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m Instruction Report W 96 2 IIl@ ll 1 September 1996 ( Updated April 1999) US Army Corps of Engineers Waterways Experiment Station Water Operations Technical Suppofl Program Simplified Procedures for Eutrophication Assessment and Prediction: User Manual by William W. Walker Approved For Public Release; Distribution Is Unlimited Prepared for Headquarters, U. S. Army Corps of Engineers The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. The findings of this report are not to be construed as an official Department of the Army position, unless so designated by other authorized documents. @ PRINTED ON RECYCLED PAPER Water Operations Technical Support Program Simplified Procedures for Eutrophication Assessment and Prediction: User Manual by William W. Walker 1127 Lowell Road Concord, MA 01742 Final report Approved for public release; distribution is unlimited Prepared for U. S. Army Corps of Engineers Washington, DC 20314 1000 Instruction Report W 96 2 September 1996 ( Updated April 1999) Monitored by U. S. Army Engineer Waterways Experiment Station Vicksburg, MS 39180 6199 ENWROWEN], T:” A. L.,! Watenvays Experiment Station Cataloging in Publication Data Walker, William W. Simplified procedures for eutrophication assessment and prediction : user manual/ by William W. Walker; prepared for U. S. Army Corps of Engineers ; monitored by U. S. Army Engineer Waterways Experiment Station. 235 p. : ill. ; 28 cm. – ( Instruction reporl; W 96 2) Includes bibliographic references. 1. Eutrophication — Mathematical models. 2. Resetvoir ecology. 3. Water quality — Evaluation — Computer programs. 1. United States. Army. Corps of Engineers. Il. U. S. Army Engineer Waterways Experiment Station. Ill. Water Quality Research Program. IV. Title. V. Series: Instruction report ( U. S. Army Engineer Waterways Experiment Station) ; w 96 2. TA7 W34i no. W 96 2 Contents Prefae . . . .. o. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. vi l— Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Eutrophication Modeling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Summary ofAssessmentProcedures . . . . . . . . . . . . . . . . . . . . . . . . . . 1 14 DataRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 18 2— FLUX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 FLUX Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 Input DataRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 2 2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 4 Program Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 2 14 Typical Application Sequence.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 26 Procedure Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2 29 Data Entry Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 2 31 DataFile Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 34 FLUX Documented Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 44 3— PROFILE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 PROFILE Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3 1 Input DataRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Mixed Layer WaterQualityData Summary . . . . . . . . . . . . . . . . . . . . . . 3 4 Oxygen Depletion Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 7 Program Operation . . . . . . . . . . . . . . . . . $. . . . . . . . . . . . . . . . . . ... 3 10 Input DataFile Format......,.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 15 Data Entry Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 20 Documented Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 3 22 4 BATHTUB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 4 1 BATHTUB Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 4 1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 4 2 Program Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 4 36 Application Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4 42 Procedure Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 51 Data Entry Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 4 53 Documented Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 59 Instructional Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 79 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. R 1 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. B 1 Appendix A: Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. A1 Appendix B: Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. B1 SF 298 List of Figures Figure 1.1. Figure 1.2. Figure 1.3. Figure 1.4. Figure 1.5. Figure 1.6. Figure 3.1. Figure 3.2. Figure 4.1. Figure 4.2. Figure 4.3. Figure 4.4. Figure 4.5. Figure 4.6. Control pathways in empirical eutrophication models developed fornorthem lake applications . . . . . . . . . . . . . . . . . 1 4 Control pathways in empirical eutrophication models developed for CEreservoirapplications . . . . . . . . . . . . . . . . . 1 5 Sensitivity analysis of first order phosphorus sedimentation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 12 Sensitivityanalysis ofsecond order phosphorus sedimentation model ...,..... . . . . . . . . . . . . . . . . . . . . . . . . . 1 13 Assessment pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 15 Estimated accuracy ofreservoirmean concentration computed from sampling designs with betweenl and 30 sampling rounds overarange oftemporal CVS . . . . . . . . 1 29 Sample PROFILE output: Surface water qualitysummary . . . 3 5 Example box plot for Beaver Reservoir . . . . . . . . . . . . . . . . . 3 7 Schematic ofBATHTUB calculations . . . . . . . . . . . . . . . . . . 4 3 Control pathways inempirica. l eutrophication models developed for CE reservoir applications . . . . . . . . . . . . . . . . . 4 5 BATHTUB segmentation schemes . . . . . . . . . . . . . . . . . . . . 4 17 Mean depth ( Z) versus hydraulic residence time( T) for Remodel developmentdataset LOGIOscales . . . . . . . . . 4 25 Relationships between nutnent residence times and hydraulic residence times in Remodel development dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 27 Phosphorus, nitrogen, turbidity relationships for CE reservoirs ( nonalgal turbidity calculated as l/ Secchi ( m) 0.025Chl a( mg/ m3)) . . . . . . . . . . . . . . . . . . . . . . . . . . 4 30 iv Figure 4.7. Phosphorus, chlorophyll a, and transparency relationships for CE reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 31 Figure 4.8. Calibration factor for linear phosphorus/ chlorophyll model versus light limitation factors . . . . . . . . . . . . . . . . . . . 4 34 Figure 4.9. Model segmentation for Lake Keystone, Oldahom& application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 59 List of Tables Table 1.1. Table 1.2. Table 1.3 Table 1.4 Table 2.1 Table 2.2 Table 2.3 Table 2.4 Table 2.5 Table 4.1 Table 4.2 Table 4.3 Table 4.4 Table 4.5 Table 4.6 Comparison of Lake and Reservoir Empirical Eutrophication Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 Mass Balance Terrnsand Data Sources . . . . . . . . . . . . . . . . 1 22 Minimal and Desirable Designs for Tributary Monitoring Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 23 General Guidelines for Designing Reservoir Pool Monitoring Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 27 Estimation Algorithms Used in FLUX Program . . . . . . . . . . . 2 5 Stratified Sample Algorithm ( Cochran 1977; Bodo and Unny 1983) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 10 Breakdown by Flow Stratum  Caddo River Example . . . . . 2 12 Typical Application Sequence . . . . . . . . . . . . . . . . . . . . . . . . 2 27 FLUX File Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 34 Symbol Definition s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 BATHTUB Model Options . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 8 Supplementary Response Models . . . . . . . . . . . . . . . . . . . . . 4 12 Error Statistics for Model Network Applied to Spatially Averaged CEReservoir Data . . . . . . . . . . . . . . . . . . . . 4 13 Diagnostic Variables and Their Interpretation . . . . . . . . . . . . 4 14 Equations for Estimating Nonalgal Turbidity, Mixed Depth, and Hypolimnetic Depths in Absence of Direct Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 4 33 Preface The information reported herein is based on a series of technical reports written by Dr. William W. Walker and published by the U. S. Army Engineer Waterways Experiment Station ( WES). These previous reports summarized work conducted as part of the Environmental and Water Quality Operational Studies Program, sponsored by the Headquarters, U. S. Army Corps of Engineers ( HQUSACE). Preparation of this report was sponsored by HQUSACE, as part of the Water Operations Technical Support ( WOTS) Program. The WOTS Program was assigned to WES under the purview of the Environmental Laboratory ( EL). Funding was provided under Department of the Army Appropriation 96X3 123, Operations and Maintenance. The WOTS was managed under the Environmental Resources Research and Assistance Programs ( ERRAP), Mr. J. L. Decell, Manager. Mr. Robert C. Gunkel was Assistant Manager, ERRAP, for the WOTS. Program Monitors for WOTS were Messrs. Frederick B. Juhle and Rixie Hardy, HQUSACE. The work was conducted under the direct WES supervision of Dr. Robert H. Kennedy, Ecosystem Processes and Effects Branch ( EPEB), Environmental Processes and Effects Division ( EPED), EL, and the general supervision of Dr. Richard E. Price, Chief, EPEB, Mr. Donald L. Robey, Chief, EPED, and Dr. John W. Keeley, Director, EL. At the time of publication of this report, Director of WES was Dr. Robert W. Whalin. Commander was COL Bruce K. Howard, EN. This report was updated in April 1999. This report should be cited as follows: Walker, W. W. ( 1996). “ Simplified procedures for eutrophication assessment and prediction: User manual,” Instruction Report W 96 2 ( Updated April 1999), U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS. lhe contents of this report are not to be used for adver~ ising, publication, or promotional putposes. Citation of trade names does not constitute an oficial endorsement or approval of the use of such commercial products. vi Background 1 Introduction This report describes simplified procedures for eutrophication assessment and prediction. These techniques, initially developed for use at U. S. Army Corps of Engineer ( CE) reservoirs, are based upon research previously described in a series of technical reports. These reports describe database development ( Report 1; Walker 1981); model testing ( Report 2; Walker 1982); model refinement ( Report 3; Walker 1985); and applications procedures ( Report 4; Walker 1987). Reported here is detailed itiormation concerning application of the latest versions of these techniques using a DOS based personal computer and also reported is an update of the original applications manual ( i. e., Report 4). Three computer programs facilitate data reduction and model implementation. While the assessment procedures and programs can be “ run” based upon the information contained in this report, their intelligent “ use” requires an understanding of basic modeling concepts and familiarity with the supporting research. Review of the above research reports and related references on this topic ( see References and Bibliography) will facilitate proper use of the techniques described below. Eutrophication can be defined as the enrichment of water bodies leading to an excessive production of organic materials by algae and/ or aquatic plants. This process has several direct and indirect impacts on reservoir water quality and beneficial uses. Common measures of eutrophication include total nutrient concentrations ( phosphorus and nitrogen), chlorophyll a ( a measure of algal density), Secchi depth ( a measure of transparency), organic nutrient forms ( nitrogen and carbon), and hypolimnetic dissolved oxygen depletion. The basis of the modeling approach described below is to relate eutrophication symptoms to external nutrient loadings, hydrology, and reservoir morphometry using statistical models derived from a representative cross section of reservoirs. When applied to existing reservoirs, the models provide a framework for interpreting water quality monitoring data and predicting Chapter 1 Introduction 1 1 effects of fhture changes in external nutrient loadings. The models can also be used to predict water quality conditions in a proposed reservoir. Three basic phases are involved in applying the methodolo~ to an existing or proposed reservoir: a. Analysis and reduction of tributary water quality data. b. Analysis and reduction of pool water quality data. c. Model implementation, A separate computer program has been developed for each phase. The datareduction phases are critical steps in the modeling process. The programs can also be used in other aspects of reservoir operation and management, including monitoring program design and generalized data analysis. The model implementation program is designed so that it can be applied to a single reservoir ( mixed or spatially segmented), networks of reservoirs ( hydrologically linked), or collections of reservoirs ( hydrologically independent). The last type of application can support regional comparative assessments of reservoir conditions and controlling factors. This report is organized in four chapters. Chapter 1 reviews basic empirical modeling concepts, presents an overview of the assessment procedures which have been developed for reservoir application, and summarizes basic data requirements and recommended monitoring strategies. Chapter 2 describes the FLUX program, which is designed for analysis and reduction of tributary monitoring data. Chapter 3 describes PROFILE, a program designed for analysis and reduction of pool monitoring data. Chapter 4 describes BATHTUB, a program designed for model implementation. Appendix A describes the necessary procedures for installing the programs on an IBM compatible personal computer. Several levels of involvement are offered to potential users of this methodology. The following steps are suggested: Step 1: Review summary information ( Chapter 1). Step 2: Review supporting research and basic reference documents. Step 3: Review program documentation ( Chapters 2,3, and 4). Step 4: Review documented output listings. Step 5: Acquire and install programs ( Appendix A) on an accessible computer system. 1 2 Step 6: Run programs using several sample input files provided. Chapter 1 Introduction Step 7: Apply program to user defined problems. The above procedures provide a gradual and logical introduction of the techniques and a foundation for their application in a reservoir management context. Eutrophication Modeling Techniques Models for reservoir eutrophication can be broadly classified as theoretical or empirical. While all models are empirical to some extent, they are distinguished by their levels of empiricism. General characteristics and limitations of these model types are discussed below. Theoretical models generally involve direct simulation of physical, chemical, and biological processes superimposed upon a simulation of reservoir hydrodynamics. These methods generally have extensive resource requirements in terms of input dat~ computing facilities, and user expertise. They can be usefbl for problems requiring high spatial and temporal resolution and/ or simulation of cause effect relationships which cannot be represented using simpler models. Their relative complexity does not guarantee that simulation models are more accurate or more reliable than simplified models for certain types of applications. Although based upon theoretical concepts ( such as mass balance and nutrient limitation of algal growth), empirical models do not attempt explicit simulation of biochemical processes and use simplified hydrodynamic representations. They generally deal with spatially and temporally averaged conditions. The simple structures, low resolution, limited number of input variables, and initial calibration to data from groups of impoundments result in relatively low data requirements. At the same time, the above characteristics limit model applicability. In one sense, empirical models attempt to “ interpolate” the gross responses of a given impoundment, based upon observed responses of other impoundments and levels of certain controlling variables. They also provide a quantitative framework for interpreting monitoring data from a given impoundment and describing eutrophication related water quality conditions and controlling factors both in absolute and relative terms. Empirical model structures and evolution Empirical prediction of reservoir eutrophication can be described as a twostage procedure involving the following types of models: a. Nutrient Balance Models. These relate pool or discharge nutrient levels to external nutrient loadings, morphometry, and hydrology. ( Note that the term “ pool” refers to the lake or reservoir impounded by a dam.) Chapter 1 Introduction 1 3 b. Eutrophication Response Models. These describe relationships among eutrophication indicators within the pool, including nutrient levels, chlorophyll a, transparency, and hypolimnetic oxygen depletion. Generally, models of each type must be linked to relate external nutrient loadings to reservoir water quality responses. In the absence of loading information, however, application of eutrophication response models alone can provide useful diagnostic tiormation on existing water quality conditions and controlling factors. The literature contains a wide array of empirical eutrophication models which have been calibrated and tested using data from various lake and/ or reservoir data sets. Many of these models, particularly the early ones, were based primarily upon data from northern, natural lakes. While the equations and coefficients vary considerably among the lake models, they share the same sets of variables and basic assumptions, as depicted in Figure 1.1. INFLOW TOTAL P MEAN DEPTH + LAKE TOTAL P CHL A— SECCHI HYDRAULIC RESIDENCE TIME Figure 1.1. Control pathways in empirical eutrophication models developed for northern lake applications Inputs to these models can be summarized in three terms: a. Inflow total phosphorus concentration. External loading/ discharge rate, a nutrient supply factor. b. Mean depth. Reservoir volume/ surface are% a morphometric factor. c. Hydraulic residence time. Reservoir volume/ discharge rate, a hydrologic fwtor. Empirical nutrient balance models have generally evolved from a simplistic “ black box” model which represents the impoundment as a continuous stirredtank reactor at steady state and the sedimentation of phosphorus as a first order reaction. Phosphorus is assumed to control algal growth and other eutrophication related water quality conditions. Response models generally consist of bivariate regression equations relating each pair of response measurements ( e. g., phosphorus/ chlorophyll, chlorophyllk. nsparency). 1 4 Chapter 1 Introduction In adapting these models for use in CE and other reservoirs ( Walker 1981, 1982, 1985), modifications have been designed to include additional input variables, controlling factors, and response variables, as depicted in Figure 1.2. Table 1.1 compares the variables and assumptions of the reservoir models documented in this manual. The reservoir modifications are designed to improve generality by incorporating additional independent variables and controlling factors found to be important in model testing. INFLOWTOTAL METALIMNETIC ~ DEPLETION RATE INFLOW ORTHO P MEANTOTAL DEPTH NYD. RESIDENCE TIME HLOROPHYLL A INFLCW TOTAL N tNFLW bNORGANIC N SECCHI SUMMER FLUSHING RATE ORGANIC N MEAN OEPTH OF TOTAL P ORTNO p MO( ED IAYER NONALGAL TRU6JDITY Figure 1.2. Control pathways in empirical eutrophication models developed for CE reservoir applications Refinements are focused in the following areas: a. Effects of nonlinear sedimentation kinetics on nutrient balances. A second order kinetic model appears to be more general than a firstorder model for predicting both among reservoir, spatially averaged variations and within reservoir, spatial variations. b. Effects of inflow nutrient partitioning ( dissolved versus particulate or organic versus inorganic) on nutrient balances and chlorophyll a levels. Because of differences in biological availability and sedimentation rates, reservoir responses appear to be much more sensitive to the orthophosphorus loading component than to the nonortho ( total minus ortho) component. Chapter 1 Introduction 1 5 Table 1.1 Comparison of Lake and Reservoir “ Empirical Eutrophication Models Model Characteristics Lake Models Reservoir Models Input Inflow total P concentration Inflow total P concentration variables Mean depth Inflow ortho P concentration Annual hydraulic residence Inflow total N concentration time Inflow inorganic N Mean hypolimnetic depth concentration Mean depth Mean hypolimnetic depth Mean depth of mixed layer Seasonal hydraulic residence time Nonalgal turbidity Spatial Mixed Mixed or spatially segmented variability Temporal Steady state Steady state variability Nutrient Linear ( first order) Nonlinear ( second order) sedimentation kinetics Factors Phosphorus Phosphorus controlling Nitrogen algal growth Light Flushing rate output Total phosphorus Total phosphorus variables Chlorophyll a Total nitrogen Transparency Chlorophyll a Hypolimnetic oxygen Transparency depletion Nonortho phosphorus Organic nitrogen Hypolimnetic oxygen depletion Metalimnetic oxygen depletion 1 6 c. Effects of seasonal variations in nutrient loadings, morphomet~, and hydrology on nutrient balances. Pool water quality conditions are related more directly to seasonal than to annual nutrient balances in impoundments with relatively high flushing rates. Chapter 1 Introduction d Effects of algal growth limitation by phosphorus, nitrogen, light, and flushing rate on chlorophyll a concentrations. Simple phosphorus/ chlorophyll a relationships are of limited use in reservoirs because nitrogen, light, and/ or flushing rate may also regulate algal growth, depending upon site specific conditions. e. Effects of spatial variations in nutrients and related variables, as controlled by reservoir morphometry, hydrology, and the spatial distribution of tributary nutrient loads. Nutrient balance models can be implemented in a spatially segmented framework which accounts for advection, dispersion, and sedimentation to predict water quality variations among and within major tributary arms. This spatial resolution can be important for evaluating impacts on reservoir uses, depending upon locations of water use points ( e. g., water supply intakes, bathing beaches, parks, fishing areas, and/ or wildlife refiges). Model structures have been tested against several independent reservoir data sets. Details on model development and testing are described in the supporting research reports ( Walker 1982, 1985). Applications Potential model applications can be classified into two general categories: diagnostic and predictive. Characteristics and limitations of these applications are described below. In a diagnostic mode, the models provide a framework for analysis and interpretation of monitoring data from a given reservoir. This yields perspective on eutrophication related water quality conditions and controlling factors. Assessments can be expressed in absolute terms ( nationwide, e. g., with respect to water quality objectives, criteri~ or standards) and/ or relative terms ( e. g., comparisons with other impoundments, or regionally). Using routines and statistical summaries included in the BATHTUB program, observed or predicted reservoir characteristics can be ranked against characteristics of CE reservoirs used in model development. In a predictive mode, the models are used to project fiture conditions in either existing or planned reservoirs. The distinction between the two types of predictive applications is important. In the first case, monitoring data from an existing reservoir can be used, in combination with the models and diagnostic analyses, as a “ starting point” for “ extrapolation” to future conditions. Because of the opportunity for site specific calibration, projections of future conditions in an existing reservoir are generally subject to less uncertainty than projections of water quality conditions in a proposed reservoir. In a predictive mode, the models project steady state responses to changes in controlling variables which are explicitly represented in the model network Chapter 1 Introduction 1 7 ( Figure 1.2). Such projections can be used in impact assessments and in evaluations of water quality control strategies. For example, fhture scenarios involving changes in seasonal or annual mean values of the following factors can be evaluated: a. Inflow nutrient concentrations or loadings ( total phosphorus, ortho phosphorus, total nitrogen, and/ or inorganic nitrogen). b. Pool elevation, as it influences mean depth, mixed layer depth, mean hypolimnetic depth, and hydraulic residence time. c. Inflow volume and changes in hydraulic residence time. d. Pool segmentation, as it influences longitudinal nutrient transport, sedimentation, and the spatial distribution of nutrients and related water quality conditions. Applications of the first type are of primary importance because control strategies for reservoir eutrophication are usually focused on external nutrient ( especially, phosphorus) supplies. Examples of impacts and control strategies which cannot be explicitly evaluated with these models include the following: a. Variations in pool level or other model input variables which occur over time scales shorter than the growing season ( typically, 6 months). b. Changes in outlet levels. c. Structural modifications, such as the construction of weirs. d. Hypolimnetic aeration or destratification. e. Other in reservoir management techniques, including dredging and chemical treatment to control internal nutrient recycling. In such cases, implementation of the models in a diagnostic mode can provide useful baseline water quality perspectives; however, simulation or other approaches must be used for predictive purposes. Although the supporting research has focused on reservoirs, the computational framework can also be applied to natural lakes. Certain procedures and concepts are essential to evaluating eutrophication problems in lakes or reservoirs. These include calculation of tributary nutrient loads, summary of observed water quality conditions, construction of water balances, and construction of mass balances. In adapting the empirical lake models ( Figure 1.1) for use in reservoirs, the goal has been to increase model generality, so that the resulting formulations can be applied within certain constraints to lakes or to 1 8 Chapter 1 Introduction reservoirs. The limits and extent of model testing against lake data sets are summarized in the supporting research reports ( Walker 1982, 1985). Options for implementing empirical models previously developed exclusively from lake data sets are also included in the software. Error, variability, and sensitivity analysis The distinction between “ error” and “ variability” is important. Error refers to a difference between an observed and a predicted mean value. Variability refers to spatial or temporal fluctuations in concentration about the mean. Prediction of temporal variability is generally beyond the scope of empirical modeling efforts, although such variability is important because it influences the precision of observed mean values calculated from limited monitoring data. Because both measurement and model errors tend to increase with concentration scale, errors are most conveniently expressed on a percentage basis or logarithmic scales. This stabilizes variance over the ranges of concentration encountered, an important requirement for application of common statistical techniques ( e. g., regression). This report frequently uses the mean coefllcient of variation ( CV) as a measure of error. The CV equals the standard error of the estimate expressed as a fraction of the predicted value. For example, a CV of 0.2 indicates that the standard error is 20 percent of the mean predicted value. Assuming that the errors are log normally distributed about the predicted value, 95 percent confidence limits can be estimated from the following equation: yme 2cv< y< yme2cv where Ym= predicted mean value CV = error mean coefficient of variation Y = 95 percent confidence range for mean value Magnitudes, sources, and interpretations of error are discussed below. Error CVS for the reservoir model network ( Figure 1.2) are on the order of 0.27 for predicting total phosphorus and 0.35 for predicting mean chlorophyll a. According to the above equation, these statistics translate into 95 percent confidence factors of 1.72 and 2.00, respectively. In applying these models in a reservoir management context, limitations imposed by errors of this magnitude are less severe than immediately apparent because of the following factors: Chapter 1 Introduction 1 9 a. Despite the relatively wide confidence bands, the models explain 91 percent and 79 percent of the observed variances in total phosphorus and chlorophyll a across reservoirs, respectively. This reflects the relatively wide ranges of conditions encountered and suggests that the models are adequate for broad comparative analyses of reservoir conditions ( i. e., ranking). b. Error statistics are calculatedfiom “ imperfect” data sets. Errors are partially attributed to random sampling, measurement, and estimation errors in the input and output ( i. e., observed) conditions, which inflate the total error but do not reflect model performance. c. Error magnitudes refer to predictions which are made without the beneJt of site specl@ c water quality information. In applications to existing reservoirs, prediction errors can be reduced by calibrating the model ( adjusting certain model coefficients) so that predictions match observed water quality conditions. The calibrated model can subsequently be used to project water quality changes likely to result from changes in nutrient loads or other controlling factors. d. Year to year water quality variations induced by climate, hydrology, nutrient loading, and other factors are substantial in many reservoirs. It would be difficult to detect modest errors in predicting average conditions without several years of intensive monitoring. e. Ability to de$ ne objective criteria or standards is limited. The “ penalty” or “ risk” associated with modest errors in predicting average responses may be low when expressed in terms of impacts on water uses. The measured and modeled variables ( chlorophyll a, etc.) are reasonable and practical, but impefiect, surrogates for potential wateruse impacts. $ Ability to predict changes in loading resultingfiom adoption of specl~ c management strategies is limited. This applies particularly to implementation of nonpoint source loading controls with performances evaluated using watershed simulation models. In such situations, errors associated with predicting reservoir response may be swamped by errors associated with predicting loadings; i. e., the reservoir response model may not be the limiting factor in the analysis. Error analysis concepts discussed below provide additional perspectives on the above points. 1 1o Differences between observed and predicted reservoir conditions can be attributed to the combined effects of a number of error sources, as described below: Chapter 1 Introduction a. Independent variable error. These are errors in the estimates of model input variables, including external nutrient loadings, flows, and reservoir morphometry. b. Dependent variable error. These are errors in the estimates of mean observed reservoir water quality conditions, based upon limited monitoring data. c. Parameter error. These errors are attributed to biases or random errors in the model coefficients estimated from cross sectional data sets. d. Model error. These errors are attributed to errors in model structure or effects of factors which are not explicitly represented. The user has direct control over the first two error sources ( i. e., independent and dependent variable error), primarily through design and implementation of appropriate monitoring programs and use of proper data reduction techniques. The last two sources ( i. e., parameter and model error) are also under user control to the extent that the user selects the model( s) deemed appropriate for specific application. Research ( Walker 1981, 1982, 1985) has been directed at minimizing the last two error sources by reviewing, screening, refining, calibrating, and testing arrays of models which are appropriate for reservoir applications under specific conditions. The impacts of errors in speci$ ing model input variables or coefficients depend upon the sensitivities of model predictions to those inputs. Sensitivities, in turn, reflect model structure and variable ranges. A sensitivity coefficient can be conveniently expressed as a normalized first derivative, or as the percent change in a model output variable induced by a 1 percent change in a model input. For example, a sensitivity coefficient of 1.0 would indicate that the output is proportional to the input; in this situation, for example, a 5 percent error in speci& ing the input would propagate through the model and cause a 5 percent error in the predicted output. For a sensitivity coefficient of 0.2, however, a 5 percent input error would cause only a 1 percent output error. Sensitivity coefficients provide insights into which model variables and coefflcients are the most important to measure or estimate accurately. Figures 1.3 and 1.4 display sensitivity coefficients for models predicting mean phosphorus concentrations in reservoirs assuming first and second order sedimentation reactions, respectively. In both cases, the output variable is the error term or the ratio of the observed to the predicted mean phosphorus concentration. Input variables used to calculate this ratio include the observed pool concentration, inflow concentration ( flow weighted over all sources), flushing rate ( outflow/ volume), and sedimentation coefficient. Sensitivities vary with flushing rate over the approximate range encountered in CE impoundments ( median value for reservoirs used in model testing = 7/ year. At low flushing rates ( or long hydraulic residence times), sensitivities Chapter 1 Introduction 1 11 1.0 0.8 0.6 0.4 0.2 0  —— — ———  SED! MENTA TION RATE   FLUSHING RATE 0.1 1 10 100 FLUSHING RATE. l/ YR SENSITIVITY COEF = I% CHANGE IN ERROR ~ 1% CHANGE Ihl FACTOR I ERROR = OBSERVE() POOL P PREDICTED POOL P P, F PREDICTED POOL P = F+ K1 WHERE: Pi = INFLOW TOTAL PHOSPHORUS CONCENTRATION ( mg/ m3) F = FLUSHING RATE ( 1/ yr ) K, = FIRST ORDER SEDIMENTATION COEFFICIENT = 2.5 1/ Yf Figure 1.3. Sensitivity analysis of first order phosphorus sedimentation model to the sedimentation coefficient and flushing rate are relatively high ( approach ing 1.0 for the first order model and 0.5 for the second order model). This reflects the relative importance of the sedimentation term in the overall phosphorus balance of the reservoir. At high flushing rates, sensitivities to the sedimentation coefficient and flushing rate approach zero for both models. In this situation, the sedimentation process is relatively unimportant, and modest errors in the specified flushing rate a. dor sedimentation coefficient can be tolerated without having major impacts on the predicted pool concentration. Because the sedimentation coefficient is estimated from highly simplified empirical models ( whereas the other input terms can be directly measured), its sensitivity characteristics have a strong influence on model performance and uncertainty over the range of flushing rates. 1 12 Chapter 1 Introduction 1.0 0.6 0.6 0.4 02 0 ——— ——— — p( J~, ,7 ~ ,0,~,,~~ , / 0 /“ ,.~”~” r r SEDIMENTATION RATE  FLUSHING RATE 1 I i 0.1 1 10 1( KI FLUSHING RATE, 1/ Yf SENSITIVITY COEF = % CHANGE IN ERROR I 11% OHANGE IN FACTOR I ERROR = OBSERVED POOL P PREDICTED POOL P + +~~” PREDICTED POOL P = 2% WHERE: F = FLUSHING RATE ( 1/ Yr) P, = INFLOW TOTAL PHOSPHORUS CONCENTRATION = 50 mg/ m3 K2 = SECOND ORDER SEDIMENTATION COEFFICIENT = .1 m3/ mg yr Figure 1.4. Sensitivity analysis of second order phosphorus sedimentation model Figures 1.3 and 1.4 are intended primarily to demonstrate sensitivity analysis concepts. They also illustrate some important basic characteristics of empirical nutrient balance models: a. Sensitivities are highest for inflow and pool phosphorus concentrations over the entire range of flushing rates. This emphasizes the importance of monitoring programs ( tributary and pool) and data reduction procedures to modeling efforts. b. Because of a higher sensitivity to phosphorus sedimentation, potential prediction errors are greater for reservoirs with lower flushing rates. Chapter 1 introduction 1 13 While pool nutrient concentrations can be predicted relatively easily from inflow concentrations in reservoirs with high flushing rates, predictions of biological responses ( as measured by chlorophyll a) may be more difficult because of temporal variability in nutrient levels ( induced by storm events, for example) and/ or controlling effects of turbidity and flushing rate. The importance of obtaining accurate inflow and pool concentration estimates for model implementation has led to the development of the computer programs described in subsequent chapters. FLUX and PROFILE are designed to make efficient use of tributary and pool monitoring da~ respectively, in calculating the required summary statistics. Summary of Assessment Procedures Figure 1.5 depicts the basic steps involved in applying the eutrophication assessment procedures described in this and subsequent chapters. The “ pathway” comprises four general stages: a. Problem identification. b. Data compilation. c. Data reduction. d. Model implementation. Once the user has developed a working understanding of the model structures, assumptions, and limitations by reviewing basic references and supporting research ( see References and Bibliography), most of the effort and cost would typically be involved in the data compilation and data reduction stages. Three computer programs have been written to assist at various stages of the analysis. The functions of these programs are outlined below: a. FLUX  estimation of tributary mass discharges ( loadings) from grab sample concentration data and continuous flow records. b. PROFILE  display and reduction of pool water quality data. c. BATHTUB  implementation of nutrient balance and eutrophication response models. Figure 1.5 summarizes the basic inputs, functions, and outputs of each supporting program. This chapter provides an overview of each analytical stage. Details are given in subsequent chapters, along with examples and guidance for use of the computer software. 1 14 Chapter 1 Introduction PATHWAY PROCEDURES PROBLEM l DESCRIBE RESERVOIR AND/ OR WATERSHED CHARACTERISTICS DEFINITION l DEFINE UATER WALITY MANAGEMENT OBJECTIVES l IDENTIFY IMPACTS/ CONTROL STRATEGIES TO BE EVALUATED l DETERMINE STUDY TYPE: DIAGNOSTIC PREDICTIVE l DETERMINE MODEL TYPE: NUTRIENT BALANCE EUTROPHICATION RESPONSE DATA CCM4PILE TRIBUTARY C( NJIPILE RESERVOIR CWPILATION AND DISCHARGE DATA POOL DATA l HYDROLOGY l HYDROLOGY l UATERSHED l MORPHWETRY CHARACTERISTICS l WATER QUALITY l UATER QUALITY DATA RUN FLUX PROGRAM RUN PROFILE PROGRAM REDUCTION l DATA ENTRY l DATA ENTRY l DIAGNOSTIC DISPLAYS l DIAGNOSTIC DISPLAYS l DATA STRATIFICATION l OXYGEN DEPLETION l LOADING CALCULATIONS CALCULATIONS ANNUAL l MIXED LAYER SUMMARIES SEASONAL M( X) EL RUN BATHTUB PROGRAM IMPLEMENTATION l SEGMENTATION l SUBMCX) EL SELECTION NUTRIENT BALANCE EUTROPHICATION RESPONSE l DATA ENTRY l CALIBRATION AND TESTING l SENSITIVITY ANALYSIS l ERROR ANALYSIS l APPLICATIONS DIAGNOSTIC PREDICTIVE Figure l. 5. Assessment pathways Problem identification The problem identification stage defines thescope ofthe modeling effort. The following factors are specified: a. The reservoir, watershed, and water uses. b. Water quality standards andmanagement objectives. c. Whether the reservoir is existing or planned. d. Specific managementstrategies orimpacts to reevaluated. Chapterl Introduction 1 15 e. Types of evaluations to be performed. ( 1) Diagnostic. ( 2) Predictive. J Classes of models to be used. ( 1) Nutrient balance. ( 2) Eutrophication response. If the analysis is not directed toward evaluating specific management strategies or impacts, the general objective may be to develop perspectives on reservoir water quality conditions and controlling factors as part of a “ diagnostic” study. This may lead, in turn, to future evaluations of specific management strategies designed for water quality control. Two general types of evaluations maybe pefiormed. In a diagnostic mode, the models are used as a framework for interpreting monitoring data from the reservoir and/ or its tributaries. A diagnostic study provides insights into factors controlling algal productivity and rankings of trophic state indicators versus water quality criteria and/ or data from other CE reservoirs. In a predictive mode, the models are applied to predict future conditions in a planned reservoir or in an existing reservoir undergoing changes in nutrient loading regime and/ or other controlling factors. Model classes are determined by the types of analyses to be performed. Both nutrient balance and eutrophication response models are required for a predictive analysis. Diagnostic studies of existing reservoirs can be based exclusively upon response models and pool water quality data; this provides a basis for defining existing conditions and controlling factors, but not for evaluating watershed/ reservoir or load/ response relationships. Monitoring requirements are generally more stringent for implementing nutrient balance models than for implementing eutrophication response models. Response models and pool monitoring data may be used in preliminary diagnostic studies aimed at defining reservoir conditions. In some reservoirs, this may be followed by implementation of a more elaborate monitoring program designed to quanti~ nutrient loadings and to support nutrient balance modeling. Priorities can be established based upon the severities of existing eutrophication related problems ( if any), intensities and types of water use, and potential for future improvement or degradation owing to changes in loading regime. 1 16 Chapter 1 Introduction Data compilation As shown in Figure 1.5 data compilation occurs in two general areas. The reservoir data required for implementation of eutrophication response models include morphometric characteristics, outflow hydrology, and pool water quality obtained over at least one complete growing season ( three preferred). The watershed data required for implementation of nutrient balance models include basic watershed characteristics ( e. g., subwatershed delineations, topography, geology, land uses, point source inventories) and tributary flow and nutrient concentration data taken at reservoir entry points over at least one full water year ( three preferred). Details on data requirements and suggested monitoring designs are given later in this chapter. Data reduction In the data reduction phase, pool and tributary water quality data are reduced or summarized in forms which can serve as model input. Since the models generally deal with conditions averaged over a growing season within defined reservoir areas ( segments), data reduction involves the averaging or integration of individual measurements, sometimes with appropriate weighting factors. The FLUX program is designed to facilitate reduction of tributary inflow monitoring data and reservoir outflow monitoring data. Using a variety of calculation techniques, FLUX estimates the average mass discharge or loading that passes a given tributary monitoring station, based upon grab sample concentration data and a continuous flow record. Potential errors in the estimates are also quantified and can be used to ( a) select the “ best” or least error loading estimate, ( b) assess data adequacy, and ( c) improve future tributary monitoring efficiency via optimal allocation of sampling effort among seasons and/ or flow regimes. Graphic displays of concentration, flow, and loading data are also provided for diagnostic purposes. The PROFILE program facilitates analysis and reduction of pool water quality data from existing reservoirs. A variety of display formats are provided to assist the user in developing perspectives on spatial and temporal water quality variations within a given reservoir. Algorithms are included for calculation of hypolirnnetic oxygen depletion rates and for robust estimation of areaweighted, surface layer mean concentrations of nutrients and other response measurements used in subsequent modeling steps. ModeI implementation The BATHTUB program applies empirical eutrophication models to morphometncally complex reservoirs or to collections of reservoirs. The program performs water and nutrient balance calculations in a steady state, Chapter 1 Introduction 1 17 spatially segmented hydraulic network which accounts for advective transport, diilbsive transport, and nutrient sedimentation. Eutrophication related water quality conditions ( expressed in terms of total phosphorus, total nitrogen, chlorophyll a, transparency, organic nitrogen, particulate phosphorus, and hypolimnetic oxygen depletion rate) are predicted using empirical relationships previously developed and tested for reservoir applications ( Walker 1983). To reflect data limitations or other sources of uncertainty, key inputs to the model can be specified in probabilistic terms ( mean and CV). Outputs are expressed in terms of a mean value and CV for each mass balance term and response variable. Output CVS are based upon a first order error analysis which accounts for input variable uncertainty and inherent model error. As shown in Figure 1.5, applications of BATHTUB would normally follow use of the FLUX program for reducing tributary monitoring data and use of the PROFILE program for reducing pool monitoring data. Use of the data reduction programs is optional if independent estimates of tributary loadings and/ or average pool water quality conditions are used. Data Requirements This section summarizes data requirements to support model applications. The following categories are discussed: a. Watershed characteristics. b. Water and nutrient loadings. c. Reservoir morphometry. d Pool water quality and hydrology. Before describing each area in detail, it is appropriate to discuss some general concepts and guidelines that may be helpful in the design of a reservoir study. IrI a typical application, most of the effort and cost would be expended in the critical data gathering phase, Information sources would generally include project design memorand~ basin planning reports, historical hydrologic and water quality dat~ and water quality data gathered specifically for the study. Data requirements can be given rather explicitly, as determined by the list of model input variables. Specific data sources and monitoring program designs cannot be dictated, however, because they are influenced by unique aspects of each reservoir and its watersheds, the extent of existing dat~ logistic considerations, and study resources. 1 18 Chapter 1 Introduction Compilation and review of existing data are important initial steps in conducting a reservoir study. Preliminary application of models using existing data ( even if inadequate) can highlight data strengths and weaknesses and help to focus fhture monitoring activities. In some cases, existing data maybe adequate to support modeling efforts. When existing data are inadequate or unavailable, a phased monitoring program is generally indicated. The first phase involves a small scale program designed to obtain preliminary data for use in designing efficient monitoring programs for subsequent years. A phased study can be a relatively cost effective means of data acquisition. Given specific objectives ( e. g., quanti@ ng annual total phosphorus load or growing season mean chlorophyll a concentration in an existing reservoir), statistical methods can be applied to improve monitoring efficiency. As the efficiency of a monitoring program increases, the amount of uncertainty ( variance) in the measured variable decreases. Monitoring efficiency may be improved by optimizing the allocation of sampling effort, subject to logistic and economic constraints. Examples of such optimization procedures include the following: a. Allocation of samples among flow regimes to estimate loadings from a given tributary. b. Allocation of samples among tributaries to estimate total reservoir loading. c. Allocation of samples among stations, depths, and dates to estimate reservoir mean concentrations. Phased studies or useful existing databases are required to implement these optimization procedures. Because of logistic constraints, multiple monitoring objectives, and other factors, “ optimal” designs are rarely implemented; instead, they can be used to indicate appropriate directions for adjusting existing sampling designs. Watershed characteristics Basic watershed information is used in the development and interpretation of hydrologic and nutrient loading dat~ in the design of tributary monitoring programs, and in the assessment of problem sources and control strategies. Maps ( U. S. Geological Survey topographic or other) are the most useful formats for this type of information. Separate maps ( or a series of transparent overlays) can be used to summarize the following types of watershed tiormation: a. Elevation contours. b. Subwatershed delineations. Chapter 1 Introduction 1 19 c. d. e. J Dominant land uses. Soil types. ( 1) Hydrologic soil groups. ( 2) Erosion potential. Point sources. Monitoring station locations. Aerial photos, regional planning agencies, design memorand~ Geographic Information System ( GIS) databases, and/ or published basin reports are generally usefid sources of watershed Mormation. Soils information would also be available from the Soil Conservation Service. The information should be summarized in a tabular form by subwatershed. Land uses, soil types, topography, and point sources are important factors in dete rmining runoff and nutrient export from a given subwatershed. This type of tiormation is used to do the following: a. Design tributary monitoring programs ( place stations). b. Interpret watershed monitoring data ( compare monitored runoff and loads from different subwatersheds to develop perspectives on regional land use/ nutrient export relationships). c. Estimate loadings from unmonitored watersheds ( use land use/ nutrientexport factors or proportion monitored loads from a nearby watershed with similar land uses and soil types, based upon drainage area). Projections of future land use and point source nutrient loads are also required for predicting impacts of watershed development. Water and nutrient loadings The formulation of water and nutrient balances for the reservoir is a critical step in the empirical modeling process. The following components are of concern: 1 20 a. Water. b. Total phosphorus. c. ortho phosphorus. Chapter 1 Introduction d. Total nitrogen. e. Inorganic nitrogen ( Ammonia+ Nitrate+ Nitrite), f Conservative substance ( e. g., chloride). Water and total phosphorus balances are essential. The other components are optional, While nitrogen balances are desirable, they may be omitted if monitoring data and/ or preliminary mass balance calculations indicate that the reservoir is clearly not nitrogen limited under existing and future loading conditions. The ortho phosphorus and inorganic nitrogen ( ammoni~ nitrate, and nitrite) loading components are required for ( optional) implementation of nutrient sedimentation models which account for the “ availability” or partitioning of total nutrient loads between dissolved and particulate ( or inorganic and organic) fractions. Conservative substance balances are useful for testing water balances and calibrating diffhsive transport rates in segmented reservoirs. The nutrient species listed above correspond to those monitored by the U. S. Environmental Protection Agency ( EPA) National Eutrophication Survey, the primary data source used in model development and testing. Monitoring of other species ( particularly, total dissolved phosphorus) may be desirable for deftig inflow nutrient partitioning and availability. Because of existing data constraints, however, the models are based upon the above species. Generally, balances should be formulated over both annual and seasonal ( e. g., May September) time periods. Annual balances should be calculated on a water year ( versus calendar year) basis. While traditional nutrient loading models deal with annual time scales, seasonal loadings are better predictors of trophic status in many reservoirs. The methodologies presented in subsequent sections can be applied separately to annual and seasonal nutrient balance data. Nutrient residence time criteria are used to assess the appropriate time scale for each reservoir. The nominal definition of seasonal ( May September) can be adjusted in specific applications, depending upon seasonal variations in inflow hydrology and, especially, pool level. For example, if a full recreational pool were maintained June through August and much lower elevations were maintained during other months for flood control purposes, then a June August time scale may be more appropriate for seasonal nutrient balances. Generally, seasonal balances are less important in projects with little or no inflow or outflow during the summer months. The formulation of both seasonal and annual balances is generally recommended for all applications and does not substantially increase monitoring requirements, since both sets of loading estimates can be derived from the same monitoring program. For each component and time scale, a control volume is drawn around the reservoir ( or reservoir segment) and the following mass balance terms are quantified: Chapter 1 Introduction 1 21 a. Total inputs. b. Total OU@ ltS. c. Increase in storage. d. Net loss. Table 1.2 outlines the specific elements of each term and general data sources. Since water is conservative, the net loss term in the water balance ( estimated by difference) reflects errors in the estimates of the other water balance terms. For nutrients, the net loss term can be estimated by difference or, in a predictive mode, by using empirical nutrient sedimentation models which have been calibrated and tested for reservoir applications. Table 1.2 Mass Balance Terms and Data Sources Mass Balance Terms General Data Sources Inputs Gauged tributaries Direct monitoring Ungauged tributaries Drainage area approximations Watershed models Direct point sources Direct monitoring Per capita loading factors Shoreline septic systems Per capita loading factors Hydrogeologic studies Direct groundwater inputs Hydrogeologic studies Atmospheric Local precipitation data Regional atmospheric deposition outputs Outflows and withdrawals Direct monitoring Evaporation Local climatologic data Increase in storage Pool elevation and morphometry data Vet loss Calculated by difference Represents error in water balance Emperical nutrient sedimentation models In general, direct monitoring is recommended to quanti& major flow and nutrient sources. Table 1.3 summarizes “ minimal” and “ desirable” designs for 1 22 tributary monitoring programs and methods for quanti& ing other loading components. These are intended as general guidelines to be modified based Chapter 1 Introduction Chapter 1 Introduction 1 23 1 24 Chapter 1 Introduction upon site specific conditions. The basic design for major tributaries and outflows consists of continuous flow monitoring and a combination of periodic grab sampling and event monitoring for concentration. A sampling program weighted toward high flow regimes is generally desirable for estimation of loadings. The multiple objectives of estimating both annual and seasonal loadings should be considered in designing surveys. The FLUX program can be applied to historical and/ or preliminary monitoring data to assist in sampling design. While balances are formulated for the study ( monitored) period, a historical hydrologic record is desirable to provide perspective on study conditions in relation to long term averages and extremes. Long term hydrologic records are usually available for reservoir discharge sites and major tributary inflows. If not, records from a nearby, long term station, possibly outside the watershed( s), can be correlated with monitoring data from study sites and used to extrapolate the record. Reservoir morphometry Reservoir morphometric information is required for nutrient balance and eutrophication response models. It is usually readily available from project design memoranda and other sources. A map indicating the following basic idormation is useful: a. Distance scale. b. Shoreline for typical and extreme pool levels. c. Bottom elevation contours or soundings. d. Tributary inflows and any direct point sources. e. Pool and tributary monitoring station locations. The following morphometric data should also be compiled in tabular form: a. Elevation/ area volume table. b. Typical operating pool elevations ( rule curve). c. Reservoir bottom elevation at each pool sampling station. d. Volumes, surface areas, and lengths of major reservoir segments at typical operating elevations. This tiormation is used in data reduction ( PROFILE) and modeling ( BATHTUB). Chapter 1 Introduction 1 25 Pool water quality and hydrology In studies of existing reservoirs, pool water quality and hydrologic data are used for the following purposes: a. Assessing trophic state, related water quality conditions, and controlling factors. b. Model testing and calibration. Expressed in terms of model variables, the primary objectives of the monitoring program are to obtain the data required for calculation of growingseason, mixed layer, average concentrations of the following variables: a. Total phosphorus. b. Dissolved ortho phosphorus. c. Total nitrogen. d Total inorganic nitrogen. e. Organic nitrogen. J Chlorophyll a ( corrected for phaeophytin). g. Transparency ( Secchi depth). J Conservative substance. In stratified reservoirs, another primary objective is to estimate hypolimnetic and metalimnetic oxygen depletion rates. Secondary objectives are to develop perspectives on spatial variations, vertical stratification, basic water chemistry, and other variables which are directly or indirectly related to eutrophication. General guidelines for designing pool monitoring programs are outlined in Table 1.4. Basic design features include component coverage, station locations, sample depths, temporal frequency, and duration. An appreciation for spatial and temporal variability of conditions within the reservoir may be obtainable from historical data and can be very useful in designing future surveys. 1 26 The objectives of identifying spatial gradients and calculating reservoirmean conditions suggest somewhat different emphasis for station placement. Generally, horizontal variations parallel to the net advective flow along the main axis of a major tributary arm are much more important than variations perpendicular to the flow. If they exist, longitudinal gradients in nutrients, algal biomass, and transparency are usually steepest in upper pool areas; this Chapter 1 Introduction Table 1.4 General Guidelines for Designing Reservoir Pool Monitoring Programs Feature Minimal Design Desirable Design Water quality Temperature Dissolved Oxygen Add: components Total P Ortho P Total Silica Total Organic Carbon Organic N Ammonia N Total Iron Total Manganese Nitrite Nitrate N Transparency True Color Sulfides Alkalinity pH Suspended Solids ( total and organic) Conductivity Turbidity Oxidation reduction potential Chlorophyll a ( corrected for Phaeophytin) Algal cell counts ( ASU) by type Dominant algal types Station locations Minimum of three stations/ reservoir Add stations in smaller tributary arms and ( near dam, midpooi, upper pool) embayments Distributed along thalweg of each major Critical reservoir use areas tributary arm in representative areas Above and below junctions of tributary Maximum distance between stations along arms thalweg = 20 km Maximum distance between stations along thalweg = 10 km Duration of sampling One growing season Three growing seasons ( typically April October) Bracket stratified period, including one round each during spring and fail isothermal periods Frequency  laboratory Monthly or biweekly Biweekly or weekly samples Depths  laboratory Mixed 1ayer composite Unstratified reservoirs: surface, samples Depth integrated hose sampling mid depth, and 1 m off bottom Stratified reservoirs: 3 samples in mixed layer 1 sample in thermocline 3 samples in hypolimnion 1 m from top of hypolimnion mid depth 1 m off bottom Frequency  field profiles Unstratified reservoirs: same as laboratory Unstratified reservoirs: same as laboratory Unstratified reservoirs: samples samples Temperature Stratified reservoirs: biweekly in spring to Stratified reservoirs: weekly in spring to Dissolved oxygen early summer ( until onset of anoxia), then early summer ( until onset of anoxia), then monthly biweekly Depths  field profiles 1 m intervals, top to bottom Increase spatial frequency in thermocline Temperature and other zones with steep gradients Dissolved oxygen Reservoir hydrology Month end values Daily values Surface elevation Monthly totals Daily totals Outflow volumes Chapter 1 Introduction 1 27 suggests that stations should be more closely spaced in upper pool areas to permit adequate resolution of gradients. Most of the reservoir volume, however, is usually located in the lower pool areas, where width and depth tend to be greater and spatial gradients tend to be less pronounced; this suggests a greater emphasis on lower pool stations for the purposes of calculating reservoir means. Because of these trade offs, it is difficult to use a statistical approach for optimizing station placement within a given reservoir. Ghen multiple sampling objectives, a reasonable design rule is to distribute stations throughout representative areas of the reservoir. The size, morphometric complexity, and loading distribution of a reservoir largely determine the required number of stations. A minimum of three stations ( upper pool, midpool, and near dam) are recommended for small projects with simple morphometry. Based upon reservoir morphometnc information, weighting factors can be applied to data from each station in calculating area weighted reservoir means ( see PROFILE). To provide bases for characterizing variability and developing robust statistical summaries, surveys should be designed to provide replication ( some overlap in information content) of measurements made in each reservoir area or segment during each sampling round. There are several ways in which replication can be built into survey designs, including the following: a. Multiple sampling at a given date, station, and depth. b. Multiple sampling with depth within the mixed layer at a given date and station. c. Multiple sampling stations within a given reservoir segment or area, d. High temporal sampling frequencies, permitting aggregation of data from adjacent sampling dates. In designing surveys, combinations of the above strategies can be employed to provide data which include at least three measurements for each reservoir segment and sampling round. In the “ desirable” design ( see Table 1.4), three samples are suggested within the mixed layer for each station and date. Since the stratum is mixed, on the average, the three samples can be treated as replicates. Other strategies listed above can be used in conjunction with depth sampling to provide replication. Another monitoring objective is to sample each station on each sampling round; this greatly simplifies reduction of the data and error analysis, as implemented in the PROFILE program. 1 28 Assuming representative station distribution and proper sampling and analytical techniques, the “ precision” of a mean, surface layer, growing season value depends largely upon the number of sampling rounds and the inherent temporal variabilities of water quality components in the reservoir being studied. For sampling periods of roughly a week or longer, the variance of the Chapter 1 Introduction mean is roughly inversely proportional to the number of rounds. Based upon analyses of variance applied to model development data sets ( Walker 1980, 198 1), temporal variance components of phosphorus, transparency, and chlorophyll a are typically 0.31,0.33, and 0.62, respectively, expressed as CVS. Figure 1.6 shows the estimated accuracies of reservoir mean concentrations computed from sampling designs with between 1 and 30 sampling rounds over a range of temporal CVS. The “ value” of each additional round, as measured by the reduction in the mean CV, decreases as the total number of rounds increases. This figure provides a rough perspective on design sensitivity and a basis for interpreting the reliability of data from historical monitoring activities, provided the sampling regimes were both specified and representative. TEMPORALCOEPflCKt4TOF VARIATION o 0.2 0.4 0.6 0.8 1.0 1 90 TYPICAL VALUES FOR GE RESERVOIRS a CHL A TOTALP ~ BIMONTH1. Y MONIHLY BIWEEKLY WEEKLY Figure 1.6. Estimated accuracy of reservoir mean concentration computed from sampling designs with between 1 and 30 sampling rounds over a range of temporal CVS The “ adequacy” of a given monitoring program is partially determined by the precision of the mean concentration estimates calculated from the data. Because of the limited pool sampling schedule employed by the EPA National Eutrophication Survey ( three to four sampling rounds per growing season), typical error CVS were on the order of 0.18 for mean total phosphorus, 0.18 for mean transparency, and 0.28 for mean chlorophyll a. More precise estimates ( e. g., mean CVS less than 0.10 for nutrients and transparency and 0.15 for mean chlorophyll a) are desirable for model applications in a reservoir management context. Chapter 1 Introduction 1 29 The purpose of sampling in and below the thermocline ( Table 1.4) is to provide information on vertical stratification and the accumulation and transformation of nutrients within the hypolimnion. Many important secondary water quality effects of eutrophication are expressed in bottom waters, including oxygen depletion, development of reducing conditions, nutrient accumulation, iron and manganese releases, and sulfide and ammonia generation. While nutrient data from the hypolimnion are not used exclusively in the models, they are important for developing an understanding of nutrient cycling and reservoir processes. Since metaiimnetic and hypolimnetic samples are less important for trophic state assessment and model implementation, however, sampling fi equencies in and below the thermocline can be lower than those used for the mixed layer. 1 30 Chapter 1 Introduction 2 FLUX FLUX Overview FLUX is an interactive program designed for use in estimating the loadings of nutrients or other water quality components passing a tributary sampling station over a given period of time. These estimates can be used in formulating reservoir nutrient balances over annual or seasonal averaging periods appropriate for application of empirical eutrophication models. Data requirements include ( a) grab sample nutrient concentrations, typically measured at a weekly to monthly frequency for a period of at least 1 year, ( b) corresponding flow measurements ( instantaneous or daily mean values), and ( c) a complete flow record ( mean daily flows) for the period of interest. Using six calculation techniques, FLUX maps the flow/ concentration relationship developed from the sample record onto the entire flow record to calculate total mass discharge and associated error statistics. An option to strati~ the data into groups based upon flow, date, and/ or season is also included. In many cases, strati& ing the data increases the accuracy and precision of loading estimates. Uncertainty is characterized by error variances of the loading estimates. A variety of graphic and tabular output formats are available to assist the user in evaluating data adequacy and in selecting the most appropriate calculation method and stratification scheme for each application. FLUX provides Mormation which can be used to improve the efficiencies of future monitoring programs designed to provide data for calculating loadings and reservoir mass balances. The succeeding sections of this chapter contain descriptions of the following topics: a. Input data requirements. b. Theory. c. Program operation. d Typical application sequence. Chapter 2 FLUX 2 1 e. Procedure outline. f Data entry screens. g. Data file formats. h. Documented session. Input Data Requirements Two data sets are required to run FLUX. One defines sample characteristics ( date of collection, concentration, and instantaneous flow). The other describes the complete flow record ( date, mean daily flow) over the period of interest. Most of the effort in applying FLUX is generally involved in setting up the required data files. To facilitate this effort, FLUX can read files in a variety of formats, as described in a subsequent section ( see Data file formats). The function of the program is to use the water quality information in the sample data set to estimate the mean ( or total) loading which corresponds to the complete flow distribution over the period of interest. All program calculations and output are in metric units, with flows expressed in million cubic meters (= cubic hectometers, hm3) per year, concentration in milligrams per cubic meter ( parts per billion), and loading in kilograms per year. The data can be stored in other units and converted to the appropriate units when accessed by FLUX ( see Appendix B). For a typical nutrient balance study, sample data sets would include the following components: instantaneous flow, total phosphorus, ortho phosphorus, total nitrogen, inorganic nitrogen, and a conservative substance such as chloride. Potential applications of the program are not restricted to these constituents, however. The sample data are normally derived from periodic grab sampling. Flow measurements stored with the water quality data should correspond to the times of sampling. Daily mean flows can be used in the absence of instantaneous flow measurements; FLUX can automatically pair sample concentrations with corresponding daily mean flows specified in the complete flow record. Generally, samples are collected periodically ( weekly to monthly) over a year and over a range of flow regimes. If intensive storm event monitoring has been conducted, resulting discrete or composite samples should be summarized before they are accessed by FLUX; in this case, each record in the sample data set includes an event mean flow and a flow weighted mean concentration for each component. Differences in the duration of composite samples are not considered in the current version of FLUX. If continuously sampled events represent a significant fraction of the total loading over the estimation period, the program may overestimate the error variance of the loading estimates. To avoid severe biases in the load estimates, special consideration must be given to 2 2 Chapter 2 FLUX the specification of sample flows in small, flashy streams or storm sewers ( see Typical application sequence). The reliability of loading estimates strongly reflects monitoring program designs. Water quality samples should be taken over the ranges of flow regime and season which are represented in the complete flow record. For a given number of concentration samples, loading estimates will usually be of greater precision if the sampling schedule is weighted toward high flow seasons and storm events, which usually account for a high percentage of the annual or seasonal loading. While the calculation methods described below are designed to make efficient use of the available datq they cannot work miracles. If the basin dynamics are such that annual loadings are dominated strongly by a few extreme events, no calculation procedure will give an acceptable answer without representative samples from at least some of the major events. FLUX provides graphic and tabular output which can help to evaluate the adequacy of the sample data set for use in load calculations. Sample data files can include up to 64 fields representing different water quality components and other sample descriptors. Loading calculations are performed for only one component at a time. Concentrations which are entered as zero or negative values are assumed to be missing. Sample records with zero or negative flow values are not used in load calculations. All FLUX calculations are performed in computer memory; source data files are not modified. The flow data set specifies the complete flow distribution, which is generally derived from continuous stage or velocity measurements made at or near the water quality monitoring site. Typically, flow records consist of a mean flow for each day in the period of interest. In the absence of daily measurements, other averaging flow periods can also be used ( weekly, monthly), but with some loss of accuracy. If a continuous flow record is not available for a particular site, one might be constructed using simulation techniques or correlating available flow measurements with simultaneous data from a nearby benchmark station with a continuous flow record and similar watershed. Missing values are permitted in the flow distribution file, but they should be avoided by estimating them independently. Zero flow values are acceptable to permit applications to intermittent streams. Negative flow values ( reverse flows) are treated as zeros. Average flow rates and loads calculated by FLUX reflect total transport in the downstream direction. This may be different from the net transport estimates appropriate for use in BATHTUB or other massbalance models. If the stream contains significant reverse flows, an option is available for calculating total transport in the upstream direction; this essentially involves reversing the sign of the sample flow and daily flow data. The net downstream transport can subsequently be calculated by subtracting the total upstream transport rates from the total downstream transport rates. It is convenient to define the time period represented in the sample data set as the “ sampling period” and that represented in flow data set as the “ averaging Chapter 2 FLUX 2 3 period.” Normally, these two periods correspond, i. e., the flow data set contains a mean daily flow value for each day in the year of water quality sampling. If the sampling and averaging periods do not correspond ( e. g., the sample set might contain data from 1978 through 1981, and the flow set might contain daily flows for 198 1), then the user is making the assumption that the flow/ concentration dynamics of the stream are stable, i. e., that concentrations measured between 1979 and 1980 are also representative of those measured in 1981. Using samples from outside the averaging period can increase the accuracy and precision of the loading estimates ( by increasing the number of samples and improving the coverage of flow regimes); this may introduce bias in the loading estimates, however, if there are significant year to year variations in the flow/ concentration relationship caused by variations in climate, hydrology, or watershed land use. In each program run, the user specifies the date ranges and/ or season ranges to be used for samples and flows; this permits estimation of both annual and seasonal loadings from source data files containing data from 1 or more years of monitoring. The flow data set may include daily flows from the year( s) of water quality monitoring, as well as other periods which may represent “ low flow,” “ average,” and “ high flow” years. Provided that a sufficiently wide range of flow regimes are sampled, this permits extrapolation of the sample record, i. e., estimation of year to year variations in loadings based upon sample data from a specific year or years. FLUX can handle problems containing up to 900 samples and 8,000 daily flow records ( 22 years), These constraints apply to data read into computer memory at the start of program execution, not the size of the input data files. Since the user is prompted for the ranges of sample and flow dates to be used in a given run, the input data files can be much larger than indicated above. Users should check the online documentation file ( accessed through the HELP option of the main menu) for maximum problem dimensions and other program changes in updated versions of FLUX ( Version 5.0 is documented here). Theory Loading calculation methods Table 2.1 lists the equations used to calculate the mean loading and error variance using six alternative methods. Method applicability depends upon flow/ concentration dynamics and sampling program design in each application. Walker ( 198 1,1987) provides details on the derivation and testing of each method. The FLUX procedure “ Calculate/ Loads” provides a one page summary of loadings calculated using each method. The user must decide which method is most appropriate for each application, based upon factors discussed below. In most cases, particularly if the data are properly stratified ( see Data stratification), the calculation methods will give estimates which are not 2 4 Chapter 2 FLUX Table 2.1 Estimation Algorithms Used in FLUX Program Method 1  Direct Mean Loading w, = Mean( w) Method 2 Flow Weighted Concentration ( Ratio Estimate) W2 = WI Mean( Q) / Mean( q) Method 3 Modified Ratio Estimate ( Bodo and Unny 1983) W3 = W2( 1 + FWJn)/( 1 + FJn) Method 4 Regression, First Order ( Walker 1981) W4 = W1[ Mean( Q)/ Mean( q) lb+’ Method 5 Regression, Second Order ( Walker 1987) W5 = W4( 1 + r FJ/( 1 + r Fq) Method 6 Regression Applied to Individual Daily Flows w= = ~ jexp [ a + ( b+ l) ln( Qi) + SE2/ 2 ] where Ci = qi = b = a = Wi = F = wq Fq = F~ = Qj = n = N = w“ = Vm = r = Xj = SE = Mean( x) Var( x) Cov( xry) measured concentration in sample i ( mg/ m3) measured flow during sample i ( hm3/ year) slope of In( c) versus In( q) regression intercept of In( c) versus In( q) regression measured flux during sample i = qi Ci ( kg/ year) Cov( w, q) / [ Mean( w) Mean( q)] Var( q) / [ Mean( q) Mean( q)] Var( Q) / [ Mean( Q) Mean( Q)] mean flow on day j ( hm3/ year) number of samples ( i) number of daily flows ( j) estimated mean flux over N days, method m ( kg/ year) variance of estimated mean flux, method m ( kg/ year) z 0.5 b( b + 1) sum over N dates in daily flow record standard error of estimate for In( c) versus In( q) regression = mean of vector x = variance of vector x = covariance of vectors x and y Chapter 2 FLUX 2 5 significantly different from each other. Thus, the choice of method will not be critical. Desired properties of the loading estimates include minimum bias and minimum variance. The distinction between bias and variance ( analogous to “ accuracy” and “ precision”) is important. A biased procedure will give the wrong answer, even for an infinite number of samples, whereas variance in the mean can generally be reduced by increasing the number of independent random samples. The seriousness of bias depends upon its size relative to the variance of the mean or the standard error of estimate. Biases less than 10 percent of the standard error account for less than 1 percent of the total mean squared error and are generally considered negligible ( Cochran 1977). Bias in a loading estimate can come from two sources: unrepresentative sampling or the use of an inappropriate calculation method. These sources are discussed below. Consistent problems with sample collection, handling, and analytical procedures can cause one type of unrepresentative sampling; there is little that can be done about these problems at the calculation stage. Another, more subtle, but generally more common type of unrepresentative sampling results from differences in the distributions of flows between the sampling dates and the entire averaging period. Sampled flows may tend to be higher or lower, on the average, than the complete distribution of flows or contain a higher or lower percentage of extreme flows. This can lead to bias in the estimate if the calculation procedure does not take the relative flow distributions into consideration by directly representing the flow/ concentration relationship and/ or by strati~ ing the sample, as described below. Even if the sampled and total flow distributions are equivalent, bias can be introduced as a result of the calculation method. For example, loading calculated as the product of the mean sample concentration and the mean flow over the averaging period would be badly biased if flow and concentration are ( even weakly) correlated ( Walker 198 1). Because of the potential bias associated with this method, it is not included in the program. The six included methods have been selected and tested so that, for representative samples, they should not introduce significant bias except under special conditions discussed below for each method. The extent to which the methods can minimize variance in the loading estimates is limited ultimately by the sample data sets. Method applicability depends upon the relationship between concentration and flow. In FLUX, this characteristic is represented by the slope of a log( Concentration) versus log( Flow) regression ( C/ Q slope) derived from the sample data set. Typically, the C/ Q slope approaches  1 at monitoring stations which are downstream of major point sources. The slope may approach or exceed 1 at monitoring stations where the load is generated as a result of runoff or high flow events, particularly for particulate components. In many watersheds, the C/ Q slope for total phosphorus varies with flow ( negative at low flows to positive at high flows). FLUX graphic and tabular output helps to 2 6 Chapter 2 FLUX characterize the concentratiordflow relationship; this characterization is essential to selecting the appropriate calculation method and developing reliable loading estimates. Method 1 ( direct load averaging) is the simplest of the calculation schemes. It gives unbiased results only if the samples are taken randomly with respect to flow regime. This method completely ignores the unsampled flow record and generally has higher variance than the other methods because the flow record on the unsampled days is not considered. This method is most appropriate for situations in which concentration tends to be inversely related to flow ( C/ Q slope approaching  1; loading does not vary with flow). This might occur, for example, at a station which is below a major point source and the flow/ concentration relationship is controlled by dilution. Method 2 bases the loading estimate on the flow weighted average concentration times the mean flow over the averaging period. This amounts to a “ ratio estimate” according to classical sampling theo~ ( Cochran 1977). This method performs best when flow and concentration are unrelated or weakly related. Some bias may occur for extreme flow/ concentration relationships. In test simulations of a stream with a C/ Q slope 0.75, Method 2 overestimated loadings by an average of 10 percent ( Walker 1987). This bias can be substantially reduced by stratifying the samples into groups of relatively homogeneous concentration and applying the method separately to each group, as described in more detail below. This is perhaps the most robust and widely applicable method, especially when applied to stratified data sets. Method 3 modifies the Method 2 estimate by a factor that is designed to adjust for potential bias in situations where concentration varies with flow. The factor was developed byBeale( 1962) and applied in a load estimation method developed by the International Joint Commission( IJC)( 1977), as described by Bodo andUnny( 1983, 1984). Trial simulations indicate that, compared with Method 2, this procedure is moderately successful at reducing bias but tends to have slightly higher mean squared error for streams with C/ Q slopes greater than or equal to zero ( Walker 1987). Method 4 is the regression method developed by Walker ( 1981). This method adjusts the flow weighted mean concentration for differences between the average sampled flow and the average total flow using the C/ Q slope. It should not be used in cases where the daily flow data set contains a significant number of zero flow values. This method petiorms well over a range of C/ Q slopes. Some bias is introduced at high C/ Q slopes. At a slope of 0.75, for example, simulated bias is 13 percent of the mean loading but accounts for only 6 percent of the total mean squared error ( Walker 1987). Additional simulations indicate that bias also occurs if the C/ Q slope is highly nonlinear ( i. e., quadratic or higher order polynomial). This problem can be resolved by strati & ing the sample so that the relationship is approximately linear within each group. Chapter 2 FLUX 2 7 Method 5 modifies the Method 4 estimate by a factor accounting for differences in variance between the sampled and total flow distributions ( Walker 1987). The derivation of the method is based upon expected value theory ( Benjamin and Cornell 1970). Method 5 should not be used in cases where the daily flow data set contains a significant number of zero flow values. As for Method 4, bias resulting from nonlinearity in the log ( c) versus log ( q) relationship can be reduced by strati$ ing the data. Method 6 is another regression based calculation method. For each stratum, the C/ Q regression equation is applied individually to each daily flow value. In contrast, Methods 4 and 5 use only the flow means and variances. A small correction for bias resulting from the log transformation is also included. This method is often appropriate for generating daily, monthly, or yearly load time series using an optional FLUX procedure designed for this purpose ( Calculate/ Series). Relatively intensive sample data sets and well defined concentration/ flow relationships are required for reliable application of this method. Method 6 is generally preferred over the other regression based methods when the flow/ concentration relationship is well defined. In applications to small, flashy streams, special consideration must be given to the specification of sample flows to avoid bias in Method 6 estimates ( see Typical application sequence). Error analysis calculations are time consuming relative to the other methods. An option to turn off the error analysis for Method 6 is included ( Utilities/ Set/ Method 6). For each method, the jackknife procedure ( Mosteller and Tukey 1978) is used to estimate error variance. This involves excluding each sampling event, one at a time, and recalculating loadings, as described in Table 2.2. While alternative, direct estimators of variance are available from classical sampling theory for most of the methods ( Cochran 1977; Walker 1981; Bodo and Unny 1983, 1984), such formulas tend to rely upon distributional assumptions. The direct estimators are generally applicable to large samples and normal distributions, neither of which is typical of this application. As described by Cochran ( 1977), the jackknife has improved properties for ratio estimators derived from small, skewed samples. Use of the jackknife procedure also provides a uniform basis for comparing calculation methods with respect to estimated variance. Simulations ( Walker 1987) indicate that jackknifing provides a reasonably unbiased estimate for error variance for a range of C/ Q slopes. Two important factors should be considered in interpreting the variance estimates. First, the estimates are themselves subject to error and are of limited accuracy in small sample sizes, particularly if the sampled flow distribution is not representative. Second, the variance estimates do not reflect effects of biases associated with some calculation methods under certain conditions, as discussed above. Thus, while the estimated variances are important factors to consider in selecting the “ best” loading estimation method, the sample characteristics and bias potential should also be considered. FLUX diagnostic procedures assist in this process, as described below. 2 8 Chapter 2 FLUX Error variance estimates developed by FLUX assume that the samples are statistically independent. This may not be the case if the file contains large numbers of discrete samples taken within relatively short periods of time. One approach to solving this problem is to composite the samples by event prior to calculating loadings. Important Wormation on the flow/ concentration relationship may be lost in compositing, however. As an alternative to compositing, discrete samples can be grouped by event only for the purposes of error analysis. In FLUX, sampling events are defined by the program parameter T. = Maximum Event Duration ( days). Samples collected within T, days of each other are considered part of the same sampling event. The default setting for T. is 1 day. This setting only influences the error variance estimates ( not the mean loading estimates). It only influences error variance estimates developed from relatively intensive sample data sets containing multiple samples on the same day or within the current N~ setting. Data stratification FLUX includes an option to divide the input flow and concentration data into a series of groups and calculate loadings separately within each group using the methods described above. Using formulas derived from classical sampling theo~ ( Cochran 1977), the mean and variance estimates within each group are subsequently combined across groups using weighting factors which are proportional to the frequency of each group in the total flow distribution ( see Table 2.2). The groups, or “ strat~” can be defined based upon flow, season, and/ or date. Stratification can serve three basic functions: a. Adjust for differences in the frequency distributions of sampled and unsampled flow regimes. b. Reduce potential biases associated with some calculation methods and/ or sampling program designs. c. Reduce the error variance of the mean loading estimate. When sample data are adequate, stratification can offer significant advantages over the direct methods and provide insights that can be used to improve sampling efficiency in future years. In most applications, the groups are defined based upon flow. The “ flowinterval” method was developed by the U. S. Army Engineer District, Buffalo ( 1975), for use in the Lake Erie Wastewater Management Study and is described by Verhoff, Yaksich, and Melfi ( 1980) and Westerdald et al. ( 198 1). This procedure applies the direct load averaging ( Method 1) separately to different data groups, defined based upon flow regimes. Since loading usually increases with flow, grouping the data based upon flow reduces the loading Chapter 2 FLUX 2 9 2 1o Table 2.2 stratified Sample Algorithm ( Cochran 1977; Bodo and Unny 1983) definitions: s = subscript indicating stratum m= subscript indicating estimation method N, = number of daily flows in stratum s N, = total number of daily flows ns,. = optimal number of samples in stratum s, given nt w = total number of sampled concentrations w= m, s mean flux in stratum s estimated by method m v= m, s variance of mean flux in stratum s estimated by m s = m, s effective standard deviation within stratum s for method m w m, t = mean flux over all strata estimated by method m v= m, t variance of mean flux over all strata estimated by method m V*= m, t variance of mean flux over all strata estimated by method m for optimal allocation of nt samples according to n~,. z= sum over all strata ( s) Equations: N, = ~ N~ % = ~ n~ w m, t = Z ( wm, JJ6)/ Nt v m, t = Z ( Vm, JJ$ 2)/ Nt2 s = m, s [ n, Vm, J0” 5 n~. = ntN~ Sm,~ / ~ ( N& J V*= m, t x ( V~, SN~ 2nJn~,.)/ N~ variance within each group and results in lower variance for the total loading estimate. A flow stratified version of Method 2 written in SAS ( Statistical Analysis System) was developed and applied to estimate phosphorus loadings in a Vermont lake study ( Walker 1983). The IJC method described by Bodo and Unny ( 1983, 1984) is a flow stratified version of Method 3. In FLUX, data groups or strata can be defined based upon flow range, date range, and/ or season range. Generally, flow ranges would be used and the data would be stratified into two or three groups based upon flow. In some situations, however, it maybe desirable to strati~ based upon sampling date or Chapter 2 FLUX season. Stratification based upon season may be usefti in situations where there is a strong seasonal variation in concentration which is independent of flow or for streams with highly regulated flows, such as a reservoir outflow station ( particularly when intake levels are varied seasonally). Flowindependent, seasonal variance components are more likely to be detected in analysis of dissolved or inorganic nutrient concentrations ( particularly nitrate) than in analysis of particulate or total nutrient concentrations. In deftig stra~ one objective is to isolate homogeneous subgroups, based upon the flow/ concentration relationship assumed by the calculation method ( constant loading for Method 1, constant concentration for Methods 2 and 3, and log linear flow/ concentration relationship for Methods 4 6). A second objective is to set stratum boundaries so that the sampled and total flow distributions are equivalent within each stratum. This protects against bias in the loading estimates and applies particularly to high flow strata. As described above, the method used to estimate error variance does not detect bias. If the flow distributions are not equivalent within each stratum, then minimum variance is less reliable as a criterion for selecting the “ best” calculation method and loading estimate. Statistical and graphical tests are provided to compare flow distributions within each stratum. Robustness of the loading estimate decreases as the number of statistical parameters which must be estimated from the sample data set increases. The number of parameters which must be estimated depends upon the calculation method and upon the number of strata. Methods 1 and 2 require one parameter estimate for each stratum. Methods 3, 4, 5, and 6 require two parameter estimates per stratum. Strati& ing the data into two or three groups based upon flow and using Method 2 is generally adequate to capture the flow/ concentration relationship while requiring the fewest parameter estimates ( in statistical terms, using up the fewest degrees of freedom). If concentration does not vary systematically with flow, the need for flow stratification decreases. Uncertainty in the loading estimate is reflected by the CV estimate reported for each calculation method. The CV equals the standard error of the mean loading divided by the mean loading. The CV reflects sampling error in the flow weighted mean concentration. Potential error variance in the flow measurements are not considered in these calculations. In practice, CV values < 0.1 are usually adequate for use in mass balance modeling, especially considering that uncertainty in flow measurements is usually in this range. Depending on stream dynamics, CV values < 0.1 may be very difficult to achieve, especially in small, flashy streams with strong C/ Q relationships. CV values between 0.1 and 0.2 may be adequate for modeling purposes, especially for minor tributaries. If higher CVS are found, the user should consider refining and extending the stream monitoring program to obtain better data sets for load estimation before proceeding with modeling efforts. This particularly applies if the CV values are high for major tributaries. Chapter 2 FLUX 2 11 For each calculation method, FLUX generates an invento~ of sample and flow data in addition to a breakdown of the flow, load, and variance components within each stratum, as well as for the total strat~ as demonstrated in Table 2.3, for the Caddo River example. Samples have been divided into three flow intervals. Complete output for this example is given at the end of this chapter. Table 2.3 Breakdown by Flow Stratum  Caddo River Example FLUX Breakdown by Stratum: FREQ FLOU FLUX VOLUME Wiss CONC CV ST NS NE DAYS HM3/ YR KG/ YR HM3 KG PPB  1 93 93 582.0 120.23 2761.4 191.58 4400.1 23.0 .050 2 61 61 407.0 397.42 14501.1 442.85 16158.7 36.5 .092 3 14 14 107.0 2070.70 259357.2 606.61 75978.7 125.3 .148 *** 168 168 1096.0 413.59 32171.8 1241.05 96537.5 77.8 .118 Optimal Sample Allocation: ST NE NE% NEOPT% FREQ% VOL% MASS% VAR% VARIANCE CV 1 :: 93 55.4 3.8 53.1 15.4 4.6 .0 . 5276E+ 04 .050 2 61 61 36.3 20.8 37.1 35.7 16.7 1.7 . 2442E+ 06 .092 3 14 14 8.3 75.5 9.8 48.9 78.7 98.3 . 1407E+ 08 .148 *** 168 168 100.0 100.0 100.0 100.0 100.0 100.0 .1432E+ 08 .118 Notes: Output from the lList/ Breakdownl Procedure for Caddo River with 3 Flow Strata The top part of the screen lists the distribution of samples, flows, fluxes, volume, and mass across strata for the current calculation method. The middle part of the screen lists the distribution of sampling effort, flow days, flow volume, mass, and error variance, each expressed as percentage of the total. The bottom part of the screen describes the potential benefit of optimizing the sample allocation across strata to obtain the lowest error variance for a fixed number of sampling events. NE% = percent of total sample events in stratun NEOPT% = optimal percent of total sample events in stratum The reduction in error CV attributed to shifting from the current sample distribution ( NE%) to the optimal distribution ( NEOPT%) is listed. This can be used to refine future monitoring program designs. Generally, a shift towards more intense sampling of high flow strata ~ ill be indicated. Typically, mostof theloadanderror varianceisinthe high flowstratum. Since the variance component is roughly inversely related to sampling frequency within each stratum, the “ breakdown by stratum” given in Table 2.3 is useful for evaluating sampling strategies. The low flow stratum accounts for 55.4 percent of the total samples but only 4.6 percent of the total mass discharge. In future sampling, moving some ofthesamples fromthelow flow to the high flow stratum would reduce the variance ofthe total loading estimate. Alternatively, to reduce monitoring costs, the low flowsampling frequencies 2 12 Chapter2 FLUX could be reduced without substantially increasing the variance of the total loading estimate. FLUX also provides an estimate of the “ optimal” sample distribution ( expressed as percent of the total sampling effort allocated to each stra~ NEOPTO/ Oin Table 2.3) which would minimize the variance of the total loading estimate for a given total number of independent samples, using the equations specified in Table 2.2. Comparing the observed variance with the optimal variance provides an approximate indication of the potential benefits of optimizing the sample design. In this case, shifting from the historical sample distribution across flow strata ( 55%/ 36%/ 8%) to the optimal sample distribution ( 4%/ 2 1%/ 76%) would decrease the CV of the load estimate from O. 118 to 0.045. As described by Bodo and Umy ( 1983, 1984), stratum breakdowns can be used to refine monitoring program designs for future years, subject to practical limitations in sample scheduling and total budget and to requirements imposed by other monitoring objectives. The “ optimal” distribution of sampling effort indicated by the program may be difficult to achieve without automated equipment. An important statistical limitation is that the “ optimal” allocation assumes that the samples are serially independent, and it may be impossible to take the recommended number of independent samples from intensively monitored strata. Five samples taken from different storm events would tend to be less serially dependent than five samples taken within one event, for example. Because of these limitations, the “ optimal” design should not be viewed as an absolute objective, but as a general direction for adjusting previous survey designs within practical constraints. Diagnostics FLUX includes several routines for generating scatter plots and histograms of flow, concentration, loading, and sample dates, as illustrated at the end of this chapter. The relationship between flow and concentration partially determines the appropriate calculation method and should be reviewed in each application. Flow frequency distributions ( sampled versus total) can also be graphically compared. These displays characterize the flow and concentration distributions and can assist the user in assessing data adequacy, identi~ ing appropriate stratification schemes, and evaluating calculation methods. The calculation methods differ with respect to the schemes used to estimate the loadings on the unsampled days or periods. For a given method, observed and predicted fluxes can be compared for each water quality sample. This provides one measure of performance. Ideally, the flux residuals ( loglO( observed flux) minus loglO( predicted flux) should be random and independent of flow season. In practice, this independence is sometimes difflcuh to achieve with the relatively simplistic models upon which the calculation methods are based. The residuals analysis procedure generates plots of observed versus predicted loadings, residuals versus flow, and residuals versus Chapter 2 FLUX 2 13 date. Alternative stratification schemes can be investigated to reduce the flowdependence and/ or time dependence of the residuals. Listings of residuals and jackknifed loading estimates are useful for identi& ing outliers and determining sensitivity of the loading estimates to individual samples. FLUX includes an outlier detection routine which can be used to delete suspected outliers from the sample data set. Outliers are detected based upon deviations of the residuals from a lognormal distribution ( Snedecor and Cochran 1989). This procedure should be used conservatively. Detection of outliers depends upon the current stratification scheme and calculation method. Important information may be lost if an apparent outlier is actually an important signal. Suspected outliers are usually apparent on the concentration versus flow scatter plots. Developing confidence with the program, stratification scheme, and calculation method are suggested before using the outlier deletion procedure. Program Operation Introduction This section describes the FLUX menu structure and operation procedures. When the program is run ( from the DOS prompt), a series of help screens summarizing model features is first encountered. If error messages appear, it generally means that one of the FLUX program files has been corrupted or that your computer does not have enough available memory. TV reinstalling the program. Try unloading any memory resident software. If you are trying to run the program from Windows, try exiting Windows and running directly from DOS. The program permits selection of ‘ user mode’ at startup after introductory screens. The selection of user mode is followed by a menu which provides interactive access to eight types of procedures with the following fhnctions: FLUX VERSION 5.0 Data Calculate Method Plot List Utilities Help Quit Data Read and/ or Strati fy Data Calculate Calculate Loads Using Current Data & Stratification Scheme Method Select Flux Calculation Method Used in Plots & Tables Plot Plot Load, Flow, and/ or Concentration Data List List Output Formats for Current Calculation Method Utilities Program Uti lities & Options Help View Help Screens Quit End Session 2 14 A procedure category is selected by moving the cursor ( using arrow keys) or by pressing the first letter of the procedure name. Selected procedures in the menu box are highlighted on the screen and underlined in the following documentation. Assistance in navigating around the menu can be obtained by Chapter 2 FLUX pressing the < F7> fiction key. A Help screen describing the selected procedure can be viewed by pressing < Fl>. After each procedure is completed, control returns to the above menu screen. Essential features of the current data set are summarized below the menu box ( not shown here). Data procedures Data procedures control input, stratification, listing, and other manipulations of sample and./ or flow data used in load calculations: Read Read New Sanple and/ or Flow Data Stratify Divide Sanples & Flows into Groups for Load Calculations Delete Delete a Specific Sanple or Delete Excluded Samples Composite Composite Samples by Date FlowSub Substitute Daily Mean Flows for Sample Flows Title Enter New Title for Labeling Output List List Sanple or Flow Input Data Four methods for reading in new sample or flow data are available under Data/ Read: Reset Read New Sa~ le & Flow Data; Reset Stratification Scheme Keep Read New Sa~ le & Flow Data; Keep Current Stratification Sch Sanples Read New Sanple Data Only; Keep Current Stratification Schern I nd, X Read Sample & Flow Data from Station Index File In the first three procedures, a data entry screen is presented for defining all input specifications ( data file names, variable labels, time periods, and units conversion factors). Use Reset to read in new flow data and reset the stratification scheme. Use Keep to read in new data without changing the current stratification scheme. Use Samples to read in new sample data only, without changing the current daily flow data or stratification scheme. Use Index to read in new data from a station index file, which is a user created ASCII file defining the storage locations and formats for concentration and flow data referring to specific stations. Using index files greatly speeds and simplifies the specification of input data. ( See Data entry screens.) If variable labels ( for daily flows, sample flows, and concentration) are left blank on data entry screens, the user is prompted to select the appropriate field from a list of all fields contained in the source data file. Screen messages track the progress of data retrieval from disk files. If the specified data set has fewer than three samples or no daily flows, an error message appears and control returns to the main menu. Note that this may occur if the file names or variable labels are entered incorrectly. If a valid data set is retrieved, subsequent screens include a listing of missing or out of sequence daily flows ( Data/ List/ Chapter 2 FLUX 2 15 Missing procedure) and a summary of the current stratification scheme ( Data/ Stratify/ List procedure). Control then returns to the main menu. Data/ Stratify procedures divide the sample and flow data into groups based upon flow, date, and/ or season. In many cases, stratification increases the accuracy and precision of load estimates. At least three samples are required in each stratum. Four options are available: Flow Define Strata Based Upon Flow; Reset Data & Season Limits Genera 1 Define General Stratification Scheme vs. Flow, Date, Season Reset Reset Stratification Scheme  Use 1 Stratum Only List List Current Strati f i cat ion Scheme & Sanple Counts Strati& ing based upon flow is often appropriate, especially when concentration is correlated with flow: 2 Strata Use 2 Flow Strata  Boundary at QMEAN 3 Strata Use 3 Flow Strata  Boundaries at QMEAN/ 2, QMEAN x 2 4 Strata Use 4 Flow Strata  Boundaries at QMEAN/ 2, QMEAN x 2, QMEAN x 8 Other Use Flows to Define Strata; Enter Flow Bounds Directly The first three procedures defineflow boundaries automatically. Dividing the dataintotwo strata based uponflow( low flow andhigh flow) is often appropriate. Three or more flow stratamaybe appropriate for relatively intensive datasetswithstrongflow/ concentration relationships. The last procedure permits direct entry offlow boundaries. Each stratum must contain atleast three sample events. Ifastratum contains fewer thenthree events, theuseris asked to redefine the flow boundaries until a valid stratification scheme is defined or the stratification scheme is reset. Data/ Delete procedures operate only on data stored in memory; they do not change disk files: One Delete a Specific Sample Excluded Delete All Sanples Excluded from Current Stratification Sche The Data/ Composite procedure combines samples collected on the same date or in the date interval into a single composite sample: 2 16 Chapter 2 FLUX Ccmposite Canposite Sanples by Date The user is prompted for the time interval ( number of days) to be used for compositing samples. This optional procedure may be appropriate for data derived from intensive monitoring programs providing multiple samples per date. The composite sample concentration is the flow weighted mean of the individual samples. The composite sample flow is the average of the sample flows. Because of possible variations in actual event duration, it is generally preferable to composite samples prior to running FLUX; i. e., to specifi event mean flows and event flow weighted mean concentrations in the source data files. The Data/ FlowSub procedure can be used to test the sensitivity of load estimates to the types of flow measurements which are paired with sample concentrations: F 1ousub Substitute Dai ly Mean Flows for Sanple Flows Depending upon source data files, input sample flows may be instantaneous flows measured at the time of sampling. The Data/ FlowSub procedure replaces sample flows with daily mean flows on the corresponding sample dates. Samples are deleted if the corresponding daily mean flow is missing or zero. This flow substitution may also be performed in the Data/ Read procedures by entering “ Lookup” in the sample flow field. Data/ List procedures summarize the sample and/ or flow data which have been retrieved from disk files: Samples List Sample Data F t OMS List F1OH Data Missing List Missing or Out of Sequence Daily Flows Before proceeding with load calculations, data listings should be reviewed to make sure that the correct sample and flow data have been retrieved from disk files. Both sample flows and corresponding daily mean flows are listed by the first two procedures. Daily flow data files read by FLUX are assumed to be sorted by date. The Data/ List/ Missing procedure lists missing or out of sequence daily flow records. If any are detected, FLUX can still operate. It is desirable, however, to estimate any missing flows independently and to sort flow files before running FLUX. Chapter 2 FLUX 2 17 Calculate procedures Calculate procedures can be accessed tier valid sample and flow data sets have been read and a valid stratification scheme has been defined. Three options are available: FLUX VERSION 5.0 Data e Method Plot List Utilities Help Quit Conpare Series Corrpare Compare Sample Flow & Total Flow Distributions Loads Calculate Loads Using Each Method Series Generate Load Time Series The Calculate/ Compare procedure provides information which can be used to assess adequacy ofthe sample dataand/ orstratificationscheme. The Calculate/ Loadsprocedure lists average flows, flux rates, flow weighted mean concentrations, and error estimates using each calculation method; this provides the basic tiormation needed for BATHTUB applications. The Calculate/ Series procedure lists flow, load, and concentration time series using the currently selected calculation method. Four options are available: Yearly Generate Load Time Series by Calendar Year WtrYearly Generate Load Time Series by Water Year Monthly Generate Monthly Load Time Series Daily Generate Daily Load Time Series Time series output does not include error estimates. These procedures are included primarily for generating load time series for use in applications other than BATHTUB which may require daily or monthly estimates. Method procedure The Method procedure asks the user to select the loading calculation method to be used in generating subsequent plots and output tables. Six choices are provided: FLUX  VERSION 5.0 Data Calculate !!! Q@ d Plot List Utilities Help Quit 1 AVG LOAD 2QWTDC 3 IJC 4 REG 1 5 REG 2 6 REG 3 1 AVG LOAD Method 1  Mean Load 2QWTDC Method 2  Flow Wtd Hean Cone. 3 IJC Method 3  Flow Wtd Nean Cone. ( IJC Modification) 4 REG 1 Method 4  Regression Model 1 5 REG 2 Method 5  Regression Model 2 6 REG 3 Method 6  Regression Model 3  log( C) vs. log( Q) Separate 2 18 Chapter2 FLUX Method 2 is initially selected as the default calculation method when the program is started. Descriptions of each method are given above ( see Loading calculation methods); summary descriptions can be viewed by selecting a method and pressing the Help key < F 1> or by running the Help procedure. Plot procedures Plot procedures provide important diagnostic information which can help in evaluating the adequacy of the current data set, stratification scheme, and calculation method: Barchart Cone Load Flow Daily Qfreq Residuals GridOpt Barcharts of Load, Mass, or Concentration Estimates Plot Sample Concentrations ( ppb) Plot Sample Loads ( kg/ yr) Plot Sample Flows ( hm3/ yr) Plot Daily Flows ( hfi/ yr) Plot Flow Frequency Distributions Plot Residuals = LOGlO ( Observed Load / Estimated Load ) Toggle Plot Grids On or Off The Plot/ Barchart procedures plot load, mass, flow weighted mean concentration, or flow as a function of calculation method or stratum: Load Load ( kg/ yr) Barcharts vs. Calculation Method or Stratum Method Plot Load Estimates ( kglyr) vs. Calculation Method Stratum Plot Load Estimates ( kg/ yr) vs. Stratwn Mass Mass ( kg) Barcharts vs. Calculation t4ethod or Stratum Method Plot Mass Estimates ( kg) vs. Calculation Method Stratun Plot Mass Estimates ( kg) vs. Stratum Cones Flow Ueighted Concentration ( ppb) vs. Calc. Method or Stratu Method Flow bleighted Concentration ( p@) vs. Calculation Method Stratun Flow Ueighted Concentration ( ppb) vs. Stratum Flow Mean Flow ( hm3/ yr) vs. Stratun Each bar chart ( exceptFlow) shows estimates+ l standard error. Plotting against method shows the sensitivityof the estimate ( total across all strata) to thecalculation method. Generally, alowsensitivity tocalculation method would support the reliability ofthe load estimates. Plotting against stratum shows estimates foreach data group using the currently selected calculation method. Plot/ Concprocedures display sample concentrations against four independent ( x axis) variables or a histogram: Chapter2 FLUX 2 19 Flow Plot Sanple Concentration ( ppb) vs. Flow ( hm3/ yr) Date Plot Sample Concentration ( ppb) vs. Date Month Plot Sample Concentration ( ppb) vs. Month Estimated Plot Observed vs. Estimated Cone. for Current Calc. Method Histogram of Observed Concentrations ( ppb) Both theobserved and theestimated sample concentrations areshown inthe first three procedures. The`` estimated'' sample concentration is based uponthe currently selected calculation method. Different symbols are usedto indicate samples indifferent strata. TheP1ot/ Loadand Plot/ Flowprocedures generate similar displays ofsarnple data: FLUX  VERSION 5.0 Data Calculate Method List Utilities Help Quit Barchart Cone Flow Daily Qfreq Residuals GridOpt Flow Date Month Estimated Histogram Flow Plot Load ( kg/ yr) vs. Flow ( hti/ yr) Date Plot Load ( kg/ yr) vs. Date t40nth Plot Load ( kg/ yr) vs. Month Estimated Plot Observed vs. Estimated Load Histogram Histogram of Observed Loads ( kg/ yr) FLUX VERSION 5.0 Data Calculate Method List Utilities Help Quit Barchart Cone Load Daily Qfreq Residuals GridOpt Date Month Histogram Comparison Both Date Plot Sample Flows ( hfi/ yr) vs. Date Uonth Plot Sanple Flows ( hm3/ yr) vs. Month Histogram Histogram of Sanple Flous ( hm3/ yr) Comparison Sample & Total Flow Histograms Both Plot Sanple Flow vs. Daily Mean Flow Plot/ Dailyprocedures display theentireflow record against date ormonth or as ahistogram: FLUX  VERSION 5.0 Data Calculate Method List Utilities Help Quit Barchart Cone Load Flow I) ailv Qfreq Residuals GridOpt Date Month Histogram Date Plot Daily Flows ( hti/ yr) vs. Date Month Plot Daily Flows ( hm3/ yr) vs. Month Histogram Histogram of Daily Flows ( hfi/ yr) Three format options are available for plotting daily flow against date: 2 20 lLinear Plot Daily Flows ( hti/ yr) vs. Date  Linear Scale 2Log Plot Daily Flows ( hm3/ yr) vs. Date  Log Scale 3Filled Plot Daily Flows ( hm3/ yr) vs. Date  Filled Chapter2 FLUX In addition to plotting the daily flow values, each of these formats also indicates daily flows on the dates of sample collection ( red squares). These displays are usefhl for identi& ing gaps in the sample record and for assessing sample coverage of major hydrographyfeatures. The lLinear and 2Log displays use different symbols to identi& strata. The 3Fi11ed display does not identifi strata. If zero flows are contained in the record, these are plotted as one half of the lowest positive flow value in the 2Log displays. The PlotiQfreq procedures display cumulative frequency distributions of sampled flow and total flow: T Freq Time Frequency Distributions for Sample & Total Flow V Freq Volune Frequency Distributions for Sample & Total Flow In the first case, they axis reflects the cumulative percentage of total samples or total flow days. In the second case, they axis is the cumulative percentage of the total sample volume or total flow volume. Plot/ Residuals procedures display residuals for the current calculation method: Cone Plot Residuals vs. Estimated Concentration ( F@) Load Plot Residuals vs. Estimated Load ( kg/ yr) Flow Plot Residuals vs. Sanple Flow ( hfi/ yr) Date Plot Residuals vs. Sample Date Month Plot Residuals vs. Sample Month Histogram Histogram of Residuals for Current Calculation Method Autocor Plot Residual Autocorrelation  Resid( t) vs. Resid( t 1) The residual is defined as log 10( observed sample flux/ estimated sample flux). Different symbols areused toidenti& strata. The Autocor procedure shows tielag l setidcomelation ofresiduds titismple order bwedupon date. As discussed above ( see Theory), serial correlation can influence the accuracy of error estimates and determine the appropriateness of time series methods for estimating loads. List procedures List procedures can be accessed only if a valid data set and stratification scheme have been defined. Three tabular output formats are provided using the currently selected calculation method: Chapter 2 FLUX 2 21 Residuals List Residuals & Screen for Outliers Breakdowns List Load & Flow Breakdowns by Stratwn; Optimal Sample Allot Jackknife List Jackknife Table for Current Calculation Method List/ Residualsprocedures provide detailed listing ofobservedandpredieted concentrations forthe currently selected calculation method: All List All Residuals Uithout Screening for Outliers Out 1 iers List Outliers Signif Set Significance Level for Outlier Screening The first procedure lists observed concentrations, estimated concentrations, and residua. ls( loglO( observed/ estimated)) foreach sample. The second procedure hwasitilm fomat, butlists odysmples wtichme suspected outliers. Outliersare detected based upon deviation from alognormal distribution; seethe associated help screen for a description oftheoutlier detection method. Ifany outliers are detected, the user may elect to delete therefrom the current sample list; source data files arenot modified. Theoutlier detection procedure is iterative mdautomaticdly repeats i~ elfmtil nooutliers we detected. The last procedure sets the significance level for outlier screening ( default= 0.05). The List/ Breakdowns procedure provides detailed information on the distribution of flow, flux, and error variance as a fuction of stratum for the current calculation method: Breakdowns List Load & Flow Breakdowns by Stratun; Optimal Sample Allot The top half of this output screen shows the sample properties. The bottom half estimates the optimal sample allocation across strata based upon the current sample properties. The optimal allocation is defined as the distribution of samp
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Title  Simplified procedures for eutrophication assessment and prediction user manual 
Subject  EutrophicationMathematical models.; Reservoir ecology.; Water qualityEvaluationComputer programs.; 41.3 P61 1999 Web Resource 
Description  Includes bibliographical references (p. R1  R3).; September 1996 (updated April 1999)." 
Creator  Walker, William W. (William Wilmot), 1949 
Publisher  U.S. Army Engineer Waterways Experiment Station 
Contributors  United States. Army. Corps of Engineers.; U.S. Army Engineer Waterways Experiment Station.; Water Quality Research Program (U.S.); Water Operations Technical Support Program. 
Type  Text 
Language  eng 
Relation  http://www.waterboards.ca.gov/losangeles/board_decisions/basin_plan_amendments/technical_documents/64_New/07_0712/BATHTUB_Manual.pdf; http://worldcat.org/oclc/489708780/viewonline 
DateIssued  1996] 
FormatExtent  239 p. in various pagings : ill. ; 18.79 MB. 
RelationRequires  Mode of access: World Wide Web. 
RelationIs Part Of  Instruction report ; W962; Instruction report (U.S. Army Engineer Waterways Experiment Station) ; W962. 
Transcript  m Instruction Report W 96 2 IIl@ ll 1 September 1996 ( Updated April 1999) US Army Corps of Engineers Waterways Experiment Station Water Operations Technical Suppofl Program Simplified Procedures for Eutrophication Assessment and Prediction: User Manual by William W. Walker Approved For Public Release; Distribution Is Unlimited Prepared for Headquarters, U. S. Army Corps of Engineers The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. The findings of this report are not to be construed as an official Department of the Army position, unless so designated by other authorized documents. @ PRINTED ON RECYCLED PAPER Water Operations Technical Support Program Simplified Procedures for Eutrophication Assessment and Prediction: User Manual by William W. Walker 1127 Lowell Road Concord, MA 01742 Final report Approved for public release; distribution is unlimited Prepared for U. S. Army Corps of Engineers Washington, DC 20314 1000 Instruction Report W 96 2 September 1996 ( Updated April 1999) Monitored by U. S. Army Engineer Waterways Experiment Station Vicksburg, MS 39180 6199 ENWROWEN], T:” A. L.,! Watenvays Experiment Station Cataloging in Publication Data Walker, William W. Simplified procedures for eutrophication assessment and prediction : user manual/ by William W. Walker; prepared for U. S. Army Corps of Engineers ; monitored by U. S. Army Engineer Waterways Experiment Station. 235 p. : ill. ; 28 cm. – ( Instruction reporl; W 96 2) Includes bibliographic references. 1. Eutrophication — Mathematical models. 2. Resetvoir ecology. 3. Water quality — Evaluation — Computer programs. 1. United States. Army. Corps of Engineers. Il. U. S. Army Engineer Waterways Experiment Station. Ill. Water Quality Research Program. IV. Title. V. Series: Instruction report ( U. S. Army Engineer Waterways Experiment Station) ; w 96 2. TA7 W34i no. W 96 2 Contents Prefae . . . .. o. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. vi l— Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Eutrophication Modeling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Summary ofAssessmentProcedures . . . . . . . . . . . . . . . . . . . . . . . . . . 1 14 DataRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 18 2— FLUX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 FLUX Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 Input DataRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 2 2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 4 Program Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 2 14 Typical Application Sequence.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 26 Procedure Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2 29 Data Entry Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 2 31 DataFile Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 34 FLUX Documented Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 44 3— PROFILE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 PROFILE Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3 1 Input DataRequirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Mixed Layer WaterQualityData Summary . . . . . . . . . . . . . . . . . . . . . . 3 4 Oxygen Depletion Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 7 Program Operation . . . . . . . . . . . . . . . . . $. . . . . . . . . . . . . . . . . . ... 3 10 Input DataFile Format......,.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 15 Data Entry Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 20 Documented Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 3 22 4 BATHTUB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 4 1 BATHTUB Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 4 1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 4 2 Program Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 4 36 Application Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4 42 Procedure Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 51 Data Entry Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 4 53 Documented Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 59 Instructional Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 79 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. R 1 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. B 1 Appendix A: Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. A1 Appendix B: Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. B1 SF 298 List of Figures Figure 1.1. Figure 1.2. Figure 1.3. Figure 1.4. Figure 1.5. Figure 1.6. Figure 3.1. Figure 3.2. Figure 4.1. Figure 4.2. Figure 4.3. Figure 4.4. Figure 4.5. Figure 4.6. Control pathways in empirical eutrophication models developed fornorthem lake applications . . . . . . . . . . . . . . . . . 1 4 Control pathways in empirical eutrophication models developed for CEreservoirapplications . . . . . . . . . . . . . . . . . 1 5 Sensitivity analysis of first order phosphorus sedimentation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 12 Sensitivityanalysis ofsecond order phosphorus sedimentation model ...,..... . . . . . . . . . . . . . . . . . . . . . . . . . 1 13 Assessment pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 15 Estimated accuracy ofreservoirmean concentration computed from sampling designs with betweenl and 30 sampling rounds overarange oftemporal CVS . . . . . . . . 1 29 Sample PROFILE output: Surface water qualitysummary . . . 3 5 Example box plot for Beaver Reservoir . . . . . . . . . . . . . . . . . 3 7 Schematic ofBATHTUB calculations . . . . . . . . . . . . . . . . . . 4 3 Control pathways inempirica. l eutrophication models developed for CE reservoir applications . . . . . . . . . . . . . . . . . 4 5 BATHTUB segmentation schemes . . . . . . . . . . . . . . . . . . . . 4 17 Mean depth ( Z) versus hydraulic residence time( T) for Remodel developmentdataset LOGIOscales . . . . . . . . . 4 25 Relationships between nutnent residence times and hydraulic residence times in Remodel development dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 27 Phosphorus, nitrogen, turbidity relationships for CE reservoirs ( nonalgal turbidity calculated as l/ Secchi ( m) 0.025Chl a( mg/ m3)) . . . . . . . . . . . . . . . . . . . . . . . . . . 4 30 iv Figure 4.7. Phosphorus, chlorophyll a, and transparency relationships for CE reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 31 Figure 4.8. Calibration factor for linear phosphorus/ chlorophyll model versus light limitation factors . . . . . . . . . . . . . . . . . . . 4 34 Figure 4.9. Model segmentation for Lake Keystone, Oldahom& application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 59 List of Tables Table 1.1. Table 1.2. Table 1.3 Table 1.4 Table 2.1 Table 2.2 Table 2.3 Table 2.4 Table 2.5 Table 4.1 Table 4.2 Table 4.3 Table 4.4 Table 4.5 Table 4.6 Comparison of Lake and Reservoir Empirical Eutrophication Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 Mass Balance Terrnsand Data Sources . . . . . . . . . . . . . . . . 1 22 Minimal and Desirable Designs for Tributary Monitoring Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 23 General Guidelines for Designing Reservoir Pool Monitoring Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 27 Estimation Algorithms Used in FLUX Program . . . . . . . . . . . 2 5 Stratified Sample Algorithm ( Cochran 1977; Bodo and Unny 1983) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 10 Breakdown by Flow Stratum  Caddo River Example . . . . . 2 12 Typical Application Sequence . . . . . . . . . . . . . . . . . . . . . . . . 2 27 FLUX File Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 34 Symbol Definition s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 BATHTUB Model Options . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 8 Supplementary Response Models . . . . . . . . . . . . . . . . . . . . . 4 12 Error Statistics for Model Network Applied to Spatially Averaged CEReservoir Data . . . . . . . . . . . . . . . . . . . . 4 13 Diagnostic Variables and Their Interpretation . . . . . . . . . . . . 4 14 Equations for Estimating Nonalgal Turbidity, Mixed Depth, and Hypolimnetic Depths in Absence of Direct Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 4 33 Preface The information reported herein is based on a series of technical reports written by Dr. William W. Walker and published by the U. S. Army Engineer Waterways Experiment Station ( WES). These previous reports summarized work conducted as part of the Environmental and Water Quality Operational Studies Program, sponsored by the Headquarters, U. S. Army Corps of Engineers ( HQUSACE). Preparation of this report was sponsored by HQUSACE, as part of the Water Operations Technical Support ( WOTS) Program. The WOTS Program was assigned to WES under the purview of the Environmental Laboratory ( EL). Funding was provided under Department of the Army Appropriation 96X3 123, Operations and Maintenance. The WOTS was managed under the Environmental Resources Research and Assistance Programs ( ERRAP), Mr. J. L. Decell, Manager. Mr. Robert C. Gunkel was Assistant Manager, ERRAP, for the WOTS. Program Monitors for WOTS were Messrs. Frederick B. Juhle and Rixie Hardy, HQUSACE. The work was conducted under the direct WES supervision of Dr. Robert H. Kennedy, Ecosystem Processes and Effects Branch ( EPEB), Environmental Processes and Effects Division ( EPED), EL, and the general supervision of Dr. Richard E. Price, Chief, EPEB, Mr. Donald L. Robey, Chief, EPED, and Dr. John W. Keeley, Director, EL. At the time of publication of this report, Director of WES was Dr. Robert W. Whalin. Commander was COL Bruce K. Howard, EN. This report was updated in April 1999. This report should be cited as follows: Walker, W. W. ( 1996). “ Simplified procedures for eutrophication assessment and prediction: User manual,” Instruction Report W 96 2 ( Updated April 1999), U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS. lhe contents of this report are not to be used for adver~ ising, publication, or promotional putposes. Citation of trade names does not constitute an oficial endorsement or approval of the use of such commercial products. vi Background 1 Introduction This report describes simplified procedures for eutrophication assessment and prediction. These techniques, initially developed for use at U. S. Army Corps of Engineer ( CE) reservoirs, are based upon research previously described in a series of technical reports. These reports describe database development ( Report 1; Walker 1981); model testing ( Report 2; Walker 1982); model refinement ( Report 3; Walker 1985); and applications procedures ( Report 4; Walker 1987). Reported here is detailed itiormation concerning application of the latest versions of these techniques using a DOS based personal computer and also reported is an update of the original applications manual ( i. e., Report 4). Three computer programs facilitate data reduction and model implementation. While the assessment procedures and programs can be “ run” based upon the information contained in this report, their intelligent “ use” requires an understanding of basic modeling concepts and familiarity with the supporting research. Review of the above research reports and related references on this topic ( see References and Bibliography) will facilitate proper use of the techniques described below. Eutrophication can be defined as the enrichment of water bodies leading to an excessive production of organic materials by algae and/ or aquatic plants. This process has several direct and indirect impacts on reservoir water quality and beneficial uses. Common measures of eutrophication include total nutrient concentrations ( phosphorus and nitrogen), chlorophyll a ( a measure of algal density), Secchi depth ( a measure of transparency), organic nutrient forms ( nitrogen and carbon), and hypolimnetic dissolved oxygen depletion. The basis of the modeling approach described below is to relate eutrophication symptoms to external nutrient loadings, hydrology, and reservoir morphometry using statistical models derived from a representative cross section of reservoirs. When applied to existing reservoirs, the models provide a framework for interpreting water quality monitoring data and predicting Chapter 1 Introduction 1 1 effects of fhture changes in external nutrient loadings. The models can also be used to predict water quality conditions in a proposed reservoir. Three basic phases are involved in applying the methodolo~ to an existing or proposed reservoir: a. Analysis and reduction of tributary water quality data. b. Analysis and reduction of pool water quality data. c. Model implementation, A separate computer program has been developed for each phase. The datareduction phases are critical steps in the modeling process. The programs can also be used in other aspects of reservoir operation and management, including monitoring program design and generalized data analysis. The model implementation program is designed so that it can be applied to a single reservoir ( mixed or spatially segmented), networks of reservoirs ( hydrologically linked), or collections of reservoirs ( hydrologically independent). The last type of application can support regional comparative assessments of reservoir conditions and controlling factors. This report is organized in four chapters. Chapter 1 reviews basic empirical modeling concepts, presents an overview of the assessment procedures which have been developed for reservoir application, and summarizes basic data requirements and recommended monitoring strategies. Chapter 2 describes the FLUX program, which is designed for analysis and reduction of tributary monitoring data. Chapter 3 describes PROFILE, a program designed for analysis and reduction of pool monitoring data. Chapter 4 describes BATHTUB, a program designed for model implementation. Appendix A describes the necessary procedures for installing the programs on an IBM compatible personal computer. Several levels of involvement are offered to potential users of this methodology. The following steps are suggested: Step 1: Review summary information ( Chapter 1). Step 2: Review supporting research and basic reference documents. Step 3: Review program documentation ( Chapters 2,3, and 4). Step 4: Review documented output listings. Step 5: Acquire and install programs ( Appendix A) on an accessible computer system. 1 2 Step 6: Run programs using several sample input files provided. Chapter 1 Introduction Step 7: Apply program to user defined problems. The above procedures provide a gradual and logical introduction of the techniques and a foundation for their application in a reservoir management context. Eutrophication Modeling Techniques Models for reservoir eutrophication can be broadly classified as theoretical or empirical. While all models are empirical to some extent, they are distinguished by their levels of empiricism. General characteristics and limitations of these model types are discussed below. Theoretical models generally involve direct simulation of physical, chemical, and biological processes superimposed upon a simulation of reservoir hydrodynamics. These methods generally have extensive resource requirements in terms of input dat~ computing facilities, and user expertise. They can be usefbl for problems requiring high spatial and temporal resolution and/ or simulation of cause effect relationships which cannot be represented using simpler models. Their relative complexity does not guarantee that simulation models are more accurate or more reliable than simplified models for certain types of applications. Although based upon theoretical concepts ( such as mass balance and nutrient limitation of algal growth), empirical models do not attempt explicit simulation of biochemical processes and use simplified hydrodynamic representations. They generally deal with spatially and temporally averaged conditions. The simple structures, low resolution, limited number of input variables, and initial calibration to data from groups of impoundments result in relatively low data requirements. At the same time, the above characteristics limit model applicability. In one sense, empirical models attempt to “ interpolate” the gross responses of a given impoundment, based upon observed responses of other impoundments and levels of certain controlling variables. They also provide a quantitative framework for interpreting monitoring data from a given impoundment and describing eutrophication related water quality conditions and controlling factors both in absolute and relative terms. Empirical model structures and evolution Empirical prediction of reservoir eutrophication can be described as a twostage procedure involving the following types of models: a. Nutrient Balance Models. These relate pool or discharge nutrient levels to external nutrient loadings, morphometry, and hydrology. ( Note that the term “ pool” refers to the lake or reservoir impounded by a dam.) Chapter 1 Introduction 1 3 b. Eutrophication Response Models. These describe relationships among eutrophication indicators within the pool, including nutrient levels, chlorophyll a, transparency, and hypolimnetic oxygen depletion. Generally, models of each type must be linked to relate external nutrient loadings to reservoir water quality responses. In the absence of loading information, however, application of eutrophication response models alone can provide useful diagnostic tiormation on existing water quality conditions and controlling factors. The literature contains a wide array of empirical eutrophication models which have been calibrated and tested using data from various lake and/ or reservoir data sets. Many of these models, particularly the early ones, were based primarily upon data from northern, natural lakes. While the equations and coefficients vary considerably among the lake models, they share the same sets of variables and basic assumptions, as depicted in Figure 1.1. INFLOW TOTAL P MEAN DEPTH + LAKE TOTAL P CHL A— SECCHI HYDRAULIC RESIDENCE TIME Figure 1.1. Control pathways in empirical eutrophication models developed for northern lake applications Inputs to these models can be summarized in three terms: a. Inflow total phosphorus concentration. External loading/ discharge rate, a nutrient supply factor. b. Mean depth. Reservoir volume/ surface are% a morphometric factor. c. Hydraulic residence time. Reservoir volume/ discharge rate, a hydrologic fwtor. Empirical nutrient balance models have generally evolved from a simplistic “ black box” model which represents the impoundment as a continuous stirredtank reactor at steady state and the sedimentation of phosphorus as a first order reaction. Phosphorus is assumed to control algal growth and other eutrophication related water quality conditions. Response models generally consist of bivariate regression equations relating each pair of response measurements ( e. g., phosphorus/ chlorophyll, chlorophyllk. nsparency). 1 4 Chapter 1 Introduction In adapting these models for use in CE and other reservoirs ( Walker 1981, 1982, 1985), modifications have been designed to include additional input variables, controlling factors, and response variables, as depicted in Figure 1.2. Table 1.1 compares the variables and assumptions of the reservoir models documented in this manual. The reservoir modifications are designed to improve generality by incorporating additional independent variables and controlling factors found to be important in model testing. INFLOWTOTAL METALIMNETIC ~ DEPLETION RATE INFLOW ORTHO P MEANTOTAL DEPTH NYD. RESIDENCE TIME HLOROPHYLL A INFLCW TOTAL N tNFLW bNORGANIC N SECCHI SUMMER FLUSHING RATE ORGANIC N MEAN OEPTH OF TOTAL P ORTNO p MO( ED IAYER NONALGAL TRU6JDITY Figure 1.2. Control pathways in empirical eutrophication models developed for CE reservoir applications Refinements are focused in the following areas: a. Effects of nonlinear sedimentation kinetics on nutrient balances. A second order kinetic model appears to be more general than a firstorder model for predicting both among reservoir, spatially averaged variations and within reservoir, spatial variations. b. Effects of inflow nutrient partitioning ( dissolved versus particulate or organic versus inorganic) on nutrient balances and chlorophyll a levels. Because of differences in biological availability and sedimentation rates, reservoir responses appear to be much more sensitive to the orthophosphorus loading component than to the nonortho ( total minus ortho) component. Chapter 1 Introduction 1 5 Table 1.1 Comparison of Lake and Reservoir “ Empirical Eutrophication Models Model Characteristics Lake Models Reservoir Models Input Inflow total P concentration Inflow total P concentration variables Mean depth Inflow ortho P concentration Annual hydraulic residence Inflow total N concentration time Inflow inorganic N Mean hypolimnetic depth concentration Mean depth Mean hypolimnetic depth Mean depth of mixed layer Seasonal hydraulic residence time Nonalgal turbidity Spatial Mixed Mixed or spatially segmented variability Temporal Steady state Steady state variability Nutrient Linear ( first order) Nonlinear ( second order) sedimentation kinetics Factors Phosphorus Phosphorus controlling Nitrogen algal growth Light Flushing rate output Total phosphorus Total phosphorus variables Chlorophyll a Total nitrogen Transparency Chlorophyll a Hypolimnetic oxygen Transparency depletion Nonortho phosphorus Organic nitrogen Hypolimnetic oxygen depletion Metalimnetic oxygen depletion 1 6 c. Effects of seasonal variations in nutrient loadings, morphomet~, and hydrology on nutrient balances. Pool water quality conditions are related more directly to seasonal than to annual nutrient balances in impoundments with relatively high flushing rates. Chapter 1 Introduction d Effects of algal growth limitation by phosphorus, nitrogen, light, and flushing rate on chlorophyll a concentrations. Simple phosphorus/ chlorophyll a relationships are of limited use in reservoirs because nitrogen, light, and/ or flushing rate may also regulate algal growth, depending upon site specific conditions. e. Effects of spatial variations in nutrients and related variables, as controlled by reservoir morphometry, hydrology, and the spatial distribution of tributary nutrient loads. Nutrient balance models can be implemented in a spatially segmented framework which accounts for advection, dispersion, and sedimentation to predict water quality variations among and within major tributary arms. This spatial resolution can be important for evaluating impacts on reservoir uses, depending upon locations of water use points ( e. g., water supply intakes, bathing beaches, parks, fishing areas, and/ or wildlife refiges). Model structures have been tested against several independent reservoir data sets. Details on model development and testing are described in the supporting research reports ( Walker 1982, 1985). Applications Potential model applications can be classified into two general categories: diagnostic and predictive. Characteristics and limitations of these applications are described below. In a diagnostic mode, the models provide a framework for analysis and interpretation of monitoring data from a given reservoir. This yields perspective on eutrophication related water quality conditions and controlling factors. Assessments can be expressed in absolute terms ( nationwide, e. g., with respect to water quality objectives, criteri~ or standards) and/ or relative terms ( e. g., comparisons with other impoundments, or regionally). Using routines and statistical summaries included in the BATHTUB program, observed or predicted reservoir characteristics can be ranked against characteristics of CE reservoirs used in model development. In a predictive mode, the models are used to project fiture conditions in either existing or planned reservoirs. The distinction between the two types of predictive applications is important. In the first case, monitoring data from an existing reservoir can be used, in combination with the models and diagnostic analyses, as a “ starting point” for “ extrapolation” to future conditions. Because of the opportunity for site specific calibration, projections of future conditions in an existing reservoir are generally subject to less uncertainty than projections of water quality conditions in a proposed reservoir. In a predictive mode, the models project steady state responses to changes in controlling variables which are explicitly represented in the model network Chapter 1 Introduction 1 7 ( Figure 1.2). Such projections can be used in impact assessments and in evaluations of water quality control strategies. For example, fhture scenarios involving changes in seasonal or annual mean values of the following factors can be evaluated: a. Inflow nutrient concentrations or loadings ( total phosphorus, ortho phosphorus, total nitrogen, and/ or inorganic nitrogen). b. Pool elevation, as it influences mean depth, mixed layer depth, mean hypolimnetic depth, and hydraulic residence time. c. Inflow volume and changes in hydraulic residence time. d. Pool segmentation, as it influences longitudinal nutrient transport, sedimentation, and the spatial distribution of nutrients and related water quality conditions. Applications of the first type are of primary importance because control strategies for reservoir eutrophication are usually focused on external nutrient ( especially, phosphorus) supplies. Examples of impacts and control strategies which cannot be explicitly evaluated with these models include the following: a. Variations in pool level or other model input variables which occur over time scales shorter than the growing season ( typically, 6 months). b. Changes in outlet levels. c. Structural modifications, such as the construction of weirs. d. Hypolimnetic aeration or destratification. e. Other in reservoir management techniques, including dredging and chemical treatment to control internal nutrient recycling. In such cases, implementation of the models in a diagnostic mode can provide useful baseline water quality perspectives; however, simulation or other approaches must be used for predictive purposes. Although the supporting research has focused on reservoirs, the computational framework can also be applied to natural lakes. Certain procedures and concepts are essential to evaluating eutrophication problems in lakes or reservoirs. These include calculation of tributary nutrient loads, summary of observed water quality conditions, construction of water balances, and construction of mass balances. In adapting the empirical lake models ( Figure 1.1) for use in reservoirs, the goal has been to increase model generality, so that the resulting formulations can be applied within certain constraints to lakes or to 1 8 Chapter 1 Introduction reservoirs. The limits and extent of model testing against lake data sets are summarized in the supporting research reports ( Walker 1982, 1985). Options for implementing empirical models previously developed exclusively from lake data sets are also included in the software. Error, variability, and sensitivity analysis The distinction between “ error” and “ variability” is important. Error refers to a difference between an observed and a predicted mean value. Variability refers to spatial or temporal fluctuations in concentration about the mean. Prediction of temporal variability is generally beyond the scope of empirical modeling efforts, although such variability is important because it influences the precision of observed mean values calculated from limited monitoring data. Because both measurement and model errors tend to increase with concentration scale, errors are most conveniently expressed on a percentage basis or logarithmic scales. This stabilizes variance over the ranges of concentration encountered, an important requirement for application of common statistical techniques ( e. g., regression). This report frequently uses the mean coefllcient of variation ( CV) as a measure of error. The CV equals the standard error of the estimate expressed as a fraction of the predicted value. For example, a CV of 0.2 indicates that the standard error is 20 percent of the mean predicted value. Assuming that the errors are log normally distributed about the predicted value, 95 percent confidence limits can be estimated from the following equation: yme 2cv< y< yme2cv where Ym= predicted mean value CV = error mean coefficient of variation Y = 95 percent confidence range for mean value Magnitudes, sources, and interpretations of error are discussed below. Error CVS for the reservoir model network ( Figure 1.2) are on the order of 0.27 for predicting total phosphorus and 0.35 for predicting mean chlorophyll a. According to the above equation, these statistics translate into 95 percent confidence factors of 1.72 and 2.00, respectively. In applying these models in a reservoir management context, limitations imposed by errors of this magnitude are less severe than immediately apparent because of the following factors: Chapter 1 Introduction 1 9 a. Despite the relatively wide confidence bands, the models explain 91 percent and 79 percent of the observed variances in total phosphorus and chlorophyll a across reservoirs, respectively. This reflects the relatively wide ranges of conditions encountered and suggests that the models are adequate for broad comparative analyses of reservoir conditions ( i. e., ranking). b. Error statistics are calculatedfiom “ imperfect” data sets. Errors are partially attributed to random sampling, measurement, and estimation errors in the input and output ( i. e., observed) conditions, which inflate the total error but do not reflect model performance. c. Error magnitudes refer to predictions which are made without the beneJt of site specl@ c water quality information. In applications to existing reservoirs, prediction errors can be reduced by calibrating the model ( adjusting certain model coefficients) so that predictions match observed water quality conditions. The calibrated model can subsequently be used to project water quality changes likely to result from changes in nutrient loads or other controlling factors. d. Year to year water quality variations induced by climate, hydrology, nutrient loading, and other factors are substantial in many reservoirs. It would be difficult to detect modest errors in predicting average conditions without several years of intensive monitoring. e. Ability to de$ ne objective criteria or standards is limited. The “ penalty” or “ risk” associated with modest errors in predicting average responses may be low when expressed in terms of impacts on water uses. The measured and modeled variables ( chlorophyll a, etc.) are reasonable and practical, but impefiect, surrogates for potential wateruse impacts. $ Ability to predict changes in loading resultingfiom adoption of specl~ c management strategies is limited. This applies particularly to implementation of nonpoint source loading controls with performances evaluated using watershed simulation models. In such situations, errors associated with predicting reservoir response may be swamped by errors associated with predicting loadings; i. e., the reservoir response model may not be the limiting factor in the analysis. Error analysis concepts discussed below provide additional perspectives on the above points. 1 1o Differences between observed and predicted reservoir conditions can be attributed to the combined effects of a number of error sources, as described below: Chapter 1 Introduction a. Independent variable error. These are errors in the estimates of model input variables, including external nutrient loadings, flows, and reservoir morphometry. b. Dependent variable error. These are errors in the estimates of mean observed reservoir water quality conditions, based upon limited monitoring data. c. Parameter error. These errors are attributed to biases or random errors in the model coefficients estimated from cross sectional data sets. d. Model error. These errors are attributed to errors in model structure or effects of factors which are not explicitly represented. The user has direct control over the first two error sources ( i. e., independent and dependent variable error), primarily through design and implementation of appropriate monitoring programs and use of proper data reduction techniques. The last two sources ( i. e., parameter and model error) are also under user control to the extent that the user selects the model( s) deemed appropriate for specific application. Research ( Walker 1981, 1982, 1985) has been directed at minimizing the last two error sources by reviewing, screening, refining, calibrating, and testing arrays of models which are appropriate for reservoir applications under specific conditions. The impacts of errors in speci$ ing model input variables or coefficients depend upon the sensitivities of model predictions to those inputs. Sensitivities, in turn, reflect model structure and variable ranges. A sensitivity coefficient can be conveniently expressed as a normalized first derivative, or as the percent change in a model output variable induced by a 1 percent change in a model input. For example, a sensitivity coefficient of 1.0 would indicate that the output is proportional to the input; in this situation, for example, a 5 percent error in speci& ing the input would propagate through the model and cause a 5 percent error in the predicted output. For a sensitivity coefficient of 0.2, however, a 5 percent input error would cause only a 1 percent output error. Sensitivity coefficients provide insights into which model variables and coefflcients are the most important to measure or estimate accurately. Figures 1.3 and 1.4 display sensitivity coefficients for models predicting mean phosphorus concentrations in reservoirs assuming first and second order sedimentation reactions, respectively. In both cases, the output variable is the error term or the ratio of the observed to the predicted mean phosphorus concentration. Input variables used to calculate this ratio include the observed pool concentration, inflow concentration ( flow weighted over all sources), flushing rate ( outflow/ volume), and sedimentation coefficient. Sensitivities vary with flushing rate over the approximate range encountered in CE impoundments ( median value for reservoirs used in model testing = 7/ year. At low flushing rates ( or long hydraulic residence times), sensitivities Chapter 1 Introduction 1 11 1.0 0.8 0.6 0.4 0.2 0  —— — ———  SED! MENTA TION RATE   FLUSHING RATE 0.1 1 10 100 FLUSHING RATE. l/ YR SENSITIVITY COEF = I% CHANGE IN ERROR ~ 1% CHANGE Ihl FACTOR I ERROR = OBSERVE() POOL P PREDICTED POOL P P, F PREDICTED POOL P = F+ K1 WHERE: Pi = INFLOW TOTAL PHOSPHORUS CONCENTRATION ( mg/ m3) F = FLUSHING RATE ( 1/ yr ) K, = FIRST ORDER SEDIMENTATION COEFFICIENT = 2.5 1/ Yf Figure 1.3. Sensitivity analysis of first order phosphorus sedimentation model to the sedimentation coefficient and flushing rate are relatively high ( approach ing 1.0 for the first order model and 0.5 for the second order model). This reflects the relative importance of the sedimentation term in the overall phosphorus balance of the reservoir. At high flushing rates, sensitivities to the sedimentation coefficient and flushing rate approach zero for both models. In this situation, the sedimentation process is relatively unimportant, and modest errors in the specified flushing rate a. dor sedimentation coefficient can be tolerated without having major impacts on the predicted pool concentration. Because the sedimentation coefficient is estimated from highly simplified empirical models ( whereas the other input terms can be directly measured), its sensitivity characteristics have a strong influence on model performance and uncertainty over the range of flushing rates. 1 12 Chapter 1 Introduction 1.0 0.6 0.6 0.4 02 0 ——— ——— — p( J~, ,7 ~ ,0,~,,~~ , / 0 /“ ,.~”~” r r SEDIMENTATION RATE  FLUSHING RATE 1 I i 0.1 1 10 1( KI FLUSHING RATE, 1/ Yf SENSITIVITY COEF = % CHANGE IN ERROR I 11% OHANGE IN FACTOR I ERROR = OBSERVED POOL P PREDICTED POOL P + +~~” PREDICTED POOL P = 2% WHERE: F = FLUSHING RATE ( 1/ Yr) P, = INFLOW TOTAL PHOSPHORUS CONCENTRATION = 50 mg/ m3 K2 = SECOND ORDER SEDIMENTATION COEFFICIENT = .1 m3/ mg yr Figure 1.4. Sensitivity analysis of second order phosphorus sedimentation model Figures 1.3 and 1.4 are intended primarily to demonstrate sensitivity analysis concepts. They also illustrate some important basic characteristics of empirical nutrient balance models: a. Sensitivities are highest for inflow and pool phosphorus concentrations over the entire range of flushing rates. This emphasizes the importance of monitoring programs ( tributary and pool) and data reduction procedures to modeling efforts. b. Because of a higher sensitivity to phosphorus sedimentation, potential prediction errors are greater for reservoirs with lower flushing rates. Chapter 1 introduction 1 13 While pool nutrient concentrations can be predicted relatively easily from inflow concentrations in reservoirs with high flushing rates, predictions of biological responses ( as measured by chlorophyll a) may be more difficult because of temporal variability in nutrient levels ( induced by storm events, for example) and/ or controlling effects of turbidity and flushing rate. The importance of obtaining accurate inflow and pool concentration estimates for model implementation has led to the development of the computer programs described in subsequent chapters. FLUX and PROFILE are designed to make efficient use of tributary and pool monitoring da~ respectively, in calculating the required summary statistics. Summary of Assessment Procedures Figure 1.5 depicts the basic steps involved in applying the eutrophication assessment procedures described in this and subsequent chapters. The “ pathway” comprises four general stages: a. Problem identification. b. Data compilation. c. Data reduction. d. Model implementation. Once the user has developed a working understanding of the model structures, assumptions, and limitations by reviewing basic references and supporting research ( see References and Bibliography), most of the effort and cost would typically be involved in the data compilation and data reduction stages. Three computer programs have been written to assist at various stages of the analysis. The functions of these programs are outlined below: a. FLUX  estimation of tributary mass discharges ( loadings) from grab sample concentration data and continuous flow records. b. PROFILE  display and reduction of pool water quality data. c. BATHTUB  implementation of nutrient balance and eutrophication response models. Figure 1.5 summarizes the basic inputs, functions, and outputs of each supporting program. This chapter provides an overview of each analytical stage. Details are given in subsequent chapters, along with examples and guidance for use of the computer software. 1 14 Chapter 1 Introduction PATHWAY PROCEDURES PROBLEM l DESCRIBE RESERVOIR AND/ OR WATERSHED CHARACTERISTICS DEFINITION l DEFINE UATER WALITY MANAGEMENT OBJECTIVES l IDENTIFY IMPACTS/ CONTROL STRATEGIES TO BE EVALUATED l DETERMINE STUDY TYPE: DIAGNOSTIC PREDICTIVE l DETERMINE MODEL TYPE: NUTRIENT BALANCE EUTROPHICATION RESPONSE DATA CCM4PILE TRIBUTARY C( NJIPILE RESERVOIR CWPILATION AND DISCHARGE DATA POOL DATA l HYDROLOGY l HYDROLOGY l UATERSHED l MORPHWETRY CHARACTERISTICS l WATER QUALITY l UATER QUALITY DATA RUN FLUX PROGRAM RUN PROFILE PROGRAM REDUCTION l DATA ENTRY l DATA ENTRY l DIAGNOSTIC DISPLAYS l DIAGNOSTIC DISPLAYS l DATA STRATIFICATION l OXYGEN DEPLETION l LOADING CALCULATIONS CALCULATIONS ANNUAL l MIXED LAYER SUMMARIES SEASONAL M( X) EL RUN BATHTUB PROGRAM IMPLEMENTATION l SEGMENTATION l SUBMCX) EL SELECTION NUTRIENT BALANCE EUTROPHICATION RESPONSE l DATA ENTRY l CALIBRATION AND TESTING l SENSITIVITY ANALYSIS l ERROR ANALYSIS l APPLICATIONS DIAGNOSTIC PREDICTIVE Figure l. 5. Assessment pathways Problem identification The problem identification stage defines thescope ofthe modeling effort. The following factors are specified: a. The reservoir, watershed, and water uses. b. Water quality standards andmanagement objectives. c. Whether the reservoir is existing or planned. d. Specific managementstrategies orimpacts to reevaluated. Chapterl Introduction 1 15 e. Types of evaluations to be performed. ( 1) Diagnostic. ( 2) Predictive. J Classes of models to be used. ( 1) Nutrient balance. ( 2) Eutrophication response. If the analysis is not directed toward evaluating specific management strategies or impacts, the general objective may be to develop perspectives on reservoir water quality conditions and controlling factors as part of a “ diagnostic” study. This may lead, in turn, to future evaluations of specific management strategies designed for water quality control. Two general types of evaluations maybe pefiormed. In a diagnostic mode, the models are used as a framework for interpreting monitoring data from the reservoir and/ or its tributaries. A diagnostic study provides insights into factors controlling algal productivity and rankings of trophic state indicators versus water quality criteria and/ or data from other CE reservoirs. In a predictive mode, the models are applied to predict future conditions in a planned reservoir or in an existing reservoir undergoing changes in nutrient loading regime and/ or other controlling factors. Model classes are determined by the types of analyses to be performed. Both nutrient balance and eutrophication response models are required for a predictive analysis. Diagnostic studies of existing reservoirs can be based exclusively upon response models and pool water quality data; this provides a basis for defining existing conditions and controlling factors, but not for evaluating watershed/ reservoir or load/ response relationships. Monitoring requirements are generally more stringent for implementing nutrient balance models than for implementing eutrophication response models. Response models and pool monitoring data may be used in preliminary diagnostic studies aimed at defining reservoir conditions. In some reservoirs, this may be followed by implementation of a more elaborate monitoring program designed to quanti~ nutrient loadings and to support nutrient balance modeling. Priorities can be established based upon the severities of existing eutrophication related problems ( if any), intensities and types of water use, and potential for future improvement or degradation owing to changes in loading regime. 1 16 Chapter 1 Introduction Data compilation As shown in Figure 1.5 data compilation occurs in two general areas. The reservoir data required for implementation of eutrophication response models include morphometric characteristics, outflow hydrology, and pool water quality obtained over at least one complete growing season ( three preferred). The watershed data required for implementation of nutrient balance models include basic watershed characteristics ( e. g., subwatershed delineations, topography, geology, land uses, point source inventories) and tributary flow and nutrient concentration data taken at reservoir entry points over at least one full water year ( three preferred). Details on data requirements and suggested monitoring designs are given later in this chapter. Data reduction In the data reduction phase, pool and tributary water quality data are reduced or summarized in forms which can serve as model input. Since the models generally deal with conditions averaged over a growing season within defined reservoir areas ( segments), data reduction involves the averaging or integration of individual measurements, sometimes with appropriate weighting factors. The FLUX program is designed to facilitate reduction of tributary inflow monitoring data and reservoir outflow monitoring data. Using a variety of calculation techniques, FLUX estimates the average mass discharge or loading that passes a given tributary monitoring station, based upon grab sample concentration data and a continuous flow record. Potential errors in the estimates are also quantified and can be used to ( a) select the “ best” or least error loading estimate, ( b) assess data adequacy, and ( c) improve future tributary monitoring efficiency via optimal allocation of sampling effort among seasons and/ or flow regimes. Graphic displays of concentration, flow, and loading data are also provided for diagnostic purposes. The PROFILE program facilitates analysis and reduction of pool water quality data from existing reservoirs. A variety of display formats are provided to assist the user in developing perspectives on spatial and temporal water quality variations within a given reservoir. Algorithms are included for calculation of hypolirnnetic oxygen depletion rates and for robust estimation of areaweighted, surface layer mean concentrations of nutrients and other response measurements used in subsequent modeling steps. ModeI implementation The BATHTUB program applies empirical eutrophication models to morphometncally complex reservoirs or to collections of reservoirs. The program performs water and nutrient balance calculations in a steady state, Chapter 1 Introduction 1 17 spatially segmented hydraulic network which accounts for advective transport, diilbsive transport, and nutrient sedimentation. Eutrophication related water quality conditions ( expressed in terms of total phosphorus, total nitrogen, chlorophyll a, transparency, organic nitrogen, particulate phosphorus, and hypolimnetic oxygen depletion rate) are predicted using empirical relationships previously developed and tested for reservoir applications ( Walker 1983). To reflect data limitations or other sources of uncertainty, key inputs to the model can be specified in probabilistic terms ( mean and CV). Outputs are expressed in terms of a mean value and CV for each mass balance term and response variable. Output CVS are based upon a first order error analysis which accounts for input variable uncertainty and inherent model error. As shown in Figure 1.5, applications of BATHTUB would normally follow use of the FLUX program for reducing tributary monitoring data and use of the PROFILE program for reducing pool monitoring data. Use of the data reduction programs is optional if independent estimates of tributary loadings and/ or average pool water quality conditions are used. Data Requirements This section summarizes data requirements to support model applications. The following categories are discussed: a. Watershed characteristics. b. Water and nutrient loadings. c. Reservoir morphometry. d Pool water quality and hydrology. Before describing each area in detail, it is appropriate to discuss some general concepts and guidelines that may be helpful in the design of a reservoir study. IrI a typical application, most of the effort and cost would be expended in the critical data gathering phase, Information sources would generally include project design memorand~ basin planning reports, historical hydrologic and water quality dat~ and water quality data gathered specifically for the study. Data requirements can be given rather explicitly, as determined by the list of model input variables. Specific data sources and monitoring program designs cannot be dictated, however, because they are influenced by unique aspects of each reservoir and its watersheds, the extent of existing dat~ logistic considerations, and study resources. 1 18 Chapter 1 Introduction Compilation and review of existing data are important initial steps in conducting a reservoir study. Preliminary application of models using existing data ( even if inadequate) can highlight data strengths and weaknesses and help to focus fhture monitoring activities. In some cases, existing data maybe adequate to support modeling efforts. When existing data are inadequate or unavailable, a phased monitoring program is generally indicated. The first phase involves a small scale program designed to obtain preliminary data for use in designing efficient monitoring programs for subsequent years. A phased study can be a relatively cost effective means of data acquisition. Given specific objectives ( e. g., quanti@ ng annual total phosphorus load or growing season mean chlorophyll a concentration in an existing reservoir), statistical methods can be applied to improve monitoring efficiency. As the efficiency of a monitoring program increases, the amount of uncertainty ( variance) in the measured variable decreases. Monitoring efficiency may be improved by optimizing the allocation of sampling effort, subject to logistic and economic constraints. Examples of such optimization procedures include the following: a. Allocation of samples among flow regimes to estimate loadings from a given tributary. b. Allocation of samples among tributaries to estimate total reservoir loading. c. Allocation of samples among stations, depths, and dates to estimate reservoir mean concentrations. Phased studies or useful existing databases are required to implement these optimization procedures. Because of logistic constraints, multiple monitoring objectives, and other factors, “ optimal” designs are rarely implemented; instead, they can be used to indicate appropriate directions for adjusting existing sampling designs. Watershed characteristics Basic watershed information is used in the development and interpretation of hydrologic and nutrient loading dat~ in the design of tributary monitoring programs, and in the assessment of problem sources and control strategies. Maps ( U. S. Geological Survey topographic or other) are the most useful formats for this type of information. Separate maps ( or a series of transparent overlays) can be used to summarize the following types of watershed tiormation: a. Elevation contours. b. Subwatershed delineations. Chapter 1 Introduction 1 19 c. d. e. J Dominant land uses. Soil types. ( 1) Hydrologic soil groups. ( 2) Erosion potential. Point sources. Monitoring station locations. Aerial photos, regional planning agencies, design memorand~ Geographic Information System ( GIS) databases, and/ or published basin reports are generally usefid sources of watershed Mormation. Soils information would also be available from the Soil Conservation Service. The information should be summarized in a tabular form by subwatershed. Land uses, soil types, topography, and point sources are important factors in dete rmining runoff and nutrient export from a given subwatershed. This type of tiormation is used to do the following: a. Design tributary monitoring programs ( place stations). b. Interpret watershed monitoring data ( compare monitored runoff and loads from different subwatersheds to develop perspectives on regional land use/ nutrient export relationships). c. Estimate loadings from unmonitored watersheds ( use land use/ nutrientexport factors or proportion monitored loads from a nearby watershed with similar land uses and soil types, based upon drainage area). Projections of future land use and point source nutrient loads are also required for predicting impacts of watershed development. Water and nutrient loadings The formulation of water and nutrient balances for the reservoir is a critical step in the empirical modeling process. The following components are of concern: 1 20 a. Water. b. Total phosphorus. c. ortho phosphorus. Chapter 1 Introduction d. Total nitrogen. e. Inorganic nitrogen ( Ammonia+ Nitrate+ Nitrite), f Conservative substance ( e. g., chloride). Water and total phosphorus balances are essential. The other components are optional, While nitrogen balances are desirable, they may be omitted if monitoring data and/ or preliminary mass balance calculations indicate that the reservoir is clearly not nitrogen limited under existing and future loading conditions. The ortho phosphorus and inorganic nitrogen ( ammoni~ nitrate, and nitrite) loading components are required for ( optional) implementation of nutrient sedimentation models which account for the “ availability” or partitioning of total nutrient loads between dissolved and particulate ( or inorganic and organic) fractions. Conservative substance balances are useful for testing water balances and calibrating diffhsive transport rates in segmented reservoirs. The nutrient species listed above correspond to those monitored by the U. S. Environmental Protection Agency ( EPA) National Eutrophication Survey, the primary data source used in model development and testing. Monitoring of other species ( particularly, total dissolved phosphorus) may be desirable for deftig inflow nutrient partitioning and availability. Because of existing data constraints, however, the models are based upon the above species. Generally, balances should be formulated over both annual and seasonal ( e. g., May September) time periods. Annual balances should be calculated on a water year ( versus calendar year) basis. While traditional nutrient loading models deal with annual time scales, seasonal loadings are better predictors of trophic status in many reservoirs. The methodologies presented in subsequent sections can be applied separately to annual and seasonal nutrient balance data. Nutrient residence time criteria are used to assess the appropriate time scale for each reservoir. The nominal definition of seasonal ( May September) can be adjusted in specific applications, depending upon seasonal variations in inflow hydrology and, especially, pool level. For example, if a full recreational pool were maintained June through August and much lower elevations were maintained during other months for flood control purposes, then a June August time scale may be more appropriate for seasonal nutrient balances. Generally, seasonal balances are less important in projects with little or no inflow or outflow during the summer months. The formulation of both seasonal and annual balances is generally recommended for all applications and does not substantially increase monitoring requirements, since both sets of loading estimates can be derived from the same monitoring program. For each component and time scale, a control volume is drawn around the reservoir ( or reservoir segment) and the following mass balance terms are quantified: Chapter 1 Introduction 1 21 a. Total inputs. b. Total OU@ ltS. c. Increase in storage. d. Net loss. Table 1.2 outlines the specific elements of each term and general data sources. Since water is conservative, the net loss term in the water balance ( estimated by difference) reflects errors in the estimates of the other water balance terms. For nutrients, the net loss term can be estimated by difference or, in a predictive mode, by using empirical nutrient sedimentation models which have been calibrated and tested for reservoir applications. Table 1.2 Mass Balance Terms and Data Sources Mass Balance Terms General Data Sources Inputs Gauged tributaries Direct monitoring Ungauged tributaries Drainage area approximations Watershed models Direct point sources Direct monitoring Per capita loading factors Shoreline septic systems Per capita loading factors Hydrogeologic studies Direct groundwater inputs Hydrogeologic studies Atmospheric Local precipitation data Regional atmospheric deposition outputs Outflows and withdrawals Direct monitoring Evaporation Local climatologic data Increase in storage Pool elevation and morphometry data Vet loss Calculated by difference Represents error in water balance Emperical nutrient sedimentation models In general, direct monitoring is recommended to quanti& major flow and nutrient sources. Table 1.3 summarizes “ minimal” and “ desirable” designs for 1 22 tributary monitoring programs and methods for quanti& ing other loading components. These are intended as general guidelines to be modified based Chapter 1 Introduction Chapter 1 Introduction 1 23 1 24 Chapter 1 Introduction upon site specific conditions. The basic design for major tributaries and outflows consists of continuous flow monitoring and a combination of periodic grab sampling and event monitoring for concentration. A sampling program weighted toward high flow regimes is generally desirable for estimation of loadings. The multiple objectives of estimating both annual and seasonal loadings should be considered in designing surveys. The FLUX program can be applied to historical and/ or preliminary monitoring data to assist in sampling design. While balances are formulated for the study ( monitored) period, a historical hydrologic record is desirable to provide perspective on study conditions in relation to long term averages and extremes. Long term hydrologic records are usually available for reservoir discharge sites and major tributary inflows. If not, records from a nearby, long term station, possibly outside the watershed( s), can be correlated with monitoring data from study sites and used to extrapolate the record. Reservoir morphometry Reservoir morphometric information is required for nutrient balance and eutrophication response models. It is usually readily available from project design memoranda and other sources. A map indicating the following basic idormation is useful: a. Distance scale. b. Shoreline for typical and extreme pool levels. c. Bottom elevation contours or soundings. d. Tributary inflows and any direct point sources. e. Pool and tributary monitoring station locations. The following morphometric data should also be compiled in tabular form: a. Elevation/ area volume table. b. Typical operating pool elevations ( rule curve). c. Reservoir bottom elevation at each pool sampling station. d. Volumes, surface areas, and lengths of major reservoir segments at typical operating elevations. This tiormation is used in data reduction ( PROFILE) and modeling ( BATHTUB). Chapter 1 Introduction 1 25 Pool water quality and hydrology In studies of existing reservoirs, pool water quality and hydrologic data are used for the following purposes: a. Assessing trophic state, related water quality conditions, and controlling factors. b. Model testing and calibration. Expressed in terms of model variables, the primary objectives of the monitoring program are to obtain the data required for calculation of growingseason, mixed layer, average concentrations of the following variables: a. Total phosphorus. b. Dissolved ortho phosphorus. c. Total nitrogen. d Total inorganic nitrogen. e. Organic nitrogen. J Chlorophyll a ( corrected for phaeophytin). g. Transparency ( Secchi depth). J Conservative substance. In stratified reservoirs, another primary objective is to estimate hypolimnetic and metalimnetic oxygen depletion rates. Secondary objectives are to develop perspectives on spatial variations, vertical stratification, basic water chemistry, and other variables which are directly or indirectly related to eutrophication. General guidelines for designing pool monitoring programs are outlined in Table 1.4. Basic design features include component coverage, station locations, sample depths, temporal frequency, and duration. An appreciation for spatial and temporal variability of conditions within the reservoir may be obtainable from historical data and can be very useful in designing future surveys. 1 26 The objectives of identifying spatial gradients and calculating reservoirmean conditions suggest somewhat different emphasis for station placement. Generally, horizontal variations parallel to the net advective flow along the main axis of a major tributary arm are much more important than variations perpendicular to the flow. If they exist, longitudinal gradients in nutrients, algal biomass, and transparency are usually steepest in upper pool areas; this Chapter 1 Introduction Table 1.4 General Guidelines for Designing Reservoir Pool Monitoring Programs Feature Minimal Design Desirable Design Water quality Temperature Dissolved Oxygen Add: components Total P Ortho P Total Silica Total Organic Carbon Organic N Ammonia N Total Iron Total Manganese Nitrite Nitrate N Transparency True Color Sulfides Alkalinity pH Suspended Solids ( total and organic) Conductivity Turbidity Oxidation reduction potential Chlorophyll a ( corrected for Phaeophytin) Algal cell counts ( ASU) by type Dominant algal types Station locations Minimum of three stations/ reservoir Add stations in smaller tributary arms and ( near dam, midpooi, upper pool) embayments Distributed along thalweg of each major Critical reservoir use areas tributary arm in representative areas Above and below junctions of tributary Maximum distance between stations along arms thalweg = 20 km Maximum distance between stations along thalweg = 10 km Duration of sampling One growing season Three growing seasons ( typically April October) Bracket stratified period, including one round each during spring and fail isothermal periods Frequency  laboratory Monthly or biweekly Biweekly or weekly samples Depths  laboratory Mixed 1ayer composite Unstratified reservoirs: surface, samples Depth integrated hose sampling mid depth, and 1 m off bottom Stratified reservoirs: 3 samples in mixed layer 1 sample in thermocline 3 samples in hypolimnion 1 m from top of hypolimnion mid depth 1 m off bottom Frequency  field profiles Unstratified reservoirs: same as laboratory Unstratified reservoirs: same as laboratory Unstratified reservoirs: samples samples Temperature Stratified reservoirs: biweekly in spring to Stratified reservoirs: weekly in spring to Dissolved oxygen early summer ( until onset of anoxia), then early summer ( until onset of anoxia), then monthly biweekly Depths  field profiles 1 m intervals, top to bottom Increase spatial frequency in thermocline Temperature and other zones with steep gradients Dissolved oxygen Reservoir hydrology Month end values Daily values Surface elevation Monthly totals Daily totals Outflow volumes Chapter 1 Introduction 1 27 suggests that stations should be more closely spaced in upper pool areas to permit adequate resolution of gradients. Most of the reservoir volume, however, is usually located in the lower pool areas, where width and depth tend to be greater and spatial gradients tend to be less pronounced; this suggests a greater emphasis on lower pool stations for the purposes of calculating reservoir means. Because of these trade offs, it is difficult to use a statistical approach for optimizing station placement within a given reservoir. Ghen multiple sampling objectives, a reasonable design rule is to distribute stations throughout representative areas of the reservoir. The size, morphometric complexity, and loading distribution of a reservoir largely determine the required number of stations. A minimum of three stations ( upper pool, midpool, and near dam) are recommended for small projects with simple morphometry. Based upon reservoir morphometnc information, weighting factors can be applied to data from each station in calculating area weighted reservoir means ( see PROFILE). To provide bases for characterizing variability and developing robust statistical summaries, surveys should be designed to provide replication ( some overlap in information content) of measurements made in each reservoir area or segment during each sampling round. There are several ways in which replication can be built into survey designs, including the following: a. Multiple sampling at a given date, station, and depth. b. Multiple sampling with depth within the mixed layer at a given date and station. c. Multiple sampling stations within a given reservoir segment or area, d. High temporal sampling frequencies, permitting aggregation of data from adjacent sampling dates. In designing surveys, combinations of the above strategies can be employed to provide data which include at least three measurements for each reservoir segment and sampling round. In the “ desirable” design ( see Table 1.4), three samples are suggested within the mixed layer for each station and date. Since the stratum is mixed, on the average, the three samples can be treated as replicates. Other strategies listed above can be used in conjunction with depth sampling to provide replication. Another monitoring objective is to sample each station on each sampling round; this greatly simplifies reduction of the data and error analysis, as implemented in the PROFILE program. 1 28 Assuming representative station distribution and proper sampling and analytical techniques, the “ precision” of a mean, surface layer, growing season value depends largely upon the number of sampling rounds and the inherent temporal variabilities of water quality components in the reservoir being studied. For sampling periods of roughly a week or longer, the variance of the Chapter 1 Introduction mean is roughly inversely proportional to the number of rounds. Based upon analyses of variance applied to model development data sets ( Walker 1980, 198 1), temporal variance components of phosphorus, transparency, and chlorophyll a are typically 0.31,0.33, and 0.62, respectively, expressed as CVS. Figure 1.6 shows the estimated accuracies of reservoir mean concentrations computed from sampling designs with between 1 and 30 sampling rounds over a range of temporal CVS. The “ value” of each additional round, as measured by the reduction in the mean CV, decreases as the total number of rounds increases. This figure provides a rough perspective on design sensitivity and a basis for interpreting the reliability of data from historical monitoring activities, provided the sampling regimes were both specified and representative. TEMPORALCOEPflCKt4TOF VARIATION o 0.2 0.4 0.6 0.8 1.0 1 90 TYPICAL VALUES FOR GE RESERVOIRS a CHL A TOTALP ~ BIMONTH1. Y MONIHLY BIWEEKLY WEEKLY Figure 1.6. Estimated accuracy of reservoir mean concentration computed from sampling designs with between 1 and 30 sampling rounds over a range of temporal CVS The “ adequacy” of a given monitoring program is partially determined by the precision of the mean concentration estimates calculated from the data. Because of the limited pool sampling schedule employed by the EPA National Eutrophication Survey ( three to four sampling rounds per growing season), typical error CVS were on the order of 0.18 for mean total phosphorus, 0.18 for mean transparency, and 0.28 for mean chlorophyll a. More precise estimates ( e. g., mean CVS less than 0.10 for nutrients and transparency and 0.15 for mean chlorophyll a) are desirable for model applications in a reservoir management context. Chapter 1 Introduction 1 29 The purpose of sampling in and below the thermocline ( Table 1.4) is to provide information on vertical stratification and the accumulation and transformation of nutrients within the hypolimnion. Many important secondary water quality effects of eutrophication are expressed in bottom waters, including oxygen depletion, development of reducing conditions, nutrient accumulation, iron and manganese releases, and sulfide and ammonia generation. While nutrient data from the hypolimnion are not used exclusively in the models, they are important for developing an understanding of nutrient cycling and reservoir processes. Since metaiimnetic and hypolimnetic samples are less important for trophic state assessment and model implementation, however, sampling fi equencies in and below the thermocline can be lower than those used for the mixed layer. 1 30 Chapter 1 Introduction 2 FLUX FLUX Overview FLUX is an interactive program designed for use in estimating the loadings of nutrients or other water quality components passing a tributary sampling station over a given period of time. These estimates can be used in formulating reservoir nutrient balances over annual or seasonal averaging periods appropriate for application of empirical eutrophication models. Data requirements include ( a) grab sample nutrient concentrations, typically measured at a weekly to monthly frequency for a period of at least 1 year, ( b) corresponding flow measurements ( instantaneous or daily mean values), and ( c) a complete flow record ( mean daily flows) for the period of interest. Using six calculation techniques, FLUX maps the flow/ concentration relationship developed from the sample record onto the entire flow record to calculate total mass discharge and associated error statistics. An option to strati~ the data into groups based upon flow, date, and/ or season is also included. In many cases, strati& ing the data increases the accuracy and precision of loading estimates. Uncertainty is characterized by error variances of the loading estimates. A variety of graphic and tabular output formats are available to assist the user in evaluating data adequacy and in selecting the most appropriate calculation method and stratification scheme for each application. FLUX provides Mormation which can be used to improve the efficiencies of future monitoring programs designed to provide data for calculating loadings and reservoir mass balances. The succeeding sections of this chapter contain descriptions of the following topics: a. Input data requirements. b. Theory. c. Program operation. d Typical application sequence. Chapter 2 FLUX 2 1 e. Procedure outline. f Data entry screens. g. Data file formats. h. Documented session. Input Data Requirements Two data sets are required to run FLUX. One defines sample characteristics ( date of collection, concentration, and instantaneous flow). The other describes the complete flow record ( date, mean daily flow) over the period of interest. Most of the effort in applying FLUX is generally involved in setting up the required data files. To facilitate this effort, FLUX can read files in a variety of formats, as described in a subsequent section ( see Data file formats). The function of the program is to use the water quality information in the sample data set to estimate the mean ( or total) loading which corresponds to the complete flow distribution over the period of interest. All program calculations and output are in metric units, with flows expressed in million cubic meters (= cubic hectometers, hm3) per year, concentration in milligrams per cubic meter ( parts per billion), and loading in kilograms per year. The data can be stored in other units and converted to the appropriate units when accessed by FLUX ( see Appendix B). For a typical nutrient balance study, sample data sets would include the following components: instantaneous flow, total phosphorus, ortho phosphorus, total nitrogen, inorganic nitrogen, and a conservative substance such as chloride. Potential applications of the program are not restricted to these constituents, however. The sample data are normally derived from periodic grab sampling. Flow measurements stored with the water quality data should correspond to the times of sampling. Daily mean flows can be used in the absence of instantaneous flow measurements; FLUX can automatically pair sample concentrations with corresponding daily mean flows specified in the complete flow record. Generally, samples are collected periodically ( weekly to monthly) over a year and over a range of flow regimes. If intensive storm event monitoring has been conducted, resulting discrete or composite samples should be summarized before they are accessed by FLUX; in this case, each record in the sample data set includes an event mean flow and a flow weighted mean concentration for each component. Differences in the duration of composite samples are not considered in the current version of FLUX. If continuously sampled events represent a significant fraction of the total loading over the estimation period, the program may overestimate the error variance of the loading estimates. To avoid severe biases in the load estimates, special consideration must be given to 2 2 Chapter 2 FLUX the specification of sample flows in small, flashy streams or storm sewers ( see Typical application sequence). The reliability of loading estimates strongly reflects monitoring program designs. Water quality samples should be taken over the ranges of flow regime and season which are represented in the complete flow record. For a given number of concentration samples, loading estimates will usually be of greater precision if the sampling schedule is weighted toward high flow seasons and storm events, which usually account for a high percentage of the annual or seasonal loading. While the calculation methods described below are designed to make efficient use of the available datq they cannot work miracles. If the basin dynamics are such that annual loadings are dominated strongly by a few extreme events, no calculation procedure will give an acceptable answer without representative samples from at least some of the major events. FLUX provides graphic and tabular output which can help to evaluate the adequacy of the sample data set for use in load calculations. Sample data files can include up to 64 fields representing different water quality components and other sample descriptors. Loading calculations are performed for only one component at a time. Concentrations which are entered as zero or negative values are assumed to be missing. Sample records with zero or negative flow values are not used in load calculations. All FLUX calculations are performed in computer memory; source data files are not modified. The flow data set specifies the complete flow distribution, which is generally derived from continuous stage or velocity measurements made at or near the water quality monitoring site. Typically, flow records consist of a mean flow for each day in the period of interest. In the absence of daily measurements, other averaging flow periods can also be used ( weekly, monthly), but with some loss of accuracy. If a continuous flow record is not available for a particular site, one might be constructed using simulation techniques or correlating available flow measurements with simultaneous data from a nearby benchmark station with a continuous flow record and similar watershed. Missing values are permitted in the flow distribution file, but they should be avoided by estimating them independently. Zero flow values are acceptable to permit applications to intermittent streams. Negative flow values ( reverse flows) are treated as zeros. Average flow rates and loads calculated by FLUX reflect total transport in the downstream direction. This may be different from the net transport estimates appropriate for use in BATHTUB or other massbalance models. If the stream contains significant reverse flows, an option is available for calculating total transport in the upstream direction; this essentially involves reversing the sign of the sample flow and daily flow data. The net downstream transport can subsequently be calculated by subtracting the total upstream transport rates from the total downstream transport rates. It is convenient to define the time period represented in the sample data set as the “ sampling period” and that represented in flow data set as the “ averaging Chapter 2 FLUX 2 3 period.” Normally, these two periods correspond, i. e., the flow data set contains a mean daily flow value for each day in the year of water quality sampling. If the sampling and averaging periods do not correspond ( e. g., the sample set might contain data from 1978 through 1981, and the flow set might contain daily flows for 198 1), then the user is making the assumption that the flow/ concentration dynamics of the stream are stable, i. e., that concentrations measured between 1979 and 1980 are also representative of those measured in 1981. Using samples from outside the averaging period can increase the accuracy and precision of the loading estimates ( by increasing the number of samples and improving the coverage of flow regimes); this may introduce bias in the loading estimates, however, if there are significant year to year variations in the flow/ concentration relationship caused by variations in climate, hydrology, or watershed land use. In each program run, the user specifies the date ranges and/ or season ranges to be used for samples and flows; this permits estimation of both annual and seasonal loadings from source data files containing data from 1 or more years of monitoring. The flow data set may include daily flows from the year( s) of water quality monitoring, as well as other periods which may represent “ low flow,” “ average,” and “ high flow” years. Provided that a sufficiently wide range of flow regimes are sampled, this permits extrapolation of the sample record, i. e., estimation of year to year variations in loadings based upon sample data from a specific year or years. FLUX can handle problems containing up to 900 samples and 8,000 daily flow records ( 22 years), These constraints apply to data read into computer memory at the start of program execution, not the size of the input data files. Since the user is prompted for the ranges of sample and flow dates to be used in a given run, the input data files can be much larger than indicated above. Users should check the online documentation file ( accessed through the HELP option of the main menu) for maximum problem dimensions and other program changes in updated versions of FLUX ( Version 5.0 is documented here). Theory Loading calculation methods Table 2.1 lists the equations used to calculate the mean loading and error variance using six alternative methods. Method applicability depends upon flow/ concentration dynamics and sampling program design in each application. Walker ( 198 1,1987) provides details on the derivation and testing of each method. The FLUX procedure “ Calculate/ Loads” provides a one page summary of loadings calculated using each method. The user must decide which method is most appropriate for each application, based upon factors discussed below. In most cases, particularly if the data are properly stratified ( see Data stratification), the calculation methods will give estimates which are not 2 4 Chapter 2 FLUX Table 2.1 Estimation Algorithms Used in FLUX Program Method 1  Direct Mean Loading w, = Mean( w) Method 2 Flow Weighted Concentration ( Ratio Estimate) W2 = WI Mean( Q) / Mean( q) Method 3 Modified Ratio Estimate ( Bodo and Unny 1983) W3 = W2( 1 + FWJn)/( 1 + FJn) Method 4 Regression, First Order ( Walker 1981) W4 = W1[ Mean( Q)/ Mean( q) lb+’ Method 5 Regression, Second Order ( Walker 1987) W5 = W4( 1 + r FJ/( 1 + r Fq) Method 6 Regression Applied to Individual Daily Flows w= = ~ jexp [ a + ( b+ l) ln( Qi) + SE2/ 2 ] where Ci = qi = b = a = Wi = F = wq Fq = F~ = Qj = n = N = w“ = Vm = r = Xj = SE = Mean( x) Var( x) Cov( xry) measured concentration in sample i ( mg/ m3) measured flow during sample i ( hm3/ year) slope of In( c) versus In( q) regression intercept of In( c) versus In( q) regression measured flux during sample i = qi Ci ( kg/ year) Cov( w, q) / [ Mean( w) Mean( q)] Var( q) / [ Mean( q) Mean( q)] Var( Q) / [ Mean( Q) Mean( Q)] mean flow on day j ( hm3/ year) number of samples ( i) number of daily flows ( j) estimated mean flux over N days, method m ( kg/ year) variance of estimated mean flux, method m ( kg/ year) z 0.5 b( b + 1) sum over N dates in daily flow record standard error of estimate for In( c) versus In( q) regression = mean of vector x = variance of vector x = covariance of vectors x and y Chapter 2 FLUX 2 5 significantly different from each other. Thus, the choice of method will not be critical. Desired properties of the loading estimates include minimum bias and minimum variance. The distinction between bias and variance ( analogous to “ accuracy” and “ precision”) is important. A biased procedure will give the wrong answer, even for an infinite number of samples, whereas variance in the mean can generally be reduced by increasing the number of independent random samples. The seriousness of bias depends upon its size relative to the variance of the mean or the standard error of estimate. Biases less than 10 percent of the standard error account for less than 1 percent of the total mean squared error and are generally considered negligible ( Cochran 1977). Bias in a loading estimate can come from two sources: unrepresentative sampling or the use of an inappropriate calculation method. These sources are discussed below. Consistent problems with sample collection, handling, and analytical procedures can cause one type of unrepresentative sampling; there is little that can be done about these problems at the calculation stage. Another, more subtle, but generally more common type of unrepresentative sampling results from differences in the distributions of flows between the sampling dates and the entire averaging period. Sampled flows may tend to be higher or lower, on the average, than the complete distribution of flows or contain a higher or lower percentage of extreme flows. This can lead to bias in the estimate if the calculation procedure does not take the relative flow distributions into consideration by directly representing the flow/ concentration relationship and/ or by strati~ ing the sample, as described below. Even if the sampled and total flow distributions are equivalent, bias can be introduced as a result of the calculation method. For example, loading calculated as the product of the mean sample concentration and the mean flow over the averaging period would be badly biased if flow and concentration are ( even weakly) correlated ( Walker 198 1). Because of the potential bias associated with this method, it is not included in the program. The six included methods have been selected and tested so that, for representative samples, they should not introduce significant bias except under special conditions discussed below for each method. The extent to which the methods can minimize variance in the loading estimates is limited ultimately by the sample data sets. Method applicability depends upon the relationship between concentration and flow. In FLUX, this characteristic is represented by the slope of a log( Concentration) versus log( Flow) regression ( C/ Q slope) derived from the sample data set. Typically, the C/ Q slope approaches  1 at monitoring stations which are downstream of major point sources. The slope may approach or exceed 1 at monitoring stations where the load is generated as a result of runoff or high flow events, particularly for particulate components. In many watersheds, the C/ Q slope for total phosphorus varies with flow ( negative at low flows to positive at high flows). FLUX graphic and tabular output helps to 2 6 Chapter 2 FLUX characterize the concentratiordflow relationship; this characterization is essential to selecting the appropriate calculation method and developing reliable loading estimates. Method 1 ( direct load averaging) is the simplest of the calculation schemes. It gives unbiased results only if the samples are taken randomly with respect to flow regime. This method completely ignores the unsampled flow record and generally has higher variance than the other methods because the flow record on the unsampled days is not considered. This method is most appropriate for situations in which concentration tends to be inversely related to flow ( C/ Q slope approaching  1; loading does not vary with flow). This might occur, for example, at a station which is below a major point source and the flow/ concentration relationship is controlled by dilution. Method 2 bases the loading estimate on the flow weighted average concentration times the mean flow over the averaging period. This amounts to a “ ratio estimate” according to classical sampling theo~ ( Cochran 1977). This method performs best when flow and concentration are unrelated or weakly related. Some bias may occur for extreme flow/ concentration relationships. In test simulations of a stream with a C/ Q slope 0.75, Method 2 overestimated loadings by an average of 10 percent ( Walker 1987). This bias can be substantially reduced by stratifying the samples into groups of relatively homogeneous concentration and applying the method separately to each group, as described in more detail below. This is perhaps the most robust and widely applicable method, especially when applied to stratified data sets. Method 3 modifies the Method 2 estimate by a factor that is designed to adjust for potential bias in situations where concentration varies with flow. The factor was developed byBeale( 1962) and applied in a load estimation method developed by the International Joint Commission( IJC)( 1977), as described by Bodo andUnny( 1983, 1984). Trial simulations indicate that, compared with Method 2, this procedure is moderately successful at reducing bias but tends to have slightly higher mean squared error for streams with C/ Q slopes greater than or equal to zero ( Walker 1987). Method 4 is the regression method developed by Walker ( 1981). This method adjusts the flow weighted mean concentration for differences between the average sampled flow and the average total flow using the C/ Q slope. It should not be used in cases where the daily flow data set contains a significant number of zero flow values. This method petiorms well over a range of C/ Q slopes. Some bias is introduced at high C/ Q slopes. At a slope of 0.75, for example, simulated bias is 13 percent of the mean loading but accounts for only 6 percent of the total mean squared error ( Walker 1987). Additional simulations indicate that bias also occurs if the C/ Q slope is highly nonlinear ( i. e., quadratic or higher order polynomial). This problem can be resolved by strati & ing the sample so that the relationship is approximately linear within each group. Chapter 2 FLUX 2 7 Method 5 modifies the Method 4 estimate by a factor accounting for differences in variance between the sampled and total flow distributions ( Walker 1987). The derivation of the method is based upon expected value theory ( Benjamin and Cornell 1970). Method 5 should not be used in cases where the daily flow data set contains a significant number of zero flow values. As for Method 4, bias resulting from nonlinearity in the log ( c) versus log ( q) relationship can be reduced by strati$ ing the data. Method 6 is another regression based calculation method. For each stratum, the C/ Q regression equation is applied individually to each daily flow value. In contrast, Methods 4 and 5 use only the flow means and variances. A small correction for bias resulting from the log transformation is also included. This method is often appropriate for generating daily, monthly, or yearly load time series using an optional FLUX procedure designed for this purpose ( Calculate/ Series). Relatively intensive sample data sets and well defined concentration/ flow relationships are required for reliable application of this method. Method 6 is generally preferred over the other regression based methods when the flow/ concentration relationship is well defined. In applications to small, flashy streams, special consideration must be given to the specification of sample flows to avoid bias in Method 6 estimates ( see Typical application sequence). Error analysis calculations are time consuming relative to the other methods. An option to turn off the error analysis for Method 6 is included ( Utilities/ Set/ Method 6). For each method, the jackknife procedure ( Mosteller and Tukey 1978) is used to estimate error variance. This involves excluding each sampling event, one at a time, and recalculating loadings, as described in Table 2.2. While alternative, direct estimators of variance are available from classical sampling theory for most of the methods ( Cochran 1977; Walker 1981; Bodo and Unny 1983, 1984), such formulas tend to rely upon distributional assumptions. The direct estimators are generally applicable to large samples and normal distributions, neither of which is typical of this application. As described by Cochran ( 1977), the jackknife has improved properties for ratio estimators derived from small, skewed samples. Use of the jackknife procedure also provides a uniform basis for comparing calculation methods with respect to estimated variance. Simulations ( Walker 1987) indicate that jackknifing provides a reasonably unbiased estimate for error variance for a range of C/ Q slopes. Two important factors should be considered in interpreting the variance estimates. First, the estimates are themselves subject to error and are of limited accuracy in small sample sizes, particularly if the sampled flow distribution is not representative. Second, the variance estimates do not reflect effects of biases associated with some calculation methods under certain conditions, as discussed above. Thus, while the estimated variances are important factors to consider in selecting the “ best” loading estimation method, the sample characteristics and bias potential should also be considered. FLUX diagnostic procedures assist in this process, as described below. 2 8 Chapter 2 FLUX Error variance estimates developed by FLUX assume that the samples are statistically independent. This may not be the case if the file contains large numbers of discrete samples taken within relatively short periods of time. One approach to solving this problem is to composite the samples by event prior to calculating loadings. Important Wormation on the flow/ concentration relationship may be lost in compositing, however. As an alternative to compositing, discrete samples can be grouped by event only for the purposes of error analysis. In FLUX, sampling events are defined by the program parameter T. = Maximum Event Duration ( days). Samples collected within T, days of each other are considered part of the same sampling event. The default setting for T. is 1 day. This setting only influences the error variance estimates ( not the mean loading estimates). It only influences error variance estimates developed from relatively intensive sample data sets containing multiple samples on the same day or within the current N~ setting. Data stratification FLUX includes an option to divide the input flow and concentration data into a series of groups and calculate loadings separately within each group using the methods described above. Using formulas derived from classical sampling theo~ ( Cochran 1977), the mean and variance estimates within each group are subsequently combined across groups using weighting factors which are proportional to the frequency of each group in the total flow distribution ( see Table 2.2). The groups, or “ strat~” can be defined based upon flow, season, and/ or date. Stratification can serve three basic functions: a. Adjust for differences in the frequency distributions of sampled and unsampled flow regimes. b. Reduce potential biases associated with some calculation methods and/ or sampling program designs. c. Reduce the error variance of the mean loading estimate. When sample data are adequate, stratification can offer significant advantages over the direct methods and provide insights that can be used to improve sampling efficiency in future years. In most applications, the groups are defined based upon flow. The “ flowinterval” method was developed by the U. S. Army Engineer District, Buffalo ( 1975), for use in the Lake Erie Wastewater Management Study and is described by Verhoff, Yaksich, and Melfi ( 1980) and Westerdald et al. ( 198 1). This procedure applies the direct load averaging ( Method 1) separately to different data groups, defined based upon flow regimes. Since loading usually increases with flow, grouping the data based upon flow reduces the loading Chapter 2 FLUX 2 9 2 1o Table 2.2 stratified Sample Algorithm ( Cochran 1977; Bodo and Unny 1983) definitions: s = subscript indicating stratum m= subscript indicating estimation method N, = number of daily flows in stratum s N, = total number of daily flows ns,. = optimal number of samples in stratum s, given nt w = total number of sampled concentrations w= m, s mean flux in stratum s estimated by method m v= m, s variance of mean flux in stratum s estimated by m s = m, s effective standard deviation within stratum s for method m w m, t = mean flux over all strata estimated by method m v= m, t variance of mean flux over all strata estimated by method m V*= m, t variance of mean flux over all strata estimated by method m for optimal allocation of nt samples according to n~,. z= sum over all strata ( s) Equations: N, = ~ N~ % = ~ n~ w m, t = Z ( wm, JJ6)/ Nt v m, t = Z ( Vm, JJ$ 2)/ Nt2 s = m, s [ n, Vm, J0” 5 n~. = ntN~ Sm,~ / ~ ( N& J V*= m, t x ( V~, SN~ 2nJn~,.)/ N~ variance within each group and results in lower variance for the total loading estimate. A flow stratified version of Method 2 written in SAS ( Statistical Analysis System) was developed and applied to estimate phosphorus loadings in a Vermont lake study ( Walker 1983). The IJC method described by Bodo and Unny ( 1983, 1984) is a flow stratified version of Method 3. In FLUX, data groups or strata can be defined based upon flow range, date range, and/ or season range. Generally, flow ranges would be used and the data would be stratified into two or three groups based upon flow. In some situations, however, it maybe desirable to strati~ based upon sampling date or Chapter 2 FLUX season. Stratification based upon season may be usefti in situations where there is a strong seasonal variation in concentration which is independent of flow or for streams with highly regulated flows, such as a reservoir outflow station ( particularly when intake levels are varied seasonally). Flowindependent, seasonal variance components are more likely to be detected in analysis of dissolved or inorganic nutrient concentrations ( particularly nitrate) than in analysis of particulate or total nutrient concentrations. In deftig stra~ one objective is to isolate homogeneous subgroups, based upon the flow/ concentration relationship assumed by the calculation method ( constant loading for Method 1, constant concentration for Methods 2 and 3, and log linear flow/ concentration relationship for Methods 4 6). A second objective is to set stratum boundaries so that the sampled and total flow distributions are equivalent within each stratum. This protects against bias in the loading estimates and applies particularly to high flow strata. As described above, the method used to estimate error variance does not detect bias. If the flow distributions are not equivalent within each stratum, then minimum variance is less reliable as a criterion for selecting the “ best” calculation method and loading estimate. Statistical and graphical tests are provided to compare flow distributions within each stratum. Robustness of the loading estimate decreases as the number of statistical parameters which must be estimated from the sample data set increases. The number of parameters which must be estimated depends upon the calculation method and upon the number of strata. Methods 1 and 2 require one parameter estimate for each stratum. Methods 3, 4, 5, and 6 require two parameter estimates per stratum. Strati& ing the data into two or three groups based upon flow and using Method 2 is generally adequate to capture the flow/ concentration relationship while requiring the fewest parameter estimates ( in statistical terms, using up the fewest degrees of freedom). If concentration does not vary systematically with flow, the need for flow stratification decreases. Uncertainty in the loading estimate is reflected by the CV estimate reported for each calculation method. The CV equals the standard error of the mean loading divided by the mean loading. The CV reflects sampling error in the flow weighted mean concentration. Potential error variance in the flow measurements are not considered in these calculations. In practice, CV values < 0.1 are usually adequate for use in mass balance modeling, especially considering that uncertainty in flow measurements is usually in this range. Depending on stream dynamics, CV values < 0.1 may be very difficult to achieve, especially in small, flashy streams with strong C/ Q relationships. CV values between 0.1 and 0.2 may be adequate for modeling purposes, especially for minor tributaries. If higher CVS are found, the user should consider refining and extending the stream monitoring program to obtain better data sets for load estimation before proceeding with modeling efforts. This particularly applies if the CV values are high for major tributaries. Chapter 2 FLUX 2 11 For each calculation method, FLUX generates an invento~ of sample and flow data in addition to a breakdown of the flow, load, and variance components within each stratum, as well as for the total strat~ as demonstrated in Table 2.3, for the Caddo River example. Samples have been divided into three flow intervals. Complete output for this example is given at the end of this chapter. Table 2.3 Breakdown by Flow Stratum  Caddo River Example FLUX Breakdown by Stratum: FREQ FLOU FLUX VOLUME Wiss CONC CV ST NS NE DAYS HM3/ YR KG/ YR HM3 KG PPB  1 93 93 582.0 120.23 2761.4 191.58 4400.1 23.0 .050 2 61 61 407.0 397.42 14501.1 442.85 16158.7 36.5 .092 3 14 14 107.0 2070.70 259357.2 606.61 75978.7 125.3 .148 *** 168 168 1096.0 413.59 32171.8 1241.05 96537.5 77.8 .118 Optimal Sample Allocation: ST NE NE% NEOPT% FREQ% VOL% MASS% VAR% VARIANCE CV 1 :: 93 55.4 3.8 53.1 15.4 4.6 .0 . 5276E+ 04 .050 2 61 61 36.3 20.8 37.1 35.7 16.7 1.7 . 2442E+ 06 .092 3 14 14 8.3 75.5 9.8 48.9 78.7 98.3 . 1407E+ 08 .148 *** 168 168 100.0 100.0 100.0 100.0 100.0 100.0 .1432E+ 08 .118 Notes: Output from the lList/ Breakdownl Procedure for Caddo River with 3 Flow Strata The top part of the screen lists the distribution of samples, flows, fluxes, volume, and mass across strata for the current calculation method. The middle part of the screen lists the distribution of sampling effort, flow days, flow volume, mass, and error variance, each expressed as percentage of the total. The bottom part of the screen describes the potential benefit of optimizing the sample allocation across strata to obtain the lowest error variance for a fixed number of sampling events. NE% = percent of total sample events in stratun NEOPT% = optimal percent of total sample events in stratum The reduction in error CV attributed to shifting from the current sample distribution ( NE%) to the optimal distribution ( NEOPT%) is listed. This can be used to refine future monitoring program designs. Generally, a shift towards more intense sampling of high flow strata ~ ill be indicated. Typically, mostof theloadanderror varianceisinthe high flowstratum. Since the variance component is roughly inversely related to sampling frequency within each stratum, the “ breakdown by stratum” given in Table 2.3 is useful for evaluating sampling strategies. The low flow stratum accounts for 55.4 percent of the total samples but only 4.6 percent of the total mass discharge. In future sampling, moving some ofthesamples fromthelow flow to the high flow stratum would reduce the variance ofthe total loading estimate. Alternatively, to reduce monitoring costs, the low flowsampling frequencies 2 12 Chapter2 FLUX could be reduced without substantially increasing the variance of the total loading estimate. FLUX also provides an estimate of the “ optimal” sample distribution ( expressed as percent of the total sampling effort allocated to each stra~ NEOPTO/ Oin Table 2.3) which would minimize the variance of the total loading estimate for a given total number of independent samples, using the equations specified in Table 2.2. Comparing the observed variance with the optimal variance provides an approximate indication of the potential benefits of optimizing the sample design. In this case, shifting from the historical sample distribution across flow strata ( 55%/ 36%/ 8%) to the optimal sample distribution ( 4%/ 2 1%/ 76%) would decrease the CV of the load estimate from O. 118 to 0.045. As described by Bodo and Umy ( 1983, 1984), stratum breakdowns can be used to refine monitoring program designs for future years, subject to practical limitations in sample scheduling and total budget and to requirements imposed by other monitoring objectives. The “ optimal” distribution of sampling effort indicated by the program may be difficult to achieve without automated equipment. An important statistical limitation is that the “ optimal” allocation assumes that the samples are serially independent, and it may be impossible to take the recommended number of independent samples from intensively monitored strata. Five samples taken from different storm events would tend to be less serially dependent than five samples taken within one event, for example. Because of these limitations, the “ optimal” design should not be viewed as an absolute objective, but as a general direction for adjusting previous survey designs within practical constraints. Diagnostics FLUX includes several routines for generating scatter plots and histograms of flow, concentration, loading, and sample dates, as illustrated at the end of this chapter. The relationship between flow and concentration partially determines the appropriate calculation method and should be reviewed in each application. Flow frequency distributions ( sampled versus total) can also be graphically compared. These displays characterize the flow and concentration distributions and can assist the user in assessing data adequacy, identi~ ing appropriate stratification schemes, and evaluating calculation methods. The calculation methods differ with respect to the schemes used to estimate the loadings on the unsampled days or periods. For a given method, observed and predicted fluxes can be compared for each water quality sample. This provides one measure of performance. Ideally, the flux residuals ( loglO( observed flux) minus loglO( predicted flux) should be random and independent of flow season. In practice, this independence is sometimes difflcuh to achieve with the relatively simplistic models upon which the calculation methods are based. The residuals analysis procedure generates plots of observed versus predicted loadings, residuals versus flow, and residuals versus Chapter 2 FLUX 2 13 date. Alternative stratification schemes can be investigated to reduce the flowdependence and/ or time dependence of the residuals. Listings of residuals and jackknifed loading estimates are useful for identi& ing outliers and determining sensitivity of the loading estimates to individual samples. FLUX includes an outlier detection routine which can be used to delete suspected outliers from the sample data set. Outliers are detected based upon deviations of the residuals from a lognormal distribution ( Snedecor and Cochran 1989). This procedure should be used conservatively. Detection of outliers depends upon the current stratification scheme and calculation method. Important information may be lost if an apparent outlier is actually an important signal. Suspected outliers are usually apparent on the concentration versus flow scatter plots. Developing confidence with the program, stratification scheme, and calculation method are suggested before using the outlier deletion procedure. Program Operation Introduction This section describes the FLUX menu structure and operation procedures. When the program is run ( from the DOS prompt), a series of help screens summarizing model features is first encountered. If error messages appear, it generally means that one of the FLUX program files has been corrupted or that your computer does not have enough available memory. TV reinstalling the program. Try unloading any memory resident software. If you are trying to run the program from Windows, try exiting Windows and running directly from DOS. The program permits selection of ‘ user mode’ at startup after introductory screens. The selection of user mode is followed by a menu which provides interactive access to eight types of procedures with the following fhnctions: FLUX VERSION 5.0 Data Calculate Method Plot List Utilities Help Quit Data Read and/ or Strati fy Data Calculate Calculate Loads Using Current Data & Stratification Scheme Method Select Flux Calculation Method Used in Plots & Tables Plot Plot Load, Flow, and/ or Concentration Data List List Output Formats for Current Calculation Method Utilities Program Uti lities & Options Help View Help Screens Quit End Session 2 14 A procedure category is selected by moving the cursor ( using arrow keys) or by pressing the first letter of the procedure name. Selected procedures in the menu box are highlighted on the screen and underlined in the following documentation. Assistance in navigating around the menu can be obtained by Chapter 2 FLUX pressing the < F7> fiction key. A Help screen describing the selected procedure can be viewed by pressing < Fl>. After each procedure is completed, control returns to the above menu screen. Essential features of the current data set are summarized below the menu box ( not shown here). Data procedures Data procedures control input, stratification, listing, and other manipulations of sample and./ or flow data used in load calculations: Read Read New Sanple and/ or Flow Data Stratify Divide Sanples & Flows into Groups for Load Calculations Delete Delete a Specific Sanple or Delete Excluded Samples Composite Composite Samples by Date FlowSub Substitute Daily Mean Flows for Sample Flows Title Enter New Title for Labeling Output List List Sanple or Flow Input Data Four methods for reading in new sample or flow data are available under Data/ Read: Reset Read New Sa~ le & Flow Data; Reset Stratification Scheme Keep Read New Sa~ le & Flow Data; Keep Current Stratification Sch Sanples Read New Sanple Data Only; Keep Current Stratification Schern I nd, X Read Sample & Flow Data from Station Index File In the first three procedures, a data entry screen is presented for defining all input specifications ( data file names, variable labels, time periods, and units conversion factors). Use Reset to read in new flow data and reset the stratification scheme. Use Keep to read in new data without changing the current stratification scheme. Use Samples to read in new sample data only, without changing the current daily flow data or stratification scheme. Use Index to read in new data from a station index file, which is a user created ASCII file defining the storage locations and formats for concentration and flow data referring to specific stations. Using index files greatly speeds and simplifies the specification of input data. ( See Data entry screens.) If variable labels ( for daily flows, sample flows, and concentration) are left blank on data entry screens, the user is prompted to select the appropriate field from a list of all fields contained in the source data file. Screen messages track the progress of data retrieval from disk files. If the specified data set has fewer than three samples or no daily flows, an error message appears and control returns to the main menu. Note that this may occur if the file names or variable labels are entered incorrectly. If a valid data set is retrieved, subsequent screens include a listing of missing or out of sequence daily flows ( Data/ List/ Chapter 2 FLUX 2 15 Missing procedure) and a summary of the current stratification scheme ( Data/ Stratify/ List procedure). Control then returns to the main menu. Data/ Stratify procedures divide the sample and flow data into groups based upon flow, date, and/ or season. In many cases, stratification increases the accuracy and precision of load estimates. At least three samples are required in each stratum. Four options are available: Flow Define Strata Based Upon Flow; Reset Data & Season Limits Genera 1 Define General Stratification Scheme vs. Flow, Date, Season Reset Reset Stratification Scheme  Use 1 Stratum Only List List Current Strati f i cat ion Scheme & Sanple Counts Strati& ing based upon flow is often appropriate, especially when concentration is correlated with flow: 2 Strata Use 2 Flow Strata  Boundary at QMEAN 3 Strata Use 3 Flow Strata  Boundaries at QMEAN/ 2, QMEAN x 2 4 Strata Use 4 Flow Strata  Boundaries at QMEAN/ 2, QMEAN x 2, QMEAN x 8 Other Use Flows to Define Strata; Enter Flow Bounds Directly The first three procedures defineflow boundaries automatically. Dividing the dataintotwo strata based uponflow( low flow andhigh flow) is often appropriate. Three or more flow stratamaybe appropriate for relatively intensive datasetswithstrongflow/ concentration relationships. The last procedure permits direct entry offlow boundaries. Each stratum must contain atleast three sample events. Ifastratum contains fewer thenthree events, theuseris asked to redefine the flow boundaries until a valid stratification scheme is defined or the stratification scheme is reset. Data/ Delete procedures operate only on data stored in memory; they do not change disk files: One Delete a Specific Sample Excluded Delete All Sanples Excluded from Current Stratification Sche The Data/ Composite procedure combines samples collected on the same date or in the date interval into a single composite sample: 2 16 Chapter 2 FLUX Ccmposite Canposite Sanples by Date The user is prompted for the time interval ( number of days) to be used for compositing samples. This optional procedure may be appropriate for data derived from intensive monitoring programs providing multiple samples per date. The composite sample concentration is the flow weighted mean of the individual samples. The composite sample flow is the average of the sample flows. Because of possible variations in actual event duration, it is generally preferable to composite samples prior to running FLUX; i. e., to specifi event mean flows and event flow weighted mean concentrations in the source data files. The Data/ FlowSub procedure can be used to test the sensitivity of load estimates to the types of flow measurements which are paired with sample concentrations: F 1ousub Substitute Dai ly Mean Flows for Sanple Flows Depending upon source data files, input sample flows may be instantaneous flows measured at the time of sampling. The Data/ FlowSub procedure replaces sample flows with daily mean flows on the corresponding sample dates. Samples are deleted if the corresponding daily mean flow is missing or zero. This flow substitution may also be performed in the Data/ Read procedures by entering “ Lookup” in the sample flow field. Data/ List procedures summarize the sample and/ or flow data which have been retrieved from disk files: Samples List Sample Data F t OMS List F1OH Data Missing List Missing or Out of Sequence Daily Flows Before proceeding with load calculations, data listings should be reviewed to make sure that the correct sample and flow data have been retrieved from disk files. Both sample flows and corresponding daily mean flows are listed by the first two procedures. Daily flow data files read by FLUX are assumed to be sorted by date. The Data/ List/ Missing procedure lists missing or out of sequence daily flow records. If any are detected, FLUX can still operate. It is desirable, however, to estimate any missing flows independently and to sort flow files before running FLUX. Chapter 2 FLUX 2 17 Calculate procedures Calculate procedures can be accessed tier valid sample and flow data sets have been read and a valid stratification scheme has been defined. Three options are available: FLUX VERSION 5.0 Data e Method Plot List Utilities Help Quit Conpare Series Corrpare Compare Sample Flow & Total Flow Distributions Loads Calculate Loads Using Each Method Series Generate Load Time Series The Calculate/ Compare procedure provides information which can be used to assess adequacy ofthe sample dataand/ orstratificationscheme. The Calculate/ Loadsprocedure lists average flows, flux rates, flow weighted mean concentrations, and error estimates using each calculation method; this provides the basic tiormation needed for BATHTUB applications. The Calculate/ Series procedure lists flow, load, and concentration time series using the currently selected calculation method. Four options are available: Yearly Generate Load Time Series by Calendar Year WtrYearly Generate Load Time Series by Water Year Monthly Generate Monthly Load Time Series Daily Generate Daily Load Time Series Time series output does not include error estimates. These procedures are included primarily for generating load time series for use in applications other than BATHTUB which may require daily or monthly estimates. Method procedure The Method procedure asks the user to select the loading calculation method to be used in generating subsequent plots and output tables. Six choices are provided: FLUX  VERSION 5.0 Data Calculate !!! Q@ d Plot List Utilities Help Quit 1 AVG LOAD 2QWTDC 3 IJC 4 REG 1 5 REG 2 6 REG 3 1 AVG LOAD Method 1  Mean Load 2QWTDC Method 2  Flow Wtd Hean Cone. 3 IJC Method 3  Flow Wtd Nean Cone. ( IJC Modification) 4 REG 1 Method 4  Regression Model 1 5 REG 2 Method 5  Regression Model 2 6 REG 3 Method 6  Regression Model 3  log( C) vs. log( Q) Separate 2 18 Chapter2 FLUX Method 2 is initially selected as the default calculation method when the program is started. Descriptions of each method are given above ( see Loading calculation methods); summary descriptions can be viewed by selecting a method and pressing the Help key < F 1> or by running the Help procedure. Plot procedures Plot procedures provide important diagnostic information which can help in evaluating the adequacy of the current data set, stratification scheme, and calculation method: Barchart Cone Load Flow Daily Qfreq Residuals GridOpt Barcharts of Load, Mass, or Concentration Estimates Plot Sample Concentrations ( ppb) Plot Sample Loads ( kg/ yr) Plot Sample Flows ( hm3/ yr) Plot Daily Flows ( hfi/ yr) Plot Flow Frequency Distributions Plot Residuals = LOGlO ( Observed Load / Estimated Load ) Toggle Plot Grids On or Off The Plot/ Barchart procedures plot load, mass, flow weighted mean concentration, or flow as a function of calculation method or stratum: Load Load ( kg/ yr) Barcharts vs. Calculation Method or Stratum Method Plot Load Estimates ( kglyr) vs. Calculation Method Stratum Plot Load Estimates ( kg/ yr) vs. Stratwn Mass Mass ( kg) Barcharts vs. Calculation t4ethod or Stratum Method Plot Mass Estimates ( kg) vs. Calculation Method Stratun Plot Mass Estimates ( kg) vs. Stratum Cones Flow Ueighted Concentration ( ppb) vs. Calc. Method or Stratu Method Flow bleighted Concentration ( p@) vs. Calculation Method Stratun Flow Ueighted Concentration ( ppb) vs. Stratum Flow Mean Flow ( hm3/ yr) vs. Stratun Each bar chart ( exceptFlow) shows estimates+ l standard error. Plotting against method shows the sensitivityof the estimate ( total across all strata) to thecalculation method. Generally, alowsensitivity tocalculation method would support the reliability ofthe load estimates. Plotting against stratum shows estimates foreach data group using the currently selected calculation method. Plot/ Concprocedures display sample concentrations against four independent ( x axis) variables or a histogram: Chapter2 FLUX 2 19 Flow Plot Sanple Concentration ( ppb) vs. Flow ( hm3/ yr) Date Plot Sample Concentration ( ppb) vs. Date Month Plot Sample Concentration ( ppb) vs. Month Estimated Plot Observed vs. Estimated Cone. for Current Calc. Method Histogram of Observed Concentrations ( ppb) Both theobserved and theestimated sample concentrations areshown inthe first three procedures. The`` estimated'' sample concentration is based uponthe currently selected calculation method. Different symbols are usedto indicate samples indifferent strata. TheP1ot/ Loadand Plot/ Flowprocedures generate similar displays ofsarnple data: FLUX  VERSION 5.0 Data Calculate Method List Utilities Help Quit Barchart Cone Flow Daily Qfreq Residuals GridOpt Flow Date Month Estimated Histogram Flow Plot Load ( kg/ yr) vs. Flow ( hti/ yr) Date Plot Load ( kg/ yr) vs. Date t40nth Plot Load ( kg/ yr) vs. Month Estimated Plot Observed vs. Estimated Load Histogram Histogram of Observed Loads ( kg/ yr) FLUX VERSION 5.0 Data Calculate Method List Utilities Help Quit Barchart Cone Load Daily Qfreq Residuals GridOpt Date Month Histogram Comparison Both Date Plot Sample Flows ( hfi/ yr) vs. Date Uonth Plot Sanple Flows ( hm3/ yr) vs. Month Histogram Histogram of Sanple Flous ( hm3/ yr) Comparison Sample & Total Flow Histograms Both Plot Sanple Flow vs. Daily Mean Flow Plot/ Dailyprocedures display theentireflow record against date ormonth or as ahistogram: FLUX  VERSION 5.0 Data Calculate Method List Utilities Help Quit Barchart Cone Load Flow I) ailv Qfreq Residuals GridOpt Date Month Histogram Date Plot Daily Flows ( hti/ yr) vs. Date Month Plot Daily Flows ( hm3/ yr) vs. Month Histogram Histogram of Daily Flows ( hfi/ yr) Three format options are available for plotting daily flow against date: 2 20 lLinear Plot Daily Flows ( hti/ yr) vs. Date  Linear Scale 2Log Plot Daily Flows ( hm3/ yr) vs. Date  Log Scale 3Filled Plot Daily Flows ( hm3/ yr) vs. Date  Filled Chapter2 FLUX In addition to plotting the daily flow values, each of these formats also indicates daily flows on the dates of sample collection ( red squares). These displays are usefhl for identi& ing gaps in the sample record and for assessing sample coverage of major hydrographyfeatures. The lLinear and 2Log displays use different symbols to identi& strata. The 3Fi11ed display does not identifi strata. If zero flows are contained in the record, these are plotted as one half of the lowest positive flow value in the 2Log displays. The PlotiQfreq procedures display cumulative frequency distributions of sampled flow and total flow: T Freq Time Frequency Distributions for Sample & Total Flow V Freq Volune Frequency Distributions for Sample & Total Flow In the first case, they axis reflects the cumulative percentage of total samples or total flow days. In the second case, they axis is the cumulative percentage of the total sample volume or total flow volume. Plot/ Residuals procedures display residuals for the current calculation method: Cone Plot Residuals vs. Estimated Concentration ( F@) Load Plot Residuals vs. Estimated Load ( kg/ yr) Flow Plot Residuals vs. Sanple Flow ( hfi/ yr) Date Plot Residuals vs. Sample Date Month Plot Residuals vs. Sample Month Histogram Histogram of Residuals for Current Calculation Method Autocor Plot Residual Autocorrelation  Resid( t) vs. Resid( t 1) The residual is defined as log 10( observed sample flux/ estimated sample flux). Different symbols areused toidenti& strata. The Autocor procedure shows tielag l setidcomelation ofresiduds titismple order bwedupon date. As discussed above ( see Theory), serial correlation can influence the accuracy of error estimates and determine the appropriateness of time series methods for estimating loads. List procedures List procedures can be accessed only if a valid data set and stratification scheme have been defined. Three tabular output formats are provided using the currently selected calculation method: Chapter 2 FLUX 2 21 Residuals List Residuals & Screen for Outliers Breakdowns List Load & Flow Breakdowns by Stratwn; Optimal Sample Allot Jackknife List Jackknife Table for Current Calculation Method List/ Residualsprocedures provide detailed listing ofobservedandpredieted concentrations forthe currently selected calculation method: All List All Residuals Uithout Screening for Outliers Out 1 iers List Outliers Signif Set Significance Level for Outlier Screening The first procedure lists observed concentrations, estimated concentrations, and residua. ls( loglO( observed/ estimated)) foreach sample. The second procedure hwasitilm fomat, butlists odysmples wtichme suspected outliers. Outliersare detected based upon deviation from alognormal distribution; seethe associated help screen for a description oftheoutlier detection method. Ifany outliers are detected, the user may elect to delete therefrom the current sample list; source data files arenot modified. Theoutlier detection procedure is iterative mdautomaticdly repeats i~ elfmtil nooutliers we detected. The last procedure sets the significance level for outlier screening ( default= 0.05). The List/ Breakdowns procedure provides detailed information on the distribution of flow, flux, and error variance as a fuction of stratum for the current calculation method: Breakdowns List Load & Flow Breakdowns by Stratun; Optimal Sample Allot The top half of this output screen shows the sample properties. The bottom half estimates the optimal sample allocation across strata based upon the current sample properties. The optimal allocation is defined as the distribution of samp 
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