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N. J. Potter, F. H. S. Chiew, A. J. Frost, R. Srikanthan, T. A. McMahon, M. C. Peel and J. M. Austin June 2008 Characterisation of Recent Rainfall and Runoff in the Murray Darling Basin A report to the Australian Government from the CSIRO Murray Darling Basin Sustainable Yields Project Murray Darling Basin Sustainable Yields Project acknowledgments The Murray Darling Basin Sustainable Yields project is being undertaken by CSIRO under the Australian Government's Raising National Water Standards Program, administered by the National Water Commission. Important aspects of the work were undertaken by Sinclair Knight Merz; Resource & Environmental Management Pty Ltd; Department of Water and Energy ( New South Wales); Department of Natural Resources and Water ( Queensland); Murray Darling Basin Commission; Department of Water, Land and Biodiversity Conservation ( South Australia); Bureau of Rural Sciences; Salient Solutions Australia Pty Ltd; eWater Cooperative Research Centre; University of Melbourne; Webb, McKeown and Associates Pty Ltd; and several individual sub contractors. Murray Darling Basin Sustainable Yields Project disclaimers Derived from or contains data and/ or software provided by the Organisations. The Organisations give no warranty in relation to the data and/ or software they provided ( including accuracy, reliability, completeness, currency or suitability) and accept no liability ( including without limitation, liability in negligence) for any loss, damage or costs ( including consequential damage) relating to any use or reliance on that data or software including any material derived from that data and software. Data must not be used for direct marketing or be used in breach of the privacy laws. Organisations include: Department of Water, Land and Biodiversity Conservation ( South Australia), Department of Sustainability and Environment ( Victoria), Department of Water and Energy ( New South Wales), Department of Natural Resources and Water ( Queensland), Murray Darling Basin Commission. CSIRO advises that the information contained in this publication comprises general statements based on scientific research. The reader is advised and needs to be aware that such information may be incomplete or unable to be used in any specific situation. No reliance or actions must therefore be made on that information without seeking prior expert professional, scientific and technical advice. To the extent permitted by law, CSIRO ( including its employees and consultants) excludes all liability to any person for any consequences, including but not limited to all losses, damages, costs, expenses and any other compensation, arising directly or indirectly from using this publication ( in part or in whole) and any information or material contained in it. Data is assumed to be correct as received from the Organisations. Acknowledgements The authors would like to thank Rodger Grayson, members of the BRS Climate Impact Sciences Program, and Dugald Black and Mark Littleboy of the NSW Department of Water and Energy for providing external review of this report. Citation Potter NJ, Chiew FHS, Frost AJ, Srikanthan R, McMahon TA, Peel MC and Austin JM ( 2008) Characterisation of recent rainfall and runoff in the Murray Darling Basin. A report to the Australian Government from the CSIRO Murray Darling Basin Sustainable Yields Project. CSIRO, Australia. 40pp. Publication Details Published by CSIRO © 2008 all rights reserved. This work is copyright. Apart from any use as permitted under the Copyright Act 1968, no part may be reproduced by any process without prior written permission from CSIRO. ISSN 1835 095X © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin Preface This is a report to the Australian Government from CSIRO. It is an output of the Murray Darling Basin Sustainable Yields Project which assessed current and potential future water availability in 18 regions across the Murray Darling Basin ( MDB) considering climate change and other risks to water resources. The project was commissioned following the Murray Darling Basin Water Summit convened by the Prime Minister of Australia in November 2006 to report progressively during the latter half of 2007. The reports for each of the 18 regions and for the entire MDB are supported by a series of technical reports detailing the modelling and assessment methods used in the project. This report is one of the supporting technical reports of the project. Project reports can be accessed at http:// www. csiro. au/ mdbsy. Project findings are expected to inform the establishment of a new sustainable diversion limit for surface and groundwater in the MDB – one of the responsibilities of a new Murray Darling Basin Authority in formulating a new Murray Darling Basin Plan, as required under the Commonwealth Water Act 2007. These reforms are a component of the Australian Government’s new national water plan ‘ Water for our Future’. Amongst other objectives, the national water plan seeks to ( i) address over allocation in the MDB, helping to put it back on a sustainable track, significantly improving the health of rivers and wetlands of the MDB and bringing substantial benefits to irrigators and the community; and ( ii) facilitate the modernisation of Australian irrigation, helping to put it on a more sustainable footing against the background of declining water resources. Summary Chapter 1 presents the MDB wide results from the analyses of the 1895 to 2006 annual rainfall series from 225 rainfall stations across the MDB. Chapter 2 presents the 1895 to 2006 annual rainfall and modelled runoff series and the assessment of recent rainfall and runoff characteristics for each of the 18 regions defined for the CSIRO Murray Darling Basin Sustainable Yields Project. Chapter 3 describes the methods used for the analyses. The analyses show high inter annual and inter decadal variability in rainfall and runoff, with long periods that are considerably wetter or drier than others. Most regions ( except the southernmost parts of the MDB) show a step change in rainfall, with a marked increase after the mid 1940s. Several dry periods are evident in the 1890s, around 1940, the mid 1960s, the early 1980s, and the last five to ten years over many parts of the MDB. The 2004 to 2006 rainfall and runoff are lower than the long term means almost everywhere in the MDB. Averaged over the entire MDB, the 2004 to 2006 mean annual rainfall ( 384 mm) is 16 percent lower than the 1895 to 2006 long term mean ( 457 mm). Averaged over the entire MDB, the 2004 to 2006 mean annual runoff ( 16.7 mm) is 39 percent lower than the 1895 to 2006 long term mean ( 27.3 mm). However, because of the inter annual variability in rainfall and runoff and the very short three year period used for comparative analysis, this difference is only statistically significant in a few small, non contiguous areas of the MDB. The 1997 to 2006 rainfall and runoff are lower than the long term means in the southern half and in the north east corner of the MDB, and are similar to the long term means in the northern half of the MDB. Averaged over the entire MDB, the 1997 to 2006 mean annual rainfall ( 440 mm) is 4 percent lower than the 1895 to 2006 long term mean ( 457 mm). Averaged over the entire MDB, the 1997 to 2006 mean annual runoff ( 21.7 mm) is 21 percent lower than the 1895 to 2006 long term mean ( 27.3 mm). However, the 1997 to 2006 rainfall and runoff are not statistically different from the 1895 to 2006 long term means when averaged over the entire MDB. Statistically significant differences are, however, observed in the southern MDB. In particular, the 1997 to 2006 rainfall in this area is lower than the long term mean, with average recurrence intervals between 20 and 100 years, and greater than 100 years in the southernmost parts. Likewise, the 1997 to 2006 runoff in the southern MDB is much lower than the long term mean, and lower than the runoff in similarly dry ten year periods in the past. This difference is also statistically significant. In the southernmost parts of the MDB, the low runoff in 1997 to 2006 is unprecedented in the historical record and has average recurrence intervals of more than 300 years. Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 The main reason for the considerably lower runoff in 1997 to 2006 compared to the runoff in similar dry periods in the past is probably the reduced rainfall in autumn and early winter. Most of the runoff in the southern MDB occurs in winter and early spring. As a result of low autumn rainfall, the soils are less saturated in winter, and this together with the lower winter rainfall results in low winter runoff when most of the runoff occurs. It should be noted that the analyses here are carried out using the 1895 to 2006 annual observed rainfall and modelled runoff time series. Some exploration of monthly patterns is included to help interpret annual changes. The purpose of the analyses is to characterise recent rainfall based solely on the historical rainfall series, and not to explore processes that may cause the observed variability. These are addressed elsewhere in other projects. It is possible that the dry conditions observed in recent years may occur more frequently in the future given the future projections for drier conditions in southeastern Australia ( IPCC, 2007; CSIRO and BoM, 2007). © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin Table of Contents 1 Basin wide assessment............................................................................................................ 1 1.1 Rainfall stations....................................................................................................................... .................................... 1 1.2 Recent rainfall ............................................................................................................................... .............................. 2 1.3 Trends and step changes in rainfall .............................................................................................................................. 4 1.4 Average recurrence interval of recent rainfall................................................................................................................ 6 2 Regional assessment ............................................................................................................... 8 2.1 Entire basin summary........................................................................................................................ .......................... 8 2.2 Recent rainfall and runoff characteristics in the southern Murray Darling Basin compared to similar dry periods ........ 14 2.3 Region by region summary ............................................................................................................................... ........ 17 2.3.1 Paroo ............................................................................................................................... ........................... 18 2.3.2 Warrego ............................................................................................................................... ....................... 19 2.3.3 Condamine Balonne........................................................................................................................ ............ 20 2.3.4 Moonie ............................................................................................................................... ......................... 21 2.3.5 Border Rivers ............................................................................................................................... ............... 22 2.3.6 Gwydir......................................................................................................................... ................................ 23 2.3.7 Namoi ............................................................................................................................... .......................... 24 2.3.8 Macquarie Castlereagh ............................................................................................................................... 25 2.3.9 Barwon Darling ............................................................................................................................... ............ 26 2.3.10 Lachlan ............................................................................................................................... ........................ 27 2.3.11 Murrumbidgee................................................................................................................... .......................... 28 2.3.12 Murray......................................................................................................................... ................................ 29 2.3.13 Ovens ............................................................................................................................... .......................... 30 2.3.14 Goulburn Broken......................................................................................................................... ................ 31 2.3.15 Campaspe....................................................................................................................... ............................ 32 2.3.16 Loddon Avoca.......................................................................................................................... ................... 33 2.3.17 Wimmera........................................................................................................................ ............................. 34 2.3.18 Eastern Mount Lofty Ranges ........................................................................................................................ 35 3 Methodology .......................................................................................................................... 36 3.1 Time series smoothing ............................................................................................................................... ............... 36 3.2 Statistical tests for trend and step change .................................................................................................................. 37 3.3 Estimation of average recurrence interval................................................................................................................... 37 3.3.1 Calculation of average recurrence interval.................................................................................................... 38 3.3.2 Interpretation of average recurrence interval ................................................................................................ 39 4 References .............................................................................................................................. 40 Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 Tables Table 2 1. Mean annual rainfall and runoff, percentage difference between recent and long term mean annual rainfall and runoff, and the average recurrence interval for the period 2004– 2006 for the 18 regions in the Murray Darling Basin................................. 9 Table 2 2. Mean annual rainfall and runoff, percentage difference between recent and long term mean annual rainfall and runoff, and the average recurrence interval for the period 1997– 2006 for the 18 regions in the Murray Darling Basin................................ 9 Figures Figure 1 1. Locations of rainfall stations used for the analyses ........................................................................................................ 1 Figure 1 2. Percentage difference between mean annual rainfall in 1895– 2006 and ( a) in 2004– 2006 and ( b) in 1997– 2006.......... 3 Figure 1 3. Results from statistical tests ( using 1895– 2006 rainfall data) for ( a) trend and ( b) step change in mean ........................ 5 Figure 1 4. Average recurrence interval of ( a) 2004– 2006 rainfall and ( b) 1997– 2006 rainfall .......................................................... 7 Figure 2 1. ( a) Linear trend and low frequency variability of rainfall, with horizontal scale from 1895 to 2006 and same vertical scale for all regions, and ( b) low frequency variability for all regions, with same vertical scale for all regions ................................. 10 Figure 2 2. ( a) Linear trend and low frequency variability of runoff, with horizontal scale from 1895 to 2006 and same vertical scale for all regions, and ( b) low frequency variability for all regions, with same vertical scale for all regions. Note that the vertical scale is different to Figure 2 1 ............................................................................................................................... .................................... 11 Figure 2 3. Percentage difference between mean annual rainfall in 1895– 2006 and ( a) in 2004– 2006 and ( b) in 1997– 2006; and percentage difference between mean annual runoff in 1895– 2006 and ( c) in 2004– 2006 and ( d) in 1997– 2006............................ 12 Figure 2 4. Average recurrence intervals for ( a) 2004– 2006 mean annual rainfall, ( b) 1997– 2006 mean annual rainfall, ( c) 2004– 2006 mean annual runoff and ( d) 1997– 2006 mean annual runoff ................................................................................................. 13 Figure 2 5. Elasticity of runoff and ratio of percentage difference in runoff to percentage difference in rainfall for three ten year dry sequences ............................................................................................................................... ..................................................... 14 Figure 2 6. Annual observed streamflow time series and low frequency variability from six catchments in the southern Murray Darling Basin ............................................................................................................................... ................................................. 15 Figure 2 7. ( a) Monthly rainfall and ( b) monthly runoff for the southern Murray Darling Basin ( Murrumbidgee, Murray, Ovens, Goulburn Broken, Campaspe, Loddon Avoca, Wimmera and Eastern Mount Lofty Ranges) averaged across selected time periods ............................................................................................................................... ...................................................................... 16 Figure 3 1. Example annual rainfall time series with Gaussian kernel ( red line) centred at 1950 and the resulting smoothed time series ( blue line) ............................................................................................................................... ............................................ 36 Figure 3 2. Definition of terms for estimation of average recurrence intervals ................................................................................ 38 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 1 1 Basin wide assessment This chapter presents the results from the analyses of 1895 to 2006 annual rainfall series from 225 rainfall stations across the Murray Darling Basin ( MDB). Section 1.1 describes the annual rainfall data used for the analyses. Section 1.2 compares the mean annual rainfall over recent years to the long term mean. Section 1.3 presents results from statistical tests for trend and step change in mean. Section 1.4 presents the average recurrence interval ( ARI) of the recent dry conditions across the MDB. 1.1 Rainfall stations Figure 1 1 shows the locations of the 225 rainfall stations used in the analyses presented in Chapter 1. The rainfall stations generally provide a good coverage across the MDB, although there is less coverage in the drier western region. The analyses use 112 years of annual rainfall series from 1895 to 2006. The data comes from the Australian Bureau of Meteorology. All stations are selected to have less than 5 percent missing data over the period 1900 to 2006. This resulted in all stations having less than 10 percent missing data over the period 1895 to 2006, and the majority ( 209) having less than 5 percent missing data over the period 1895 to 2006. The data gaps are infilled with the patched point data from SILO ( see http:// www. nrm. qld. gov. au/ silo and Jeffrey et al., 2001). Figure 1 1. Locations of rainfall stations used for the analyses 2 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 1.2 Recent rainfall Figure 1 2 ( a) shows the percentage difference between the mean annual rainfall in the past three years ( 2004 to 2006) and in 1895 to 2006. Figure 1 2 ( b) shows the percentage difference between the mean annual rainfall in the past ten years ( 1997 to 2006) and in 1895 to 2006. In areas within the black contour line, the mean annual rainfall over the recent period is statistically significantly lower ( at a = 0.1) than the 1895 to 2006 mean. There are no stations where the recent mean is statistically significantly higher than the long term mean. The statistical significance is determined using the Student’s t test ( see Section 3.2) on the difference between the means of the two periods, ( a) 1895 to 2003 and 2004 to 2006, and ( b) 1895 to 1996 and 1997 to 2006. The statistically significant stations identified by the parametric Student’s t test are almost identical to those identified by the non parametric Rank Sum test ( see Section 3.2). Although the analyses are carried out for each of the 225 rainfall stations, Figure 1 2 shows contours derived from interpolation of these values because it is easier to visualise the spatial pattern across the MDB. An iterative finite difference interpolation technique is used ( TOPOGRID command in ArcInfo with the drainage enforcement option turned off). The resulting contours are essentially identical to those produced from other interpolation methods. Figure 1 2 ( a) indicates that in most parts of the MDB the 2004 to 2006 rainfall is lower than the long term mean. Averaged over the entire MDB the 2004 to 2006 mean annual rainfall ( 384 mm) is 16 percent lower than the 1895 to 2006 mean ( 457 mm). However, there are other three year periods in the historical data that have similar rainfall ( see Section 1.4 and Chapter 2), and the lower rainfall in 2004 to 2006 compared to the long term mean is not statistically significant, except at a few stations in several non contiguous regions across the MDB. The rainfall over the longer 1997 to 2006 period over much of the higher runoff producing regions in the southern MDB is lower than the long term mean by up to 20 percent. In the southernmost MDB, the lower rainfall is statistically different from the long term mean. The mean annual rainfall in the northern half of the MDB in 1997 to 2006 is similar or slightly higher compared to the long term mean. Averaged over the entire MDB the 1997 to 2006 mean annual rainfall ( 440 mm) is 4 percent lower than the 1895 to 2006 mean ( 457 mm). © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 3 Figure 1 2. Percentage difference between mean annual rainfall in 1895– 2006 and ( a) in 2004– 2006 and ( b) in 1997– 2006 4 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 1.3 Trends and step changes in rainfall Figure 1 3 presents results from statistical tests for trend and step change in mean in the 1895 to 2006 annual rainfall series from the 225 stations in the MDB. Figure 1 3 ( a) shows results from the three statistical tests for trend ( Mann Kendall, Spearman’s Rho and Linear Regression) and Figure 1 3 ( b) shows results from the three statistical tests for step change in mean ( Distribution Free CUSUM, Cumulative Deviation and Worsley Likelihood Ratio). The step change tests also identify the year of step change. All six tests are widely used in the literature and are briefly described in Section 3.2. Figure 1 3 ( a) shows that the results from the three tests for trend are almost identical. Figure 1 3 ( b) also shows that the results from the three step change tests are similar, particularly in the eastern half of the MDB. Except for the southernmost and northernmost parts of the MDB, annual rainfall in 1895 to 2006 over much of the MDB shows an increasing trend, and about half of these trends are statistically significant ( at α = 0.1). About half of the rainfall stations show a statistically significant positive step change in mean, about three quarters of them in the mid 1940s. This suggests that the biggest overall signal in 1895 to 2006 rainfall is the higher rainfall after the mid 1940s compared to before the mid 1940s, particularly in the eastern half of the MDB. © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 5 Figure 1 3. Results from statistical tests ( using 1895– 2006 rainfall data) for ( a) trend and ( b) step change in mean 6 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 1.4 Average recurrence interval of recent rainfall Figure 1 4 ( a) and ( b) present the average recurrence interval ( ARI) of the 2004 to 2006 rainfall ( past three years) and 1997 to 2006 rainfall ( past ten years), respectively, based on the 1895 to 2006 rainfall series. The ARI for a specific n year rainfall threshold is defined here as the average number of years between successive n year rainfall falling below the threshold. For example, an ARI of 50 years for 1997 to 2006 rainfall means that once a ten year mean rainfall is below the 1997 to 2006 mean, it will take, on average, another 50 years before another ‘ independent’ ten year mean rainfall falls below the 1997 to 2006 mean. There is no generally accepted method for defining the ARI of an n year low rainfall sequence. The ARI presented here must therefore be used cautiously and with full knowledge of the method used to estimate it ( see Section 3.3). There is also no generally accepted method of quantifying drought severity ( magnitude and duration) that is equally relevant for different applications. The three year mean rainfall and ten year mean rainfall are used here as objective measures of dry conditions because they can be easily understood. It should also be noted that the 2004 to 2006 and 1997 to 2006 rainfalls may be part of a more severe dry sequence with higher ARIs than that presented here ( see Section 3.3.2). Although the analyses are carried out for each of the 225 rainfall stations, Figure 1 4 shows contours derived from interpolation of these values because it is easier to visualise the spatial pattern across the MDB. An iterative finite difference interpolation technique ( TOPOGRID command in ArcInfo with the drainage enforcement option turned off) is used. The resulting contours are essentially identical to those produced from other interpolation methods. Although the recent rainfall in the southern half of the MDB is lower than the long term mean ( Section 1.2), there are similar dry periods in the historical data. Figure 1 4 ( a) shows that the 2004 to 2006 rainfall in parts of the southern and northeastern regions of the MDB have ARIs of 20 to 50 years. Figure 1 4 ( b) shows that the low rainfall over the longer 1997 to 2006 period is more extreme, with ARIs of more than 50 years in the northeastern and southern parts of the MDB, and more than 100 years in the southernmost parts. The ARIs elsewhere are generally less than 20 years, suggesting that there are many other three year and ten year rainfalls similar to or lower than the recent rainfall. © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 7 Figure 1 4. Average recurrence interval of ( a) 2004– 2006 rainfall and ( b) 1997– 2006 rainfall 8 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2 Regional assessment This chapter presents the 1895 to 2006 annual rainfall and runoff series, and the assessment of recent rainfall and runoff characteristics, for each of the 18 regions defined for the Murray Darling Basin Sustainable Yields Project. Section 2.1 summarises MDB wide rainfall and runoff and characterises recent rainfall and runoff. Section 2.2 discusses the recent rainfall and runoff characteristics in the southern parts of the MDB compared to previous dry periods. Section 2.3 summarises the rainfall and runoff characteristics in one page for each of the 18 MDB regions. The source of the rainfall data is the SILO 0.05 o x 0.05 o (~ 5 km x 5 km) gridded daily rainfall data ( see http:// www. nrm. qld. gov. au/ silo and Jeffrey et al., 2001). The runoff data comes from the rainfall runoff modelling over 0.05 o x 0.05 o grid cells across the MDB carried out for the CSIRO Murray Darling Sustainable Yields Project. The modelled daily runoff series for 1895 to 2006 is for ‘ current’ land use conditions. The modelled runoff series therefore does not consider development over time, but reflects the historical climate signal in runoff for ‘ current’ land use conditions ( see Chiew et al., 2008). Modelled runoff data is used for the analyses because there are relatively few long streamflow records, observed streamflow data is affected by changes in land use, and gauged unimpaired streamflow data is available for less than 1 percent of the MDB. The annual rainfall and runoff series for each region is calculated as the average of the rainfall and runoff from all 0.05 o x 0.05 o grid cells that are in the region. Entire basin summary Table 2 1 summarises recent rainfall and runoff for 2004 to 2006 compared to the long term means for the 18 MDB regions. Table 2 2 provides the same comparative summary for the period 1997 to 2006. Figure 2 1 and Figure 2 2 show the linear trends and low frequency variability of rainfall and runoff, respectively, in the 18 MDB regions. Figure 2 1 indicates that over the period 1895 to 2006, annual rainfall over much of the MDB shows an increasing trend. The plots also show inter decadal oscillations in the rainfall series with long periods that are considerably wetter or drier than others. Most regions show a marked step increase in rainfall after the mid 1940s ( particularly in the east), while dry periods are observed over many parts of the MDB in the 1890s, around 1940, the mid 1960s, the early 1980s, and the last five to ten years. The trend and low frequency variability of runoff ( Figure 2 2) are similar to those for rainfall, but are more clearly seen in the high runoff regions in the south east because the standard deviation of annual runoff in these regions is larger relative to the northern regions of the MDB. Values for the interannual variability ( coefficient of variation) of rainfall and runoff are presented in each regional summary page in Section 2.3. The coefficient of variation for annual rainfall ranges from 0.21 to 0.43, and the coefficient of variation for annual runoff ranges from 0.5 to 1.3, with the drier regions generally having larger variability than the wetter regions. The interannual variability of runoff in the MDB is almost twice that of similar river basins elsewhere in the world ( Peel et al., 2004). Figure 2 3 presents the percentage difference between the 2004 to 2006 rainfall and runoff and the 1895 to 2006 longterm means, as well as the percentage difference between the 1997 to 2006 rainfall and runoff and the 1895 to 2006 long term means for the 18 MDB regions. Figure 2 4 presents the average recurrence intervals ( ARIs, see Sections 1.4 and 3.3) for 2004 to 2006 rainfall and runoff and 1997 to 2006 rainfall and runoff for the 18 MDB regions. The characteristics of the recent rainfall have been presented and discussed in Chapter 1. Like rainfall, runoff has reduced recently, but to a larger degree compared to previous dry periods, particularly in the southern MDB, as discussed in Section 2.2. © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 9 Table 2 1. Mean annual rainfall and runoff, percentage difference between recent and long term mean annual rainfall and runoff, and the average recurrence interval for the period 2004– 2006 for the 18 regions in the Murray Darling Basin 2004– 2006 rainfall 2004– 2006 runoff Region 1895– 2006 mean annual rainfall mean percent change from 1895– 2006 ARI* 1895– 2006 mean annual runoff mean percent change from 1895– 2006 ARI* Paroo 311 209  33% 20 17 6.2  64% < 20 Warrego 422 338  20% < 20 7.2 3.1  57% < 20 Condamine Balonne 514 436  15% < 20 19 11  44% < 20 Moonie 528 490  7% < 20 17 15  16% < 20 Border Rivers 641 611  5% < 20 32 27  18% < 20 Gwydir 644 692 8% < 20 41 47 16% < 20 Namoi 633 650 3% < 20 24 22  11% < 20 Macquarie Castlereagh 544 453  17% < 20 35 19  46% < 20 Barwon Darling 328 270  18% < 20 6.0 3.7  39% < 20 Lachlan 461 358  22% 20 23 13  44% < 20 Murrumbidgee 530 409  23% 29 54 31  44% 27 Murray 340 281  17% < 20 24 16  35% < 20 Ovens 1004 794  21% 26 231 137  41% < 20 Goulburn Broken 764 601  21% 32 149 81  46% 35 Campaspe 594 482  19% < 20 69 29  59% 34 Loddon Avoca 430 353  18% < 20 21 8.8  57% 24 Wimmera 403 313  22% 28 16 6.7  59% 31 Eastern Mount Lofty Ranges 463 427  8% < 20 30 19  39% < 20 * Average recurrence interval, see Section 3.3. Table 2 2. Mean annual rainfall and runoff, percentage difference between recent and long term mean annual rainfall and runoff, and the average recurrence interval for the period 1997– 2006 for the 18 regions in the Murray Darling Basin 1997– 2006 rainfall 1997– 2006 runoff Region 1895– 2006 mean annual rainfall mean percent change from 1895– 2006 ARI* 1895– 2006 mean annual runoff mean percent change from 1895– 2006 ARI* Paroo 311 310 0% < 20 17 16  10% < 20 Warrego 422 427 1% < 20 7.2 6.6  8% < 20 Condamine Balonne 514 503  2% < 20 19 15  23% 23 Moonie 528 541 2% < 20 17 17  3% < 20 Border Rivers 641 641 0% < 20 32 32  1% < 20 Gwydir 644 688 7% 23 41 48 18% 23 Namoi 633 663 5% < 20 24 29 17% 22 Macquarie Castlereagh 544 547 1% < 20 35 33  5% < 20 Barwon Darling 328 339 3% < 20 6.0 6.5 8% < 20 Lachlan 461 425  8% < 20 23 18  24% 23 Murrumbidgee 530 471  11% 39 54 37  31% 106 Murray 340 313  8% 21 24 19  21% 36 Ovens 1004 895  11% 41 231 172  26% 36 Goulburn Broken 764 649  15% 156 149 89  41% 850 Campaspe 594 517  13% 47 69 34  50% 594 Loddon Avoca 430 381  11% 36 21 10  52% 420 Wimmera 403 350  13% 54 16 8.1  51% 385 Eastern Mount Lofty Ranges 463 429  7% 26 30 19  36% 105 * Average recurrence interval, see Section 3.3. 10 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 1895 1915 1935 1955 1975 1995 ( b) Paroo Warrego Condamine Balonne Moonie Border Rivers Gwydir Namoi Macquarie Castlereagh Barwon Darling Lachlan Murrumbidgee Murray Ovens Goulburn Broken Campaspe Loddon Avoca Wimmera Eastern Mount Lofty Ranges Figure 2 1. ( a) Linear trend and low frequency variability of rainfall, with horizontal scale from 1895 to 2006 and same vertical scale for all regions, and ( b) low frequency variability for all regions, with same vertical scale for all regions © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 11 1895 1915 1935 1955 1975 1995 Condamine Balonne Moonie Border Rivers Gwydir Namoi Ovens Goulburn Broken Campaspe Loddon Wimmera Eastern Mount Lofty Ranges Lachlan Murrumbidgee Murray Macquarie Castlereagh Barwon Darling Paroo Warrego ( b) Figure 2 2. ( a) Linear trend and low frequency variability of runoff, with horizontal scale from 1895 to 2006 and same vertical scale for all regions, and ( b) low frequency variability for all regions, with same vertical scale for all regions. Note that the vertical scale is different to Figure 2 1 12 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 Figure 2 3. Percentage difference between mean annual rainfall in 1895– 2006 and ( a) in 2004– 2006 and ( b) in 1997– 2006; and percentage difference between mean annual runoff in 1895– 2006 and ( c) in 2004– 2006 and ( d) in 1997– 2006 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 13 Figure 2 4. Average recurrence intervals for ( a) 2004– 2006 mean annual rainfall, ( b) 1997– 2006 mean annual rainfall, ( c) 2004– 2006 mean annual runoff and ( d) 1997– 2006 mean annual runoff 14 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.2 Recent rainfall and runoff characteristics in the southern Murray Darling Basin compared to similar dry periods The 2004 to 2006 and 1997 to 2006 rainfall and runoff across the southern MDB generally have ARIs greater than 20 years ( Table 2 1, and Figure 2 4). The 2004 to 2006 runoff ARIs in the southern MDB are generally similar to or slightly higher than the 2004 to 2006 rainfall ARIs. However, the 1997 to 2006 runoff ARIs in the southern MDB are much higher than the 1997 to 2006 rainfall ARIs, particularly in the Goulburn Broken, Campaspe, Loddon Avoca and Wimmera regions where the runoff ARIs are greater than 300 years. Although the 2004 to 2006 mean annual runoff is similar to or lower than the 1997 to 2006 mean annual runoff, persistent low runoff over the longer ten year period is more statistically significant and therefore has higher ARIs than the three year period. The eight southernmost regions in the MDB are the Murrumbidgee, Murray, Ovens, Goulburn Broken, Campaspe, Loddon Avoca, Wimmera and Eastern Mount Lofty Ranges. In these regions, almost all of the three year and ten year low rainfall means ( 37 out of 48) and low runoff means ( 32 out of 48) identified in Section 2.3 occur in the following three time periods: 1895 to 1904; 1936 to 1946; and 1997 to 2006. These time periods are also identified as dry periods in many of the other MDB regions. The remainder of this section compares the 1997 to 2006 rainfall and runoff with the 1895 to 1904 and 1936 to 1945 dry periods. 0 1 2 3 4 5 6 Paroo Warrego Condamine Balonne Moonie Border Rivers Gwydir Namoi Macquarie Castlereagh Barwon Darling Lachlan Murrumbidgee Murray Ovens Goulburn Broken Campa spe Loddon Avoca Wimmera Eastern Mt Lofty Rang es Ratio of percentage difference in runoff to percentage difference in rainfall 1895– 1904 1936– 1945 1997– 2006 Long term elasticity Figure 2 5. Elasticity of runoff and ratio of percentage difference in runoff to percentage difference in rainfall for three ten year dry sequences Figure 2 5 shows the long term rainfall elasticity of runoff for the 18 MDB regions, estimated from the 1895 to 2006 annual rainfall and runoff data using a nonparametric estimator ( Chiew, 2006). The rainfall elasticity of runoff is defined here as the average percentage change in mean annual runoff for a given percentage change in mean annual rainfall. This elasticity varies from about 2 to 3 across the MDB ( Figure 2 5), indicating that a 1 percent change in mean annual rainfall in the MDB will be amplified as a 2 to 3 percent change in mean annual runoff. Figure 2 5 also shows the percentage difference of recent and long term mean annual runoff divided by the percentage difference of recent and long term mean annual rainfall ( i. e. values in ‘ runoff, percent change from 1895– 2006’ column divided by values in the ‘ rainfall, percent change from 1895– 2006’ column in ). The ratios are only plotted if rainfall over a ten year period is more than 5 percent lower than the long term mean to avoid extremely large and meaningless ratios when the ten year rainfall is close to the long term mean. The ratios shown in Figure 2.5 for 1936 to 1945 are generally similar to the long term rainfall elasticities of runoff, but slightly higher in the north east and slightly lower in the southern MDB. The ratios for 1895 to 1904 are generally higher than the long term rainfall elasticities of runoff. For the southern MDB, the ratios for 1997 to 2006 are greater than the © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 15 ratios for 1895 to 1904, the ratios for 1936 to 1945, and the long term rainfall elasticities of runoff. This indicates that the runoff over the last ten years ( 1997 to 2006) is considerably lower than the runoff in similar low rainfall periods in the historical record. 0 50 100 150 200 250 300 1895 1915 1935 1955 1975 1995 401215 ( Upper Murray) 0 200 400 600 800 1000 1200 1400 1895 1915 1935 1955 1975 1995 403205 ( Ovens) 0 200 400 600 800 1000 1200 1895 1915 1935 1955 1975 1995 405205 ( Goulburn Broken) 0 50 100 150 200 250 1895 1915 1935 1955 1975 1995 405212 ( Goulburn Broken) 0 50 100 150 200 250 300 350 400 1895 1915 1935 1955 1975 1995 407217 ( Loddon) 0 20 40 60 80 100 120 140 160 180 1895 1915 1935 1955 1975 1995 415206 ( Wimmera) Figure 2 6. Annual observed streamflow time series and low frequency variability from six catchments in the southern Murray Darling Basin As mentioned on page 8, the analyses in this report are based on modelled ‘ natural’ runoff data. In order to check that the recent low runoff is not an artefact of the rainfall runoff modelling, annual streamflow series from six representative streamflow gauges in the southern MDB are shown in Figure 2 6. The streamflow gauges are chosen to have data starting before 1950 and to have less than 5 percent of the data missing during the period 1975 to 2006. The years with 16 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 missing data are not shown in the plots. The Gaussian smooth shown in the plots assumes mean annual streamflow values for the missing years. The recorded streamflow series from all these six catchments also show significantly lower streamflow in recent years. ( a) ( b) 0 10 20 30 40 50 60 J F M A M J J A S O N D mm / month 1895– 2006 1997– 2006 1936– 1945 1895– 1904 a) 0 1 2 3 4 5 6 7 8 J F M A M J J A S O N D mm / month 1997– 2006 1936– 1945 1895– 1904 1895– 2006 b) Figure 2 7. ( a) Monthly rainfall and ( b) monthly runoff for the southern Murray Darling Basin ( Murrumbidgee, Murray, Ovens, Goulburn Broken, Campaspe, Loddon Avoca, Wimmera and Eastern Mount Lofty Ranges) averaged across selected time periods Figure 2 7 shows the mean monthly rainfall and runoff averaged over the eight southern MDB regions ( Murrumbidgee, Murray, Ovens, Goulburn Broken, Campaspe, Loddon Avoca, Wimmera and Eastern Mount Lofty Ranges) for the entire 1895 to 2006 period and the three ten year dry periods. The plots indicate that most of the rainfall reduction in the 1997 to 2006 dry period is in the autumn and early winter. In contrast, in both the 1895 to 1904 and 1936 to 1945 periods, there is at least one month in autumn or winter that has a mean rainfall greater than the long term mean. Rainfall in the southern MDB is higher in the winter half of the year and most of the runoff in the southern MDB occurs in winter and early spring. As a result of low autumn rainfall, the soils are less saturated in winter, and this together with the lower winter rainfall results in low winter runoff when most of the runoff occurs. This is probably the main reason for the much lower runoff in the past ten years ( 1997 to 2006) compared to similar past dry periods. It is also likely that after a prolonged dry period, subsurface storage is low or has lost connection with the river system, and significant amounts of rainfall and diffused recharge are required to fill the storage or to re establish the connection with the river system before significant runoff can occur. Other possible reasons for the higher runoff reduction in the past ten years compared to similar past dry periods include: higher recent temperature , accentuating the impact of low rainfall; changes in the daily rainfall distribution ( however, the analyses here also indicate that extreme daily rainfall characteristics in 1997 to 2006 are similar to the long term characteristics); and changes in the sequencing of rainfall events. The mean annual runoff over the past ten years in the Goulburn Broken, Campaspe, Loddon Avoca and Wimmera regions is also similar to the projected decrease in mean annual runoff in the extreme dry 2030 climate change scenario ( see Chiew et al., 2008). However, because the analysis is based on a relatively short ten years of data, it is not sufficient evidence that the hydroclimate has shifted to a new regime. Nevertheless, if the hydroclimate has shifted to a new regime ( like in the extreme dry climate change scenario), the dry conditions observed over the past ten years will occur more frequently. Murphy and Timbal ( 2007) examined rainfall over south eastern Australia ( mostly the same area as the southern MDB defined here but with the inclusion of the coastal fringe around the southern MDB) and also observe lower than normal autumn rainfall over 1997 2006 compared with the 1936 1945 period. Furthermore they demonstrate that average maximum daily temperature has been higher and annual year to year variability of rainfall is smaller compared with the 1936 1945 period. They suggest that these three climatic conditions taken together have contributed to the recent very low inflows into the southern MDB. © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 17 2.3 Region by region summary The following analyses are presented for each region from page 18 onwards: · annual rainfall and runoff series for 1895 to 2006 and low frequency variability of rainfall and runoff. The low frequency variability ( smoothed time series) is calculated using the kernel smoothing method described in Section 3.1 · mean, standard deviation, coefficient of variation, coefficient of skewness and lag one autocorrelation coefficient of mean annual rainfall and runoff · a table showing the three lowest independent mean annual rainfall and runoff for three year non overlapping periods and their ARIs ( method described in Section 3.3), and the corresponding values for the past three years ( 2004 to 2006) · a table showing the three lowest independent mean annual rainfall and runoff for ten year non overlapping periods and their ARIs ( method described in Section 3.3), and the corresponding values for the past ten years ( 1997 to 2006) · maps of the spatial distribution of mean annual rainfall and mean annual runoff. The three lowest independent three year and ten year rainfall and runoff means are selected from the period 1895 to 2006. To ensure that the events are independent and do not come from the same dry sequence, an event cannot overlap a previously selected period. For example, if the rank one ten year rainfall mean occurs in 1957 to 1966, subsequent events cannot be selected from the previous ten year period ( 1948 to 1957) to the following ten year period ( 1966 to 1975) inclusive. 18 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.1 Paroo Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 311 mm Standard deviation of annual rainfall: 135 mm Coefficient of variation of annual rainfall: 0.43 Coefficient of skewness of annual rainfall: 0.81 Lag one serial correlation of annual rainfall: 0.087 Mean annual runoff: 17.4 mm Standard deviation of annual runoff: 20.3 mm Coefficient of variation of annual runoff: 1.17 Coefficient of skewness of annual runoff: 2.75 Lag one serial correlation of annual runoff: 0.114 Three year rainfall Rank Period Mean ARI 1 1927– 1929 151 209 2 1900– 1902 171 71 3 1944– 1946 175 62 Past three years 2004– 2006 209 20 Three year runoff Rank Period Mean ARI 1 1944– 1946 2.5 169 2 2001– 2003 2.8 119 3 1899– 1901 3.0 107 Past three years 2004– 2006 6.2 < 20 Ten year rainfall Rank Period Mean ARI 1 1957– 1966 243 53 2 1937– 1946 247 47 3 1896– 1905 252 38 Past ten years 1997– 2006 310 < 20 Ten year runoff Rank Period Mean ARI 1 1957– 1966 8.4 65 2 1896– 1905 8.9 54 3 1927– 1936 10.1 35 Past ten years 1997– 2006 15.6 < 20 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 19 2.3.2 Warrego Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 422 mm Standard deviation of annual rainfall: 148 mm Coefficient of variation of annual rainfall: 0.35 Coefficient of skewness of annual rainfall: 0.89 Lag one serial correlation of annual rainfall: 0.094 Mean annual runoff: 7.2 mm Standard deviation of annual runoff: 8.6 mm Coefficient of variation of annual runoff: 1.19 Coefficient of skewness of annual runoff: 3.07 Lag one serial correlation of annual runoff: 0.087 Three year rainfall Rank Period Mean ARI 1 1900– 1902 260 90 2 1944– 1946 264 79 3 1965– 1967 282 43 Past three years 2004– 2006 338 < 20 Three year runoff Rank Period Mean ARI 1 1944– 1946 1.5 101 2 1899– 1901 1.5 100 3 1965– 1967 2.2 31 Past three years 2004– 2006 3.1 < 20 Ten year rainfall Rank Period Mean ARI 1 1896– 1905 344 60 2 1937– 1946 347 55 3 1926– 1935 361 33 Past ten years 1997– 2006 427 < 20 Ten year runoff Rank Period Mean ARI 1 1896– 1905 3.4 109 2 1926– 1935 4.1 46 3 1937– 1946 4.2 40 Past ten years 1997– 2006 6.6 < 20 20 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.3 Condamine Balonne Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 80 100 120 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 514 mm Standard deviation of annual rainfall: 139 mm Coefficient of variation of annual rainfall: 0.27 Coefficient of skew of annual rainfall: 0.63 Lag one serial correlation of annual rainfall: 0.029 Mean annual runoff: 18.9 mm Standard deviation of annual runoff: 17.4 mm Coefficient of variation of annual runoff: 0.92 Coefficient of skewness of annual runoff: 2.73 Lag one serial correlation of annual runoff: 0.050 Three year rainfall Rank Period Mean ARI 1 1900– 1902 345 130 2 1944– 1946 348 118 3 1965– 1967 397 25 Past three years 2004– 2006 436 < 20 Three year runoff Rank Period Mean ARI 1 1900– 1902 5.3 126 2 1944– 1946 7.2 36 3 2001– 2003 7.3 35 Past three years 2004– 2006 10.6 < 20 Ten year rainfall Rank Period Mean ARI 1 1937– 1946 452 41 2 1896– 1905 453 39 3 1927– 1936 476 21 Past ten years 1997– 2006 503 < 20 Ten year runoff Rank Period Mean ARI 1 1896– 1905 10.0 134 2 1929– 1938 12.4 39 3 1960– 1969 12.9 33 Past ten years 1997– 2006 14.5 23 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 21 2.3.4 Moonie Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 80 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 528 mm Standard deviation of annual rainfall: 144 mm Coefficient of variation of annual rainfall: 0.27 Coefficient of skewness of annual rainfall: 0.38 Lag one serial correlation of annual rainfall: 0.023 Mean annual runoff: 17.4 mm Standard deviation of annual runoff: 15.3 mm Coefficient of variation of annual runoff: 0.88 Coefficient of skewness of annual runoff: 1.91 Lag one serial correlation of annual runoff: 0.045 Three year rainfall Rank Period Mean ARI 1 1900– 1902 356 82 2 1944– 1946 376 47 3 1965– 1967 379 44 Past three years 2004– 2006 490 < 20 Three year runoff Rank Period Mean ARI 1 1900– 1902 4.0 147 2 1944– 1946 6.5 28 3 1979– 1981 6.5 27 Past three years 2004– 2006 14.6 < 20 Ten year rainfall Rank Period Mean ARI 1 1935– 1944 433 131 2 1895– 1904 470 32 3 1964– 1973 489 21 Past ten years 1997– 2006 541 < 20 Ten year runoff Rank Period Mean ARI 1 1896– 1905 8.5 156 2 1927– 1936 9.8 73 3 1937– 1946 11.8 32 Past ten years 1997– 2006 16.8 < 20 22 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.5 Border Rivers Rainfall 0 200 400 600 800 1000 1200 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 641 mm Standard deviation of annual rainfall: 142 mm Coefficient of variation of annual rainfall: 0.22 Coefficient of skewness of annual rainfall: 0.17 Lag one serial correlation of annual rainfall:  0.018 Mean annual runoff: 32.4 mm Standard deviation of annual runoff: 23.1 mm Coefficient of variation of annual runoff: 0.71 Coefficient of skewness of annual runoff: 2.20 Lag one serial correlation of annual runoff: 0.015 Three year rainfall Rank Period Mean ARI 1 1918– 1920 480 60 2 1900– 1902 492 43 3 1939– 1941 504 32 Past three years 2004– 2006 611 < 20 Three year runoff Rank Period Mean ARI 1 1900– 1902 14.4 49 2 1938– 1940 15.7 33 3 1992– 1994 16.7 26 Past three years 2004– 2006 26.7 < 20 Ten year rainfall Rank Period Mean ARI 1 1935– 1944 541 169 2 1918– 1927 567 51 3 1895– 1904 606 < 20 Past ten years 1997– 2006 641 < 20 Ten year runoff Rank Period Mean ARI 1 1935– 1944 19.2 210 2 1922– 1931 23.1 43 3 1906– 1915 24.6 31 Past ten years 1997– 2006 32.2 < 20 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 23 2.3.6 Gwydir Rainfall 0 200 400 600 800 1000 1200 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 200 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 644 mm Standard deviation of annual rainfall: 153 mm Coefficient of variation of annual rainfall: 0.24 Coefficient of skewness of annual rainfall: 0.23 Lag one serial correlation of annual rainfall: 0.063 Mean annual runoff: 40.6 mm Standard deviation of annual runoff: 30.4 mm Coefficient of variation of annual runoff: 0.75 Coefficient of skewness of annual runoff: 1.86 Lag one serial correlation of annual runoff: 0.112 Three year rainfall Rank Period Mean ARI 1 1965– 1967 454 85 2 1944– 1946 476 48 3 1980– 1982 492 35 Past three years 2004– 2006 692 < 20 Three year runoff Rank Period Mean ARI 1 1925– 1927 15.9 51 2 1965– 1967 16.4 45 3 1938– 1940 18.1 31 Past three years 2004– 2006 47.0 < 20 Ten year rainfall Rank Period Mean ARI 1 1935– 1944 530 193 2 1918– 1927 572 38 3 1897– 1906 575 36 Past ten years 1997– 2006 688 < 20 Ten year runoff Rank Period Mean ARI 1 1935– 1944 22.2 218 2 1896– 1905 27.3 49 3 1923– 1932 28.4 40 Past ten years 1997– 2006 47.9 < 20 24 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.7 Namoi Rainfall 0 200 400 600 800 1000 1200 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 633 mm Standard deviation of annual rainfall: 155 mm Coefficient of variation of annual rainfall: 0.25 Coefficient of skewness of annual rainfall: 0.31 Lag one serial correlation of annual rainfall: 0.104 Mean annual runoff: 24.4 mm Standard deviation of annual runoff: 20.1 mm Coefficient of variation of annual runoff: 0.82 Coefficient of skewness of annual runoff: 2.20 Lag one serial correlation of annual runoff: 0.095 Three year rainfall Rank Period Mean ARI 1 1944– 1946 464 47 2 1980– 1982 471 39 3 1965– 1967 475 36 Past three years 2004– 2006 650 < 20 Three year runoff Rank Period Mean ARI 1 1938– 1940 7.9 90 2 1965– 1967 9.7 36 3 1935– 1937 10.5 28 Past three years 2004– 2006 21.7 < 20 Ten year rainfall Rank Period Mean ARI 1 1937– 1946 527 113 2 1918– 1927 560 36 3 1897– 1906 564 32 Past ten years 1997– 2006 663 < 20 Ten year runoff Rank Period Mean ARI 1 1935– 1944 13.1 185 2 1896– 1905 17.2 34 3 1923– 1932 17.3 33 Past ten years 1997– 2006 28.6 < 20 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 25 2.3.8 Macquarie Castlereagh Rainfall 0 200 400 600 800 1000 1200 1400 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 200 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 544 mm Standard deviation of annual rainfall: 159 mm Coefficient of variation of annual rainfall: 0.29 Coefficient of skewness of annual rainfall: 0.86 Lag one serial correlation of annual rainfall:  0.014 Mean annual runoff: 34.6 mm Standard deviation of annual runoff: 30.3 mm Coefficient of variation of annual runoff: 0.88 Coefficient of skewness of annual runoff: 2.65 Lag one serial correlation of annual runoff: 0.050 Three year rainfall Rank Period Mean ARI 1 1965– 1967 390 45 2 1944– 1946 396 37 3 1938– 1940 409 27 Past three years 2004– 2006 453 < 20 Three year runoff Rank Period Mean ARI 1 1938– 1940 13.9 40 2 1965– 1967 14.8 31 3 1944– 1946 15.4 27 Past three years 2004– 2006 18.8 < 20 Ten year rainfall Rank Period Mean ARI 1 1937– 1946 434 210 2 1895– 1904 471 42 3 1910– 1919 484 29 Past ten years 1997– 2006 547 < 20 Ten year runoff Rank Period Mean ARI 1 1932– 1941 18.9 207 2 1906– 1915 20.4 109 3 1895– 1904 21.8 67 Past ten years 1997– 2006 32.9 < 20 26 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.9 Barwon Darling Rainfall 0 200 400 600 800 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 328 mm Standard deviation of annual rainfall: 117 mm Coefficient of variation of annual rainfall: 0.36 Coefficient of skewness of annual rainfall: 0.60 Lag one serial correlation of annual rainfall: 0.088 Mean annual runoff: 6.0 mm Standard deviation of annual runoff: 7.9 mm Coefficient of variation of annual runoff: 1.30 Coefficient of skewness of annual runoff: 4.16 Lag one serial correlation of annual runoff: 0.011 Three year rainfall Rank Period Mean ARI 1 1900– 1902 194 94 2 1965– 1967 195 86 3 1927– 1929 212 44 Past three years 2004– 2006 270 < 20 Three year runoff Rank Period Mean ARI 1 1965– 1967 1.2 153 2 1900– 1902 1.3 114 3 1943– 1945 1.7 48 Past three years 2004– 2006 3.7 < 20 Ten year rainfall Rank Period Mean ARI 1 1937– 1946 250 146 2 1896– 1905 266 60 3 1918– 1927 283 30 Past ten years 1997– 2006 339 < 20 Ten year runoff Rank Period Mean ARI 1 1937– 1946 2.9 117 2 1897– 1906 3.1 94 3 1910– 1919 3.3 66 Past ten years 1997– 2006 6.5 < 20 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 27 2.3.10 Lachlan Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 80 100 120 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 461 mm Standard deviation of annual rainfall: 130 mm Coefficient of variation of annual rainfall: 0.28 Coefficient of skewness of annual rainfall: 0.39 Lag one serial correlation of annual rainfall: 0.024 Mean annual runoff: 23.1 mm Standard deviation of annual runoff: 19.0 mm Coefficient of variation of annual runoff: 0.82 Coefficient of skewness of annual runoff: 2.20 Lag one serial correlation of annual runoff: 0.003 Three year rainfall Rank Period Mean ARI 1 1944– 1946 323 50 2 1901– 1903 331 40 3 1897– 1899 338 33 Past three years 2004– 2006 358 20 Three year runoff Rank Period Mean ARI 1 1944– 1946 8.4 46 2 1901– 1903 9.1 34 3 1897– 1899 9.1 33 Past three years 2004– 2006 13.0 < 20 Ten year rainfall Rank Period Mean ARI 1 1895– 1904 366 220 2 1937– 1946 371 163 3 1918– 1927 424 20 Past ten years 1997– 2006 425 < 20 Ten year runoff Rank Period Mean ARI 1 1895– 1904 12.3 193 2 1932– 1941 13.6 92 3 1906– 1915 15.0 49 Past ten years 1997– 2006 17.6 23 28 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.11 Murrumbidgee Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 200 250 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 530 mm Standard deviation of annual rainfall: 136 mm Coefficient of variation of annual rainfall: 0.26 Coefficient of skewness of annual rainfall: 0.46 Lag one serial correlation of annual rainfall: 0.042 Mean annual runoff: 54.3 mm Standard deviation of annual runoff: 32.4 mm Coefficient of variation of annual runoff: 0.60 Coefficient of skewness of annual runoff: 1.82 Lag one serial correlation of annual runoff: 0.049 Three year rainfall Rank Period Mean ARI 1 1943– 1945 385 55 2 2004– 2006 409 29 3 1897– 1899 414 26 Past three years 2004– 2006 409 29 Three year runoff Rank Period Mean ARI 1 1927– 1929 29.1 34 2 1943– 1945 30.0 29 3 1901– 1903 30.1 28 Past three years 2004– 2006 30.6 27 Ten year rainfall Rank Period Mean ARI 1 1895– 1904 444 120 2 1937– 1946 450 88 3 1997– 2006 471 39 Past ten years 1997– 2006 471 39 Ten year runoff Rank Period Mean ARI 1 1895– 1904 36.8 122 2 1997– 2006 37.2 106 3 1905– 1914 38.7 72 Past ten years 1997– 2006 37.2 106 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 29 2.3.12 Murray Rainfall 0 200 400 600 800 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 80 100 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 340 mm Standard deviation of annual rainfall: 92 mm Coefficient of variation of annual rainfall: 0.27 Coefficient of skewness of annual rainfall: 0.73 Lag one serial correlation of annual rainfall: 0.129 Mean annual runoff: 24.0 mm Standard deviation of annual runoff: 12.0 mm Coefficient of variation of annual runoff: 0.50 Coefficient of skewness of annual runoff: 1.40 Lag one serial correlation of annual runoff: 0.164 Three year rainfall Rank Period Mean ARI 1 1943– 1945 222 131 2 1965– 1967 244 45 3 1927– 1929 250 36 Past three years 2004– 2006 281 < 20 Three year runoff Rank Period Mean ARI 1 1901– 1903 12.0 62 2 1912– 1914 12.8 42 3 1943– 1945 12.8 41 Past three years 2004– 2006 15.7 < 20 Ten year rainfall Rank Period Mean ARI 1 1936– 1945 285 80 2 1895– 1904 285 76 3 1926– 1935 306 27 Past ten years 1997– 2006 313 21 Ten year runoff Rank Period Mean ARI 1 1895– 1904 15.3 282 2 1936– 1945 16.4 122 3 1907– 1916 18.7 39 Past ten years 1997– 2006 18.9 36 30 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.13 Ovens Rainfall 0 500 1000 1500 2000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 200 400 600 800 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 1004 mm Standard deviation of annual rainfall: 250 mm Coefficient of variation of annual rainfall: 0.25 Coefficient of skewness of annual rainfall: 0.30 Lag one serial correlation of annual rainfall:  0.024 Mean annual runoff: 231.3 mm Standard deviation of annual runoff: 140.0 mm Coefficient of variation of annual runoff: 0.61 Coefficient of skewness of annual runoff: 1.19 Lag one serial correlation of annual runoff: 0.078 Three year rainfall Rank Period Mean ARI 1 1943– 1945 747 53 2 2004– 2006 794 26 3 1901– 1903 797 25 Past three years 2004– 2006 794 26 Three year runoff Rank Period Mean ARI 1 1901– 1903 99.4 53 2 1895– 1897 100.8 49 3 1943– 1945 113.9 31 Past three years 2004– 2006 136.6 < 20 Ten year rainfall Rank Period Mean ARI 1 1895– 1904 862 99 2 1936– 1945 888 49 3 1997– 2006 895 41 Past ten years 1997– 2006 895 41 Ten year runoff Rank Period Mean ARI 1 1895– 1904 129.8 498 2 1997– 2006 171.9 36 3 1905– 1914 180.0 28 Past ten years 1997– 2006 171.9 36 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 31 2.3.14 Goulburn Broken Rainfall 0 200 400 600 800 1000 1200 1400 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 100 200 300 400 500 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 764 mm Standard deviation of annual rainfall: 172 mm Coefficient of variation of annual rainfall: 0.22 Coefficient of skewness of annual rainfall: 0.17 Lag one serial correlation of annual rainfall:  0.022 Mean annual runoff: 149.2 mm Standard deviation of annual runoff: 77.3 mm Coefficient of variation of annual runoff: 0.52 Coefficient of skewness of annual runoff: 0.94 Lag one serial correlation of annual runoff: 0.030 Three year rainfall Rank Period Mean ARI 1 1943– 1945 562 72 2 1936– 1938 588 41 3 2004– 2006 601 32 Past three years 2004– 2006 601 32 Three year runoff Rank Period Mean ARI 1 1912– 1914 75.4 52 2 1936– 1938 78.9 41 3 2004– 2006 81.0 35 Past three years 2004– 2006 81.0 35 Ten year rainfall Rank Period Mean ARI 1 1997– 2006 649 156 2 1936– 1945 669 66 3 1895– 1904 703 27 Past ten years 1997– 2006 649 156 Ten year runoff Rank Period Mean ARI 1 1997– 2006 88.6 850 2 1895– 1904 116.2 39 3 1940– 1949 117.6 36 Past ten years 1997– 2006 88.6 850 32 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.15 Campaspe Rainfall 0 200 400 600 800 1000 1200 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 200 250 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 594 mm Standard deviation of annual rainfall: 147 mm Coefficient of variation of annual rainfall: 0.25 Coefficient of skewness of annual rainfall: 0.02 Lag one serial correlation of annual rainfall: 0.036 Mean annual runoff: 68.9 mm Standard deviation of annual runoff: 48.3 mm Coefficient of variation of annual runoff: 0.70 Coefficient of skewness of annual runoff: 0.89 Lag one serial correlation of annual runoff: 0.009 Three year rainfall Rank Period Mean ARI 1 1943– 1945 387 138 2 1936– 1938 427 51 3 1925– 1927 439 40 Past three years 2004– 2006 482 < 20 Three year runoff Rank Period Mean ARI 1 1943– 1945 25.0 52 2 2001– 2003 25.4 50 3 2004– 2006 28.5 34 Past three years 2004– 2006 28.5 34 Ten year rainfall Rank Period Mean ARI 1 1937– 1946 480 230 2 1997– 2006 517 47 3 1895– 1904 518 46 Past ten years 1997– 2006 517 47 Ten year runoff Rank Period Mean ARI 1 1997– 2006 34.2 594 2 1895– 1904 40.3 135 3 1940– 1949 44.9 60 Past ten years 1997– 2006 34.2 594 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 33 2.3.16 Loddon Avoca Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 80 100 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 430 mm Standard deviation of annual rainfall: 112 mm Coefficient of variation of annual rainfall: 0.26 Coefficient of skewness of annual rainfall: 0.17 Lag one serial correlation of annual rainfall: 0.055 Mean annual runoff: 20.7 mm Standard deviation of annual runoff: 15.5 mm Coefficient of variation of annual runoff: 0.75 Coefficient of skewness of annual runoff: 1.26 Lag one serial correlation of annual runoff: 0.034 Three year rainfall Rank Period Mean ARI 1 1943– 1945 277 152 2 1925– 1927 313 41 3 1900– 1902 319 35 Past three years 2004– 2006 353 < 20 Three year runoff Rank Period Mean ARI 1 1943– 1945 6.8 55 2 2001– 2003 6.9 54 3 1925– 1927 8.3 29 Past three years 2004– 2006 8.8 24 Ten year rainfall Rank Period Mean ARI 1 1936– 1945 346 215 2 1895– 1904 370 57 3 1997– 2006 381 36 Past ten years 1997– 2006 381 36 Ten year runoff Rank Period Mean ARI 1 1997– 2006 9.9 420 2 1940– 1949 12.6 70 3 1896– 1905 13.0 60 Past ten years 1997– 2006 9.9 420 34 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.17 Wimmera Rainfall 0 200 400 600 800 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 403 mm Standard deviation of annual rainfall: 96 mm Coefficient of variation of annual rainfall: 0.24 Coefficient of skewness of annual rainfall: 0.04 Lag one serial correlation of annual rainfall: 0.050 Mean annual runoff: 16.5 mm Standard deviation of annual runoff: 11.8 mm Coefficient of variation of annual runoff: 0.71 Coefficient of skewness of annual runoff: 1.13 Lag one serial correlation of annual runoff: 0.073 Three year rainfall Rank Period Mean ARI 1 1943– 1945 276 97 2 1965– 1967 298 43 3 1938– 1940 301 39 Past three years 2004– 2006 313 28 Three year runoff Rank Period Mean ARI 1 1943– 1945 4.7 103 2 1965– 1967 6.3 38 3 2004– 2006 6.7 31 Past three years 2004– 2006 6.7 31 Ten year rainfall Rank Period Mean ARI 1 1936– 1945 350 55 2 1997– 2006 350 54 3 1895– 1904 359 36 Past ten years 1997– 2006 350 54 Ten year runoff Rank Period Mean ARI 1 1997– 2006 8.1 385 2 1895– 1904 10.3 63 3 1937– 1946 10.8 48 Past ten years 1997– 2006 8.1 385 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 35 2.3.18 Eastern Mount Lofty Ranges Rainfall 0 200 400 600 800 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 80 100 120 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 463 mm Standard deviation of annual rainfall: 97 mm Coefficient of variation of annual rainfall: 0.21 Coefficient of skewness of annual rainfall: 0.38 Lag one serial correlation of annual rainfall:  0.053 Mean annual runoff: 30.1 mm Standard deviation of annual runoff: 20.5 mm Coefficient of variation of annual runoff: 0.68 Coefficient of skewness of annual runoff: 1.34 Lag one serial correlation of annual runoff: 0.015 Three year rainfall Rank Period Mean ARI 1 1965– 1967 334 241 2 1912– 1914 372 37 3 1957– 1959 378 30 Past three years 2004– 2006 427 < 20 Three year runoff Rank Period Mean ARI 1 1912– 1914 11.3 110 2 1965– 1967 11.4 106 3 1975– 1977 13.5 44 Past three years 2004– 2006 18.5 < 20 Ten year rainfall Rank Period Mean ARI 1 1993– 2002 420 45 2 1958– 1967 433 24 3 1895– 1904 441 < 20 Past ten years 1997– 2006 429 26 Ten year runoff Rank Period Mean ARI 1 1997– 2006 19.3 105 2 1976– 1985 22.8 30 3 1932– 1941 23.7 23 Past ten years 1997– 2006 19.3 105 36 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 3 Methodology This section describes the methodology used to obtain the results presented in Chapter 1 and Chapter 2. Section 3.1 describes the time series smoothing method used to calculate the low frequency variability of rainfall in Chapter 2. Section 3.2 describes the statistical tests used to test for trend and step changes in mean of the rainfall time series in Section 1.2 and Section 1.3. Section 3.3 describes the method used to estimate the average recurrence intervals ( ARIs) of n year rainfall in Section 1.4 and Chapter 2. 3.1 Time series smoothing The time series smoothing is used to calculate the low frequency rainfall variability in Chapter 2. A kernel smoother, essentially a weighted moving average, is used. In the kernel smoother, the smoothed estimate at t0 of a time series Y( t) of length T is given by ( Fan and Yao, 2005): ( ) ( ) [ ( ) ] Σ [ ( ) ] Σ = =   = T t T t K t t h Y t K t t h Y t 1 0 1 0 0 / / ˆ for a given kernel function K( t) and bandwidth parameter h. A Gaussian kernel is used here ( Figure 3 1). The Gaussian kernel places more emphasis on years close to t0 than a moving average filter, and so results in a smoother signal. The Gaussian kernel is a normal distribution function with a mean of zero and a standard deviation of one: KG( t ) = ( 2 p )  1/ 2 exp(  t 2 / 2) A bandwidth of 5.4 is used here, which corresponds to 95 percent of the kernel lying ten years either side of the current year. This bandwidth can be derived from normal probability tables. 0 250 500 750 1000 1250 1895 1905 1915 1925 1935 1945 1955 1965 1975 1985 1995 2005 Annual rainfall ( mm) 0 0.1 0.2 0.3 0.4 0.5 Value of kernel Figure 3 1. Example annual rainfall time series with Gaussian kernel ( red line) centred at 1950 and the resulting smoothed time series ( blue line) Since the Gaussian kernel smooths are actually two sided averages, care needs to be taken in interpreting the values at the endpoints. For example, if rainfall in the next ten years ( 2007 to 2016) is decreasing, the value of the smoothed rainfall signal using these data would be slightly lower than if rainfall in the next ten years is increasing. Therefore, if we are currently at the trough of a drought, the smoothed rainfall signal would be slightly larger if we incorporated this extra information ten years from now. The mean absolute magnitude of the edge effect is small, approximately 5 percent of mean annual rainfall only. © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 37 3.2 Statistical tests for trend and step change Six statistical tests are used in Section 1.3 to test the 1895 to 2006 annual rainfall series for trend and step change in mean. Three statistical tests are used for trend: Mann Kendall, Spearman’s Rho and Linear Regression. Three statistical tests are used for step change in mean and year of step change: Distribution Free CUSUM, Cumulative Deviation and Worsley Likelihood Ratio. The Student’s t test is used in Section 1.2 to test whether the mean annual rainfall over the recent years is significantly different from the 1895 to 2006 mean. The Rank Sum test is also used to check the t test results. These non parametric and parametric tests are widely used in the literature, and details can be found in the TREND software package ( http:// www. toolkit. net. au/ trend and Chiew and Siriwardena, 2005) and the WMO UNESCO Expert Workshop on Trend/ Change Detection report ( Kundzewicz and Robson, 2000; Kundzewicz and Robson, 2004). The tests are summarised briefly below: · Mann Kendall Test is a non parametric test that determines the significance of a trend by analysing the relative frequency of ranked data values. · Spearman’s Rho is a non parametric test that determines the significance of a trend by analysing the correlation coefficient between the ranked response and time. · Linear regression is a parametric test that determines the significance of a trend by analysing the slope of the linear regression between the data values and time. · Distribution Free CUSUM is a non parametric test that determines the significance of a step change in mean by analysing the relative cumulative deviations from the median. The change point is given by the maximum absolute value of the test statistic. · Cumulative Deviation is a parametric test that determines the significance of a step change in mean by analysing the relative cumulative deviations from the mean. The change point is given by the maximum absolute value of the test statistic. · Worsley Likelihood Ratio is a parametric test that determines the significance of a step change in mean by analysing the relative cumulative deviations from the mean with higher weights given to the start and end of the time series. The change point is given by the maximum absolute value of the test statistic. · Student’s t test is a parametric test that determines whether the means from two specified data periods are statistically different by comparing the two means and taking into account the variability in the data. · Rank Sum is a non parametric test that determines whether the medians from two specified data periods are statistically different by comparing the sum of ranked data in each period. In all cases a two sided 90 percent significance level ( i. e. α = 0.1) is used. Specifically, a test statistic is statistically significant if the value of the statistic lies outside the 5 th or 95 th percentile of the relevant cumulative distribution function. 3.3 Estimation of average recurrence interval The method used to estimate the ARI of n year rainfall and runoff averages ( see Section 1.4 and Chapter 2) is described here. The ARI for a specific n year mean rainfall or runoff threshold is defined here as the average number of years between successive n year mean rainfall or runoff falling below the threshold, or the average time between successive down crossings ( see Section 3.3.1) of the threshold ( Fernandez and Salas, 1999). For example, an ARI of 50 years for ten year mean rainfall falling below 500 mm means that once a ten year mean rainfall is below 500 mm, it will take on average another 50 years before another ‘ independent’ ten year mean rainfall below 500 mm occurs, given there must be at least one ten year mean rainfall above the 500 mm threshold between two successive events/ down crossings. There is no generally accepted method for defining the ARI of an n year low rainfall or runoff sequence. The ARI defined here is somewhat different to the standard flood return period found in many textbooks. This is because unlike most flood frequency analysis, consecutive n year rainfall and runoff events, as used here, are not independent. There is also no generally accepted method of quantifying drought severity ( magnitude and duration) that is equally relevant for different applications ( Heim, 2002; Keyantash and Dracup, 2002). This is evident from the hundreds of 38 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 drought indices used in the literature. The three year mean rainfall and runoff and ten year mean rainfall and runoff are used here as objective measures of dry conditions because they can be easily understood. 3.3.1 Calculation of average recurrence interval Figure 3 2 provides a graphical explanation of the terms used here. This is important because different studies use slightly different definitions of terms. In this project: · Up crossing is defined as a crossing of the threshold from below. · Down crossing is defined as a crossing of the threshold from above. · Event duration is defined as the time between a down crossing and the subsequent up crossing. · Inter arrival time is defined as the time between an up crossing and the subsequent down crossing. · Recurrence interval is defined as the time between successive down crossings. Inter arrival time Recurrence interval Event duration Dow n crossing Up crossing Figure 3 2. Definition of terms for estimation of average recurrence intervals To estimate the ARI, based on an 1895 to 2006 annual rainfall or runoff series, the lag one autoregressive model of Frost et al. ( 2007) is first used to generate stochastic annual rainfall and runoff. This model also allows for non Gaussian distributions using Box Cox transformation and considers parameter uncertainty using Bayesian methods with Markov Chain Monte Carlo parameter estimation. The runoff modelling is more problematic because of the high skewness and apparent multimodality for some regions. For this reason, the prior distribution of the Box Cox lambda parameter is bounded between – 2 and 2 for the rainfall modelling, and between 0 and 2 for the runoff modelling. Verification of the stochastic simulations are carried out by comparing a series of standard statistics ( mean, standard deviation, coefficient of skewness, and lag one to lag 15 autocorrelation coefficients) and distribution plots of annual rainfall and runoff and ten year rainfall and runoff sums. The verification indicates that most statistics from most of the historical series lie within the 90 percent confidence limits of 50,000 112 year replicates from the model, and the mean, standard deviation, skew and lag one autocorrelation coefficient of the historical data from most sites/ regions are similar to the median of the replicates. For each station/ region, the model is used to generate 100 replicates of 100,000 years of annual rainfall or runoff. The ARI for any specified n year rainfall or runoff threshold can be calculated directly from a 100,000 years annual replicate as the mean of the recurrence intervals. As 100 stochastic replicates are used, there are 100 estimates of the ARI for any specified n year rainfall or runoff threshold. The 100 replicates – each with a different parameter chosen randomly from the posterior distribution – are used to take into account sampling variability and parameter uncertainty. As the distribution of the ARI estimates can be highly skewed, particularly for the higher ARIs, the median ARI from the 100 estimates is presented as the ARI for n year rainfall and runoff thresholds in Section 1.4 and Chapter 2. © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 39 3.3.2 Interpretation of average recurrence interval The ARI for a specific n year rainfall or runoff threshold is defined here as the average number of years between successive down crossings of the threshold ( Fernandez and Salas, 1999). The ARI defined here is somewhat different to the standard flood return period found in many textbooks. This is because unlike most flood frequency analysis, consecutive n year rainfall or runoff events are not independent. For example, the ten year mean rainfalls for a given year and the previous year are calculated using nine years of the same annual rainfall data. Furthermore, serial correlation of annual rainfall and runoff is explicitly included in the model, as described in Section 3.3.1, which also increases the recurrence interval of any rainfall or runoff threshold ( Yevjevich, 1972). The traditional method of calculating ARIs ( i. e. the exceedance probability method) will correspond to the recurrence interval as defined in Section 3.3.1 for independent events ( Stedinger et al., 1993), but will greatly underestimate the ARI for highly correlated time series. It should also be noted that the past three year and past ten year rainfall and runoff ( as presented in Section 1.4 and in the last row of the tables in Chapter 2) may be part of a more severe dry sequence. For example, the ARI for 1995 to 2004 rainfall may be higher than the ARI for the 1997 to 2006 rainfall presented in Section 1.4 and Chapter 2. As such, where n year rainfall or runoff has been increasing over the past couple of years, the ARIs estimated for 2004 to 2006 rainfall and runoff and 1997 to 2006 rainfall and runoff ( as presented in Section 1.4 and in the last row of the tables in Chapter 2) may be lower than the maximum ARI for the recent dry sequence. In contrast, the ARIs for the lowest three independent three year and ten year rainfall and runoff means in the tables in Chapter 2 do not have this problem because they are independent non overlapping lowest, second lowest and third lowest n year rainfall and runoff means in the 1895 to 2006 rainfall and runoff series. ARIs for values of recent rainfall and runoff above the long term mean as well as ARIs less than 20 years are not reported in Section 1.4 and Chapter 2. For values above the long term mean the inter arrival time decreases as the threshold increases, but the event duration increases as the threshold increases. Therefore for the method defined here, the ARI will increase as recent rainfall or runoff increases above the long term mean. Recent rainfall or runoff above the long term mean can be considered as a rare event, but ARIs in this report are specifically for dry sequences. Also, values of the recent rainfall or runoff lower but close to the long term mean can be considered frequent events. The purpose of reporting ARIs in Section 1.4 and Chapter 2 is to estimate the recurrence interval of uncommon low rainfall and runoff events, so values of the ARI below 20 years are also not reported in those sections. 40 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 4 References Chiew FHS and Siriwardena L ( 2005) TREND user guide. CRC for Catchment Hydrology, Clayton, Vic., http:// www. toolkit. net. au/ trend. Chiew FHS ( 2006) Estimation of rainfall elasticity of streamflow in Australia. Hydrological Sciences Journal 51, 613– 625. Chiew FHS, Vaze J, Viney NR, Jordan PW, Perraud J M, Zhang L, Teng J, Young WJ, Peña Arancibia J, Morden RA, Freebairn A, Austin JM, Hill PI, Wiesenfeld CR and Murphy R. ( 2008) Rainfall runoff modelling across the Murray Darling Basin. A report to the Australian government from the CSIRO Murray Darling Basin Sustainable Yields Project. CSIRO, Australia. 71 pp. CSIRO and Bureau of Meteorology ( 2007) Climate change in Australia. Technical report, http:// www. climatechangeinaustralia. gov. au. Fan J and Yao Q ( 2005) Nonlinear time series: Nonparametric and parametric methods. Springer, New York. Fernandez B and Salas JD ( 1999) Return period and risk of hydrologic events, I. Mathematical formulation, Journal of Hydrologic Engineering 4, 297– 307. Frost AJ, Thyer MA, Srikanthan R and Kuczera G ( 2007) A general Bayesian framework for calibrating and evaluating stochastic models of annual multi site hydrological data. Journal of Hydrology 340, 129– 148, doi: 10.1016/ j. jhydrol. 2007.03.023. Heim Jr RR ( 2002) A review of the twentieth century drought indices used in the United States. Bulletin of the American Meteorological Society 83, 1146– 1165. IPCC ( 2007) Climate Change 2007: The Physical Science Basis – Summary for Policymakers. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, http:// ipcc wg1. ucar. edu/ wg1/ wg1 report. html. Jeffrey SJ, Carter JO, Moodie KB and Beswick AR ( 2001) Using spatial interpolation to construct a comprehensive archive of Australian climate data. Environmental Modelling & Software 16, 309– 330. Keyantash J and Dracup JA ( 2002) The quantification of drought: an evaluation of drought indices. Bulletin of the American Meteorological Society 83, 1167– 1180. Kundzewicz ZW and Robson AJ ( 2000) Detecting trend and other changes in hydrological data. WCDMP, no. 45, WMO TD, no. 1013, World Meteorological Organization, Geneva, Switzerland. Kundzewicz ZW and Robson AJ ( 2004) Change detection in hydrological records – A review of the methodology. Hydrological Sciences Journal 49, 7– 19. Murphy BF and Timbal B ( 2007) A review of recent climate variability and climate change in southeastern Australia. International Journal of Climatology, published online, doi: 10.1002/ joc. 1627 Peel MC, McMahon TA, Finlayson, BL ( 2004) Continental differences in the variability of annual runoff – Update and reassessment. Journal of Hydrology 295, 185– 197, doi: 10.1016/ j. jhydrol. 2004.03.004 Stedinger JR, Vogel RM and Foufoula Georgiou E ( 1993) Frequency analysis of extreme events. In Handbook of Hydrology, edited by DR Maidment, chapter 18, McGraw Hill, New York. Yevjevich VM ( 1972) Stochastic processes in hydrology. Water Resources Publications, Fort Collins, Colorado.
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Title  Characterisation of recent rainfall and runoff in the MurrayDarling Basin a report to the Australian Government from the CSIRO MurrayDarling Basin Sustainable Yields Project 
Subject  Rain and rainfallAustraliaMurray River Watershed (N.S.W.S. Aust.)Mathematical models.; Rain and rainfallAustraliaUpper Murray Region (N.S.W. and Vic.)Mathematical models.; Rain and rainfallAustraliaDarling River Watershed (Qld. and N.S.W.); Rain and rainfallAustraliaDarling River Valley (Qld. and N.S.W.); RunoffAustraliaMurray River Watershed (N.S.W.S. Aust.); RunoffAustraliaUpper Murray Region (N.S.W. and Vic.); RunoffAustraliaDarling River Watershed (Qld. and N.S.W.); RunoffAustraliaDarling River Valley (Qld. and N.S.W.); G893 P828 Web Resource 
Description  "June 2008."; Includes bibliographical references (p. 40). 
Creator  Potter, N. J. 
Publisher  CSIRO 
Contributors  Srikanthan, R. (Ratnasingham); CSIRO MurrayDarling Basin Sustainable Yields Project.; Water for a Healthy Country Flagship 
Type  Text 
Identifier  http://www.csiro.au/files/files/pmax.pdf 
Language  eng 
Relation  http://worldcat.org/oclc/648772422/viewonline 
DateIssued  2008 
FormatExtent  [48] p. : digital PDF file, col. ill., col. map, charts, tables ; 3.52 MB. 
RelationRequires  Mode of access: World Wide Web 
RelationIs Part Of  Water for a healthy country, 
Transcript  N. J. Potter, F. H. S. Chiew, A. J. Frost, R. Srikanthan, T. A. McMahon, M. C. Peel and J. M. Austin June 2008 Characterisation of Recent Rainfall and Runoff in the Murray Darling Basin A report to the Australian Government from the CSIRO Murray Darling Basin Sustainable Yields Project Murray Darling Basin Sustainable Yields Project acknowledgments The Murray Darling Basin Sustainable Yields project is being undertaken by CSIRO under the Australian Government's Raising National Water Standards Program, administered by the National Water Commission. Important aspects of the work were undertaken by Sinclair Knight Merz; Resource & Environmental Management Pty Ltd; Department of Water and Energy ( New South Wales); Department of Natural Resources and Water ( Queensland); Murray Darling Basin Commission; Department of Water, Land and Biodiversity Conservation ( South Australia); Bureau of Rural Sciences; Salient Solutions Australia Pty Ltd; eWater Cooperative Research Centre; University of Melbourne; Webb, McKeown and Associates Pty Ltd; and several individual sub contractors. Murray Darling Basin Sustainable Yields Project disclaimers Derived from or contains data and/ or software provided by the Organisations. The Organisations give no warranty in relation to the data and/ or software they provided ( including accuracy, reliability, completeness, currency or suitability) and accept no liability ( including without limitation, liability in negligence) for any loss, damage or costs ( including consequential damage) relating to any use or reliance on that data or software including any material derived from that data and software. Data must not be used for direct marketing or be used in breach of the privacy laws. Organisations include: Department of Water, Land and Biodiversity Conservation ( South Australia), Department of Sustainability and Environment ( Victoria), Department of Water and Energy ( New South Wales), Department of Natural Resources and Water ( Queensland), Murray Darling Basin Commission. CSIRO advises that the information contained in this publication comprises general statements based on scientific research. The reader is advised and needs to be aware that such information may be incomplete or unable to be used in any specific situation. No reliance or actions must therefore be made on that information without seeking prior expert professional, scientific and technical advice. To the extent permitted by law, CSIRO ( including its employees and consultants) excludes all liability to any person for any consequences, including but not limited to all losses, damages, costs, expenses and any other compensation, arising directly or indirectly from using this publication ( in part or in whole) and any information or material contained in it. Data is assumed to be correct as received from the Organisations. Acknowledgements The authors would like to thank Rodger Grayson, members of the BRS Climate Impact Sciences Program, and Dugald Black and Mark Littleboy of the NSW Department of Water and Energy for providing external review of this report. Citation Potter NJ, Chiew FHS, Frost AJ, Srikanthan R, McMahon TA, Peel MC and Austin JM ( 2008) Characterisation of recent rainfall and runoff in the Murray Darling Basin. A report to the Australian Government from the CSIRO Murray Darling Basin Sustainable Yields Project. CSIRO, Australia. 40pp. Publication Details Published by CSIRO © 2008 all rights reserved. This work is copyright. Apart from any use as permitted under the Copyright Act 1968, no part may be reproduced by any process without prior written permission from CSIRO. ISSN 1835 095X © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin Preface This is a report to the Australian Government from CSIRO. It is an output of the Murray Darling Basin Sustainable Yields Project which assessed current and potential future water availability in 18 regions across the Murray Darling Basin ( MDB) considering climate change and other risks to water resources. The project was commissioned following the Murray Darling Basin Water Summit convened by the Prime Minister of Australia in November 2006 to report progressively during the latter half of 2007. The reports for each of the 18 regions and for the entire MDB are supported by a series of technical reports detailing the modelling and assessment methods used in the project. This report is one of the supporting technical reports of the project. Project reports can be accessed at http:// www. csiro. au/ mdbsy. Project findings are expected to inform the establishment of a new sustainable diversion limit for surface and groundwater in the MDB – one of the responsibilities of a new Murray Darling Basin Authority in formulating a new Murray Darling Basin Plan, as required under the Commonwealth Water Act 2007. These reforms are a component of the Australian Government’s new national water plan ‘ Water for our Future’. Amongst other objectives, the national water plan seeks to ( i) address over allocation in the MDB, helping to put it back on a sustainable track, significantly improving the health of rivers and wetlands of the MDB and bringing substantial benefits to irrigators and the community; and ( ii) facilitate the modernisation of Australian irrigation, helping to put it on a more sustainable footing against the background of declining water resources. Summary Chapter 1 presents the MDB wide results from the analyses of the 1895 to 2006 annual rainfall series from 225 rainfall stations across the MDB. Chapter 2 presents the 1895 to 2006 annual rainfall and modelled runoff series and the assessment of recent rainfall and runoff characteristics for each of the 18 regions defined for the CSIRO Murray Darling Basin Sustainable Yields Project. Chapter 3 describes the methods used for the analyses. The analyses show high inter annual and inter decadal variability in rainfall and runoff, with long periods that are considerably wetter or drier than others. Most regions ( except the southernmost parts of the MDB) show a step change in rainfall, with a marked increase after the mid 1940s. Several dry periods are evident in the 1890s, around 1940, the mid 1960s, the early 1980s, and the last five to ten years over many parts of the MDB. The 2004 to 2006 rainfall and runoff are lower than the long term means almost everywhere in the MDB. Averaged over the entire MDB, the 2004 to 2006 mean annual rainfall ( 384 mm) is 16 percent lower than the 1895 to 2006 long term mean ( 457 mm). Averaged over the entire MDB, the 2004 to 2006 mean annual runoff ( 16.7 mm) is 39 percent lower than the 1895 to 2006 long term mean ( 27.3 mm). However, because of the inter annual variability in rainfall and runoff and the very short three year period used for comparative analysis, this difference is only statistically significant in a few small, non contiguous areas of the MDB. The 1997 to 2006 rainfall and runoff are lower than the long term means in the southern half and in the north east corner of the MDB, and are similar to the long term means in the northern half of the MDB. Averaged over the entire MDB, the 1997 to 2006 mean annual rainfall ( 440 mm) is 4 percent lower than the 1895 to 2006 long term mean ( 457 mm). Averaged over the entire MDB, the 1997 to 2006 mean annual runoff ( 21.7 mm) is 21 percent lower than the 1895 to 2006 long term mean ( 27.3 mm). However, the 1997 to 2006 rainfall and runoff are not statistically different from the 1895 to 2006 long term means when averaged over the entire MDB. Statistically significant differences are, however, observed in the southern MDB. In particular, the 1997 to 2006 rainfall in this area is lower than the long term mean, with average recurrence intervals between 20 and 100 years, and greater than 100 years in the southernmost parts. Likewise, the 1997 to 2006 runoff in the southern MDB is much lower than the long term mean, and lower than the runoff in similarly dry ten year periods in the past. This difference is also statistically significant. In the southernmost parts of the MDB, the low runoff in 1997 to 2006 is unprecedented in the historical record and has average recurrence intervals of more than 300 years. Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 The main reason for the considerably lower runoff in 1997 to 2006 compared to the runoff in similar dry periods in the past is probably the reduced rainfall in autumn and early winter. Most of the runoff in the southern MDB occurs in winter and early spring. As a result of low autumn rainfall, the soils are less saturated in winter, and this together with the lower winter rainfall results in low winter runoff when most of the runoff occurs. It should be noted that the analyses here are carried out using the 1895 to 2006 annual observed rainfall and modelled runoff time series. Some exploration of monthly patterns is included to help interpret annual changes. The purpose of the analyses is to characterise recent rainfall based solely on the historical rainfall series, and not to explore processes that may cause the observed variability. These are addressed elsewhere in other projects. It is possible that the dry conditions observed in recent years may occur more frequently in the future given the future projections for drier conditions in southeastern Australia ( IPCC, 2007; CSIRO and BoM, 2007). © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin Table of Contents 1 Basin wide assessment............................................................................................................ 1 1.1 Rainfall stations....................................................................................................................... .................................... 1 1.2 Recent rainfall ............................................................................................................................... .............................. 2 1.3 Trends and step changes in rainfall .............................................................................................................................. 4 1.4 Average recurrence interval of recent rainfall................................................................................................................ 6 2 Regional assessment ............................................................................................................... 8 2.1 Entire basin summary........................................................................................................................ .......................... 8 2.2 Recent rainfall and runoff characteristics in the southern Murray Darling Basin compared to similar dry periods ........ 14 2.3 Region by region summary ............................................................................................................................... ........ 17 2.3.1 Paroo ............................................................................................................................... ........................... 18 2.3.2 Warrego ............................................................................................................................... ....................... 19 2.3.3 Condamine Balonne........................................................................................................................ ............ 20 2.3.4 Moonie ............................................................................................................................... ......................... 21 2.3.5 Border Rivers ............................................................................................................................... ............... 22 2.3.6 Gwydir......................................................................................................................... ................................ 23 2.3.7 Namoi ............................................................................................................................... .......................... 24 2.3.8 Macquarie Castlereagh ............................................................................................................................... 25 2.3.9 Barwon Darling ............................................................................................................................... ............ 26 2.3.10 Lachlan ............................................................................................................................... ........................ 27 2.3.11 Murrumbidgee................................................................................................................... .......................... 28 2.3.12 Murray......................................................................................................................... ................................ 29 2.3.13 Ovens ............................................................................................................................... .......................... 30 2.3.14 Goulburn Broken......................................................................................................................... ................ 31 2.3.15 Campaspe....................................................................................................................... ............................ 32 2.3.16 Loddon Avoca.......................................................................................................................... ................... 33 2.3.17 Wimmera........................................................................................................................ ............................. 34 2.3.18 Eastern Mount Lofty Ranges ........................................................................................................................ 35 3 Methodology .......................................................................................................................... 36 3.1 Time series smoothing ............................................................................................................................... ............... 36 3.2 Statistical tests for trend and step change .................................................................................................................. 37 3.3 Estimation of average recurrence interval................................................................................................................... 37 3.3.1 Calculation of average recurrence interval.................................................................................................... 38 3.3.2 Interpretation of average recurrence interval ................................................................................................ 39 4 References .............................................................................................................................. 40 Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 Tables Table 2 1. Mean annual rainfall and runoff, percentage difference between recent and long term mean annual rainfall and runoff, and the average recurrence interval for the period 2004– 2006 for the 18 regions in the Murray Darling Basin................................. 9 Table 2 2. Mean annual rainfall and runoff, percentage difference between recent and long term mean annual rainfall and runoff, and the average recurrence interval for the period 1997– 2006 for the 18 regions in the Murray Darling Basin................................ 9 Figures Figure 1 1. Locations of rainfall stations used for the analyses ........................................................................................................ 1 Figure 1 2. Percentage difference between mean annual rainfall in 1895– 2006 and ( a) in 2004– 2006 and ( b) in 1997– 2006.......... 3 Figure 1 3. Results from statistical tests ( using 1895– 2006 rainfall data) for ( a) trend and ( b) step change in mean ........................ 5 Figure 1 4. Average recurrence interval of ( a) 2004– 2006 rainfall and ( b) 1997– 2006 rainfall .......................................................... 7 Figure 2 1. ( a) Linear trend and low frequency variability of rainfall, with horizontal scale from 1895 to 2006 and same vertical scale for all regions, and ( b) low frequency variability for all regions, with same vertical scale for all regions ................................. 10 Figure 2 2. ( a) Linear trend and low frequency variability of runoff, with horizontal scale from 1895 to 2006 and same vertical scale for all regions, and ( b) low frequency variability for all regions, with same vertical scale for all regions. Note that the vertical scale is different to Figure 2 1 ............................................................................................................................... .................................... 11 Figure 2 3. Percentage difference between mean annual rainfall in 1895– 2006 and ( a) in 2004– 2006 and ( b) in 1997– 2006; and percentage difference between mean annual runoff in 1895– 2006 and ( c) in 2004– 2006 and ( d) in 1997– 2006............................ 12 Figure 2 4. Average recurrence intervals for ( a) 2004– 2006 mean annual rainfall, ( b) 1997– 2006 mean annual rainfall, ( c) 2004– 2006 mean annual runoff and ( d) 1997– 2006 mean annual runoff ................................................................................................. 13 Figure 2 5. Elasticity of runoff and ratio of percentage difference in runoff to percentage difference in rainfall for three ten year dry sequences ............................................................................................................................... ..................................................... 14 Figure 2 6. Annual observed streamflow time series and low frequency variability from six catchments in the southern Murray Darling Basin ............................................................................................................................... ................................................. 15 Figure 2 7. ( a) Monthly rainfall and ( b) monthly runoff for the southern Murray Darling Basin ( Murrumbidgee, Murray, Ovens, Goulburn Broken, Campaspe, Loddon Avoca, Wimmera and Eastern Mount Lofty Ranges) averaged across selected time periods ............................................................................................................................... ...................................................................... 16 Figure 3 1. Example annual rainfall time series with Gaussian kernel ( red line) centred at 1950 and the resulting smoothed time series ( blue line) ............................................................................................................................... ............................................ 36 Figure 3 2. Definition of terms for estimation of average recurrence intervals ................................................................................ 38 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 1 1 Basin wide assessment This chapter presents the results from the analyses of 1895 to 2006 annual rainfall series from 225 rainfall stations across the Murray Darling Basin ( MDB). Section 1.1 describes the annual rainfall data used for the analyses. Section 1.2 compares the mean annual rainfall over recent years to the long term mean. Section 1.3 presents results from statistical tests for trend and step change in mean. Section 1.4 presents the average recurrence interval ( ARI) of the recent dry conditions across the MDB. 1.1 Rainfall stations Figure 1 1 shows the locations of the 225 rainfall stations used in the analyses presented in Chapter 1. The rainfall stations generally provide a good coverage across the MDB, although there is less coverage in the drier western region. The analyses use 112 years of annual rainfall series from 1895 to 2006. The data comes from the Australian Bureau of Meteorology. All stations are selected to have less than 5 percent missing data over the period 1900 to 2006. This resulted in all stations having less than 10 percent missing data over the period 1895 to 2006, and the majority ( 209) having less than 5 percent missing data over the period 1895 to 2006. The data gaps are infilled with the patched point data from SILO ( see http:// www. nrm. qld. gov. au/ silo and Jeffrey et al., 2001). Figure 1 1. Locations of rainfall stations used for the analyses 2 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 1.2 Recent rainfall Figure 1 2 ( a) shows the percentage difference between the mean annual rainfall in the past three years ( 2004 to 2006) and in 1895 to 2006. Figure 1 2 ( b) shows the percentage difference between the mean annual rainfall in the past ten years ( 1997 to 2006) and in 1895 to 2006. In areas within the black contour line, the mean annual rainfall over the recent period is statistically significantly lower ( at a = 0.1) than the 1895 to 2006 mean. There are no stations where the recent mean is statistically significantly higher than the long term mean. The statistical significance is determined using the Student’s t test ( see Section 3.2) on the difference between the means of the two periods, ( a) 1895 to 2003 and 2004 to 2006, and ( b) 1895 to 1996 and 1997 to 2006. The statistically significant stations identified by the parametric Student’s t test are almost identical to those identified by the non parametric Rank Sum test ( see Section 3.2). Although the analyses are carried out for each of the 225 rainfall stations, Figure 1 2 shows contours derived from interpolation of these values because it is easier to visualise the spatial pattern across the MDB. An iterative finite difference interpolation technique is used ( TOPOGRID command in ArcInfo with the drainage enforcement option turned off). The resulting contours are essentially identical to those produced from other interpolation methods. Figure 1 2 ( a) indicates that in most parts of the MDB the 2004 to 2006 rainfall is lower than the long term mean. Averaged over the entire MDB the 2004 to 2006 mean annual rainfall ( 384 mm) is 16 percent lower than the 1895 to 2006 mean ( 457 mm). However, there are other three year periods in the historical data that have similar rainfall ( see Section 1.4 and Chapter 2), and the lower rainfall in 2004 to 2006 compared to the long term mean is not statistically significant, except at a few stations in several non contiguous regions across the MDB. The rainfall over the longer 1997 to 2006 period over much of the higher runoff producing regions in the southern MDB is lower than the long term mean by up to 20 percent. In the southernmost MDB, the lower rainfall is statistically different from the long term mean. The mean annual rainfall in the northern half of the MDB in 1997 to 2006 is similar or slightly higher compared to the long term mean. Averaged over the entire MDB the 1997 to 2006 mean annual rainfall ( 440 mm) is 4 percent lower than the 1895 to 2006 mean ( 457 mm). © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 3 Figure 1 2. Percentage difference between mean annual rainfall in 1895– 2006 and ( a) in 2004– 2006 and ( b) in 1997– 2006 4 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 1.3 Trends and step changes in rainfall Figure 1 3 presents results from statistical tests for trend and step change in mean in the 1895 to 2006 annual rainfall series from the 225 stations in the MDB. Figure 1 3 ( a) shows results from the three statistical tests for trend ( Mann Kendall, Spearman’s Rho and Linear Regression) and Figure 1 3 ( b) shows results from the three statistical tests for step change in mean ( Distribution Free CUSUM, Cumulative Deviation and Worsley Likelihood Ratio). The step change tests also identify the year of step change. All six tests are widely used in the literature and are briefly described in Section 3.2. Figure 1 3 ( a) shows that the results from the three tests for trend are almost identical. Figure 1 3 ( b) also shows that the results from the three step change tests are similar, particularly in the eastern half of the MDB. Except for the southernmost and northernmost parts of the MDB, annual rainfall in 1895 to 2006 over much of the MDB shows an increasing trend, and about half of these trends are statistically significant ( at α = 0.1). About half of the rainfall stations show a statistically significant positive step change in mean, about three quarters of them in the mid 1940s. This suggests that the biggest overall signal in 1895 to 2006 rainfall is the higher rainfall after the mid 1940s compared to before the mid 1940s, particularly in the eastern half of the MDB. © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 5 Figure 1 3. Results from statistical tests ( using 1895– 2006 rainfall data) for ( a) trend and ( b) step change in mean 6 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 1.4 Average recurrence interval of recent rainfall Figure 1 4 ( a) and ( b) present the average recurrence interval ( ARI) of the 2004 to 2006 rainfall ( past three years) and 1997 to 2006 rainfall ( past ten years), respectively, based on the 1895 to 2006 rainfall series. The ARI for a specific n year rainfall threshold is defined here as the average number of years between successive n year rainfall falling below the threshold. For example, an ARI of 50 years for 1997 to 2006 rainfall means that once a ten year mean rainfall is below the 1997 to 2006 mean, it will take, on average, another 50 years before another ‘ independent’ ten year mean rainfall falls below the 1997 to 2006 mean. There is no generally accepted method for defining the ARI of an n year low rainfall sequence. The ARI presented here must therefore be used cautiously and with full knowledge of the method used to estimate it ( see Section 3.3). There is also no generally accepted method of quantifying drought severity ( magnitude and duration) that is equally relevant for different applications. The three year mean rainfall and ten year mean rainfall are used here as objective measures of dry conditions because they can be easily understood. It should also be noted that the 2004 to 2006 and 1997 to 2006 rainfalls may be part of a more severe dry sequence with higher ARIs than that presented here ( see Section 3.3.2). Although the analyses are carried out for each of the 225 rainfall stations, Figure 1 4 shows contours derived from interpolation of these values because it is easier to visualise the spatial pattern across the MDB. An iterative finite difference interpolation technique ( TOPOGRID command in ArcInfo with the drainage enforcement option turned off) is used. The resulting contours are essentially identical to those produced from other interpolation methods. Although the recent rainfall in the southern half of the MDB is lower than the long term mean ( Section 1.2), there are similar dry periods in the historical data. Figure 1 4 ( a) shows that the 2004 to 2006 rainfall in parts of the southern and northeastern regions of the MDB have ARIs of 20 to 50 years. Figure 1 4 ( b) shows that the low rainfall over the longer 1997 to 2006 period is more extreme, with ARIs of more than 50 years in the northeastern and southern parts of the MDB, and more than 100 years in the southernmost parts. The ARIs elsewhere are generally less than 20 years, suggesting that there are many other three year and ten year rainfalls similar to or lower than the recent rainfall. © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 7 Figure 1 4. Average recurrence interval of ( a) 2004– 2006 rainfall and ( b) 1997– 2006 rainfall 8 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2 Regional assessment This chapter presents the 1895 to 2006 annual rainfall and runoff series, and the assessment of recent rainfall and runoff characteristics, for each of the 18 regions defined for the Murray Darling Basin Sustainable Yields Project. Section 2.1 summarises MDB wide rainfall and runoff and characterises recent rainfall and runoff. Section 2.2 discusses the recent rainfall and runoff characteristics in the southern parts of the MDB compared to previous dry periods. Section 2.3 summarises the rainfall and runoff characteristics in one page for each of the 18 MDB regions. The source of the rainfall data is the SILO 0.05 o x 0.05 o (~ 5 km x 5 km) gridded daily rainfall data ( see http:// www. nrm. qld. gov. au/ silo and Jeffrey et al., 2001). The runoff data comes from the rainfall runoff modelling over 0.05 o x 0.05 o grid cells across the MDB carried out for the CSIRO Murray Darling Sustainable Yields Project. The modelled daily runoff series for 1895 to 2006 is for ‘ current’ land use conditions. The modelled runoff series therefore does not consider development over time, but reflects the historical climate signal in runoff for ‘ current’ land use conditions ( see Chiew et al., 2008). Modelled runoff data is used for the analyses because there are relatively few long streamflow records, observed streamflow data is affected by changes in land use, and gauged unimpaired streamflow data is available for less than 1 percent of the MDB. The annual rainfall and runoff series for each region is calculated as the average of the rainfall and runoff from all 0.05 o x 0.05 o grid cells that are in the region. Entire basin summary Table 2 1 summarises recent rainfall and runoff for 2004 to 2006 compared to the long term means for the 18 MDB regions. Table 2 2 provides the same comparative summary for the period 1997 to 2006. Figure 2 1 and Figure 2 2 show the linear trends and low frequency variability of rainfall and runoff, respectively, in the 18 MDB regions. Figure 2 1 indicates that over the period 1895 to 2006, annual rainfall over much of the MDB shows an increasing trend. The plots also show inter decadal oscillations in the rainfall series with long periods that are considerably wetter or drier than others. Most regions show a marked step increase in rainfall after the mid 1940s ( particularly in the east), while dry periods are observed over many parts of the MDB in the 1890s, around 1940, the mid 1960s, the early 1980s, and the last five to ten years. The trend and low frequency variability of runoff ( Figure 2 2) are similar to those for rainfall, but are more clearly seen in the high runoff regions in the south east because the standard deviation of annual runoff in these regions is larger relative to the northern regions of the MDB. Values for the interannual variability ( coefficient of variation) of rainfall and runoff are presented in each regional summary page in Section 2.3. The coefficient of variation for annual rainfall ranges from 0.21 to 0.43, and the coefficient of variation for annual runoff ranges from 0.5 to 1.3, with the drier regions generally having larger variability than the wetter regions. The interannual variability of runoff in the MDB is almost twice that of similar river basins elsewhere in the world ( Peel et al., 2004). Figure 2 3 presents the percentage difference between the 2004 to 2006 rainfall and runoff and the 1895 to 2006 longterm means, as well as the percentage difference between the 1997 to 2006 rainfall and runoff and the 1895 to 2006 long term means for the 18 MDB regions. Figure 2 4 presents the average recurrence intervals ( ARIs, see Sections 1.4 and 3.3) for 2004 to 2006 rainfall and runoff and 1997 to 2006 rainfall and runoff for the 18 MDB regions. The characteristics of the recent rainfall have been presented and discussed in Chapter 1. Like rainfall, runoff has reduced recently, but to a larger degree compared to previous dry periods, particularly in the southern MDB, as discussed in Section 2.2. © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 9 Table 2 1. Mean annual rainfall and runoff, percentage difference between recent and long term mean annual rainfall and runoff, and the average recurrence interval for the period 2004– 2006 for the 18 regions in the Murray Darling Basin 2004– 2006 rainfall 2004– 2006 runoff Region 1895– 2006 mean annual rainfall mean percent change from 1895– 2006 ARI* 1895– 2006 mean annual runoff mean percent change from 1895– 2006 ARI* Paroo 311 209  33% 20 17 6.2  64% < 20 Warrego 422 338  20% < 20 7.2 3.1  57% < 20 Condamine Balonne 514 436  15% < 20 19 11  44% < 20 Moonie 528 490  7% < 20 17 15  16% < 20 Border Rivers 641 611  5% < 20 32 27  18% < 20 Gwydir 644 692 8% < 20 41 47 16% < 20 Namoi 633 650 3% < 20 24 22  11% < 20 Macquarie Castlereagh 544 453  17% < 20 35 19  46% < 20 Barwon Darling 328 270  18% < 20 6.0 3.7  39% < 20 Lachlan 461 358  22% 20 23 13  44% < 20 Murrumbidgee 530 409  23% 29 54 31  44% 27 Murray 340 281  17% < 20 24 16  35% < 20 Ovens 1004 794  21% 26 231 137  41% < 20 Goulburn Broken 764 601  21% 32 149 81  46% 35 Campaspe 594 482  19% < 20 69 29  59% 34 Loddon Avoca 430 353  18% < 20 21 8.8  57% 24 Wimmera 403 313  22% 28 16 6.7  59% 31 Eastern Mount Lofty Ranges 463 427  8% < 20 30 19  39% < 20 * Average recurrence interval, see Section 3.3. Table 2 2. Mean annual rainfall and runoff, percentage difference between recent and long term mean annual rainfall and runoff, and the average recurrence interval for the period 1997– 2006 for the 18 regions in the Murray Darling Basin 1997– 2006 rainfall 1997– 2006 runoff Region 1895– 2006 mean annual rainfall mean percent change from 1895– 2006 ARI* 1895– 2006 mean annual runoff mean percent change from 1895– 2006 ARI* Paroo 311 310 0% < 20 17 16  10% < 20 Warrego 422 427 1% < 20 7.2 6.6  8% < 20 Condamine Balonne 514 503  2% < 20 19 15  23% 23 Moonie 528 541 2% < 20 17 17  3% < 20 Border Rivers 641 641 0% < 20 32 32  1% < 20 Gwydir 644 688 7% 23 41 48 18% 23 Namoi 633 663 5% < 20 24 29 17% 22 Macquarie Castlereagh 544 547 1% < 20 35 33  5% < 20 Barwon Darling 328 339 3% < 20 6.0 6.5 8% < 20 Lachlan 461 425  8% < 20 23 18  24% 23 Murrumbidgee 530 471  11% 39 54 37  31% 106 Murray 340 313  8% 21 24 19  21% 36 Ovens 1004 895  11% 41 231 172  26% 36 Goulburn Broken 764 649  15% 156 149 89  41% 850 Campaspe 594 517  13% 47 69 34  50% 594 Loddon Avoca 430 381  11% 36 21 10  52% 420 Wimmera 403 350  13% 54 16 8.1  51% 385 Eastern Mount Lofty Ranges 463 429  7% 26 30 19  36% 105 * Average recurrence interval, see Section 3.3. 10 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 1895 1915 1935 1955 1975 1995 ( b) Paroo Warrego Condamine Balonne Moonie Border Rivers Gwydir Namoi Macquarie Castlereagh Barwon Darling Lachlan Murrumbidgee Murray Ovens Goulburn Broken Campaspe Loddon Avoca Wimmera Eastern Mount Lofty Ranges Figure 2 1. ( a) Linear trend and low frequency variability of rainfall, with horizontal scale from 1895 to 2006 and same vertical scale for all regions, and ( b) low frequency variability for all regions, with same vertical scale for all regions © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 11 1895 1915 1935 1955 1975 1995 Condamine Balonne Moonie Border Rivers Gwydir Namoi Ovens Goulburn Broken Campaspe Loddon Wimmera Eastern Mount Lofty Ranges Lachlan Murrumbidgee Murray Macquarie Castlereagh Barwon Darling Paroo Warrego ( b) Figure 2 2. ( a) Linear trend and low frequency variability of runoff, with horizontal scale from 1895 to 2006 and same vertical scale for all regions, and ( b) low frequency variability for all regions, with same vertical scale for all regions. Note that the vertical scale is different to Figure 2 1 12 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 Figure 2 3. Percentage difference between mean annual rainfall in 1895– 2006 and ( a) in 2004– 2006 and ( b) in 1997– 2006; and percentage difference between mean annual runoff in 1895– 2006 and ( c) in 2004– 2006 and ( d) in 1997– 2006 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 13 Figure 2 4. Average recurrence intervals for ( a) 2004– 2006 mean annual rainfall, ( b) 1997– 2006 mean annual rainfall, ( c) 2004– 2006 mean annual runoff and ( d) 1997– 2006 mean annual runoff 14 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.2 Recent rainfall and runoff characteristics in the southern Murray Darling Basin compared to similar dry periods The 2004 to 2006 and 1997 to 2006 rainfall and runoff across the southern MDB generally have ARIs greater than 20 years ( Table 2 1, and Figure 2 4). The 2004 to 2006 runoff ARIs in the southern MDB are generally similar to or slightly higher than the 2004 to 2006 rainfall ARIs. However, the 1997 to 2006 runoff ARIs in the southern MDB are much higher than the 1997 to 2006 rainfall ARIs, particularly in the Goulburn Broken, Campaspe, Loddon Avoca and Wimmera regions where the runoff ARIs are greater than 300 years. Although the 2004 to 2006 mean annual runoff is similar to or lower than the 1997 to 2006 mean annual runoff, persistent low runoff over the longer ten year period is more statistically significant and therefore has higher ARIs than the three year period. The eight southernmost regions in the MDB are the Murrumbidgee, Murray, Ovens, Goulburn Broken, Campaspe, Loddon Avoca, Wimmera and Eastern Mount Lofty Ranges. In these regions, almost all of the three year and ten year low rainfall means ( 37 out of 48) and low runoff means ( 32 out of 48) identified in Section 2.3 occur in the following three time periods: 1895 to 1904; 1936 to 1946; and 1997 to 2006. These time periods are also identified as dry periods in many of the other MDB regions. The remainder of this section compares the 1997 to 2006 rainfall and runoff with the 1895 to 1904 and 1936 to 1945 dry periods. 0 1 2 3 4 5 6 Paroo Warrego Condamine Balonne Moonie Border Rivers Gwydir Namoi Macquarie Castlereagh Barwon Darling Lachlan Murrumbidgee Murray Ovens Goulburn Broken Campa spe Loddon Avoca Wimmera Eastern Mt Lofty Rang es Ratio of percentage difference in runoff to percentage difference in rainfall 1895– 1904 1936– 1945 1997– 2006 Long term elasticity Figure 2 5. Elasticity of runoff and ratio of percentage difference in runoff to percentage difference in rainfall for three ten year dry sequences Figure 2 5 shows the long term rainfall elasticity of runoff for the 18 MDB regions, estimated from the 1895 to 2006 annual rainfall and runoff data using a nonparametric estimator ( Chiew, 2006). The rainfall elasticity of runoff is defined here as the average percentage change in mean annual runoff for a given percentage change in mean annual rainfall. This elasticity varies from about 2 to 3 across the MDB ( Figure 2 5), indicating that a 1 percent change in mean annual rainfall in the MDB will be amplified as a 2 to 3 percent change in mean annual runoff. Figure 2 5 also shows the percentage difference of recent and long term mean annual runoff divided by the percentage difference of recent and long term mean annual rainfall ( i. e. values in ‘ runoff, percent change from 1895– 2006’ column divided by values in the ‘ rainfall, percent change from 1895– 2006’ column in ). The ratios are only plotted if rainfall over a ten year period is more than 5 percent lower than the long term mean to avoid extremely large and meaningless ratios when the ten year rainfall is close to the long term mean. The ratios shown in Figure 2.5 for 1936 to 1945 are generally similar to the long term rainfall elasticities of runoff, but slightly higher in the north east and slightly lower in the southern MDB. The ratios for 1895 to 1904 are generally higher than the long term rainfall elasticities of runoff. For the southern MDB, the ratios for 1997 to 2006 are greater than the © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 15 ratios for 1895 to 1904, the ratios for 1936 to 1945, and the long term rainfall elasticities of runoff. This indicates that the runoff over the last ten years ( 1997 to 2006) is considerably lower than the runoff in similar low rainfall periods in the historical record. 0 50 100 150 200 250 300 1895 1915 1935 1955 1975 1995 401215 ( Upper Murray) 0 200 400 600 800 1000 1200 1400 1895 1915 1935 1955 1975 1995 403205 ( Ovens) 0 200 400 600 800 1000 1200 1895 1915 1935 1955 1975 1995 405205 ( Goulburn Broken) 0 50 100 150 200 250 1895 1915 1935 1955 1975 1995 405212 ( Goulburn Broken) 0 50 100 150 200 250 300 350 400 1895 1915 1935 1955 1975 1995 407217 ( Loddon) 0 20 40 60 80 100 120 140 160 180 1895 1915 1935 1955 1975 1995 415206 ( Wimmera) Figure 2 6. Annual observed streamflow time series and low frequency variability from six catchments in the southern Murray Darling Basin As mentioned on page 8, the analyses in this report are based on modelled ‘ natural’ runoff data. In order to check that the recent low runoff is not an artefact of the rainfall runoff modelling, annual streamflow series from six representative streamflow gauges in the southern MDB are shown in Figure 2 6. The streamflow gauges are chosen to have data starting before 1950 and to have less than 5 percent of the data missing during the period 1975 to 2006. The years with 16 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 missing data are not shown in the plots. The Gaussian smooth shown in the plots assumes mean annual streamflow values for the missing years. The recorded streamflow series from all these six catchments also show significantly lower streamflow in recent years. ( a) ( b) 0 10 20 30 40 50 60 J F M A M J J A S O N D mm / month 1895– 2006 1997– 2006 1936– 1945 1895– 1904 a) 0 1 2 3 4 5 6 7 8 J F M A M J J A S O N D mm / month 1997– 2006 1936– 1945 1895– 1904 1895– 2006 b) Figure 2 7. ( a) Monthly rainfall and ( b) monthly runoff for the southern Murray Darling Basin ( Murrumbidgee, Murray, Ovens, Goulburn Broken, Campaspe, Loddon Avoca, Wimmera and Eastern Mount Lofty Ranges) averaged across selected time periods Figure 2 7 shows the mean monthly rainfall and runoff averaged over the eight southern MDB regions ( Murrumbidgee, Murray, Ovens, Goulburn Broken, Campaspe, Loddon Avoca, Wimmera and Eastern Mount Lofty Ranges) for the entire 1895 to 2006 period and the three ten year dry periods. The plots indicate that most of the rainfall reduction in the 1997 to 2006 dry period is in the autumn and early winter. In contrast, in both the 1895 to 1904 and 1936 to 1945 periods, there is at least one month in autumn or winter that has a mean rainfall greater than the long term mean. Rainfall in the southern MDB is higher in the winter half of the year and most of the runoff in the southern MDB occurs in winter and early spring. As a result of low autumn rainfall, the soils are less saturated in winter, and this together with the lower winter rainfall results in low winter runoff when most of the runoff occurs. This is probably the main reason for the much lower runoff in the past ten years ( 1997 to 2006) compared to similar past dry periods. It is also likely that after a prolonged dry period, subsurface storage is low or has lost connection with the river system, and significant amounts of rainfall and diffused recharge are required to fill the storage or to re establish the connection with the river system before significant runoff can occur. Other possible reasons for the higher runoff reduction in the past ten years compared to similar past dry periods include: higher recent temperature , accentuating the impact of low rainfall; changes in the daily rainfall distribution ( however, the analyses here also indicate that extreme daily rainfall characteristics in 1997 to 2006 are similar to the long term characteristics); and changes in the sequencing of rainfall events. The mean annual runoff over the past ten years in the Goulburn Broken, Campaspe, Loddon Avoca and Wimmera regions is also similar to the projected decrease in mean annual runoff in the extreme dry 2030 climate change scenario ( see Chiew et al., 2008). However, because the analysis is based on a relatively short ten years of data, it is not sufficient evidence that the hydroclimate has shifted to a new regime. Nevertheless, if the hydroclimate has shifted to a new regime ( like in the extreme dry climate change scenario), the dry conditions observed over the past ten years will occur more frequently. Murphy and Timbal ( 2007) examined rainfall over south eastern Australia ( mostly the same area as the southern MDB defined here but with the inclusion of the coastal fringe around the southern MDB) and also observe lower than normal autumn rainfall over 1997 2006 compared with the 1936 1945 period. Furthermore they demonstrate that average maximum daily temperature has been higher and annual year to year variability of rainfall is smaller compared with the 1936 1945 period. They suggest that these three climatic conditions taken together have contributed to the recent very low inflows into the southern MDB. © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 17 2.3 Region by region summary The following analyses are presented for each region from page 18 onwards: · annual rainfall and runoff series for 1895 to 2006 and low frequency variability of rainfall and runoff. The low frequency variability ( smoothed time series) is calculated using the kernel smoothing method described in Section 3.1 · mean, standard deviation, coefficient of variation, coefficient of skewness and lag one autocorrelation coefficient of mean annual rainfall and runoff · a table showing the three lowest independent mean annual rainfall and runoff for three year non overlapping periods and their ARIs ( method described in Section 3.3), and the corresponding values for the past three years ( 2004 to 2006) · a table showing the three lowest independent mean annual rainfall and runoff for ten year non overlapping periods and their ARIs ( method described in Section 3.3), and the corresponding values for the past ten years ( 1997 to 2006) · maps of the spatial distribution of mean annual rainfall and mean annual runoff. The three lowest independent three year and ten year rainfall and runoff means are selected from the period 1895 to 2006. To ensure that the events are independent and do not come from the same dry sequence, an event cannot overlap a previously selected period. For example, if the rank one ten year rainfall mean occurs in 1957 to 1966, subsequent events cannot be selected from the previous ten year period ( 1948 to 1957) to the following ten year period ( 1966 to 1975) inclusive. 18 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.1 Paroo Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 311 mm Standard deviation of annual rainfall: 135 mm Coefficient of variation of annual rainfall: 0.43 Coefficient of skewness of annual rainfall: 0.81 Lag one serial correlation of annual rainfall: 0.087 Mean annual runoff: 17.4 mm Standard deviation of annual runoff: 20.3 mm Coefficient of variation of annual runoff: 1.17 Coefficient of skewness of annual runoff: 2.75 Lag one serial correlation of annual runoff: 0.114 Three year rainfall Rank Period Mean ARI 1 1927– 1929 151 209 2 1900– 1902 171 71 3 1944– 1946 175 62 Past three years 2004– 2006 209 20 Three year runoff Rank Period Mean ARI 1 1944– 1946 2.5 169 2 2001– 2003 2.8 119 3 1899– 1901 3.0 107 Past three years 2004– 2006 6.2 < 20 Ten year rainfall Rank Period Mean ARI 1 1957– 1966 243 53 2 1937– 1946 247 47 3 1896– 1905 252 38 Past ten years 1997– 2006 310 < 20 Ten year runoff Rank Period Mean ARI 1 1957– 1966 8.4 65 2 1896– 1905 8.9 54 3 1927– 1936 10.1 35 Past ten years 1997– 2006 15.6 < 20 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 19 2.3.2 Warrego Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 422 mm Standard deviation of annual rainfall: 148 mm Coefficient of variation of annual rainfall: 0.35 Coefficient of skewness of annual rainfall: 0.89 Lag one serial correlation of annual rainfall: 0.094 Mean annual runoff: 7.2 mm Standard deviation of annual runoff: 8.6 mm Coefficient of variation of annual runoff: 1.19 Coefficient of skewness of annual runoff: 3.07 Lag one serial correlation of annual runoff: 0.087 Three year rainfall Rank Period Mean ARI 1 1900– 1902 260 90 2 1944– 1946 264 79 3 1965– 1967 282 43 Past three years 2004– 2006 338 < 20 Three year runoff Rank Period Mean ARI 1 1944– 1946 1.5 101 2 1899– 1901 1.5 100 3 1965– 1967 2.2 31 Past three years 2004– 2006 3.1 < 20 Ten year rainfall Rank Period Mean ARI 1 1896– 1905 344 60 2 1937– 1946 347 55 3 1926– 1935 361 33 Past ten years 1997– 2006 427 < 20 Ten year runoff Rank Period Mean ARI 1 1896– 1905 3.4 109 2 1926– 1935 4.1 46 3 1937– 1946 4.2 40 Past ten years 1997– 2006 6.6 < 20 20 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.3 Condamine Balonne Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 80 100 120 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 514 mm Standard deviation of annual rainfall: 139 mm Coefficient of variation of annual rainfall: 0.27 Coefficient of skew of annual rainfall: 0.63 Lag one serial correlation of annual rainfall: 0.029 Mean annual runoff: 18.9 mm Standard deviation of annual runoff: 17.4 mm Coefficient of variation of annual runoff: 0.92 Coefficient of skewness of annual runoff: 2.73 Lag one serial correlation of annual runoff: 0.050 Three year rainfall Rank Period Mean ARI 1 1900– 1902 345 130 2 1944– 1946 348 118 3 1965– 1967 397 25 Past three years 2004– 2006 436 < 20 Three year runoff Rank Period Mean ARI 1 1900– 1902 5.3 126 2 1944– 1946 7.2 36 3 2001– 2003 7.3 35 Past three years 2004– 2006 10.6 < 20 Ten year rainfall Rank Period Mean ARI 1 1937– 1946 452 41 2 1896– 1905 453 39 3 1927– 1936 476 21 Past ten years 1997– 2006 503 < 20 Ten year runoff Rank Period Mean ARI 1 1896– 1905 10.0 134 2 1929– 1938 12.4 39 3 1960– 1969 12.9 33 Past ten years 1997– 2006 14.5 23 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 21 2.3.4 Moonie Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 80 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 528 mm Standard deviation of annual rainfall: 144 mm Coefficient of variation of annual rainfall: 0.27 Coefficient of skewness of annual rainfall: 0.38 Lag one serial correlation of annual rainfall: 0.023 Mean annual runoff: 17.4 mm Standard deviation of annual runoff: 15.3 mm Coefficient of variation of annual runoff: 0.88 Coefficient of skewness of annual runoff: 1.91 Lag one serial correlation of annual runoff: 0.045 Three year rainfall Rank Period Mean ARI 1 1900– 1902 356 82 2 1944– 1946 376 47 3 1965– 1967 379 44 Past three years 2004– 2006 490 < 20 Three year runoff Rank Period Mean ARI 1 1900– 1902 4.0 147 2 1944– 1946 6.5 28 3 1979– 1981 6.5 27 Past three years 2004– 2006 14.6 < 20 Ten year rainfall Rank Period Mean ARI 1 1935– 1944 433 131 2 1895– 1904 470 32 3 1964– 1973 489 21 Past ten years 1997– 2006 541 < 20 Ten year runoff Rank Period Mean ARI 1 1896– 1905 8.5 156 2 1927– 1936 9.8 73 3 1937– 1946 11.8 32 Past ten years 1997– 2006 16.8 < 20 22 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.5 Border Rivers Rainfall 0 200 400 600 800 1000 1200 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 641 mm Standard deviation of annual rainfall: 142 mm Coefficient of variation of annual rainfall: 0.22 Coefficient of skewness of annual rainfall: 0.17 Lag one serial correlation of annual rainfall:  0.018 Mean annual runoff: 32.4 mm Standard deviation of annual runoff: 23.1 mm Coefficient of variation of annual runoff: 0.71 Coefficient of skewness of annual runoff: 2.20 Lag one serial correlation of annual runoff: 0.015 Three year rainfall Rank Period Mean ARI 1 1918– 1920 480 60 2 1900– 1902 492 43 3 1939– 1941 504 32 Past three years 2004– 2006 611 < 20 Three year runoff Rank Period Mean ARI 1 1900– 1902 14.4 49 2 1938– 1940 15.7 33 3 1992– 1994 16.7 26 Past three years 2004– 2006 26.7 < 20 Ten year rainfall Rank Period Mean ARI 1 1935– 1944 541 169 2 1918– 1927 567 51 3 1895– 1904 606 < 20 Past ten years 1997– 2006 641 < 20 Ten year runoff Rank Period Mean ARI 1 1935– 1944 19.2 210 2 1922– 1931 23.1 43 3 1906– 1915 24.6 31 Past ten years 1997– 2006 32.2 < 20 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 23 2.3.6 Gwydir Rainfall 0 200 400 600 800 1000 1200 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 200 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 644 mm Standard deviation of annual rainfall: 153 mm Coefficient of variation of annual rainfall: 0.24 Coefficient of skewness of annual rainfall: 0.23 Lag one serial correlation of annual rainfall: 0.063 Mean annual runoff: 40.6 mm Standard deviation of annual runoff: 30.4 mm Coefficient of variation of annual runoff: 0.75 Coefficient of skewness of annual runoff: 1.86 Lag one serial correlation of annual runoff: 0.112 Three year rainfall Rank Period Mean ARI 1 1965– 1967 454 85 2 1944– 1946 476 48 3 1980– 1982 492 35 Past three years 2004– 2006 692 < 20 Three year runoff Rank Period Mean ARI 1 1925– 1927 15.9 51 2 1965– 1967 16.4 45 3 1938– 1940 18.1 31 Past three years 2004– 2006 47.0 < 20 Ten year rainfall Rank Period Mean ARI 1 1935– 1944 530 193 2 1918– 1927 572 38 3 1897– 1906 575 36 Past ten years 1997– 2006 688 < 20 Ten year runoff Rank Period Mean ARI 1 1935– 1944 22.2 218 2 1896– 1905 27.3 49 3 1923– 1932 28.4 40 Past ten years 1997– 2006 47.9 < 20 24 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.7 Namoi Rainfall 0 200 400 600 800 1000 1200 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 633 mm Standard deviation of annual rainfall: 155 mm Coefficient of variation of annual rainfall: 0.25 Coefficient of skewness of annual rainfall: 0.31 Lag one serial correlation of annual rainfall: 0.104 Mean annual runoff: 24.4 mm Standard deviation of annual runoff: 20.1 mm Coefficient of variation of annual runoff: 0.82 Coefficient of skewness of annual runoff: 2.20 Lag one serial correlation of annual runoff: 0.095 Three year rainfall Rank Period Mean ARI 1 1944– 1946 464 47 2 1980– 1982 471 39 3 1965– 1967 475 36 Past three years 2004– 2006 650 < 20 Three year runoff Rank Period Mean ARI 1 1938– 1940 7.9 90 2 1965– 1967 9.7 36 3 1935– 1937 10.5 28 Past three years 2004– 2006 21.7 < 20 Ten year rainfall Rank Period Mean ARI 1 1937– 1946 527 113 2 1918– 1927 560 36 3 1897– 1906 564 32 Past ten years 1997– 2006 663 < 20 Ten year runoff Rank Period Mean ARI 1 1935– 1944 13.1 185 2 1896– 1905 17.2 34 3 1923– 1932 17.3 33 Past ten years 1997– 2006 28.6 < 20 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 25 2.3.8 Macquarie Castlereagh Rainfall 0 200 400 600 800 1000 1200 1400 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 200 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 544 mm Standard deviation of annual rainfall: 159 mm Coefficient of variation of annual rainfall: 0.29 Coefficient of skewness of annual rainfall: 0.86 Lag one serial correlation of annual rainfall:  0.014 Mean annual runoff: 34.6 mm Standard deviation of annual runoff: 30.3 mm Coefficient of variation of annual runoff: 0.88 Coefficient of skewness of annual runoff: 2.65 Lag one serial correlation of annual runoff: 0.050 Three year rainfall Rank Period Mean ARI 1 1965– 1967 390 45 2 1944– 1946 396 37 3 1938– 1940 409 27 Past three years 2004– 2006 453 < 20 Three year runoff Rank Period Mean ARI 1 1938– 1940 13.9 40 2 1965– 1967 14.8 31 3 1944– 1946 15.4 27 Past three years 2004– 2006 18.8 < 20 Ten year rainfall Rank Period Mean ARI 1 1937– 1946 434 210 2 1895– 1904 471 42 3 1910– 1919 484 29 Past ten years 1997– 2006 547 < 20 Ten year runoff Rank Period Mean ARI 1 1932– 1941 18.9 207 2 1906– 1915 20.4 109 3 1895– 1904 21.8 67 Past ten years 1997– 2006 32.9 < 20 26 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.9 Barwon Darling Rainfall 0 200 400 600 800 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 328 mm Standard deviation of annual rainfall: 117 mm Coefficient of variation of annual rainfall: 0.36 Coefficient of skewness of annual rainfall: 0.60 Lag one serial correlation of annual rainfall: 0.088 Mean annual runoff: 6.0 mm Standard deviation of annual runoff: 7.9 mm Coefficient of variation of annual runoff: 1.30 Coefficient of skewness of annual runoff: 4.16 Lag one serial correlation of annual runoff: 0.011 Three year rainfall Rank Period Mean ARI 1 1900– 1902 194 94 2 1965– 1967 195 86 3 1927– 1929 212 44 Past three years 2004– 2006 270 < 20 Three year runoff Rank Period Mean ARI 1 1965– 1967 1.2 153 2 1900– 1902 1.3 114 3 1943– 1945 1.7 48 Past three years 2004– 2006 3.7 < 20 Ten year rainfall Rank Period Mean ARI 1 1937– 1946 250 146 2 1896– 1905 266 60 3 1918– 1927 283 30 Past ten years 1997– 2006 339 < 20 Ten year runoff Rank Period Mean ARI 1 1937– 1946 2.9 117 2 1897– 1906 3.1 94 3 1910– 1919 3.3 66 Past ten years 1997– 2006 6.5 < 20 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 27 2.3.10 Lachlan Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 80 100 120 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 461 mm Standard deviation of annual rainfall: 130 mm Coefficient of variation of annual rainfall: 0.28 Coefficient of skewness of annual rainfall: 0.39 Lag one serial correlation of annual rainfall: 0.024 Mean annual runoff: 23.1 mm Standard deviation of annual runoff: 19.0 mm Coefficient of variation of annual runoff: 0.82 Coefficient of skewness of annual runoff: 2.20 Lag one serial correlation of annual runoff: 0.003 Three year rainfall Rank Period Mean ARI 1 1944– 1946 323 50 2 1901– 1903 331 40 3 1897– 1899 338 33 Past three years 2004– 2006 358 20 Three year runoff Rank Period Mean ARI 1 1944– 1946 8.4 46 2 1901– 1903 9.1 34 3 1897– 1899 9.1 33 Past three years 2004– 2006 13.0 < 20 Ten year rainfall Rank Period Mean ARI 1 1895– 1904 366 220 2 1937– 1946 371 163 3 1918– 1927 424 20 Past ten years 1997– 2006 425 < 20 Ten year runoff Rank Period Mean ARI 1 1895– 1904 12.3 193 2 1932– 1941 13.6 92 3 1906– 1915 15.0 49 Past ten years 1997– 2006 17.6 23 28 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.11 Murrumbidgee Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 200 250 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 530 mm Standard deviation of annual rainfall: 136 mm Coefficient of variation of annual rainfall: 0.26 Coefficient of skewness of annual rainfall: 0.46 Lag one serial correlation of annual rainfall: 0.042 Mean annual runoff: 54.3 mm Standard deviation of annual runoff: 32.4 mm Coefficient of variation of annual runoff: 0.60 Coefficient of skewness of annual runoff: 1.82 Lag one serial correlation of annual runoff: 0.049 Three year rainfall Rank Period Mean ARI 1 1943– 1945 385 55 2 2004– 2006 409 29 3 1897– 1899 414 26 Past three years 2004– 2006 409 29 Three year runoff Rank Period Mean ARI 1 1927– 1929 29.1 34 2 1943– 1945 30.0 29 3 1901– 1903 30.1 28 Past three years 2004– 2006 30.6 27 Ten year rainfall Rank Period Mean ARI 1 1895– 1904 444 120 2 1937– 1946 450 88 3 1997– 2006 471 39 Past ten years 1997– 2006 471 39 Ten year runoff Rank Period Mean ARI 1 1895– 1904 36.8 122 2 1997– 2006 37.2 106 3 1905– 1914 38.7 72 Past ten years 1997– 2006 37.2 106 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 29 2.3.12 Murray Rainfall 0 200 400 600 800 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 80 100 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 340 mm Standard deviation of annual rainfall: 92 mm Coefficient of variation of annual rainfall: 0.27 Coefficient of skewness of annual rainfall: 0.73 Lag one serial correlation of annual rainfall: 0.129 Mean annual runoff: 24.0 mm Standard deviation of annual runoff: 12.0 mm Coefficient of variation of annual runoff: 0.50 Coefficient of skewness of annual runoff: 1.40 Lag one serial correlation of annual runoff: 0.164 Three year rainfall Rank Period Mean ARI 1 1943– 1945 222 131 2 1965– 1967 244 45 3 1927– 1929 250 36 Past three years 2004– 2006 281 < 20 Three year runoff Rank Period Mean ARI 1 1901– 1903 12.0 62 2 1912– 1914 12.8 42 3 1943– 1945 12.8 41 Past three years 2004– 2006 15.7 < 20 Ten year rainfall Rank Period Mean ARI 1 1936– 1945 285 80 2 1895– 1904 285 76 3 1926– 1935 306 27 Past ten years 1997– 2006 313 21 Ten year runoff Rank Period Mean ARI 1 1895– 1904 15.3 282 2 1936– 1945 16.4 122 3 1907– 1916 18.7 39 Past ten years 1997– 2006 18.9 36 30 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.13 Ovens Rainfall 0 500 1000 1500 2000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 200 400 600 800 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 1004 mm Standard deviation of annual rainfall: 250 mm Coefficient of variation of annual rainfall: 0.25 Coefficient of skewness of annual rainfall: 0.30 Lag one serial correlation of annual rainfall:  0.024 Mean annual runoff: 231.3 mm Standard deviation of annual runoff: 140.0 mm Coefficient of variation of annual runoff: 0.61 Coefficient of skewness of annual runoff: 1.19 Lag one serial correlation of annual runoff: 0.078 Three year rainfall Rank Period Mean ARI 1 1943– 1945 747 53 2 2004– 2006 794 26 3 1901– 1903 797 25 Past three years 2004– 2006 794 26 Three year runoff Rank Period Mean ARI 1 1901– 1903 99.4 53 2 1895– 1897 100.8 49 3 1943– 1945 113.9 31 Past three years 2004– 2006 136.6 < 20 Ten year rainfall Rank Period Mean ARI 1 1895– 1904 862 99 2 1936– 1945 888 49 3 1997– 2006 895 41 Past ten years 1997– 2006 895 41 Ten year runoff Rank Period Mean ARI 1 1895– 1904 129.8 498 2 1997– 2006 171.9 36 3 1905– 1914 180.0 28 Past ten years 1997– 2006 171.9 36 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 31 2.3.14 Goulburn Broken Rainfall 0 200 400 600 800 1000 1200 1400 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 100 200 300 400 500 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 764 mm Standard deviation of annual rainfall: 172 mm Coefficient of variation of annual rainfall: 0.22 Coefficient of skewness of annual rainfall: 0.17 Lag one serial correlation of annual rainfall:  0.022 Mean annual runoff: 149.2 mm Standard deviation of annual runoff: 77.3 mm Coefficient of variation of annual runoff: 0.52 Coefficient of skewness of annual runoff: 0.94 Lag one serial correlation of annual runoff: 0.030 Three year rainfall Rank Period Mean ARI 1 1943– 1945 562 72 2 1936– 1938 588 41 3 2004– 2006 601 32 Past three years 2004– 2006 601 32 Three year runoff Rank Period Mean ARI 1 1912– 1914 75.4 52 2 1936– 1938 78.9 41 3 2004– 2006 81.0 35 Past three years 2004– 2006 81.0 35 Ten year rainfall Rank Period Mean ARI 1 1997– 2006 649 156 2 1936– 1945 669 66 3 1895– 1904 703 27 Past ten years 1997– 2006 649 156 Ten year runoff Rank Period Mean ARI 1 1997– 2006 88.6 850 2 1895– 1904 116.2 39 3 1940– 1949 117.6 36 Past ten years 1997– 2006 88.6 850 32 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.15 Campaspe Rainfall 0 200 400 600 800 1000 1200 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 50 100 150 200 250 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 594 mm Standard deviation of annual rainfall: 147 mm Coefficient of variation of annual rainfall: 0.25 Coefficient of skewness of annual rainfall: 0.02 Lag one serial correlation of annual rainfall: 0.036 Mean annual runoff: 68.9 mm Standard deviation of annual runoff: 48.3 mm Coefficient of variation of annual runoff: 0.70 Coefficient of skewness of annual runoff: 0.89 Lag one serial correlation of annual runoff: 0.009 Three year rainfall Rank Period Mean ARI 1 1943– 1945 387 138 2 1936– 1938 427 51 3 1925– 1927 439 40 Past three years 2004– 2006 482 < 20 Three year runoff Rank Period Mean ARI 1 1943– 1945 25.0 52 2 2001– 2003 25.4 50 3 2004– 2006 28.5 34 Past three years 2004– 2006 28.5 34 Ten year rainfall Rank Period Mean ARI 1 1937– 1946 480 230 2 1997– 2006 517 47 3 1895– 1904 518 46 Past ten years 1997– 2006 517 47 Ten year runoff Rank Period Mean ARI 1 1997– 2006 34.2 594 2 1895– 1904 40.3 135 3 1940– 1949 44.9 60 Past ten years 1997– 2006 34.2 594 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 33 2.3.16 Loddon Avoca Rainfall 0 200 400 600 800 1000 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 80 100 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 430 mm Standard deviation of annual rainfall: 112 mm Coefficient of variation of annual rainfall: 0.26 Coefficient of skewness of annual rainfall: 0.17 Lag one serial correlation of annual rainfall: 0.055 Mean annual runoff: 20.7 mm Standard deviation of annual runoff: 15.5 mm Coefficient of variation of annual runoff: 0.75 Coefficient of skewness of annual runoff: 1.26 Lag one serial correlation of annual runoff: 0.034 Three year rainfall Rank Period Mean ARI 1 1943– 1945 277 152 2 1925– 1927 313 41 3 1900– 1902 319 35 Past three years 2004– 2006 353 < 20 Three year runoff Rank Period Mean ARI 1 1943– 1945 6.8 55 2 2001– 2003 6.9 54 3 1925– 1927 8.3 29 Past three years 2004– 2006 8.8 24 Ten year rainfall Rank Period Mean ARI 1 1936– 1945 346 215 2 1895– 1904 370 57 3 1997– 2006 381 36 Past ten years 1997– 2006 381 36 Ten year runoff Rank Period Mean ARI 1 1997– 2006 9.9 420 2 1940– 1949 12.6 70 3 1896– 1905 13.0 60 Past ten years 1997– 2006 9.9 420 34 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 2.3.17 Wimmera Rainfall 0 200 400 600 800 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 403 mm Standard deviation of annual rainfall: 96 mm Coefficient of variation of annual rainfall: 0.24 Coefficient of skewness of annual rainfall: 0.04 Lag one serial correlation of annual rainfall: 0.050 Mean annual runoff: 16.5 mm Standard deviation of annual runoff: 11.8 mm Coefficient of variation of annual runoff: 0.71 Coefficient of skewness of annual runoff: 1.13 Lag one serial correlation of annual runoff: 0.073 Three year rainfall Rank Period Mean ARI 1 1943– 1945 276 97 2 1965– 1967 298 43 3 1938– 1940 301 39 Past three years 2004– 2006 313 28 Three year runoff Rank Period Mean ARI 1 1943– 1945 4.7 103 2 1965– 1967 6.3 38 3 2004– 2006 6.7 31 Past three years 2004– 2006 6.7 31 Ten year rainfall Rank Period Mean ARI 1 1936– 1945 350 55 2 1997– 2006 350 54 3 1895– 1904 359 36 Past ten years 1997– 2006 350 54 Ten year runoff Rank Period Mean ARI 1 1997– 2006 8.1 385 2 1895– 1904 10.3 63 3 1937– 1946 10.8 48 Past ten years 1997– 2006 8.1 385 © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 35 2.3.18 Eastern Mount Lofty Ranges Rainfall 0 200 400 600 800 1895 1915 1935 1955 1975 1995 Annual rainfall ( mm) Runoff 0 20 40 60 80 100 120 1895 1915 1935 1955 1975 1995 Annual runoff ( mm) Mean annual rainfall: 463 mm Standard deviation of annual rainfall: 97 mm Coefficient of variation of annual rainfall: 0.21 Coefficient of skewness of annual rainfall: 0.38 Lag one serial correlation of annual rainfall:  0.053 Mean annual runoff: 30.1 mm Standard deviation of annual runoff: 20.5 mm Coefficient of variation of annual runoff: 0.68 Coefficient of skewness of annual runoff: 1.34 Lag one serial correlation of annual runoff: 0.015 Three year rainfall Rank Period Mean ARI 1 1965– 1967 334 241 2 1912– 1914 372 37 3 1957– 1959 378 30 Past three years 2004– 2006 427 < 20 Three year runoff Rank Period Mean ARI 1 1912– 1914 11.3 110 2 1965– 1967 11.4 106 3 1975– 1977 13.5 44 Past three years 2004– 2006 18.5 < 20 Ten year rainfall Rank Period Mean ARI 1 1993– 2002 420 45 2 1958– 1967 433 24 3 1895– 1904 441 < 20 Past ten years 1997– 2006 429 26 Ten year runoff Rank Period Mean ARI 1 1997– 2006 19.3 105 2 1976– 1985 22.8 30 3 1932– 1941 23.7 23 Past ten years 1997– 2006 19.3 105 36 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 3 Methodology This section describes the methodology used to obtain the results presented in Chapter 1 and Chapter 2. Section 3.1 describes the time series smoothing method used to calculate the low frequency variability of rainfall in Chapter 2. Section 3.2 describes the statistical tests used to test for trend and step changes in mean of the rainfall time series in Section 1.2 and Section 1.3. Section 3.3 describes the method used to estimate the average recurrence intervals ( ARIs) of n year rainfall in Section 1.4 and Chapter 2. 3.1 Time series smoothing The time series smoothing is used to calculate the low frequency rainfall variability in Chapter 2. A kernel smoother, essentially a weighted moving average, is used. In the kernel smoother, the smoothed estimate at t0 of a time series Y( t) of length T is given by ( Fan and Yao, 2005): ( ) ( ) [ ( ) ] Σ [ ( ) ] Σ = =   = T t T t K t t h Y t K t t h Y t 1 0 1 0 0 / / ˆ for a given kernel function K( t) and bandwidth parameter h. A Gaussian kernel is used here ( Figure 3 1). The Gaussian kernel places more emphasis on years close to t0 than a moving average filter, and so results in a smoother signal. The Gaussian kernel is a normal distribution function with a mean of zero and a standard deviation of one: KG( t ) = ( 2 p )  1/ 2 exp(  t 2 / 2) A bandwidth of 5.4 is used here, which corresponds to 95 percent of the kernel lying ten years either side of the current year. This bandwidth can be derived from normal probability tables. 0 250 500 750 1000 1250 1895 1905 1915 1925 1935 1945 1955 1965 1975 1985 1995 2005 Annual rainfall ( mm) 0 0.1 0.2 0.3 0.4 0.5 Value of kernel Figure 3 1. Example annual rainfall time series with Gaussian kernel ( red line) centred at 1950 and the resulting smoothed time series ( blue line) Since the Gaussian kernel smooths are actually two sided averages, care needs to be taken in interpreting the values at the endpoints. For example, if rainfall in the next ten years ( 2007 to 2016) is decreasing, the value of the smoothed rainfall signal using these data would be slightly lower than if rainfall in the next ten years is increasing. Therefore, if we are currently at the trough of a drought, the smoothed rainfall signal would be slightly larger if we incorporated this extra information ten years from now. The mean absolute magnitude of the edge effect is small, approximately 5 percent of mean annual rainfall only. © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 37 3.2 Statistical tests for trend and step change Six statistical tests are used in Section 1.3 to test the 1895 to 2006 annual rainfall series for trend and step change in mean. Three statistical tests are used for trend: Mann Kendall, Spearman’s Rho and Linear Regression. Three statistical tests are used for step change in mean and year of step change: Distribution Free CUSUM, Cumulative Deviation and Worsley Likelihood Ratio. The Student’s t test is used in Section 1.2 to test whether the mean annual rainfall over the recent years is significantly different from the 1895 to 2006 mean. The Rank Sum test is also used to check the t test results. These non parametric and parametric tests are widely used in the literature, and details can be found in the TREND software package ( http:// www. toolkit. net. au/ trend and Chiew and Siriwardena, 2005) and the WMO UNESCO Expert Workshop on Trend/ Change Detection report ( Kundzewicz and Robson, 2000; Kundzewicz and Robson, 2004). The tests are summarised briefly below: · Mann Kendall Test is a non parametric test that determines the significance of a trend by analysing the relative frequency of ranked data values. · Spearman’s Rho is a non parametric test that determines the significance of a trend by analysing the correlation coefficient between the ranked response and time. · Linear regression is a parametric test that determines the significance of a trend by analysing the slope of the linear regression between the data values and time. · Distribution Free CUSUM is a non parametric test that determines the significance of a step change in mean by analysing the relative cumulative deviations from the median. The change point is given by the maximum absolute value of the test statistic. · Cumulative Deviation is a parametric test that determines the significance of a step change in mean by analysing the relative cumulative deviations from the mean. The change point is given by the maximum absolute value of the test statistic. · Worsley Likelihood Ratio is a parametric test that determines the significance of a step change in mean by analysing the relative cumulative deviations from the mean with higher weights given to the start and end of the time series. The change point is given by the maximum absolute value of the test statistic. · Student’s t test is a parametric test that determines whether the means from two specified data periods are statistically different by comparing the two means and taking into account the variability in the data. · Rank Sum is a non parametric test that determines whether the medians from two specified data periods are statistically different by comparing the sum of ranked data in each period. In all cases a two sided 90 percent significance level ( i. e. α = 0.1) is used. Specifically, a test statistic is statistically significant if the value of the statistic lies outside the 5 th or 95 th percentile of the relevant cumulative distribution function. 3.3 Estimation of average recurrence interval The method used to estimate the ARI of n year rainfall and runoff averages ( see Section 1.4 and Chapter 2) is described here. The ARI for a specific n year mean rainfall or runoff threshold is defined here as the average number of years between successive n year mean rainfall or runoff falling below the threshold, or the average time between successive down crossings ( see Section 3.3.1) of the threshold ( Fernandez and Salas, 1999). For example, an ARI of 50 years for ten year mean rainfall falling below 500 mm means that once a ten year mean rainfall is below 500 mm, it will take on average another 50 years before another ‘ independent’ ten year mean rainfall below 500 mm occurs, given there must be at least one ten year mean rainfall above the 500 mm threshold between two successive events/ down crossings. There is no generally accepted method for defining the ARI of an n year low rainfall or runoff sequence. The ARI defined here is somewhat different to the standard flood return period found in many textbooks. This is because unlike most flood frequency analysis, consecutive n year rainfall and runoff events, as used here, are not independent. There is also no generally accepted method of quantifying drought severity ( magnitude and duration) that is equally relevant for different applications ( Heim, 2002; Keyantash and Dracup, 2002). This is evident from the hundreds of 38 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 drought indices used in the literature. The three year mean rainfall and runoff and ten year mean rainfall and runoff are used here as objective measures of dry conditions because they can be easily understood. 3.3.1 Calculation of average recurrence interval Figure 3 2 provides a graphical explanation of the terms used here. This is important because different studies use slightly different definitions of terms. In this project: · Up crossing is defined as a crossing of the threshold from below. · Down crossing is defined as a crossing of the threshold from above. · Event duration is defined as the time between a down crossing and the subsequent up crossing. · Inter arrival time is defined as the time between an up crossing and the subsequent down crossing. · Recurrence interval is defined as the time between successive down crossings. Inter arrival time Recurrence interval Event duration Dow n crossing Up crossing Figure 3 2. Definition of terms for estimation of average recurrence intervals To estimate the ARI, based on an 1895 to 2006 annual rainfall or runoff series, the lag one autoregressive model of Frost et al. ( 2007) is first used to generate stochastic annual rainfall and runoff. This model also allows for non Gaussian distributions using Box Cox transformation and considers parameter uncertainty using Bayesian methods with Markov Chain Monte Carlo parameter estimation. The runoff modelling is more problematic because of the high skewness and apparent multimodality for some regions. For this reason, the prior distribution of the Box Cox lambda parameter is bounded between – 2 and 2 for the rainfall modelling, and between 0 and 2 for the runoff modelling. Verification of the stochastic simulations are carried out by comparing a series of standard statistics ( mean, standard deviation, coefficient of skewness, and lag one to lag 15 autocorrelation coefficients) and distribution plots of annual rainfall and runoff and ten year rainfall and runoff sums. The verification indicates that most statistics from most of the historical series lie within the 90 percent confidence limits of 50,000 112 year replicates from the model, and the mean, standard deviation, skew and lag one autocorrelation coefficient of the historical data from most sites/ regions are similar to the median of the replicates. For each station/ region, the model is used to generate 100 replicates of 100,000 years of annual rainfall or runoff. The ARI for any specified n year rainfall or runoff threshold can be calculated directly from a 100,000 years annual replicate as the mean of the recurrence intervals. As 100 stochastic replicates are used, there are 100 estimates of the ARI for any specified n year rainfall or runoff threshold. The 100 replicates – each with a different parameter chosen randomly from the posterior distribution – are used to take into account sampling variability and parameter uncertainty. As the distribution of the ARI estimates can be highly skewed, particularly for the higher ARIs, the median ARI from the 100 estimates is presented as the ARI for n year rainfall and runoff thresholds in Section 1.4 and Chapter 2. © CSIRO 2008 Characterisation of recent rainfall and runoff in the Murray Darling Basin ▪ 39 3.3.2 Interpretation of average recurrence interval The ARI for a specific n year rainfall or runoff threshold is defined here as the average number of years between successive down crossings of the threshold ( Fernandez and Salas, 1999). The ARI defined here is somewhat different to the standard flood return period found in many textbooks. This is because unlike most flood frequency analysis, consecutive n year rainfall or runoff events are not independent. For example, the ten year mean rainfalls for a given year and the previous year are calculated using nine years of the same annual rainfall data. Furthermore, serial correlation of annual rainfall and runoff is explicitly included in the model, as described in Section 3.3.1, which also increases the recurrence interval of any rainfall or runoff threshold ( Yevjevich, 1972). The traditional method of calculating ARIs ( i. e. the exceedance probability method) will correspond to the recurrence interval as defined in Section 3.3.1 for independent events ( Stedinger et al., 1993), but will greatly underestimate the ARI for highly correlated time series. It should also be noted that the past three year and past ten year rainfall and runoff ( as presented in Section 1.4 and in the last row of the tables in Chapter 2) may be part of a more severe dry sequence. For example, the ARI for 1995 to 2004 rainfall may be higher than the ARI for the 1997 to 2006 rainfall presented in Section 1.4 and Chapter 2. As such, where n year rainfall or runoff has been increasing over the past couple of years, the ARIs estimated for 2004 to 2006 rainfall and runoff and 1997 to 2006 rainfall and runoff ( as presented in Section 1.4 and in the last row of the tables in Chapter 2) may be lower than the maximum ARI for the recent dry sequence. In contrast, the ARIs for the lowest three independent three year and ten year rainfall and runoff means in the tables in Chapter 2 do not have this problem because they are independent non overlapping lowest, second lowest and third lowest n year rainfall and runoff means in the 1895 to 2006 rainfall and runoff series. ARIs for values of recent rainfall and runoff above the long term mean as well as ARIs less than 20 years are not reported in Section 1.4 and Chapter 2. For values above the long term mean the inter arrival time decreases as the threshold increases, but the event duration increases as the threshold increases. Therefore for the method defined here, the ARI will increase as recent rainfall or runoff increases above the long term mean. Recent rainfall or runoff above the long term mean can be considered as a rare event, but ARIs in this report are specifically for dry sequences. Also, values of the recent rainfall or runoff lower but close to the long term mean can be considered frequent events. The purpose of reporting ARIs in Section 1.4 and Chapter 2 is to estimate the recurrence interval of uncommon low rainfall and runoff events, so values of the ARI below 20 years are also not reported in those sections. 40 ▪ Characterisation of recent rainfall and runoff in the Murray Darling Basin © CSIRO 2008 4 References Chiew FHS and Siriwardena L ( 2005) TREND user guide. 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