Assessing future droughts in Australia - a nesting model to correct for long-term persistence in general circulation model precipitation simulations

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1 18 th World IMACS / MODSIM Congress, Carns, Australa July 09 Assessng future droughts n Australa - a nestng model to correct for long-term persstence n general crculaton model precptaton smulatons Johnson, F.M. 1 and A. Sharma 1 1 School of Cvl and Envronmental Engneerng, Unversty of New South Wales, Sydney, Australa Emal: fona.johnson@student.unsw.edu.au Abstract: To produce meanngful predctons for water resources assessments, we need to be able to correctly model clmate varablty on a range of tme scales. Inablty to represent low-frequency varablty n precptaton and streamflow leads to a poor smulaton of droughts, and can result n based estmates of the securty of water resources systems. Ths s partcularly mportant n regons, such as Australa, where clmate teleconnectons lead to varablty at nterannual and nterdecadal scales. The mpacts of clmate change on ths varablty are mportant to consder. The precptaton outputs of General Crculaton Models (GCMs) are based compared to observatons at a range of tme scales. At the daly scale, ranfall occurrence s poorly modelled wth ranfall occurrng too often, wth too low ntenstes. At monthly and annual scales, the dstrbutons of ranfall amounts can be based, n some cases over-predctng ranfall amounts and n others, especally n coastal areas, underpredctng ranfall totals. Interannual varablty s also poorly modelled. We demonstrate the extent of ths bas by comparng the precptaton from the CSIRO Mk3.5 model to observed data over Australa. We propose a framework to address and correct for these weaknesses n the GCM outputs. The model nvolves nestng the GCM smulatons nto monthly and annual tme seres of observed data, such that monthly and annual means, varances and lag correlatons are approprately smulated. Daly precptaton outputs from the CSIRO Mk3.5 model are corrected usng the above model. The nestng model () s also compared to a smple monthly correcton (), and s found to provde better performance n terms of predcton error at annual and nterannual tme scales. At monthly tme scales, the gves slghtly better predctons. The root mean square errors of the predctons compared to the observed Bureau of Meteorology data are presented n Table 1 for a range of statstcs at dfferent tme scales. Ths data s presented for the valdaton perod of 1951 to 00. Table 1. Comparson of raw and bas corrected ( and ) predcton errors for key statstcs. Statstc RMSE RMSE RMSE Annual Mean Annual Std. Dev Annual Lag 1 Cor Monthly Mean Monthly Std. Dev Year Mnmum Sum Year Mnmum Sum th Percentle 1 Year SPI th Percentle 2 Year SPI th Percentle 5 Year SPI The results of the models are also used to assess the dfference n drought predctons usng the Standardsed Precptaton Index (SPI). Predctons of the SPI are compared for the raw GCM precptaton and the bas corrected outputs. The fnal three rows of Table 1 present the results of ths analyss for the perod 1951 to 00, showng the superor performance of the methodology. For future clmate projectons, usng the SRESA2 scenaro for 80, t s found that drought frequences are overestmated when usng the raw GCM precptaton outputs. Overall the study demonstrates that bas correcton wth nestng at multple tme scales can address some of the weaknesses of GCM precptaton felds. Keywords: Clmate change, bas correcton, precptaton, general crculaton model (GCM) 3935

2 1. INTRODUCTION The mpacts of clmate change on water resources systems are of concern to a range of stakeholders from governments to water utltes, agrculturalsts to urban consumers. Impact assessments seek to answer questons regardng future rsks to water resources systems, partcularly at a regonal or watershed scale. To produce meanngful predctons for these assessments, we need to be able to correctly model clmate varablty on a range of tme scales. But there are problems wth general crculaton model (GCM) ranfall outputs on all temporal scales. Frstly, although GCMs are expected to provde more relable results at seasonal to annual tme frames, there can stll be sgnfcant bases n the annual and monthly statstcs of precptaton when compared to observatons. Fgure 1 shows the observed annual mean ranfall and Fgure 1 the bas n the annual means from the CSIRO Mk3.5 GCM for Australa for 1961 to 00. We see that over the relatvely dry, flat nteror of Australa, the model overpredcts the annual ranfall by up to 0% n some locatons. In coastal areas, annual average ranfall s underestmated. In Fgure 1(c) we present a comparson of the rato of the projected changes n annual average ranfall by 80 to the bas n the annual average ranfall for the th century. Areas shown n lght grey are those where the rato of the change s larger than the bas, medum grey shows areas where the change and bas are of the same order of magntude. Areas shown n black ndcate where the bas s much larger than the projected changes for the SRESA2 scenaro (c) <50% >50% >0% Fgure 1. Bases n mean annual GCM ranfall outputs a) observed mean annual ranfall (mm/yr) for 1901 to 00, b) mean annual bas (observed modelled) n mean annual ranfall (mm/yr), c) rato of changes projected for SRESA2 for 61 to 00 compared to bas for 1901 to 00. Secondly, at a fner tme scale t s well known that there are problems n the modellng of daly ranfall both n ranfall occurrence and ranfall ntensty. Sun et al. (06) found that GCMs tend to overestmate the number of days wth ranfall less than mm, whlst underestmatng more ntense events, wth the errors cancellng each other out to gve seasonal totals that can be reasonably realstc, although ths s very model dependent (Randall et al., 07). Other problems related to the modellng of daly ranfalls nclude preservng observed dry and wet spell lengths (Ines and Hansen, 06). Thrdly, nterannual varablty of ranfall s dependent on regonal and global clmate teleconnectons, and the nature and extent of ths varablty changes around the world. In Australa, major clmate teleconnectons that affect nterannual ranfall varablty nclude the El Nno Southern Oscllaton (ENSO), the Interdecadal Pacfc Oscllaton (IPO), the Southern Annular Mode (SAM) and the Indan Ocean Dpole (IOD). Inablty to represent low-frequency varablty n precptaton and flow, results n a poor smulaton of droughts and based estmates of the securty offered by exstng water resources systems n a warmer clmate. The modellng of ENSO n GCMs has been assessed n many studes. ArchutaRao and Sperber (06) nvestgated how well ENSO was modelled n the GCMs submtted to the 3rd Coupled Model Intercomparson Project (CMIP3) for the IPCC Fourth Assessment Report. They attrbuted overall mprovements snce one of the earlest assessments of ENSO modellng (Neeln et al., 1992) to mproved coupled model formulatons. However, they note the mportance of reducng systematc model error (AchutaRao and Sperber, 06) to ensure the accuracy of precptaton clmatologes. Despte the problems wth GCM ranfall outputs, mpact assessment studes stll requre future projectons of ranfall for a range of applcatons. Stochastc and dynamc downscalng have both been used n many studes n an attempt to provde better future ranfall projectons. However both stochastc and dynamc downscalng studes tend to be hghly specalzed and hence are developed for a partcular regon or specfc queston. We 3936

3 are nterested n whether smple methods, whch can quckly and easly be appled over dfferent regons, could be used to mprove some of the shortcomngs of GCM ranfall. The remander of ths paper s organsed as follows. In Secton 2, we examne technques that have been proposed n the lterature to bas correct GCM ranfall. Secton 3 descrbes our proposed bas correcton technque. Secton 4 presents the results of the model appled to th century GCM smulatons over Australa and future drought projectons, and Secton 5 presents the conclusons. 2. BIAS CORRECTION FOR GCM OUTPUTS Bas correcton technques have been developed to allow the use of GCM outputs drectly, whlst acceptng that there are problems n GCM modellng of ranfall. Combned wth a spatal dsaggregaton step, they can provde nputs at a scale that s sutable for hydrologc modellng. Wthout spatal dsaggregaton, bas correcton can be used to make regonal assessments of water avalablty. Wood et al. (04) compared three smple statstcal downscalng approaches, ncludng lnear nterpolaton, spatal dsaggregaton and a combned bas correcton and spatal dsaggregaton model. The bas correcton method used quantle mappng to correct the monthly model clmatology to the observed clmatology. The bas correcton wth spatal dsaggregaton was the only method to produce hydrologcally plausble results (Wood et al., 04). Areas suggested by Wood et al (04) for future work ncluded modellng of nterannual varablty and sub-grd spatal varablty. Maurer and Hdalgo (08) compared the monthly quantle mappng of Wood et al (04) to a constructed analogue downscalng approach. They commented that the advantage of the quantle mappng s that t allows the mean and varablty of a GCM to evolve n accordance wth the GCM smulaton, whle matchng all statstcal moments between the GCM and observatons for the base perod (Maurer and Hdalgo, 08). Ines and Hansen (06) also appled the quantle mappng technque, ths tme to daly ranfalls nstead of monthly totals. The model was more successful than multplcatve scalng of monthly data at predctng monthly means, and daly ntensty and occurrence. However, they found that crop yelds were generally under-predcted usng the bas corrected ranfalls whch they attrbuted to the modelled wet and dry spell lengths n the raw GCM outputs, whch were not changed by the bas correcton technques. 3. NESTING METHODOLOGY The bas correcton methods descrbed n the precedng secton focused on monthly or daly statstcs of ranfall. However, longer term varatons n ranfall also need to be well modelled to enable accurate estmates of drought and water resources avalablty. In ths study, we propose a method that addresses the mssng nterannual varablty by usng statstcs from the observed ranfall at two tme scales monthly and annual, rather than just one tme scale. The ssue of correctly modellng nterannual varablty n precptaton has been addressed by researchers lookng at stochastc ranfall generaton models. Srkanthan (09) descrbes a nested two part model: daly, stochastcally generated, ranfalls are modfed by nestng n monthly and annual data to ensure that the daly, monthly and annual statstcs of the observed ranfall are reproduced. A nestng procedure was also used by Wang and Nathan (07), although n ths case the nestng of the daly generated ranfall sequences was only carred out at the monthly level. To adapt the nestng model to bas correcton, we use the daly GCM outputs nstead of generatng daly ranfall. The daly GCM sequences are then modfed by nestng n the observed monthly and annual tme seres. The process for the nestng s now descrbed. We use the 0.25 degree grdded ranfall data product from the Australa Bureau of Meteorology (BOM), whch has data from 1900 onwards. We splt the observed data nto two perods, a calbraton perod to derve the model parameters of 1901 to 1950, and a valdaton perod of 1951 to 00. The method s appled to daly precptaton from the CSIRO Mk3.5 model. The observed and modeled ranfalls are aggregated to monthly data and parameters for the nestng model are calculated for each month of the year, usng the all the years n the calbraton perod. For example, all January ranfalls from 1901 to 1950 are collated and the mean and standard devaton of these 50 values calculated. The tme seres of raw GCM monthly ranfalls (y) s then standarzed to create y for each month n the tme seres by removng the model monthly mean and standard devaton for that month () as shown n (1). 3937

4 y y μ mod, = (1) σ mod, We then remove the monthly lag one autocorrelatons (ρ mod, ) that are present n the model results from the standardzed tme seres and nstead apply the observed monthly lag one autocorrelatons (ρ obs, ) to create y" as shown. Monthly lag one autocorrelatons are defned as the correlaton of the tme seres of the values from month wth the tme seres of month -1. For example, the monthly autocorrelaton for February s calculated as the correlaton of the February values from 1901 to 1950, wth the tme seres of January values from 1901 to y ρ mod, y 1 y = ρ obs. y ρobs. (2) 2 1 ρ mod, We now rescale the observed means and standard devatons to create the nested tme seres (y ) at the monthly level. y = y σ + μ (3) obs, obs, The nested monthly values (y ) are then aggregated to the annual scale (z). The monthly process s repeated for the annual tme step, wth the dfference that there s no need to allow for seasonalty, as s done n the monthly model by calculatng the model parameters separately for each month. Begnnng wth the annual tme seres (z), we modfy by standardsng wth the mean and standard devaton of the annual ranfall, such that for year j, where j s between 1901 to 1950 for the calbraton perod: z z μ j mod j = (4) σ mod We then remove any modelled lag one autocorrelatons and apply the observed lag one autocorrelatons. Yearly lag one autocorrelatons are calculated as the correlaton between the ranfall n one year and the next. As the observed lag one autocorrelatons are generally qute small, ths step does not generally lead to large changes compared to the standardsed annual seres (z ). z = ρ z + 1 ρ 2 j obs j 1 obs z ρ z j mod j ρmod The last step s to create the fnal annual tme seres by rescalng wth the observed annual means and standard devatons. z = z σ + μ (6) j j obs obs We now have four tme seres that we wll use to correct the daly GCM tme seres (x), the uncorrected monthly tme seres (y), the nested monthly tme seres (y ), the aggregated yearly tme seres (z) and the nested annual tme seres (z ). From Srkanthan (09), the correctons at the monthly and annual level can be appled to the daly tme seres at the same tme to create a one step correcton as follows, where for day t whch s n month m n year n, the weghtng factor s the rato of the monthly corrected ranfall to the raw GCM ranfall for month m, multpled by the rato of the yearly corrected ranfall to the aggregated GCM ranfall for year n. y z = xt m n xˆ t ym zn For future perods, we use the observed and modelled statstcs for the observaton perod to adjust the future model results, and thereby assumng that the bases n the model for observed perod reman the same n the future. In more detal, the future bas correcton steps wth equatons (1), (2), (4) and (5) use the monthly and annual statstcs from the GCM for the current clmate and equatons (3) and (6) use the observed statstcs as before. The form of equaton (7) s unchanged for the future perod. We use the SRESA2 scenaro, wth data from the perod 61 to 20. Results are presented for the average of ths perod, nomnally termed 80. (5) (7) 3938

5 4. RESULTS 4.1. Modellng of Seasonal and Annual Ranfall Statstcs We compare the results of the nestng bas correcton to those from a bas correcton method that corrects just the monthly means and standard devatons. In the followng text, the monthly mean and standard devaton correcton s term the Monthly Bas Correcton (), whlst the nested algorthm outlned n Secton 3 s term the Nested Bas Correcton (). Fgure 2 shows the bas corrected results for the and methods at the annual level for the valdaton perod of 1951 to 00. In Fgures 2 to 4, each ndvdual pont on the graph represents the respectve annual statstc for each grd cell (.e. each locaton where the bas correcton has been appled). Both methods gve good mprovements for the mean annual ranfall, whlst the shows mprovement n the annual standard devatons and lag one autocorrelatons compared to both the raw GCM outputs and the. Ths demonstrates that mprovng the modellng of mean ranfall s not enough to correct model ranfall varablty. The lag one autocorrelatons do not show as good mprovement as the means and standard devatons. Ths s because the autocorrelatons of the observed data are not as smlar as the other statstcs between the calbraton and valdaton perods. Despte ths, by bas correctng wth the nested model, whch ncludes correctng the lag one autocorrelatons, we model nterannual varablty much better. Ths s demonstrated n the followng secton. Modelled Mean Annual Ranfall (mm) Modelled Annual Standard Devaton (mm) Modelled Lag 1 Cor Observed Mean Annual Ranfall (mm) Observed Annual Standard Devaton (mm) Observed Lag 1 Cor Fgure 2: Modelled vs observed statstcs of annual ranfall for raw GCM outputs and and bas corrected models for a) annual mean, b) annual standard devaton and c) annual lag one autocorrelaton Modellng of Interannual Ranfall Varablty Lookng at the statstcs of nterannual varablty, we frstly consder the 2 and 5 year mnmum ranfall totals. These statstcs are standardsed by the mean annual ranfall to allow comparsons of the statstcs across Australa. Fgure 3 presents plots of modelled vs observed for the valdaton perod of By correctng the GCM outputs at the annual level for the lag one autocorrelaton, we mprove the modellng of these mnmum ranfall totals. Ths s mportant for ensurng that drought and flood perods are modelled correctly, partcularly f the GCM outputs are beng consdered for analyss of dam capactes. The results from both Fgure 2 and Fgure 3 are summarsed n Table 1, whch presents the root mean square errors (RMSE) of the raw GCM outputs compared to observatons and also the results from applyng the and methods. Modelled 2 Year Mnmum Standardsed Ranfall Observed 2 Year Mnmum Standardsed Ranfall Modelled 5 Year Mnmum Standardsed Ranfall Observed 5 Year Mnmum Standardsed Ranfall Fgure 3. a) 2 year and b) 5 year mnmum ranfall totals, standardsed by mean annual ranfall 3939

6 4.3. Modellng of Current and Future Drought Frequences We now also present the results from an applcaton of the bas corrected outputs for drought analyss usng the Standardsed Precptaton Index (SPI). The SPI was developed to provde a smple calculaton of drought (Guttman, 1999). A tme seres of precptaton s ftted to a standard normal dstrbuton and the quantles of the ftted dstrbuton are used to assess the severty of the drought. Negatve values of the ndex occur durng dry perods, wth postve values ndcatng wet condtons. The SPI can be calculated for varyng ntervals; ntervals of 1, 2 and 5 years are assessed n ths study. We undertake two calculatons usng the SPI. The frst compares the modellng of drought frequences across Australa from the raw and bas corrected GCM outputs for the valdaton perod of 1951 to 00. Fgure 4 shows scatter plots of the estmated 5 th percentle of the SPI at each grd cell compared to the observed data for SPI values calculated for the three tme perods. The 5 th percentle has prevously been defned as severe drought by Burke and Brown (08). 5th percentle 1 year SPI 5th percentle 2 year SPI 5th percentle 5 year SPI Modelled Modelled Modelled (c) Observed Observed Observed Fgure 4. Modelled vs observed 5 th percentle SPI values for a) 1 year SPI, b) 2 year SPI and c) 5 year SPI Both bas correcton methods mprove the modellng of severe drought. The s found to provde the best estmate of the magntude of observed severe drought at each locaton. Table 1 presents the predcton error for each of the scenaros n Fgure 4. For both bas correcton methods, performance s best when we calculate the SPI at a one year nterval and decreases for ncreasng SPI ntervals. Ths s to be expected as our nestng model only corrects for lag one autocorrelatons. We would requre a measure of longer term persstence n our model to capture the varatons of drought over longer perods. Ths s an area of ongong research. Wth confdence that the nested bas Frequency of Severe Drought - Frequency of Severe Drought - correcton method can mprove the modellng of droughts, we move to assessng the frequency of future severe droughts. To do ths, we use the observed th percentle SPI value to defne a severe Frequency of Severe Drought - Severe Drought Frequency Comp. drought threshold at each grd cell. We (d) then use the future GCM projectons (both (c) raw and bas corrected) to see how frequently we expect severe droughts to occur n the future (Burke and Brown, 08). The results of ths analyss hghlght the mpact of ncorrectly modellng nterannual varablty n GCM outputs. Fgure 5 shows the predctons of drought frequency for the future across Australa. The mean frequency of severe droughts Raw Fgure 5. Maps of severe drought frequency n 80 for a) raw GCM, b) monthly and c) nested bas correcton. A comparson of the dstrbuton of values for the three cases s shown n d). 3940

7 occurrng n the future usng the raw GCM outputs s approxmately % - meanng that n any one year, % of the country s lkely to be sufferng from a severe drought. If we only bas correct the GCM outputs usng a monthly scalng, then the pattern of severe droughts s qute smlar, and the mean occurrence frequency s approxmately 18%. On the other hand, usng the nestng bas correcton technque, we fnd that severe droughts are less lkely than t would seem from the raw GCM outputs. The mean occurrence frequency s 15% n ths case, and we can see the dfference n the spatal patterns of severe drought frequency, wth decreases n occurrence frequency partcularly n Western Australa. It s mportant to note that we are stll seeng ncreases n the frequency of severe droughts over 90% of the country. Also, f we assessed drought usng a combned precptaton and temperature based ndex (e.g. the Palmer Drought Severty Index), then wth the combnaton of ncreasng temperatures we would expect droughts to occur even more frequently. Further research s beng undertaken whether these fndngs are specfc to the CSIRO GCM or they apply to other GCMs as well. 5. CONCLUSIONS Ths paper has presented the detals of a nestng bas correcton methodology that can be appled to GCM ranfall outputs to address known weaknesses n the modellng of monthly, annual and nterannual statstcs of ranfall. The nested bas correcton model performs better than smple monthly means correctons, whch have often been used n clmate change mpact assessments. Future work wll nvolve extensons to the model to account for longer term persstence. It s also proposed to apply the nestng model to multple GCMs. ACKNOWLEDGMENTS Fundng for ths research came from the Australan Research Councl and the Sydney Catchment Authorty. Ther support for ths work s gratefully acknowledged. We acknowledge the modellng groups, the Program for Clmate Model Dagnoss and Intercomparson (PCMDI) and the WCRP s Workng Group on Coupled Modellng (WGCM) for ther roles n makng avalable the WCRP CMIP3 mult-model dataset. Support of ths dataset s provded by the Offce of Scence, U.S. Department of Energy. REFERENCES AchutaRao, K. and Sperber, K.R. (06), ENSO smulaton n coupled ocean-atmosphere models: are the current models better? Clmate Dynamcs, 27, Burke, E.J. and Brown, S.J. (08), Evaluatng uncertantes n the projecton of future drought. Journal of Hydrometeorology, 9, Guttman, N.B. (1999), Acceptng the standardzed precptaton ndex: A calculaton algorthm. Journal of the Amercan Water Resources Assocaton, 35, Ines, A. V. M. and Hansen, J.W. (06), Bas correcton of daly GCM ranfall for crop smulaton studes. Agrcultural and Forest Meteorology, 138, Maurer, E. P. and Hdalgo, H.G. (08), Utlty of daly vs. monthly large-scale clmate data: an ntercomparson of two statstcal downscalng methods. Hydrology and Earth System Scences, 12, 551. Neeln, J.D., Latf, M., Allaart, M. A. F., Cane, M. A., Cubasch, U., Gates, W. L., Gent, P. R., Ghl, M., Gordon, C., Lau, N. C., Mechoso, C. R., Meehl, G. A., Oberhuber, J. M., Phlander, S. G. H., Schopf, P. S., Sperber, K. R., Sterl, K. R., Tokoka, T., Trbba, J., and Zebak, S. E. (1992), Tropcal ar-sea nteracton n general crculaton models. Clmate Dynamcs, 7, Randall, D.A., Wood, R. A., Bony, S., Colman, R., Fchefet, T., Fyfe, J., Kattsov, V., Ptman, A., Shukla, J., and Srnvasan, J. (07), Clmate Models and Ther Evaluaton. Clmate Change 07: The Physcal Scence Bass. Contrbuton of Workng Group I to the Fourth Assessment Report of the Intergovernmental Panel on Clmate Change, S. Solomon, D. Qn, M. Mannng, Z. Chen, M. Marqus, K. B. Averyt, M. Tgnor, and H. L. Mller, Eds., Cambrdge Unversty Press,. Srkanthan, R. (09), A nested multste daly ranfall stochastc generaton model, Journal of Hydrology, do:.16/j.jhydrol Sun, Y., S. Solomon, A. Da, and R. W. Portmann (06), How often does t ran? Journal of Clmate, 19, Wang, Q. J. and Nathan, R.J. (07), A method for couplng daly and monthly tme scales n stochastc generaton of ranfall seres. Journal of Hydrology, 346, Wood, A. W., Leung, L.R., Srdhar, V., and Lettenmaer, D.P. (04), Hydrologc mplcatons of dynamcal and statstcal approaches to downscalng clmate model outputs. Clmatc Change, 62,