potential improvements to statistical downscaling of general circulation model outputs to catchment...

8/11/2019 Potential Improvements to Statistical Downscaling of General Circulation Model Outputs to Catchment Streamflow

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ORIGINAL PAPER

Potential improvements to statistical downscaling of generalcirculation model outputs to catchment streamflowswith downscaled precipitation and evaporation

D. A. Sachindra & F. Huang & A. Barton & B. J. C. Perera

Received: 12 December 2013 /Accepted: 18 September 2014# Springer-Verlag Wien 2014

Abstract An existing streamflow downscaling model(SDM (original) ), was modified with the outputs of a precipitationdownscaling model (PDM) and an evaporation downscalingmodel (EDM) as additional inputs, for improving streamflow projections. For this purpose, lag 0, lag 1 and lag 2 outputs of PDM were individually introduced to SDM (original) as additionalinputs, and then it was calibrated and validated. Performances of the resulting modified models were assessed using Nash-Sutcliffe efficiency (NSE) during calibration and validation. It was found that the use of lag 0 precipitation as an additionalinput to SDM (original) improves NSE in calibration and valida-tion. This modified streamflow downscaling model is calledSDM (lag0_preci) . Then lag 0, lag 1 and lag 2 evaporation of EDM were individually introduced to SDM (lag0_preci) as addi-tional inputs and it was calibrated and validated. The resultingmodels showed signs of over-fitting in calibration and under-fitting in validation. Hence, SDM (lag0_preci) was selected as the best model. When SDM (lag0_preci) was run with observed lag 0 precipitation, a large improvement in NSE was seen. This proved that if precipitation produced by the PDM can accuratelyreproduce the observations, improved precipitation predictionswill produce better streamflow predictions.

1 Introduction

General Circulation Models (GCMs) are considered as themost widely used tools for projection of global climate into

the future (Bastola and Misra 2013 ). GCMs use the funda-mentals of physics for describing the global climate. Whenforced with plausible scenarios of future greenhouse gas(GHG) concentrations, they are capable of projecting theglobal climate hundreds of years into the future (Tripathiet al. 2006 ). The spatial resolution of a current GCM is inthe order of a few hundred kilometres and GCMs are capableof correctly simulating the global and continental climate.However, since GCMs coarsely represent the topographyand land use, they are unable to correctly simulate the catch-ment scale climate. Therefore, statistical and dynamic down-scaling techniques are used for translating the coarse scaleinformation in the GCM outputs to catchment scalehydroclimatic information (e.g. Hertig and Jacobeit ( 2008 );Can et al. ( 2011 ); Samadi et al. ( 2012 ); Flint and Flint (2012 )).

In dynamic downscaling, a Regional Climate Model(RCM) is nested in a GCM for simulation of regional climate(Murphy 1998 ). In this process, initial and lateral boundaryconditions to the RCM are provided by the GCM at multiplevertical and horizontal levels (Wilby and Fowler 2011 ). In theRCM, the information provided by the GCM is processedusing the fundamentals of physics of the atmosphere, andhence regional patterns of climate variables are generated(Rummukainen 2010 ). When the difference of the spatialresolutions between the GCM and the RCM is high, multiplenesting which involves downscaling starting from a larger domain with coarser spatial resolution and progressively mi-grating to smaller domains with finer spatial resolution (untilthe desired spatial resolution is attained) is performed (Rojas2006 ). RCMs are also to simulate the climate over a catchment at a spatial resolution of a few kilometres (e.g. 5 50 km).Dynamic downscaling techniques can produce spatially con-tinuous fields of climatic variables while maintaining thespatial coherence (Maurer et al. 2008 ). Since RCMs operateat relatively higher spatial resolutions, the improved

D. A. Sachindra ( * ) : F. Huang : A. Barton : B. J. C. Perera College of Engineering and Science, Victoria University, FootscrayPark Campus, P.O. Box 14428, Melbourne, Victoria 8001, Australia e-mail: [email protected]

A. BartonFederation University, PO Box 663, Ballarat, Victoria 3353,Australia

Theor Appl ClimatolDOI 10.1007/s00704-014-1288-7


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representation of topographic features such as mountains,water bodies and other land use features aid in the simulationof local climate more accurately (Rummukainen 2010 ;Horvath et al. 2012 ). However, RCMs suffer from high computational costs associated with their complex physics-basedstructure (Haas and Pinto 2012 ). The computational cost of a dynamic downscaling exercise largely increases with the spa-tial resolution of the RCM and the extent of the domains (Qianand Zubair 2010 ). Owing to the high computation costs asso-ciated with dynamic downscaling, use of multiple GCMs andGHG emission scenarios in a dynamic downscaling studymay not be always feasible. Also, the simulations produced by a RCM during its spin-up period (time taken to attainclimate equilibrium) which can be in the order of a fewmonths or a few years (Denis et al. 2002 ) are discarded.

Statistical downscaling techniques are dependent on thestatistical relationships developed between the GCM outputsand the catchment-scale hydroclimatic variables (Fowler et al.2007 ). Owing to the simplicity, statistical downscaling tech-niques are associated with much less computational costs(Bedia et al. 2013 ). Statistical downscaling techniques can be used to produce projections of hydroclimatic variables suchas streamflows, leaf wetness etc. which are not simulated byGCMs. Also, unlike dynamic downscaling, statisticalmethods enab le downsca l ing o f GCM outpu t s tohydroclimatic variables at specific points in the catchment.On the other hand, statistical downscaling techniques are not able to produce spatially continuous fields of hydroclimaticvariables. For proper calibration and validation of a statisticaldownscaling model, long series of observations are preferred.This is because a long series of observations can possiblyexpose the downscaling model to the full variance of the localscale climate and make the downscaling model more robust (Sachindra et al. 2014a ). In statistical downscaling, it is as-sumed that the statistical relationships determined between thelarge-scale atmospheric variables (e.g. GCM outputs, reanal-ysis outputs) and catchment scale climatic variables (e.g. precipitation) for the past climate are also valid for the chang-ing climate in the future (Benestad et al. 2008 ). This assump-tion is similar to that of the validity of parameterisationschemes in the RCMs for future climate. According to Wilbyet al. (2004 ), statistical downscaling techniques can be classi-fied into three categories; (1) regression techniques (e.g.Tareghian and Rasmussen 2013 ), (2) weather classificationtechniques (e.g. Gutirrez et al. 2013 ) and (3) weather gener-ation techniques (e.g. Wilks 1999 ). Regression based statisti-cal downscaling techniques are regarded as the most widelyused statistical downscaling techniques (Nasseri et al. 2013 ).

Reliable forecasts of streamflows are useful in the manage-ment of water resources in a catchment. These management activities include flood control, water supply, hydroelectricitygeneration and also the maintenance of environmental flows.Therefore, it is realised that the projection of catchment scale

streamflows into the future under changing climate is of highimportance.

Landman et al. ( 2001 ) used bias-corrected moisture andcirculation outputs of a GCM in canonical correlation analysis(CCA)-based statistical downscaling model for simulation of seasonal streamflows at 12 locations in South Africa. Cannonand Whitfield ( 2002 ) used multi-linear regression (MLR) andartificial neural networks (ANN) for downscaling GCM outputs to 5-day average streamflows at 21 locations in Canada.They used variables representative of the atmospheric circula-tions at the Earth s surface and the mid troposphere, tempera-ture at lower troposphere and boundary layer moisture vari-ables. In that study, it was commented that ANN was morecapable compared to MLR in downscaling GCM outputs tostreamflows. Hence, it was realised that non-linear techniquesare able to better capture the complex association between theatmospheric variables and streamflows. Ghosh and Mujumdar (2008 ) used support vector machine (SVM) and relevancevector machine (RVM) regression techniques for downscalingGCM outputs to monthly streamflows at a site in India. Theyused principal component analysis (PCA) for derivation of PCsfrom GCM outputs and applied fuzzy c-mean clustering toclassify the PCs into classes before introducing them to thedownscaling models. It was found that the RVM-based down-scaling model was less prone to over-fitting unlike the SVM- based downscaling model which suffered severe over-fitting.Tisseuil et al. ( 2010 ) employed ANN, generalized additivemodels, aggregated boosted trees andgeneralized linear modelsfor downscaling NCEP/NCAR reanalysis and GCM outputs todaily streamflows, at 51 stations in France. In that study, usinghierarchical ascending cluster (HAC) analysis, predictor vari-ables were separated into several clusters based on their simi-larity, and then the first PC of each cluster was used as inputs tothe downscaling model. It was found that aggregated boostedtrees (non-linear technique) were more efficient in downscalinglarge-scale atmospheric variables to streamflows. Sachindra et al. (2013 ) used least square support vector machine regres-sion (LS-SVM-R) and MLR to downscale NCEP/NCAR re-analysis outputs to monthly streamflows at a station in north-western Victoria, Australia. Unlike in the former streamflowdownscaling studies, they used soil moisture content as aninput to the downscaling model and found that it is highlyinfluential on streamflows. Furthermore they commented that both LS-SVM-R and MLR produced very comparable perfor-mances. However, both techniques were unable to simulate theextremes of streamflow.

The main advantage of downscaling GCM outputs directlyto streamflows in a catchment is that it allows the quick estimation of streamflows without the need of a hydrologicmodel. However, direct downscaling of GCM outputs tostreamflows can only be used for simulation of unregulatedflows in a catchment. Since many complex hydrological pro-cesses (e.g. infiltration) are not explicitly modelled in a direct

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streamflow downscaling exercise, errors to streamflow simu-lations may be introduced.

Precipitation and evaporation are two highly influentialclimatic variables on the availability of water resources in a catchment. Precipitation is regarded as the main driver of streamflow in many catchments. In past literature, there aremany case studies on downscaling GCM outputs to precipi-tation at the catchment scale (e.g. Tripathi et al. ( 2006 ),Anandhi et al. ( 2008 ), Timbal et al. ( 2009 ), Jeong et al.(2012 ), Sachindra et al. ( 2014a )). Evaporation is one of themany processes responsible for the loss of water from a catchment. Some examples for downscaling GCM outputsto evaporation are found in the studies of Timbal et al.(2009 ), Yang et al. ( 2012 ), Goyal and Ojha ( 2012 ).

As stated earlier, Sachindra et al. ( 2013 ) detailed the de-velopment of a s ta t is t ical model for downscal ing NCEP/NCAR reanalysis outputs direct ly to monthlystreamflows at a location in north-western Victoria, Australia.The current paper provides the details of further potentialimprovements to that streamflow downscaling model and alsothe streamflow projections produced into the future using theimproved model. As stated previously, precipitation and evap-oration are influential on the streamflows in a catchment. Inthis study, outputs of downscaling models for precipitationand evaporation at a station located close to the streamflowsite were used as additional inputs to the original streamflowdownscaling model, for improving its performances. The performances of the new streamflow downscaling model werecompared with those of the original streamflow downscalingmodel graphically and numerically. Following the improve-ments to the streamflow downscalingmodel, using the outputsof HadCM3, ECHAM5 and GFDL2.0 pertaining to A2 andB1 GHG emission scenarios, the streamflow at the site of interest was projected into the future period 2000 2099.

Smith and Chandler ( 2010 ) stated that HadCM3, ECHAM5and GFDL2.0 are capable in correctly simulating the precipita-tion over Australia and also able to produce accuratesimulationsof El Nio Southern Oscillation (ENSO). They also argued that a GCM which can correctly simulate precipitation should beable to simulate other climatic variables with a good degree of accuracy. Therefore, for the present study, the outputs of HadCM3, ECHAM5 and GFDL2.0 were used.

In this paper, Section 2 details the study area and the data used in this study. Section 3 provides the details of the genericmethodology. The application of this methodology is de-scribed in Section 4 with results. Finally, Section 5 presentsthe summary of the study and conclusions.

2 Study area and data

The operational area of Grampians Wimmera Mallee Water Corporation (GWMWater) is located in the north-western

region of Victoria, Australia. The streamflow site consideredin this study (same as in Sachindra et al. 2013 ) is located closeto the southern boundary of the operational area of GWMWater. The projection of streamflow in the operationalarea of GWMWater (about 62,000 km 2) into the future is animportant task, as the water supply system located in this area provides water to a large number of domestic and industrialcustomers, and to the surrounding environment. Figure 1shows the location of the streamflow site and its catchment in the operational area of GWMWater.

The streamflow site (Lat. 37.17, Lon. 142.54) consid-ered in this study is located on the Fyans Creek at LakeBellfield (refer to Fig. 1). In other words, this site representsthe inflow to Lake Bellfield (GWMWater 2011a ). LakeBellfield provides water to nearby towns of Halls Gap andPomonal, and also many recreational activities such as swim-ming, fishing and boating that take place at this lake. Thecatchment area demarcated by this streamflow site is about 96 km 2 (GWMWater 2011a ) and it is located within theGrampians national park (GWMWater 2011b ). Since thecatchment area is located within a national park, the land usehas remained stationary over the last few centuries and also it is expected to remain constant in the future. The catchment of Lake Bellfield contains soils composed of mainly sandstonesand some mudstones (Cayley and Taylor 1997 ). The inflow toLake Bellfield is usually of good quality with low salinity andturbidity (Sachindra et al. 2013 ). The inflow to Lake Bellfield provided by the Fyans Creek is influenced by some diversionsinto the catchment and also some extractions out of it. Theunregulated inflow (naturalised) to Lake Bellfield have beencomputed by Sinclair ( 2004 ). There is no weather observationstation located within the catchment of the Bellfield Lake. Theclosest weather observation station at Halls Gap post office(Lat. 37.14, Lon. 142.52), which is situated about 10 kmoutside the boundary of the catchment, was selected as thestation representative of the climate of this catchment (refer toFig. 1).

In order to provide inputs to the statistical downscalingmodels (precipitation, evaporation and streamflow) for their calibration and validation, monthly reanalysis outputs of Na-tional Centers for Environmental Predictions/National Center for Atmospheric Research (NCEP/NCAR) were obtainedfrom the website of National Oceanic and AtmosphericAdministration/Earth System Research Laboratory(NOAA/ESRL) Physical Sciences Division at http://www.esrl.noaa.gov/psd/ , for the period 1950 2010. For calibrationand validation of the precipitation and evaporationdownscaling models, observations of monthly precipitationand evaporation of the station at Halls Gap post office wereobtained from the SILO database of Queensland ClimateChange Centre of Excellence at http://www.longpaddock.qld.gov.au/silo/ for the period 1950 2010. For calibrationand validation of the streamflow downscaling model, the

Potential improvements to statistical downscaling of streamflows
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unregulated monthly streamflow data of the site (inflow toLake Bellfield) considered in this study were obtained fromGWMWater for the period 1950 2010.

In order to identify the bias in the outputs of downscalingmodels and for correction of bias, past observations of month-ly precipitation, evaporation and streamflows have to bereproduced. For this purpose, the twentieth century climateexperiment (20C3M) outputs of HadCM3, ECHAM5 andGFDL2.0 were extracted from the website of the Programmefor Climate Model Diagnosis and Inter-comparison (PCMDI)at https://esgcet.llnl.gov:8443/index.jsp , for the period 1950

1999. For validation of the bias-correction, HadCM3 outputsfor COMMIT GHG emission scenario were also obtainedfrom the same web site for the period 2000 2099.

For projection of precipitation and evaporation, and hencestreamflow into the future, the outputs of HadCM3, ECHAM5and GFDL2.0 pertaining to the A2 and B1 GHG emissionscenario were also obtained from the PCMDI ( https://esgcet.llnl.gov:8443/index.jsp ), for the period 2000 2099.

3 Generic methodology

In this study, a statistical model that was developed for down-scaling reanalysis outputs to monthly streamflows was mod-ified for improving its performances. For this purpose, twoadditional separate statistical downscaling models (one for

precipitation and the other for evaporation) were developedwith reanalysis outputs for downscaling them to monthly precipitation and evaporation at a station which is locatedclose to the streamflow site. The outputs of these two down-scaling models were introduced to the streamflow downscal-ing model to enhance its performances. The development of the original model for downscaling large-scale atmosphericvariables to monthly streamflows using the MLR techniquewas detailed in Sachindra et al. ( 2013 ). This originalstreamflow downscaling model is referred to as SDM (original)throughout this paper.

3.1 Downscaling models for precipitation and evaporation

Sachindra et al. ( 2014a ) found that the MLR technique wascapable of successfully capturing the relationships betweenthe reanalysis outputs and precipitation observations. Hence,in this study, downscaling models for monthly precipitationand evaporation were built using the MLR technique. The precipitation downscaling model and evaporation downscal-ing model used in this study are referred to as PDM and EDMthroughout this paper. The procedure employed in this studyfor the development of PDM and EDM was quite similar tothat used in developing SDM (original) using MLR. For extrac-tion of large-scale climate information, the same atmosphericdomain used in the development of SDM (original) was selected.

Fig. 1 Streamflow site and itscatchment within operational area of GWMWater

https://esgcet.llnl.gov:8443/index.jsphttps://esgcet.llnl.gov:8443/index.jsphttps://esgcet.llnl.gov:8443/index.jsphttps://esgcet.llnl.gov:8443/index.jsphttps://esgcet.llnl.gov:8443/index.jsphttps://esgcet.llnl.gov:8443/index.jsp


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Two pools of probable predictors were selected for PDMand EDM by considering the past literature and fundamentalsof hydrology. These probable predictors were the variablesthat are likely to influence precipitation and evaporation.Potential predictors are the subsets of probable predictorswhich highly influence the predictand of interest. The poten-tial predictors were extracted from the pools of probable predictors for each calendar month for each predictand sepa-rately. This was performed because the set of predictors influ-ential on a certain predictand can vary with the seasonalchanges in the atmosphere (Karl et al. 1990 ).

To extract potential predictors from the pools of probable predictors, the Pearson correlation coefficient (Pearson 1895 )was used. For each predictand, the record of observations andthe reanalysis data pertaining to the probable predictors weresplit into 20-year time slices. Then the Pearson correlationcoefficients between the observations of the predictand of interest and the reanalysis data pertaining to probable predic-tors were computed for all 20-year time slices and the whole period of the records. This procedure was performed at eachgrid point in the atmospheric domain and for each calendar month separately. The probable predictors which showedstatistically significant ( p 0.05) good correlations with theobservations in all time slices and the whole period of thestudy were selected as the potential predictors for each calen-dar month for each predictand.

The first two thirds of the observations of each predictandand the reanalysis data pertaining to the potential predictors,for each calendar month, were allocated for calibration of thedownscaling models. The rest of these data sets were used for validation of the downscaling models. The reanalysis data for both calibration and validation phases of the downscalingmodels were standardised with their means and the standarddeviations corresponding to the calibration period. Initially,the standardised reanalysis data of the potential predictor which showed the best correlation with the observations of the predictand over the whole period of the study was intro-duced to the downscaling model. Then, by minimising thesum of squared errors between the model outputs (e.g. pre-cipitation) and the observations, the optimum values of thecoefficient and the constant of the linear regression equationwere determined. The downscaling model was then validated by introducing the rest of the reanalysis data of that potential predictor to the model. During the validation, the optimumvalues of the coefficient and the constant determined in thecalibration phase of the downscaling model were kept con-stant. The model performances in the calibration and valida-tion phases were measured using the Nash-Sutcliffe efficiency(NSE) (Nash and Sutcliffe 1970 ). Thereafter, the next best potential predictors were introduced to the downscaling mod-el, one at a time, and the model calibration and validation were performed as stated previously. This stepwise addition of po te nt ia l pr ed ic to rs wa s cont in ue d un ti l th e mo de l

performance in validation reached a maximum in terms of the NSE. The maximum performance in the validation wasconsidered in selecting the best model for each calendar month for each predictand, as it aided in avoiding any modelswhich displayed over-fitting in calibration and under-fitting invalidation. This procedure yielded the best sets of potential predictors and the optimum downscaling models for eachcalendar month of each predictand. Note that all downscalingmodels detailed in this paper had common calibration andvalidation periods.

3.2 Potential improvements to streamflow downscaling model

Initially, the precipitation and evaporation outputs of the PDMand the EDM pertaining to both calibration and validation phases of the models were standardised for each calendar month using the means and the standard deviations of theobservations of the calibration period. Then, for each calendar month, the standardised lag 0 precipitation output of the PDM pertaining to its calibration phase was introduced to theSDM (original) . Following the introduction of the standardisedlag 0 precipitation, this model was calibrated, and the opti-mum values for its parameters (coefficients and constants of MLR equations) were found for each calendar month. TheSDM (original) modified with lag 0 precipitation is calledSDM (lag0_preci) . In the validation of SDM (lag0_preci) , the opti-mum values of the constants and the coefficients of MLR equa t ions de te rmined in the ca l ib ra t ion phase o f SDM (lag0_preci) were kept fixed. Then, the standardised lag 0 precipitation outputs of the PDM pertaining to the validation phase were introduced to SDM (lag0_preci) for reproducing theobserved streamflow for that period. The performance of SDM (lag0_preci) was monitored using the NSE and scatter plotsin the calibration and validation phases.

Similarly, SDM (original) was again calibrated and validated by separately introducing the standardised lag 1 and lag 2 precipitat ion outputs of the PDM, yielding modifi edstreamflow downscaling models SDM (lag1_preci) andSDM (lag2_preci) , respectively. Then, considering the NSEs inva l ida t ion , the bes t mode l ou t o f SDM ( l a g 0 _ p r e c i ) ,SDM (lag1_preci) and SDM (lag2_preci) was selected for the next step of the model improvement. This best model is calledSDM (lag i _preci) .

In the next step, SDM (lag i _preci) was further modified byindividually introducing the standardised lag 0, lag 1 and lag 2evaporation outputs of the EDM pertaining to the calibration phase. This yielded SDM (lag i _preci_ & _lag0_evap) (i.e. SDM (lag i _- preci) with lag 0 evaporation), SDM (lag i _preci_ & _lag1_evap) (i.e.SDM (lag i _pr eci ) with lag 1 evaporation) and SDM (lag i _- preci_ & _lag2_evap) (i.e. SDM (lag i _preci) with lag 2 evaporation).The optimum values of the coefficients and constants of MLR equations were found for each calendar month in the calibra-tion of above models, and then they were validated using the



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standardised lag 0, lag 1 and lag 2 evaporation outputs of theEDM pertaining to the validation phase as described previ-ously. The performances of these three SDMs were monitoredusing NSE and scatter plots, in their calibration and validation phases. The best SDM was selected based on the NSE in thevalidation phase. This best model is referred to as SDM (lag i _- preci_ & _lag j _evap) , where i and j refer to lags of precipitation andevaporation. The above stepwise modification process appliedto SDM (original) is graphically illustrated in Fig. 2.

Another SDM was developed (calibrated and validated) byintroducing observed lag i precipitation and lag j evaporationto SDM (original) corresponding to the best SDM identified previously. The lags i and j refer to lags of precipitation andevaporation used in the best SDM. This downscaling modeldeveloped using the observed lag i precipitation and lag j evaporation as additional inputs to SDM (original) is calledSDM (original+OBS) . It allowed the quantification of the maxi-mum potential improvement to SDM (original) with observa-tions of precipitation and evaporation. Numerical and graph-ical performance comparisons between the SDM (original) ,SDM (lag i _preci_ & _lag j _evap) and SDM (original+OBS) were per-formed. This enabled the quantification of the actual and potential improvements to SDM (original) following the modifi-cations made in this study.

3.3 Reproduction of precipitation, evaporation and hencestreamflow using GCM outputs and bias-correction

Once the PDM and the EDM were developed, they were runwith the 20C3M outputs of each GCM. For this purpose, the20C3M outputs of each GCM corresponding to potential predictors used in the PDM and EDM were standardised withthe means and the standard deviations of reanalysis data relevant to the calibration phase of the downscaling models.The reproduction of precipitation and evaporation using the20C3M outputs of each GCM enabled the quantification of bias introduced to precipitation and evaporation simulations by each GCM and its subsequent correction. Once precipita-tion and evaporation observations for the past werereproduced by the PDM and the EDM using 20C3M outputsof the GCMs, the statistics of reproduced precipitation andevaporation were compared with those of observations for thequantification of bias. Then, the equidistant quantile mapping(EQM) technique (Li et al. 2010 ) was used to correct the bias

in precipitation and evaporation reproduced by PDM andEDM.

For the application of the EQM technique, empirical cu-mulative distribution functions (CDFs) were derived from theoutputs of PDM and EDM pertaining to the past climate(using 20C3M outputs of each GCM) and also from the precipitation and evaporation observations, for each calendar month separately. Then, for each calendar month, the CDFsderived from the outputs of PDM and EDM for the past climate were mapped onto the CDFs developed from the precipitation and evaporation observations respectively. Inthis mapping process, first, for a given value of the predictandof interest (e.g. precipitation) downscaled by the model (e.g.PDM), the corresponding CDF value was found from theCDF derived from the values of that predictand of interest downscaled by the model. Then pertaining to that CDF value,the value of the predictand of interest was found from the CDFderived from the past observations. This value of the predictand of interest obtained from the CDF derived fromthe past observations is the bias-corrected value of the predictand downscaled by the model. The above processwas applied to all values of the predictand of interest down-scaled by the model and it yielded the bias-corrected CDF.The application of the EQM technique allowed the correctionof bias in all statistical moments of precipitation and evapo-ration downscaled by the PDM and the EDM for the past climate with GCM outputs. A detailedapplication of the EQMtechnique is found in Li et al. ( 2010 ), Salvi et al. ( 2011 ) andSachindra et al. ( 2014b ).

The time series of precipitation and evaporation were de-rived from their bias-corrected CDFs and for each calendar month precipitation and evaporation data were standardisedusing the means and the standard deviations of their observa-tions relevant to the calibration period of the downscalingmodel. The 20C3M data relevant to the potential predictorsused in the SDM (original) were also standardised with themeans and the standard deviations of reanalysis data of thecalibration phase of the downscaling models. Then, theSDM (lag i _preci_ & _lag j _evap) was run with the bias-corrected outputs of the PDM and the EDM produced in the above stepalong with 20C3M outputs of each GCM pertaining to theinputs to SDM (original) . The EQM technique was used tocorrect the bias in the streamflow downscaled by SDM (lag i _- preci_ & _lag j _evap) , run with the bias-corrected outputs of thePDM and the EDM along with 20C3M outputs of each

SDM (original) SDM (lag i _preci)Select bestmodel

Lag i (i = 0, 1, 2) precipitation

SDM (lag i _preci_&_lag j _evapo)

Lag j ( j = 0, 1, 2)evaporation

Select bestmodel

Fig. 2 Flow chart for modification of SDM (original)



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GCM. For this purpose, the same procedure used for thecorrection of bias in the outputs of PDM and EDM wasemployed.

For validating the performances of the EQM technique for precipitation and evaporation, statistics of bias-corrected pre-cipitation and evaporation downscaled using the outputs of a GCM pertaining to the COMMIT GHG emission scenario for the future climate were compared with those of observed precipitation and evaporation. For validatingthe performancesof the EQM technique for streamflow, statistics of bias-corrected streamflow downscaled using the outputs of theGCM and the bias-corrected precipitation and evaporationrelevant to the COMMIT GHG emission scenario were compared with those of observed streamflow. The COMMITGHG emission scenario assumes that the GHG concentrationsobserved at the end of the twentieth century (CO 2 concentra-tion in the atmosphere 370 ppm) will remain the samethroughout the twenty-first century. Assuming that the risein the GHG concentrations in the atmosphere in the latter half of the twentieth century is small, it can be argued that theclimate simulated by a GCM over the latter half of the twen-tieth century is in close agreement with the climate projectedinto the future by the same GCM under the COMMIT GHGemission scenario (argument proven by Sachindra et al.(2014b )).

The GCM outputs pertaining to the COMMIT GHG emis-sion scenario were standardised using the means and thestandard deviations of reanalysis outputs. Then, PDM andEDM were run with the COMMIT GHG emission scenariooutputs of the GCM. Thereafter, the empirical CDFs werederived from the precipitation and evaporation time series projected into the future under the COMMIT GHG emissionscenario. Then for each calendar month, the difference be-tween the CDF of the predictand of interest (precipitation or evaporation) produced into the future under the COMMITGHG emission scenario and the CDF simulated for the past corresponding to 20C3M was added to the CDF of the obser-vations of the predictand. This process yielded the bias-corrected CDFs of precipitation and evaporation for the futureclimate characterised by the COMMIT scenario. Followingthis bias-correction, for the validation of the EQM technique,the statistics of precipitation and evaporation downscaledfrom GCM outputs for COMMIT GHG emission scenariowere compared with those of past observations.

The bias-corrected time series of precipitation and evapo-ration were standardised with the means and the standarddeviations of observations relevant to the model calibration period for each calendar month. The GCM outputs of theCOMMIT GHG emission scenario for SDM (lag i _preci_ & _lag j _-evap) were also standardised with the corresponding means andstandard deviations of reanalysis outputs of the model calibra-tion period for each calendar month. Then, SDM (lag i _- preci_ & _lag j _evap) was run with these bias-corrected outputs of

the PDM and the EDM and the GCM outputs of COMMITGHG emission scenario. The streamflow produced in theabove step was bias-corrected using the EQM technique,following the same procedure used for the correction of biasin precipitation and evaporation produced by the downscalingmodel for the COMMIT GHG emission scenario. Then, thestatistics of bias-corrected streamflow produced by SDM (lag i _- preci_ & _lag j _evap) for the COMMIT GHG emission scenariowere compared with those of past observed streamflow. Thiscomparison of statistics enabled the assessment of effective-ness of the EQM technique (or validation of EQM) incorrecting the bias in streamflow projections.

Figure 3 shows the main steps involved in the applicationand validation of the bias-correction for precipitation, evapo-ration and streamflows in a flow chart. In that flow chart, thesteps shown above the dashed line (in dark print black) refer to the application of the bias-correction to precipitation, evap-oration and streamflows for the past climate. The steps shown below the dashed line (in light print blue) refer to the vali-dation of the bias-correction with COMMIT GHG emissionscenario and the same set of steps were followed for the bias-correction of projections of precipitation, evaporation andstreamflows produced into the future with another GHG emis-sion scenario (e.g. A2) as described in the next section.

3.4 Projection of precipitation, evaporation and hencestreamflow into the future, and bias-correction

The outputs of each GCM for the PDM and EDM pertaining tofuture climate (e.g. A2, B1 GHG emission scenario) werestandardised using the corresponding means and standard devi-ations of reanalysis outputs relevant to the model calibration period for each calendar month. Then, the PDM and the EDMwere run with these standardised outputs of each GCM for thefuture climate. Following the procedure described in Section 3.3used for the validation of effectiveness of the EQM technique(refer to Fig. 3), it was used to correct the bias in the precipitationand evaporation projected into the future. The bias-correctedtime series of precipitation and evaporation for future werestandardised with the means and the standard deviations of observations relevant to the model calibration period for eachcalendar month. The outputs of each GCM for the SDM (lag i _- preci_ & _lag j _evap) for future climate were standardised using thecorresponding means and standard deviations of reanalysis outputs relevant to the model calibration period.

The bias-corrected standardised outputs of PDM and EDMfor future climate along with other standardised outputs of eachGCM were introduced to SDM (lag i _preci_ & _lag j _evap) for the projection of streamflow at the point of interest into the future.This procedure was performed for each calendar month sepa-rately. Following the same procedure used in correcting thebiasin the projections of precipitation and evaporation for theCOMMIT GHG scenario (refer to Section 3.3), bias in the



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streamflow projected into the future by SDM (lag i _preci_ & _lag j _-evap) was corrected using the EQM technique. Then, the sea-sonal statistics of observed streamflow were compared withthose of streamflow projected into the future. Also, the ensemble average streamflow time series was computed from thestreamflow outputs of SDM (lag i _preci_ & _lag j _evap) when it wasrun with the outputs of each GCM and the outputs of PDM andEDM. The probability exceedance curves for projected ensemble average streamflow and observed streamflows were compared for each season for the assessment of possible changes inthe streamflow regime in the future.

4 Application

4.1 Downscaling models for precipitation and evaporation

4.1.1 Domain and predictor selection for downscaling models

Before developing the downscaling models, an atmosphericdomain spanning over the study area was defined. This atmo-spheric domain spanned over the longitudes 135 150 E andlatitudes 30 42.5 S. It included seven and six grid points inthe longitudinal and latitudinal direction respectively. The

PDM/EDM

20C3M GCMoutputs

Application

of EQM tocorrect bias

SDM (lag0_preci)

20C3M GCMoutputs

CDF of precipitation/

evaporation for pastclimate

Bias-corrected CDF of precipitation/


CDF of streamflow for past climate

Bias-corrected CDF of streamflow for past

climate

Applicationof EQM tocorrect bias

Bias-corrected timeseries of precipitation/


PDM/EDM

COMMIT GCMoutputs/any future

scenario


SDM (lag0_preci)

COMMIT GCMoutputs/any future

scenario

CDF of precipitation/evaporation for

COMMIT/any futurescenario

Bias-corrected CDF of

precipitation/evaporation for COMMIT/any future scenario

CDF of streamflowfor COMMIT/ any

future scenario

Bias-corrected CDF of streamflow for

COMMIT/ any futurescenario


Bias-corrected timeseries of precipitation/

evaporation for COMMIT/any future

scenario

Difference betweentwo CDFs (past and future) Bias-corrected time

series of streamflowfor past climate

CDF of observed precipitation/


CDF of observedstreamflow for past

climate

Difference between two

CDFs

Bias-corrected timeseries of streamflowfor COMMIT/ any

future scenario

Application of bias-correction

Validation of bias-correction

Fig. 3 Main steps involved inapplication and validation of bias-correction



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spatial resolution of the atmospheric domain was selected as2.5 in both directions in order to be consistent with the spatialresolution of NCEP/NCAR reanalysis outputs. This atmo-spheric domain is shown in Fig. 4.

The predictor selection, the calibration and validation, the bias-correction and the projection of precipitation into thefuture using a precipitation downscaling model at the HallsGap post office was detailed in the studies by Sachindra et al.(2014a , b). That precipitation downscaling model was used inthe current study as the PDM. Therefore, for more detailsabout the PDM used in this study, readers are referred toSachindra et al. ( 2014a , b). The details on the EDM developedin this study are provided in this section.

Once the atmospheric domain was defined, a pool of prob-able predictors for evaporation was selected. Timbal et al.(2009 ) used meteorological analogues for downscalingGCM outputs to daily precipitation, pan evaporation, mini-mum temperature, maximum temperatureand dew point temperature over the southern half of Australia. Since the present study area is also located in the southern region of Australia,the predictors used in that study for downscaling evaporationwere also used in the present study.

The NCEP/NCAR reanalysis data pertaining to the probable predictors and the observations of evaporation at the Halls Gap post office for the period 1950 2010 were split into three timeslices; 1950 1969, 1970 1989 and 1990 2010. Following the procedure detailed in Section 3.1, potential predictors for evap-oration for each calendar month were identified from the pool of probable predictors. Then, the NCEP/NCAR reanalysis data pertaining to the potential predictors and the observations of

evaporation were separated into two chronological groups;1950 1989, 1990 2010. The former group of data was usedfor the calibration, while the latter group was used for thevalidation of the downscaling model. As described in Sec-tion 3.1, the MLR-based statistical downscaling models weredeveloped for each calendar month for evaporation, and the best sets of potential variables were identified. The same procedurewas practised by Sachindra et al. ( 2013 , 2014a ) in developingthe SDM (original) and PDM, respectively. The best sets of poten-tial predictors identified for precipitation and evaporation for each calendar month are shown in Table 1.

Table 2 shows the best sets of potential predictors used inSDM (original) for each calendar month with their gird locations. Note that in December, volumetric moisture content in soil layer 10 200 cm at grid points (4,3) and (4,4) used as inputs toSDM (original) were removed from the set of input. This was because the volumetric moisture content in soil layer 10

200 cm at grid points (4,3) and (4,4) simulated by HadCM3indicated presence of large bias in its variance (in comparison to NCEP/NCAR reanalysis data). SDM (original) was re-calibratedand validated only for December without the volumetric mois-ture content in soil layer 10 200 cm at grid points (4,3) and (4,4),and it was found that the removal of the above two variablesfrom the model does not change its performance significantly.

4.1.2 Performances of precipitation and evaporationdownscaling models

The performances of the PDM and the EDM were monitoredduring their calibration and validation periods using statistical

Fig. 4 Atmospheric domain for downscaling



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and graphical techniques. Table 3 shows the statistics of theobserved and EDM reproduced evaporation for the calibrationand validation period. Performances of PDM were detailed inSachindra et al. ( 2014b , c).

According to Table 3, it was seen that the EDM was able toreproduce thestatisticsof observed evaporation with good degreeof accuracy in both calibration and validation periods. EDMshowed NSEs of 0.97 and 0.98 in its calibration and validation periods respectively, and PDM displayed NSEs of 0.74 and 0.70for the same periods (Sachindra et al. 2014b ). In general,

precipitation shows high levels of fluctuations than evaporation(which usually displays smooth regular variations over time).This allows downscaling large-scale atmospheric variables toevaporation with higher degree of accuracy in comparison to precipitation. Overall, both PDM and EDM showed good per-formances in the calibration and validation phases.

4.2 Potential improvements to streamflow downscaling model

As described in Section 3.2, the SDM (original) was modifiedusing the precipitation and evaporation reproduced by PDM

Table 1 Best sets of potential predictors for each calendar month of PDM and EDM

Month Potential variables used in the PDM and EDM with grid locations

Precipitation Evaporation

January Surface precipitation rate {(3,3),(4,4)} 1000 hPa air temperature {(3,4)}

1000 hPa specific humidity {(3,3),(3,4),(4,4)}

850 hPa meridional wind {(2,6),(3,5),(3,6)}850 hPa relative humidity {(1,2)}

2 m specific humidity {(3,3),(3,4)}

February Surface precipitation rate {(3,4),(4,4),(4,5)} 1000 hPa relative humidity {(3,3),(4,4)}

925 hPa relative humidity {(3,3),(3,4),(4,4),(4,5)}

March Surface precipitation rate {(3,3),(3,4),(3,5),(4,3),(4,4),(4,5),(4,6)} 1000 hPa air temperature {(2,5)}

April 850 hPa relative humidity {(4,3),(4,4)} 925 hPa relative humidity {(2,1)}

Surface precipitation rate {(4,3)}

May Surface precipitation rate {(4,4),(5,5)} 1000 hPa relative humidity {(4,4)}

850 hPa geopotential height {(4,3)}

June Surface precipitation rate {(3,2),(3,3),(4,2),(4,3),(4,4),(4,5)} 1000 hPa relative humidity {(4,4)}

Mean sea level pressure {(4,3),(5,3)}

850 hPa zonal wind {(2,4)}Surface pressure {(4,3),(5,3),(5,4)}

July 850 hPa zonal wind {(1,3),(1,4)} 1000 hPa relative humidity {(2,2),(2,3),(3,4)}

850 hPa geopotential height {(4,3),(4,4),(4,5)} 925 hPa relative humidity {(2,3),(3,4)}

Surface precipitation rate {(1,4),(1,5),(1,6),(2,5)}

August Surface precipitation rate {(4,3),(5,4),(5,5)} 1000 hPa relative humidity {(3,1)}

925 hPa relative humidity {(2,3),(3,3)}

September Surface precipitation rate {(2,1),(2,2),(3,2),(3,3), (3,5),(4,2),(4,3),(4,4),(4,5)} 1000 hPa relative humidity {(2,2),(3,2),(3,3)}

850 hPa relative humidity {(3,3)}


October Surface precipitation rate {(3,2),(4,2),(4,3),(4,4)} 700 hPa geopotential height {(1,1)}



November 850 hPa relative humidity {(3,2),(3,3)} 850 hPa air temperature {(2,5),(3,5)}

Surface precipitation rate {(4,3),(4,5)} 700 hPa geopotential height {(2,3),(2,4),(2,5)}

December Surface precipitation rate {(2,1),(3,2),(4,3),(4,4),(5,5)} 1000 hPa air temperature {(2,2)}

850 hPa relative humidity {(3,2)} 925 hPa relative humidity {(3,2)}

Surface skin temperature {(2,1),(2,2),(2,3),(3,5)}

The locations are given within brackets (see Fig. 1)

hPa atmospheric pressure in hectopascal



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and EDM. Table 4 provides the statistics of observed andmodel simulated streamflows for the calibration and

validation periods before and after the modification of SDM (original) . As can be seen from Table 4, when theSDM (original) was modified using the lag 0 and lag 1 precipi-tation produced by the PDM, NSEs in both calibration andvalidation period increased equally (refer to SDM (lag0_preci)and SDM (lag1_preci) in Table 4). However, when lag 2 precip-itation was introduced to SDM (original) , the model performancein terms of NSE increased in calibration, but decreased invalidation. This indicated that with the introduction of lag 2 precipitation, SDM (lag2_preci) tends to show signs of over-fitting in calibration and under-fitting in validation. Consider-ing the improvement in NSE in validation, SDM (lag0_preci) wasselected for further modification with evaporation produced by the EDM. After the modification of SDM (lag0_preci) with lag0, lag 1 and lag 2 evaporation, Table 4 shows that further improvement to this model was not possible. Furthermore,when lag 0 and lag 1 precipitation together, lag 0, lag 1 and lag2 precipitation together, lag 1 precipitation and lag 0 evapo-ration together, lag 1 precipitation and lag 1 evaporationtogether and lag 1 precipitation and lag 0 and lag 1 evapora-tion together were used as additional inputs to SDM (original) , nofurther improvement to the model was seen. HenceSDM (lag0_preci) was selected as the best streamflow downscal-ing model.

As seen in Table 2, for SDM (original) , in all seasonsvolumetric soil moisture content and humidity variables(relative or specific humidity at different pressure levels)have been selected as best potential variables. The rate of evaporation from a catchment is dependent on factors suchas: wind speeds, air temperature, atmospheric humidity,sunshine hours (Wang et al. 2012 ) and also the soil mois-ture content (Shang et al. 2007 ). Therefore, it can beargued that the inclusion of variables representative of atmospheric humidity and soil moisture content in thedownscaling model can compensate the exclusion of evap-oration to a certain degree.

In Table 4, it was seen that with the introduction of lag zeroevaporation to SDM (lag0_preci) , the performance of theSDM (lag0_preci_ & _lag0_evap) in terms of NSE does not showany significant change. In fact, with the introduction of lagzero evaporation the performance of SDM (lag0_preci_ & _lag0_evap)in terms of NSE has slightly increased in model calibration period and slightly decreased in model validation period withrespect to that of SDM (lag0_preci) . The SDM (lag0_preci) alreadycontains atmospheric humidity and soil moisture variables (seeTable 2) which can indirectly explain the influence of evapo-ration on streamflow. Therefore, when evaporation is intro-duced to SDM (lag0_preci) it brings redundant information to themodel. This redundant information fed into the model does not cause any significant improvement to the model performance.In other words, the inclusion of evaporation in theSDM (lag0_preci) does not lead to any significant improvement in model performance.

Table 2 Best sets of potential predictors for each calendar month of SDM (original)

Month Potential variables used for MLR model with grid locations

January 1000 hPa relative humidity {(1,2),(2,2),(2,3),(3,4)}

February Volumetric soil moisture content 0 10 cm {(4,3)}

Volumetric soil moisture content 10 200 cm

{(2,2),(3,1),(3,2)}March 1000 hPa relative humidity {(5,6),(6,6),(6,7)}

April 700 hPa relative humidity {(4,2),(4,3)}


May Volumetricsoil moisturecontent 0 10 cm {(4,3),(4,4),(4,5)}

June Volumetric soil moisture content 0 10 cm{(4,3),(4,4),(5,2),(5,3),(5,4),(6,3)}


July 700 hPa geopotential height {(4,4)}

850 hPa geopotential height {(4,3),(4,4),(4,5)}

August 700 hPa geopotential height {(5,4),(5,5)}

850 hPa geopotential height {(5,4),(5,5),(5,6)}

September 700 hPa geopotential height {(2,1),(3,2),(3,3)}October Volumetric soil moisturecontent 0 10 cm {(4,3),(4,4),(5,3)}

November 700 hPa geopotential height {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}

December 700 hPa relative humidity {(4,3)}



850 hPa specific humidity {(5,5)}

Volumetric soil moisturecontent 0 10 cm {(4,4),(4,5),(5,4)}

Volumetric soil moisture content 10 200 cm{(3,2),(4,3) a ,(4,4) a }

The locations are given within brackets (see Fig. 1)

hPa atmospheric pressure in hectopascala Variables were removed from the model due to large bias in variance inHadCM3 outputs

Table 3 Performances of EDM in calibration and validation

Statistic Calibration (1950 1989) Validation (1990 2010)

Observations EDM Observations EDM

Avg 110.3 110.3 109.7 109.4Std 67.3 66.5 65.7 65.6

Min 21.8 22.2 23.8 22.8

Max 277.7 259.3 262.0 251.3

NSE 0.97 0.98

R 2 0.97 0.98

Avg average of monthly evaporation in mm, Std standard deviation of monthly evaporation in mm, Min minimum of monthly evaporation inmm, Max maximum of monthly evaporation in mm, NSE Nash-Sutcliffeefficiency, R2 coefficient of determination



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Then, in order to quantify the maximum potential improve-ment to SDM (original) , observed lag 0 precipitation was intro-duced to SDM (original) as an additional input and the modelwas calibrated and validated; this model is called SDM (original+OBS) . SDM (original+OBS) showed a significant increase in NSEin both calibration and validation periods as seen in Table 4.Also, the average, the standard deviation and the maximum of streamflow reproduced by SDM (original+OBS) was in better agreement with those of observations in both calibration andvalidation periods. The rise in NSE of SDM (original+OBS) wasmuch higher than that of SDM (lag0_preci) . This indicated that if the PDM is able to perfectly mimic the observed precipitation,then a significant improvement to SDM (original) can be intro-duced by using the lag 0 precipitation of PDM as an input. It was concluded that any significant improvement to PDM willimprove the performances of SDM (lag0_preci) .

Figure 5 shows the scatter of streamflow produced bySDM (original) , SDM (lag0_preci) and SDM (original+OBS) during thecalibration (1950 1989) and the validation (1990 2010) pe-riods. Though a rise in NSEs in both calibration and validation periods was seen, the reduction of scatter in streamflow down-scaled by SDM (lag0_preci) in its calibration and validation phaseswas minimum in comparison to the scatter of streamflow down-scaled by SDM (original) . However, the streamflow output of SDM (original+OBS) indicated a clear reduction of its scatter in bothcalibration and validation periods in comparison to scatter of streamflow of SDM (original) and SDM (lag0_preci) .

4.3 Reproduction of precipitation and hence streamflow usingoutputs HadCM3, ECHAM5 and GFDL2.0

4.3.1 Reproduction of precipitation and bias-correction

As stated in Section 3.3, the PDM was run with the20C3M outputs of HadCM3, ECHAM5 and GFDL2.0

for reproduction of observed precipitation over the period1950 1999. This allowed the quantification of bias in the precipitation downscaled by the PDM and its subsequent correction. Since SDM (lag0_preci) does not need evaporationas an input, the EDM was not used for the rest of thestudy. The statistics of precipitation reproduced by thePDM with NCEP/NCAR reanalysis and 20C3M outputsof HadCM3, ECHAM5 and GFDL2.0 and the statistics of observed precipitation (for the observation station locatedat Halls Gap post office) were shown in Sachindra et al.(2014c ). In that study, it was seen that with 20C3Moutputs HadCM3 and GFDL2.0, the PDM was able toreproduce the standard deviation, the minimum and themaximum of precipitation with good accuracy during the period 1950 1999. However, with 20C3M outputs of ECHAM5, the PDM over-estimated (presence of bias)the average, the standard deviation, and the minimumand the maximum of precipitation. Also, the average of precipitation was largely over-estimated by the PDM withthe 20C3M outputs of HadCM3 and GFDL2.0. For cor-rection of this bias, in the study by Sachindra et al.(2014c ), the EQM technique was applied to the precipita-tion simulated by the PDM run with the 20C3M outputsof HadCM3, ECHAM5 and GFDL2.0 for the period1950 1999 as described in Section 3.3. In that study, after the application of the EQM technique, the average, thestandard deviation and the maximum of precipitation were perfectly corrected, though the scatter of downscaled pre-cipitation still remained large indicated by small R2 and NSE.

In Sachindra et al. ( 2013 c, d), for validating the effective-ness of the EQM technique for precipitation, statistics of bias-corrected precipitation downscaled using the outputs of HadCM3 pertaining to COMMIT GHG emission scenariofor the period 2000 2099 were compared with those of

Table 4 Performances of SDMs in calibration and validation

Model Calibration (1950 1989) Validation (1990 2010)

Avg Std Min Max NSE Avg Std Min Max NSE

Observations 2129.3 2387.3 0.0 12,427.0 N/A 1318.6 1788.1 0.0 9387.0 N/A

SDM (original) 2132.4 1984.5 0.0 9773.5 0.69 2022.3 2123.7 0.0 11,255.2 0.33

SDM (lag0_preci) 2131.0 2019.1 0.0 10,770.9 0.72 2048.4 2157.7 0.0 11,539.8 0.36SDM (lag1_preci) 2133.7 2023.4 0.0 9231.9 0.72 2011.4 2169.0 0.0 11,759.2 0.36

SDM (lag2_preci) 2134.3 2021.2 0.0 9739.9 0.72 2024.1 2176.7 0.0 11,915.1 0.28

SDM (lag0_preci_ & _lag0_evap) 2131.3 2044.0 0.0 10,256.5 0.73 2039.7 2179.0 0.0 11,239.6 0.35



SDM (original+OBS) 2133.5 2145.1 0.0 12,072.7 0.81 1867.8 2006.0 0.0 10,741.8 0.60

Avg average of monthly stream flow in 10 3 m3 , Std standard deviation of monthly streamflow in 10 3 m3 , Min minimum of monthly streamflow in103 m3 , Max maximum of monthly streamflow in 10 3 m3 , NSE Nash-Sutcliffe efficiency



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observed precipitation for the period 1950 1999. This proce-dure was briefly described in Section 3.3 of this paper.Sachindra et al. ( 2014c ) commented that in validation, EQMwas able to successfully reduce the bias in precipitation

downscaled with HadCM3 outputs of the COMMIT GHGemission scenario for the period 2000 2099 and also it wasassumed that EQM is able to reduce the bias in the precipita-tion downscaled with the outputs of ECHAM5 and GFDL2.0.

0

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SDM (lag0_preci)

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Fig. 5 Scatter plots for calibration and validation phasesof SDMs



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4.3.2 Reproduction of streamflow and bias-correction

For reproduction of past observed streamflow, SDM (lag0_preci)was run with the 20C3M outputs of HadCM3, ECHAM5 andGFDL2.0 and the bias-corrected precipitation simulated bythe PDM, as described in Section 3.3. This allowed the quan-tification of bias in the streamflow downscaled by theSDM (lag0_preci) and its subsequent correction. The statisticsof observed streamflow and those of streamflow simulated by SDM (lag0_preci) during the period 1950 1999 are shown inTable 5. It can be seen from Table 5 that when theSDM (lag0_preci) was run with the 20C3M outputs of HadCM3,ECHAM5 and GFDL2.0 and outputs of PDM, it tended toover-estimate the average, the standard deviation, and themaximum of streamflow. This indicated the influence of biasin 20C3M outputs of HadCM3, ECHAM5 and GFDL2.0 ondownscaled streamflow. Once the EQM technique was applied to the streamflow produced by SDM (lag0_preci) , the biasin the average, the standard deviation and the maximum of streamflow was corrected to a good degree. However, theimprovement in NSE and R2 were small. This indicated that though the statistics of streamflow were well corrected, thescatter of the downscaled streamflow has not reduced much.This leads to the conclusion that projections of streamflow produced into the future should not be used as time series,instead they should be used in terms of probability distributionand statistics such as seasonal average, standard deviation andminimum/maximum etc.

4.3.3 Validation of bias-correction for streamflow

After the EQM technique was applied to the streamflowoutputs of SDM (lag0_preci) for past climate, a validation of this bias-correction was performed. For validation of ef-fectiveness of the EQM-based bias-correction for streamflow, the SDM (lag0_preci) was run with the outputs

of HadCM3 pertaining to COMMIT GHG emission sce-nario. Then, the EQM technique was applied to thestreamflow projection produced into the future period2000 2099 under COMMIT GHG emission scenario, asdescribed in Section 3.3.

In Tables 6 and 7, the statistics of bias-corrected streamflowdownscaled using COMMIT HadCM3 outputs for the period2000 2099 were comparedwith those of observedstreamflowof the period 1950 1999. As shown in Tables 6 and 7, it wasseen that prior to the application of the EQM bias-correction,the average of streamflow was over-estimated by the down-scaling model in all seasons. However, with the application of the EQM technique, this over-estimation has largely reduced.The standard deviation and the maximum of streamflow insummer and autumn were also corrected with good accuracy by EQM. Following the EQM bias-correction, the mismatch between the minimum of observed streamflow and that of streamflow projected into the future also reduced largely. Asthe influence of bias in 20C3M outputs of HadCM3,ECHAM5 and GFDL2.0 on downscaled streamflow weresimilar in nature (see Table 5), it was assumed that the influ-ence of bias in COMMIT outputs of HadCM3, ECHAM5 andGFDL2.0 on downscaled streamflow were also similar innature. Hence, it was realised that the EQM technique shouldalso be able to correct the bias in the streamflows projectedinto the future by the downscaling model run with the outputsof ECHAM5 and GFDL2.0.

4.4 Projection of precipitation and hence streamflowinto the future

4.4.1 Projection of precipitation into the future

In order to produce streamflow projections into the futureusing SDM (lag0_preci) , projections of precipitation are required.In the study by Sachindra et al ( 2014c ), by introducing the

Table 5 Performances of SDM (lag0_preci) with NCEP/NCAR and HadCM3 outputs before and after bias-correction

Statistic Period (1950 1999)

Observations With NCEP/NCAR outputs With HadCM3 outputs With ECHAM5 outputs With GFDL2.0 outputs

Before bias-correction

After bias-correction





Avg 2048.7 2144.5 3515.5 2035.4 3507.4 2034.9 3506.6 2035.2

Std 2339.4 2031.3 2724.1 2350.1 2719.5 2350.5 2706.0 2350.3

Min 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Max 12,427.0 11,255.2 13,791.1 12,427.0 13,997.3 12,427.0 12,873.7 12,427.0

NSE 0.69 0.79 0.20 0.77 0.15 0.80 0.25

R 2 0.69 0.17 0.16 0.17 0.18 0.16 0.14

Avg average of monthly streamflow in 10 3 m3 , Std standard deviation of monthly streamflow in 10 3 m3 , Min minimum of monthly streamflow in103 m3 , Max maximum of monthly streamflow in 10 3 m3 , NSE Nash-Sutcliffe efficiency, R2 coefficient of determination



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standardised outputs of HadCM3, ECHAM5 and GFDL2.0 pertaining to the A2 and B1 GHG emission scenarios to thePDM, precipitation projections were produced over the period

2000 2099, and those projections were bias-corrected usingthe EQM technique. For a more detailed description on theapplication of the EQM technique in correcting bias in the precipitation output of a downscaling model, readers are re-ferred to Sachindra et al ( 2014b ).

The A2 and B1 GHG emission scenario refer to high andlow levels of GHG emissions in the twenty-first centuryrespectively (A2/B1 CO 2 concentration of about 850/ 550 ppm at the end of the twenty-first century) (IPCC 2000 ).The use of A2 and B1 GHG emission scenarios in a statisticaldownscaling study allows the quantification of impacts of relatively high and low levels of GHG emissions on thecatchment scale hydroclimatology, respectively (Sachindra et al. 2014b ).

In the study by Sachindra et al ( 2014c ), it was found that when the HadCM3 outputs corresponding to A2 and B1 GHGemission scenarios were used as inputs to the PDM, theaverage of precipitation at the observation station at Halls

Gap post office in the period 2000 2099 showed an increasein autumn and winter, and a decrease in summer and spring incomparison to the corresponding seasonal averages of ob-

served precipitation of the period 1950 1999. In the samestudy, when the ECHAM5 outputs for the A2 and B1 GHGemission scenarios were used as inputs to the PDM, theaverage of precipitation in the period 2000 2099 showed anincrease in summer and a decline in winter and spring incomparison to the corresponding seasonal averages of ob-served precipitation of the period 1950 1999. With the useof outputs of GFDL2.0 pertaining to A2 and B1 GHG emis-sion scenarios to the PDM, the average of precipitation in the period 2000 2099 showed a rise in spring and a decline inautumn in comparison to the corresponding seasonal averagesof observed precipitation of the period 1950 1999.

4.4.2 Projection of streamflow into the future

Once precipitation was projected into the future (2000 2099)and bias-corrected, it was standardised for each calendar month using the mean and the standard deviation of observed

Table 6 Statistics of observed streamflow of the period 1950 1999 and streamflow downscaled using HadCM3 COMMIT outputs for 2000 2099(summer and autumn)

Statistic Summer Autumn

Observed SDM (lag0_preci) with HadCM3COMMIT outputs (2000 2099)

Observed SDM (lag0_preci) with HadCM3COMMIT outputs (2000 2099)

Before bias-correction After bias-correction Before bias-correction After bias-correction

Avg 836.0 997.6 822.0 603.2 1424.9 754.5

Std 850.4 793.8 865.6 936.2 1473.8 925.9

Min 0.0 0.0 0.0 0.0 0.0 0.0

Max 8041.0 3357.0 8714.9 8017.0 4640.6 8207.0

Avg average of monthly streamflow in 10 3 m3 , Std standard deviation of monthly streamflow in 10 3 m3 , Min minimum of monthly streamflow in103 m3 , Max maximum of monthly streamflow in 10 3 m3

Table 7 Statistics of observed streamflow of the period 1950 1999 and streamflow downscaled using HadCM3 COMMIT outputs for 2000 2099(winter and spring)

Statistic Winter Spring

Observed SDM (lag0_preci) with HadCM3COMMIT outputs (2000 2099) Observed SDM(lag0_preci) with HadCM3COMMIT outputs (2000 2099)

Before bias-correction After bias-correction Before bias-correction After bias-correction

Avg 3394.3 3888.0 3448.8 3361.4 4620.9 2453.6

Std 2496.1 1930.3 3294.9 2651.4 2398.5 3045.4

Min 0.0 510.4 0.0 0.0 0.0 0.0

Max 11,162.0 13,180.6 17,540.7 12,427.0 13,933.8 16,162.3

Avg average of monthly streamflow in 10 3 m3 , Std standard deviation of monthly streamflow in 10 3 m3 , Min minimum of monthly streamflow in103 m3 , Max maximum of monthly streamflow in 10 3 m3



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precipitat ion of period 1950 1989. Then, the HadCM3,ECHAM5 and GFDL2.0 outputs pertaining to the A2 andB1 GHG emission scenarios for SDM (lag0_preci) correspondingto future climate were also standardised for each calendar month using the means and the standard deviations of NCEP/NCAR reanalysis outputs of period 1950 1989. Usingthe above standardised precipitation of the PDM and outputsof HadCM3, ECHAM5 and GFDL2.0 pertaining to A2 andB1 GHG emission scenarios as inputs to SDM (lag0_preci) , projections of streamflow for each calendar month was produced.

Table 8 shows the seasonal statistics of observed and projected streamflows (inflow to Lake Bellfield in north-western Victoria, Australia) corresponding to A2 and B1GHG emission scenarios for periods 1950 1999 and 2000

2099, respectively. Also, the ensemble average streamflowtime series was computed from the streamflow outputs of SDM (lag0_preci) when it was run with the outputs of HadCM3,ECHAM5 and GFDL2.0 and the precipitation outputs of PDM. Statistics of streamflow derived from the ensembleaverage streamflow time series are also shown in Table 8. Notethat in Table 8, changes in the average of precipitation pro-duced by PDM over the period 2000 2099 with respect to theaverage of observed precipitation in the period 1950 1999 arealso provided (for more details, refer to footnote of Table 8).

According to Table 8, it was seen that the average of streamflow corresponding to both A2 andB1 emission scenarios,indicated a decline in summer, autumn and spring and showed anincrease in winter, for all GCMs and for the ensemble. However,as shown in Table 8, the precipitation outputs of the PDM did not show such decline in summer, autumn and spring and an increasein winter for all three GCMs and for both GHG emissionscenarios. Instead, average of precipitation projected by PDMindicated mixed results in above seasons, depending on theGCM and the GHG emission scenario of interest. It was realisedthat an increase (or decrease) in precipitation in a season does not guarantee an increase (or decrease) in the streamflow in that season. This is possibly because though precipitation is the maindriver of streamflow, variables such as soil moisture content andatmospheric moisture content (influence the evaporation rate)can significantly influence the streamflow generation process.As an example, a dry catchment (i.e. low soil moisture content and atmospheric moisture content) can absorb large amount of the precipitation and cause either small increase or even somedecrease in the average of streamflow.

Similar to precipitation, streamflow also showed a rise inits standard deviation and the maximum, in all seasons corre-sponding to all three GCMs and both GHG emission scenar-ios. This indicated that there will be more fluctuations in the

Table 8 Seasonal statistics of observed and projected streamflow

Season Statistic Observed (1950 99) HadCM3 (2000 99) ECHAM5 (2000 99) GFDL2.0 (2000 99) Ensemble average (2000 99)

A2 B1 A2 B1 A2 B1 A2 B1

Summer Avg 835.9 421.7a

758.9a

767.1 b

764.3 b

775.3 b

772.4a

654.7c

765.2a

Std 850.4 808.7 988.6 969.8 962.3 928.6 923.2 641.0 905.9

Min 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Max 8041.0 9275.7 11,055.1 11,230.5 11,000.3 10,911.7 10,716.8 7380.7 10,924.0

Autumn Avg 603.2 524.8 b 499.8 a 512.0 c 504.9 b 484.8 a 491.6 a 507.2 a 498.8 a

Std 936.1 1054.1 1047.2 1046.4 1047.7 1046.2 1046.0 1030.4 1026.6

Min 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Max 8017.0 9260.3 9268.0 9258.7 9258.7 9261.1 9257.8 9260.0 9261.5

Winter Avg 3394.3 3797.1 b 3823.7 b 3487.4 a 3588.7 a 3736.7 c 3869.1 b 3673.7 a 3760.5 b

Std 2496.1 3184.5 2891.5 2739.8 2804.7 3023.2 3017.3 2612.9 2474.2

Min 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 29.2

Max 11,162.0 19,964.9 15,435.5 14,753.4 14,509.1 14,229.4 13,849.2 15,494.7 13,426.9

Spring Avg 3361.4 2509.2 a 2375.5 a 2051.7 a 2173.2 a 2812.3 b 2965.9 b 2457.8 a 2504.9 a Std 2651.4 3042.3 2734.5 2579.5 2533.1 2922.6 2949.3 2384.5 2242.8

Min 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Max 12,427.0 15,863.1 13,841.3 13,722.9 12,768.3 14,133.1 14,944.9 12,500.1 11,424.7

Avg average of monthly streamflow in 10 3 m3 , Std standard deviation of monthly streamflow in 10 3 m3 , Min minimum of monthly streamflow in103 m3 , Max maximumof monthly streamflow in 10 3 m3 , Ensembleaverage average time series computed from the outputs of SDM (lag0_preci) whenit was run with the outputs of HadCM3, ECHAM5 and GFDL2.0 and precipitation outputs of PDMa Average of precipitation showed a decrease with respect to that of observations of period 1950 99 b Average of precipitation showed an increase with respect to that of observations of period 1950 99c Average of precipitation did not show any change with respect to that of observations of period 1950 99



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streamflow regime in the future and the magnitude of theextremely high streamflows tend to increase in all seasons.Also, it was noticed that in general, the maximum of streamflow was higher for the A2 GHG emission scenarioscompared to that of B1, for the majority of GCMs in allseasons.

Figure 6 shows the probability exceedance curves for ob-served streamflow for the period 1950 1999 and the probability exceedance curves for streamflow projected into thefuture period 2000 2099 derived using the multi-model en-semble average streamflow time series, for each season. It wasclear that in all seasons, except spring, the magnitude of theextremely high streamflow tends to show a rise for both A2and B1 emission scenarios. In summer, for most of the ex-ceedance probabilities (particularly for smaller exceedance probabilities), streamflow shows a decrease under both sce-narios; however still the extremely high streamflow tends toshow a rise. This decrease in streamflow was probably due tothe dryness of the catchment in summer caused by the declinein precipitation in spring (see Table 8 for decline in average precipitation in spring).

In autumn, for smaller exceedance probabilities (highstreamflows), streamflow showed a rising trend and for higher exceedance probabilities (low streamflows) a decreasing trendwas seen. In winter, streamflow for both A2 and B1 GHGemission scenarios showed a rising trend for the majority of the exceedance probabilities (low to high streamflows). Inspring, for the majority of exceedance probabilitiesstreamflow showed a decrease corresponding to both A2and B1 GHG emission scenarios. Furthermore, according tothe exceedance curves in Fig. 6, it was realised that in thefuture there will be more months with zero flows particularlyin summer and autumn.

The long-term seasonal statistics (e.g. average, standarddeviation, minimum and maximum) of monthly streamflowsobtained from the bias-corrected time series are useful for themanagement of water resources in a catchment. The averageof streamflow in each season determined in this study pro-vides an idea of the availability of water in Lake Bellfield inthe future, hence the availability of water to Halls Gap andPomonal towns and also for the recreational activities whichtake place at this lake can be determined. This allows theappropriate allocation of water to various needs dependingon the availability. The standard deviation of streamflowshows the degree of fluctuations in inflow to Lake Bellfieldin the future. In this study, a rise in the standard deviation of inflow to Lake Bellfield was seen in all seasons. The rise in thestandard deviation of inflow to Lake Bellfield indicated morefluctuations in the streamflow regime in the future. Thesefluctuations in the inflow to the lake should be taken intoaccount in its future operations and any modification, as theyimpact the reliability of water supply to customers. Theknowledge of the extremes in the streamflow regimeis helpful

in the management of droughts and floods. Since the number of months with zero inflow and the magnitude of the peak inflow to Lake Bellfield in all seasons have increased, newdrought and flood mitigation measures may be needed in themanagement of droughts and floods in the catchment in thefuture.

4.5 Uncertainties associated with streamflow projections

It should be noted that the projections of streamflows pro-duced in this study using statistical downscaling are subject toa cascade of uncertainties originating from a number of sources. These sources of uncertainties include; GHG emis-sion scenarios, GCMs, the downscaling technique, methodol-ogy followed in developing the downscaling model (e.g. predictor selection and pre-processing, selection of calibration period) and predictor-predictand stationar ity assumption(Sachindra et al. 2014d ).

The actual amounts of GHG emissions in the future worldare unknown as they are dependent on a number of factorssuch as population, technological development and govern-ment policies, which can largely change in the future over time. Therefore, several equally likely but different GHGemission scenarios have been defined for the future (e.g.SRES GHG emission scenarios (IPCC 2000 ), Representativeconcentration pathways (van Vuuren et al. 2011 )). The use of several equally likely but different GHG emission scenarios in producing catchment scale hydroclimatic projections into thefuture enables the quantification of uncertainties introduced by GHG emissions to the projections. In this study, the projections of streamflows were produced corresponding to theA2 and B1 GHG emission scenarios for the quantification of relatively high and low impacts of GHG emissions onstreamflows in the future. The streamflow projections pro-duced in this study should be treated as plausible rather thandefinite as the GHG emission scenarios on which they are based are on are plausible realisations of future GHGemissions.

The projections produced using a downscaling model canvary from GCM to GCM as the approximations and assump-tions employed in the structures of GCMs vary from oneanother. In the present study, outputs of HadCM3, ECHAM5and GFDL2.0 were used to produce inputs to the downscalingmodels. Using sets of outputs from different GCMs on thedownscaling models and hence deriving an ensemble of projections can better explain the uncertainties (e.g. visualize theupper and lower uncertainty bounds of the projections of the predictand) introduced by different GCMs to the projectionsof the predictand of interest. Furthermore, combination of ensemble of projections using an ensemble modelling tech-nique (e.g. averaging) can reduce the dependence of projec-tions of one specific GCM. In this study, for the derivation of the ensemble projections, the simple averaging technique was



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used. In simple averaging, each projection produced by thestatistical downscaling model is assigned the same weightage.In other words, it is assumed that all GCMs perform equally.However, this assumption can be coarse and assigningweightages to each projection based on the performance of each GCM for each calendar month and hence deriving anensemble projection can be regarded as a better approach(Zhang and Huang 2013 ). However, such procedure is com- putationally expensive.

Since different downscaling techniques can represent the predictor-predictand relationships differently, the downscalingtechnique used in a study can also introduce a certain degreeof uncertainty to the projections. However, in comparison tothe uncertainties introduced by the GHG emission scenariosand GCMs, the uncertainties introduced by different downscaling techniques are negligible. Sachindra et al(2013 ) used LS-SVM and MLR for statistically downscalingmonthly GCM outputs to monthly streamflows andcommented that both techniques yielded similar results.Also, Tripathi et al. ( 2006 ) found that LS-SVM is marginally be tte r th an ANN in do wns ca ling GCM ou tpu ts to

precipitation. Furthermore, they commented that both tech-niques failed to correctly capture the extremes of precipitation.

The methodology used in the development of a downscal-ing model can also introduce some uncertainty to the projec-tion. The overall methodology of a downscaling exerciseincludes the selection of potential predictors, standardisationof predictor data, selection of the calibration period and modelcalibration and validation. Each of the above steps can be performed in a number of different manners. As an example,in a downscaling exercise, instead of using traditional calibra-tion and validation approach, a cross-validation approach can be adopted. Therefore, depending on the methodologyemployed, the outputs of a downscaling model can vary.

Almost all statistical downscaling models are dependent onthe assumption that the relationships derived between the predictors and predictands for the past climate will be validfor the future, under changing climate. In other words, thevalidity of the stationarity of predictor-predictand relation-ships under non-stationary climate is assumed. However, thevalidity of the above assumption is questionable under non-stationary climate. A few attempts to handle the non-

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Multi-model ensemble projected streamflow inwinter A2 2000-2099

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Fig. 6 Seasonal probability exceedance curves for observed streamflow and bias-corrected streamflow for future climate under A2 and B1 GHGemission scenarios



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stationarity of predictor-predictand relationships under non-stationary climate are documented in Raje and Mujumdar (2010 ), Duan et al ( 2012 ) and Hertig and Jacobeit ( 2013 ). Inthis study, like most of the other downscaling studies, it wasassumed that the predictor-predictand relationships will bestationary under changing climate (non-stationary climate).Further investigation is needed for the confirmation of theimpact of the above assumption on the streamflow projections produced in this study.

Furthermore, it should be noted that in direct downscalingof GCM outputs to catchment scale streamflows, the changesin the land use patterns and water diversions in and out of a catchment are not considered as such catchment scale changesare not characterised in the GCM outputs.

5 Conclusions

The following conclusions were drawn from this study:

1. When the precipitation downscaled from large-scale at-mospheric variables is used as an additional input to a statistical model developed for downscaling large-scaleatmospheric vari

potential improvements to statistical downscaling of general circulation model outputs to catchment...

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