Using a key station approach, statistical downscaling of monthly general circulation model outputs to monthly precipitation, evaporation, minimum temperature and maximum temperature at 17 observation stations located in Victoria, Australia was performed. Using the observations of each predictand, over the period 1950–2010, correlations among all stations were computed. For each predictand, the station which showed the highest number of correlations above 0.80 with other stations was selected as the first key station. The stations that were highly correlated with that key station were considered as the member stations of the first cluster. By employing this same procedure on the remaining stations, the next key station was found. This procedure was performed until all stations were segregated into clusters. Thereafter, using the observations of each predictand, regression equations (inter-station regression relationships) were developed between the key stations and the member stations for each calendar month. The downscaling models at the key stations were developed using reanalysis data as inputs to them. The outputs of HadCM3 pertaining to A2 emission scenario were introduced to these downscaling models to produce projections of the predictands over the period 2000–2099. Then the outputs of these downscaling models were introduced to the inter-station regression relationships to produce projections of predictands at all member stations.

INTRODUCTION

Climate change due to rising concentrations of atmospheric greenhouse gases (GHG) (Wilks 2010) is a major issue in the present world. It is believed that the spatio-temporal changes in precipitation pattern, increase in the intensity and frequency of extreme precipitation events, rise in the global temperature, and heat waves are some of the consequences of the increasing concentrations of GHG in the atmosphere (Nicholls 2008). It is believed that the climate of earth will continue to change in the future (Hundecha & Bardossy 2008). The study of the impact of changing climate on water resources is of great importance, particularly at the catchment scale, as water is essential for the existence of life.

General circulation models (GCMs) are the most widely used tools for projection of global climate into the future (Anandhi et al. 2008), considering the GHG concentrations in the atmosphere. GCMs are based on the physics of the atmosphere, and they employ various assumptions and approximations to simplify the naturally complex atmosphere in modelling (Sachindra et al. 2013). However, due to the coarse spatial resolution of the GCM outputs, they cannot be used directly in catchment scale studies which need climatic data at finer spatial resolutions (Jeong et al. 2012). As a solution to the issue of coarse spatial resolution of GCM outputs, downscaling techniques have been developed. They link the coarse resolution GCM outputs with fine resolution hydroclimatic variables at the catchment scale. There are two broad classes of downscaling methods in use: (1) dynamic downscaling and (2) statistical downscaling (Wilby & Dawson 2007; Liu et al. 2013).

Dynamic downscaling involves the introduction of boundary and initial conditions obtained from a GCM to a regional climate model (RCM) (Murphy 1998). RCMs are also atmospheric physics based models capable of producing their outputs at spatial resolutions finer than the outputs of GCMs. Dynamic downscaling techniques produce spatially continuous projections of climatic variables, while maintaining their correlations over space (Maurer & Hidalgo 2008). The major issue with dynamic downscaling techniques is the high computational costs and the long simulation time involved in their implementation.

In statistical downscaling, mathematical relationships are first developed between the GCM outputs and the catchment scale hydroclimatic variable of interest using the data of past climate. Then these relationships are used in downscaling GCM outputs pertaining to future climate. Therefore, all statistical downscaling techniques assume that the relationships developed between the GCM outputs and catchment scale hydroclimatic variable using the data of past climate will remain the same in the future. Furthermore, statistical downscaling techniques can only produce point scale projections of climate, while the dynamic downscaling techniques produce spatially continuous fields of outputs. Nevertheless, statistical downscaling methods are computationally cheaper compared to dynamic downscaling techniques and also faster in producing their outputs.

Statistical downscaling techniques are further subdivided into three groups: (1) regression methods, (2) weather classification and (3) weather generation (Wilby et al. 2004). In regression downscaling methods, either linear or non-linear relationships between the GCM outputs and the catchment scale hydroclimatic variables are constructed (Chen et al. 2010). Weather classification involves the determination of the values of catchment scale hydroclimatic variables by matching the current state of large scale weather with past similar conditions in the record (Wilby et al. 2004). Weather generators produce synthetic sequences of the climatic variable, which capture the statistics of the observations (Kou et al. 2007).

Statistical downscaling studies are conducted at individual stations without explicitly preserving the observed cross-correlation structures between stations (e.g. Tripathi et al. 2006; Anandhi et al. 2008; Sachindra et al. 2013), and also at multiple stations attempting to maintain the observed cross-correlation structures (or spatial covariance structure) between the stations (e.g. Jeong et al. 2012). In a statistical downscaling study which involves downscaling at a large number of stations over a study area, the preservation of the cross-correlation structure among stations is an important objective, as it enables the plausible representation of spatial variations of the climatic variables over the study area. However, under changing climate in the future, the cross-correlation structures among stations may also tend to change. Jeong et al. (2012) used the multivariate multi-linear regression technique for downscaling National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis outputs to daily precipitation, simultaneously at nine observation stations in Canada. Wilks (1999) used a weather generation technique to generate daily precipitation, minimum temperature, maximum temperature and solar radiation, simultaneously at 62 stations in the western part of the USA. The same weather generation technique was used by Qian et al. (2002) for generating the daily precipitation, minimum temperature and maximum temperature at six observation stations in Portugal. Wilby et al. (2003) used the conditional resampling method to downscale GCM outputs to daily precipitation at multiple stations in the UK. However, the multi-site downscaling methods employed in the past were of a high degree of complexity.

Gupta (2008) stated that a short streamflow data set at a station can be lengthened by using a linear regression equation fitted between the data of that station and data of another station, which has a long record of data and also displays a high correlation with the former station. Anandhi et al. (2008) successfully used this regression technique to estimate missing data of minimum and maximum temperature at a station. This simple idea can be extended to a statistical downscaling exercise in which multiple stations are involved. This paper demonstrates the application of the following relatively simple yet effective multi station downscaling approach based on the above idea.

Initially, a station at which the observed data of the predictand (e.g. precipitation) are highly correlated with those at some other stations in the study area is identified. This station is referred to as the key station. Thereafter, regression relationships are developed between the key station and the other stations which are correlated with the key station, using observed data. A statistical downscaling model is then developed for the key station. The outputs of this downscaling model are used in the regression relationships developed between the key station and the other stations, to produce the values of the predictand at the other stations. In this study, the aforementioned key station approach was employed in order to determine the values of monthly precipitation, evaporation, minimum and maximum temperature at multiple stations in an area, using the outputs of the downscaling models developed at a few key stations. Precipitation is the predominant factor which determines the amount of water available in a catchment, while evaporation is a key process which governs the loss of water from a catchment. Temperature is directly influential on the rate of evaporation. Therefore precipitation, evaporation and temperature are three climatic variables which largely influence the water resources in a catchment. Hence, the study of the variations of these three climatic variables under changing climate in the future is immensely helpful in determining the availability of surface water resources in a catchment.

The operational area of Grampians Wimmera Mallee Water Cooperation in the north western region of Victoria, Australia was selected as the study area to demonstrate the key station approach employed in this study. This area is sensitive to severe droughts (Barton et al. 2011), therefore reliable information on the likely future water availability is quite important.

The one assumption of the key station approach is that the observed cross-correlation structure among the stations in the past climate for a certain climate variable is also valid for the climatic projections produced into the future. However, for the successful implementation of the key station approach, the correlations between the observations of the predictand of interest at the key station and the corresponding observations at the other stations in the study area should be high. If the above condition is satisfied, the key station approach can be used effectively over any geographic region. If the cross-correlations are low, the relationships between the key station and the other stations become weaker. Furthermore, in the key station approach, downscaling models are only developed at the key stations. Hence, it avoids the need of selecting predictors, developing downscaling models and correction of bias (described in detail later in this paper) for each individual station in the study area. The innovation of the key station approach is associated with the effective yet simple clustering algorithm which assigns stations into clusters based on the similarity of characteristics of the hydroclimatic variable of interest.

The next section of this paper provides the details of the study area and the data used in this research, followed by a section explaining the generic methodology. The application of the generic methodology to the study area is detailed in the following section, together with the results of the application. The final section provides the broad conclusions derived from this study.

STUDY AREA AND DATA

For the case study, monthly precipitation, evaporation, minimum temperature and maximum temperature measured at 17 stations were used. These stations were located within the operational area of Grampians Wimmera Mallee Water Cooperation (GWMWater) (www.gwmwater.org.au) in north-western Victoria, Australia. The operational area of GWMWater is shown in Figure 1 and is about 62,000 km2 in extent. The elevation of the study area varies from about 25 to 1,200 m (above mean sea level) from north to south. The northern part of the study area is relatively flatter and its climate is persistently dry and warm (Bureau of Meteorology 2013). On the other hand, the southern region of the study area is mountainous and has a less pronounced dry season (Bureau of Meteorology 2013).
Figure 1

Study area.

Figure 1

Study area.

Table 1 shows the 17 stations considered in this study with their latitudes and longitudes.

Table 1

Stations considered in this study

Name of the station Station ID Latitude Longitude 
Eversley 79014 –37.18 143.15 
Ouyen post office 76047 –35.07 142.32 
Birchip post office 77007 –35.98 142.92 
Swan Hill post office 77042 –35.34 143.55 
Rainbow 77083 –35.90 141.99 
Great Western 79019 –37.18 142.86 
Polkemmet 79023 –36.66 142.07 
Lake Lonsdale 79026 –37.03 142.58 
Longerenong 79028 –36.67 142.30 
Moyston post office 79034 –37.30 142.77 
Wartook reservoir 79046 –37.09 142.43 
Hamilton airport 90173 –37.65 142.06 
Halls Gap post office 79074 –37.14 142.52 
Tottington 79079 –36.79 143.12 
Stawell 79080 –37.07 142.79 
Balmoral post office 89003 –37.25 141.84 
Ararat prison 89085 –37.28 142.98 
Name of the station Station ID Latitude Longitude 
Eversley 79014 –37.18 143.15 
Ouyen post office 76047 –35.07 142.32 
Birchip post office 77007 –35.98 142.92 
Swan Hill post office 77042 –35.34 143.55 
Rainbow 77083 –35.90 141.99 
Great Western 79019 –37.18 142.86 
Polkemmet 79023 –36.66 142.07 
Lake Lonsdale 79026 –37.03 142.58 
Longerenong 79028 –36.67 142.30 
Moyston post office 79034 –37.30 142.77 
Wartook reservoir 79046 –37.09 142.43 
Hamilton airport 90173 –37.65 142.06 
Halls Gap post office 79074 –37.14 142.52 
Tottington 79079 –36.79 143.12 
Stawell 79080 –37.07 142.79 
Balmoral post office 89003 –37.25 141.84 
Ararat prison 89085 –37.28 142.98 

Station ID is as defined by the Bureau of Meteorology Australia from www.bom.gov.au/climate/data/stations/.

Monthly observed precipitation, evaporation (class A pan evaporation), maximum temperature and minimum temperature for the 17 stations shown in Table 1 were obtained from the SILO database of Queensland Climate Change Centre of Excellence at www.longpaddock.qld.gov.au/silo/, for the period 1950–2010. These data were used for identification of key stations and also for calibration and validation of the downscaling models. The observed records of precipitation, evaporation, maximum temperature and minimum temperature were also used in the bias-correction of the outputs of the downscaling models as the reference data set. For providing inputs to the downscaling models in calibration and validation, monthly NCEP/NCAR reanalysis outputs were extracted from the physical sciences division of the National Oceanic and Atmospheric Administration/Earth System Research Laboratory (NOAA/ESRL) at www.esrl.noaa.gov/psd/.

For reproducing the past observed precipitation, evaporation, maximum temperature and minimum temperature using the downscaling models, monthly outputs of HadCM3 for the 20th century climate experiment (20C3M) were downloaded from the Programme for Climate Model Diagnosis and Inter-comparison (PCMDI) (https://esgcet.llnl.gov:8443/index.jsp) for the period 1950–1999. For producing projections of catchment scale precipitation, evaporation, maximum temperature and minimum temperature into the future, using the downscaling models, GCM outputs corresponding to future GHG emissions are required. For this purpose, outputs of HadCM3 (a GCM) pertaining to the A2 GHG emission scenario were downloaded from https://esgcet.llnl.gov:8443/index.jsp.

Smith & Chandler (2009) stated that HadCM3 is among the few GCMs which are capable of properly simulating the precipitation over Australia and produce credible predictions of El Niño Southern Oscillation (ENSO). In that study, they argued that any GCM capable of simulating precipitation with a good degree of accuracy should also simulate other climatic variables plausibly. Therefore, HadCM3 was selected for the present study. The distinct link between ENSO and precipitation in Australia is discussed in detailed by Chiew et al. (1998). The use of the A2 GHG emission scenario in the current study enables the projection of the worst plausible impacts of the rising GHG concentrations on the climate over the study area, as this scenario refers to high levels of emissions of GHG, owing to the rapid economic growth of the future world. The A2 GHG emission scenario provides similarities to the severe drought experienced by the study region from 1997 to 2009 (Barton et al. 2011), which now provides the basis for many government planning efforts (for example refer to Victorian Government Department of Sustainability & Environment 2011).

GENERIC METHODOLOGY

The procedure for application of the key station approach used in this study is shown in brief in the flow chart provided in Figure 2. The steps shown in Figure 2 are described in detail later. This multi-station downscaling approach relies on the downscaling models at the key stations and the regression relationships between the key stations and the member stations. Therefore, identification of key stations, clusters, member stations and development of regression relationships between the key stations and the member stations are major steps of this approach.
Figure 2

Steps involved in application of the key station approach.

Figure 2

Steps involved in application of the key station approach.

Identification of key stations and clusters

In this paper, a key station is defined as an observation station whose data for a specific climatic variable (e.g. monthly precipitation) are highly correlated with those of a set of other observation stations in the same study area. The key station and the other observation stations (member stations) which are highly correlated with it are called a cluster. A study area can have several clusters; each cluster contains a key station, and a cluster can have any number of member stations.

For identification of key stations and clusters for each climatic variable, initially the Pearson correlation coefficients (Pearson 1895) between each station and the rest of the stations were computed for the past climate, considering all calendar months together. This yielded a matrix of correlation coefficients among all stations in the study area. Once the correlation matrix was computed, by examining it, a station at which the data of the considered climatic variable are highly correlated (magnitude of 0.80 or above preferred) with those at other stations in the study area was identified. This station was the key station and the other stations which were highly correlated with it were the member stations of the cluster, for the climatic variable considered.

If one such key station for the whole study area cannot be found, then multiple key stations for the study area were identified. In such a case, first, a threshold value of 0.80 was imposed on the correlation matrix of a climatic variable of interest. Note that the threshold value of 0.80 refers only to the magnitude of the correlation. Once the threshold value was imposed on the correlation matrix, the station which has the highest number of correlations above the threshold with other stations was selected as the first key station, and the stations which showed high correlation with this station were considered as the members of the first cluster. When multiple stations showed the same number of stations with which they have correlations above 0.80, any such station was selected as the first key station. Thereafter, the same procedure which was used in identifying the first key station was applied on the correlation matrix which included only the stations which were not included in the first cluster. In this manner, the second key station and the member stations of the second cluster were identified. This procedure was repeated until all stations are assigned to clusters. Also, the different clusters should be as uncorrelated as possible. Clusters and key stations were identified for each variable considered in this study separately. If there is any station which does not display a correlation above the threshold with any other station, that station should be treated as a solitary key station (not any member stations in the cluster).

The magnitude of the correlation threshold can be changed based on the correlations in the matrix. However, if the correlations among the stations for a certain predictand were relatively low, the advantage of application of the key station approach becomes limited. This is because low correlations refer to poor linear associations between a predictand at the key station and that at the member stations in the cluster. These poor linear associations will cause the regression relationships built between a predictand at a key station and that at member stations to be less effective.

Relationships between key stations and member stations in clusters

Once the key stations were identified, simple linear regression relationships were developed for each predictand between the key station and the member stations, using the observations. This was done for each cluster and for each calendar month separately. In this paper, these relationships are referred to as inter-station regression relationships. The first two-thirds of the observations at the key and the member stations were used to calibrate these linear regression relationships. Then, these linear regression relationships were validated using the remaining observations.

Atmospheric domain and predictor selection

After the development of the inter-station regression relationships, an atmospheric domain over the study area was defined. The atmospheric domain allows the inclusion of influences of the large scale atmospheric circulations on the catchment scale climate in the downscaling models. This atmospheric domain was used for the development of downscaling models for all predictands at all key stations.

For this study, probable predictors which are the likely variables to influence a predictand at the catchment scale were selected based on a review of past literature and hydrological principles. Probable predictors can vary from predictand to predictand and also geographically. The potential predictors are a subset of probable predictors and they are the most influential predictors on the predictand considered. Potential predictors also vary from predictand to predictand and also spatiotemporally.

The potential predictors for each calendar month at each key station were selected from the set of probable predictors, based on their correlations with the observations of the predictand. The selection of potential predictors for each calendar month enables the consideration of seasonal variations of the atmosphere, and hence it allows better modelling of the predictand (Sachindra et al. 2013). The data corresponding to the probable predictors were obtained from a reanalysis database. These reanalysis data and observations of the predictand (pertaining to a key station) were chronologically separated into 20-year time slices. Then the Pearson correlation coefficients between the observations and the reanalysis data were computed for each time slice and for the whole time period of the study. This was performed at each grid point in the atmospheric domain, for each calendar month separately. The probable predictors which displayed the best correlations (statistical significance: p ≤ 0.05) consistently over the 20-year time slices and the whole period of the study were selected as the potential predictors for each calendar month.

Development of downscaling models at key stations

Downscaling models were developed (calibrated and validated) for the key stations using the potential predictors identified in the previous section. The first two-thirds of the observations of predictands and the reanalysis data corresponding to the potential predictors were used for the calibration of the downscaling models and the remaining data were used for the validation. The reanalysis data for potential predictors for both calibration and validation were standardised using the means and standard deviations of the reanalysis data corresponding to the calibration phase of the downscaling model. This was done as the means and standard deviations of the reanalysis data become a fixed component of the downscaling model throughout its development (calibration and validation) and projection phases (Sachindra et al. 2014b). For the calibration of the downscaling model, initially the potential predictor which displayed the best correlation with the predictand over the whole period of the study at the station of interest was introduced to the downscaling model. By minimising the sum of squared errors between the observations and the outputs of the downscaling model, the optimum values for the coefficient and constant in the multi-linear regression (MLR) equation (in this case a simple linear regression equation, as there is only one independent variable) were computed. Following this, the downscaling model was validated as an independent simulation. The model performance in calibration and validation was measured using the Nash–Sutcliffe efficiency (NSE) (Nash & Sutcliffe 1970) by comparing the model outputs with the corresponding observations. Then, one at a time, the next best potential predictors were introduced to the downscaling model, and it was calibrated and validated. This stepwise introduction of predictors was continued until the performance of the downscaling model attains a maximum in validation, in terms of the NSE. The stepwise model development allowed the identification of the best set of predictors and the development of the best downscaling model for each calendar month. Following the same procedure, downscaling models were developed for all calendar months at each key station for each predictand, separately. The performances of the downscaling models during the calibration and validation phases were assessed by comparing the statistics of the model outputs with those of observations. Graphical comparisons (scatter plots) of outputs of downscaling models and observations were also performed.

Reproduction of past climate at key stations and bias-correction

After the development of downscaling models at the key stations, the 20C3M outputs of the GCM pertaining to the calibration and validation phases of the downscaling models were standardised with the means and the standard deviations of the reanalysis outputs corresponding to the calibration phase of the downscaling models. Then, by introducing these standardised 20C3M outputs of the GCM to the downscaling models, the observations of the predictands (e.g. precipitation) were reproduced for the past climate. This was performed to analyse the performances of the downscaling models in reproducing the past observations when these were run with the GCM outputs pertaining to the past climate. It was an important investigation as the downscaling models have been developed with better quality reanalysis data for the past climate, and for the projection of climate into the future they will be used with GCM outputs which are associated with greater uncertainties. If any bias was seen in the outputs of the downscaling models when run with the 20C3M outputs of the GCM, a correction to bias was applied.

In this study, the monthly bias-correction (Johnson & Sharma 2012) was applied on the outputs of the downscaling models (e.g. precipitation) produced with the 20C3M outputs of the GCM. The monthly bias-correction is based on the assumption that the bias in the mean and the standard deviation of the outputs of the downscaling models (with respect to past observations) for the past climate will remain the same in the future (Johnson & Sharma 2012). The procedure for the application of the monthly bias-correction is described below.

This bias-correction was applied to the calibration period of the downscaling model, by replacing the means and the standard deviations of the outputs of the downscaling models produced with the 20C3M outputs of the GCM, with those of observations relevant to the calibration period of the downscaling models. For the validation of the bias-correction, outputs of the downscaling models produced with the 20C3M outputs of the GCM pertaining to the validation period of the downscaling models were standardised with the means and the standard deviations of the outputs of the downscaling models pertaining to the calibration period. Then, those standardised outputs were transformed back with the means and the standard deviations of the observations relevant to the calibration period of the downscaling models. The bias-correction was applied to each predictand in each calendar month separately.

Development of a downscaling model at a member station

It was important to compare the statistics of the outputs (e.g. monthly precipitation) produced by the inter-station regression relationships against the statistics of outputs of a downscaling model developed at a member station for the past climate since this enables the determination of how well the key station approach can replace the need of having individual downscaling models at member stations. For this purpose, for a predictand, a downscaling model was developed at a member station. The downscaling model developed at a member station refers to relationships between the observations at a member station and reanalysis data. In the development of the downscaling model at this member station, the same procedure which was adopted in building downscaling models at the key stations was employed. The outputs of the inter-station regression relationships and the corresponding outputs of the downscaling model built at the member station were compared both numerically and graphically with each other.

Projections into future

In order to produce catchment scale projections of the predictands into the future, GCM outputs pertaining to the future climate were obtained. Then these were standardised with the means and the standard deviations of the reanalysis data corresponding to the calibration phase of the downscaling models. These standardised GCM outputs were introduced to the downscaling models developed at key stations for producing the projections of predictands into the future. In the same way as the bias-correction was validated (refer to ‘Reproduction of past climate at key stations and bias-correction’ above), it was applied to the projections produced into the future by the downscaling models developed at the key stations. Using the inter-station regression relationships, the projections produced into the future at key stations were extended to the member stations.

APPLICATION

The generic methodology described above under ‘Generic methodology’ was applied to downscale monthly GCM outputs to precipitation, evaporation, minimum temperature and maximum temperature at 17 stations (see Table 1) located in the operational area of GWMWater (see Figure 1).

Identification of key stations and clusters

Key stations and clusters for precipitation

For identification of key stations, first the correlations of monthly precipitation among the stations were computed for the period 1950–2010, considering all calendar months together. Then the correlations above 0.80 (p ≤ 0.05) in the matrix were identified. This correlation matrix is shown in Table 2. The correlations above 0.80 are highlighted in bold text. For monthly precipitation, the stations 79023 (Polkemmet) and 79046 (Wartook reservoir) showed the highest number of correlations above 0.80 with the rest of the stations in the study area. Therefore, one of these stations, in this case station 79046, was selected as the first key station for monthly precipitation. The stations which displayed correlations above 0.80 with station 79046 (first key station) were identified as the member stations of the first cluster. These member stations were 79014, 79019, 79023, 79026, 79028, 79034, 90173, 79074, 79079, 79080, 89003 and 89085.

Table 2

Correlations among the 17 stations for monthly observed precipitation over the period 1950–2010

 
 

Bold correlations are above the correlation threshold 0.80.

After the delineation of the first cluster, the rest of the stations (76047, 77007, 77042 and 77083) in the study area were considered for the identification of the next key stations. The correlations among these stations for monthly precipitation are highlighted in the box shown in Table 2. Similar to the selection of the first key station, a threshold of 0.80 was imposed on the correlation matrix in this box. Since each station highlighted in the box in Table 2 (76047, 77007, 77042 and 77083) had only one correlation above 0.80 with other stations, one of these stations, in this case station 76047 (Ouyen post office), was selected as the second key station. Due to the high correlation displayed by the precipitation data at station 77042 (Swan Hill post office) with those at station 76047 (Ouyen post office), station 76042 was identified as the only member of the second cluster. Then, again a correlation threshold of 0.80 was imposed on the last two stations left (77007 and 77083). Since these two stations were highly correlated with each other for precipitation, station 77007 (Birchip post office) was defined as the third and the last key station, and station 77083 (Rainbow) was identified as the only member station of the third cluster. It was understood that the key station approach was able to segregate the precipitation observation stations in the study area into a number of clusters, depending on the spatial correlation structures seen in the past precipitation observations. The stations in different clusters were least correlated with each other. This allowed the maintenance of adequate independence between the stations in different clusters. Figure 3 shows the key stations, member stations and the clusters delineated over the study area for monthly precipitation.
Figure 3

Clusters of stations for precipitation.

Figure 3

Clusters of stations for precipitation.

Key stations and clusters for evaporation, minimum temperature and maximum temperature

In the same manner as for monthly precipitation, correlation matrices for the monthly observed evaporation, minimum temperature and maximum temperature were also calculated for the period 1950–2010 (not shown in the paper). It was seen that the correlations among stations for monthly evaporation, minimum and maximum temperature were much higher than those for monthly precipitation. The minimum correlation among the 17 stations for evaporation, which was about 0.94, was seen between stations 90173 and 76047, as these two stations are located in two different climatic zones and are separated by a large distance. The lowest correlations for both minimum temperature and maximum temperature were seen between the stations 90173 and 77042, which were 0.96 and 0.98, respectively. These two stations are located far apart from each other (see Figure 4) in two distinctly different climatic zones (refer to ‘Study area and data’ above).
Figure 4

Cluster of stations for evaporation, minimum temperature and maximum temperature.

Figure 4

Cluster of stations for evaporation, minimum temperature and maximum temperature.

Considering the very high correlations (higher than the correlation threshold of magnitude of 0.80) seen between the stations for evaporation, minimum temperature and maximum temperature, it was realised that any station in the study area can be regarded as a key station, for those climatic variables. Therefore, for evaporation, minimum temperature and maximum temperature, station 79046 (Wartook reservoir) was selected as the sole key station. The rest of the stations were considered as the member stations of the cluster. Figure 4 shows the key station and the cluster for evaporation, minimum temperature and maximum temperature over the study area.

Relationships between key stations and member stations in clusters

As described above under ‘Relationships between key stations and member stations in clusters’, simple linear regression relationships were developed (calibrated and validated) between the key stations and the member stations of each cluster, for each predictand and for each calendar month separately. The constants and coefficients of the MLR equations in the inter-station regression relationships determined for the past climate were assumed to be valid for the future, under changing climate.

Relationships between key stations and member stations for precipitation

Table 3 shows the statistics of the calibration (1950–1989) and validation (1990–2010) phases of inter-station regression relationships for precipitation. In all four seasons in all clusters, and at all member stations during the calibration phase of the inter-station regression relationships, the average of the monthly precipitation was near-perfectly reproduced. However, during the calibration period, the standard deviation of the precipitation was under-estimated at all member stations, in all clusters and in all seasons. In cluster 1 in the calibration period, the NSEs ranged between 0.57–0.83 (summer), 0.68–0.90 (autumn), 0.68–0.84 (winter) and 0.68– 0.90 (spring).

Table 3

Statistics for calibration and validation of inter-station regression relationships for precipitation

        Period 1950–1989 (Calibration)
 
Period 1990–2010 (Validation)
 
    Average
 
Std
 
  Average
 
Std
 
  
Season Key station Cluster Member station Obs Inter Obs Inter NSE Obs Inter Obs Inter NSE 
Summer 79046 79014 33.5 33.7 33.1 28.1 0.73 36.5 32.5 28.0 25.5 0.61 
79019 32.7 32.9 33.5 28.7 0.75 28.2 31.5 22.7 25.6 0.49 
79023 25.2 25.2 23.6 19.5 0.68 24.3 24.4 18.6 17.1 0.34 
79026 30.5 30.5 26.7 22.9 0.73 30.4 29.7 26.0 21.2 0.80 
79028 25.0 25.2 26.7 21.3 0.66 24.1 24.2 20.9 18.3 0.39 
79034 33.4 33.4 32.3 26.7 0.68 31.0 32.4 27.4 26.0 0.70 
90173 36.1 36.1 26.9 20.3 0.57 33.2 35.7 25.3 22.2 0.37 
79074 40.7 40.7 33.7 30.8 0.83 42.9 40.0 41.0 31.9 0.82 
79079 29.6 29.6 28.5 21.4 0.57 28.7 29.2 25.8 21.0 0.50 
79080 30.3 30.3 28.6 24.2 0.72 31.3 29.5 26.5 21.9 0.67 
89003 28.5 28.5 23.8 18.2 0.59 28.4 27.9 20.4 18.6 0.41 
89085 34.8 34.9 34.3 29.5 0.75 36.2 33.5 28.2 26.8 0.64 
76047 77042 24.3 24.3 27.0 20.3 0.56 24.1 24.1 22.1 18.8 0.60 
77007 77083 23.1 23.1 25.2 19.9 0.62 25.5 21.1 32.6 12.9 0.39 
Autumn 79046 79014 46.8 46.8 33.1 28.2 0.73 36.0 36.8 25.3 21.7 0.71 
79019 47.1 47.1 34.0 28.1 0.69 32.2 37.0 24.9 22.0 0.71 
79023 36.6 36.6 28.2 24.7 0.77 24.9 27.9 19.5 18.9 0.72 
79026 49.2 49.3 40.1 35.0 0.77 32.8 36.9 26.3 26.8 0.86 
79028 35.6 35.7 30.2 25.2 0.70 22.4 26.6 19.3 19.5 0.66 
79034 48.8 48.8 34.9 29.2 0.70 32.4 38.4 25.6 23.5 0.62 
90173 53.2 53.2 32.8 28.2 0.74 39.8 43.6 24.0 22.9 0.51 
79074 73.7 73.7 58.8 55.7 0.90 54.1 53.8 43.1 41.5 0.89 
79079 46.2 46.2 35.5 29.3 0.68 30.3 35.7 26.9 22.5 0.74 
79080 46.5 46.5 36.6 31.2 0.73 30.5 35.1 23.6 24.4 0.74 
89003 47.9 47.9 34.1 30.4 0.80 31.9 37.6 21.7 23.6 0.73 
89085 50.7 50.7 32.8 27.8 0.72 33.5 40.9 23.1 22.0 0.70 
76047 77042 32.8 32.8 27.9 22.8 0.67 21.1 24.0 20.7 19.0 0.63 
77007 77083 31.1 31.1 27.5 23.3 0.72 21.1 20.7 21.6 15.8 0.76 
Winter 79046 79014 62.7 62.7 29.0 25.4 0.77 63.8 60.6 29.4 24.0 0.71 
79019 63.0 63.0 32.1 28.3 0.78 60.9 60.4 30.4 26.5 0.72 
79023 48.3 48.3 24.9 21.1 0.72 49.2 47.4 27.0 20.9 0.77 
79026 72.4 72.4 38.6 33.7 0.76 72.9 70.3 39.3 32.9 0.88 
79028 44.2 44.2 23.3 19.8 0.73 43.1 43.1 26.1 19.5 0.73 
79034 63.0 63.0 32.3 28.0 0.75 60.3 60.6 28.6 26.3 0.75 
90173 73.6 73.6 29.2 25.2 0.74 70.6 72.2 28.7 24.4 0.55 
79074 125.1 125.1 64.5 59.2 0.84 119.4 120.3 61.2 56.6 0.86 
79079 58.9 58.9 28.2 23.3 0.68 55.0 57.7 32.7 22.8 0.67 
79080 60.1 60.1 31.0 26.4 0.73 61.0 58.4 32.8 25.9 0.81 
89003 73.6 73.6 33.4 29.7 0.79 66.5 71.1 31.3 28.1 0.78 
89085 64.3 64.3 29.3 26.5 0.82 60.9 62.3 27.0 25.1 0.74 
76047 77042 35.9 35.9 23.0 19.5 0.72 30.8 32.9 18.7 16.2 0.55 
77007 77083 36.8 36.8 20.4 17.3 0.72 37.1 33.1 21.5 15.9 0.66 
Spring 79046 79014 55.7 55.7 32.8 27.9 0.72 51.7 49.7 29.6 23.9 0.66 
 79019 53.0 53.0 32.2 28.2 0.77 49.0 46.9 28.9 23.7 0.58 
 79023 42.6 42.6 27.2 23.1 0.73 40.9 37.0 26.2 18.7 0.72 
 79026 53.2 53.2 33.9 30.2 0.80 50.2 46.6 30.7 25.0 0.84 
 79028 40.5 40.5 28.1 23.2 0.68 35.8 34.9 23.3 18.3 0.73 
   79034 56.3 56.3 33.9 29.1 0.74 48.5 49.4 25.3 24.4 0.72 
   90173 63.5 63.5 29.1 25.2 0.75 59.8 58.4 26.8 21.5 0.70 
   79074 87.7 87.7 53.5 50.8 0.90 78.3 78.5 48.4 45.8 0.83 
   79079 50.4 50.4 32.8 27.2 0.69 44.1 44.5 30.8 22.4 0.64 
   79080 50.5 50.5 32.1 27.7 0.74 47.1 44.5 29.2 22.9 0.74 
   89003 57.2 57.2 31.4 27.9 0.79 48.9 51.4 27.5 23.8 0.85 
   89085 58.7 58.7 34.0 30.4 0.80 49.9 51.6 23.9 25.5 0.65 
 76047 77042 34.0 34.0 23.7 20.1 0.72 34.0 31.3 29.6 18.1 0.72 
 77007 77083 36.0 36.0 26.2 21.9 0.70 31.6 31.6 24.8 17.7 0.65 
        Period 1950–1989 (Calibration)
 
Period 1990–2010 (Validation)
 
    Average
 
Std
 
  Average
 
Std
 
  
Season Key station Cluster Member station Obs Inter Obs Inter NSE Obs Inter Obs Inter NSE 
Summer 79046 79014 33.5 33.7 33.1 28.1 0.73 36.5 32.5 28.0 25.5 0.61 
79019 32.7 32.9 33.5 28.7 0.75 28.2 31.5 22.7 25.6 0.49 
79023 25.2 25.2 23.6 19.5 0.68 24.3 24.4 18.6 17.1 0.34 
79026 30.5 30.5 26.7 22.9 0.73 30.4 29.7 26.0 21.2 0.80 
79028 25.0 25.2 26.7 21.3 0.66 24.1 24.2 20.9 18.3 0.39 
79034 33.4 33.4 32.3 26.7 0.68 31.0 32.4 27.4 26.0 0.70 
90173 36.1 36.1 26.9 20.3 0.57 33.2 35.7 25.3 22.2 0.37 
79074 40.7 40.7 33.7 30.8 0.83 42.9 40.0 41.0 31.9 0.82 
79079 29.6 29.6 28.5 21.4 0.57 28.7 29.2 25.8 21.0 0.50 
79080 30.3 30.3 28.6 24.2 0.72 31.3 29.5 26.5 21.9 0.67 
89003 28.5 28.5 23.8 18.2 0.59 28.4 27.9 20.4 18.6 0.41 
89085 34.8 34.9 34.3 29.5 0.75 36.2 33.5 28.2 26.8 0.64 
76047 77042 24.3 24.3 27.0 20.3 0.56 24.1 24.1 22.1 18.8 0.60 
77007 77083 23.1 23.1 25.2 19.9 0.62 25.5 21.1 32.6 12.9 0.39 
Autumn 79046 79014 46.8 46.8 33.1 28.2 0.73 36.0 36.8 25.3 21.7 0.71 
79019 47.1 47.1 34.0 28.1 0.69 32.2 37.0 24.9 22.0 0.71 
79023 36.6 36.6 28.2 24.7 0.77 24.9 27.9 19.5 18.9 0.72 
79026 49.2 49.3 40.1 35.0 0.77 32.8 36.9 26.3 26.8 0.86 
79028 35.6 35.7 30.2 25.2 0.70 22.4 26.6 19.3 19.5 0.66 
79034 48.8 48.8 34.9 29.2 0.70 32.4 38.4 25.6 23.5 0.62 
90173 53.2 53.2 32.8 28.2 0.74 39.8 43.6 24.0 22.9 0.51 
79074 73.7 73.7 58.8 55.7 0.90 54.1 53.8 43.1 41.5 0.89 
79079 46.2 46.2 35.5 29.3 0.68 30.3 35.7 26.9 22.5 0.74 
79080 46.5 46.5 36.6 31.2 0.73 30.5 35.1 23.6 24.4 0.74 
89003 47.9 47.9 34.1 30.4 0.80 31.9 37.6 21.7 23.6 0.73 
89085 50.7 50.7 32.8 27.8 0.72 33.5 40.9 23.1 22.0 0.70 
76047 77042 32.8 32.8 27.9 22.8 0.67 21.1 24.0 20.7 19.0 0.63 
77007 77083 31.1 31.1 27.5 23.3 0.72 21.1 20.7 21.6 15.8 0.76 
Winter 79046 79014 62.7 62.7 29.0 25.4 0.77 63.8 60.6 29.4 24.0 0.71 
79019 63.0 63.0 32.1 28.3 0.78 60.9 60.4 30.4 26.5 0.72 
79023 48.3 48.3 24.9 21.1 0.72 49.2 47.4 27.0 20.9 0.77 
79026 72.4 72.4 38.6 33.7 0.76 72.9 70.3 39.3 32.9 0.88 
79028 44.2 44.2 23.3 19.8 0.73 43.1 43.1 26.1 19.5 0.73 
79034 63.0 63.0 32.3 28.0 0.75 60.3 60.6 28.6 26.3 0.75 
90173 73.6 73.6 29.2 25.2 0.74 70.6 72.2 28.7 24.4 0.55 
79074 125.1 125.1 64.5 59.2 0.84 119.4 120.3 61.2 56.6 0.86 
79079 58.9 58.9 28.2 23.3 0.68 55.0 57.7 32.7 22.8 0.67 
79080 60.1 60.1 31.0 26.4 0.73 61.0 58.4 32.8 25.9 0.81 
89003 73.6 73.6 33.4 29.7 0.79 66.5 71.1 31.3 28.1 0.78 
89085 64.3 64.3 29.3 26.5 0.82 60.9 62.3 27.0 25.1 0.74 
76047 77042 35.9 35.9 23.0 19.5 0.72 30.8 32.9 18.7 16.2 0.55 
77007 77083 36.8 36.8 20.4 17.3 0.72 37.1 33.1 21.5 15.9 0.66 
Spring 79046 79014 55.7 55.7 32.8 27.9 0.72 51.7 49.7 29.6 23.9 0.66 
 79019 53.0 53.0 32.2 28.2 0.77 49.0 46.9 28.9 23.7 0.58 
 79023 42.6 42.6 27.2 23.1 0.73 40.9 37.0 26.2 18.7 0.72 
 79026 53.2 53.2 33.9 30.2 0.80 50.2 46.6 30.7 25.0 0.84 
 79028 40.5 40.5 28.1 23.2 0.68 35.8 34.9 23.3 18.3 0.73 
   79034 56.3 56.3 33.9 29.1 0.74 48.5 49.4 25.3 24.4 0.72 
   90173 63.5 63.5 29.1 25.2 0.75 59.8 58.4 26.8 21.5 0.70 
   79074 87.7 87.7 53.5 50.8 0.90 78.3 78.5 48.4 45.8 0.83 
   79079 50.4 50.4 32.8 27.2 0.69 44.1 44.5 30.8 22.4 0.64 
   79080 50.5 50.5 32.1 27.7 0.74 47.1 44.5 29.2 22.9 0.74 
   89003 57.2 57.2 31.4 27.9 0.79 48.9 51.4 27.5 23.8 0.85 
   89085 58.7 58.7 34.0 30.4 0.80 49.9 51.6 23.9 25.5 0.65 
 76047 77042 34.0 34.0 23.7 20.1 0.72 34.0 31.3 29.6 18.1 0.72 
 77007 77083 36.0 36.0 26.2 21.9 0.70 31.6 31.6 24.8 17.7 0.65 

Average, average of monthly precipitation in mm; Std, standard deviation of monthly precipitation in mm; Inter, inter-station regression relationships; NSE, Nash–Sutcliffe efficiency.

In the calibration phase of the inter-station regression relationships, the highest NSEs in all clusters, in all four seasons, were seen at station 79074 (Halls Gap post office). This was due to the very high correlation (0.95 in Table 2) which prevailed between the observed precipitation at the key station of cluster 1 (79046) and that at station 79074. Also, these stations were located geographically close to each other (see Figure 3). In cluster 1, during the calibration phase, the lowest NSEs in summer, autumn and winter were seen at station 79079. In the calibration period in clusters 2 and 3, NSEs were relatively low in summer, and the highest NSEs in those clusters were seen in winter.

In the validation phase of the inter-station regression relationships for precipitation, despite some under-predictions in all seasons, the average of precipitation was well reproduced at all member stations in the three clusters. During the same period, the standard deviation of the precipitation was well reproduced at the majority of member stations in cluster 1, in all seasons, despite some under and over-predictions. Under-prediction of the standard deviation of precipitation was evident at all member stations in clusters 2 and 3 in all seasons. In cluster 1 during validation, NSEs for precipitation at member stations varied between 0.34–0.82 (summer), 0.51–0.89 (autumn), 0.55–0.88 (winter) and 0.58–0.85 (spring). In summer and autumn, station 79074 showed the highest NSEs in all clusters during the validation phase. In winter and spring, station 79026 displayed the highest NSEs in all clusters.

Considering the performances of the outputs of inter-station regression relationships seen in their calibration and validation phases, it was realised that they are robust enough for satisfactory modelling of precipitation at the member stations.

Relationships between key stations and member stations for evaporation and temperature

At the majority of member stations, the NSEs for the calibration (1950–1989) and validation (1990–2010) phases of the inter-station regression relationships for evaporation, minimum temperature and maximum temperature were quite high in all four seasons (results not shown in the paper). It was realised that these high NSEs were due to the high correlations seen between the key station and member stations (see above under ‘Key stations and clusters for evaporation, minimum temperature and maximum temperature’) for evaporation, minimum temperature and maximum temperature. Furthermore, it was seen that NSEs for the inter-station regression relationships developed for evaporation, minimum temperature and maximum temperature were relatively higher than those for precipitation. Also, in the calibration phase the inter-station regression relationships near-perfectly reproduced the averages of evaporation, minimum temperature and maximum temperature, at all member stations, in all seasons. Also, at the majority of stations the standard deviations of evaporation, minimum temperature and maximum temperature were near-perfectly reproduced by the inter-station regression relationships during the calibration period. In the validation phase, despite slight over and under-predictions, the inter-station regression relationships built for evaporation, minimum temperature and maximum temperature were able to capture the average and the standard deviations of these variables well in all seasons, at all member stations. It was realised that the inter-station regression relationships developed between the key station and member stations for evaporation, minimum temperature and maximum temperature are quite robust.

Atmospheric domain and predictor selection

As shown in Figure 5, an atmospheric domain with seven points in the longitudinal direction and six points in the latitudinal direction was demarcated over the study area for the current study. This atmospheric domain had a spatial resolution of 2.5° in both longitudinal and latitudinal directions.
Figure 5

Atmospheric domain for downscaling.

Figure 5

Atmospheric domain for downscaling.

The probable predictors for the current study were selected mainly based on the study by Timbal et al. (2009). Timbal et al. (2009) used the method of meteorological analogues to statistically downscale GCM outputs to daily precipitation, pan evaporation, minimum temperature, maximum temperature, and dew point temperature over six regions in the southern half of Australia. In that study, they identified the best predictors for each predictand for each season over the six regions. Since the current study area is also located in south eastern Australia, the predictors used in the study by Timbal et al. (2009) were included in the probable predictor pool of the current study. Some of the predictors used by Anandhi et al. (2008, 2009) in downscaling GCM outputs to monthly precipitation, minimum temperature and maximum temperature were also included in the pool of probable predictors used in the current study. The probable predictors which were selected for the present study based on past literature and hydrology are shown in Table 4.

Table 4

Probable predictors for precipitation, evaporation and temperature

Probable predictor Level Precipitation Evaporation Tmin/max 
Geopotential height 200 hPa ✓ ✓ ✓ 
500 hPa ✓ ✓ ✓ 
700 hPa ✓ ✓ ✓ 
850 hPa ✓ ✓ ✓ 
1,000 hPa ✓ ✓ ✓ 
Relative humidity 500 hPa ✓ ✓ ✓ 
700 hPa ✓ ✓ ✓ 
850 hPa ✓ ✓ ✓ 
925 hPa  ✓ ✓ 
1,000 hPa ✓ ✓ ✓ 
Specific humidity 2 m height ✓ ✓ ✓ 
500 hPa ✓ ✓ ✓ 
850 hPa ✓ ✓ ✓ 
1,000 hPa ✓ ✓ ✓ 
Air temperature 2 m height ✓ ✓ ✓ 
500 hPa ✓ ✓ ✓ 
850 hPa ✓ ✓ ✓ 
1,000 hPa ✓ ✓ ✓ 
Skin temperature Surface ✓ ✓ ✓ 
Pressure Surface ✓ ✓ ✓ 
Mean sea level ✓ ✓ ✓ 
Precipitation rate Surface ✓ ✓  
Precipitable water N/A  ✓  
Zonal wind speed 850 hPa ✓ ✓ ✓ 
Meridional wind speed 850 hPa ✓ ✓ ✓ 
Probable predictor Level Precipitation Evaporation Tmin/max 
Geopotential height 200 hPa ✓ ✓ ✓ 
500 hPa ✓ ✓ ✓ 
700 hPa ✓ ✓ ✓ 
850 hPa ✓ ✓ ✓ 
1,000 hPa ✓ ✓ ✓ 
Relative humidity 500 hPa ✓ ✓ ✓ 
700 hPa ✓ ✓ ✓ 
850 hPa ✓ ✓ ✓ 
925 hPa  ✓ ✓ 
1,000 hPa ✓ ✓ ✓ 
Specific humidity 2 m height ✓ ✓ ✓ 
500 hPa ✓ ✓ ✓ 
850 hPa ✓ ✓ ✓ 
1,000 hPa ✓ ✓ ✓ 
Air temperature 2 m height ✓ ✓ ✓ 
500 hPa ✓ ✓ ✓ 
850 hPa ✓ ✓ ✓ 
1,000 hPa ✓ ✓ ✓ 
Skin temperature Surface ✓ ✓ ✓ 
Pressure Surface ✓ ✓ ✓ 
Mean sea level ✓ ✓ ✓ 
Precipitation rate Surface ✓ ✓  
Precipitable water N/A  ✓  
Zonal wind speed 850 hPa ✓ ✓ ✓ 
Meridional wind speed 850 hPa ✓ ✓ ✓ 

✓, included in the pool of probable predictors; N/A, not applicable; hPa, atmospheric pressure in hectopascal; Tmin/max, minimum temperature and maximum temperature.

Following the procedure described above under ‘Atmospheric domain and predictor selection’, potential predictors from the pool of probable predictors were extracted for each predictand at each key station for each calendar month.

Development of downscaling models at key stations

Using the procedure described above under ‘Development of downscaling models at key stations’, downscaling models were developed at the key stations for precipitation, evaporation, minimum temperature and maximum temperature. In statistical downscaling, it is common practice to use reanalysis data corresponding to the potential predictors as inputs to the downscaling models (predictor-predictand relationships) and then compare the outputs of the downscaling models against the observations (e.g. Anandhi et al. 2009; Sachindra et al. 2013). Corresponding to each GCM (or reanalysis) output, observations are not always readily available. As an example, observations of geopotential height at 200 hpa pressure level are not readily available but reanalysis outputs are available for geopotential height at 200 hpa pressure level. Therefore, reanalysis data were used in the development of downscaling models in this study.

These models were calibrated and validated over the periods 1950–1989 and 1990–2010, respectively. The sections below entitled ‘Downscaling models developed at key stations for precipitation’, ‘Downscaling models developed at key stations for evaporation and temperature’ and ‘Bias-correction of the outputs produced by downscaling models with 20C3M outputs of HadCM3 at key stations’ detail the performances of the downscaling models developed at the key stations for precipitation, evaporation, minimum temperature and maximum temperature, respectively. All downscaling models in this study were developed using the MLR option available in the statistics toolbox of MATLAB (Version–R2008b) software.

Downscaling models developed at key stations for precipitation

As stated above under ‘Key stations and clusters for precipitation’, three key stations were identified for precipitation. Table 5 shows the statistics of the precipitation reproduced by the downscaling model developed at the key station 79046 of cluster 1. The statistics of the precipitation reproduced by the downscaling models developed at key stations 76047 (cluster 2) and 77007 (cluster 3) are not shown in tabular form. During the calibration phase of the downscaling models at key stations 79046, 76047 and 77007, the average of the precipitation was near-perfectly reproduced in all seasons. In validation at all three key stations, the average of precipitation was successfully reproduced, in all seasons, despite some under and over-predictions. In the majority of seasons, the standard deviation of precipitation was under-estimated by the downscaling models at all three key stations, during both the calibration and validation periods. During calibration at all three key stations, the maximum of precipitation was under-predicted in all seasons. In validation, the maximum of precipitation was under-predicted in all seasons at station 79046 (key station 1). At the other two key stations, this pattern was evident in the majority of seasons. The R2 values and NSEs of the precipitation reproduced by the downscaling models at the three key stations were also comparable with each other in the calibration and validation periods. Reanalysis data are the outputs of a GCM quality controlled and corrected against observations (a process called ‘data assimilation’) (Kalnay et al. 1996). The reanalysis data are not as accurate as observations (Mooney et al. 2011). Therefore, the comparison between the outputs of a statistical downscaling model run with reanalysis data with the observations does not always guarantee an excellent agreement between model outputs and observations (e.g. Sachindra et al. 2013).

Table 5

Statistics of precipitation reproduced by downscaling model developed at station 79046 (Key station 1)

    Calibration (1950–1989)
 
Validation (1990–2010)
 
  Season
 
Season
 
Model Statistic Summer Autumn Winter Spring Summer Autumn Winter Spring 
Observed Avg 40.9 67.9 108.5 80.8 39.3 50.2 106.3 72.3 
Model output 40.9 67.9 108.5 80.8 47.8 56.5 110.9 76.9 
Observed Std 32.2 49.6 50.2 43.2 31.6 36.7 49.1 37.9 
Model output 20.4 39.8 41.6 32.2 24.3 28.3 40.1 30.2 
Observed Min 2.3 3.1 14.5 10.4 0.0 4.0 25.2 9.0 
Model output 8.5 0.0 11.1 23.8 15.8 0.0 21.4 18.3 
Observed Max 163.4 246.7 273.7 246.2 155.0 137.8 234.2 189.6 
Model output 123.7 182.1 240.4 166.6 112.7 117.5 221.6 164.4 
Model output NSE 0.40 0.65 0.69 0.56 0.41 0.56 0.74 0.73 
Model output R2 0.40 0.65 0.69 0.56 0.49 0.59 0.75 0.75 
    Calibration (1950–1989)
 
Validation (1990–2010)
 
  Season
 
Season
 
Model Statistic Summer Autumn Winter Spring Summer Autumn Winter Spring 
Observed Avg 40.9 67.9 108.5 80.8 39.3 50.2 106.3 72.3 
Model output 40.9 67.9 108.5 80.8 47.8 56.5 110.9 76.9 
Observed Std 32.2 49.6 50.2 43.2 31.6 36.7 49.1 37.9 
Model output 20.4 39.8 41.6 32.2 24.3 28.3 40.1 30.2 
Observed Min 2.3 3.1 14.5 10.4 0.0 4.0 25.2 9.0 
Model output 8.5 0.0 11.1 23.8 15.8 0.0 21.4 18.3 
Observed Max 163.4 246.7 273.7 246.2 155.0 137.8 234.2 189.6 
Model output 123.7 182.1 240.4 166.6 112.7 117.5 221.6 164.4 
Model output NSE 0.40 0.65 0.69 0.56 0.41 0.56 0.74 0.73 
Model output R2 0.40 0.65 0.69 0.56 0.49 0.59 0.75 0.75 

Avg, average of monthly precipitation in mm; Std, standard deviation of monthly precipitation in mm; Min, minimum of monthly precipitation in mm; Max, maximum of monthly precipitation in mm; NSE, Nash–Sutcliffe efficiency; R2, coefficient of determination.

Figure 6 shows the scatter plots for the precipitation reproduced by the downscaling models developed at the key stations 79046, 76047 and 77007, for the calibration and validation phases. The best model performance in terms of the NSE (0.75) was seen at key station 79046 in its validation. Similarly, a good NSE of 0.70 was also seen in its calibration phase. The other two key stations showed low NSEs in both calibration and validation, relative to those of key station 79046. At all three key stations, the scatter of precipitation reproduced by the downscaling models in their calibration and validation periods was comparable with each other. According to the six scatter plots in Figure 6, it was seen that the high precipitation values were under-predicted by the downscaling models at all key stations, during both the calibration and validation periods. Also, all three downscaling models in general displayed an over-predicting pattern for the low precipitation values in the calibration and validation periods.
Figure 6

Scatter plots for precipitation reproduced by downscaling models developed at key stations 79046, 76047 and 77007.

Figure 6

Scatter plots for precipitation reproduced by downscaling models developed at key stations 79046, 76047 and 77007.

Downscaling models developed at key stations for evaporation and temperature

As stated above under ‘Key stations and clusters for evaporation, minimum temperature and maximum temperature’, for the entire study area one single key station was identified for evaporation, minimum temperature and maximum temperature. The statistics of the monthly evaporation, minimum temperature and maximum temperature reproduced by the downscaling models developed at the key station 79046 were compared with the statistics of corresponding observations (results not shown).

During the calibration phase, the average of evaporation was perfectly reproduced by the downscaling model at key station 79046, in all seasons. Despite negligible over and under-predictions seen during the validation period of this downscaling model, in all seasons, the average of evaporation was well reproduced. The standard deviation of evaporation was reproduced with good accuracy in both calibration and validation, in all seasons, despite slight over- and under-predictions. For evaporation, relatively high NSE and R2 values were seen in the calibration and validation phases of the downscaling model, in all seasons. According to the statistics of the monthly evaporation reproduced by the downscaling model developed at key station 79046, it was realised that this model is quite capable of reproducing the statistics of observations of evaporation.

In all seasons, the averages of the minimum temperature and maximum temperature were near-perfectly reproduced by the downscaling models which were developed for the key station 79046, in both the calibration and validation periods. Despite slight under- and over-estimations, the standard deviation of the minimum temperature was well reproduced in the calibration and the validation phases of the downscaling model, in all seasons. However, both in calibration and validation, the standard deviation of the maximum temperature was slightly under-estimated by the downscaling model in all four seasons. In all seasons, an over-prediction of the minimum of the minimum temperature was seen in both calibration and validation. The minimum of the minimum temperature was important as it referred to extreme minimum temperature. In both the calibration and validation periods, despite slight over and under-predictions, the maximum of the maximum temperature were reproduced with good accuracy by the downscaling model, in all seasons. The maximum of the maximum temperature was important as it referred to extreme maximum temperature.

Figure 7 shows the scatter plots for evaporation, minimum temperature and maximum temperature reproduced by the downscaling models developed at key station 79046. It was evident that, for evaporation, minimum temperature and maximum temperature, the scatter was small and quite comparable in both the calibration and validation periods. However, the scatter of evaporation (see Figure 7(a) and 7(b)) and maximum temperature (see Figure 7(e) and 7(f)) in both the calibration and validation periods was relatively smaller for lower values and larger for higher values. On the other hand, the scatter of the minimum temperature was almost even along the 45° line in both the calibration and validation periods (see Figure 7(c) and 7(d)).
Figure 7

Scatter plots for evaporation, minimum temperature and maximum temperature reproduced by downscaling model developed at key station 79046.

Figure 7

Scatter plots for evaporation, minimum temperature and maximum temperature reproduced by downscaling model developed at key station 79046.

Bias-correction of the outputs produced by downscaling models with 20C3M outputs of HadCM3 at key stations

Following the procedure detailed above under ‘Reproduction of past climate at key stations and bias-correction’, the monthly bias-correction (Johnson & Sharma 2012) was applied over the period 1950–1989 and it was validated for the period 1990–2010. Table 6 shows the statistics of precipitation reproduced by the downscaling model developed at key station 79046 when it was run with the 20C3M outputs of HadCM3, before and after the application of the monthly bias-correction. Note that the statistics of evaporation, minimum temperature and maximum temperature reproduced by the downscaling model developed at key station 79046 before and after the monthly bias-correction are not shown in tabular form.

Table 6

Statistics of precipitation reproduced by downscaling model at key station 79046, with 20C3M outputs of HadCM3, before and after bias-correction

    Application (1950–1989)
 
Validation (1990–1999)
 
  Season
 
Season
 
Model Statistic Summer Autumn Winter Spring Summer Autumn Winter Spring 
Observed Avg 40.9 67.9 108.5 80.8 42.3 53.1 119.0 77.8 
Before B-C 66.3 102.2 156.5 83.4 69.9 106.1 137.0 82.6 
After B-C 41.1 68.1 108.5 80.8 44.5 75.4 101.8 81.1 
Observed Std 32.2 49.6 50.2 43.2 37.2 42.9 57.8 41.8 
Before B-C 32.1 34.4 137.0 47.6 35.1 39.4 93.6 52.5 
After B-C 31.9 49.2 50.2 43.2 35.0 70.7 37.1 47.5 
Observed Min 2.3 3.1 14.5 10.4 0.0 4.0 29.8 21.8 
Before B-C 17.7 18.4 0.0 0.0 21.3 46.3 0.0 0.0 
After B-C 0.0 0.0 2.4 17.0 0.0 9.0 3.5 20.6 
Observed Max 163.4 246.7 273.7 246.2 155.0 137.8 234.2 189.6 
Before B-C 183.7 189.6 1091.1 187.9 145.4 212.7 420.7 163.7 
After B-C 144.0 245.4 323.6 193.5 126.2 298.1 209.3 236.8 
Before B-C NSE –1.17 –0.40 –9.29 –1.00 –1.30 –1.91 –2.70 –0.87 
After B-C –0.54 –0.27 –1.03 –0.90 –0.64 –2.46 –0.48 –1.22 
    Application (1950–1989)
 
Validation (1990–1999)
 
  Season
 
Season
 
Model Statistic Summer Autumn Winter Spring Summer Autumn Winter Spring 
Observed Avg 40.9 67.9 108.5 80.8 42.3 53.1 119.0 77.8 
Before B-C 66.3 102.2 156.5 83.4 69.9 106.1 137.0 82.6 
After B-C 41.1 68.1 108.5 80.8 44.5 75.4 101.8 81.1 
Observed Std 32.2 49.6 50.2 43.2 37.2 42.9 57.8 41.8 
Before B-C 32.1 34.4 137.0 47.6 35.1 39.4 93.6 52.5 
After B-C 31.9 49.2 50.2 43.2 35.0 70.7 37.1 47.5 
Observed Min 2.3 3.1 14.5 10.4 0.0 4.0 29.8 21.8 
Before B-C 17.7 18.4 0.0 0.0 21.3 46.3 0.0 0.0 
After B-C 0.0 0.0 2.4 17.0 0.0 9.0 3.5 20.6 
Observed Max 163.4 246.7 273.7 246.2 155.0 137.8 234.2 189.6 
Before B-C 183.7 189.6 1091.1 187.9 145.4 212.7 420.7 163.7 
After B-C 144.0 245.4 323.6 193.5 126.2 298.1 209.3 236.8 
Before B-C NSE –1.17 –0.40 –9.29 –1.00 –1.30 –1.91 –2.70 –0.87 
After B-C –0.54 –0.27 –1.03 –0.90 –0.64 –2.46 –0.48 –1.22 

Avg, average of monthly precipitation in mm; Std, standard deviation of monthly precipitation in mm; Min, minimum of monthly precipitation in mm; Max, maximum of monthly precipitation in mm; NSE, Nash–Sutcliffe efficiency; Before B-C, before bias-correction; After B-C, after bias-correction.

As shown in Table 6, the downscaling model at the key station 79046, when it was run with the 20C3M outputs of HadCM3, tended to over-estimate the average of precipitation in the application and validation periods of the bias-correction, in all seasons, before the bias-correction. After the application of the monthly bias-correction the average of precipitation reproduced by the downscaling model was corrected with good accuracy, in all seasons in the application period. During the validation period of the bias-correction in summer and spring, the average of precipitation was successfully corrected. The correction to the standard deviation of precipitation reproduced by the downscaling model was successful in the majority of seasons in the application and validation phases of the bias-correction. In both the application and validation periods of the bias-correction, the minimum of precipitation was well corrected in all seasons except spring. However, the correction to the maximum of precipitation was limited in the majority of seasons, in both application and validation periods.

In the application and validation periods, before the implementation of the bias-correction, the NSEs were quite low during all seasons for precipitation. This indicated that there is a large mismatch in the precipitation reproduced by the downscaling model when it was run with the 20C3M outputs of HadCM3 (i.e. considerable bias) and the observed precipitation. The limited performance of the precipitation downscaling model was due to the bias in the 20C3M outputs of HadCM3 rather than due to a failure of the downscaling model. This was proven as the downscaling was able to well reproduce the precipitation when run with reanalysis data (see Table 5) in comparison to the precipitation reproduced by the downscaling model with the 20C3M outputs of HadCM3. Sachindra et al. (2014a) had demonstrated the large bias in the 20C3M outputs of HadCM3 over the same study area and also the impact of bias on the outputs of the downscaling models. After the application of the bias-correction, the NSEs in all seasons in the application period and also in summer and winter in the validation period showed some increase. This hinted at some improvement to the time series of the variable following the application of monthly bias-correction.

For evaporation in general, the over and under-predictions in the statistics were quite small in comparison with those for precipitation. During the application period of the bias-correction, the bias in the average of evaporation was perfectly corrected in all seasons. In the validation phase of the bias-correction, the bias in the average of evaporation reproduced by the downscaling model increased in the majority of seasons. The standard deviation of the evaporation reproduced by the downscaling model was well corrected in the application phase of the bias-correction. In the validation phase, the bias in the standard deviation of the evaporation decreased in winter and spring. The maximum of the evaporation reproduced by the downscaling model was well corrected by the bias-correction in summer during both the application and validation periods. The NSEs for the evaporation reproduced by the downscaling model when it was run with the 20C3M outputs of HadCM3 were relatively higher than those for precipitation, in both the application and validation periods.

The bias in the average of the minimum temperature and the maximum temperature reproduced by the downscaling model at key station 79046, when it was run with the 20C3M outputs of HadCM3, was quite small in all seasons even before the bias-correction. The over-prediction of the standard deviation of the minimum temperature that was seen in summer and spring in the application and validation periods of the bias-correction was successfully corrected. Also, the under and over-predictions in the standard deviation of the maximum temperature in the application and validation periods of the bias-correction were successfully corrected in all seasons. Furthermore, the monthly bias-correction was able to successfully correct the bias in the minimum of minimum temperature and the maximum of maximum temperature in both application and validation periods.

Development of a downscaling model at a member station

Using the same procedure used in developing downscaling models at key stations (see above under ‘Development of downscaling models at key stations’), a downscaling model was built for precipitation at member station 89003. This was performed to compare the performances of the inter-site regression relationship (between the key station 79046 and the member station 89003) against the performances of the downscaling model developed at this member station in reproducing the observed precipitation. Table 7 shows the statistics of precipitation reproduced by the downscaling models at station 89003, and also the statistics of precipitation reproduced at station 89003 by applying the precipitation outputs of the downscaling model developed at key station 79046 on the inter-site regression relationship. Note that both downscaling models at stations 89003 and 79046 were run with NCEP/NCAR reanalysis outputs as inputs, for this analysis.

Table 7

Statistics of precipitation reproduced at station 89003 by downscaling models and inter-site regression relationship

    Calibration (1950–1989)
 
Validation (1990–2010)
 
  Season
 
Season
 
Model Statistic Summer Autumn Winter Spring Summer Autumn Winter Spring 
Observed Avg 28.5 47.9 73.6 57.2 28.4 31.9 66.5 48.9 
Model output 28.5 48.0 73.6 57.2 33.3 37.9 73.1 54.8 
Inter-station Reg 28.5 47.9 73.6 57.2 32.3 41.3 74.7 54.7 
Observed Std 23.8 34.1 33.4 31.4 20.4 21.7 31.3 27.5 
Model output 14.1 27.3 28.2 23.3 17.3 19.6 27.0 23.3 
Inter-station Reg 12.2 24.3 24.7 20.4 14.3 18.5 23.8 19.4 
Observed Min 0.0 0.0 5.7 4.4 0.0 0.0 10.0 3.2 
Model output 12.0 0.0 1.7 18.8 13.3 0.0 17.8 0.0 
Inter-station Reg 8.9 2.5 18.3 18.2 14.9 2.5 23.9 14.6 
Observed Max 143.7 136.8 182.9 184.0 85.8 90.7 147.7 125.2 
Model output 88.6 114.8 161.7 148.5 81.6 88.0 143.1 111.1 
Inter-station Reg 79.8 111.3 158.4 112.3 73.4 76.9 136.3 109.4 
Model output NSE 0.35 0.65 0.72 0.55 0.44 0.45 0.66 0.60 
Inter-station Reg 0.36 0.50 0.65 0.46 0.46 0.31 0.66 0.64 
    Calibration (1950–1989)
 
Validation (1990–2010)
 
  Season
 
Season
 
Model Statistic Summer Autumn Winter Spring Summer Autumn Winter Spring 
Observed Avg 28.5 47.9 73.6 57.2 28.4 31.9 66.5 48.9 
Model output 28.5 48.0 73.6 57.2 33.3 37.9 73.1 54.8 
Inter-station Reg 28.5 47.9 73.6 57.2 32.3 41.3 74.7 54.7 
Observed Std 23.8 34.1 33.4 31.4 20.4 21.7 31.3 27.5 
Model output 14.1 27.3 28.2 23.3 17.3 19.6 27.0 23.3 
Inter-station Reg 12.2 24.3 24.7 20.4 14.3 18.5 23.8 19.4 
Observed Min 0.0 0.0 5.7 4.4 0.0 0.0 10.0 3.2 
Model output 12.0 0.0 1.7 18.8 13.3 0.0 17.8 0.0 
Inter-station Reg 8.9 2.5 18.3 18.2 14.9 2.5 23.9 14.6 
Observed Max 143.7 136.8 182.9 184.0 85.8 90.7 147.7 125.2 
Model output 88.6 114.8 161.7 148.5 81.6 88.0 143.1 111.1 
Inter-station Reg 79.8 111.3 158.4 112.3 73.4 76.9 136.3 109.4 
Model output NSE 0.35 0.65 0.72 0.55 0.44 0.45 0.66 0.60 
Inter-station Reg 0.36 0.50 0.65 0.46 0.46 0.31 0.66 0.64 

Avg, average of monthly precipitation in mm; Std, standard deviation of monthly precipitation in mm; Min, minimum of monthly precipitation in mm; Max, maximum of monthly precipitation in mm; NSE, Nash–Sutcliffe efficiency; Inter-station Reg, inter-station regression relationship.

As shown in Table 7, in all seasons the average of precipitation was near-perfectly reproduced by the downscaling model at station 89003 and the inter-station regression relationship in the calibration period. In the validation period, the average of precipitation was over-estimated in all seasons by the downscaling model at station 89003 and the inter-station regression relationship. However, still these results were quite comparable with each other. In both calibration and validation, the standard deviation of precipitation was under-predicted in all seasons by the downscaling model at station 89003 and the inter-station regression relationship. Nevertheless, in all seasons, the standard deviation of precipitation reproduced by the downscaling model at station 89003 and the inter-station regression relationship were comparable with each other. Also, the maximum of precipitation reproduced by the downscaling model at station 89003 and that by inter-station regression relationship was comparable in all seasons. In both the calibration and validation periods, in the majority of seasons, the NSEs of the downscaling model at station 89003 and the inter-station regression relationship were quite comparable with each other.

In summary, it was seen that the statistics of the precipitation reproduced by the downscaling model developed for station 89003 and the inter-station regression relationship between the key station 79046 and station 89003 are comparable with each other in the majority of instances. It was then assumed that the inter-station regression relationships can reproduce precipitation, evaporation and minimum temperature and maximum temperature quite well at all stations, in comparison with the individual downscaling models developed for them.

Projections into the future

The A2 GHG emission scenario of the Intergovernmental Panel on Climate Change (IPCC) defined in the Special Report on Emission Scenarios (SRES) (IPCC 2000) was used for the projection of precipitation, evaporation, minimum temperature and maximum temperature into the future, at the 17 stations considered in this study. The monthly outputs of HadCM3 for the period 2000–2099 pertaining to the A2 GHG emission scenario were used for producing inputs to the downscaling models developed at the key stations. Following the procedure detailed above under ‘Projections into the future’, projections of precipitation, evaporation, minimum temperature and maximum temperature were produced into the future at the 17 stations.

The percentage changes in the statistics of monthly precipitation, evaporation, minimum temperature and maximum temperature, for each season, over the period 2000–2099, were compared with the statistics of the observations of those predictands of the period 1950–1989. In Table 8 the comparison of average of monthly precipitation, evaporation, minimum temperature and maximum temperature, for each season, over the period 2000–2099 with that of observations of the period 1950–1989 is shown.

Table 8

Percentage changes in the average of precipitation, evaporation, minimum temperature and maximum temperature over the period 2000–2099

Predictand Season 79014 76047 77007 77042 77083 79019 79023 79026 79028 79034 79046 90173 79074 79079 79080 89003 89085 
Precipitation Summer –9 ↓ –10 ↓ +28 ↑ –9 ↓ 21 ↑ –10 ↓ –10 ↓ –10 ↓ –9 ↓ –9 ↓ –10 ↓ –6 ↓ –9 ↓ –8 ↓ –9 ↓ –7 ↓ –10 ↓ 
Autumn +4 ↑ +36 ↑ +40 ↑ +23 ↑ +35 ↑ +6 ↑ +7 ↑ +9 ↑ +9 ↑ +8 ↑ +4 ↑ +7 ↑ +5 ↑ +5 ↑ +8 ↑ +6 ↑ +6 ↑ 
Winter +14 ↑ +23 ↑ –1 ↓ 21 ↑ –1 ↓ +15 ↑ +15 ↑ +16 ↑ +15 ↑ +15 ↑ +16 ↑ +11 ↑ +17 ↑ +13 ↑ +15 ↑ +14 ↑ +14 ↑ 
Spring –26 ↓ –18 ↓ –15 ↓ –14 ↓ –11 ↓ –27 ↓ –29 ↓ –30 ↓ –30 ↓ –27 ↓ –27 ↓ –19 ↓ –28 ↓ –28 ↓ –28 ↓ –24 ↓ –27 ↓ 
Evaporation Summer +7 ↑ +8 ↑ +9 ↑ +8 ↑ +9 ↑ +13 ↑ +11 ↑ +12 ↑ +11 ↑ +13 ↑ +13 ↑ +7 ↑ +13 ↑ +12 ↑ +12 ↑ +12 ↑ +13 ↑ 
Autumn +6 ↑ +11 ↑ +9 ↑ +8 ↑ +9 ↑ +11 ↑ +10 ↑ +11 ↑ +10 ↑ +11 ↑ +12 ↑ +6 ↑ +11 ↑ +11 ↑ +11 ↑ +10 ↑ +11 ↑ 
Winter +2 ↑ +4 ↑ +3 ↑ +3 ↑ +3 ↑ +4 ↑ +4 ↑ +5 ↑ +4 ↑ +5 ↑ +5 ↑ +2 ↑ +5 ↑ +5 ↑ +5 ↑ +4 ↑ +4 ↑ 
Spring +13 ↑ +19 ↑ +18 ↑ +16 ↑ +18 ↑ +21 ↑ +20 ↑ +22 ↑ +19 ↑ +22 ↑ +23 ↑ +11 ↑ +22 ↑ +24 ↑ +21 ↑ +18 ↑ +21 ↑ 
Min Temp Summer +1 ↑ +1 ↑ +0 ↑ +0 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ 
Autumn +22 ↑ +21 ↑ +22 ↑ +20 ↑ +23 ↑ +22 ↑ +22 ↑ +22 ↑ +24 ↑ +23 ↑ +25 ↑ +21 ↑ +24 ↑ +22 ↑ +21 ↑ +22 ↑ +23 ↑ 
Winter +40 ↑ +31 ↑ +36 ↑ +28 ↑ +36 ↑ +41 ↑ +39 ↑ +37 ↑ +41 ↑ +41 ↑ +49 ↑ +32 ↑ +44 ↑ +38 ↑ +34 ↑ +37 ↑ +46 ↑ 
Spring +29 ↑ +21 ↑ +26 ↑ +21 ↑ +26 ↑ +30 ↑ +26 ↑ +27 ↑ +29 ↑ +31 ↑ +34 ↑ +28 ↑ +32 ↑ +27 ↑ +26 ↑ +29 ↑ +33 ↑ 
Max Temp Summer +2 ↑ +2 ↑ +2 ↑ +1 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ 
Autumn +5 ↑ +4 ↑ +5 ↑ +4 ↑ +5 ↑ +6 ↑ +5 ↑ +5 ↑ +5 ↑ +6 ↑ +6 ↑ +5 ↑ +6 ↑ +5 ↑ +5 ↑ +5 ↑ +6 ↑ 
Winter +24 ↑ +21 ↑ +23 ↑ +22 ↑ +22 ↑ +25 ↑ +23 ↑ +24 ↑ +23 ↑ +25 ↑ +28 ↑ +21 ↑ +26 ↑ +24 ↑ +24 ↑ +22 ↑ +24 ↑ 
Spring +21 ↑ +16 ↑ +18 ↑ +16 ↑ +18 ↑ +22 ↑ +20 ↑ +21 ↑ +20 ↑ +23 ↑ +24 ↑ +20 ↑ +23 ↑ +20 ↑ +21 ↑ +20 ↑ +23 ↑ 
Predictand Season 79014 76047 77007 77042 77083 79019 79023 79026 79028 79034 79046 90173 79074 79079 79080 89003 89085 
Precipitation Summer –9 ↓ –10 ↓ +28 ↑ –9 ↓ 21 ↑ –10 ↓ –10 ↓ –10 ↓ –9 ↓ –9 ↓ –10 ↓ –6 ↓ –9 ↓ –8 ↓ –9 ↓ –7 ↓ –10 ↓ 
Autumn +4 ↑ +36 ↑ +40 ↑ +23 ↑ +35 ↑ +6 ↑ +7 ↑ +9 ↑ +9 ↑ +8 ↑ +4 ↑ +7 ↑ +5 ↑ +5 ↑ +8 ↑ +6 ↑ +6 ↑ 
Winter +14 ↑ +23 ↑ –1 ↓ 21 ↑ –1 ↓ +15 ↑ +15 ↑ +16 ↑ +15 ↑ +15 ↑ +16 ↑ +11 ↑ +17 ↑ +13 ↑ +15 ↑ +14 ↑ +14 ↑ 
Spring –26 ↓ –18 ↓ –15 ↓ –14 ↓ –11 ↓ –27 ↓ –29 ↓ –30 ↓ –30 ↓ –27 ↓ –27 ↓ –19 ↓ –28 ↓ –28 ↓ –28 ↓ –24 ↓ –27 ↓ 
Evaporation Summer +7 ↑ +8 ↑ +9 ↑ +8 ↑ +9 ↑ +13 ↑ +11 ↑ +12 ↑ +11 ↑ +13 ↑ +13 ↑ +7 ↑ +13 ↑ +12 ↑ +12 ↑ +12 ↑ +13 ↑ 
Autumn +6 ↑ +11 ↑ +9 ↑ +8 ↑ +9 ↑ +11 ↑ +10 ↑ +11 ↑ +10 ↑ +11 ↑ +12 ↑ +6 ↑ +11 ↑ +11 ↑ +11 ↑ +10 ↑ +11 ↑ 
Winter +2 ↑ +4 ↑ +3 ↑ +3 ↑ +3 ↑ +4 ↑ +4 ↑ +5 ↑ +4 ↑ +5 ↑ +5 ↑ +2 ↑ +5 ↑ +5 ↑ +5 ↑ +4 ↑ +4 ↑ 
Spring +13 ↑ +19 ↑ +18 ↑ +16 ↑ +18 ↑ +21 ↑ +20 ↑ +22 ↑ +19 ↑ +22 ↑ +23 ↑ +11 ↑ +22 ↑ +24 ↑ +21 ↑ +18 ↑ +21 ↑ 
Min Temp Summer +1 ↑ +1 ↑ +0 ↑ +0 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ +1 ↑ 
Autumn +22 ↑ +21 ↑ +22 ↑ +20 ↑ +23 ↑ +22 ↑ +22 ↑ +22 ↑ +24 ↑ +23 ↑ +25 ↑ +21 ↑ +24 ↑ +22 ↑ +21 ↑ +22 ↑ +23 ↑ 
Winter +40 ↑ +31 ↑ +36 ↑ +28 ↑ +36 ↑ +41 ↑ +39 ↑ +37 ↑ +41 ↑ +41 ↑ +49 ↑ +32 ↑ +44 ↑ +38 ↑ +34 ↑ +37 ↑ +46 ↑ 
Spring +29 ↑ +21 ↑ +26 ↑ +21 ↑ +26 ↑ +30 ↑ +26 ↑ +27 ↑ +29 ↑ +31 ↑ +34 ↑ +28 ↑ +32 ↑ +27 ↑ +26 ↑ +29 ↑ +33 ↑ 
Max Temp Summer +2 ↑ +2 ↑ +2 ↑ +1 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ +2 ↑ 
Autumn +5 ↑ +4 ↑ +5 ↑ +4 ↑ +5 ↑ +6 ↑ +5 ↑ +5 ↑ +5 ↑ +6 ↑ +6 ↑ +5 ↑ +6 ↑ +5 ↑ +5 ↑ +5 ↑ +6 ↑ 
Winter +24 ↑ +21 ↑ +23 ↑ +22 ↑ +22 ↑ +25 ↑ +23 ↑ +24 ↑ +23 ↑ +25 ↑ +28 ↑ +21 ↑ +26 ↑ +24 ↑ +24 ↑ +22 ↑ +24 ↑ 
Spring +21 ↑ +16 ↑ +18 ↑ +16 ↑ +18 ↑ +22 ↑ +20 ↑ +21 ↑ +20 ↑ +23 ↑ +24 ↑ +20 ↑ +23 ↑ +20 ↑ +21 ↑ +20 ↑ +23 ↑ 

Min Temp, minimum temperature; Max Temp, maximum temperature; ↑, increase in the average of predictand during 2000-2099 with respect to that during 1950–1989, ↓, decrease in the average of predictand during 2000–2099 with respect to that during 1950–1989.

As seen in Table 8, the average of the monthly precipitation showed a decline in summer and spring at the majority of stations in the period 2000–2099, in comparison with the average of the observed precipitation 1950–1989. In autumn and winter, the average of precipitation displayed a rise at the majority of stations. It was realised that, with respect to the past climate of the period 1950–1989, summer and spring in the period 2000–2099 will be dryer and autumn and winter tend to be wetter, over the study area. In all seasons except autumn, the standard deviation of the monthly precipitation over the period 2000–2099 indicated a drop at most of the stations. The maximum of the monthly precipitation indicated a rise in magnitude at the majority of stations in summer, autumn and winter during the period 2000–2099.

According to Table 8, the average of the monthly evaporation displayed a rise in all seasons, at all stations, over the period 2000–2099, in comparison with that of observations of the period 1950–1989. This implies that in the future, throughout the study area, the loss of water into the atmosphere due to evaporation will tend to increase. In the period 2000–2099, the standard deviation of the monthly evaporation showed a rise in summer, autumn and spring at the majority of stations. In all four seasons, the maximum of the monthly evaporation indicated an increase at the majority of stations in the period 2000–2099.

At all stations, the average (see Table 8) and the standard deviation of the monthly minimum temperature displayed a rise over the period 2000–2099, with respect to those statistics of the observations of the minimum temperature of the period 1950–1989. However, the increase in the average of the monthly minimum temperature in summer was negligible at all stations. Except in summer, the minimum of the monthly minimum temperature also indicated a rise at the majority of stations.

According to Table 8, at all stations, the average of the monthly maximum temperature showed an increase in all four seasons over the period 2000–2099, in comparison with that of observations of the period 1950–1989. This rise in the average of the monthly maximum temperature was relatively higher in winter and spring at all stations. Only in summer, at all stations, the standard deviation of the monthly maximum temperature indicated a decline in the period 2000–2099. The maximum of the monthly maximum temperature showed a rise in all seasons, at all stations, in the period 2000–2099.

The Victorian Government Department of Sustainability & Environment (2008a, 2008b) stated that according to the median estimates obtained from the raw outputs of number of GCMs under B1 (low emissions), A1B (medium emissions) and A1F1 (high emissions) emission scenarios, the average temperature and evaporation are likely to increase in all seasons, across the Wimmera and Mallee regions which include the present study area. These findings of the Victorian Government Department of Sustainability and Environment further reinforced the findings of the present study.

CONCLUSIONS

The following broad conclusions were drawn from this study:

  1. The key station approach was proven to be a simple and yet effective methodology for downscaling GCM outputs to a predictand of interest at multiple stations concurrently. The key station approach is able to segregate the stations in a study area into separate clusters according to the spatial variations of the predictand of interest seen in the past observations. This enforces the maintenance of independence among stations in different clusters while preserving dependence structure among the station in individual clusters.

  2. Nevertheless, for the effective application of the key station approach, the presence of high correlations (preferably magnitudes above 0.80 at p 0.05) among the observation stations (in a cluster) for the predictand of interest is a prerequisite. However, when the correlations between the stations for a predictand of interest are less strong (limited linear association), a non-linear regression technique can be used for developing effective inter-station regression relationships.

  3. In the application of the key station approach, downscaling models are developed for the predictand of interest only at the key stations. Therefore, unlike downscaling at each individual station separately, in this approach the selection of potential predictors and the correction of bias have to be performed only at several stations.

  4. When the bias is limited, the monthly bias-correction was found to be very effective in correcting the bias in the monthly mean and the standard deviation of a climatic variable (e.g. output of a GCM or downscaling model). In monthly bias-correction, though no explicit measure is employed to correct the bias in the minimum and the maximum of a climatic variable, yet it is capable of effectively reducing the bias in the minimum and the maximum of the variable when the bias is limited. Therefore, monthly bias-correction is recommended for variables which show little bias in their statistics.

ACKNOWLEDGEMENTS

The authors acknowledge the financial assistance provided by the Australian Research Council Linkage Grant scheme and the Grampians Wimmera Mallee Water Corporation for this project.

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