The studies of climate change impacts on water resources have become an interesting topic since the late twentieth century. The main source of discussion in assessment studies is supported by the outputs from a Global  Climate  Model  (GCM)  under  different  emission scenarios. A GCM is a three-dimensional numerical model of a planetary, ocean and atmosphere that employs many principles of physics, mathematics and fluid mechanics. However, the resolution of GCMs is not high enough to be  used  directly  in a regional study such as a hydrological simulation. In this way, downscaling tools are employed to localize the results of different GCM as an input to hydrological models.

Among the outputs of the GCMs, the temperature and precipitation data were frequently used to force impact model such as hydrological models. In addition, both temperature and precipitation are the main atmospheric variables affected by the Greenhouse Gases (GHG) emissions. For instance, in the Fourth Assessment Report (AR4) of Intergovernmental Panel on Climate Change (IPCC), the climate change effect on fresh water systems is due to increases in temperature and sea level as well as precipitation variability (Fiseha et al., 2012). For the temperature, the report of IPCC AR4 shows the increase of global mean surface temperatures by 0.74ºC over the last 100 years (1906-2005) (Solomon et al., 2007).

The output of GCMs in the simulation of the climate system has coarse resolution that is not enough to match with sub-grid scale features such as topography and landuse. To bridge this gap, downscaling is commonly a method to investigate the impact of climate change on water resources at a regional scale. The basic assumption in downscaling is that the large-scale atmospheric system influences the local scale system considerably, but the inverse effects from regional scales to global scales are insignificant (Fowler et al., 2007; Hewitson and Crane, 1996; Maraun et al., 2010; Teutschbein et al., 2011; Wilby et al., 2004; Xu, 1999).

The existing downscaling methods have two broad categories, namely dynamical downscaling and statistical downscaling, which have been created using atmospheric physics and empirical statistics, respectively. The extensive discussion on these downscaling classes includes theories, application, and advantage and deficiency of them can be found in many previous research works (Hewitson and Crane, 1996;Xu, 1999; Wilby et al., 2004; Fowler et al., 2007; Teutschbein et al., 2011).

Statistical downscaling methods are used by the hydrologist to obtain the local-scale data as an input to the hydrological models. Statistical downscaling approach could be further categorized in weather type, regression method, and weather generator (Wilby et al., 2004). The weather type technique engaged meteorological data to a given weather type in accordance with their similarity concerning synoptic patterns. Regression-based models involve developing a linear or nonlinear empirical relationship between a local climate variable as predictand (e.g. temperature and precipitation)   and    large-scale   GCM    parameters   as predictors. A Weather Generator (WG) is a stochastic model that can be used to simulate daily weather based on parameters determined by historical records (Wilks and Wilby, 1999). Multiple regression and weather generator methods are more utilized than others, as they are computationally less demanding data, easy to apply, and efficient (Dibike and Coulibaly, 2005; Hashmi et al., 2011; Semenov et al., 1998; Solomon et al., 2007; Tavakol‐Davani et al., 2013). Moreover, other offered methods, range from Markov Chain (Gregory et al., 1993), and multiple regression (Murphy, 1999)to more complicated hybrid models such as Statistical Downscaling Model (SDSM) (Wilby et al., 1999)and automated regression-based statistical downscaling (Hessami et al., 2008). The comparison of artificial neural network and multiple regression (linear and nonlinear) is the subject of other studies in downscaling climate parameters (Khan et al., 2006; Schoof and Pryor, 2001). However, none of these downscaling methods are robust and precise enough to simulate the diversity in the climate system. Thus, a comparative study of different downscaling models in capturing the temporal characteristics of climate variable would be beneficial (e.g., mean, variance, wet/dry spell length) (Hashmi et al., 2011; Khan et al., 2006; Muluye, 2012). This study investigates and evaluates two statistical downscaling methods in regression category from multiple linear regression (SDSM) to fully nonlinear regression (ANN) in capturing the climatic characteristics in a tropical climate of Malaysia.

Study area

The study area is the Langat River Basin, which is one of the most urbanized catchments in Malaysia, located in the southern parts of Klang Valley in which the capital city of Kuala Lumpur is located (Figure  1). It supplies two third of water required for the state of Selangor for different water usage. This watershed experienced rapid development in urbanization, agriculture, and industrialization. The total area of the Langat River Basin is approximately 2,352 km². It lies between latitudes 2° 40ËŠ 15ʺ to 3° 16ʹ 15ʺ N and longitudes 101° 17ʹ 20ʺ to 101° 55ʹ 10ʺ E. The northern part of the basin is a mountainous area; while its central and western parts consist of the flat area. The mean areal annual rainfall of the Langat River Basin is 1994 mm, while the highest recorded monthly rainfall is approximately 327 mm in November, and the lowest is 97.6 mm in June. A summary    of     the      geographic     characteristics     of meteorological stations within the study area is presented in Table 11.

 

 

 

The closest grid cell for the study area has coordinates of 1.86°N and 101.25°E (X=28 and Y=24). In this research, the current climate as the base line period was set for the starting date of recording until the end of the year 2000 (Table 2). Two projection time slices, namely 2020-2049 (2030s) and 2070-2099 (2080s) exist, which allow the assessment of climate change impacts on water resource in the watershed.

 

 

While the original predictor dataset of NCEP/NCAR contained 26 daily predictors (describing atmospheric circulation, thickness and moisture content at the surface, geopotential heights at 850 and 500 hPa), the candidate predictors are only eight predictors in Malaysia. This limitation is for an area near the equator (this study area) where Coriolis forces tend to be zero (Predictors, 2008). The candidate lists of large-scale predictor variables from NCEP/NCAR and CGCM3.1 used in downscaling the climate variables are presented in Table  3. The values of predictors were normalized by their respective mean and standard deviation.

 

Artificial neural network

The second downscaling method is the Artificial Neural Network (ANN) under the Multilayer Perceptron (MLP) architecture with variation of learning algorithms, transfer functions, and number of neurons. The ANN is a nonlinear regression type which the network learned by supervised and unsupervised learning to create a developed relationship between a few selected large-scale atmospheric predictors and basin scale meteorological predictands.

The MLP is one of the most popular neural network, which consists of three layers of neurons namely, input, hidden and output layer. The information flows in the forward direction and network trained using a back propagation learning algorithm to minimize the least square error (LSE) between realized and target outputs. As weights in MLP computed by a developed back-propagation learning algorithm, these networks are the most popular among researcher and users of ANNs (Jain et al., 1996). The Multi-layer perceptron with one hidden layer and three learning algorithms include Momentum (M) (Harpham and Wilby, 2005), Levenberg-Marquardt (LM) (Govindaraju and Rao, 2010), and Conjugate Gradient (CG) learnings (Charalambous, 1992) which were investigated for downscaling the precipitation, maximum and minimum temperatures at 10 stations. The transfer functions in hidden layer were Sigmoid (Sig) and Hyperbolic Tangent (HT) and also linear transfer function in the output layer. The numbers of hidden layer neurons were found through simple trial-and-error method in all applications. Then, the performances of different networks were examined using correlation coefficient (R), and MAE.

Validation of models

The parameters established during the calibration process that explain the statistical agreement between observed and simulated data were then used for the model validation and for daily and monthly time scales.

The performance of downscaling models in generating the mean daily precipitation, mean dry spell and wet spell length for precipitation in a month and mean daily and variance for temperature in a month were examined using the Standard Error (SE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) as follows:

Where, y_obs is the observed data, y_sim is the simulated value, k is the number of independent variables, and n is the number of recorded data in the validation dataset. The y refers to daily maximum temperature, minimum temperature and precipitation at each station. In this study, a dry day is defined as a day with an amount of less than 1 mm precipitation during a day (Deni et al., 2010).

Uncertainty analysis

In the statistical downscaling, confidence intervals in the estimates of means and variances provide special view about uncertainty in the estimates of mean and variances (Khan et al., 2006). In the current study, the most commonly used non-parametric technique, bootstrapping has been applied to obtain the confidence intervals of means and variances. The main part of bootstrapping is to resample a large number of new data sets with replacement from the original data set. The algorithm for uncertainty analysis in this study includes the following steps:

1. Draw a new sample of size n with replacement from the original sample.

2. Compute the mean or variance of the new sample.

3. Repeat steps 1 and 2, 1000 times, and calculate the mean and variance.

4. Plot the distribution of these 1000 sample means or variances.

5. Compute the 95% confidence interval for the mean or variances by finding the 2.5th and 97.5th percentiles of this constructed distribution.

Selection of Predictors

The selection of predictors mainly ascertains the character of the downscaled climate scenario. As the correlation analysis between the predictands of the Langat River Basin and the NCEP/NCAR re-analysis predictors was discovered to have extremely poor results, an offline statistical analysis was carried out to improve the correlations between predictand and predictors (Hashmi et al., 2011). A Cross Correlation Analysis (CCA) between each pair of predictands and the NCEP/NCAR predictors is an attempt in this regard to find the optimum lags, which correspond with maximum correlation between each pair of predictand-predictors.

The correlation amounts before and after CCA at six out of 10 stations are shown in Figure  2 as an example. While for  many  of  the  NCEP/NCAR  predictors   at  the stations, the CCA improved the correlation between the large-scale predictors and local-scale predictand, few of the NCEP/NCAR predictors did not show any lag for the improvement of the correlation. The examination of the results of the CCA indicates that improvements in the predictors include MSLP, P500, and P850, which were more than that for S850, SHUM, and TEMP. The comparison between predictand-predictors correlation shows that the correlation coefficient for maximum and minimum temperatures are higher than that for daily precipitation as a predictand. This lagged NCEP/NCAR predictors and the local precipitation as well as maximum and minimum temperatures are then employed to screen the predictors as a process in the calibration of the statistical downscaling models.

 

 

The stepwise regression with both directions (backward and forward) was adapted to screen the predictors and select the best combination of them by reaching the smallest Akaike Information Criterion (AIC) (Hessami et al., 2008; Tavakol‐Davani et al., 2013). Table 4 shows the identified significant NCEP/NCAR predictors for predictand and stations at the significant level of p <0.001 under consideration.

 

 

From the selected predictors in Table 3, it was discovered that the local variables were controlled by non-atmospheric parameters. For instance, both of temperature  and  precipitation  are  sensitive to pressure fields at geopotential heights of 500 hPa, and near surface specific humidity.

While, the Mean Sea Level Pressure (MSLP) is a measure control variable for temperature, it was not a significant predictor for precipitation in all sites. The mean temperature at 2 m height (TEMP) controls both the maximum and minimum temperatures and precipitation observed at each station except minimum temperature at Station 9.

The selected predictors at all stations were used for the calibration and validation of different downscaling models including SDSM version 4.2.9 (Wilby et al., 2002), and artificial neural network with different structures. The observed historical dataset until the year 2001 was split into two equal parts of the calibration and validation processes of the downscaling methods as defined in Table 2. The calibration of two statistical downscaling approaches was carried out for every single site during the calibration period and validated through the data outside the calibration period.

Comparisons of model performance

Two downscaling approaches were examined in simulating the predictand time series during the validation period (independent  data  set)  as  described  in  Table 2 and Table 5 at all stations in the Langat River Basin. The performance results of the validation criteria include the SE, RMSE, and MAE of the satisfactory calibrated downscaling models, which are presented in Table6. The results of the validation analysis indicated that the SDSM technique performed lower value of error (SE, RMSE, and MAE) in reproducing the observed time series of temperature and precipitation than the ANN model. Therefore, the SDSM model was more efficient in reproducing the inter-annual variability (less error value) of the mean daily precipitation and daily maximum and minimum  temperatures   compared   to  the  other  model (Sachindra et al., 2013). The result also showed less error values in downscaling the maximum and minimum temperatures than the precipitation by the two models. It is noted that the lower error (SE, RMSE, and MAE) values during the calibration and validation lead to the better performance of the model.

 

 

 

The results of the Kolmogorov-Smirnov (KS) test in Table6 indicated no significant difference between the produced mean values of precipitation by SDSM and the observed values at the 95% confidence level. The only acceptable modeling by the ANN was produced at Station 10 in  downscaling  the T_Min  during  the validation period. The results of KS test also showed that none of these downscaling models were capable to reproduce the mean monthly T_Min at Station 11.

The statistical characteristics of daily precipitation time series are important for the future projection of downscaling models.

Table  7 illustrates the statistical characteristics of downscaled precipitation including the ratio of dry days, which were bracketed by downscaling models as well as mean and standard deviation (SD) in the validation period at the stations of the Langat River Basin. In addition to the better accuracy of the SDSM in simulating the historical observed time series, its skill in reproducing the number of dry days (P <1 mm) and SD of time series was more acceptable. In comparison, in these two downscaling techniques, it seems that the SDSM is more capable in simulating the number of dry day, wet day and SD of rainfall data.

 

 

It is not unusual to receive negative  precipitation  value forecasts from the ANN models (Muluye, 2012). From this point of view, while the SDSM model was smart in generating non-negative values, the ANN technique performed negative values in daily rainfall during the validation period, respectively.

For the maximum and minimum temperatures, while, the performance of the ANN method was acceptable in reproducing the mean observed values, the SDSM model produces qualified time series in reproducing the standard deviation of the observation (Table 8).

 

 

 

 

This study examined the effects of the complexity of regression models in downscaling the climate variables in a tropical watershed in Malaysia. The performance of a multiple linear regression, called SDSM, and non-linear regression, called artificial neural network with three significant learning rules were evaluated in simulating presence and projecting the two future periods (2020-2049, 2070-2099) of daily precipitation, maximum and minimum temperatures under the A2 emission scenario using CGCM3.1. The three learning algorithms were Momentum, Levenberg-Marquardt, and Conjugate Gradient. The daily precipitation, maximum and minimum temperatures from the beginning of recording period were used as weather inputs to the downscaling model. These two downscaling models were calibrated and validated using large-scale predictors NCEP/NCAR reanalysis data and   regional   climate   variables.   The   comparison   of generated time series illustrated that the SDSM was more accurate than the ANN model. While the SDSM showed more ability to catch the wet-spell and dry-spell length, the other model overestimated the wet-spell length, and underestimated the mean monthly precipitation and dry-spell length. The calibrated models for precipitation and temperature devised here performed relatively better in simulating the temperature, but relatively poor to capture the variability of precipitation.

The SDSM predicted an increase in the mean monthly precipitation, while, the other model anticipated a decline in this value by the 2030s period. The range of these rates was wider for the 2080s than the 2030s period. The results of the SDSM showed an increasing change in rainfall through the southwest monsoon season rainfall in the 2030s compared to the baseline period. The time series of daily precipitation in the two future periods generated by the ANN downscaling model indicated a decrease in the dry spell and an increase in the wet spell length in the 2030s and the 2080s, which did not conform to the SDSM results. The downscaling models indicated that most of the sites in the river basin experience an increase for T_Max during the two future periods, but the rate of change is more during the southwest monsoon month (May to August) and slightly less during the northeast monsoon (November to February). Therefore, warmer weather conditions in the two future periods were predicted by the downscaling models. The results of the SDSM and other downscaling model found different expectations in the prediction of T_Min for the southwest monsoon season months.

The SDSM predicted a decrease and the other downscaling model predicted an increasing trend by the 2030s and the 2080s periods. Almost all the generated downscaling time series under the A2 scenario showed the highest rate of change percentage by the 2030s and the 2080s at Station 8, which located in a mountainous area in comparison with the stations in flat areas.

The uncertainty in the estimation of means of the observed and downscaled daily precipitation as well as daily maximum and minimum temperatures has been measured by estimating confidence intervals about means and variance at different stations (Figure7). The uncertainty analysis of the estimates of mean and variance is performed by calculating the 95% non-parametric bootstrap confidence intervals of these variables using the available data (Error! Reference source not found.2). The uncertainty of mean and variance of the observed daily precipitation as well as maximum and minimum temperatures have been compared with the uncertainty of the downscaled mean and variance daily precipitation and maximum and minimum temperatures. The graphical plots of those uncertainty estimates are shown in Figure7. In the case of daily precipitation downscaling, This figure indicates that the ANN model variability is not close enough  with   the   observed   variability   but  the  SDSM variability are closer to the observed variability at all stations. The uncertainty of ANN and SDSM models indicated that the variability between the observed and simulated daily maximum and minimum temperatures cannot be considered equal at most of stations.

 

The authors have not declared any conflict of interests.

The authors would like to thank the Department of Irrigation and Drainage (DID) and the Malaysian Meteorological Department (MMD), both under the Ministry of Natural Resources and Environment Malaysia (NRE), for providing the data and technical support. The authors would also like to thank the Ministry of Science, Technology and Innovation (MOSTI) sincerely for the financial support provided for the project.