## 3 Methodology
### Bias Correction Methods
#### 3.1.1 Linear Scaling (LS) of Precipitation and Temperature  
LS method is a simple bias correction method and is widely used to adjust precipitation and temperature from GCM [29]. This method reduces the biases by comparing the mean of the bias-corrected values with the observed values [21]. The function of the LS method is used to calculate the corrected values based on the differences between the observed and GCM-simulated data. Precipitation data are rectified using a multiplier term where the simulated precipitation data are multiplied by the scaling factor. On the other hand, temperature is corrected using an additive term, where the simulated temperature data are added to the scaling factor. LS equations of precipitation and temperature are given in (2) and (3):  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Name** & **Country** & **Modeling Center** & **Resolution** \\ \hline ACCESS1.3 & Australia & Australian Community Climate and Earth System & 1.875\({}^{\circ}\)\(\times\) 1.25\({}^{\circ}\) \\  & & Simulator Coupled Model & 1.875\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\) \\ \hline CMCC-CESM & Italy & Euro-Mediterranean Center on Climate Change & 1.875\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\) \\ \hline CNRM-CM5 & France & Centre National de Recherches Méeorologiques & 1.4\({}^{\circ}\)\(\times\) 1.4\({}^{\circ}\) \\ \hline GFDL-CM3 & United States & Geophysical Fluid Dynamics Laboratory & 2.0\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\) \\ \hline HadCM3 & United Kingdom & Met Office Hadley Centre & 3.75\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\) \\ \hline HADGEM2-ES & United Kingdom & Met Office Hadley Centre and the Climatic Research Unit & 1.875\({}^{\circ}\)\(\times\) 1.875\({}^{\circ}\) \\ \hline INM-CM4 & Russia & Institute of Numerical Mathematics (INM) of the Russian & 2.8\({}^{\circ}\)\(\times\) 2.8\({}^{\circ}\) \\  & & Academy of Sciences & \\ \hline MIROC5 & Japan & Japan Agency for Marine-Earth Science and Technology (JAMSTEC), the National Institute for Environmental & 1.4\({}^{\circ}\)\(\times\) 1.4\({}^{\circ}\) \\  & & Studies (NIES), and the University of Tokyo & \\ \hline MPI-ESM-P & Germany & Max Planck Institute for Meteorology (MPI-M), Germany & 1.9\({}^{\circ}\)\(\times\) 1.9\({}^{\circ}\) \\ \hline MRI-CGCM3 & Japan & Meteorological Research Institute (MRI) in Japan. The institute under the Japan Meteorological Agency (JMA) & 1.125\({}^{\circ}\)\(\times\) 1.125\({}^{\circ}\) \\ \hline MRI-ESM1 & Japan & Meteorological Research Institute (MRI) in Japan. The institute under the Japan Meteorological Agency (JMA) & 1.125\({}^{\circ}\)\(\times\) 1.875\({}^{\circ}\) \\ \hline NorESM1\_M & Norway & Norwegian Climate Centre, a part of the Norwegian & \\  & & Meteorological Institute, and the Bjerknes Centre for & 1.9\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\) \\  & & Climate Research, a collaborative research center involving & \\  & & Norwegian institutions. & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Detailed information on the 12 CMIP5 models datasets used.  
For precipitation,  
\[\mathrm{P_{cor,m,d}}=\mathrm{P_{raw,m,d}}\times\frac{\mu(P_{obs,m})}{\mu(P_{raw,m})} \tag{2}\]  
For temperature,  
\[\mathrm{T_{cor,m,d}}=\mathrm{T_{raw,m,d}}+(\mu(\mathrm{T_{obs,m}})-\mu(\mathrm{T_ {raw,m}})) \tag{3}\]  
where \(\mathrm{P_{cor,m,d}}\) and \(\mathrm{T_{cor,m,d}}\) are corrected precipitation and temperature on the dth day of mth month, respectively; \(\mathrm{P_{raw,m,d}}\) and \(\mathrm{T_{raw,m,d}}\) are raw precipitation and temperature on the dth day of mth month, respectively; \(\mu(\mathrm{P_{obs,m}})\) and \(\mu(\mathrm{T_{obs,m}})\) are mean values of observed precipitation and temperature at month m, respectively; and \(\mu(\mathrm{P_{raw,m}})\) and \(\mu(\mathrm{T_{raw,m}})\) are mean values of raw precipitation and temperature at month m, respectively.