## 4 Results and Discussion
### Statistical Analysis of Kolmogorov-Smirnov Test
#### 4.2.1 Precipitation  
The four bias correction methods were applied to correct the GCM-simulated raw daily precipitation data. To check its performance, the K-S test is used and bias-corrected outputs are compared with the observed data. Figure 3 illustrates the K-S test applied in July for the observed series with the model-simulated raw data (Figure 3a), the data corrected using LS (Figure 3b), the data corrected by LOCI (Figure 3c), the data corrected by PT (Figure 3d), the and data corrected by DM (Figure 3e). Figure 3 shows the plot of cumulative frequency distributions on the same graph along with the maximum difference D and \(p\)-value. Table 5 synthesizes the results of D (14) and the level of significance of the cumulative distribution function (\(p\)-value) of the observed precipitation data, the model-simulated raw data, and the data corrected using the LS, LOCI, PT, and DM methods. Table 5 indicates that the bias correction improves the model-simulated raw data, enhancing the K-S test statistic D and its level of significance, i.e., \(p\)-values. For better understanding, the K-S test statistic D = 0.3871 and \(p\)-value 0.013 means that the two distribution functions of the observed data and model-simulated data are different at \(p\) = 0.013, i.e., at a 98.7% confidence level. The null hypothesis has been defined and both cumulative distribution functions are equal. The K-S test statistic D value is decreased to some extent after the application of bias correction methods, which reveals that it gives \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Models** & **MBE** & **MAE** & **RMSE** & **NSE** & **Correlation Coefficient** \\ \hline ACCESS1.3 & 0.87 & 1.693 & 6.862 & 0.208 & 0.472 \\ CMCC-CESM & 0.914 & 1.924 & 6.914 & 0.196 & 0.459 \\ CNRM-CM5 & 0.846 & 1.762 & 6.895 & 0.201 & 0.462 \\ GFDL-CM3 & 0.89 & 1.792 & 6.93 & 0.193 & 0.454 \\ HadCM3 & 0.905 & 2.181 & 7.005 & 0.175 & 0.435 \\ HADGEM2-ES & 0.893 & 2.135 & 7.074 & 0.159 & 0.417 \\ INM-CM4 & 0.893 & 1.757 & 6.9 & 0.2 & 0.462 \\ MIROC5 & 0.773 & 1.895 & 6.908 & 0.198 & 0.456 \\ MPI-ESM-P & 0.847 & 1.818 & 6.819 & 0.218 & 0.482 \\ MRI-CGCM3 & 0.907 & 1.83 & 6.771 & 0.229 & 0.497 \\ MRI-ESM1 & 0.862 & 1.854 & 6.944 & 0.189 & 0.449 \\ NorESM1\_M & 0.793 & 1.958 & 6.956 & 0.186 & 0.444 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical summary of the climate models for minimum temperature. better results than the GCM model data. Table 5 illustrates that most of the D values are improved, i.e., decreased after applying the bias correction methods. In the LS bias correction method, except for the month of January, all remaining 11 months show decreased D values with respect to the data without correction, although the \(p\)-value is less than 5%. Similarly, after LOCI correction, except for the month of April, all remaining 11 months show decreased D values. In comparison to the LS and LOCI correction methods, the PT and DM methods give better results. In the PT method, the D value is reduced in all months except April, which has an increased D value. The DM is very effective, which significantly reduces the D value in all months throughout the year. The \(p\)-value is also near 1, which signifies that the observed data's cumulative distribution and DM-corrected data's cumulative distribution are equal. Figure 3: Illustration of the K–S test for the month of July for the (**a**) simulated data without correction, and the (**b**) LS-corrected, (**c**) LOCI-corrected, (**d**) PT-corrected, and (**e**) DM-corrected precipitation data. The K-S test assessment index D represents the maximum difference between the cumulative distribution functions of the model-simulated data and observed data in each month, as shown in Figure 4. The line chart (Figure 4) shows that the K-S test statistics D value in each month is maximum in the model-simulated uncorrected data series with respect to the observed data and the results of the K-S test, which are improved after applying all four correction techniques.