## 4 Results and Discussion
### Statistical Analysis of Kolmogorov-Smirnov Test
#### 4.2.2 Maximum and Minimum Temperature (T\({}_{\text{max}}\) and T\({}_{\text{min}}\))  
Similarly, three bias correction methods were applied to correct the GCM-simulated raw maximum and minimum temperature data and the K-S test is applied to check the performance of the bias-corrected outputs with respect to the observed data. Plots of both the cumulative frequency distributions on the same graph, along with the maximum difference D and \(p\)-values, are illustrated in Figure 5 (maximum temperature) and Figure 6 (minimum temperature). Figure 4: K–S test statistic D for bias correction methods with respect to observed precipitation data. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Month**} & \multicolumn{2}{c}{**No**} & \multicolumn{2}{c}{**Linear**} & \multicolumn{2}{c}{**Local**} & \multicolumn{2}{c}{**Power**} & \multicolumn{2}{c}{**Distribution**} \\  & \multicolumn{2}{c}{**Correction**} & \multicolumn{2}{c}{**Scaling**} & \multicolumn{2}{c}{**Intensity Scaling**} & \multicolumn{2}{c}{**Transformation**} & \multicolumn{2}{c}{**Mapping**} \\ \cline{2-10}  & **D** & \(p\) & **D** & \(p\) & **D** & \(p\) & **D** & \(p\) & **D** & \(p\) \\ \hline January & 0.3871 & 0.013 & 0.4839 & 0.00  
Figure 5: Illustration of the K-S test for the month of July for the (**a**) simulated data without correction, (**b**) LS-corrected, (**c**) VS-corrected, and (**d**) DM-corrected maximum temperature data. Figure 6: Illustration of the K-S test for the month of July for (**a**) simulated data without correction, (**b**) LS-corrected, (**c**) VS-corrected, and (**d**) DM-corrected minimum temperature data. Table 6 gives information on the results of the D value and its level of significance (\(p\)-value) regarding the cumulative distribution function of the observed maximum temperature data, the model-simulated data without correction, and the data corrected using the LS, VS, and DM methods. As Table 6 specifies the K-S statistics D and \(p\)-value, it clearly shows that, in the simulated data without correction, 4 out of 12 months give a maximum difference value of 1, and, without correction data series, also shows zero significance throughout the year. As bias correction methods are applied, all D values throughout the year are decreased and \(p\)-values are increased to some extent. In the LS method, though all 12 months have decreased D values in comparison to the uncorrected data, 6 months show a significant \(p\)-value of more than 0.9. The VS method gave better results than the LS method and it improved the \(p\)-value by more than 0.9 in 8 months except for July, August, November, and December. Also, the months of January and February give 100% significance. The DM methods give the best results compared to the other methods. In the DM method, D values during all months of the year are decreased and 11 months also show a significance value of more than 0.9, except August which has a significance value of 0.778. In the case of minimum temperature (Table 7), the months of April and May show greater values in comparison to the other months, even without correction. The plot in Figure 6a shows both cumulative frequency distributions on the graph along with the maximum difference D = 0.0968 and significance \(p\)-value = 0.998. Out of the 12 months, 7 show a significance value of zero in the uncorrected data. In the LS and VS methods, all D and \(p\)-values show enhanced results with decreased D values and increased \(p\)-values of more than 0.9. The DM method has better results than the LS and VS methods, as 4 months out of 12 show 100% significance, and also decreased D values than uncorrected data. Similarly, for maximum and minimum temperature, all three correction techniques improved the K-S test assessment index D and significance \(p\)-value. The K-S test assessment index D for maximum temperature and minimum temperature are shown in Figures 7 and 8, respectively.