Although several studies (Fang et al. 2015; Shrestha et al. 2017; Mendez et al. 2020; Enayati et al. 2021) have proven that the quantile mapping method can correct the mean, standard deviation, quantile, and frequency of wet days, its performance may vary depending on the topographical area and the weather characteristics. Therefore, the effectiveness of quantile mapping is basically evaluated in terms of statistical indices (Table 3), namely the percent bias (PBIAS), root mean square error (RMSE), and normalised standard deviation (
) to validate the accuracy between observed and corrected GCMs data during the baseline period (1985–2014). If the values of these indices are closer to the perfect fit than before bias correction, it indicates that there are better correlations. The statistical relationship between the GCM outputs and observations during that period will be applied for future rainfall projections by assuming that the statistical relationships observed in the past will continue to hold in the future.
Statistical indices used for performance evaluation of the bias correction method
| Statistic Index | Unit | Equation | Range | Perfect Fit |
|---|---|---|---|---|
| Percent Bias (PBIAS) | Percent (%) |  |  | 0 |
| Root Mean Square Error (RMSE) | Millimetre (mm) |  |  | 0 |
Normalised standard deviation ( ) | Dimensionless (−) |  |  | +1 |
| Statistic Index | Unit | Equation | Range | Perfect Fit |
|---|---|---|---|---|
| Percent Bias (PBIAS) | Percent (%) | | | 0 |
| Root Mean Square Error (RMSE) | Millimetre (mm) | | | 0 |
| Normalised standard deviation () | Dimensionless (−) | | | +1 |
Note: obs refers to the observed data, mod refers the GCM data, and n refers the number of data.