*3.4. Downscaling of the Weighted Precipitation*

Based on the verification of EDBF results, the algorithm was employed in the downscaling process. During the downscaling process, a distinction between the low-resolution (upscaling) and the high-resolution (downscaling) was made by using Equation (5). By subtracting the weighted precipitation *PD*.*WTPLR* (i.e., also called the low-resolution weighted precipitation) (Figure 7b) from the original *Avg*\_*MTGPM* precipitation (Figure 7a), the residuals - *RWTPLR* of the regression model (i.e., also called as the low-resolution weighted residuals) at 0.75◦ resolution were obtained as shown in Figure 7c, which represents the amount of precipitation that could not be predicted by the weighted precipitation via EDBF algorithm according to Equation (15). Subsequently, the generated residuals were interpolated to 0.05◦ resolution (Figure 7d), also called the high-resolution weighted residuals (*RWTPHR*), by applying a spline tension interpolator [59]. Finally, the high-resolution weighted precipitation (*PD*.*WTPHR*) at 0.05◦ resolution (Figure 7e) was obtained using Equation (5). Using Equation (16) to add the high-resolution weighted precipitation to the high-resolution weighted residuals, the final downscaled high-resolution weighted precipitation *PDs*.*PWTPHR* (Figure 7f) for the humid region of Mainland China was obtained:

$$R\_{WTP\_{LR}} = A \upsilon \mathcal{g}\_{\text{GPM}} - P\_{D.WTP\_{LR}} \tag{15}$$

$$P\_{D5.PWM\_{HR}} = P\_{D.WTP\_{HR}} + R\_{WTP\_{HR}} \tag{16}$$

**Figure 7.** Stepwise downscaling process to predict the high-resolution multitemporal weighted precipitation: (**a**) the GPM-based average multitemporal precipitation at 0.75◦ resolution; (**b**) the EDBF-based weighted precipitation at 0.75◦ resolution; (**c**) the low-resolution weighted residuals at 0.75◦ resolution generated from the difference between (**a**) and (**b**); (**d**) the high-resolution weighted residuals at 0.05◦ resolution generated by interpolating (**c**) via Spline Interpolation; (**e**) the EDBF-based high-resolution weighted precipitation at 0.05◦ resolution; and (**f**) the final high-resolution downscaled multitemporal weighted precipitation, at 0.05◦ resolution, as a product of adding (**d**) into (**e**), respectively.

#### **4. Discussion**

In this study, a new downscaling methodology, namely GMWPA at 0.05◦ resolution, was developed and investigated in the humid region of Mainland China. A two-stepped procedure [38,39,41], based on a scale-dependent regression analysis and downscaling of the predicted multitemporal weighted precipitation at a refined scale, was adopted during the execution of proposed methodology. For this purpose, the multitemporal GPM precipitation dataset (2001 to 2015) at 0.1◦ and ASTER 30 m DEM-based geospatial predictors, i.e., elevation, longitude, and latitude were taken as input variables to predict the low-resolution—for the residual generation at optimal resolution scale—and the high-resolution weighted precipitation, and were used in the final downscaling process.

Furthermore, the regression analysis was performed in two phases. In the first phase, each geospatial predicator was assessed through developing a relationship (Table 1) with each individual precipitation variable via a fitting line—polynomial fit. Moreover, it was observed that latitude showed the highest correlation with all precipitation variables and achieved the highest R2 value. Compared to previous studies [3,34,59] which used either one or two independent variables (NDVI, elevation), the authors in [38] used several independent variables, i.e., latitude, longitude, elevation, slope, aspect, NDVI, Max\_NDVI, Range\_NDVI, and Min\_NDVI, to establish regression models for deriving the annual precipitation over continental China. From the study, it was concluded that, apart from latitude, all variables including NDVI showed relatively weak empirical relationships with the observed precipitation, especially over the humid region of China. Specifically, for NDVI, a possible reason may be that NDVI-related predictors are better indicator of precipitation in arid and semi-arid areas. The NDVI values would not increase with the increased rainfall amount in humid areas, which makes a relatively weak empirical relationship between precipitation and saturated NDVI. Keeping in view, latitude was selected as the proxy of precipitation and employed in assigning initial weight value (e.g., based on *r* value calculated for each precipitation variable with respect to latitude) to each individual precipitation variable from the multitemporal precipitation dataset, and which was then processed in EDBF algorithm [58] to predict the weighted precipitation.

Likewise, in the second phase, the output precipitation variable from EDBF, e.g., the weighted precipitation was assessed via developing the relationship with latitude through linear fitting. Moreover, the correlation between latitude and the weighted precipitation was increased for each of the low-resolution scale, and the highest R<sup>2</sup> was achieved at 100 km (e.g., between 0.75◦, 1.0◦, 1.25◦ resolutions), which showed that the weighted precipitation was well captured by latitude at 100 km resolution. Although the highest correlation between latitude and the weighted precipitation was achieved at 1.0◦ (100 km), but due to certain reasons, 0.75◦ resolution was selected as an optimal low resolution (e.g., for the upscaling) during the downscaling process. First, there was not much difference between the two resolution scales for the achieved R2, i.e., 0.75◦ (R<sup>2</sup> = 0.7918) and 1.0◦ (R2 = 0.7977) resolution. Secondly, 0.75◦ resolution had more pixels, i.e., 195, as compared to 111 pixels for 1.0◦ resolution to cover the whole study area. Considering, to convert points into pixels, the Spline Interpolation method [51,60] was used, which estimates values using a mathematical function that minimizes the overall surface curvature, resulting in a smooth surface that passes exactly through a specified number of nearest input points while passing through the sample points. Thus, using 0.75◦ resolution, which had a closer specified number of nearest input points, i.e., 12 points, than 1.0◦ resolution, tends to produce a smoother surface by minimizing the surface curvature.

From the EDBF algorithm perspective, it is a general framework rather than a specific algorithm, which is easy to implement and can easily accommodate any existing multi-parent crossover algorithms (MCAs). Moreover, the existing MCA-based coefficients [61–63] follow a uniform distribution, which also violates constraints, thus propagate error. Errors cascade exponentially, with even a slight increase in the hybrid scale, which leads to the increase in time consumption. To address such problem, EDBF is the best solution which takes multiple MCAs as its constituent members. In addition, the number of iterations during the execution of EDBF algorithm at the low-resolution scale, i.e., 0.25◦, 0.50◦, 0.75◦, 1.0◦, 1.25◦ and 1.50◦ was set to 3 <sup>×</sup> <sup>10</sup><sup>4</sup> with the reason that a possible number of iterations

be available for the stabilization of convergence before the ending of simulation process. Moreover, the process was repeated for all the low resolutions. Though the convergence stabilized before a <sup>3</sup> <sup>×</sup> 104 number of iterations, still a slight improvement could be observed, and further improvement in the regression value(s) could be expected. Instead, by terminating simulation during the execution, we let simulation process to be completed until the last iteration. Owing to that, the number of iterations was reduced during the simulation of high-resolution (i.e., 0.05◦ resolution) weighted precipitation, and the convergence was well stabilized within the set number of iterations.

During the verification process, the weighted precipitation was first compared with its contributing multitemporal precipitation variables at all the low and the original resolution scales. It outperformed all input variables for the achieved R<sup>2</sup> and outperformed the annual precipitation and underperformed compared to the seasonal and the monthly precipitation variables for the achieved RMSE. Furthermore, the weighted precipitation was compared with different classified precipitations, extracted either as an individual or grouped variables from the original multitemporal precipitation dataset used in the prediction of EDBF-based weighted precipitation at the original 0.1◦ resolution. The results are shown in Table 5, in which the weighted precipitation showed the highest correlation with its predictor (R2 = 0.772) as compared to other used variables. In addition, the weighted precipitation had a lower RMSE value (e.g., RMSE = 141.113 mm) than the Avg-An (01–15) + Wet Ppt+ Dry Ppt, Avg-An (01–15) + Dry Ppt, Avg-An (01–15) + Wet Ppt, Wet Ppt + Dry Ppt, Avg-An (01–15) and Avg-MT (−01 & −04) Ppt with the observed RMSE value of 179.248, 206.353, 182.762, 178.025, 192.537 and 197.434 mm, respectively. Also, it had a higher RMSE than the Avg-MT Ppt variable, i.e., 135.370 mm. The reason of low RMSE value for the average multitemporal GPM precipitation was that the average output was equally contributed by each precipitation variable from the multitemporal dataset. Out of the eight used variables from the multitemporal precipitation dataset, the five variables consisted of the seasonal and the monthly precipitation, which had lower received pixel precipitation. Adding to this, the number of days counted during each of the seasonal component (e.g., average 90 days) is lower than the annual component (e.g., 365 days) and there is less probability of variation in the seasonal precipitation than the annual precipitation. Despite lower R2 values, less variability from the mean precipitation was observed in the seasonal and the monthly precipitation as compared to the annual precipitation. On the contrary, the EDBF-based weighted precipitation was mainly predicted on the basis of assigned weights via calculated *r* values. In this regard, higher the *r* value, the more weight was assigned to that variable and more contribution from that variable in the prediction of weighted precipitation. Additionally, it was compared with neutral variables, wherein it outperformed all comparing variables for the achieved R<sup>2</sup> and RMSE values.


**Table 5.** Comparison between the weighted precipitation and classified extracted precipitation variables.

Note: Avg-MT Ppt is the average multitemporal precipitation; Avg-An(01-15) + Wet + Dry Ppt is the average precipitation as product of the average annual, the wet year (2004) and the dry year (2001) precipitation; Avg-An + Dry Ppt is the average precipitation as product of the average annual (2001–2015) and the dry year (2001) precipitation; Avg-An(01-15) + Wet Ppt is the average precipitation as product of the average annual (2001–2015) and the wet year (2004) precipitation; Wet + Dry Ppt is the average precipitation as product of the wet year (2004) and the dry year (2001) precipitation; Avg-An (01-15) is the average annual (2001–2015) precipitation; Avg-MT(-01 & -04) Ppt is the average multitemporal precipitation excluding the dry year (2001) and the wet year (2004) precipitations.

The downscaling methodology applied in this study was mainly based on the work presented in [39], where the basis function was selected at an optimum resolution and by interpolating the residuals. After successfully applying the proposed methodology, the EDBF algorithm was employed in downscaling of the dry year (2001), the wet year (2004) and the average annual (2001–2015) precipitation at 0.05◦ resolution by following the same process as for downscaling the *Avg*\_*MTGPM* precipitaiton. Before downscaling, a graphical relationship between the weighted precipitiaon and the dry year (2001), the wet year (2004) and the average annual (2001–2015) precipitation was developed through a scatter plot as shown in Figure 5g–i, respectively. The weighted precipitation showed the highest correlation with the dry year (2001) followed by the average annual (2001–2015) and the wet year (2004) for the achieved R<sup>2</sup> = 0.9869, 0.8929 and 0.4154, respectively.

Moreover, during downscaling, the low-resolution weighted residuals (Figure S6d–f) were generated by subtracting the low-resolution weighted precipitation *PD*.*WTPLR* (Figure 7b) from the original dry year (2001), the wet year (2004) and the average annual (2001–2015) precipitation (Figure S6a–c) at 0.75◦ resolution, respectively. Afterward, the high-resolution weighted residuals (Figure S6g–i) at 0.05◦ were obtained by interpolating the low-resolution residuals at 0.75◦ resolution. Finally, by adding the obtained high-resolution interpolated residuals to the high-resolution weighted precipitation (Figure 7e), the downscaled high-resolution weighted precipitation at 0.05◦ resolution for the dry year (2001) (Figure 8d), the wet year (2004) (Figure 8e) and the average annual (2001–2015) precipitation (Figure 8f) was obtained. From Figure 8, it shows that the high-resolution weighted precipitation captured the same precipitation pattern as that of the original GPM dry year (2001), the wet year (2004) and the average annual (2001–2015) precipitation at 0.1◦. Moreover, by analyzing the class wise pattern (Table 6) for the obtained precipitation, the algorithm accurately captured the wet year (2004) (Figure 8e) and the average annual (2001–2015) precipitation, whereas some classes, e.g., class 4 (gold color) and 5 (light green) were not very well captured during downscaling of the dry year (2001) precipitation, such as between 111◦ to 115◦E and 25◦ to 27◦N, and 117◦ to 118◦E and 24◦ to 25◦N.

**Figure 8.** Comparison between the downscaled weighted precipitation at 0.05◦ resolution for (**d**–**f**) and the original GPM precipitation at a nominal resolution of 0.1◦ for (**a**) the dry year (2001), (**b**) the wet year (2004), and (**c**) the average annual (2001–2015), respectively.


**Table 6.** Comparison of spatial pattern between GPM based precipitations with its corresponding weighted precipitation for different precipitation classes.

Note: Green colored values show the average difference of less than 5 mm, Blue colored values show the average difference of about 10 mm, Pink colored values show the average difference of about 20 mm, Red colored values show the average difference of about 30 mm between the GMP and weighted precipitation at particular pattern class, respectively.

Subsequently, to analyze difference in the range of precipitation classes (i.e., difference between the upper and the lower boundary of captured precipitation pattern) between the original dry year (2001), the wet year (2004) and the average annual (2001–2015) precipitation at 0.1◦ resolution, their corresponding weighted precipitation at 0.05◦ resolution was found to be in close proximity with the average difference of less than 5 mm for most classes. Apart from that, EDBF algorithm slightly underpredicted extreme precipitation for the dry year (2001) and the wet year (2004) with the average difference of 30 mm, and overpredicted the average annual (2001–2015) precipitation with a difference of 20 mm. On the contrary, for low precipitation EDBF underpredicted the dry year (2001) and the average annual (2001–2015), and overpredicted the wet year (2004) precipitation with the average difference of 10, 4 and 23 mm, respectively. Similarly, considering the individual precipitation variable, EDBF accurately predicted the wet year (2003) and the average annual (2001–2015) precipitation with the average difference of less than 5 mm, whereas it slightly overpredicted the dry year (2001) with an average difference of 10 mm between the original and the corresponding weighted precipitation.
