*3.1. Regional Evaluation of SM2RAIN-CCI Dataset*

Accuracy of daily precipitation estimates from the SM2RAIN-CCI and SM2RAIN-ASCAT were assessed using the RGs data as a benchmark for each climate region during the period 2000–2015 and 2007–2015, respectively. The continuous metrics (listed in Table 2) values are statistical quantification of variations in the amount of precipitation from SM2RAIN-CCI/ASCAT datasets from the RGs data at the pixel scale (considered only the common pixels). The ordinary kriging method is used to interpolate the pixel base data over entire Pakistan (climate regions) to comprehensively understand the spatial distribution trend of error characteristics.

Figure 3 shows the spatial distribution of statistical metrics of SM2RAIN-CCI over four distinct climate regions, i.e., glacial, humid, arid and hyper-arid regions in Pakistan. Precipitation data for SM2RAIN-CCI is not available in the glacial region and high elevated areas of humid region due to masking, i.e., precipitation data of SM2RAIN-CCI is masked out in frozen soil, snow-dominated regions and complex topography.

Figure 3a represents the spatial distribution of SM2RAIN-CCI biases (B) across Pakistan in comparison with RG observations for the study period (2000–2015) on a daily temporal scale. In the humid region, larger negative biases (underestimation) are evident over north-east of the humid region but decreases gradually towards the west (slightly overestimated). The north-east of humid region consists of the Mangla dam, barrages, headworks and an extensively developed integrated irrigation canal system (comprised of 12 interlink canals and 43 independent irrigation canals commands) of the country (hereinafter called hydraulically developed areas), which results in the groundwater level rise in the vicinity of these structures and the soil water saturation in irrigated land after irrigation. Besides, the area is also subjected to heavy and intense precipitation that may saturate the soil in a quick span of time. Since the SM2RAIN-based products work on the principles of soil–water balance, the excessive precipitation cannot be considered when the soil gets saturated, and hence resulting in

higher biases (higher underestimation). The sign of biases shows an interesting feature along the west of arid region indicating a considerable underestimation of precipitation. Western side of arid regions is comprised of mild elevated mountainous ranges (i.e., Koh-e-Suleman, Koh-e-Chiltan, Koh-e-Murdaar, and Koh-e-Takatu) having cold weather in winter and hot in summer with mean annual precipitation of 317 mm [47]. Precipitation is underestimated in this region due to the low infiltration capacity (the area is mostly covered with rocks) and also due to the snow factor in the winter season. However, precipitation is overestimated in the plain agricultural areas of the arid region (east and south-east). Hyper-arid region is the hottest region located at the coast of the Arabian Sea and experience mean annual precipitation of 133 mm. Precipitation is overestimated in the region by SM2RAIN-CCI, which may be due to seawater intrusion from the Arabian Sea [66]. High overestimation is observed in the south-east coastal area which gradually decreases towards the west.

Figure 3b presents the spatial distribution of ubRMSE over different climate regions of Pakistan. A common trend of lower ubRMSE towards the west in comparison to the east of each climate region is observed in the figure. Higher ubRMSE is observed in the hydraulically developed areas in the north-east of humid region. Lower ubRMSE is observed in the hyper-arid region, most specifically near the coast of the Arabian Sea. The hyper-arid region is a precipitation deficit region where there is plenty of time for precipitation to infiltrate and saturate the soil. The reason for lower ubRMSE in the hyper-arid region is low intensity and low magnitude precipitation. Higher ubRMSE was observed at HRG23 (12.44 mm/day) while minimum at HARG8 (1.83 mm/day).

Figure 3c depicts the distribution of Theil's U coefficient that shows the accuracy of SM2RAIN-CCI to accurately detect a precipitation event. Smaller values (close to zero) represent better forecasting accuracy, while values closer to 1 depicts poor forecasting. The figure reveals better forecasting accuracies at ARG16 (0.24) and ARG8 (0.23), with poor forecasting accuracies in north-east of humid region, more specifically at HRG23 (0.66) and HRG24 (0.69), respectively. Locations of high accuracies (minimum Theil's U) in the arid region are in the vicinity of the agricultural region (ARG9) and the Thar desert (ARG16) where soil is mostly unsaturated. The only source of water for agriculture is irrigation water. Agriculture in the location helps to preserve the water in the soil. Beside the arid region, moderate accuracy is depicted in south-east of the hyper-arid region near HARG18, HARG19, HARG20, and HARG21. The average values of Theil's U in the humid, arid and hyper-arid regions were 0.51, 0.40, and 0.42, and the median values were 0.53, 0.43, and 0.41, respectively.

Spatial distributions of mean square error components, i.e., random and systematic errors, in SM2RAIN-CCI across Pakistan are presented in Figure 3d,e. Before the integration of any PP in the hydrological application, the knowledge about systematic and random errors for implementation of any statistical adjustment and bias correction is extremely vital [61]. In comparison with the random error component, systematic errors have larger contributions over Pakistan. The analysis depicts that SM2RAIN-CCI needs proper adjustments in biases before assimilating into any hydrological application. Larger systematic errors are observed in the hyper-arid and downstream portion of arid regions while minimum values are in the humid region.

Figure 3f presents the spatial distribution of KGE score for the SM2RAIN-CCI product as compared to RGs observation. Results shows smaller KGE scores in the humid region, which increases to maximum values in the middle of the arid region, then decreasing at the end of the arid region. Smaller KGE scores in north-east of the humid region might be due to the relatively poor performance of SM2RAIN-CCI in the hydraulically developed areas. Besides that, the uncertainties in gauge-based estimates associated with sparse gauge density also play a vital role. The highest KGE scores were observed at ARG3 (0.78), HRG11 (0.74), and ARG15 (0.73). The minimum KGE score was observed at HRG24 (0.13).

**Figure 3.** Spatial distribution of bias (**a**), ubRMSE (**b**), Theil's U coefficient (**c**), systematic error (**d**), random error (**e**), and KGE score (**f**) based on a daily scale across Pakistan from SM2RAIN-CCI compared to RGs data for the period of 2000–2015.
