**3. Results**

*3.1. Evaluation of Precipitation Amount-Based Indices*

Multi-year annual PRCPTOT, R85p, R95p, and R99p from observational precipitation were generally characterized by a decrease from southeastern to northwestern, with the HRB means of 812.60 mm, 441.15 mm, 233.68 mm, and 76.64 mm, respectively (Figure 2a1–a4). Overall, the PERSIANN-CDR could capture a similar spatial distribution for each amountbased index, with spatial *R*s of 0.94 for PRCPTOT, 0.92 for R85p, 0.89 for R95p, and 0.81 for R99p (Figure 2b1–b4). Despite that, evident differences in the climatological values of these amount-based indices existed between observation and PERSIANN-CDR (Figure 2b1–b4); the HRB *β* > 1.0 indicated that the PERSIANN-CDR overestimated the climatological values of the amount-based indices. Meanwhile, the spatial variabilities of the climatological values were all overestimated, with HRB *γ* values of 1.40, 1.32, 1.45, and 1.56 for PRCPTOT, R85p, R95p and R99p, respectively. To have an integrative consideration of *β*, *γ*, and *R*, the PERSIANN-CDR showed high (i.e., *KGE*s ≥ 0.38) performance overall in spatially representing the climatological value of each amount-based index, especially for R95p with a *KGE* of 0.58.

**3. Results** 

*3.1. Evaluation of Precipitation Amount-Based Indices* 

cially for R95p with a *KGE* of 0.58.

Multi-year annual PRCPTOT, R85p, R95p, and R99p from observational precipitation were generally characterized by a decrease from southeastern to northwestern, with the HRB means of 812.60 mm, 441.15 mm, 233.68 mm, and 76.64 mm, respectively (Figure 2a1–a4). Overall, the PERSIANN-CDR could capture a similar spatial distribution for each amount-based index, with spatial *R*s of 0.94 for PRCPTOT, 0.92 for R85p, 0.89 for R95p, and 0.81 for R99p (Figure 2b1–b4). Despite that, evident differences in the climatological values of these amount-based indices existed between observation and PERSIANN-CDR (Figure 2b1–b4); the HRB *β* > 1.0 indicated that the PERSIANN-CDR overestimated the climatological values of the amount-based indices. Meanwhile, the spatial variabilities of the climatological values were all overestimated, with HRB *γ* values of 1.40, 1.32, 1.45, and 1.56 for PRCPTOT, R85p, R95p and R99p, respectively. To have an integrative consideration of *β*, *γ*, and *R*, the PERSIANN-CDR showed high (i.e., *KGE*s ≥ 0.38) performance overall in spatially representing the climatological value of each amount-based index, espe-

**Figure 2.** Spatial patterns of multi-year annual means of observational amount-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**–**a4** (**b1**–**b4**) are for PRCPTOT, R85p, R95p, and R99p, respectively. In **a1**–**a4**, the blue numbers represent the HRB mean for a given extreme precipitation index. The red dashed line within **b1**−**b4** is the 1:1 line. **Figure 2.** Spatial patterns of multi-year annual means of observational amount-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**–**a4** (**b1**–**b4**) are for PRCPTOT, R85p, R95p, and R99p, respectively. In **a1**–**a4**, the blue numbers represent the HRB mean for a given extreme precipitation index. The red dashed line within **b1**–**b4** is the 1:1 line.

Generally, each of the four amount-based indices was differently overestimated at > 90% of grids by the PERSIANN-CDR (Figure 3a1–a4). Larger overestimations (i.e., *β* > 1.4) for PRCPTOT and R85p were mainly located in the southern part (Figure 3a1,a2), while for R95p and R99p larger overestimations were widely distributed across the HRB except for small part of southern HRB (Figure 3a3,a4). For PRCPTOT (R85p), *γ* values were between 1.0 and 1.2 at >90% of grids, corresponding to overestimated temporal variability; generally, in southwestern and easternmost HRB, temporal variability at <10% of grids was underestimated (Figure 3b1,b2). Regarding R95p and R99p (Figure 3b3,b4), overestimated temporal variabilities existed at >90% of grids, of which >30% of grids had *γ* > 1.2, mainly in the central-northern part for R95p and in the northern and southeastern parts for R99p. Checking temporal *R*s for PRCPTOT at all the grids (Figure 3c1), the values were all >0.50, with 81% of grids showing *R*s > 0.70 widely distributed across the HRB. As for R85p (Figure 3c2), most (>85%) grids showed temporal *R*s > 0.50, especially for western, southeastern, and northeastern HRB, with temporal *R*s > 0.70, while it was noted that there were still some grids with *R*s < 0.40 sporadically in the central-northern part. Seen in Figure 3c3, 50% of grids showed *R*s > 0.50 for R95p, accompanied by <10% of grids with *R*s > 0.70 in

(Figure 3d4).

southwestern HRB; of the remaining grids, their corresponding *R*s < 0.2 indicated that the PERSIANN-CDR had much limited ability in reproducing temporal fluctuations of R95p. Figure 3c4 illustrates that the PERSIANN-CDR could capture temporal fluctuations of R99p at only 15% of grids, mainly in western HRB; moreover, negative *R*s in northeastern HRB suggested that the product had no capacity in reproducing temporal fluctuations of R99p. At > 90% of grids, *KGE*s for both PCPTOT and R85p were >0.20, especially in centralnorthern HRB, with *KGE*s > 0.40 indicating better overall performance (Figure 3d1,d2). For R95p (Figure 3d3), there existed 66% of grids with *KGE*s > 0.2, particularly those in the southern part with *KGE*s > 0.40, whereas in the northern part around 30% of grids with *KGE*s < 0.20 showed limited overall performance for representing R95p. Except for the 16% of grids in the southwestern part with *KGE*s between 0.2 and 0.4, the PERSIANN-CDR lacked the ability to represent R99p over the remaining grids (Figure 3d4). 0.70 in southwestern HRB; of the remaining grids, their corresponding *R*s < 0.2 indicated that the PERSIANN-CDR had much limited ability in reproducing temporal fluctuations of R95p. Figure 3c4 illustrates that the PERSIANN-CDR could capture temporal fluctuations of R99p at only 15% of grids, mainly in western HRB; moreover, negative *R*s in northeastern HRB suggested that the product had no capacity in reproducing temporal fluctuations of R99p. At > 90% of grids, *KGE*s for both PCPTOT and R85p were >0.20, especially in central-northern HRB, with *KGE*s > 0.40 indicating better overall performance (Figure 3d1,d2). For R95p (Figure 3d3), there existed 66% of grids with *KGE*s > 0.2, particularly those in the southern part with *KGE*s > 0.40, whereas in the northern part around 30% of grids with *KGE*s < 0.20 showed limited overall performance for representing R95p. Except for the 16% of grids in the southwestern part with *KGE*s between 0.2 and 0.4, the PERSIANN-CDR lacked the ability to represent R99p over the remaining grids

*Remote Sens.* **2021**, *13*, x FOR PEER REVIEW 7 of 20

Generally, each of the four amount-based indices was differently overestimated at > 90% of grids by the PERSIANN-CDR (Figure 3a1–a4). Larger overestimations (i.e., *β* > 1.4) for PRCPTOT and R85p were mainly located in the southern part (Figure 3a1,a2), while for R95p and R99p larger overestimations were widely distributed across the HRB except for small part of southern HRB (Figure 3a3,a4). For PRCPTOT (R85p), *γ* values were between 1.0 and 1.2 at > 90% of grids, corresponding to overestimated temporal variability; generally, in southwestern and easternmost HRB, temporal variability at < 10% of grids was underestimated (Figure 3b1,b2). Regarding R95p and R99p (Figure 3b3,b4), overestimated temporal variabilities existed at > 90% of grids, of which > 30% of grids had *γ* > 1.2, mainly in the central-northern part for R95p and in the northern and southeastern parts for R99p. Checking temporal *R*s for PRCPTOT at all the grids (Figure 3c1), the values were all > 0.50, with 81% of grids showing *R*s > 0.70 widely distributed across the HRB. As for R85p (Figure 3c2), most (>85%) grids showed temporal *R*s > 0.50, especially for western,

ure 3c3, 50% of grids showed *R*s > 0.50 for R95p, accompanied by <10% of grids with *R*s >

**Figure 3.** Spatial patterns of different validation metrics for the amount-based indices. **Figure 3.** Spatial patterns of different validation metrics for the amount-based indices.

At space, the observational PRCPTOT, R85p, R95p, and R99p trends had a similar distribution, i.e., decreased over western and southeastern parts, but increased in other At space, the observational PRCPTOT, R85p, R95p, and R99p trends had a similar distribution, i.e., decreased over western and southeastern parts, but increased in other regions, with the HRB trends of 4.17 mm/yr, 3.68mm/yr, 3.13 mm/yr, and 1.69mm/yr, respectively (Figure 4a1–a4). Moreover, the percentage of the grids with positive trends for each index was always ≥ 56%. As shown in Figure 4b1–b4, each of the PERSIANN-CDR amount-based indices corresponded to underestimated trends at most (>50%) grids; for the regional mean, the HRB *β* < 0.5 suggested that the PERSIANN-CDR seriously underestimated the trends of these amount-based indices, especially for the PRCPTOT with opposite changes (i.e., *β* = −0.18) between the observation and the PERSIANN-CDR. Except for PRCPTOT, the spatial variabilities of R85p, R95p, and R99p trends were overestimated with the HRB *γ* values >1.00. The PERSIANN-CDR showed a moderate performance (spatial *R* = 0.39) in producing spatial patterns of PRCPTOT trends, but much limited capacity (spatial *R*s < 0.20) existed for the other three indices. Based on *KGE*, it is evident that the PERSIANN-CDR had no ability (i.e., *KGE*s < 0) to present the trends of these amount-based indices.

based indices.

regions, with the HRB trends of 4.17 mm/yr, 3.68mm/yr, 3.13 mm/yr, and 1.69mm/yr, respectively (Figure 4a1–a4). Moreover, the percentage of the grids with positive trends for each index was always ≥ 56%. As shown in Figure 4b1–b4, each of the PERSIANN-CDR amount-based indices corresponded to underestimated trends at most (>50%) grids; for the regional mean, the HRB *β* < 0.5 suggested that the PERSIANN-CDR seriously underestimated the trends of these amount-based indices, especially for the PRCPTOT with opposite changes (i.e., *β* = −0.18) between the observation and the PERSIANN-CDR. Except for PRCPTOT, the spatial variabilities of R85p, R95p, and R99p trends were overestimated with the HRB *γ* values >1.00. The PERSIANN-CDR showed a moderate performance (spatial *R* = 0.39) in producing spatial patterns of PRCPTOT trends, but much limited capacity (spatial *R*s < 0.20) existed for the other three indices. Based on *KGE*, it is evident that the PERSIANN-CDR had no ability (i.e., *KGE*s < 0) to present the trends of these amount-

**Figure 4.** Spatial patterns of the temporal trends of the observational amount-based indices (**a1**– **a4**), and the scatterplots between observation and PERSIANN-CDR. **a1**–**a4** (**b1**–**b4**) are for PRCPTOT, R85p, R95p, and R99p, respectively. In **a1**–**a4**, the black numbers represent the HRB trends of the observational amount-based indices, while the blue (red) numbers indicate grid percentages with increasing (decreasing) trend across the HRB. The red dashed line in **b1**–**b4** is the 1:1 line. **Figure 4.** Spatial patterns of the temporal trends of the observational amount-based indices (**a1**–**a4**), and the scatterplots between observation and PERSIANN-CDR. **a1**–**a4** (**b1**–**b4**) are for PRCPTOT, R85p, R95p, and R99p, respectively. In **a1**–**a4**, the black numbers represent the HRB trends of the observational amount-based indices, while the blue (red) numbers indicate grid percentages with increasing (decreasing) trend across the HRB. The red dashed line in **b1**–**b4** is the 1:1 line.

#### *3.2. Evaluation of Precipitation Duration-Based Indices*

*3.2. Evaluation of Precipitation Duration-Based Indices*  For the HRB, the observational multi-year annual means of CDD and CWD were 45.22 days and 5.08 days, respectively (Figure 5a1,a2), corresponding to spatial distributions of a decrease from northwest to southeast and an increase from northwest to southeast. Based on spatial *R*s of 0.86 for CDD and 0.71 for CWD (Figure 5b1,b2), the PERSIANN-CDR better detected spatial distributions of climatological characteristics of these two durationbased indices. It is evident that for the HRB, the PERSIANN-CDR seriously underestimated and overestimated magnitudes of climatological CDD and CWD values, respectively, with *β* values of 0.68 and 1.95 (Figure 5b1,b2). For spatial variability, larger overestimation existed for CDD with the HRB *γ* of 1.44, while CWD corresponded to a slight underestimation (*γ* = 0.98). In terms of *KGE*, this PERSIANN-CDR had no ability to represent CWD, while better overall performance (*KGE* = 0.44) existed for CDD (Figure 5b1,b2).

5b1,b2).

**Figure 5.** Spatial patterns of multi-year annual means of observational duration-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**,**a2** (**b1**,**b2**) are for CDD and CWD, respectively. In **a1**,**a2**, the blue numbers represent the HRB mean for a given extreme precipitation index. The red dashed line in **b1**,**b2** is the 1:1 line. **Figure 5.** Spatial patterns of multi-year annual means of observational duration-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**,**a2** (**b1**,**b2**) are for CDD and CWD, respectively. In **a1**,**a2**, the blue numbers represent the HRB mean for a given extreme precipitation index. The red dashed line in **b1**,**b2** is the 1:1 line.

For the HRB, the observational multi-year annual means of CDD and CWD were 45.22 days and 5.08 days, respectively (Figure 5a1,a2), corresponding to spatial distributions of a decrease from northwest to southeast and an increase from northwest to southeast. Based on spatial *R*s of 0.86 for CDD and 0.71 for CWD (Figure 5b1,b2), the PER-SIANN-CDR better detected spatial distributions of climatological characteristics of these two duration-based indices. It is evident that for the HRB, the PERSIANN-CDR seriously underestimated and overestimated magnitudes of climatological CDD and CWD values, respectively, with *β* values of 0.68 and 1.95 (Figure 5b1,b2). For spatial variability, larger overestimation existed for CDD with the HRB *γ* of 1.44, while CWD corresponded to a slight underestimation (*γ* = 0.98). In terms of *KGE*, this PERSIANN-CDR had no ability to represent CWD, while better overall performance (*KGE* = 0.44) existed for CDD (Figure

At all the grids, CDD were underestimated (*β* < 1.00), followed by > 95% of grids with larger underestimations (*β* < 0.80) (Figure 6a1). Conversely, the PERSIANN-CDR much overestimated CWD (*β* > 1.40) across the HRB (Figure 6a2). Based on *γ*, temporal variabilities of CDD were underestimated at > 90% of grids (Figure 6b1), and larger underestimations (*γ* < 0.9) mainly appeared in western HRB, followed by some grids with overestimations (*γ* > 1.00), mainly in some parts of eastern HRB. For CWD (Figure 6b2), overestimations (underestimations) of temporal variabilities occurred at 25% (75%) of grids but were characterized by sporadic distribution across the study region. Regarding CDD (Figure 6c1), the PERSIANN-CDR had strong ability (*R* > 0.50) to represent temporal fluctuations at 40% of grids in northwestern HRB, but moderate or limited ability at other grids. Except for only 5% of grids with a certain capacity, the PERSIANN-CDR had limited or no capacity (*R* < 0.20) in reproducing temporal fluctuations of CWD across the HRB (Figure 6c2). Seen in Figure 6d1, the PERSIANN-CDR had the ability (*KGE* > 0.30) to represent CDD at >60% of grids in northern HRB, followed by no ability, mainly in southern HRB. Smaller (near to 0) and negative *KGE*s at all the grids suggested the PERSIANN-CDR had no ability in capturing CWD across the HRB (Figure 6d2). At all the grids, CDD were underestimated (*β* < 1.00), followed by > 95% of grids with larger underestimations (*β* < 0.80) (Figure 6a1). Conversely, the PERSIANN-CDR much overestimated CWD (*β* > 1.40) across the HRB (Figure 6a2). Based on *γ*, temporal variabilities of CDD were underestimated at > 90% of grids (Figure 6b1), and larger underestimations (*γ* < 0.9) mainly appeared in western HRB, followed by some grids with overestimations (*γ* > 1.00), mainly in some parts of eastern HRB. For CWD (Figure 6b2), overestimations (underestimations) of temporal variabilities occurred at 25% (75%) of grids but were characterized by sporadic distribution across the study region. Regarding CDD (Figure 6c1), the PERSIANN-CDR had strong ability (*R* > 0.50) to represent temporal fluctuations at 40% of grids in northwestern HRB, but moderate or limited ability at other grids. Except for only 5% of grids with a certain capacity, the PERSIANN-CDR had limited or no capacity (*R* < 0.20) in reproducing temporal fluctuations of CWD across the HRB (Figure 6c2). Seen in Figure 6d1, the PERSIANN-CDR had the ability (*KGE* > 0.30) to represent CDD at >60% of grids in northern HRB, followed by no ability, mainly in southern HRB. Smaller (near to 0) and negative *KGE*s at all the grids suggested the PERSIANN-CDR had no ability in capturing CWD across the HRB (Figure 6d2).

In view of observations, the two duration-based indices for the HRB differently increased, with a rate of 0.24 days/yr for CDD and 0.02 days/yr for CWD (Figure 7a1,a2). Spatially, the positive trends of the observational CDD occurred at 84% of grids, followed by decreasing trends at 16% of grids in central-northern and southwestern parts (Figure 7a1). There existed >30% of grids with decreased CWD, generally in western HRB, while increased CWD was widely distributed across eastern HRB, with a grid percentage around 70% (Figure 7a2). For the HRB, the CDD trends were overestimated by the PERSIANN-CDR, with *β* of 1.20 (Figure 7b1), while the product seriously underestimated (*β* = 0.12) the CWD trends (Figure 7b2). In terms of *γ*, the PERSIANN-CDR overestimated spatial variabilities of both CDD and CWD trends, especially for CWD, with a serious overestimation (*γ* = 10.58) (Figure 7b1,b2). Overall, there was no ability (*R* < 0.10) for the PERSIANN-CDR to produce spatial patterns of the trends of the duration-based indices, accompanied by no *KGE*-based ability (*KGE* near to 0 and even < 0) (Figure 7b1,b2).

*Remote Sens.* **2021**, *13*, x FOR PEER REVIEW 10 of 20

**Figure 6.** Spatial patterns of different validation metrics for the duration-based indices. **Figure 6.** Spatial patterns of different validation metrics for the duration-based indices. SIANN-CDR to produce spatial patterns of the trends of the duration-based indices, ac-

companied by no *KGE*-based ability (*KGE* near to 0 and even < 0) (Figure 7b1,b2).

In view of observations, the two duration-based indices for the HRB differently in-

**Figure 7.** Spatial patterns of the temporal trends of the observational duration-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**,**a2** (**b1**,**b2**) are for CDD and CWD, **Figure 7.** Spatial patterns of the temporal trends of the observational duration-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**,**a2** (**b1**,**b2**) are for CDD and CWD, respectively. In **a1**,**a2**, the black numbers represent the HRB trends of the observational durationbased indices, while the blue (red) numbers indicate grid percentages with increasing (decreasing) trend across the HRB. The red dashed line in **b1**,**b2** is the 1:1 line.

#### *3.3. Evaluation of Precipitation Frequency-Based Indices*

**Figure 7.** Spatial patterns of the temporal trends of the observational duration-based indices and Multi-year annual R10mm, R20mm, and Rnnmm from observational precipitation were characterized by a decrease from northwest to southeast, with the HRB means of 22.93 days, 11.73 days, and 8.86 days, respectively (Figure 8a1–a3). Overall, the PERSIANN-CDR could better capture spatial distributions of climatological R10mm, R20mm, and Rnnmm, with spatial *R*s of 0.96, 0.91, and 0.90, respectively (Figure 8b1–b3). For the HRB, magnitudes and spatial variabilities for climatological value of each frequency index were differently underestimated and overestimated by the PERSIANN-CDR, respectively (Figure 8b1–b3). Specifically,

the PERSIANN-CDR showed the largest Rnnmm underestimation in magnitude (spatial variability) with the HRB *β* (*γ*) of 0.68 (1.30) (Figure 8b1–b3). Based on *KGE*, this product had better overall performance (i.e., *KGE* > 0.55) in representing the three frequency-based indices, particularly for R10mm and R20mm, with *KGE*s > 0.60 (Figure 8b1–b3). (Figure 8b1–b3). Specifically, the PERSIANN-CDR showed the largest Rnnmm underestimation in magnitude (spatial variability) with the HRB *β* (*γ*) of 0.68 (1.30) (Figure 8b1–b3). Based on *KGE*, this product had better overall performance (i.e., *KGE* > 0.55) in representing the three frequency-based indices, particularly for R10mm and R20mm, with *KGE*s > 0.60 (Figure 8b1–b3).

respectively. In **a1**,**a2**, the black numbers represent the HRB trends of the observational durationbased indices, while the blue (red) numbers indicate grid percentages with increasing (decreasing)

Multi-year annual R10mm, R20mm, and Rnnmm from observational precipitation were characterized by a decrease from northwest to southeast, with the HRB means of 22.93 days, 11.73 days, and 8.86 days, respectively (Figure 8a1–a3). Overall, the PER-SIANN-CDR could better capture spatial distributions of climatological R10mm, R20mm, and Rnnmm, with spatial *R*s of 0.96, 0.91, and 0.90, respectively (Figure 8b1–b3). For the HRB, magnitudes and spatial variabilities for climatological value of each frequency index were differently underestimated and overestimated by the PERSIANN-CDR, respectively

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trend across the HRB. The red dashed line in **b1**,**b2** is the 1:1 line.

*3.3. Evaluation of Precipitation Frequency-Based Indices* 

**Figure 8.** Spatial patterns of multi-year annual means of observational frequency-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**–**a3** (**b1**–**b3**) are for R10mm, R20mm, and Rnnmm, respectively. In **a1**–**a3**, the blue numbers represent the HRB mean for a given extreme precipitation index. The red dashed line in **b1**–**b3** is the 1:1 line. **Figure 8.** Spatial patterns of multi-year annual means of observational frequency-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**–**a3** (**b1**–**b3**) are for R10mm, R20mm, and Rnnmm, respectively. In **a1**–**a3**, the blue numbers represent the HRB mean for a given extreme precipitation index. The red dashed line in **b1**–**b3** is the 1:1 line.

Seen in Figure 9a1, except for 4% of grids in the southern part with smaller overestimations (*β* between 1.00 and 1.10), the PERSIANN-CDR differently underestimated R10mm at the remaining grids. Regarding R20mm and Rnnmm, the underestimations (*β* < 1.00) occurred at an overwhelming majority (>98%) of grids, of which > 80% of grids corresponded to larger underestimations (*β* < 0.60) (Figure 9a2,a3). Based on *γ*, temporal variabilities of the three frequency-based indices were differently underestimated at >75% of grids (Figure 9b1–b3); larger underestimations (*γ* < 0.8) for R20mm in northern HRB Seen in Figure 9a1, except for 4% of grids in the southern part with smaller overestimations (*β* between 1.00 and 1.10), the PERSIANN-CDR differently underestimated R10mm at the remaining grids. Regarding R20mm and Rnnmm, the underestimations (*β* < 1.00) occurred at an overwhelming majority (>98%) of grids, of which > 80% of grids corresponded to larger underestimations (*β* < 0.60) (Figure 9a2,a3). Based on *γ*, temporal variabilities of the three frequency-based indices were differently underestimated at >75% of grids (Figure 9b1–b3); larger underestimations (*γ* < 0.8) for R20mm in northern HRB and for Rnnmm in northern and central-southern parts (Figure 9b2,b3). Moreover, there were some grids with overestimated temporal variabilities (*γ* > 1.00) of the frequency-based indices, e.g., R10mm and R20mm at >15% of grids, generally in southern HRB (Figure 9b1,b2). It is evident that the PERSIANN-CDR had strong ability (*R* > 0.50) to represent temporal fluctuations of R10mm at 89% of grids, which were widely distributed across the HRB; for R20mm and Rnnmm, there existed >50% of grids with *R* > 0.50, mainly in southern HRB (Figure 9c1–c3). Obviously, the PERSIANN-CDR exhibited a better overall performance (*KGE* > 0.40) in detecting R10mm at all the grids (Figure 9d1). Except for <15% of grids, generally in northwestern and northeastern HRB with no estimation ability, southern HRB corresponded to *KGE*s > 0.20 for Rn20mm and Rnnmm (Figure 9d2,d3), particularly for most grids of southern HRB, with *KGE*s > 0.5.

10b1–b3).

particularly for most grids of southern HRB, with *KGE*s > 0.5.

and for Rnnmm in northern and central-southern parts (Figure 9b2,b3). Moreover, there were some grids with overestimated temporal variabilities (*γ* > 1.00) of the frequencybased indices, e.g., R10mm and R20mm at > 15% of grids, generally in southern HRB (Figure 9b1,b2). It is evident that the PERSIANN-CDR had strong ability (*R* > 0.50) to represent temporal fluctuations of R10mm at 89% of grids, which were widely distributed across the HRB; for R20mm and Rnnmm, there existed > 50% of grids with *R* > 0.50, mainly in southern HRB (Figure 9c1–c3). Obviously, the PERSIANN-CDR exhibited a better overall performance (*KGE* > 0.40) in detecting R10mm at all the grids (Figure 9d1). Except for < 15% of grids, generally in northwestern and northeastern HRB with no estimation ability,

**Figure 9.** Spatial patterns of different validation metrics for the frequency-based indices. **Figure 9.** Spatial patterns of different validation metrics for the frequency-based indices.

As shown in Figure 10a1–a3, the HRB R10mm, R20mm, and Rnnmm increased by 0.03 days/yr, 0.03 days/yr, and 0.02 days/yr, respectively. At space, the trends of the observational frequency-based indices generally had a decrease in the western part and an increase in eastern parts; moreover, there were always ≥ 65% of grids with positive trends for the three indices. For the HRB, the PERSIANN-CDR seriously underestimated (*β* < 0.50) the trends of all the frequency-based indices, and even for R20mm and Rnnmm, the PERSIANN-CDR showed the opposite trends (Figure 10b1–b3). The metric of *γ* suggested As shown in Figure 10a1–a3, the HRB R10mm, R20mm, and Rnnmm increased by 0.03 days/yr, 0.03 days/yr, and 0.02 days/yr, respectively. At space, the trends of the observational frequency-based indices generally had a decrease in the western part and an increase in eastern parts; moreover, there were always ≥ 65% of grids with positive trends for the three indices. For the HRB, the PERSIANN-CDR seriously underestimated (*β* < 0.50) the trends of all the frequency-based indices, and even for R20mm and Rnnmm, the PERSIANN-CDR showed the opposite trends (Figure 10b1–b3). The metric of *γ* suggested that this product overestimated spatial variabilities of R10mm (Figure 10b1). There was no ability (*R* ≤ 0.11) for the PERSIANN-CDR to produce spatial patterns of R10mm, R20mm, and Rnnmm trends, accompanied by no *KGE*-based ability (*KGE* < 0) (Figure 10b1–b3).

that this product overestimated spatial variabilities of R10mm (Figure 10b1). There was no ability (*R* ≤ 0.11) for the PERSIANN-CDR to produce spatial patterns of R10mm, R20mm, and Rnnmm trends, accompanied by no *KGE*-based ability (*KGE* < 0) (Figure

**Figure 10.** Spatial patterns of the temporal trends of the observational frequency-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**–**a3** (**b1**–**b3**) are for R10mm, R20mm, and Rnnmm, respectively. In **a1**–**a3**, the black numbers represent the HRB trends of the **Figure 10.** Spatial patterns of the temporal trends of the observational frequency-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**–**a3** (**b1**–**b3**) are for R10mm, R20mm, and Rnnmm, respectively. In **a1**–**a3**, the black numbers represent the HRB trends of the observational frequency-based indices, while the blue (red) numbers indicate grid percentages with increasing (decreasing) trend across the HRB. The red dashed line in **b1**–**b3** is the 1:1 line.

#### with increasing (decreasing) trend across the HRB. The red dashed line in **b1**–**b3** is the 1:1 line. *3.4. Evaluation of Precipitation Intensity-Based Indices*

*3.4. Evaluation of Precipitation Intensity-Based Indices*  For Rx1day, Rx5day, and SDII, the observational multi-year annual means were 96.05 mm/day, 148.97 mm/(5 days), and 12.99 mm/day for the HRB, respectively, generally characterized by an increase from the northwest to southeast (Figure 11a1–a3). The spatial *R*s of 0.25 for Rx1day, 0.38 for Rx5day, and 0.52 for SDII indicated that the PERSIANN-CDR could reproduce spatial patterns of climatological characteristics of the intensity-based indices (Figure 11b1–b3). The HRB *β* values < 0.80 for the intensity-based indices suggested that the three indices were underestimated by the PERSIANN-CDR, especially for For Rx1day, Rx5day, and SDII, the observational multi-year annual means were 96.05 mm/day, 148.97 mm/(5 days), and 12.99 mm/day for the HRB, respectively, generally characterized by an increase from the northwest to southeast (Figure 11a1–a3). The spatial *R*s of 0.25 for Rx1day, 0.38 for Rx5day, and 0.52 for SDII indicated that the PERSIANN-CDR could reproduce spatial patterns of climatological characteristics of the intensity-based indices (Figure 11b1–b3). The HRB *β* values < 0.80 for the intensity-based indices suggested that the three indices were underestimated by the PERSIANN-CDR, especially for SDII (*β* = 0.49), followed by R1xday (*β* = 0.64). For Rx1day and Rx5day, the HRB *γ* values < 1.0 indicated that spatial variabilities of the two PERSIANN-CDR intensity-based indices were smaller than the observations (Figure 11b1,b2), followed by SDII with *γ* of 1.37. Based on *KGE*, this product had a moderate overall performance (*KGE* > 0.20) in representing the three intensity-based indices.

SDII (*β* = 0.49), followed by R1xday (*β* = 0.64). For Rx1day and Rx5day, the HRB *γ* values < 1.0 indicated that spatial variabilities of the two PERSIANN-CDR intensity-based indi-

Based on *KGE*, this product had a moderate overall performance (*KGE* > 0.20) in repre-

observational frequency-based indices, while the blue (red) numbers indicate grid percentages

senting the three intensity-based indices.

**Figure 11.** Spatial patterns of multi-year annual means of the observational intensity-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**–**a3** (**b1**–**b3**) are for Rx1day, Rx5day, and SDII, respectively. In **a1**–**a3**, the blue numbers represent the HRB mean for a given extreme precipitation index. The red dashed line in **b1**–**b3** is the 1:1 line. **Figure 11.** Spatial patterns of multi-year annual means of the observational intensity-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**–**a3** (**b1**–**b3**) are for Rx1day, Rx5day, and SDII, respectively. In **a1**–**a3**, the blue numbers represent the HRB mean for a given extreme precipitation index. The red dashed line in **b1**–**b3** is the 1:1 line.

In general, the intensity-based indices were underestimated by PERSIANN-CDR except for only 3% of grids with slight overestimations (*β* between 1.00 and 1.20) for Rx5day in the northeastern part (Figure 12a1–a3). There were more than 80% of grids with overestimated temporal variabilities for the three indices, especially in northwestern and central-eastern HRB, with *γ* > 1.40 for Rx1day and Rx5day, and in northwestern and southeastern HRB, with *γ* > 1.30 for SDII (Figure 12b1–b3). The PERSIANN-CDR had strong or moderate ability (*R* > 0.30) in detecting temporal fluctuations of R1xday at 39% of grids, but ability was sporadically distributed across the HRB (Figure 12c1). For Rx5day (Figure 12c2), there existed 68% of grids with *R* > 0.30, of which 30% of grids with better *R*-based performance (*R* > 0.50) were generally in southern HRB; moreover, the PERSIANN-CDR showed limited (*R* < 0.30) or no ability in reproducing temporal variability, particularly in the northern part with *R* < 0.20 and even negative. For SDII (Figure 12c3), >90% of grids with *R* > 0.30 suggested that the PERSIANN-CDR had the ability to reproduce temporal variability across the HRB, especially for western and southeastern parts, with better *R*based performance (*R* > 0.50). Spatially, the product had the ability (*KGE* > 0.20) to represent Rx1day at 28% of grids, mainly in middle HRB, but no ability at 72% of grids (Figure 9d1). With exception of 40% of grids having no ability, generally in northern HRB, the PERSIANN-CDR corresponded to a better overall performance for Rx5day across southern HRB, especially in the southeastern part, with *KGE* > 0.40 (Figure 9d2). The PER-SIANN-CDR exhibited a certain overall performance (*KGE* > 0.20) in detecting SDII at 59% of grids, followed by 41% of grids with limited and even no ability (Figure 12d3). In general, the intensity-based indices were underestimated by PERSIANN-CDR except for only 3% of grids with slight overestimations (*β* between 1.00 and 1.20) for Rx5day in the northeastern part (Figure 12a1–a3). There were more than 80% of grids with overestimated temporal variabilities for the three indices, especially in northwestern and central-eastern HRB, with *γ* > 1.40 for Rx1day and Rx5day, and in northwestern and southeastern HRB, with *γ* > 1.30 for SDII (Figure 12b1–b3). The PERSIANN-CDR had strong or moderate ability (*R* > 0.30) in detecting temporal fluctuations of R1xday at 39% of grids, but ability was sporadically distributed across the HRB (Figure 12c1). For Rx5day (Figure 12c2), there existed 68% of grids with *R* > 0.30, of which 30% of grids with better *R*-based performance (*R* > 0.50) were generally in southern HRB; moreover, the PERSIANN-CDR showed limited (*R* < 0.30) or no ability in reproducing temporal variability, particularly in the northern part with *R* < 0.20 and even negative. For SDII (Figure 12c3), >90% of grids with *R* > 0.30 suggested that the PERSIANN-CDR had the ability to reproduce temporal variability across the HRB, especially for western and southeastern parts, with better *R*based performance (*R* > 0.50). Spatially, the product had the ability (*KGE* > 0.20) to represent Rx1day at 28% of grids, mainly in middle HRB, but no ability at 72% of grids (Figure 9d1). With exception of 40% of grids having no ability, generally in northern HRB, the PERSIANN-CDR corresponded to a better overall performance for Rx5day across southern HRB, especially in the southeastern part, with *KGE* > 0.40 (Figure 9d2). The PERSIANN-CDR exhibited a certain overall performance (*KGE* > 0.20) in detecting SDII at 59% of grids, followed by 41% of grids with limited and even no ability (Figure 12d3).

10b1–b3).

**Figure 12.** Spatial patterns of different validation metrics for the intensity-based indices. **Figure 12.** Spatial patterns of different validation metrics for the intensity-based indices.

All the observational precipitation intensity-based indices for the HRB increased but at different rates, i.e., 0.23 mm/(day yr) for Rx1day, 0.76 mm/(5 days yr) for Rx5day, and 0.03 mm/(day yr) for SDII (Figure 13a1–a3). Generally, the measured Rx1day increased at most (59%) grids, followed by 41% of grids with decreased Rx1day, while the spatial distribution was scattered (Figure 13a1). For the observational Rx5day, 74% of grids corresponded to an increase, particularly in western HRB (excluding southwestern part) with a rate 1.00 mm/(5 days yr), while the remaining grids, generally in the southwestern and southeastern parts, showed different reductions (Figure 13a2). There were 34% of grids with decreased SDII, mainly in the southwestern and southeastern parts, followed by increases at the remaining grids (Figure 13a3). Broadly, the HRB *β* values for the intensitybased indices were all ≤ 0.52, suggesting underestimated trends by the PERSIANN-CDR, especially for Rx5day trends, with many underestimations (*β* = 0.20) (Figure 13b1–b3). In terms of the HRB γ, the PERSIANN-CDR underestimated spatial variabilities (*γ* < 0.90) for the HRB Rx1day and SDII trends but overestimated (*γ* < 1.31) Rx5day trends (Figure 10b1–b3). The PERSIANN-CDR had a certain *R*-based performance (spatial *R* around 0.20 All the observational precipitation intensity-based indices for the HRB increased but at different rates, i.e., 0.23 mm/(day yr) for Rx1day, 0.76 mm/(5 days yr) for Rx5day, and 0.03 mm/(day yr) for SDII (Figure 13a1–a3). Generally, the measured Rx1day increased at most (59%) grids, followed by 41% of grids with decreased Rx1day, while the spatial distribution was scattered (Figure 13a1). For the observational Rx5day, 74% of grids corresponded to an increase, particularly in western HRB (excluding southwestern part) with a rate 1.00 mm/(5 days yr), while the remaining grids, generally in the southwestern and southeastern parts, showed different reductions (Figure 13a2). There were 34% of grids with decreased SDII, mainly in the southwestern and southeastern parts, followed by increases at the remaining grids (Figure 13a3). Broadly, the HRB *β* values for the intensity-based indices were all ≤ 0.52, suggesting underestimated trends by the PERSIANN-CDR, especially for Rx5day trends, with many underestimations (*β* = 0.20) (Figure 13b1–b3). In terms of the HRB γ, the PERSIANN-CDR underestimated spatial variabilities (*γ* < 0.90) for the HRB Rx1day and SDII trends but overestimated (*γ* < 1.31) Rx5day trends (Figure 10b1–b3). The PERSIANN-CDR had a certain *R*-based performance (spatial *R* around 0.20 or > 0.30) in producing spatial patterns of these indices' trends (Figure 13b1–b3). There was no ability (*KGE* < 0.10) for the PERSIANN-CDR to represent these trends (Figure 10b1–b3).

**Figure 13.** Spatial patterns of the temporal trends of the observational intensity-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**–**a3** (**b1**–**b3**) are for Rx1day, Rx5day, and SDII, respectively. In **a1**–**a3**, the black numbers represent the HRB trends of the observational intensity-based indices, while the blue (red) numbers indicate grid percentages with increasing (decreasing) trend across the HRB. The red dashed line in **b1**–**b3** is the 1:1 line. **Figure 13.** Spatial patterns of the temporal trends of the observational intensity-based indices and the scatterplots between observation and PERSIANN-CDR. **a1**–**a3** (**b1**–**b3**) are for Rx1day, Rx5day, and SDII, respectively. In **a1**–**a3**, the black numbers represent the HRB trends of the observational intensity-based indices, while the blue (red) numbers indicate grid percentages with increasing (decreasing) trend across the HRB. The red dashed line in **b1**–**b3** is the 1:1 line.

#### **4. Conclusions and Discussion 4. Conclusions and Discussion**

Attempts to validate various satellite-based precipitation products' capacity in representing precipitation characteristics from different perspectives have been widely conducted all over the world. However, information about their capacity in detecting extreme precipitation and related changes (i.e., linear trends) is scarce. As a result, we collected daily observations from 182 gauges across the HRB during 1983–2012 and examined the PERSIANN-CDR capacity to represent precipitation amount- (PRCPTOT, R85p, R95p, and R99p), duration- (CDD and CWD), frequency- (R10mm, R20mm, and Rnnmm), and intensity-based (Rx1day, R5xday, and SDII) indices and their linear trends. The conclusions can be summarized as follows. Attempts to validate various satellite-based precipitation products' capacity in representing precipitation characteristics from different perspectives have been widely conducted all over the world. However, information about their capacity in detecting extreme precipitation and related changes (i.e., linear trends) is scarce. As a result, we collected daily observations from 182 gauges across the HRB during 1983–2012 and examined the PERSIANN-CDR capacity to represent precipitation amount- (PRCPTOT, R85p, R95p, and R99p), duration- (CDD and CWD), frequency- (R10mm, R20mm, and Rnnmm), and intensity-based (Rx1day, R5xday, and SDII) indices and their linear trends. The conclusions can be summarized as follows.


it underestimated and overestimated climatological values of the HRB CDD and CWD, respectively. For spatial variabilities, overestimations existed for the climatological CDD, but underestimations for the climatological CWD. The PERSIANN-CDR showed no *KGE*-based ability and better overall performance in representing the climatological CWD and CDD, respectively. Over most of the HRB, CDD (CWD) were underestimated (overestimated), with underestimations of temporal variabilities. For most grids, the PERSIANN-CDR had strong and moderate ability to represent temporal fluctuations of CDD, with moderate *KGE*-based performance; however, the opposite results were found for CWD. The HRB CDD and CWD trends were overestimated and underestimated, respectively, followed by overestimated spatial variabilities. Overall, the PERSIANN-CDR had no *R*-based ability in producing spatial patterns of the trends of the duration-based indices, accompanied with no *KGE*-based ability.


A comprehensive assessment of the PERSIANN-CDR extreme precipitation over the HRB was conducted by comparing here with gauge measurements. However, it should be noted that there existed some issues—e.g., mismatch in spatial scale between point-scale gauge and areal satellite precipitation, inherent uncertainties for gauge observations (including calibration flaws, wind-related undercatch, wetting-evaporation losses, etc.), and inhomogeneity of observations—influencing the confidence level of our findings [39,47–52]. Because of precipitation with large variability at a small spatial extent, a sparse gauge network is difficult to use to fully detect precipitating processes at a given PERSIANN-CDR grid. Therefore, to minimize the related uncertainties into validation results, a sufficient number of gauges should be collected [47]. Commonly, gauges have flaws in calibration, consequently resulting in measured values with uncertainties. For instance, some studies have stated that calibration flaws tended to underestimate gauge observations, particu-

larly for greater rainfall intensities [48]. Under wind-related undercatch effect, the catch efficiency of gauges becomes lower, more or less, mainly due to raindrops missing the funnel or falling at an inclination. As a result, the gauged-recorded precipitation is often smaller than the true values, and underestimations are closely associated with ambient wind speed, raindrop size distribution, and gauge design [49]. Moreover, the gauge values are likely to be underestimated because of evaporation from water adhering to the inside walls of the gauges (i.e., wetting losses) and exposure of the water surface within a gauge to atmosphere (i.e., evaporation losses) [50]. Simply, these influential factors of gauge measurements have an aggregate impact of underestimating gauge precipitation, which then propagate impact into our results [51]. In this study, although gauges with inhomogeneous observations were removed with the Pettitt test (a better method to examine observations' homogeneity when lacking meta-data for gauges; [40]), no guarantee shows that the records at the remaining gauges were all homogenous, potentially weakening the confidence level of this study.

Regardless, our study provides some significant reference data for PERSIANN-CDR developers and potential users in the HRB and other regions. For example, the different capacity of PERSIANN-CDR to detect various extreme precipitation indices suggests that PERSIANN-CDR developers might try to develop specific algorithms and/or correction procedures for increasing a certain validation metric-based performance; for potential users, some PERSIANN-CDR extreme precipitation indices (e.g., CWD, Rx1day, and Rx5day) with poor performance should be excluded from use. The poor performance of PERSIANN-CDR for detecting linear trends of all the selected indices implies that more effort should be devoted by the developers to improving PERSIANN-CDR's abilities; moreover, more attention should be paid by potential users of PERSIANN-CDR when conducting studies of long-term changes in extreme precipitation.

**Author Contributions:** S.S., J.W., and W.S. conceived and designed this study. S.S., J.W., W.S., and R.C. were the main authors, whose work included data collection and analysis, interpretation of results, and manuscript preparation. G.W. played a supervisory role. S.S., J.W., W.S., and R.C. contributed by processing data and providing rain gauge observations. All authors discussed the results and revised the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was jointly supported by the National Key Research and Development Program of China (Grant NOs. 2018YFC1507101 and 2017YFA0603701), the National Natural Science Foundation of China (Grant NOs. 42075189, 41605042, and 41875094), and the Qinglan Project of Jiangsu Province of China.

**Acknowledgments:** PERSIANN-CDR daily precipitation data were downloaded from the Centre for Hydrometeorology and Remote Sensing (CHRS) data portal with a website at http://chrsdata. eng.uci.edu (accessed on 1 January 2021), while DEM data of SRTM3 are available from http://srtm. csi.cgiar.org/index.asp (accessed on 1 January 2021). Notably, daily precipitation observations at more than 200 gauge sites are not available to the public, but they can be obtained and used through cooperation with the CMA. We thank all data developers and their managers and funding agencies, whose work and support were essential for obtaining the datasets, without which the analyses conducted in this study would have been impossible. In addition, source code for conducting this study is available from the authors upon request (sun.s@nuist.edu.cn).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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