Evaluation and Correction of IMERG Late Run Precipitation Product in Rainstorm Over the Southern Basin of China

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Article Evaluation and Correction of IMERG Late Run Precipitation Product in Rainstorm over the Southern Basin of China

Chen Yu 1,2, Jianchun Zheng 3,*, Deyong Hu 1,2,*, Yufei Di 1,2, Xiuhua Zhang 1 and Manqing Liu 1

1 College of Resource Environment and Tourism, Capital Normal University, Beijing 100048, China; [email protected] (C.Y.); [email protected] (Y.D.); [email protected] (X.Z.); [email protected] (M.L.) 2 Laboratory Cultivation Base of Environment Process and Digital Simulation, Beijing 100048, China 3 Beijing Research Center of Urban Systems Engineering, Beijing 100035, China * Correspondence: [email protected] (J.Z.); [email protected] (D.H.)

Abstract: Satellite precipitation products play an essential role in providing effective global or re- gional precipitation. However, there are still many uncertainties in the performance of satellite precipitation products, especially in extreme precipitation analysis. In this study, a Global Precip- itation Measurement (GPM) Integrated Multi-satellite Retrievals for GPM (IMERG) late run (LR) product was used to evaluate the rainstorms in the southern basin of China from 2015 to 2018. Three correction methods, multiple linear regression (MLR), artificial neural network (ANN), and geographically weighted regression (GWR), were used to get correction products to improve the precipitation performance. This study found that IMERG LR’s ability to characterize rainstorm events was limited, and there was a significant underestimation. The observation error and detection ability of IMERG LR decrease gradually from the southeast coast to the northwest inland. The error test shows that in the eastern coastal area (zone I and II), the central area (zone III), and the western inland area (zone IV and V), the optimal correction method is MLR, ANN, and GWR, respectively.



 The performance of three correction products is slightly better compared with the original product IMERG LR. From zone I to V, correlation coefficient (CC) and root mean square error (RMSE) show Citation: Yu, C.; Zheng, J.; Hu, D.; Di, Y.; Zhang, X.; Liu, M. Evaluation and a decreasing trend. Zone II has the highest relative bias (RB), and the deviation is relatively large. Correction of IMERG Late Run The categorical indices of inland area performed better than coastal area. The correction product’s Precipitation Product in Rainstorm precipitation is slightly lower than the observed value from April to November with a mean error over the Southern Basin of China. of 8.03%. The correction product’s precipitation was slightly higher than the observed values in Water 2021, 13, 231. https://doi.org/ other months, with an average error of 12.27%. The greater the observed precipitation, the higher 10.3390/w13020231 the uncertainty of corrected precipitation result. The coefficient of variation showed that zone II had the highest uncertainty, and zone V had the lowest uncertainty. MLR had a high uncertainty Received: 30 November 2020 with an average of 9.72%. The mean coefficient of variation of ANN and GWR is 7.74% and 7.29%, Accepted: 18 January 2021 respectively. This study aims to generate a set of precipitation products with good accuracy through Published: 19 January 2021 the IMERG LR evaluation and correction to support regional extreme precipitation research.

Publisher’s Note: MDPI stays neutral Keywords: satellite precipitation product; southern basin of China; correction; IMERG; rainstorm; with regard to jurisdictional claims in uncertainty published maps and institutional affil- iations.

1. Introduction Measuring the temporal and spatial distribution of precipitation based on satellite Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. remote sensing is one of the most challenging scientific research goals in recent years [1,2]. This article is an open access article Early satellite precipitation relied on visible light, infrared, and active/passive microwave distributed under the terms and sensors on geostationary and low earth orbit satellites. The Tropical Rainfall Measuring conditions of the Creative Commons Mission (TRMM), launched in November 1997, carried the world’s first space-borne pre- Attribution (CC BY) license (https:// cipitation radar, ushering in a new era of global precipitation monitoring [3]. At present, creativecommons.org/licenses/by/ a series of satellite precipitation products have been released and opened to the public, 4.0/). such as Precipitation Estimation from Remotely Sensed Information using Artificial Neural

Water 2021, 13, 231. https://doi.org/10.3390/w13020231 https://www.mdpi.com/journal/water Water 2021, 13, 231 2 of 17

Networks (PERSIANN) [4], Climate Prediction Center Morphing Technique (CMORPH) [5], Climate Hazards Group Infrared Precipitation with Station data (CHIRPS) [6], TRMM Multi-satellite Precipitation Analysis (TMPA) [7], and Global Precipitation Measurement (GPM) [8]. These products have been widely used in hydrological simulation [9], flood management [10], drought monitoring [11,12], and climate change analysis [13]. Some studies have evaluated the accuracy of satellite precipitation products [14–16]. However, further evaluation of satellite precipitation products is needed to improve the reliability in estimating extreme precipitation. Satellite-based precipitation estimation has become a vital data resource and has been applied in extreme precipitation events worldwide. Tashima et al. [17] confirmed the effectiveness of Global Satellite Mapping of Precipitation (GSMaP) products in monitoring extreme precipitation in East Asia and Western Pacific. Kiany et al. [18] evaluated TRMM’s ability to detect extreme precipitation in southwestern Iran from 1998 to 2016. It showed that precipitation products could capture the temporal and spatial behavior of most extreme precipitation indices. The evaluation of extreme precipitation in Tunisia in 2007–2009 demonstrated that satellite precipitation products need to be combined with other near- real-time data to make a reliable estimation [19]. Lockhoff et al. [20] asserted that satellite precipitation products could reliably reproduce extreme precipitation characteristics over Europe. However, some studies had found that satellite precipitation products had limited ability to characterize extreme precipitation. Palharini et al. [21] found that precipitation products’ ability to retrieve extreme precipitation in tropical South America depends on geographical location and large-scale rainfall conditions. Paska et al. [22] measured extreme precipitation in Malaysia. The correlation between satellite precipitation products and rain gauge data was usually low in heavy precipitation. Precipitation products showed an underestimation in terms of the extreme precipitation index results. Evaluation in the Amazon region of Brazil indicated that satellite precipitation products tended to underestimate the month’s highest precipitation [23]. Similarly, the evaluation in the United States suggested that precipitation products are not ideal for detecting extreme precipitation [24]. With the increase of extreme precipitation threshold, the performance of precipitation products tended to deteriorate. Some scholars have also used satellite precipitation products to carry out extreme precipitation evaluation in China. Studies showed that satellite precipitation products still have limited resolution and accuracy in their application to extreme precipitation [25–27]. Precipitation products produced a good estimation of extreme precipitation with 1050 yearly recurrence intervals but exhibited consistent underestimation in these periods [28]. Moreover, there are spatial and seasonal differences in precipitation products’ ability to detect extreme precipitation [29]. It is of great significance to improve the accuracy of satellite precipitation products by using appropriate correction methods [30]. The mean error of the precipitation product is closely related to the rainfall intensity of the rain gauge data and can be characterized by polynomial fitting, thus providing useful information for correction [31]. The relationship between precipitation products and ground observations can correct satellite precipitation data, showing the spatial variation of precipitation [32]. Lu et al. [33] showed that the correction product by stepwise regression model had excellent performance in Xinjiang, China. The correction methods have been tested in French Guiana and the Mekong river basin [34,35]. The results proved that the correction method can effectively improve the performance of precipitation products and has the potential to solve the precipitation bias problem. Previous studies focused on the overall evaluation of precipitation products, and relatively few regional correction experiments have restricted the application of precipita- tion products. The comparative studies on multi-satellite precipitation products showed that Integrated Multi-satellite Retrievals for GPM (IMERG) has good performance in pre- cipitation monitoring [28,36,37]. However, how IMERG performs in extreme precipitation requires further study to evaluate and calibrate error. This study has two main purposes. One is to evaluate the performance of IMERG under extreme precipitation conditions. The other is to use correction methods to improve Water 2021, 13, x FOR PEER REVIEW 3 of 17

Water 2021, 13, 231 3 of 17 This study has two main purposes. One is to evaluate the performance of IMERG under extreme precipitation conditions. The other is to use correction methods to improve the precipitation product’s accuracy. The samples with daily precipitation above 50 mm the precipitation product’s accuracy. The samples with daily precipitation above 50 mm in in the southern basin of China from 2015 to 2018 were selected as rainstorm events to the southern basin of China from 2015 to 2018 were selected as rainstorm events to evaluate evaluate the performance of the IMERG and reveal its error characteristics. Three correc- the performance of the IMERG and reveal its error characteristics. Three correction methods, tion methods, multiple linear regression (MLR), artificial neural network (ANN), and ge- multiple linear regression (MLR), artificial neural network (ANN), and geographically ographically weighted regression (GWR), were adopted to improve the accuracy of the weighted regression (GWR), were adopted to improve the accuracy of the IMERG product IMERG product in measuring precipitation during rainstorms. Then, the precipitation re- in measuring precipitation during rainstorms. Then, the precipitation results of correction sults of correction products were analyzed, along with the uncertainty associated with products were analyzed, along with the uncertainty associated with each correction method. each correction method. This study can refer users to decide whether and how to correct This study can refer users to decide whether and how to correct precipitation products to precipitation products to better use them in specific study areas. better use them in specific study areas.

2. The Study2. Area The and Study Datasets Area and Datasets 2.1. The Study2.1. Area The Study Area The geographicalThe geographical location, elevation, location, and elevation, spatial distribution and spatial of distribution rainstorm offrequency rainstorm frequency in the study inarea the are study shown area in are Figure shown 1. inThe Figure study1 .area The is study the southern area is the basin southern of China, basin of China, including Huaiheincluding river Huaihe basin, Yangtze river basin, river Yangtze basin, Southeast river basin, basin, Southeast and Pearl basin, river and basin. Pearl river basin. The study areaThe is study located area at is 90°2 located2′–122°4 at 90◦0′22 E,0–122 18°1◦403′–037°0E, 188′◦ 13N,0–37 with◦08 a0 N,total with area a total of 2.72 area of 2.72 mil- million km2. lionThe kmsouth2. Theof the south study of area the studyis close area to a is tropical close to climate, a tropical and climate, the north and is thea north is a temperate climate.temperate The climate.mean annual The mean precipitation annual precipitation in the study in area the studyranges area from ranges 400 mm from 400 mm in in the westernthe region western to region1800 mm to 1800in the mm eastern in the region. eastern The region. precipitation The precipitation mainly mainlyconcen- concentrated trated in summerin summer (June (Juneto August) to August) and mostly and mostly in the in form the form of rainstorms. of rainstorms. Moreover, Moreover, the the temporal temporal andand spatial spatial distribution distribution of ofextreme extreme precipitation precipitation in in the the study study area area is is uneven. uneven. Rainstorm Rainstorm eventsevents in in the the southeast southeast coast coast have have high high frequency, frequency, and and the the frequency frequency gradually gradually decreases decreases towardtoward the the inland inland area area (Figure (Figure 1c).1c). The The regional regional division division of of extreme extreme precipita- precipitation and its tion and its relatedrelated statistical characteristics basedbased onon thethe satellite satellite precipitation precipitation products products are worthy of are worthy ofin-depth in-depth analysis. analysis.

Figure 1. (a) TheFigure location 1. (a) of The the location study area of the in studyChina, area (b) inthe China, study (area’sb) the DEM study and area’s basins, DEM (c and) the basins, rainstorm (c) the frequency rainstorm frequency distribution indistribution the study area in the from study 2015 area to 2018. from 2015 to 2018.

2.2. IMERG Precipitation2.2. IMERG Product Precipitation Product As a new generationAs a new of generation satellite precipitation of satellite precipitation product, GPM product, IMERG’s GPM core IMERG’s satellite core satellite was launchedwas in launchedFebruary 2014 in February and can 2014 provide and canglobal provide rain and global snow rain data and at snow an interval data at an interval of 0.5 h. GPMof IMERG 0.5 h. GPMfirst used IMERG a dual first-frequency used a dual-frequency precipitation radar precipitation including radar Ka and including Ku Ka and bands to provideKu bands physical to provide information physical about information cloud aboutprecipitation cloud precipitation particles (shape, particles (shape, intensity, and convective processes of raindrops). This can depict the spatial distribution of precipitation particles more accurately. GPM IMERG data are verified by precipitation

Water 2021, 13, 231 4 of 17

inversion mechanism based on ground-based observation tests and fusion verification oriented by hydrometeorological application [38]. GPM IMERG has three run products (early, late, and final run products). This study uses a daily IMERG late run (IMERG LR) product (https://gpm.nasa.gov/data/directory). IMERG LR is a quasi real time product with a release delay of 12 h and spatial resolution of 0.1◦. Compared with early run (ER) product, IMERG LR has backward propagation, which improves product accuracy. The final run (FR) product reveals the good qual- ity, but the performance level of LR and FR is comparable according to the evaluation values [37,39,40]. Moreover, IMERG LR has a better time response than FR product with 3.5 months release delay.

2.3. Rain Gauge Data The rain gauge daily data provided by the China Meteorological Administration (http://data.cma.cn/) were used. Rain gauge data have undergone strict quality control, and are reliable and suitable for satellite precipitation products evaluation [41]. The rain gauge data were screened in the following two steps. First is to remove gauges with incomplete observation data; then to select gauges with rainstorm records. Finally, 242 rain gauges were selected for this study. These rain gauges have passed the uniformity test and have high accuracy and reliability [42,43]. The criterion for judging a rainstorm is to set the precipitation threshold (50 mm/day). If the daily precipitation exceeds this value, it will be judged as a rainstorm.

2.4. Normalized Difference Vegetation Index (NDVI) The NDVI data were used as the input parameter of the correction methods and were obtained from the Atmosphere Archive and Distribution System (https://ladsweb.modaps. eosdis.nasa.gov/search/). The product has a temporal resolution of one month and a spatial resolution of 1 km. The annual NDVI data were obtained by averaging the monthly NDVI data.

3. Methods 3.1. Statistical and Categorical Indices In this study, the correlation coefficient (CC), root mean square error (RMSE), and relative bias (RB) were used to evaluate the accuracy of precipitation products. CC reflects the linear correlation between IMERG LR and rain gauge data. The higher the value, the higher the correlation between them. RMSE describes the difference between IMERG LR and rain gauge data. The closer the RMSE is to 0, the more accurate the precipitation product is. RB describes precipitation products’ systematic error, and its positive or negative value indicates that IMERG LR overestimates or underestimates the rain gauge data. The calculation formula of each statistical index is shown below.

n ∑ (Gi − G)(Si − S) i=1 CC = s s (1) n 2 n 2 ∑ (Gi − G) ∑ (Si − S) i=1 i=1

s n 1 2 RMSE = ∑ (Si − Gi) (2) n i=1 n ∑ (Si − Gi) i=1 RB = n − 1 (3) ∑ Gi i=1 where G is the rain gauge data, and S is the satellite precipitation product. G and S denote mean value. Water 2021, 13, 231 5 of 17

The probability of detection (POD), false alarm ratio (FAR), and critical success index (CSI) were adopted to reflect the detection ability of precipitation products to the rainstorm. POD represents the detection hit ratio of precipitation products on whether daily precipita- tion events occur, and the value range is 0–1. The higher the value, the higher the detection hit ratio of precipitation products. FAR reflects the probability of precipitation products misreporting precipitation events, and the value range is 0–1. The lower the value, the lower the degree of vacancy and false ability of precipitation products. CSI comprehen- sively reflects the ability of precipitation products to estimate whether precipitation events occur, and the value range is 0–1. The larger the value, the stronger the comprehensive performance of precipitation products.

H POD = (4) H + M F FAR = (5) H + F H CSI = (6) H + M + F where H (hit) is the frequency of rainstorm events observed and detected. F (false alarm) is the frequency of rainstorm events not observed but detected; M (miss) is the frequency of rainstorm events observed but not detected.

3.2. Evaluation Regional Division Based on Hot Spot Clustering The spatial clustering factor was used to identify the statistically significant clustering zones of precipitation evaluation indices. Hot spot clustering analysis can determine the spatial clustering of high or low value features. According to the z score, when z > 2.58, it is regarded as the significant high value spatial clustering (hot spot). When z < −2.58, it is regarded as the significant low value spatial clustering (cold spot). When |z| < 2.58, there is no significant spatial clustering. The clustering distributions of statistical and categorical indices were obtained, and the number of hot and cold spots at each rain gauge was counted. Rain gauges with the same clustering characteristics were identified as the same type. The spatial region of the same gauge type was obtained by the processing of Tyson polygon. In this way, based on the aggregation of spots, the regional division based on evaluation performance was realized.

3.3. Precipitation Product Correction Methods Three correction methods were used in this study, including multiple linear regression (MLR), artificial neural network (ANN), and geographically weighted regression (GWR). The correction methods aim to eliminate the precipitation difference (the y of Formulas (7)– (9)) between the observed value and the precipitation product. MLR contains trend and residual term. The difference between rain gauge data and precipitation product was taken as a dependent variable, while longitude, latitude, elevation, and NDVI were taken as multiple independent variables.

y = β0 + β1x1 + β2x2 + β3x3 + β4x4 (7)

where x1–x4 are longitude, latitude, altitude, and NDVI. β0–β4 are the corresponding parameters. ANN is an efficient method that can handle the complicated relationship between different variables and has a powerful nonlinear mapping capability. The ANN used in this study is a three-layer back propagation network structure, including an input layer, a hidden layer, and an output layer. The input layer contains four nodes, which are longitude, Water 2021, 13, 231 6 of 17

latitude, elevation, and NDVI; the output layer is precipitation data; the number of hidden layer nodes is determined as ten by trial and error method.

2N+1 y = ϕ( ∑ ωixi + b) (8) i=1

where x is the input layer parameter, ω is the weight of parameter, b is the bias, and N is the number of input layer nodes. GWR uses the idea of local regression to explore the spatial relationship between independent and dependent variables. GWR selects test samples based on geographical distance and assigns them different weights. GWR introduces spatial relationship weight into the operation and establishes the regression model by estimating different spatial position parameters. n yi = βi0(ui, vi) + ∑ βik(ui, vi)xik + εi (9) k=1

where (ui, vi) is the position of grid i, βi0 (ui, vi) is the constant estimation value, βik (ui, vi) is the parameter estimation value, which refers to NDVI and elevation. εi is the residual estimation value. To avoid multicollinearity and overfitting of the regression equation, the stepwise regression method was used in MLR construction. No correlation was found between the four parameters and IMERG LR. Before the training network, ANN preprocessed the input and output vectors to normalize them to (−1,1), avoiding slow convergence and long training time caused by inconsistent data units or extensive range. For all sample data, approximately 2/3 were used as training samples and the remaining 1/3 as validation samples.

3.4. Correction Method Verification and Uncertainty Evaluation The mean squared error (MSE), mean absolute error (MAE), and standard deviation (SD) were used to evaluate the correction methods. MSE is the square of the difference between estimated and real values. The smaller MSE indicates that the correction method has better accuracy. MAE is the average of absolute errors. MAE can reflect the actual level of correction error. SD is the arithmetic square root of the variance. SD can reflect the discrete degree of a data set. Through the coefficient of variation, the precipitation evaluation uncertainty by cor- rection products was studied. The larger the coefficient, the greater the discrete degree of the correction product, and the higher the uncertainty. s n ∑ (xi − x)/n i=1 C = × 100% (10) |x|

where xi is the precipitation value of each correction method, and x is the mean value of all correction methods.

4. Results 4.1. IMERG LR Performance Evaluation for Rainstorm All daily rainstorm events recorded by rain gauges in the southern basin from 2015 to 2018 were obtained, and the scatter points corresponding to IMERG LR were plotted (Figure2) . The fitting results showed that IMERG LR significantly underestimates rain- storms. IMERG LR underestimated 90.72% of the rainstorm events, and only overestimated 9.28% of the rainstorm events. The density center of precipitation scatter point appeared at (56.8, 10.6) mm, and the IMERG LR precipitation was much lower than the rain gauge data. In Figure2, the proportion of rainstorm events in each month is listed. Heavy rainfall Water 2021, 13, x FOR PEER REVIEW 7 of 17

4. Results 4.1. IMERG LR Performance Evaluation for Rainstorm All daily rainstorm events recorded by rain gauges in the southern basin from 2015 to 2018 were obtained, and the scatter points corresponding to IMERG LR were plotted (Figure 2). The fitting results showed that IMERG LR significantly underestimates rain- storms. IMERG LR underestimated 90.72% of the rainstorm events, and only overesti- Water 2021, 13, 231 7 of 17 mated 9.28% of the rainstorm events. The density center of precipitation scatter point ap- peared at (56.8, 10.6) mm, and the IMERG LR precipitation was much lower than the rain gauge data. In Figure 2, the proportion of rainstorm events in each month is listed. Heavy eventsrainfall were event relativelys were relatively concentrated concentrated in summer in from summer June from to August, June to accounting August, accounting for 58.33% offor the 58.33% total. of the total.

FigureFigure 2.2. PrecipitationPrecipitation scatter plot of rain rain gauge gauge data data and and Integrated Integrated Multi Multi-satellite-satellite Retrievals Retrievals for for GlobalGlobal PrecipitationPrecipitation MeasurementMeasurement (GPM)(GPM)(IMERG) (IMERG)late laterun run (LR).(LR).

BasedBased onon statisticalstatistical andand categoricalcategorical indices,indices, thethe performanceperformance of IMERGIMERG LRLR forfor rain-rain- stormstorm was was evaluated. evaluated. In addition, In addition, the evaluation the evaluation results of all results rainfall of events all (>0.1rainfall mm/day) events were(>0.1mm/day) obtained forwere comparison obtained for (Table comparison1). IMERG (Table LR had 1). aIMERG low correlation LR had a with low rainstormcorrelation (CCwith was rainstorm 0.30), RMSE (CC was was 0.30), 7.66 mm,RMSE and was RB 7.66 was mm,−0.52 and mm. RBIMERG was −0.52 LR’s mm. POD IMERG decreased LR’s fromPOD 0.73decreased for all from rainfall 0.73 to for 0.20 all for rainfall rainstorm. to 0.20 The for FAR rainstorm. of IMERG The LRFAR in of rainstorms IMERG LR was in 0.68,rainstorms and the was CSI 0.68, was 0.18.and the On CSI the was whole, 0.18. IMERG On the LR’s whole, evaluation IMERG indices LR’s evaluation for rainstorm indices are worsefor rainstorm than all are rainfall. worse than all rainfall.

Table 1.TablePerformance 1. Performance comparison comparison of IMERG of IMERG LR in rainstorms LR in rainstorms and all rainfalland all events.rainfall events.

StatisticalStatistical Indices Indices CategoricalCategorical Indices Indices CCCC RMSE RMSE (mm)(mm) RBRB (mm) (mm) PODPOD FARFAR CSICSI RainstormRainstorm 0.300.30 7.66 −0.52−0.52 0.200.20 0.680.68 0.180.18 AllAll rainfall rainfall 0.420.42 4.41 −0.05−0.05 0.730.73 0.440.44 0.450.45

TheThe spatialspatial distribution of of IMERG IMERG LR LR statistical statistical and and categorical categorical indices indices is isshown shown in inFigure Figure 3. 3CC. CC had had poor poor spatial spatial differentiation differentiation (Figure (Figure 3a). Some3a). Somerain gauges rain gauges in the northern in the northernregion showed region showedhigh CC high values, CC values,and the and rainstorm the rainstorm frequency frequency in these in theseregions regions was rela- was relativelytively low. low. RMSE RMSE decreased decreased gradually gradually from from the the southeast southeast coast coast to to the northwest inlandinland (Figure(Figure3 b). 3b). The The southeast southeast coast coast was was a subtropical a subtropical monsoon monsoon climate climate zone, where zone, whererainstorms rain- frequentlystorms frequently occur, leading occur, leading to high to error high results. error results. The spatial The spatial distribution distribution of RB of shows RB shows that the IMERG LR precipitation is generally lower than the observed value in the study area (Figure3c). CSI performs relatively well in the southeast coastal region (Figure3d) . In the western region, POD is low and FAR is high (Figure3e,f). The evaluation indices performed slightly better in the eastern region, but IMERG LR’s detection ability of rainstorms needs to be further improved. Water 2021, 13, x FOR PEER REVIEW 8 of 17

that the IMERG LR precipitation is generally lower than the observed value in the study area (Figure 3c). CSI performs relatively well in the southeast coastal region (Figure 3d). Water 2021, 13, 231 In the western region, POD is low and FAR is high (Figure 3e,f). The evaluation indices8 of 17 performed slightly better in the eastern region, but IMERG LR’s detection ability of rain- storms needs to be further improved.

FigureFigure 3.3. TheThe spatialspatial distributiondistribution ofof IMERGIMERG LRLR statisticalstatistical indices indices (( ((a)a) CC, CC, ( b(b)) RMSE, RMSE, and and (c ()c RB)) RB) and categoricaland categorical indices indices ((d) CSI,((d) (CSI,e) POD, (e) POD, and (andf) FAR). (f) FAR).

4.2.4.2. HotHot SpotSpot ClusteringClustering andand RegionalRegional DivisionDivision AccordingAccording toto the the evaluation evaluation indices, indices, the the spatial spatial clustering clustering characteristics characteristics of the of resultsthe re- weresults obtained.were obtained. Among Among statistical statistical indices, indices, CC hadCC had 15 hot 15 spotshot spots clustered clustered in the in the northern north- regionern region of Yangtze of Yangtze river river basin. basin. Cold Cold spots spots appeared appeared in in the the western western Yangtze Yangtze river river basinbasin andand thethe southeastsoutheast cornercorner ofof HuaiheHuaihe riverriver basin.basin. A totaltotal ofof 80.99%80.99% ofof thethe gaugesgauges hadhad nono significantsignificant CC cluster clustering.ing. RMSE RMSE showed showed cold cold clustering clustering in inthe the western western and and northern northern re- regions.gions. There There was was a hot a hot clustering clustering phenomenon phenomenon in the in thesouth south through through the transition the transition of non of- non-significantsignificant gauges gauges in the in central the central region. region. RB’sRB’s clustering clustering mainly mainly occurred occurred in the in west the west (hot (hotspot) spot) and andsout southh (cold (cold spot). spot). TheThe categoricalcategorical indicesindices clusteringclustering characteristics were similar in spatialspatial distribution. PODPOD showedshowed coldcold spotsspots inin thethe westernwestern regionregion andand hothot spotsspots inin thethe easterneastern region.region. FARFAR clusteringclustering distribution was was the the opposite, opposite, and and the the range range of hot of hotspot spotss was small. was small. The south- The southeasteast coastal coastal area was area the was CSI the hot CSI clustering hot clustering range, range,indicating indicating that IMERG that IMERG LR had LR the had op- thetimal optimal ability ability to detect to detect rainstorms rainstorms in inthis this area. area. Correspondingly, Correspondingly, the the western inland inland showed cold spots, and the central and northern regions of the study area were non- showed cold spots, and the central and northern regions of the study area were non-sig- significant clustering as shown in Figure4. nificant clustering as shown in Figure 4.

Water 2021, 13, 231 9 of 17 Water 2021, 13, x FOR PEER REVIEW 9 of 17

FigureFigure 4. 4.The The spatial spatial clustering clustering ofof statisticalstatistical indicesindices ((((aa)) CC,CC, ((bb)) RMSE,RMSE, andand ((cc)) RB)RB) andand categoricalcategorical indicesindices (( ((dd)) CSI, CSI, ( e(e)) POD, POD, and and ( f()f) FAR). FAR).

TheThe spatial spatial clustering clustering phenomenon phenomenon of of the the evaluation evaluationindices indicesreflects reflects the the different different performanceperformance characteristicscharacteristics ofof IMERGIMERG LRLR inin different different zones zones of of the the study study area. area. Based Based on on clusteringclustering characteristics,characteristics, thethe regionalregional divisiondivision waswas considered. considered. TheThe evaluationevaluation perfor-perfor- mancemance ofof IMERGIMERG LR to to rainstorm rainstorm will will be be impr improvedoved effectively effectively by byexploring exploring a unique a unique pre- precipitationcipitation product product correction correction scheme scheme for for different different zones. zones. Therefore,Therefore, the the study study area area was was divided divided into into five five zones zones according according to the to spatial the spatial clustering clus- characteristicstering characteristics of evaluation of evaluation indices. indices. The southeast The southeast coastal regioncoastal containedregion contained zone I and zone II. Ⅰ Zoneand Ⅱ III. Zone was locatedⅢ was located in the central in the region.central region. North andNorth west and of west the studyof the areastudy were area Zone were IVZone and Ⅳ V, and respectively. Ⅴ, respectively. The performance The performance of IMERG of IMERG LR in LR zone in zone I and I IIand was II satisfactory.was satisfac- Intory. these In zones,these zones, correlations correlations were strongwere strong (CC 0.39 (CC and 0.39 0.37), and 0.37), and the and categorical the categor indexical index CSI showedCSI showed relatively relatively good good performance performance (0.16 and(0.16 0.14) and but0.14) had but high had RMSEhigh RMSE (both 7.75(both mm) 7.75 andmm) RB and (− 0.78RB (−0.78 and− and−0.630.63 mm). mm). From From zone zone III to Ⅲ zone to zone V, the Ⅴ performance, the performance of CSI of gradually CSI grad- decreasedually decreased from 0.11 from to 0.11 0.03, to and 0.03, the and correlation the correlation was relatively was relatively weakened weakened (CC was (CC 0.36, was 0.25,0.36, and 0.25, 0.11, and respectively), 0.11, respectively) see Figure, see Figure5. 5.

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Figure 5. RegionalFigure division 5. Regional and evaluation division indices and evaluation of each zone. indices of each zone.

4.3.4.3. Correction Statistics Results in Different Zones MLR, ANN, and GWR were used to correct the IMERG LR. Here, the three correctioncorrection methods were used in each zone to improve precipitation product performance and com- pare thethe correctioncorrection differences.differences. The The error error results results of of correction correction methods methods are are summarized summarized in Tablein Table2. The 2. The correction correction errors errors of of MLR MLR in in three three zones zones were were the the smallest, smallest, which which were were zone zone I,Ⅰ, II,Ⅱ, and V.Ⅴ. ANNANN performedperformed relativelyrelatively betterbetter inin zonezone III,Ⅲ, andand GWRGWR performedperformed relativelyrelatively better in zone IV.Ⅳ. It should be noted that in each zone, the errors of the three correction methods were Table 2. Error test of precipitation product correction method (the shadow represents the best roughly at the same magnitude. On the whole, MLR correction had the best effect, with performing method of test index in each zone). mean MSE equal to 129.98 mm, MAE 8.50 mm, and SD 11.19 mm. GWR mean error results were: MSEZone was 135.31 mm, MAE I was 8.83 IImm, and SD III was 11.43 mm. IV The ANN V mean error results were:MLR MSE was 138.17 71.85 mm, MAE 121.99 was 8.91 101.34 mm, and SD 226.53 was 11.52 128.17mm. The orderMSE of (mm) correctionANN error in each 88.96 zone from 123.11 good to bad 90.50 was: Ⅰ > Ⅲ > 248.59 Ⅱ > Ⅴ > Ⅳ. 139.70 GWR 83.68 125.63 103.82 227.06 136.34 Table 2. Error test MLRof precipitation 6.26 product correction 8.47 method 7.73(the shadow 11.13represents the 8.91best performingMAE (mm) methodANN of test index 7.68in each zone). 8.52 7.33 11.67 9.36 GWR 7.35 8.63 7.92 11.11 9.15 ZoneMLR 8.47Ⅰ 11.04Ⅱ 10.07Ⅲ 15.05Ⅳ 11.32Ⅴ SD (mm) ANNMLR 9.4371.85 11.09121.99 9.51101.34 15.77226.53 128.17 11.82 MSE (mm) GWRANN 9.0588.96 11.21123.11 10.1590.50 15.07248.59 139.70 11.67 GWR 83.68 125.63 103.82 227.06 136.34 It should be noted thatMLR in each6.26 zone, the errors8.47 of the7.73 three correction11.13 methods 8.91 were roughlyMAE at (mm) the same magnitude.ANN On7.68 the whole,8.52 MLR correction7.33 had11.67 the best effect,9.36 with mean MSE equal to 129.98GWR mm, MAE7.35 8.50 mm,8.63 and SD 11.197.92 mm. GWR11.11 mean error9.15 results were: MSE was 135.31 mm,MLR MAE was8.47 8.83 mm,11.04 and SD was10.07 11.43 mm.15.05 The ANN11.32 mean error results were: MSE was 138.17 mm, MAE was 8.91 mm, and SD was 11.52 mm. The SD (mm) ANN 9.43 11.09 9.51 15.77 11.82 order of correction error in each zone from good to bad was: I > III > II > V > IV. The precipitation differencesGWR between9.05 correction11.21 products10.15 and observation15.07 data11.67 were calculated, and the difference result of the original product of IMERG LR was added for comparisonThe precipitation (Figure6). differences It can be seen between that in correction each zone, products the precipitation and observation difference data of were the correctioncalculated, products and the difference was significantly result of improved the original compared product with of IMERG the original LR was product. added The for differencecomparison range (Figure of the 6). originalIt can be product seen that IMERG in each LR zone, in all the zones precipitation was 42.48–55.09 difference mm. of After the correction,correction products the mean was difference significantly was reduced improved to − compared0.42–1.36 mm.with the original product. The difference range of the original product IMERG LR in all zones was 42.48–55.09 mm. After correction, the mean difference was reduced to −0.42–1.36 mm.

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The mean difference in the original precipitation product from zone Ⅰ to Ⅴ increased gradually. After correction, the differences in all zones were reduced to the same range. WaterWater2021 2021, 13, 13, 231, x FOR PEER REVIEWThe difference near the zero value means low correction deviation and good correction1111 ofof 17 17

effect. The differences of MLR (zone Ⅰ) and GWR (zone Ⅳ) were relatively clustered, sim- ilar to the error test results in Table 2. The mean difference in the original precipitation product from zone Ⅰ to Ⅴ increased gradually. After correction, the differences in all zones were reduced to the same range. The difference near the zero value means low correction deviation and good correction effect. The differences of MLR (zone Ⅰ) and GWR (zone Ⅳ) were relatively clustered, sim- ilar to the error test results in Table 2.

FigureFigure 6. 6.The The precipitationprecipitation differencedifference ofof originaloriginal IMERGIMERG LRLR productproduct (Origin) and threethree correction productsproducts (multiple(multiple linearlinear regressionregression (MLR),(MLR), artificial artificial neural network network ( (ANN),ANN), and and geographically geographically weighted regression (GWR)) compared with observation data. weighted regression (GWR)) compared with observation data. Sample gauges were selected to verify the error of correction methods (Figure 7). The The mean difference in the original precipitation product from zone I to V increased gradually.gauge with After the highest correction, rainstorm the differences frequency in in all each zones zone were was reduced selected. to The the samebest method range. forFigure rain 6. gauge The precipitation No.59,087 difference (zone Ⅰ) andof original No.58,538 IMERG (zone LR product Ⅱ) was (Origin) MLR with and tahree difference correction of Theproducts difference (multiple near linear the zeroregression value (MLR), means artificial low correction neural network deviation (ANN), and and good geographically correction 0.37 and 2.26 mm, respectively. The ANN difference of rain gauge No.58,506 (zone Ⅲ) effect.weighted The regression differences (GWR)) of MLR compared (zone I) with and observation GWR (zone data. IV) were relatively clustered, similar towas the the error smallest test results (0.67 in mm). Table The2. best method for rain gauge No.57,447 (zone Ⅳ) and Ⅴ No.59,021SampleSample (zone gauges gauges ) werewas were GWR selected selected with to to a verify dverifyifference the the error errorof 5.11 of of correction andcorrection 4.45 mm, methods methods respectively. (Figure (Figure7 ).From 7). The The a gaugecomprehensivegauge with with the the highest evaluation,highest rainstorm rainstorm MLR, frequency ANN,frequency and in inGWR each each zoneis zone the was optimalwas selected. selected. correction The The best bestmethod method method for Ⅰ Ⅱ Ⅲ forthefor rain easternrain gauge gauge coastal No.59,087 No.59,087 area (zone (zone (zone and I) Ⅰ) and and ), No.58,538 centralNo.58,538 area (zone (zone (zone II) Ⅱ ) was was), and MLR MLR the with westernwith a a difference difference inland area of of Ⅳ Ⅴ 0.37(zone0.37 and and 2.26 and2.26 mm, mm,), respectively. respectively. respectively. The The ANN ANN difference difference of of rain rain gauge gauge No.58,506 No.58,506 (zone (zone III) Ⅲ) waswas the the smallest smallest (0.67 (0.67 mm). mm). TheThe bestbest methodmethod forfor rain rain gauge gauge No.57,447 No.57,447 (zone (zone IV) Ⅳ) and and No.59,021No.59,021 (zone (zone V) Ⅴ) was was GWR GWR with with a a difference difference of of 5.11 5.11 and and 4.45 4.45 mm, mm, respectively. respectively. From From a a comprehensivecomprehensive evaluation, evaluation, MLR, MLR, ANN, ANN, and and GWR GWR is is the the optimal optimal correction correction method method for for thethe eastern eastern coastal coastal area area (zone (zone I Ⅰ and and II), Ⅱ), central central area area (zone (zone III), Ⅲ), and and the the western western inland inland area area (zone IV and V), respectively. (zone Ⅳ and Ⅴ), respectively.

Figure 7. The precipitation difference comparison of the correction methods for sample gauges in zone Ⅰ–Ⅴ (a–e).

4.4. Spatio-Temporal Comparison of Correction Products The evaluation indices results of three correction products in each zone were ana- lyzed (Table 3). On the whole, the performance of correction products was improved com- FigureFigure 7. 7.The The precipitation precipitation difference difference comparisoncomparison ofof thethe correctioncorrection methodsmethods for sample gauges in paredⅠ withⅤ that of original products. For the statistical indices of the study area, CC was zonezone I–V – (a (–ae–).e). 0.30 before correction and 0.40 after correction. RMSE decreased from 7.66 to 5.43 mm, 4.4.4.4. Spatio-Temporal Spatio-Temporal Comparison Comparison of of Correction Correction Products Products TheThe evaluation evaluation indices indices results results of of three three correction correction products products inin each each zonezone werewere ana-ana- lyzedlyzed (Table (Table3 ).3). OnOn the whole, whole, the the performance performance of of correction correction products products was was improved improved com- comparedpared with with that that of original of original products. products. For the For statistical the statistical indices indices of the study of the area, study CC area, was CC0.30 was before 0.30 correction before correction and 0.40 and after 0.40 correction. after correction. RMSE decreased RMSE decreased from 7.66 from to 5. 7.6643 mm, to

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5.43 mm, and RB decreased from −0.52 to −0.07 mm. For categorical indices, the correction products performed well. CSI reached 0.72, POD rose to 0.75, and FAR decreased to 0.13. Compared with Table1, it can be seen that the statistical indices of correction products in rainstorm events were lower than all rainfall events, but the categorical indices had improved significantly.

Table 3. Evaluation indices results of correction products.

Statistical Indices Categorical Indices Correction Methods CC RMSE RB POD FAR CSI MLR 0.48 5.71 −0.04 0.77 0.16 0.71 I ANN 0.46 5.75 −0.04 0.76 0.15 0.71 GWR 0.47 5.72 −0.06 0.74 0.16 0.68 MLR 0.53 5.78 −0.12 0.63 0.21 0.55 II ANN 0.52 5.80 −0.13 0.62 0.20 0.54 GWR 0.46 5.79 −0.12 0.62 0.20 0.54 MLR 0.42 5.37 −0.02 0.86 0.08 0.83 III ANN 0.48 5.36 −0.02 0.86 0.08 0.83 GWR 0.43 5.38 −0.03 0.84 0.11 0.80 MLR 0.29 5.49 −0.03 0.80 0.09 0.77 IV ANN 0.29 5.50 −0.04 0.80 0.12 0.76 GWR 0.31 5.50 −0.04 0.83 0.11 0.79 MLR 0.16 4.76 0.00 0.84 0.08 0.81 V ANN 0.16 4.78 −0.01 0.83 0.06 0.81 GWR 0.17 4.74 0.00 0.82 0.07 0.79

There were some differences in the evaluation indices under different zones. From zone I to V, CC and RMSE showed a decreasing trend. Zone II had the highest RB, and the deviation is relatively large. Compared with the coastal region, the inland region had better performance in categorical indices. The best correction method for each zone was similar to the statistical conclusions through the evaluation indices. The precipitation product performance can be effectively improved by selecting the optimal correction method in different zones. The absolute precipitation differences between the original product and the correction products based on rain gauge data were compared, and the results are displayed by gauge interpolation (Figure8). The difference of the original product in zone I and II was relatively low, while zone V was relatively high. The correction product improved the performance of zone V based on the overall reduction of the difference. The difference results were relatively high in the southwest area of zone V due to the lack of gauges. The spatial distribution trend of the absolute difference of correction products was consistent. The north of zone I and the west of zone III were good correction regions. Water 2021, 13, 231 13 of 17 Water 2021, 13, x FOR PEER REVIEW 13 of 17

FigureFigure 8. 8.Spatial Spatial distribution distribution of of the the absolute absolute precipitation precipitation difference difference between between the the (a) ( originala) original product prod- anduct threeand three correction correction products products ((b) MLR,((b) MLR, (c) ANN, (c) ANN, and (andd) GWR). (d) GWR).

TheThe observation observation mean mean value value forfor rainstorms rainstorms in in each each month month was was obtained obtainedby byrain rain gaugegauge data, data, and and the the differences differences of of precipitation precipitation products products before before and and after after correction correction were were comparedcompared (Figure (Figure9 ).9). The The difference difference between between the the original original product product and and the the observed observed value value waswas large, large, which which showed showed that that the the precipitation precipitation is is significantly significantly underestimated, underestimated, and and the the relativerelative error error ranged ranged from from 14.24% 14.24% to to 68.93%. 68.93%. After After correction, correction, the the relative relative error error is is reduced reduced toto 2.50–19.64%. 2.50–19.64%. The The precipitation precipitation of of the the correction correction products products from from April April to to November November was was slightlyslightly lowerlowerthan thanthe the observed observed value,value, withwith a a mean mean error error of of 8.03%, 8.03%, which which could could better better characterizecharacterize the the rainstorm rainstorm events. events. In In other other months, months, the the precipitation precipitation of ofthe the correction correction productsproducts was was slightly slightly higher higher than than the the observed observed values. values.

FigureFigure 9. 9.Difference Difference comparison comparison of of monthly monthly precipitation precipitation products products before before and and after after correction. correction.

5.5. Discussion Discussion PreviousPrevious studies studies have have shown shown that that IMERG IMERG products’ products’ performance performance inin describingdescribing pre-pre- cipitationcipitation is is highly highlydependent dependent on on regional regional topography topography [ 44[44,45],45].. The The conclusion conclusion of of this this study supports that topographic conditions may affect the precipitation product. Figure8a study supports that topographic conditions may affect the precipitation product. Figure showed a large error between the precipitation product and observed data in the western 8a showed a large error between the precipitation product and observed data in the west- high altitude region. The main reason may be that the snow covered surface and cloud ice ern high altitude region. The main reason may be that the snow covered surface and cloud

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ice mixing meteorological conditions easily lead to signal acquisition difficulty [36]. Com- mixingpared with meteorological the original conditions product, easilythe correction lead to signal products acquisition have a difficultysignificant [36 improvement]. Compared within categorical the original indices. product, This the is because correction the products product’s have precipitation a significant value improvement can be directly in cate- im- gorical indices. This is because the product’s precipitation value can be directly improved proved through regression and weighting processing to meet the indices’ statistical re- through regression and weighting processing to meet the indices’ statistical requirements. quirements. The correction method of this study is based on latitude and longitude, DEM, and The correction method of this study is based on latitude and longitude, DEM, and NDVI data. Satellite precipitation products have regional and seasonal errors [46]. These NDVI data. Satellite precipitation products have regional and seasonal errors [46]. These errors will disturb the correlation between precipitation and environmental factors, leading errors will disturb the correlation between precipitation and environmental factors, lead- to uncertainty in precipitation correction [47]. With the increase of observed precipitation, ing to uncertainty in precipitation correction [47]. With the increase of observed precipi- correction products’ uncertainty presented an upward trend (Figure 10). The uncertainty tation, correction products’ uncertainty presented an upward trend (Figure 10). The un- bandwidth changed steadily in the range of observed precipitation (50.20, 71.72) mm, certainty bandwidth changed steadily in the range of observed precipitation (50.20, 71.72) increasing from 12.14 to 18.44 mm. With the observed precipitation improvement, the mm, increasing from 12.14 to 18.44 mm. With the observed precipitation improvement, uncertainty error also increased from 20.23 to 68.90 mm. the uncertainty error also increased from 20.23 to 68.90 mm.

FigureFigure 10.10. UncertaintyUncertainty ofof correctioncorrection productsproducts (gray(gray bandband representsrepresents errorerror range).range).

TheThe coefficient coefficient of of variation variation was was used used to reflect to reflect the uncertainty the uncertainty of the correction of the correction method inmethod processing in processing precipitation precipitation products products (Table4). (Table The mean 4). The coefficient mean coefficient in five regions in five ranged regions fromranged 3.87% from to 3.87% 12.95%. to 12.95%. Zone II Zone had the Ⅱ had highest the highest uncertainty, uncertainty, and zone and V hadzone the Ⅴ had lowest the uncertainty.lowest uncertainty. The mean The coefficients mean coefficients of ANN of and ANN GWR and were GWR 7.74% were and 7.74% 7.29%, and respectively, 7.29%, re- showingspectively, good showing correction good correction results. Comparing results. Comparing the correction the correction methods, methods, MLR had MLR a high had uncertainty.a high uncertainty. The coefficient The coefficient is 5.83–12.88%, is 5.83 with–12.88%, an average with an of average 9.72%. The of mean9.72%. coefficients The mean ofcoefficients ANN and of GWR ANN are and 7.74% GWR and are 7.29%, 7.74% respectively, and 7.29%, andrespectively, the correction and resultsthe correction are stable. re- sults are stable. Table 4. The coefficient of variation of the correction methods. Table 4. The coefficient of variation of the correction methods. Zone MLR ANN GWR ZoneI MLR 12.03% ANN 4.31% GWR 8.80% ⅠII 12.03% 12.88% 4.31% 13.06% 12.92%8.80% ⅡIII 12.88% 5.83% 13.06% 8.52% 12.92% 7.24% IV 11.37% 9.30% 5.90% Ⅲ 5.83% 8.52% 7.24% V 6.51% 3.54% 1.57% Ⅳ 11.37% 9.30% 5.90% Ⅴ 6.51% 3.54% 1.57% There are still some limitations to this study. The study period of IMERG LR was 2015–2018.There Inare terms still some of the limitations time span, to the this 4-year study. data The are study relatively period less, of which IMERG will LR bring was errors2015–2018. to the In test. terms In of the the correction time span, process, the 4-year only data the are correlations relatively amongless, which precipitation, will bring DEM,errors and to the NDVI test. were In the considered. correction The process, influence only of the other correlations factors, such among as humidity, precipitation, wind speed,DEM, and temperature,NDVI were considered. were ignored. The Other influence environmental of other factors, factors such affecting as humidity, precipitation wind distributionspeed, and temperature, should be considered were ignored. as much Other as possible environmental in the follow-up factors affecti study.ng The precipita- spatial variationtion distribution of the rainfall should field be [48considered] was not consideredas much as in possible this study. in the The follow spatial-up inconsistency study. The ofspatial the rain variation gauge (point) of the rainfalland the fieldIMERG [48] LR was (area) not may considered cause potential in this study.uncertainty The spatial to the

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evaluation results. It is of great significance to further quantify and summarize the error characteristics of IMERG products in a rainstorm.

6. Conclusions This study evaluated IMERG LR precipitation product’s performance in the southern basin of China from 2015 to 2018. Furthermore, the regional division was realized based on the hot spot clustering of the evaluation indices. MLR, ANN, and GWR correction methods were used to improve precipitation products’ performance and accuracy. The main conclusions are as follows. (1) Based on evaluation indices, IMERG LR’s performance ability of reproducing a rain- storm is limited and needs to be further improved. IMERG LR underestimates heavy precipitation. The correlation between IMERG LR and rain gauge data is relatively good in the northern region with low rainstorm frequency. The observation error and detection ability gradually decrease from the southeast coast to the northwest inland. (2) The statistical indices performance of correction products in rainstorm events is lower than that of all rainfall events, but categorical indices have improved significantly. The precipitation of the correction precipitation product from April to November is slightly lower than the observed value, with an average error of 8.03%. The correction product’s precipitation was slightly higher than the observed values in other months, with an average error of 12.27%. (3) Through error tests and sample gauges analysis, the optimal correction method in the eastern coastal area (zone I and II), the central area (zone III), and the western inland area (zone IV and V) is MLR, ANN, and GWR, respectively. From zone I to V, CC and RMSE show a decreasing trend. Zone II has the highest RB, and the deviation is relatively large. The categorical indices of the inland region perform better than the coastal region. The correction product improves the performance of rainstorms, and the excellent correction range is in the north of zone I and the west of zone III. (4) With the increase of observed precipitation, the correction product’s uncertainty shows an upward trend. The coefficient of variation shows that the uncertainty range of all regions is 3.87–12.95%. Zone II has the highest uncertainty, and zone V has the lowest uncertainty. MLR has high uncertainty, with an average of 9.72%. The mean coefficients of ANN and GWR were 7.74% and 7.29%, respectively.

Author Contributions: Conceptualization, C.Y. and J.Z.; methodology, C.Y. and D.H.; validation, C.Y., Y.D. and X.Z.; data curation, X.Z.; writing—original draft preparation, C.Y.; writing—review and editing, J.Z. and D.H.; project administration, M.L.; funding acquisition, J.Z. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the National Key R&D Program of China (Grant No. 2018YFC0809900) and Beijing Municipal Science and Technology Project (Z181100009018009). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The rain gauge data provided by China Meteorological Administration ensure this study can proceed successfully. The NDVI data provided by Atmosphere Archive and Distri- bution System ensure this study can proceed successfully. The authors would like to express their gratitude to the GPM IMERG teams for their effort in making the data available. Conflicts of Interest: The authors declare no conflict of interest. Water 2021, 13, 231 16 of 17

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