Evaluation and Error Decomposition of IMERG Product Based on Multiple Satellite Sensors

The Integrated Multisatellite Retrievals for GPM (IMERG) is designed to derive precipitation by merging data from all the passive microwave (PMW) and infrared (IR) sensors. While the input source errors originating from the PMW and IR sensors are important, their structure, characteristics, and algorithm improvement remain unclear. Our study utilized a four-component error decomposition (4CED) method and a systematic and random error decomposition method to evaluate the detectability of IMERG dataset and identify the precipitation errors based on the multi-sensors. The 30 min data from 30 precipitation stations in the Tunxi Watershed were used to evaluate the IMERG data from 2018 to 2020. The input source includes five types of PMW sensors and IR instruments. The results show that the sample ratio for IR (Morph, IR + Morph, and IR only) is much higher than that for PMW (AMSR2, SSMIS, GMI, MHS, and ATMS), with a ratio of 72.8% for IR sources and a ratio of 27.2% for PMW sources. The high false ratio of the IR sensor leads to poor detectability performance of the false alarm ratio (FAR, 0.5854), critical success index (CSI, 0.3014), and Brier score (BS, 0.1126). As for the 4CED, Morph and Morph + IR have a large magnitude of high total bias (TB), hit overestimate bias (HOB), hit underestimate bias (HUB), false bias (FB), and miss bias (MB), which is related to the prediction ability and sample size. In addition, systematic error is the prominent component for AMSR2, SSMIS, GMI, and Morph + IR, indicating some inherent error (retrieval algorithm) that needs to be removed. These findings can support improving the retrieval algorithm and reducing errors in the IMERG dataset.


Introduction
Precipitation is an essential hydro-meteorological variable that plays a vital role in the water and energy cycles of the terrestrial ecosystem [1]. Accurate precipitation data with high spatiotemporal resolution are crucial for flood, drought, and water resource management [2,3]. However, obtaining such precipitation data has been a longstanding challenge because of its strong spatiotemporal heterogeneity.
There are three mainstream methods to measure precipitation: rain gauge measurement, radar observation, and satellite retrieval. Each of these methods has different advantages and disadvantages due to the inability to achieve high spatiotemporal resolution and precision. Rain gauge measurement is a traditional and direct method to obtain relatively reliable and high-precision precipitation with a high temporal resolution at a specific point, while it cannot completely cover an area and capture spatial variability [4]. For radar observation, its spatial and temporal resolution is superior to other sensors, but there are several drawbacks, such as non-precipitation radar echoes, radar artifacts, beam blockage, range degradation and earth curvature, non-uniform beam filling, and bright banding. Satellite retrieval has high temporal resolution and global spatial coverage, particularly in remote regions where gauge or radar observation is sparse or nonexistent [5,6].
Satellite precipitation estimates derive from several sensor observations based on different platforms [7][8][9]. Sensor types mainly include infrared (IR) and passive microwave (PMW) sensors. Although IR has a high spatiotemporal resolution, it lacks a physical relationship with rain rates, which is an indirect estimate resulting in the insufficient accuracy of instantaneous precipitation rate [10][11][12]. The PMW can provide more direct precipitation estimates by using a direct physical connection with hydrometeor profiles, while it has sparse time-space sampling [13,14]. Combining the advantages of IR and PMW, several satellite precipitation products (SPPs) have been developed, including the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) [15], Climate Prediction Center Morphing Technique (CMORPH) [16], Global Satellite Mapping of Precipitation (GSMaP) [17], Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) [9], and Global Precipitation Measurement (GPM). The Integrated Multisatellite Retrievals for GPM (IMERG) was developed to merge precipitation estimates from passive microwave (PMW), microwave-calibrated infrared (IR) satellite estimates, additional satellite estimates, and precipitation gauge data. First, the PMW data from low-Earth-orbit (leo) platforms, including GPM Microwave Imager (GMI), Advanced Microwave Scanning Radiometer (AMSR), Special Sensor Microwave Imager/Sounder (SS-MIS), Special Sensor Microwave Imager (SSMI), Microwave Humidity Sounder (MHS), and Advanced Technology Microwave Sounder (ATMS), were morphed by using as many leosatellites as possible. Then, the IR data from geosynchronous-Earth-orbit (geo) platforms were augmented to compensate for the limited PMW sampling.
Although significant progress has been made in satellite remote sensing of precipitation, the retrieval algorithm, data source, and error correction can introduce inevitable errors. Therefore, identifying and analyzing error input sources will benefit the retrieval algorithm and error correction of satellite precipitation estimates [18,19]. In general, the rain detection capability, hit biases, and the systematic and random errors are important metrics in evaluating the satellite precipitation data. For the rain detection capability, the probability of detection (POD), false alarm ratio (FAR), and critical success index (CSI) are always used. For the error decomposition, Tian et al. [20] proposed a new method to decompose the total bias (TB) into three independent components, namely hit bias (HB), false bias (FB), and miss bias (MB). It can overcome the underestimation of the TB because of the cancelation between the positive FB and the negative MB. Among the three components, the positive/negative sign of HB is uncertain, depending on the satellite estimate and the gauge observation. Furthermore, Chaudhary and Dhanya [21] and Zhang, et al. [22] put forward the 4CED method to decompose TB into four independent components, and the HB is decomposed into the hit overestimate (positive) and hit underestimate (negative) bias. For the rainfall correctly detected by satellite, the error can be characterized by systematic and random error based on the additive or multiplicative model [23][24][25]. The systematic error comes from the remote sensing measurement or retrieval algorithm characteristics, while the random error arises from sensor sampling and design. However, the above studies mainly focus on the dataset evaluation of the integrated satellite precipitation products without distinguishing the difference among different input sources. There is still a lack of research about SPPs evaluation at sensor scale [6,13,[26][27][28][29]. Consequently, the sample frequency and error components originating from multi-sensors can be quantified and evaluated independently at the sensor level.
"Floods in the south, droughts in the north" are the typical features of East China for the East Asian monsoon [30]. The Tunxi Watershed, located in the southeastern China humid zone, has frequent intense and uneven spatiotemporal rainfall distribution. Its rapid response to hydrological processes can easily lead to natural disasters. Several hydrolog-ical models were used to explore the runoff mechanism and improve the flood accuracy and forecast ability [31][32][33]. The low density gauge data were used as the input of the hydrological model. The gauge data are spatial discontinuous and cannot capture the variability of precipitation. According to the existing research and the recent Intergovernmental Panel on Climate Change (IPCC) report 2020, climate change and change-induced hydro-meteorological extremes will continue and become more intense and severe in the future [34][35][36]. The Xin'anjiang Nested Experimental Watershed was implemented in 2017 in Tunxi Watershed to strengthen the observation of the water cycle [37]. Tunxi Watershed is among the best regions in southeast China because dense and well-maintained gauges are available. Nevertheless, conventional rain gauges cannot fully capture the spatial distribution of rainfall. To some extent, the satellite estimate can compensate for the drawback of gauge observation. However, the satellite estimate's data quality is still questionable and needs to be comprehensively evaluated for its indirect observation. To this end, the IMERG data originating from PMW and IR sensors contributing to the combined estimates were segregated and assessed independently, including sample frequency, detectability, and error structure. Therefore, the objectives of this study are: (1) to evaluate the effect of different sensor sources with rainfall gauge data over a typical humid hill area in southern China; (2) to identify and track precipitation errors by the 4CED method and the systematic and random error decomposition method; and (3) to provide insights for improving satellite estimates.

Study Area
Tunxi Watershed is located in Huangshan City, southeastern China. It is situated between 29.47 • N-30.09 • N and 117.65 • E-118.47 • E, and the total area is 2674 km 2 ( Figure 1). It is located in the transitional zone between the Jianghuai plain and the East China mountains and has typical north-south interlacing geographical features. The watershed is located in the subtropical monsoon humid climate zone, characterized by hot and humid summers and cool to mild winters [38][39][40]. The average annual precipitation is about 1800 mm, concentrated in May-September. It has the obvious characteristics of high precipitation and temperature in summer. The average annual temperature is approximately 17 • C. The dominant vegetation types in this region are evergreen broadleaf forest, evergreen needle-leaf trees, and bamboo [37,41,42]. The terrain in the middle of the basin is relatively flat, and the topographic conditions at the edges are complex. The elevation has an apparent spatial heterogeneity with the highest altitude of 1257 m and the lowest altitude of 123 m. The complex terrain, high intensity, and uneven spatiotemporal precipitation can easily lead to flash floods.

Rain Gauge Data
Precipitation data covering 2018-2020 from 30 precipitation gauges in the Tunxi Watershed were selected as the reference data for evaluating the performance of the IMERG datasets. Precipitation was sampled every 5 min using tipping-bucket rain gauges with a 0.5 mm resolution. The 5 min precipitation was temporally aggregated to 30 min precipitation. The 30 precipitation gauges are evenly distributed across the Tunxi Watershed with a density of 0.011 set/km 2 . The precipitation data were provided by the Xin'anjiang Nested Experimental Watershed (http://hydro-lab.hhu.edu.cn/, accessed on 1 February 2023) [37].

IMERG Dataset
The Integrated Multi-satellite Retrievals for GPM (IMERG) algorithm fuses information from several satellite-based microwave and infrared precipitation estimates. The IMERG system is run three times, namely, early (~4 h), late (~14 h), and final (~3.5 months) runs (hereafter IMERG-E, IMERG-L, and IMERG-F). IMERG-F includes additional satellite data and was merged with monthly gauge information. Several data fields are included in each IMERG dataset showing how the estimates were computed to provide data quality information The HQprecipitation fields represent the merged microwave-only precipitation estimate and can identify the microwave satellite source from the HQprecipSource fields. IRprecipitation is IR-only precipitation estimate and can identify the weight of IR-only precipitation relative to the morphed merged microwave-only precipitation by IRkalman-FilterWeight. The IRkalmanFilterWeight values range from 0 to 100, where 0 is morph only, 100 is entirely based on IR, and anything in between is IR + morph. The IMERG-F precipi-tationUncal fields are recorded in the original multi-satellite-only half-hourly data. The IMERG-F precipitationcal fields are recorded precipitation data after gauge correction [43].
Global Precipitation Measurement Mission Integrated Multi-satellite Final Run V6B (hereafter, IMERG-F V6B) [43,44], which has been released as the latest version, is used to perform the data quality analysis. The IMERG-F V6B precipitationUncal dataset without monthly gauge adjustment is compared against the rain gauge. The IMERG-F precipitatio-nUncal provides precipitation data with 30 min and 0.1 × 0.1 degree resolutions at global scale. We chose an overlapping time span from 2018 to 2020 as our study period. The bilinear interpolation method was used to downscale coarser satellite precipitation data to a fine spatial resolution (1 km). The input source includes five types of passive microwave (PMW) instruments (Table 1) and infrared (IR) observations.

. Evaluation of Detection Capability
The detection capability of IMERG was evaluated against gauge observation using a point-to-pixel method. Several statistical indexes were adopted to evaluate the performance of IMERG [25,27,[45][46][47]. The threshold to distinguish rain/no rain events was set to 0.5 mm based on the resolution of the rain gauge. Hit events (H) represent the precipitation events detected by IMERG and gauge. False events (F) represent the precipitation events detected by IMERG but not observed by the gauge. Miss events (M) represent the precipitation events not detected by IMERG but observed by the gauge. Nonevents events (N) represent the precipitation events not detected by both IMERG and gauge. The probability of detection (POD), false alarm ratio (FAR), and critical success index (CSI) were used to evaluate the precipitation detection capability ( Table 2). The Brier score (BS) is a function to measure the accuracy of probabilistic predictions [48]. A model with good performance has a score of 0, while the worst has a score of 1. All these statistical indexes can calculate the occurrence and nonoccurrence of precipitation events between IMERG and precipitation gauge data.  Note: Ps is the probability of precipitation (0/1) from satellite (IMERG); P G is the precipitation (0/1) from gauge observation.

Four-Component Error Decomposition Method
In order to better quantify and trace the error sources of IMERG, based on the detection capability and estimation capacity, the total bias (TB) can be decomposed into several independent error components. Here, we used the 4CED to perform the IMERG data quality analysis. The traditional error decomposition method (hereafter called the threecomponent error decomposition method, 3CED) proposed by Tian et al. [20] decomposes the TB into three components, namely, hit bias (HB), false bias (FB), and miss bias (MB) ( Table 3). Among the three independent error components, FB is always positive, and MB is always negative, while HB can be either positive or negative. Furthermore, the HB is further decomposed into the hit overestimate bias (HOB), hit underestimate bias (HUB), and true hit (bias = 0). Therefore, the 4CED includes HOB, HUB, FB, and MB [21,22]. The detailed mathematical formulas are listed in Table 3. HOB and FB are always positive among the four error components, while HUB and MB are always negative. Therefore, the TB can be decomposed into the overestimate bias (OB) and the underestimate bias (UB) using the two-component error decomposition method (2CED). OB is calculated as the sum of HOB and FB, and UB is calculated as the sum of HUB and MB. Moreover, the relationships between TN, OB, UB, HOB, HUB, FB, and MB is TB = OB + UB = (HOB + FB) + (HUB + MB) = HB + FB + MB (Figure 2). Table 3. The statistical metrics used to quantify the performance of IMERG.

Statistical Index Formula Perfect Value
Total bias (TB) Hit bias (HB) Hit overestimate bias (HOB) Hit underestimate bias (HUB) Overestimate bias (OB) OB = HOB + FB 0 Underestimate bias (UB) UB = HUB + MB 0 Note: S and G represent the precipitation estimates from satellite (IMERG) and gauge, respectively. n is the number of precipitation events. h, f, m, ho, and hu represent the number of hit, false, miss, hit overestimate and hit underestimate precipitation events, respectively.

Systematic and Random Error Decomposition
IMERG data derived from the retrieval results of multiple satellite sensors has its characteristics. Systematic error and random error decomposition can be used to perform error tracing. Systematic errors can reflect the characteristics of sensors and precipitation retrieval algorithms, while random errors are ubiquitous and unavoidable in observations. The mean square error was decomposed into systematic and random components as follows [4,24,49]: whereŜ represents the precipitation, which is calculated by the additive error model. E S is the systematic error ratio, and E G is the random error ratio. a and b are the slope and intercept of the additive error model, respectively.

General Analysis
The precipitation derived from the IMERG product was extracted over the Tunxi Watershed and compared with the gauge observations. The average annual precipitation at points or grids for gauge observation and IMERG were 1874 and 1676 mm, respectively. A preliminary comparison of IMERG with the reference data is shown in Figure 3. In general, IMERG is more consistent with the reference for Tunxi Watershed, except for a slight underestimation over mountain area. Figure 3a, the bias between the IMERG and gauge observation shows that IMERG tends to slightly underestimate the precipitation (bias < −200 mm) in mountainous terrain areas. The precipitation detected by IMERG at the elevation between 135 m and 369 m is close to the gauge measurements (−200 mm < bias < 200 mm). Elevation significantly influenced the accuracy of IMERG, and the accuracy of IMERG decreased with the increase of elevation. The relative bias is within 20% at 93.33% of the gauges in the Tunxi Watershed (Figure 3b). The correlation coefficient on the 30 min time scale ranges from 0.39 to 0.52 (Figure 3c), demonstrating a relatively poor performance on the data consistency, which is consistent with previous studies [13,46,50]. IMERG has closer annual precipitation with a poor correlation coefficient on the 30 min time scale, indicating that the detectability performance may cause a larger impact on the data quality on the 30 min time scale.

Detectability Performance
It is critical to analyze and trace the error contribution of IMERG and identify the input source (sensor type) and its features. Figure 4 shows the sample ratio and four types of precipitation events for all input sensor sources. Clearly, the sample ratio for IR (Morph, IR + Morph, and IR only) sources is 72.8%, which is much higher than the sample ratio for PMW (AMSR2, SSMIS, GMI, MHS, and ATMS) sources (27.2%). The precipitation data from IR sensor accounts for a significant proportion in the IMERG data. It means the precipitation data quality from the IR sources plays an important role in IMERG. Obviously, PMW sources had low HR, FR, and high MR. On the other hand, IR has high HR, FR, corresponding to a low MR. It indicates that IR sources overestimate rain rate occurrences because of the high HR, FR, and low MR. In summary, it is worth noting that IR has a high rate sample, and its detection capability contributed much error to IMERG.  Figure 5 shows the results of POD, FAR, and CSI for each input source used in IMERG. The POD values for Morph and Morph + IR are higher than 60%, while all the PMW sources have values between 36.3% and 38.8%, with tiny differences. On the other hand, for FAR, all the IR sources are higher than 50%, which is much higher than PWM sensors (27.5-31.8%). It indicates that IR tends to estimate false rainfall events. The CSI for PMW (32.5%) is higher than IR (30.1%), showing that PMW sensors have a good ability to detect precipitation for all precipitation events.  The BS was used to further analyze the IMERG precipitation detection and its accuracy. Compared with the sounder passive microwave sensor, the imager passive microwave sensor has a higher BS, indicating that the imager's precipitation detection accuracy is slightly lower (Figure 6). Among the individual data sources, GMI has the lowest BS, indicating the high rate of prediction accuracy and low proportion of misreported and underreported precipitation events. It is worth noting that Morph + IR has the highest BS and the lowest accuracy rate, mainly due to its high false positive rate. Since that Morph + IR contributes the most to IMERG precipitation, improving its accuracy is crucial for improving the overall accuracy of IMERG data. Based on the analysis in Figures 4-6, we can conclude that the detection errors, including false events and miss events, are the main error source of IMERG. Moreover, it is worth noting that GMI has the highest precision among all the sensors. GMI instruments aboard the GPM Core Observatory are designed to provide key information for sensing light and solid precipitation.  Figure 7 shows the total bias and the four error decomposed components for the eight input sources of IMERG. Generally, the TB for all sensors is negative, which means all the sensors underestimate precipitation. Morph has the biggest |TB| of 4.08%, Morph + IR has the highest FB and |HUB|. For all the PMW sensors, |MB| is an important component among the four components, which leads to negative TB. Bias is not only related to the data quality but also to data quantity. IR only has a little effect on the quality of IMERG data because of its small sample size, despite its poor detectability performance. Morph and Morph + IR have a significant sample size and a considerable TB due to their poor detectability performance, resulting in a large TB. Therefore, improving the detectability and precision of the Morph and Morph + IR is essential to reduce the HOB, |HUB|, FB, and |MB|. For the TB, the Morph + IR is smaller than Morph, while Morph + IR has larger |HUB|, FB, and |MB|. The performance of Morph + IR is still questionable since the magnitude of TB may be adjusted due to the cancellation of positive values (HOB and FB) and negative values (HUB and MB).

Systematic and Random Error Decomposition
The systematic and random error components of each sensor were estimated using an additive error model performed over Tunxi Watershed from 2018 to 2020. Figure 8 displays each sensor's systematic and random components of total error. Clearly, all the PMW-sounder sensors exhibit a lower systematic error ratio (<27.94%), while PMW-imager sensors exhibit less random error (<39.0%). Systematic error is the prominent component for AMSR2, SSMIS, GMI, and Morph + IR. It should be noted that ATMS has the lowest systematic error of 7.8%, showing that most of the systematic error is removed.

Error Decomposition
There are close connections between 2CED, 3CED, and 4CED (Section 3.2). 2CED and 3CED can be derived based on the 4CED. In Section 4.3, the 4CED has been used to identify the IMERG data error for each sensor. In addition, the relationships and differences between 2CED, 3CED, and 4CED are discussed. Figure 9 depicts the three components of bias (HB, FB, and MB) for the eight input sources of IMERG. Compared to 4CED, 3CED has the same FB and MB as 4CED. Morph + IR has the biggest |HB| (9.26%) of all the sensors, followed by Morph (5.72%). For Morph + IR, the |HB|, HOB, and |HUB| are 9.26%, 6.12%, and 15.38%, respectively. The |HB|, HOB, and |HUB| for Morph are 5.723%, 8.10%, and 13.83%. Obviously, HB is underrepresented due to the cancelation of the positive HOB and the negative HUB. 4CED can describe the error component more comprehensively. For the PMW-sounder sensors, the HB is always positive. Based on the 4CED method, TB can be further divided into OB and UB. OB is the sum of HOB and FB, while UB is the sum of HUB and MB. For all the sensors, |UB| is bigger than OB, suggesting that |UB| is the dominant factor of the error source ( Figure 10). Additionally, Morph + IR has the biggest OB and |UB|, while the TB is smaller than Morph, indicating a cancellation effect of the overestimate and underestimate bias.

Error Source Analysis
The satellite precipitation estimate is retrieved from the PMW and IR sensors to meet the spatial and temporal requirements. The sampling frequency and precision from PMW and IR sensors are related to the accuracy of IMERG data. Figures 4-7 show the sample ratio, detection ability, four-component error decomposition, and systematic and random error for each input source. In summary, PMW sensors (AMSR2, SSMIS, GMI, MHS, and ATMS) have the low sample ratio with high accuracy, while IR sensors (Morph, Morph + IR, IR only) have the high sample ratio with low accuracy.
IMERG is designed to inter-calibrate, merge, and interpolate satellite microwave precipitation estimates together with microwave-calibrated infrared (IR) satellite estimates. The sample ratio for PMW sensors is 27.2%. To compensate for the limited available sampling, microwave-calibrated IR satellite estimates are used when the PMW samples are too sparse. Therefore, it is important to launch more leo-satellites to obtain more PMW information for precipitation estimates.
The frequent sampling and poor detection ability result in significant error in IMERG data. Therefore, it is essential to improve the detectability of IR sensors. The indirect relationship between IR brightness temperature and precipitation is used to calculate the precipitation. For PERSIANN-CSS, the 60 • N-S latitude belt is divided into 24 sub-regions to perform regional training and parallel processing [51]. Chen et al. [52] found that the input source error of GPM-GSMaP is impacted by geographic and climatic factors. For the improvement of IMERG, more sub-regions related to latitude, topography, climatic, and other factors should be considered to get more accurate indirect relationship between IR brightness temperature and precipitation. In addition, the three temperature levels (220 K, 235 K, and 253 K) are used to extract cloud features at different altitudes. More temperature levels can be divided to perform precipitation calculations at different altitudes and regions. Recently, intelligent algorithms have demonstrated good predictive capability in many fields [53][54][55][56][57][58]. The development of intelligent algorithms provides new insight into precipitation prediction based on IR sensor.

Uncertainty of Gauge Observation
The evaluation of satellite precipitation estimates depends on surface gauge observations. When using rain gauge measurements as a benchmark, considering their density is important [8]. In the Tunxi Watershed, there is a typical catchment of 0.55 km 2 , and 13 precipitation stations are evenly distributed in the typical catchment at different elevations, slopes, and aspects. The method of measuring precipitation in the typical catchment is the same as in the Tunxi Watershed, using the same rain gauge and recording the data every 5 min. The annual precipitationfor the 13 precipitation stations are 2214, 2172, 2303, 2206, 2180, 2231, 2126, 2137, 1882, 1685, 2268, 2157, and 2289 mm, respectively. The coefficient of variation (Cv) for annual precipitation is 0.0809, with the mean, maximum, and minimum values of 2142, 2303, and 1685 mm, respectively. The observations show that the precipitation has small spatial heterogeneity in the typical catchment. In addition, it has been demonstrated by previous research that the spatial variability of precipitation across the Tunxi Watershed follows simple scaling and increases as the drainage area increases, leading to larger spatial heterogeneity [37]. The annual precipitation in the Tunxi watershed is 1874 mm, and the corresponding Cv is 0.1122. The annual precipitation and Cv of typical catchment and Tunxi Watershed are very close. Therefore, the rain gauge can capture the spatial pattern of the Tunxi Watershed, indicating that the rain gauge density can reach the requirement for the satellite evaluation.

Conclusions
In this study, the 4CED and systematic and random error decomposition are used to quantify and trace the error characteristics of the eight input sources used in the IMERG dataset. The evaluation of IMERG data includes detectability performance, 4CED, and systematic and random errors. The primary conclusions are as follows.
(1) For detectability, the sample ratio for IR (Morph, IR + Morph, and IR only) is much higher than for PMW (AMSR2, SSMIS, GMI, MHS, and ATMS). The IR sensor has a high HR, FR, POD, and FAR, indicating that IR is sensitive to light precipitation events and tends to predict a false signal for the satellite estimate. The poor performance of CSI and BS for IR sensors is mainly due to the high false ratio. (2) Based on the 4CED, the TB can be decomposed into HOB, HUB, FB, and MB. HOB and FB are always positive among the four error components, while HUB and MB are always negative. The magnitude of HOB and |HUB| is higher than |HB| because of the unavoidable cancellation during the HB calculations process. Generally, the TB for all sensors is negative, meaning that all the sensors underestimate precipitation. Morph and Morph + IR have considerable bias related to the prediction ability and the sample size. It is crucial to reduce the FR to improve the detectability of IR sensors due to their high sample size. (3) The systematic and random error components were assessed using the additive error model. Systematic error is the prominent component for AMSR2, SSMIS, GMI, and Morph + IR, indicating that the retrieval algorithm for these sensors needs further improvement.

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