Impacts of Gauge Data Bias on the Performance Evaluation of Satellite-Based Precipitation Products in the Arid Region of Northwestern China

Abstract

It has been reported that systematic bias exists in gauge measurements, which are usually used as the evaluation benchmark, so it is crucial to investigate the impacts of gauge data bias on the evaluation of satellite precipitation products. Six satellite precipitation products (IMERG, CMORPH, GSMaP, PERSIANN, PERSIANN−CCS, and PDIR−Now) and gauge data are collected from 2003 to 2015 in the arid region of Northwestern China. A daily correction for precipitation biases from wind-induced undercatch, wetting loss, and trace error is made for gauge measurements. The changes in metrics, including four continuous and four categorical metrics, are calculated to illustrate how the gauge data bias impacts the evaluation of six satellite precipitation products. The results show the following: The overall performances of six satellite precipitation products are undervalued by the gauge bias. Compared to other satellite products, the performance of IMERG is the best, whether before or after bias correction. However, the performances of all six satellite products are still not good enough even after bias correction and need to be improved. The impacts of gauge bias on the evaluation of the satellite precipitation products also differ by subregion, season, satellite precipitation product, precipitation intensity, and precipitation phase. In conclusion, the impacts of the gauge bias on the performance assessment of satellite products are obvious over the study region, implying that bias correction for gauge measurements is needed to obtain an accurate understanding of the performance of satellite precipitation products if choosing the gauge data as the evaluation benchmark.

1. Introduction

As the main driver of the water cycle and the most active variable in atmospheric circulation, precipitation plays a vital role in hydrological, climatic, and agricultural applications, for instance, extreme precipitation analysis [1], drought monitoring [2], flood forecasting [3], and agricultural decision-making [4]. Despite its importance in many applications, reliable and accurate precipitation measurement remains a challenging task due to the significant heterogeneity of precipitation processes [1].

Conventional precipitation gauges are considered to provide the most accurate precipitation observations in many parts of the world. However, the difficulty and the cost associated with their maintenance limit their area of coverage. While the ground networks of precipitation gauges in developed regions are dense enough, in developing countries and remote areas, the data coverage is usually insufficient to accurately characterize the spatial variability of precipitation. The satellite remote-sensing technology, with its consistent periodicity and broad coverage, presents a promising alternative way to measure precipitation [2].

Satellite precipitation products (SPPs) are normally derived from sensors on board geostationary and low-earth orbit satellites. Geostationary satellites employ visible and infrared sensors to retrieve precipitation estimates with high spatial and temporal resolutions (e.g., 0.5–2 km and 10–15 min for the Advanced Himawari Imager [5] onboard Himawari-8/-9, manufactured by Mitsubishi Electric, Tokyo, Japan). Low earth orbit satellites use passive microwave sensors to provide worldwide precipitation measurements with two observations per day and a spatial resolution typically larger than 25 km [6]. The latter is typically more accurate because microwave sensors are more directly responsive to cloud internal processes and precipitation formation mechanisms [7]. Several SPPs have been developed to exploit the complementary strengths of geostationary observations and low-earth orbit retrievals.

These SPPs include the following: Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) [8], Climate Prediction Center (CPC) morphing technique (CMORPH) [9], Global Precipitation Measurement (GPM) Integrated Multi-satellitE Retrievals (IMERG) [10], Global Satellite Mapping of Precipitation (GSMaP) [11], Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) [12], PERSIANN−Cloud Classification System (CCS) [13], and PERSIANN−Dynamic Infrared Rain Rate near-real-time (PDIR−Now) [14]. These SPPs are especially valuable in regions where precipitation observations from hydrometeorological networks are scarce or totally absent.

Although SPPs can provide quasi-global high-quality precipitation estimation, they are subject to bias and systematic errors caused by various factors such as sampling frequency, the nonuniform field of view of the sensors, and uncertainties in the retrieval algorithms [15]. Therefore, it is necessary to evaluate and intercompare the performance of these datasets before application. Characterized by a reliable and direct way to measure precipitation, observations from precipitation gauges are often selected as the evaluation reference. A number of studies have been performed to evaluate SPPs against gauge data [16,17,18,19,20,21,22,23]. For example, Alijanian et al. [17] evaluated five satellite rainfall estimates (CMORPH, PERSIANN−CDR, PERSIANN, TRMM, and MSWEP) against gauge data based on different rainfall regimes over Iran. They found that the performance of satellite rainfall estimates varies with climatic regimes; for example, the best correlation was observed in the south, on the shore of the Persian Gulf, with a “very hot and humid” climate for MSWEP, TRMM, and PERSIANN−CDR. Yu et al. [22] analyzed and evaluated the spatiotemporal accuracy features of the following three high spatial resolution SPPs: CHIRPS, GPM−IMERG, and PERSIANN−CCS. They concluded that the performance of SPPs is relatively good in summer but slightly weak in winter, and SPPs perform better in the eastern humid basin than in the western arid basin.

However, the measurements from precipitation gauges often include systematic biases, which could weaken the reliability of the assessment results of SPPs. These biases include wind-induced precipitation undercatch, evaporation losses, the underestimation of trace precipitation events, and wetting losses. Of the biases, the wind-induced undercatch is generally the source of the greatest error. In the low-precipitation areas, the wetting losses and trace precipitation are also significant biases [24,25,26,27]. The World Meteorological Organization (WMO) began the Solid Precipitation Measurement Intercomparison Project in 1985 to assess various national methods of solid precipitation observations [28]. This project involves thirteen countries, including China. New bias-correction techniques have been developed for a variety of commonly used precipitation gauges across the world, such as the Canadian Nipher snow gauge, the United States standard 8” non-recording gauge, the Hellmann gauge, and the Russian Tretyakov gauge. The WMO bias-corrected methods have been applied in several regions and countries, such as Mongolia [27], Greenland [25], and the northern regions [29]. The results clearly show that precipitation amounts are much higher than previously reported, especially in high-latitude regions [30].

In China, research on bias correction of gauge data has been carried out since the 1980s [26,31,32,33,34,35,36,37]. Analysis of the intercomparison data of precipitation measurements at Daxigou Meteorological Station in 1986 indicated the relationship between the catch efficiency of the Chinese standard precipitation gauge (CSPG) and the average wind speed at 10 m height for different precipitation phases [33,34]. Ye et al. [26] developed a new bias-correction method for gauge measurements and generated a reliable climatology for China based on the bias-corrected data. They found that annual precipitation has increased by 6–62% relative to gauge-measured yearly total precipitation over China. Li et al. [31] used the bias-corrected daily precipitation from a gauge to re-divide the climatic zones in China. The findings demonstrate that the severe arid areas declined while the severe humid areas grew, indicating that the actual climate conditions of China should be wetter than presently assessed. Yao et al. [35] investigated the effects of gauge data bias on aridity and drought assessment in China. They concluded that the spatial and temporal characteristics of drought assessment were altered by precipitation bias. These studies imply that the bias of gauge measurements will affect all research fields that use gauge data, of course, including SPPs evaluation. However, to our knowledge, there have been no relevant studies that investigate the impacts of gauge bias on the performance assessment of SPPs in China. Such studies will contribute to a more accurate understanding of SPPs’ performance and thus help users select appropriate SPPs for different applications.

The arid region of Northwestern China (ARNC) is one of the important parts of the arid region of Central Asia. The terrain in the region is complex; mountains and basins are distributed alternately, deserts and oases coexist, and the spatial and temporal distribution of natural elements, including precipitation, is very uneven [38]. SPPs can provide valuable precipitation information, which is beneficial to studies on climate change, prevention and control of desertification, protection and restoration of ecosystems, etc., for this area. Correcting the biases due to wind-induced undercatch, wetting loss, and underestimation of trace precipitation events for gauge measurements, Ye et al. [26] found the correction factor (computed as corrected minus measured data, divided by measured data) is more significant in northwestern China than southeastern China. Ma et al. [39] found the correction factor can be up to 180% in the winter over the ARNC. This illustrates that it is indeed necessary to investigate the impact of gauge bias on the performance assessment of SPPs before applications in ARNC.

In this paper, the impacts of bias in gauge data on evaluating six major SPPs (IMERG, CMORPH, GSMaP, PERSIANN, PERSIANN−CCS, PDIR−Now) over ARNC were investigated on a spatial/seasonal scale, different ranges of precipitation intensity, and different precipitation phases. We first corrected for the bias inherent in gauge-measured precipitation. Then, the changes in the performance assessment of SPPs were presented by calculating the changes in evaluation metrics. The structure of this study is as follows: Section 2 describes the study area and datasets, the preprogressing of datasets, the bias correction method for gauge measurements, and evaluation metrics, Section 3 presents the results, and Section 4 makes the summary and discussion, while the conclusions are given in Section 5.

2. Materials and Methods

2.1. Study Area

The arid region of Northwestern China (ARNC), located in central Asia between 73–107° E and 35–50° N and far from the ocean, is an extremely arid and arid region with regional mean annual precipitation of less than 200 mm, which belongs to a temperate continental climate [40]. ARNC is bounded by Helan Mountains in the east, Kunlun Mountains–Alkun Mountains–Qilian Mountains in the south, and Chinese borders in the north and west. This region covers the entire Xinjiang Uygur Autonomous, the Hexi Corridor in Gansu Province, the Alxa Plateau in Inner Mongolia, and areas west of Helan Mountain in Ningxia Hui Autonomous Region (Figure 1a).

In the study, there are two major inland basins (Tarim Basin and Junggar Basin) and some major mountains (Altai Mountains, Tianshan Mountains, Kunlun Mountains, Alkun Mountains, and Qilian Mountains) area.

The spatial distributions of precipitation based on the gauge data from 1970 to 2000, the gauge data without bias correction from 2003 to 2015, and the bias-corrected gauge data from 2003 to 2015 all exhibit a decreasing trend from mountainous areas to plains on both sides (Figure 1d−f), which is due to the influence of atmospheric circulation and topography [41]. Southwest monsoon and East Asian monsoon deliver humid airflow and produce precipitation with the uplift of the terrain in Qilian Mountains. The northern part of ARNC is the channel of westerly wind circulation, which can bring moist airflow from the Atlantic Ocean. With the influence of high mountains, there is abundant precipitation in Tianshan Mountains. However, the humid airflow cannot enter Tarim Basin, Junggar Basin, Kexi Corridor, and Alxa Plateau due to the blockade of high mountains, which gives rise to small precipitation there.

According to previous studies [38,41] and regional differences in topography, ARNC is divided into six subregions (Figure 1b) (I) Northern Xinjiang (NX), (II) Tianshan Mountains (TM), (III) Southern Xinjiang (SX), (IV) Qilian Mountains (QM), (V) Hexi Corridor (HC), (VI) Alxa Plateau (AP).

2.2. Datasets

2.2.1. Ground Observation Data

Daily observation of precipitation, temperature, and wind speed at 10 m height for the period from 2003 to 2015 were used in this study. These data are from 91 weather stations as a part of the Chinese network of weather stations, shown in Figure 1c. China Meteorological Administration (CMA) operates this network, and all collected data go through strict quality control and inspection.

Precipitation data are recorded by the Chinese standard precipitation gauge (CSPG) with manual observation. CSPG has been the standard instrument to measure both solid and liquid precipitation in China since the late 1950s. CSPG, a 65-cm long and 20-cm in diameter galvanized iron cylinder, is placed 0.7 m above the ground without a windshield [26,37]. Besides, daily mean air temperature and daily mean wind speed at 10 m height from 91 CMA stations were gathered to classify precipitation phases (i.e., rain, snow, and mixed precipitation) and calculate the gauge’s catch ratio [31].

2.2.2. Satellite Precipitation Products

Building upon the success of the Tropical Rainfall Measuring Mission (TRMM), NASA and the Japan Aerospace Exploration Agency initiated the Global Precipitation Measurement (GPM) mission. The Integrated Multi-satellitE Retrievals for GPM (IMERG) algorithm combines microwave precipitation estimates from the GPM constellation, microwave-calibrated infrared satellite estimates, Global Precipitation Climatology Centre (GPCC) monthly gauge analyses, and data from other sensors [10]. The latest Version 06B of IMERG has extended the data period back to June 2000 by incorporating precipitation estimates collected during the TRMM era. IMERG contains two real-time products (Early Run and Late Run) and one research-level product (Final Run). The IMERG Final Run product includes the following two precipitation variables: the multi-satellite-only precipitation estimates (IMERG_uncal) and the multi-satellite precipitation estimates with gauge calibration based on GPCC monthly gauge analysis (IMERG_cal). Since the precipitation records from 91 CMA weather stations used in this study have been shared with GPCC monthly analysis [42], we used IMERG_uncal (hereafter IMERG) for independent evaluation. As for the rest SPPs, the unadjusted version was selected for the same reason. The half-hourly 0.1° IMERG Final Run precipitation estimates were gathered from Goddard Earth Sciences Data and Information Services Center (GES DISC) (https://disc.gsfc.nasa.gov/ accessed on 28 February 2022).

The Climate Prediction Center (CPC) morphing technique (CMORPH) [9] generates global precipitation analyses at very high spatial and temporal resolution (8 km and 30 min) by taking advantage of the high temporal resolution observations from the geosynchronous orbit (GEO) infrared (IR) sensors and the more accurate precipitation estimates from low earth orbit (LEO) passive microwave (PMW) sensors. Through the cross-correlation technique, the cloud systems’ motion vectors are first defined by the consecutive GEO IR images. The instantaneous PMW precipitation estimates are then propagated along the cloud motion vectors. CMORPH Version 0.x is generated using an evolving algorithm with inputting PMW retrievals of changing versions over the entire data period, resulting in discontinuities in the time series of the data. To address this problem, CMORPH Version 1.0 is created using a fixed algorithm with the inputs of identical versions throughout the data period [43]. CMORPH Version 1.0 includes the raw (satellite only) and bias−corrected (gauge-satellite blended) precipitation products. In this study, we used the three hourly 0.25° CMORPH Version 1.0 Raw dataset (hereafter CMORPH), which is available at the Research Data Archive (RDA; https://rda.ucar.edu/ accessed on 25 February 2022) managed by National Center for Atmospheric Research (NCAR).

Global Satellite Mapping of Precipitation (GSMaP) is a blended PMW−IR precipitation product, which has been developed in Japan as the Japanese GPM standard product [11]. PMW precipitation retrieval algorithm [44], PMW−IR combined algorithm [45], and gauge-adjustment algorithm [46] comprise the core algorithms of GSMaP. The GSMaP products in the GPM era comprise the “standard product”, “near-real-time product”, “real-time product”, and “reanalysis product”. The standard products include satellite-only precipitation estimates (GSMaP_MVK) and gauge-calibrated precipitation estimates (GSMaP_Gauge), which are processed three days after observations. Reanalysis products (GSMaP_RNL and GSMaP_RNL_Gauge) are calculated with Japanese 55-year reanalysis (JRA55) [47]. The preliminary analyses by developers show that the differences between the reanalysis and the standard products are small [11]. The data period of the latest version 7 for standard products starts from March 2014. Before this time, the latest version 6 for reanalysis products could be used. Daily 0.1° V7 GSMaP_MVK coupled with V6 GSMaP_RNL (hereafter GSMaP) were used in this paper and downloaded on the website https://sharaku.eorc.jaxa.jp/GSMaP/ accessed on 25 February 2022.

Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) [12], PERSIANN−Cloud Classification System (CCS) [13], and PERSIANN−Dynamic Infrared Rain Rate near-real-time (PDIR−Now) [14] as members of PERSIANN family primarily depend on IR data. As its name implies, PERSIANN provides rainfall estimates using artificial neural networks (ANNs). However, the 2-day latency of PERSIANN as a result of using PMW observations as input made it not applicable to applications with real-time requirement. To address this problem, PERSIANN−CCS discarded PWM data and utilized a collection of classified cloud groups with calibrated cloud-top temperature and rainfall (Tb−R) relationships trained by self-organizing feature maps (SOFMs) to estimate rainfall. The main features of PERSIANN−CCS include the short data latency and sole reliance on IR data. However, without PMW data, the accuracy of PERSIANN−CCS severely weakened compared with PERSIANN. Therefore, PDIR−Now was developed mainly based on the framework of PERSIANN−CCS. The difference is that PDIR adopted dynamical rather than static Tb−R curves and used rainfall climatology data to shift the curve’s position. In this study, six-hourly 0.25° PERSIANN, six-hourly 0.04° PERSIANN−CCS (hereafter CCS), and six-hourly 0.04° PDIR−Now (hereafter PDIR) were collected from the Center for Hydrometeorology and Remote Sensing (CHRS) Data Portal (https://chrsdata.eng.uci.edu/ accessed on 25 February 2022).

The basic information and references of six SPPs are summarized in

Table 1. Summary of SPPs used in this study.

Dataset	Version	Resolution	Period	Reference
IMERG	Final Run v06B IMERG_uncal	0.1°/0.5 h	2003–2015	Huffman et al. [10]
CMORPH	V1.0 Raw, satellite-only	0.25°/3 h	2003–2015	Joyce et al. [9]
GSMaP	GSMaP_MVK v7/GSMaP_RNL v6	0.1°/1 d	2003–2015	Kubota et al. [11]
PERSIANN	—	0.25°/6 h	2003–2015	Hsu et al. [12]
PERSIANN−CCS	—	0.04°/6 h	2003–2015	Hong et al. [13]
PDIR−Now	—	0.04°/6 h	2003–2015	Nguyen et al. [14]

.

2.3. Methods

Several steps were carried out to investigate the impacts of the gauge bias on the performance assessment of SPPs (Figure 2). First, the local time of gauge data and SPPs should be unified. The gauge data uses the Beijing Time (UTC +8) but the SPPs use the UTC time. The precipitation values from the specific grids of SPPs were extracted using the geographic location of weather stations, which is called pixel-to-point strategy. These values were then evaluated against the corresponding gauge observations. Second, the wind and temperature were used to correct the bias of gauge data. Last, the original gauge data and the bias-corrected gauge data were used to investigate the impacts of the gauge bias on the performance assessment of SPPs in the whole ARNC and different subregions, different seasons, different precipitation intensities, and different precipitation types. More details of these procedures were explained in the following sections.

2.3.1. Preprocessing of the Datasets

It should be noted that CMA stations record daily precipitation from 8:00 p.m. Beijing time of the previous day to 8:00 p.m. Beijing time of the current day, which is equivalent to 12:00 Coordinated Universal Time (UTC) to 12:00 UTC. To keep the consistent definition of daily precipitation with CMA, the precipitation estimates for each SPP falling between 12:00 and 12:00 UTC were aggregated to obtain daily precipitation.

The spatial mismatch exists between the point measurements of precipitation gauges and the areal estimates of SPPs. There are two possible ways to solve this problem. One is to average multiple gauge observations within a grid of SPPs. However, the network of weather stations is relatively sparse in the study area, where the grids of SPPs contain at most one station. The other is to use interpolation methods to unify the spatial scales of gauge observations and SPPs. However, the uncertainties incurred are hard to quantify, especially in remote and mountainous areas.

Therefore, to preserve the accuracy of gauge data and SPPs, we adopted the pixel-to-point strategy, which many other authors also adopt [16,22,48,49,50,51]. This strategy assumes the area-scale satellite precipitation is equal to point-scale gauge precipitation regardless of the position of gauges in the grid. Precipitation values from the specific grids of SPPs were extracted using the geographic location of weather stations and were evaluated against the corresponding gauge observations.

2.3.2. Evaluation Metrics

Several continuous metrics, including Pearson correlation coefficient (CC), relative bias (BIAS), normalized root mean square error (NRMSE), and the modified Kling–Gupta efficiency (KGE′), were adopted to evaluate and compare the accuracy of SPPs. The CC, with the range between 0 and 1, was utilized to describe the degree of linear correlation between the target (i.e., satellite) and the reference (i.e., precipitation gauge) datasets. The higher the value, the better the correlation. The RB (in percentage), with the optimal value of 0, was used to describe the systematic bias of target datasets relative to the reference dataset. A smaller absolute value of RB indicates a smaller deviation. Positive values of RB indicate overestimation of precipitation amounts. Negative values indicate underestimation of precipitation amounts. The NRMSE, with the optimal value of 0, normalizing the root mean square error (RMSE) to eliminate dimensional effects, was used to measure the error of the target datasets. A larger value of NRMSE indicates a larger error. The KGE′, synthesizing correlation, bias, and variability components, describes the overall accuracy of target datasets. KGE′ ranges in (−∞,1] with large values indicating better accuracy.

To further examine the ability of SPPs to detect precipitation events, a set of categorical metrics was also calculated, including the probability of detection (POD), false alarm ratio (FAR), frequency bias (FB), and critical success index (CSI). The POD, with the optimal value of 1, presents the ratio of precipitation events detected by satellites among all precipitation events gauges observe. The FAR, with the optimal value of 0, gives the ratio of error-detected events among all the events satellites detect. The FB, with the optimal value of 0, shows the extent to which SPPs overestimate or underestimate the number of precipitation events. Similar to RB, the positive values of FB indicate overestimation of the number of precipitation events. The negative values indicate underestimation. The CSI, ranging in [0, 1], combines the features of POD and FAR to demonstrate the overall detection ability of SPPs. The larger the value, the better detection ability.

The calculation formulas can be found in

Table 2. Statistical metrics.

Name	Formula	Optimal Value	Value Range
Correlation coefficient/CC	$\frac{\frac{1}{\mathrm{N}}{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}\left({\mathrm{S}}_{\mathrm{i}}-\overline{\mathrm{S}}\right)\left({\mathrm{G}}_{\mathrm{i}}-\overline{\mathrm{G}}\right)}{{\mathsf{\sigma }}_{\mathrm{S}}{\mathsf{\sigma }}_{\mathrm{G}}}$	1	[0, 1]
Relative bias/RB	$\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}\left({\mathrm{S}}_{\mathrm{i}}-{\mathrm{G}}_{\mathrm{i}}\right)}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{G}}_{\mathrm{i}}}\left(100\right)$	0	(−∞,+∞)
Normalized root mean square error/NRMSE	$\frac{\sqrt{\frac{1}{\mathrm{N}}{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{S}}_{\mathrm{i}}-{\mathrm{G}}_{\mathrm{i}}\right)}^2}}{\frac{1}{\mathrm{N}}{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{G}}_{\mathrm{i}}}$	0	(−∞,+∞)
Modified Kling–Gupta efficiency/KGE′	$1-\sqrt{{\left(\mathrm{CC}-1\right)}^2+{\left(\mathsf{\beta }-1\right)}^2+{\left(\mathsf{\gamma }-1\right)}^2}$	1	(−∞,1]
Probability of detection/POD	$\frac{\mathrm{HIT}}{\mathrm{HIT}+\mathrm{MISS}}$	1	[0, 1]
False alarm ratio/FAR	$\frac{\mathrm{FALSE}}{\mathrm{HIT}+\mathrm{FALSE}}$	0	[0, 1]
Frequency bias/FB	$\frac{\mathrm{HIT}+\mathrm{FALSE}}{\mathrm{HIT}+\mathrm{MISS}}-1$	0	(−∞,+∞)
Critical success index/CSI	$\frac{1}{1/\left(1-\mathrm{FAR}\right)+1/\mathrm{POD}-1}$	1	[0, 1]

Note: N represents number of samples; S_i and G_i represent the ith satellite precipitation estimate and gauge record, respectively; $\overline{\mathrm{S}}$ and $\overline{\mathrm{G}}$ represent the corresponding mean values; σ_S and σ_G represent the corresponding standard deviations. β is bias ratio, of which the calculation formula is $\overline{\mathrm{S}}/\overline{\mathrm{G}}$; γ is variability ratio, of which the calculation formula is (σ_S/$\overline{\mathrm{S}}$)/(σ_G/$\overline{\mathrm{G}}$). HIT represents the number of precipitation events that are detected by satellite and observed by the gauge; MISS represents the number of events that are observed but not detected; FALSE represents the number of events that are detected but not observed.

.

For more details and comments on the aforementioned continuous and categorical metrics, one can refer to the literature [22,52,53,54].

At last, the changes of evaluation metrics, which are calculated by the evaluation metrics computed using the corrected gauge precipitation as baseline minus those using the raw gauge precipitation as the baseline, are denoted as ∆CC, ∆NRMSE, ∆RB, ∆KGE′, ∆POD, and so on. They are used to illustrate the impacts of gauge bias on the performance evaluation of six SPPs. In this paper, we think the bias-corrected gauge precipitation is more actual than the gauge precipitation without bias correction. Therefore, the positive ∆CC, ∆NRMSE, ∆KGE′, ∆POD, ∆FAR, and ∆CSI indicate that the gauge bias makes the correlation, error, accuracy, probability of detection, false alarm ratio, and detection ability of SPPs undervalued, respectively, and vice versa. Due to the fact that the estimates from SPPs remain unchanged in the process of correcting the gauge bias, the negative ∆RB and ∆FB indicate the following: After removing the gauge bias, the precipitation amount and the number of precipitation events from gauge increase.

2.3.3. Bias-Correction Method

Bias correction technique has been developed for CSPG through gauge intercomparison experiments carried out in the Urumqi River basin, northwestern China [34,55] and applied in the research on precipitation climatology and drought assessment over China [26,31,35,37]. The bias correction procedure used in this paper follows those studies. The bias in gauge−measured precipitation was caused by wind, wetting, evaporation, and trace events losses [56]. The general correction formula for the gauge precipitation was the following [26]:

$$P_c=K\left(P_m+\Delta P_w+\Delta P_e+\Delta P_t\right), K=1/CR$$

(1)

where $P_c$ is the corrected gauge precipitation; $P_m$ is the raw gauge-measured precipitation; $\Delta P_w$, $\Delta P_e$, and $\Delta P_t$ are wetting losses, evaporation losses, and trace precipitation, respectively; $CR$ is the catch ratio (%); $K$ is the correction coefficient for wind-induced errors.

Evaporation losses are time-varying and site-dependent. Daily variation and seasonal change in evaporation losses are significant. Estimating the daily evaporation losses at one site is difficult using the experimental results obtained from other gauge sites [26]. Therefore, the evaporation loss is neglected in this study. In addition, due to the usage of a funnel and a container during the high evaporation period, the annual evaporation loss in China is expected to be small. The results of bias corrections will not be greatly affected if ignoring this type of error [39].

A precipitation event with a reading less than 0.1 mm is outside the resolution of CSPG, and hence it is recorded as a trace precipitation event. Officially, all trace precipitation events are treated as zero amounts. The day during which trace precipitation event was recorded, however, is considered a precipitation day. Two trace precipitation events have been sometimes reported in a single trace precipitation day, according to the precipitation observations in China. The gauge cannot identify precipitation events with precipitation less than the wetting loss. To be conservative, we did not correct the wetting loss and wind undercatch for trace precipitation days. A value of 0.10 mm was assigned for any trace day, regardless of the number of trace observations reported [26,31,35,37,39]. Trace precipitation days are marked with 32,700 in the gauge records.

Wetting losses depend on precipitation phase, gauge type, and the daily gauge emptying times. According to the wetting loss experiments for the CSPG in China [33,34], the average wetting loss of the CSPG per observation was 0.23 mm, 0.30 mm, and 0.29 mm for rain, snow, and mixed precipitation, respectively. Precipitation is measured twice a day in China, at 08:00 and 20:00 Local Time (Beijing time). To be conservative, wetting losses were adjusted once a measurable day (daily gauge-measured precipitation ≥ 0.10 mm).

Wind loss correction is relatively complicated and depends on precipitation phases, with snow generally more susceptible to wind. Precipitation phase is classified by daily mean air temperature in this work [26,27]. The temperature thresholds were set at −2 °C and +2 °C, that is, snow below −2 °C, rain above +2 °C, and mixed precipitation between −2 and +2 °C. In the WMO intercomparison, the catch ratio was defined as the ratio of the amount of precipitation (including the gauge measured amount and wetting loss) caught by the gauge to the true precipitation [28]. Based on the gauge intercomparison experiments in the Urumqi River basin, which used the octagonal vertical double fence (DFIR) as the reference gauge, the relation between catch ratio and wind speed has been developed for different precipitation phases [34,36]. The catch ratio (percent) versus daily mean wind speed at 10 m height are presented below for rain, snow, and mixed precipitation, as follows:

$$C{R}_{snow}=100\exp \left(-0.056U_{10}\right)$$

(2)

$$C{R}_{rain}=100\exp \left(-0.041U_{10}\right)$$

(3)

$$C{R}_{mixed}=C{R}_{snow}-\left(C{R}_{snow}-C{R}_{rain}\right)\times \left(T+2\right)/4$$

(4)

where, $C{R}_{snow}$, $C{R}_{rain}$, and $C{R}_{mixed}$ are catch ratios for snow, rain, and mixed precipitation, respectively; $U_{10}$ is the daily mean wind speed at 10 m height; $T$ is the daily mean temperature.

After determining each component of bias, Equation (1) is finally simplified as follows:

$$P_c=\left\{\begin{array}{c}\left(P_m+\Delta P_w\right)/CR\\ \Delta P_t\end{array}\right.\hspace{1em}\begin{array}{c}\mathrm{for} \mathrm{measurable} \mathrm{day} (P_m\ge 0.1 \mathrm{mm})\hfill \\ \mathrm{for} \mathrm{trace} \mathrm{precipitation} \mathrm{day} (0<P_m<0.1 \mathrm{mm})\hfill \end{array}$$

(5)

For each measurable day, wind loss and wetting loss were corrected. For each trace precipitation day, only trace loss was corrected. More details on the bias correction method are referred to [26,31,34,35,36,37].

3. Results

3.1. Spatial Variations of the Changes of Evaluation Metrics

To provide a general idea of how the impacts of gauge bias on the evaluation of six SPPs vary spatially, we first showed the spatial patterns (Figure 3) and regional variability (

Table 3. The changes of continuous metrics of SPPs in each subregion.

Subregion		NX	TM	SX	QM	HC	AP	ARNC
∆CC	IMERG	0.004	0.004	0.010	0.005	0.003	0.009	0.005
	CMORPH	0.002	0.001	0.013	0.002	0.005	0.005	0.004
	GSMaP	0.005	0.002	0.006	0.005	0.006	0.008	0.004
	PERSIANN	0.006	0.003	0.010	0.007	0.008	0.009	0.007
	CCS	0.007	0.004	0.005	0.005	0.007	0.007	0.005
	PDIR	0.009	0.006	0.015	0.001	0.008	0.012	0.008
	Mean	0.006	0.003	0.010	0.004	0.006	0.008	0.006
∆NRMSE	IMERG	−0.81	−0.27	−2.19	−0.23	−1.05	−0.89	−0.77
	CMORPH	−0.77	−0.32	−1.68	−0.14	−0.78	−0.74	−0.66
	GSMaP	−2.35	−1.11	−9.52	−0.41	−1.51	−1.16	−2.63
	PERSIANN	−1.10	−0.39	−2.60	−0.30	−1.22	−0.97	−0.98
	CCS	−2.39	−1.37	−7.03	−0.81	−2.90	−2.55	−2.54
	PDIR	−0.71	−0.27	−1.70	−0.27	−1.13	−0.75	−0.70
	Mean	−1.36	−0.62	−4.12	−0.36	−1.43	−1.18	−1.38
∆RB	IMERG	−28.5%	−15.9%	−41.6%	−14.4%	−32.3%	−28.5%	−25.0%
	CMORPH	−29.2%	−17.2%	−40.7%	−14.8%	−32.4%	−39.1%	−25.8%
	GSMaP	−52.6%	−33.2%	−122.1%	−20.8%	−38.3%	−36.5%	−48.7%
	PERSIANN	−41.8%	−19.7%	−86.8%	−15.1%	−39.3%	−33.3%	−36.5%
	CCS	−93.6%	−53.1%	−266.8%	−33.6%	−101.2%	−87.6%	−95.6%
	PDIR	−45.1%	−20.4%	−81.4%	−21.8%	−53.5%	−41.6%	−40.1%
	Mean	−48.5%	−26.6%	−106.6%	−20.1%	−49.5%	−44.4%	−45.3%
∆KGE′	IMERG	0.10	−0.02	0.33	−0.08	0.26	0.20	0.09
	CMORPH	0.11	−0.01	0.31	−0.04	0.21	0.30	0.10
	GSMaP	0.43	0.26	1.19	0.04	0.31	0.30	0.40
	PERSIANN	0.31	0.04	0.83	−0.04	0.29	0.21	0.26
	CCS	0.91	0.49	2.66	0.23	0.98	0.84	0.93
	PDIR	0.34	0.04	0.76	0.07	0.47	0.32	0.30
	Mean	0.37	0.13	1.01	0.03	0.42	0.36	0.35

) of the changes in continuous metrics.

In terms of ∆CC, it shows small values for all six SPPs. The majority of weather stations have ∆CC in the range of 0~0.02. The ∆CCs for six subregions range from 0.001 in TM for CMORPH to 0.012 in AP for PDIR. The small values of ∆CC show that the bias in gauge measurements has little effect on the CC of SPPs. The RB decreases with negative ∆RB in every weather station for each SPP. This is because the precipitation from the gauge increases after removing the negative bias. The negative ∆NRMSEs at all weather stations for six SPPs illustrate that the errors of SPPs will be overvalued if no bias correction is made. The ∆KGE′s are positive at most weather stations for SPPs, except IMERG and CMORPH. IMERG and CMORPH have negative ∆KGE′s at weather stations in TM and QM. For ARNC as a whole, the ∆KGE′s for six SPPs are all positive, and the values range from 0.09 for IMERG to 0.93 for CCS. This result indicates that the accuracies of six SPPs are overall undervalued over ARNC. On the other hand, this also means the gauge bias has the most significant impact on the accuracy assessment of CCS among six selected SPPs. On the regional scale, the ∆KGE′ ranges from −0.08 in QM for IMERG to 2.66 in SX for CCS. Among six subregions, each SPP has the largest |∆KGE′| in SX. This indicates that the accuracy assessment of six SPPs in SX is most affected by gauge bias than in other subregions. The changes in continuous metrics are also varied by different SPPs. Compared to other SPPs, CCS has the largest |∆KGE′| whether in each subregion or ARNC as a whole. This result shows the following: Among six selected SPPs, the gauge bias has the largest impact on the accuracy assessment of CCS, making the accuracy significantly undervalued.

To quantify the impacts of gauge bias on the precipitation detectability assessment of SPPs, we further calculated the changes in categorical metrics. The spatial patterns and regional variability of the changes in categorical metrics were displayed in Figure 4 and

Table 4. The changes of categorical metrics of SPPs in each subregion.

Subregion		NX	TM	SX	QM	HC	AP	ARNC
∆POD	IMERG	−0.06	−0.07	−0.12	−0.05	−0.07	−0.08	−0.08
	CMORPH	−0.04	−0.06	−0.10	−0.03	−0.07	−0.04	−0.07
	GSMaP	−0.05	−0.06	−0.08	−0.04	−0.05	−0.06	−0.06
	PERSIANN	−0.04	−0.06	−0.08	−0.02	−0.04	−0.06	−0.05
	CCS	−0.05	−0.05	−0.09	−0.01	−0.03	−0.04	−0.05
	PDIR	−0.04	−0.05	−0.05	−0.03	−0.03	−0.04	−0.04
	Mean	−0.05	−0.06	−0.09	−0.03	−0.05	−0.05	−0.06
∆FAR	IMERG	−0.19	−0.13	−0.26	−0.09	−0.18	−0.15	−0.18
	CMORPH	−0.18	−0.12	−0.25	−0.08	−0.12	−0.08	−0.15
	GSMaP	−0.21	−0.14	−0.28	−0.09	−0.20	−0.16	−0.20
	PERSIANN	−0.17	−0.12	−0.15	−0.09	−0.13	−0.10	−0.15
	CCS	−0.17	−0.12	−0.12	−0.09	−0.11	−0.08	−0.13
	PDIR	−0.17	−0.13	−0.17	−0.09	−0.13	−0.10	−0.15
	Mean	−0.18	−0.13	−0.21	−0.09	−0.15	−0.11	−0.16
∆FB	IMERG	−0.52	−0.44	−1.13	−0.21	−0.65	−0.65	−0.60
	CMORPH	−0.45	−0.43	−1.11	−0.31	−0.93	−1.40	−0.66
	GSMaP	−0.44	−0.41	−1.28	−0.22	−0.60	−0.65	−0.58
	PERSIANN	−0.70	−0.51	−2.45	−0.24	−0.91	−0.94	−0.90
	CCS	−0.69	−0.54	−2.70	−0.24	−1.11	−1.16	−0.97
	PDIR	−0.87	−0.63	−2.73	−0.29	−1.24	−1.29	−1.09
	Mean	−0.61	−0.49	−1.90	−0.25	−0.91	−1.02	−0.80
∆CSI	IMERG	0.08	0.06	0.10	0.03	0.09	0.08	0.07
	CMORPH	0.05	0.05	0.10	0.05	0.07	0.06	0.06
	GSMaP	0.07	0.05	0.15	0.03	0.10	0.09	0.09
	PERSIANN	0.10	0.06	0.11	0.04	0.08	0.06	0.09
	CCS	0.10	0.07	0.09	0.04	0.07	0.06	0.08
	PDIR	0.12	0.09	0.14	0.06	0.10	0.08	0.11
	Mean	0.09	0.06	0.12	0.04	0.09	0.07	0.08

, respectively.

The categorical metrics were calculated for six SPPs with a precipitation threshold of 0.1 mm/day. The negative ∆POD, negative ∆FAR, negative ∆FB, and positive ∆CSI are seen in almost every station and each cell in Table 4. This demonstrates that gauge bias makes the probability of detection and false alarm rate of six SPPs both overvalued, but the precipitation detectability is undervalued. The increasing number of precipitation events causes negative ∆FB. After correcting the trace loss, the trace precipitation day previously classified as a no precipitation day was presently classified as a precipitation day under the precipitation threshold of 0.1 mm/day, which inevitably increased the number of precipitation events. Among six subregions, each SPP has the largest |∆CSI| in SX. Compared to other SPPs, PDIR has the largest |∆CSI| whether in each subregion or ARNC as a whole. The results show the following: the precipitation detectability assessment of SPPs in SX is most affected compared to that in other subregions. Moreover, among the six selected SPPs, the gauge bias has the largest impact on the precipitation detectability assessment of PDIR, making the precipitation detectability significantly undervalued.

3.2. Seasonal Variations of the Changes of Evaluation Metrics

To explore the seasonal variability of the impacts of gauge bias on the performance evaluation of SPPs, we calculated the changes of continuous metrics and categorical metrics on the seasonal scale, as shown in Figure 5 and Figure 6, respectively.

As seen in Figure 5, the |∆CC|s for all SPPs show low values (smaller than 0.012) in all four seasons. ∆NRMSEs, ∆RBs, and ∆KGE′s for all SPPs show negative, negative, and positive values in all four seasons, respectively, except that ∆KGE′ for IMERG in the spring and ∆KGE′s for IMERG and CMORPH in the winter have negative values. This suggests that the accuracy of six SPPs is undervalued in four seasons by the gauge biases, except for the accuracy of IMERG in the spring and the accuracy of IMERG and CMORPH in the winter, which are overvalued. The ∆NRMSE, ∆RB, and ∆KGE′ show seasonal variation for six SPPs. The ∆NRMSE for each SPP shows the largest value in the winter but the smallest value in the summer. This indicates that the error of SPPs is most overvalued in the winter and least overvalued in the summer. The ∆KGE′s for different SPPs display different seasonal patterns. For example, PERSIANN, CCS, and PDIR have the highest ∆KGE′ in the winter and the lowest ∆KGE′ in the summer. IMERG has negative ∆KGE′ in the spring and winter but positive ∆KGE′ in the summer and autumn. This suggests that the impacts of gauge bias on the accuracy assessment of SPPs show seasonal variations, but the seasonal patterns of the impacts are different for different SPPs.

The same as in Figure 4 and Table 4, the categorical metrics in Figure 6 were also calculated for six SPPs with a precipitation threshold of 0.1 mm/day. The ∆PODs, ∆FARs, ∆FBs, and ∆CSIs for all SPPs show negative, negative, and positive values in all four seasons, respectively. In four seasons, the probability of detection, false alarm rate, and precipitation detectability for six SPPs are overvalued, overvalued, and undervalued, respectively, as indicated by negative ∆PODs, negative ∆FARs, and ∆CSIs. The correction for trace events increases the number of precipitation events, leading to negative ∆FBs. The ∆POD, ∆FAR, ∆FB, and ∆CSI for each SPP all show seasonal variation. For example, the |∆POD|s for IMERG, CMORPH, GSMaP, PERSIANN, and CCS are most significant in summer but most minor in winter. The |∆FAR|s for CMORPH, GSMaP, PERSIANN, CCS, and PDIR are largest in summer but smallest in winter. The ∆CSIs for IMERG, CMORPH, GSMaP, PERSIANN, and PDIR are largest in summer but smallest in winter.

3.3. The Changes of Detection Ability for Different Ranges of Precipitation Intensity

To explore the impacts of gauge data bias on different ranges of precipitation intensity, the ∆CSI for eight ranges of precipitation (i.e., 0–0.1 mm/day, 0.1–1 mm/day, 1–5 mm/day, 5–10 mm/day, 10–15 mm/day, 15–20 mm/day, 20–25 mm/day, and >25 mm/day) were calculated and shown in Figure 7. For 0–0.1 mm/day, the ∆CSIs for six SPPs except PDIR are negative, with the values ranging from −0.03 to −0.01, indicating the detection ability of precipitation events with 0–0.1 mm/day for IMERG, CMORPH, GSMaP, PERSIANN, and CCS is overvalued. For 0.1–1 mm/day, the ∆CSIs for six SPPs, except for CCS and PDIR, range from 0.05 to 0.07, demonstrating the detection ability of precipitation events with 0.1–1 mm/day for IMERG, CMORPH, GSMaP, and PERSIANN is significantly undervalued. As for other ranges of precipitation intensity (>1 mm/day), the |∆CSI|s for six SPPs are within 0.01, indicating the bias of gauge data generally has a relatively small impact on detecting precipitation events with >1 mm/day.

3.4. The Changes of Accuracy for Different Precipitation Phases

The changes in continuous metrics of six SPPs for rain, mixed precipitation, and snow are displayed in

Table 5. The changes of continuous metrics of six SPPs for different precipitation phases.

Metrics	Type	IMERG	CMORPH	GSMaP	PERSIANN	CCS	PDIR
∆CC	Rain	0.007	0.007	0.006	0.007	0.004	0.009
	Mixed	0.005	0.004	0.003	0.009	0.006	0.016
	Snow	0.006	−0.001	0.000	0.008	0.006	0.014
∆NRMSE	Rain	−0.65	−0.53	−1.69	−0.66	−1.52	−0.55
	Mixed	−0.50	−0.48	−3.76	−1.24	−3.70	−0.64
	Snow	−1.34	−1.84	−13.42	−4.46	−13.75	−1.68
∆RB	Rain	−24.7%	−24.9%	−41.1%	−28.3%	−57.9%	−35.8%
	Mixed	−13.1%	−17.9%	−38.6%	−40.1%	−157.9%	−35.4%
	Snow	−21.6%	−26.3%	−135.4%	−128.2%	−531.2%	−78.6%
∆KGE′	Rain	0.14	0.13	0.36	0.17	0.54	0.27
	Mixed	−0.10	−0.03	0.03	0.28	1.56	0.21
	Snow	−0.21	−0.22	0.94	1.20	5.30	0.62

. The ∆CCs for six SPPs are still small, with the values ranging from −0.001 to 0.016, showing bias in gauge data has a small impact on the correlation evaluation of SPPs for three precipitation phases. The ∆NRMSEs and ∆RBs of six SPPs are negative for rain, mixed precipitation, and snow. This suggests the errors and relative biases of SPPs for three precipitation types are all overvalued. The ∆KGE′s of SPPs are positive for all three precipitation phases, except IMERG and CMORPH have negative ∆KGE′s for mixed precipitation and snow. This result manifests that the accuracies of six SPPs for rain, mixed precipitation, and snow are undervalued, except that the accuracies of IMERG and CMORPH are overvalued for mixed precipitation and snow. Moreover, the |∆NRMSE|s, |∆RB|s, and |∆KGE′|s of six SPPs for snow are generally higher than those for rain, which demonstrates that gauge data bias has greater impact on the accuracy assessment of snow estimation than that of rain estimation for six SPPs. This might be caused by the lower catch ratio of snow than rain. Besides, the accuracy assessment of CCS for rain, mixed precipitation, and snow is most affected by gauge data bias compared to that of other SPPs, as shown by that the |∆NRMSE|, |∆RB|, and |∆KGE′| of CCS are all the largest among six SPPs for each precipitation phase.

3.5. The Performance of SPPs before Bias Correction and after Bias Correction

Due to the synthesized attributes of KGE′ and CSI, we used them to evaluate the overall accuracy and detection capability of precipitation events for six SPPs, respectively. The KGE′s and CSIs of SPPs before bias correction and after bias correction are shown in

Table 6. The RB, KGE′, FB, and CSI of SPPs before bias correction and after bias correction over the whole ARNC.

Product		IMERG	CMORPH	GSMaP	PERSIANN	CCS	PDIR
RB	RB_B	28.8%	33.1%	150.9%	88.2%	393.2%	106.9%
	RB_A	3.8%	7.3%	102.3%	51.7%	297.5%	66.8%
KGE′	KGE′_B	0.40	0.27	−0.69	−0.20	−3.05	−0.38
	KGE′_A	0.49	0.37	−0.29	0.06	−2.12	−0.08
FB	FB_B	0.57	0.71	0.50	1.34	1.52	1.84
	FB_A	−0.04	0.05	−0.08	0.44	0.55	0.74
CSI	CSI_B	0.35	0.28	0.34	0.25	0.23	0.26
	CSI_A	0.42	0.34	0.43	0.34	0.31	0.37

Note: RB_B, KGE′_B, FB_B, and CSI_B represent the RB, KGE′, FB, and CSI of six SPPs before bias correction of gauge data. RB_A, KGE′_A, FB_A, and CSI_A represent the corresponding metrics after bias correction of gauge data.

.

To explain why the changes in KGE′ and CSI happened after bias correction, we also calculated RB and FB of SPPs before bias correction and after bias correction, which are also displayed in Table 6. The FB and CSI were calculated with a precipitation threshold of 0.1 mm/day. As seen from Table 6, the KGE′s and CSIs of all six SPPs increase after bias correction, which means that the accuracy and precipitation detection capability of all six SPPs are undervalued if evaluating using the unadjusted gauge data. The reason for this result is as follows: The six SPPs all overestimate the precipitation amount and the number of precipitation events, which is confirmed by the positive RBs and FBs both before bias correction and after bias correction. After removing the negative bias inherent in gauge measurements, the gauge precipitation amount increases. Moreover, after correcting the trace events loss, a number of trace events previously classified as no precipitation events were now classified as precipitation events, leading to the increasing number of precipitation events from the gauge. As a result, the bias magnitudes of six SPPs in precipitation amount and the number of precipitation events both significantly decrease after bias correction, which is demonstrated by the decreasing absolute value of RB and FB. This in turn causes the increasing KGE′s and CSIs of all the six SPPs. Over the whole ARNC, whether before bias correction or after bias correction, IMERG has the largest KGE′ among the six SPPs. For CSI, the two largest CSIs occur for IMERG and GSMaP, and these values are very close. Taking these together, it can be concluded that IMERG has the highest performance among six SPPs and therefore is the most appropriate product for applications over the ARNC. In addition, although PERSIANN, CCS, and PDIR provide more precipitation detail with high resolution (0.04°), their performance is relatively bad (low KGE′ and CSI) in ARNC. Last but not the least, the performances of all six SPPs are still not good enough with the highest KGE′ and CSI just reaching 0.49 and 0.43, respectively. Therefore, further efforts are needed to further improve the performance of SPPs.

4. Summary and Discussion

Summarizing the above results, we found that the bias of the gauge makes the overall performances of all six SPPs undervalued over the whole ARNC, which indicates that the application potential of SPPs in ARNC will be underestimated if directly using gauge data as an evaluation benchmark without removing bias. After removing the negative bias inherent in gauge measurements, the precipitation amount and the number of precipitation events from the gauge increase, which reduced the overestimation magnitude of six SPPs in precipitation amount and the number of precipitation events. Therefore, the absolute values of RB and FB decline along with decreasing RMSE, POD, and FAR, which contribute to the increasing KGE′ and CSI. These results suggest that the performance evaluation of SPPs in other regions may also be affected by the gauge bias and further works should be performed to investigate the impacts of gauge bias on the performance assessment of SPPs in other regions. In addition, the CC of SPPs after bias correction hardly changes, which indicates that the correlation between SPPs and gauge data is robust to the bias in gauge measurements. This is because the bias-corrected gauge data has a significant linear correlation with the original measured gauge data (see Figure 8; the determination coefficient R² reaches 0.99).

Among six SPPs, IMERG shows the best performance, which can be explained by the massive input data and advanced retrieval algorithms. IMERG integrates “all” satellite microwave precipitation estimates, microwave-calibrated infrared (IR) satellite estimates, and potentially other precipitation estimators for the TRMM and GPM eras over the entire globe [10]. The algorithm of IMERG incorporates multiple techniques from other SPPs, that is, the morphing technique from CMORPH, the IR precipitation estimation method from PERSIANN, and intercalibration and bias-adjustment algorithms from TMPA (Tropical Rainfall Measuring Mission Multi-Satellite Precipitation Analysis) [10]. Three IR-based precipitation estimation products, PERSIANN, CCS, and PDIR, although with higher resolution, do not show superior performance to a passive microwave (PMW)-based IMERG. This is because IR imagery only provides information on cloud-top characteristics, but PMW sensors provide rich information on the vertical profile of the atmosphere and hydrometeors directly related to precipitation [14]. Moreover, the performances of all six SPPs over ARNC are still not very satisfactory over ARNC. This might be caused by the sub-cloud evaporation [57] and the complex terrain. Over arid regions, the atmospheric conditions beneath the clouds are mostly dry. As a consequence, precipitation detected by satellites will evaporate before reaching the surface. The terrain is complex over ARNC; mountains and basins are distributed alternately, and deserts and oases coexist. Therefore, the variability of precipitation patterns over this region is high and hard to be completely captured by the satellites. Besides, efforts are needed to develop more advanced algorithms and integrate more earth observation data for SPPs to provide more accurate gridded SPPs over ARNC. Alternatively, SPPs can be merged with ground precipitation observation (gauge or radar observations) and reanalysis precipitation products to provide multi-source precipitation fusion products with high accuracy, which will especially be useful for regions with scarce ground precipitation observations, for example, ARNC.

The impacts of gauge data bias on the performance assessment of SPPs are different for different SPPs and vary by different subregions, seasons, ranges of precipitation intensity, and precipitation phases. Two reasons may account for this result. First, different algorithms of six SPPs lead to different performances of the SPPs. The algorithms of PERSIANN, CCS, and PDIR belong to the category of techniques called the “Euler approach” [14,58]. Using collocated IR and PMW data, this category develops a spatiotemporally dependent empirical link between precipitation intensity and cloud-top temperature. The algorithms of CMORPH, GSMaP, and IMERG adopted the second category of techniques, the “Lagrangian approach” [43,58]. Using the precipitation cloud system moving vector computed from consecutive IR images, the “Lagrangian approach” propagates and interpolates the estimated instantaneous rain rates from the PMW observations. Second, the correction factors (the ratio of the corrected gauge precipitation to the measured gauge precipitation) differ by different regions, seasons, precipitation phases, and ranges of precipitation intensity. Ye et al. [26] found the correction factor varies from 15% to 250% over the arid region in Northwest China. Zhang et al. [37] found the correction factor for light rain intensity could reach 40%, and the correction factor for rainstorm events could reach as high as 18% in some regions of northwest China. Because snow dominates in winter (the ratio of snow in precipitation events is 84.3% in winter) and almost all the precipitation events are rain in summer (the ratio of rain in precipitation events is near 100% in summer) in the study area, the correction factor is larger in winter than in summer. The catch ratio of snow is less than that of rain because snow is more susceptible to wind than rain [26,27,35]. This leads to a higher correction factor for snow than for rain.

This study belongs to the family of studies on the impacts of the gauge bias on downstream applications of gauge data over China. Zhang et al. [37] investigated the effect of the gauge bias on precipitation climatology over Mainland China, and they found that the actual amounts of precipitation, snowfall, and intense rainfall were much higher than previously measured over China. Li et al. [31] redivided the climatic zones in China using the bias-corrected gauge data, and they found that the areas of severe arid decreased, but the areas of severe humid areas increased compared to the climate zone division using the original gauge data. Yao et al. [35] studied the effects of the gauge bias on aridity and drought assessment in China. The results show that climate type changed after correcting the gauge bias, for example, some sites from severe arid to arid and others from arid to semi-arid. These studies and the results of this paper prove that the bias of gauge data will inevitably affect applications that use gauge data as an input. Therefore, further efforts are needed to study the effects of gauge bias on other downstream applications of gauge data.

The network of weather stations used in this study is uneven and relatively sparse, with a density of 0.43 stations per 10,000 km². The weather stations in NX and SX are mainly distributed on the edges of the Junggar Basin and the Tarim Basin. Only four weather stations are located in AP. A high-density network of weather stations will substantially improve the reliability of the impact analyses of gauge data bias on the evaluation of SPPs. Limited by the density of the weather station, we adopted a pixel-to-point strategy with the assumption that the point-scale precipitation observation is equal to the areal precipitation estimates and the mismatch between point-measured gauge data and areal estimates from SPPs is neglected. Last but not least, some uncertainties exist in the bias-correction method for gauge measurements. We used two air temperature thresholds to classify the precipitation phase. This simple scheme may cause misclassification of the precipitation phase in some cases. It is expected to develop a parameterization scheme for more accurate precipitation phase classification based on the relationship between various geophysical variables and the precipitation phase. It has been suggested that the wind speed at the gauge level should be used to establish equations for catch ratios [59]. The wind speed at gauge orifice height can be estimated from the wind speed at standard height. Reducing wind at standard height to the gauge orifice height should consider gauge exposure. However, the station metadata about gauge exposure was not available, so wind speed at the gauge orifice height could not be obtained to calculate the catch ratios. The daily mean wind speed at 10 m height available at the weather station was used instead. Moreover, wind speed can vary during a 24-h day, and therefore the daily mean wind speed applied to correct wind undercatch may not accurately reflect the simultaneous wind speed at the time of the precipitation occurs in some cases. Hourly data is desirable, but high-quality hourly precipitation and wind speed data are currently unavailable.

5. Conclusions

This study has analyzed the impacts of gauge data bias on the performance evaluation of IMERG, CMOPRH, GSMaP, PERSIANN, CCS, and PDIR. Calculating the evaluation metrics of the six SPPs using the measured gauge precipitation and the corrected gauge precipitation as a baseline, respectively, the changes in evaluation metrics of these SPPs can be obtained. Based on the results of current analyses, the impact of bias in gauge measurements can be concluded as follows:

• Over ARNC, the overall performances of six SPPs are undervalued by the gauge bias. For different aspects of performance, the bias makes the error, the probability of detection, and the false alarm rate of SPPs overvalued, and the relative bias and frequency bias undervalued. The correlation of SPPs is robust to the bias in gauge measurements;
• Whether before bias correction or after bias correction, the performance of IMERG is best over ARNC among six SPPs. PERSIANN, CCS, and PDIR, despite providing more precipitation details (higher resolution), do not show superior performance among the selected SPPs. The performances of all six SPPs are still not very satisfactory even after bias correction and needed to be improved for applications in ARNC;
• For different subregions, seasons, SPP, precipitation intensity, and precipitation phase, the impacts of gauge bias on the performance assessment are different. Among six subregions, the performance (accuracy and the detectability of precipitation events) assessment is most affected by gauge bias in SX. Compared to other SPPs, the accuracy of CCS and the detection ability of PDIR are the most undervalued, respectively. Each SPP shows a seasonal pattern of the impacts of bias, but the seasonal patterns vary across different SPPs. For different ranges of precipitation intensity, the detection ability of precipitation events with 0.1–1 mm/day for IMERG, CMORPH, GSMaP, and PERSIANN is significantly undervalued, but the impact of bias on the detection ability of precipitation events with >1 mm/day for six SPPs seems small. The impact of gauge bias on the accuracy assessment of snow estimation is more significant than that of rain estimation for six SPPs.