Does ERA5-Land Effectively Capture Extreme Precipitation in the Yellow River Basin?

Abstract

ERA5-Land is a valuable reanalysis data resource that provides near-real-time, high-resolution, multivariable data for various applications. Using daily precipitation data from 301 meteorological stations in the Yellow River Basin from 2001 to 2013 as benchmark data, this study aims to evaluate ERA5-Land’s capability of monitoring extreme precipitation. The evaluation study is conducted from three perspectives: precipitation amount, extreme precipitation indices, and characteristics of extreme precipitation events. The results show that ERA5-Land can effectively capture the spatial distribution patterns and temporal trends in precipitation and extreme precipitation; however, it also exhibits significant overestimation and underestimation errors. ERA5-Land significantly overestimates total precipitation and indices for heavy precipitation and extreme precipitation (R95pTOT and R99pTOT), with errors reaching up to 89%, but underestimates the Simple Daily Intensity Index (SDII). ERA5-Land tends to overestimate the duration of extreme precipitation events but slightly underestimates the total and average precipitation of these events. These findings provide a scientific reference for optimizing the ERA5-Land algorithm and for users in selecting data.

1. Introduction

Extreme precipitation refers to the phenomenon of a large amount of rainfall occurring in a short period. Extreme precipitation poses numerous hazards, including flooding, collapses, landslides, mudslides, urban waterlogging, and the triggering of secondary disasters such as debris flows. These events threaten human safety and economic and social development [1,2,3,4,5]. In the context of climate change, the frequency and intensity of extreme precipitation events in China have increased in recent years [6,7]. Studies indicate that, in future scenarios, the intensity and frequency of extreme precipitation are expected to further increase in most regions of China [8,9].

Currently, precipitation data come from various sources, mainly including station observations, remote sensing retrievals, and reanalysis data. Station observations are typically obtained through rain gauges or ground-based weather radar. Rain gauges are widely regarded as providing accurate ground data, but they are influenced by factors such as the time of station establishment, uneven station distribution, instrument accuracy, unique terrain, and human operation, which result in poor spatial representation [10]. Ground-based weather radar can provide areal precipitation data but is expensive, has limited spatial coverage, and exhibits significant uncertainty in complex terrains [11,12].

Remote sensing data have the advantages of wide coverage and good spatial representation, but their accuracy is affected by the choice of retrieval algorithm and the source of the remote sensing data [13,14]. Reanalysis of precipitation data is generated by integrating meteorological models with observational data, combining multiple data sources to provide high consistency, strong continuity, high timeliness, high spatial and temporal resolution, and long time series. This is particularly important in data-scarce regions [15]. However, the accuracy of reanalysis of precipitation data also varies depending on data sources and analysis models [15,16].

ERA5 is a global reanalysis dataset released by the European Centre for Medium-Range Weather Forecasts (ECMWF) [17]. It provides continuous atmospheric fields from 1979 to the present, covering multiple parameters of the surface, atmosphere, and ocean. This dataset is characterized by high spatial and temporal resolution, fast updates, and a wide range of parameters, making it widely recognized and utilized. Research indicates that ERA5 represents a significant improvement over ECMWF’s fourth-generation reanalysis product, ERA-Interim [18,19]. ERA5-Land is a global land reanalysis dataset produced by ECMWF based on ERA5, specifically targeting land surfaces. It provides high-spatial- and high-temporal-resolution data (0.1 degrees monthly/hourly) for over 50 variables [17]. This dataset offers valuable resources for studying land surface processes, monitoring terrestrial hydrological changes, and analyzing vegetation dynamics [20].

In recent years, many scholars have increasingly studied the applicability of ERA5-Land, making significant progress in areas such as precipitation, drought, and temperature [21,22,23,24,25,26,27,28]. Some scholars have conducted systematic quantitative analyses of the accuracy of ERA5 in terms of precipitation [15,23,29,30,31,32]. Research has found that ERA5 precipitation data effectively reflect the actual spatial distribution patterns and seasonal changes in precipitation, although various errors still exist [15,30]. For example, the accuracy of ERA5 precipitation data is affected by complex terrains and arid climates [33,34,35], leading to poor performance in hydrological simulations [23]. Jiao et al. [30] found that the accuracy of ERA5-Land precipitation products is strongly correlated with topography and climate. Some scholars have also evaluated the error characteristics of ERA5-Land in extreme precipitation. For instance, Espinosa et al. [27] evaluated the accuracy of ERA5-Land in capturing extreme precipitation over 42 hydrological years in Portugal based on station observations, finding potential for its application in extreme precipitation scenarios. Xu et al. [36] compared ERA5-Land with remote sensing precipitation retrieval data in China, finding that ERA5-Land effectively reflects the spatial distribution patterns of actual precipitation but significantly underestimates extreme precipitation. Conversely, Wang et al. [37] pointed out that ERA5-Land tends to overestimate precipitation. Jiang et al. [15] noted significant regional differences in the performance of ERA5-Land in China, with weak capability in capturing precipitation events, particularly for moderate to heavy precipitation events exceeding 10 mm/day.

Most of the above studies have evaluated the capability of ERA5-Land to capture precipitation or extreme precipitation based on precipitation statistical indices or extreme precipitation indices, overlooking the continuity and persistence characteristics of precipitation. Precipitation events are continuous over time, and extreme precipitation is an extreme type within these events [38]. Therefore, it is necessary to assess the accuracy of ERA5-Land precipitation data from various perspectives such as precipitation capture capability, extreme precipitation indices, and extreme precipitation events. This approach would be beneficial for improving ERA5-Land precipitation retrieval algorithms.

The Yellow River Basin faces ecological fragility, and frequent occurrences of extreme precipitation events, which easily trigger floods, exacerbate soil erosion, and threaten the safety of people’s lives and property. Studies have found that the intensity of extreme precipitation events in the Yellow River Basin has significantly increased, which is a key factor contributing to changes in the basin’s water–sediment relationship [39,40]. However, to our knowledge, there has been no systematic evaluation of ERA5-Land’s ability to capture extreme precipitation in the Yellow River Basin.

This study plans to systematically evaluate the error characteristics of ERA5-Land precipitation products in extreme precipitation aspects using data from 301 meteorological stations in the Yellow River Basin from 2001 to 2013. The evaluation was conducted from three perspectives: precipitation error, extreme precipitation index error, and characteristics of extreme precipitation event errors. This will be achieved through conventional error evaluation metrics, extreme precipitation indices, and run theory methods. The objective is to confirm the accuracy and utility of ERA5-Land in capturing extreme precipitation events, thereby validating its applicability for similar studies in other regions. Meanwhile, it can provide scientific references for improving ERA5-Land algorithms and support the implementation of national strategies for ecological protection and high-quality development in the Yellow River Basin.

2. Data and Methods

2.1. Study Area

The Yellow River Basin is located in East Asia (32.15° N–41.87° N, 95.87° E–119.07° E). The terrain slopes from west to east with significant surface undulations (Figure 1c). Figure 1a shows the geographical location of the Yellow River Basin in China. Originating in the Bayan Har Mountains on the Tibetan Plateau, the mainstream of the Yellow River extends 5464 km. The basin covers an area of 795,000 km² [41]. The upper river, above Toktor Hekou, primarily flows through the Tibetan Plateau and Inner Mongolia Plateau. The middle river, from Toktor Hekou to Taohuayu, traverses the Loess Plateau. The lower river, below Taohuayu, flows through the North China Plain. The region has a diverse and complex climate, with annual precipitation ranging from 200 mm to 600 mm, exhibiting significant spatial distribution differences. It encompasses arid, semi-arid, and semi-humid regions, with uneven seasonal precipitation distribution, substantial interannual variability, low humidity, high evaporation, and frequent droughts. Most of the upper basin and middle basin lies west of the 400 mm isohyet, characterized by arid and low rainfall conditions, with the long-term average precipitation being only 40% of that in the Yangtze River Basin.

2.2. Datasets

2.2.1. Station Observations

The observed precipitation data from meteorological stations were obtained from the China Meteorological Administration (http://data.cma.cn, accessed on 11 August 2022). All stations are national-level meteorological stations. The station data used in this study underwent strict quality control and inspection, including removing invalid values, extreme value tests, internal consistency checks, and spatial consistency checks [10]. To ensure the scientific validity and reliability of the study, we excluded stations with missing precipitation data between January 2001 and December 2013. Ultimately, we retained 301 stations with complete data that had a data availability rate of 100% during the study period. There are 115 stations in the upper basin, 159 stations in the middle basin, and 27 stations in the lower basin. The distribution of these stations is shown in Figure 1c.

2.2.2. ERA5-Land Dataset

ERA5-Land originates from the European Centre for Medium-Range Weather Forecasts (ECMWF) website (https://cds.climate.copernicus.eu, accessed on 20 October 2023). Its original spatial resolution is 0.1° × 0.1° with a temporal resolution of hourly or monthly scales [17,20,42], and it provides data on over fifty land surface variables, including precipitation, temperature, and evaporation. The ERA5-Land dataset has significant advantages such as high resolution, long time series, and multiple meteorological variables [43]. These advantages make it widely applicable for various small-scale climate and environmental studies, and it provides a solid foundation for climate change trend analysis and long-term climate research. In this study, hourly precipitation data from 2001 to 2013 were obtained. To maintain consistency with the station observations, the hourly precipitation data were aggregated to daily scales.

2.3. Methods

2.3.1. Evaluation Indices

This study uses relative bias (RB), correlation coefficient (CC), and root mean square error (RMSE) to quantify the evaluation of ERA5-Land’s ability to capture precipitation, reproduce extreme precipitation, and replicate the characteristics of extreme precipitation events [44]. The specific formulas are provided in

Table 1. The formula of evaluation indices.

Name	Formula	Optimal Value
Relative bias (RB)	RB =${\displaystyle \frac{{\sum }_{i=1}^n(S_i-O_i)}{{\sum }_{i=1}^n{O}_i}}\times 100\%$	0
Correlation coefficient (CC)	CC =${\displaystyle \frac{{\sum }_{i=1}^n\left(S_i-\overline{S}\right)\left(O_i-\overline{O}\right)}{\sqrt{{\sum }_{i=1}^n(S_i-\overline{S}{)}^2}\sqrt{{\sum }_{i=1}^n(O_i-\overline{O}{)}^2}}}$	1
Root mean square error (RMSE)	RMSE =$\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n(S_i-O_i{)}^2}$	0

$S_i$ represents the ERA5-Land precipitation values, $O_i$ represents the observed precipitation values from meteorological stations, $\overline{S}$ and $\overline{O}$ are the mean values of the ERA5-Land and station-observed precipitation sequences over the evaluation period, respectively, and n is the total number of samples.

.

CC represents the correlation coefficient, signifying the level of agreement between ERA5-Land model outputs and in situ observational data. RB quantifies the proportional discrepancy between the ERA5-Land estimates and ground-truth measurements. RMSE assesses the average magnitude of the deviations across all data points.

2.3.2. Extreme Precipitation Indices

This study uses ten extreme precipitation indices defined by the World Meteorological Organization (WMO) Commission for Climatology and the Expert Team on Climate Change Detection and Indices (ETCCDI) to evaluate the capability of ERA5-Land in capturing various aspects of extreme precipitation [45]. These indices include PRCPTOT, R20mm, R10mm, CDD, CWD, RX1day, RX5day, SDII, R95pTOT, and R99pTOT. Among them, PRCPTOT, RX1day, RX5day, R95pTOT, and R99pTOT are precipitation amount indices; CDD, CWD, R20mm, and R10mm are precipitation frequency indices; and SDII is a precipitation intensity index. The specific extreme precipitation indices and their definitions are provided in

Table 2. Definition of extreme precipitation indices.

Index	Description	Unit
PRCPTOT	Total wet day precipitation (mm) in the year	mm
R10mm	Number of days in the year with rainfall greater than 10 mm	days
R20mm	Number of days in the year with rainfall greater than 20 mm	days
RX1day	Maximum daily rainfall amount (mm) in the year	mm
RX5day	Maximum rainfall amount (mm) over five consecutive days in the year	mm
R95pTOT	Total rainfall (mm) in the year from days exceeding the 95th percentile	mm
R99pTOT	Total rainfall (mm) in the year from days exceeding the 99th percentile	mm
CDD	Maximum number of consecutive drought days (<1 mm) in the year	days
CWD	Maximum number of consecutive wet days (≥1 mm) in the year	days
SDII	Simple Daily Intensity Index. The ratio of total yearly rainfall to the number of yearly wet days (≥1 mm)	mm/day

.

2.3.3. Extreme Precipitation Event and Its Characteristics

A precipitation event is defined as a sequence of precipitation days where at least one day exceeds the effective precipitation threshold of 1 mm/day. If during this sequence, at least one day exceeds the extreme precipitation threshold, the event is classified as an extreme precipitation event (EPE); otherwise, it is classified as a regular precipitation event [46]. Due to the varied precipitation patterns at each station, establishing a single, uniform threshold for extreme precipitation does not reflect the actual variability. Consequently, this study employs the percentile approach to ascertain the threshold for extreme precipitation, specifically utilizing the 90th percentile of daily rainfall as the benchmark.

Once EPEs are identified, their characteristics can be quantified. The capacity of remote sensing data to detect EPEs can be assessed through these quantified attributes. To characterize an EPE, five fundamental metrics are primarily utilized: event duration (ED), event total precipitation (ET), event mean precipitation (EM), event peak value (EP) and event frequency (EF). ED is the time difference between the end time (TE) and the start time (TS) of an EPE, primarily measuring the length of the event. ET is the total precipitation during an EPE, used to assess the severity of the event. The ratio of the ET to ED gives the EM, describing the event’s intensity. Additionally, the maximum precipitation during an EPE is referred to as EP, also indicating the event’s intensity. Figure 2 illustrates the definition and characteristics of EPEs. Furthermore, by counting the total number of EPEs within a specified time frame, we can determine EF, which describes the variation in the occurrence of EPEs across different regions.

$$ED=TE-TS$$

(1)

$$EP=\underset{\mathit{TS}\le t\le \mathit{TE}}{\mathit{max}}{P}_t$$

(2)

$$ET={\int }_{TS}^{TE}{P}_t$$

(3)

$$EM={\displaystyle \frac{ET}{ED}}={\displaystyle \frac{{\int }_{TS}^{TE}{P}_t}{TE-TS}}$$

(4)

3. Results

This study is divided into three phases. Initially, the study focuses on the acquisition and preprocessing of both station observations and ERA5-Land. Subsequently, the second phase entails the computation of quantitative precipitation metrics, including those specific to extreme precipitation events. The final phase involves an in-depth spatiotemporal analysis to assess the efficacy of ERA5-Land in capturing the nuances of extreme precipitation. Figure A1 shows the details.

3.1. Evaluation of ERA5-Land for Reflecting Precipitation Amount

Precipitation in the Yellow River Basin generally exhibits a pattern of higher amounts in summer and autumn and lower amounts in winter and spring, with the majority of rainfall occurring from May to September (Figure 1b). Precipitation levels fluctuate across different sub-basins and throughout the months. Notably, the upper basin typically receives less monthly rainfall than the overall basin average. Except during May, June, and October, there is a general downward trend in precipitation in the lower basin, middle basin, and upper basin during the year.

The average annual precipitation and annual precipitation days in the Yellow River Basin based on ERA5-Land and station observations have the same variation trend. They all show an increasing trend from the northwest to the south. However, the average annual precipitation and annual precipitation days in the upper basin have great spatial differences. The middle basin and lower basin are relatively small. According to statistics, ERA5-Land significantly overestimated stations with annual precipitation greater than 600 mm/year (Figure 3a), and stations with annual precipitation days greater than 60 days (Figure 3b). Only forty-nine station observations monitor annual precipitation between 600 mm and 800 mm per year, while ERA5-Land captures one hundred and thirty-one stations within this range. The number of ERA5-Land monitoring stations with annual precipitation greater than 800 mm/year is thirty-seven more than that of stations based on observations. The number of stations with precipitation days between 60 days and 120 days based on station observations is one hundred and fifty-seven fewer than that of stations with precipitation days captured by ERA5-Land. ERA5-Land has identified thirty-two stations with more than 120 days of precipitation. Meanwhile, the number of precipitation days of three hundred and one stations based on station observations is less than 120 days.

To assess the performance of ERA5-Land in estimating precipitation, this section evaluates it from two perspectives: spatial distribution patterns and temporal evolution. Figure 4a–c show the spatial distribution of RB, CC, and RMSE for daily precipitation from ERA5-Land and station observations from 2001 to 2013.

More than 72% of the stations have an RB within the range of −20% to 40%, primarily distributed in the lower basin, most of the middle basin, parts of the Ordos Plateau in the upper basin, and some central areas of the Loess Plateau (Figure 4a). The RB is larger in most areas of the western and central upper basin, with RB reaching up to 100%. The CC is relatively high (greater than 0.5) in the southern middle basin and some southeastern parts of the upper basin, while the correlation is lower (CC < 0.5) in most areas of the upper basin and lower basin (Figure 4b). The spatial distribution of RMSE shows a pattern of low values in the northwest and high values in the southeast. The RMSE is generally below 6 mm/day in the upper basin, slightly higher in the middle basin, and exceeds 7 mm/day at most stations in the lower basin (Figure 4c). This pattern is mainly related to the overall rainfall distribution in the region, with less rainfall in the northwest and more in the southeast.

3.2. Evaluation of ERA5-Land for Reflecting Extreme Precipitation Indices

Extreme precipitation indices are vital for evaluating extreme precipitation. This study assesses ERA5-Land’s ability to capture extreme precipitation amounts and frequencies based on ten extreme precipitation indices. Figure 5 illustrates the spatial distribution of the relative errors in extreme precipitation indices between ERA5-Land and station observations.

Figure 5a shows the RB of the SDII, ranging from −40.52% to 8%, with 98% of areas showing negative SDII and 96% of stations having an SDII between −30% and 10%, indicating relatively small relative bias. The RB of the SDII in the lower basin is −26.31% (

Table A1. Extreme precipitation index error evaluation table in the Yellow River Basin.

	Yellow River Basin			Upper			Middle			Lower
	RB	CC	RMSE	RB	CC	RMSE	RB	CC	RMSE	RB	CC	RMSE
PRCPTOT	26.02	0.72	156.06	38.12	0.68	172.16	20.79	0.64	142.71	7.78	0.73	134.01
SDII	−18.35	0.53	2.13	−16.03	0.42	1.60	−18.68	0.60	2.21	−26.31	0.57	3.97
R10mm	21.13	0.60	5.18	25.73	0.46	5.23	18.91	0.67	5.23	15.55	0.76	4.82
R20mm	1.36	0.47	2.69	3.38	0.35	2.28	0.93	0.55	2.88	−3.60	0.51	3.39
RX1day	−11.15	0.17	25.49	−6.32	0.17	17.90	−13.26	0.17	27.95	−19.33	0.12	43.33
RX5day	3.03	0.38	31.37	8.23	0.33	24.57	0.80	0.45	32.47	−6.01	0.17	53.84
R95pTOT	28.71	0.40	53.17	43.67	0.38	48.77	20.78	0.43	54.01	12.65	0.28	68.50
R99pTOT	38.28	0.18	34.69	27.94	0.22	23.82	40.47	0.17	37.03	97.73	−0.02	63.24
CDD	−24.45	0.48	18.36	−35.16	0.36	25.85	−18.73	0.53	13.90	−12.38	0.69	12.69
CWD	61.38	0.42	3.83	76.61	0.38	4.60	49.54	0.48	3.33	64.90	0.25	3.43

Note: The RB units are in % for all extreme precipitation indices. The RMSE units are in mm for PRCPTOT, RX1day, RX5day, R95pTOT, and R99pTOT; mm/day for SDII; and days for R10mm, R20mm, CDD, and CWD.

). Specifically, the SDII of the stations in the middle basin is concentrated at 9–11 mm/day, and the SDII of ERA5-Land is concentrated at 7–9 mm/day (Figure A2a,b). This suggests that ERA5-Land tends to underestimate average daily precipitation intensity.

PRCPTOT increases from north to south in the Yellow River Basin (Figure A2c,d). The RB of the PRCPTOT in the upper basin is 38.12% (Table A1). Figure 5b displays the RB of the PRCPTOT, ranging from −28.63% to 153.26%. About 94.7% of the stations show an overestimation error (RB > 0%), with 22.6% of stations having PRCPTOT overestimation errors exceeding 40%, mainly in the southwestern upper basin. This indicates a severe overestimation of total precipitation by ERA5-Land. Sub-basin analysis shows the upper basin has the highest RB and RMSE, performing the worst, while the middle basin and lower basin perform relatively better.

Using ERA5-Land, the R95pTOT and R99pTOT are too high in the southern Yellow River Basin (Figure A2i,j and Figure A3a,b). For R95pTOT and R99pTOT, ERA5-Land also shows significant overestimation issues, with 89.7% and 68.44% of stations, respectively, showing overestimation errors. The RB of R95pTOT in the upper basin is 43.67% (Table A1). For R95pTOT, 16.9% of stations have an RB greater than 50%, and only about 10% of stations show slight underestimation errors, mainly in the middle basin and lower basin (Figure 5e). The RB of R99pTOT is larger, with 36% of stations having R99pTOT overestimation errors greater than 50%, most notably in the northern and lower basin (Figure 5f). The RB of R99pTOT in the lower basin is 97.73% (Table A1).

Additionally, The RX1day values of the stations in the middle basin are widely distributed from 60 mm to 70 mm, and the RX1day values using ERA5-Land are widely distributed from 40 mm to 50 mm. In the lower basin, 92.6% of stations have an RX1day larger than 70 mm, but only 25.9% of ERA5-Land’s RX1day is greater than 70 mm (Figure A2e,f). ERA5-Land tends to underestimate RX1day in the Yellow River Basin, with 74.1% of stations having negative RB, but overestimates RX5day, with 68.4% of stations showing overestimation errors (Figure 5c,d).

R10mm and R20mm increase from northwest to southeast in the basin (Figure A3c–f). In terms of the number of rainy days, ERA5-Land tends to overestimate the number of days with precipitation greater than 10 mm/day, with 88.7% of stations showing overestimation and 47.5% of stations having an average overestimation error greater than 20% (Figure 5g). For the RB values of R20mm in the Yellow River Basin, 55.5% are negative, and 8.0% are greater than 40%, mainly in the southern basin (Figure 5h). This indicates a significant overestimation of low-intensity rainy days by ERA5-Land.

The CDD values obtained based on ERA5-Land in the middle and south of the basin are significantly lower than those observed at the stations. In the middle basin and southern Yellow River Basin, the calculated CDD of ERA5-Land is less than 35 days, but the CDD of the stations is between 35 days and 70 days (Figure A3g,h). In the Yellow River Basin, ERA5-Land significantly underestimates the CDD and overestimates the CWD, with 99.3% of stations having a negative RB of the CDD, averaging −23.81% (Figure 5i). ERA5-Land overestimates the CWD at all stations, with 42.9% of stations having CWD relative biases greater than 60% (Figure 5j). The CWD of most stations is less than 9 days, but the CWD of 23.3% of stations calculated based on ERA5-Land is greater than 9 days (Figure A3i,j).

Figure 6 depicts the spatial distribution of correlation coefficients for ten extreme precipitation indices derived from both ERA5-Land and station observations. Regarding precipitation intensity, the correlation coefficients for SDII span from −0.67 to 0.92 between ERA5-Land and station observations. Approximately 53.2% of the stations exhibit SDII correlations within the range of 0.5 to 0.8, while 8% of the stations demonstrate correlations surpassing 0.8. The correlation coefficients are generally lower in the upper basin (CC = 0.42), peak in the middle basin (CC = 0.6), and are moderate in the lower basin (CC = 0.57), as illustrated in Figure 6a and detailed in Table A1. Regarding total precipitation, ERA5-Land shows good agreement, with 62.1% of stations indicating PRCPTOT correlations between 0.5 and 0.8, and 31.2% of stations showing correlations from 0.8 to 1. In particular, the highest correlations are seen in the central and northern parts of the upper basin and the southern parts of the middle basin (Figure 6b). This suggests that ERA5-Land observations, despite overestimation in some areas, are consistent with station observations for total precipitation. However, for extreme precipitation indices (RX1day and RX5day), the correlation between ERA5-Land and station observations is relatively low, with regional average correlations below 0.4. Only 11.3% and 32.9% of stations have correlations above 0.5, and 32.9% and 26.9% of stations exhibit negative correlations, respectively (Figure 6c,d). This is also the case for the indices R95pTOT and R99pTOT, with average CC values of 0.40 and 0.18, respectively (Figure 6e,f and Table A1). Comparatively, ERA5-Land better represents heavy precipitation than extreme precipitation. The correlation is lower in the western upper basin, central middle basin, and lower basin.

ERA5-Land effectively captures the number of precipitation days, with more than 75.1% and 51.8% of stations exhibiting a CC above 0.5 for R10mm and R20mm, respectively. Additionally, over 19.3% and 5.6% of stations show a CC surpassing 0.8 for these indices. The correlation is particularly robust for the R10mm and R20mm indices in the northern regions and central parts of the upper basin, as well as throughout the middle basin and lower basin (Figure 6g,h).

Similarly, for CDD and CWD indices, ERA5-Land shows high consistency with station observations. The mean CDD correlation is 0.48, with 51.8% and 43.2% of stations having correlation coefficients above 0.5. Interestingly, like the precipitation amount and intensity indices, stations with high CWD correlations are mainly distributed in the southern upper basin and south of the middle basin (Figure 6i,j).

Among the RMSEs of the ten extreme precipitation indices, the SDII has the smallest overall error (Figure 7a), with 98% of stations showing errors less than 5 mm/day. The RMSEs of the SDII in the upper basin, middle basin and lower basin are 1.6, 2.21 and 3.97, respectively (Table A1). The PRCPTOT has a larger RMSE (Figure 7b), with all stations across the entire basin showing errors greater than 20 mm. The RMSEs of the PRCPTOT in the upper basin, middle basin and lower basin are 172.16, 142.71 and 134.01, respectively (Table A1). RX1day has a considerable error, with 7.8% of stations showing errors less than 10 mm and 50.5% showing errors greater than 20 mm, with the western upper basin having smaller errors than the middle basin and lower basin (Figure 7c). For RX5day, 7.3% of stations show errors less than 10 mm, and 31.6% show errors greater than 20 mm, with an uneven distribution of errors throughout different parts of the basin (Figure 7d). The RMSE of R95pTOT is generally large, with 99.3% of stations showing errors greater than 20 mm (Figure 7e). The RMSEs of R95pTOT in the upper basin, middle basin and lower basin are 48.77, 54.01 and 68.5, respectively (Table A1). Similarly, R99pTOT has large errors, with the eastern regions showing larger errors than the western regions (Figure 7f). The R10mm error is relatively small overall, with 95.3% of stations showing errors below than 10 days, and 58.1% showing errors below 5 days (Figure 7g). The R20mm error is also small across the basin, with 98.0% of stations showing errors below 5 days and at an average of 2.7 days (Figure 7h). For the CDD, 13.3% of stations have an RMSE below 10 days. Errors in the upper basin (RMSE = 25.85) are larger than those in the middle basin (RMSE = 13.9) and lower basin (RMSE = 12.69), with the overall western regions showing larger errors, and the middle basin and lower basin showing errors in the range of 10 days to 15 days (Figure 7i and Table A1). The CWD has a smaller RMSE, with 97% of stations showing errors below 10 days, and 84.4% showing errors below 5 days, with slightly larger errors in the western upper basin (Figure 7j). The RMSEs for R10mm, R20mm, and CWD are relatively small, these being 5.18 days, 2.69 days, and 3.83 days, respectively.

To evaluate the temporal error characteristics of ERA5-Land data on extreme precipitation indices, we calculated regional average extreme precipitation indices based on both station observations and ERA5-Land. Figure 8 presents a comparison of the temporal distribution of extreme precipitation indices.

The ten extreme precipitation indices, derived from both ERA5-Land and station observations, exhibit analogous fluctuation patterns across the Yellow River Basin for the period from 2001 to 2013. These indices reflect similar temporal variation traits within the basin itself and across its three sub-basins, indicating a coherent response to climatic and meteorological phenomena. Most of the ten extreme precipitation indices based on station observations exhibit minor fluctuations in most years. Among them, SDII, RX1day, RX5day, R99pTOT, R10mm, R20mm, and CDD show a slight overall increasing trend. ERA5-Land effectively captures this basic trend. Except for CDD, the other nine indices show significant high values in 2003, which aligns with the observations from meteorological stations. This is mainly due to the occurrence of pronounced extreme precipitation events in the upper basin in 2003, which ERA5-Land can detect as an abnormality. However, ERA5-Land exhibits apparent overestimation or underestimation for different extreme precipitation indices.

Within the Yellow River Basin, distinct zones exhibit varying degrees of accuracy in capturing precipitation by ERA5-Land. Specifically, ERA5-Land tends to overestimate the PRCPTOT, R95pTOT, R99pTOT, R10mm, and RX5day, while it underestimates the SDII, RX1day, CDD, and CWD. This indicates that while ERA5-Land has a good grasp of total precipitation, it shows less precision when detailing specific aspects of precipitation intensity and the occurrence of consecutive dry or wet days. This observation corresponds to the overestimation and underestimation patterns identified in Figure 5. RX5day and R20mm show a good agreement with the measurements from meteorological stations over the years, but ERA5-Land calculations of RX5day, R20mm, and R99pTOT exhibit overestimation or underestimation in different years (Figure 8). Figure 8d indicates an underestimation of the RX5day in 2005, 2012, and 2013, while overestimation is observed in the remaining years. Figure 8h shows that ERA5-Land tends to overestimate R20mm in 2001, 2003, 2005, 2007, and 2010, while underestimation occurs in other years. In a comparative analysis of sub-basins within the Yellow River Basin, it is observed that in the lower basin, indices such as SDII, PRCPTOT, RX1day, RX5day, R95pTOT, R10mm, and R20mm surpass the basin’s average. Furthermore, these indices are more pronounced in the upper basin compared to the middle basin. Conversely, they are least significant in the lower basin. The CDD and CWD, as derived from ERA5-Land, significantly exceed the values obtained from station observations across the sub-basins. Nevertheless, the interannual variability of CDD and CWD exhibits minimal fluctuation within the different sub-basins of the Yellow River Basin.

3.3. Evaluation of ERA5-Land for Capturing Extreme Precipitation Event

EPE is a continuous process, so to better evaluate the ability of ERA5-Land to detect extreme precipitation events, we redefine extreme precipitation events and their characteristics. From the perspective of event processes, we extract EPE and calculate their characteristics based on station observations and ERA5-Land. Figure 9 shows the spatial distribution of the average total frequency, duration, and total precipitation of EPEs in the Yellow River Basin from 2001 to 2013. It should be noted that since the frequency of EPEs varies across different stations, for comparison purposes, we divide the ED, ET, and EM of EPEs at each station by the corresponding frequency, resulting in the averaged characteristics, namely average duration (MED), average total precipitation (MET), and average mean precipitation (MEM).

The EF of EPE across all stations in the Yellow River Basin is 42 times, with a decreasing trend from west to east and from south to north. The upper basin has the highest frequency, followed by most parts of the middle basin, while the central and northeastern parts of the lower basin have fewer events (Figure 9a). According to ERA5-Land, the EF in the Yellow River Basin is 75 times, which is higher than the actual average frequency (Figure 9b). Figure 9c shows the difference in EF between ERA5-Land and station observations, with all stations exhibiting varying degrees of EF overestimation, ranging from 11 times to 96 times. The overestimation is most severe in the western and central upper basin, while the northeastern upper basin, middle basin, and lower basin show less overestimation.

The ET reflects the severity of these events. The MET of EPEs calculated from station observations from 2001 to 2013 shows a trend of more precipitation in the southeast and less in the northwest, consistent with the annual average precipitation distribution in the Yellow River Basin. The MET ranges from 18.92 mm to 81.59 mm, with 80.1% of the stations having MET values between 20 mm and 50 mm (Figure 9j). ERA5-Land effectively captures this southeast high MET and northwest low MET spatial distribution trend, with MET ranging from 16.54 mm to 64.4 mm. In total, 89.7% of the stations in the Yellow River Basin have MET values between 20 mm and 50 mm (Figure 9k), and 80.1% of ERA5-Land stations underestimate the MET, mainly in the southern middle basin and parts of the central and lower basin (Figure 9l).

The MED of EPEs calculated from station observations ranges from 1 day to 1.51 days (Figure 9d). The MED of EPEs based on ERA5-Land data is between 1.13 and 1.66 days, generally overestimating the actual duration of extreme precipitation (Figure 9e). Except for 15 stations with slight underestimation, the remaining stations show overestimation. The lower basin exhibits a smaller overestimation of the duration by ERA5-Land (Figure 9f). These conclusions are consistent with the overestimation findings for R10mm and R20mm.

The MEM values calculated from station observations show an increasing trend from the upper basin to the lower basin, with a maximum value of 73.7 mm/day and a minimum value of 14.6 mm/day (Figure 9g). In contrast, the MEM from ERA5-Land has a maximum value of only 44.3 mm/day and a minimum value of 11.27 mm/day (Figure 9h). ERA5-Land predominantly overestimates MEM in the upper basin and middle basin, while it tends to slightly underestimate MEM in the lower basin (Figure 9i).

Figure 10 illustrates the interannual variation curves of the annual average frequency, duration, peak, total precipitation, and average precipitation of extreme precipitation events in the Yellow River Basin from 2001 to 2013, based on data extracted from ground stations and ERA5-Land. Overall, the annual EF remained stable, ranging between two times and four times per year. On the whole, the duration of these events showed a slight upward trend, while ET, EP, and EM exhibited significant fluctuation and upward trends. In summary, the duration of events show a slight increasing trend, while ET, EP, and EM display significant fluctuations and upward trends. Notably, EF exhibited a trend of increasing initially and then decreasing, with 2003 and 2008 as the pivotal years (Figure 10a). EP, ET, and EM rose from 2001 to 2005, plummeted from 2005 to 2008, and surged after 2008 (Figure 10c–e). The annual variation in ED was distinct, characterized by a pattern of decrease, increase, decrease again, and finally an increase, with 2004, 2007, and 2009 as the transitional years (Figure 10b). The trends in ERA5-Land and ground station observations for the annual average frequency, duration, total precipitation, and average precipitation of extreme precipitation events were generally consistent, although notable overestimation and underestimation issues were present.

Specifically, from 2001 to 2013, ERA5-Land significantly overestimated the EF (Figure 10a) and ED (Figure 10b) of extreme precipitation events in the Yellow River Basin. The most severe overestimation EF occurred in 2003, where the overestimate reached up to four times (Figure 10a). Conversely, ERA5-Land significantly underestimated the EP (Figure 10c) and ET (Figure 10d), which aligns with the conclusion from Figure 5 that ERA5-Land underestimates R20mm and is consistent with the spatial distribution observed in Figure 9, with the most significant underestimation of EP occurring in 2005 (Figure 10c). However, ERA5-Land’s ability to capture EM was relatively accurate, with smaller margins of overestimation and underestimation (Figure 10e).

ERA5-Land’s detection of extreme precipitation events frequency differs by station and month (Figure 11). ERA5-Land’s annual cumulative extreme precipitation frequency from 2001 to 2013 exceeds station observations, mirroring the trend in Figure 10a. Data from ERA5-Land and station observations indicate that extreme precipitation typically falls from April to August, with a hiatus from November to February. The Yellow River Basin’s extreme precipitation pattern over thirteen years is similar, with events in the upper basin from April to August, in the middle basin from June to August, and in the lower basin concentrated in July and August.

Figure 12 displays that the EF of extreme precipitation events was higher in the upper basin, while the EP, ET and EM of extreme precipitation events were higher in the upper basin lowest in the lower basin from 2001 to 2013. ERA5-Land overestimated the EF and ED of the same month in the upper basin and middle basin, and underestimated Ethe P, ET and EM. To be specific, the EF of ERA5-Land in the upper basin was from 2.4 times to 4.2 times higher than the station observations of it, while the EF of ERA5-Land was about 2 times higher than the station observations of it in the middle basin and lower basin (Figure 12a). ERA5-Land’s overestimation of ED was even more significant in the lower basin, at up to 0.24 days (Figure 12b). ERA5-Land’s underestimation of ET was even more significant in the middle basin, at up to 2.16 mm (Figure 12d). ERA5-Land underestimated EP highest in the lower basin (EP = 7.39 mm/day), followed by the middle basin (EP = 5.38 mm/day), and lowest in the upper basin (EP = 3.62 mm/day). In different sub-basins of the Yellow River Basin, ERA5-Land underestimated the EM in the same way as it did the EP (Figure 12c,e).

4. Discussion

Based on the station observations, this study systematically assesses ERA5-Land’s capacity to capture extreme precipitation events. ERA5-Land tends to overestimate the EF and ED, potentially due to its inherent overestimation when analyzing precipitation in the basin, as indicated in Figure 3. The findings reveal a general congruence between ERA5-Land and station observations regarding total precipitation, albeit with persistent overestimation issues. By comparison, we found that the ability of ERA5-Land to monitor extreme precipitation is correlated with that for precipitation. The different ability of ERA5-Land to capture precipitation leads to the difference in capturing results of extreme precipitation events (Figure 3 and Figure 9).

Station observations have been widely used in previous studies. However, these data have limitations such as difficulty in acquisition, low density in high-altitude and complex terrain areas, and limited spatial representativeness. Consequently, error assessments based on station observations also have potential inaccuracies [47,48]. As station density decreases, the impact of spatial scale on data accuracy leads to increased precipitation assessment errors [49]. The stations used in this study are all national meteorological stations with strict quality control, but they still face the following potential errors: (1) The density of meteorological stations in the Yellow River Basin is relatively low. Therefore, this study uses ERA5-Land grid points corresponding to station locations as evaluation objects. While this approach cannot explicitly represent ERA5-Land performance in unobserved areas, it still provides valuable reference information. (2) Station observations reflect precipitation measurements at specific locations, whereas ERA5-Land data, with a spatial resolution of 0.1° × 0.1°, represent average precipitation on a pixel scale. This spatial scale mismatch may introduce certain uncertainties in the evaluation. Spatial discrepancies are a prevalent issue in current data evaluations, yet ERA5-Land provides a significant enhancement in horizontal resolution with a 9 km grid spacing, surpassing its predecessors, ERA5 and ERA-Interim. This advancement is particularly crucial for enhancing the precision of extreme precipitation capture. While the above limitations might introduce some level of uncertainty in the assessment, they exert a negligible influence on the overarching conclusions drawn from this study.

5. Conclusions

This study conducts a comprehensive assessment of ERA5-Land’s performance in capturing extreme precipitation in the Yellow River Basin, focusing on three key aspects: its precipitation capture capability, the representation of extreme precipitation indices, and the capacity to reproduce extreme precipitation events from daily observations. Statistical evaluation metrics are employed to gauge both the precipitation capture capability and the fidelity of extreme precipitation indices as provided by ERA5-Land. This study involved extracting extreme precipitation events and their characteristics from the ERA5-Land and comparing these with the findings from station observations. The comparative analysis revealed the following insights:

(1)

ERA5-Land effectively captures the spatial distribution and temporal trends in precipitation, indices, and extreme precipitation events in the Yellow River Basin. However, there are significant overestimation and underestimation errors. ERA5-Land generally overestimates the daily precipitation amounts across the basin, with the best capture ability in the middle basin, followed by the upper basin and lower basin. ERA5-Land generally overestimates the annual precipitation days in the Yellow River Basin.

(2)

ERA5-Land severely overestimates the total precipitation, with an error reaching up to 153%. It also significantly overestimates R95pTOT and R99pTOT, with 89.7% and 68.44% of stations showing overestimation errors, respectively. More stations exhibit underestimation errors for RX1day and overestimation errors for RX5day. For the number of rainy days, ERA5-Land tends to overestimate the number of days with precipitation greater than R10mm and CDD. Additionally, ERA5-Land systematically underestimates SDII. ERA5-Land can capture the temporal variation characteristics of extreme precipitation indicators in different regions of the Yellow River Basin.

(3)

ERA5-Land captures the spatiotemporal distribution characteristics of extreme precipitation events but consistently overestimates the frequency of these events, particularly in the western and central upper basin. It overestimates the duration of extreme precipitation for 95% of the stations in the basin while generally underestimating the average precipitation amount and total precipitation of extreme precipitation events. Specifically, EF, ED and ET are overestimated in the upper basin, middle basin and lower basin in each month, and the overestimation is more obvious in the upper basin.

In summary, ERA5-Land’s ability to monitor extreme precipitation in the Yellow River Basin is mainly reflected in capturing the basic trends in spatiotemporal distribution. However, there are significant overestimation and underestimation errors in precipitation amounts, extreme precipitation indices, and characteristics of extreme precipitation events, with most being systematic errors. Therefore, it is recommended to apply error correction when using ERA5-Land for extreme precipitation research. This study serves as a reference for enhancing the ERA5-Land algorithm by meticulously analyzing the frequency, timing, and intensity of extreme precipitation events. The findings affirm the precision and practicality of ERA5-Land in capturing these events, thereby validating its utility for similar studies in other regions. The conclusions drawn from this research not only bolster ecological conservation and disaster warning initiatives in the Yellow River Basin but also provide practical guidance for users of the ERA5-Land in this critical geographical area.