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. 2025 Jan 2;15:156. doi: 10.1038/s41598-024-84076-x

Long-term variability of extreme precipitation with WRF model at a complex terrain River Basin

Yinchi Zhang 1,2,3, Chao Deng 1,2,3, Wanling Xu 13, Yao Zhuang 4,5,6, Lizhi Jiang 5, Caiying Jiang 7, Xiaojun Guan 5, Jianhui Wei 8, Miaomiao Ma 9, Ying Chen 1,2,3,12, Jian Peng 10,11, Lu Gao 1,2,3,12,✉
PMCID: PMC11696463  PMID: 39747505

Abstract

Global warming has profound effects on precipitation patterns, leading to more frequent and extreme precipitation events over the world. These changes pose significant challenges to the sustainable development of socio-economic and ecological environments. This study evaluated the performance of the new generation of the mesoscale Weather Research and Forecasting (WRF) model in simulating long-term extreme precipitation events over the Minjiang River Basin (MRB) of China from 1981 to 2020. We calculated 12 extreme precipitation indices from the WRF simulations and compared them with observations. The spatio-temporal variations of extreme precipitation were further analyzed in terms of intensity, frequency, and duration. The results indicated that the WRF model can appropriately reproduce the spatial distribution of extreme precipitation indices with acceptable biases. The performance is significantly better for intensity and frequency indices compared to duration indices. Except for PRCPTOT and R10mm, WRF accurately captures the interannual variations of extreme precipitation. Meanwhile, the results of the pre-whitening Mann-Kendall (PWMK) test suggested that WRF can identify significant increasing trends in extreme precipitation, particularly for R95p, R99p, and R50mm. This study provides valuable insights for extreme precipitation forecasting and warning in other mountainous regions.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-84076-x.

Keywords: Dynamical downscaling, WRF, Extreme precipitation, Spatio-temporal variations, Minjiang River Basin

Subject terms: Environmental sciences, Hydrology, Natural hazards

Introduction

The sixth assessment report of the Intergovernmental Panel on Climate Change (IPCC) demonstrates that the global surface temperature has warmed by 1.1℃ from 2011 to 2020 compared to the period from 1850 to 19001. In the context of global warming, human activities lead to a significant increase in the frequency and intensity of extreme weather and climate events. The losses and damages inflicted on both natural and social systems far exceed the variability of natural climate2–4. Climate warming is also accompanied by the enhancement of hydrological cycle, manifested by the increase of both total precipitation and extreme precipitation worldwide5,6. The changes in precipitation variability will affect the climate resilience of social and ecological systems, which is an important issue that must be considered in the response to climate change7. It is forecasted that the enhanced hydrological cycle caused by global warming will lead to more extreme intra-annual precipitation patterns, characterized by stronger precipitation events and longer intervals between events8. Zhang et al. pointed out that the extreme precipitation in the global monsoon regions has shown an increasing trend in the past century, with a significant increasement in the contrast between wet and dry seasons9. Different combinations of precipitation mean state and variability will cause various types of hydrological, agricultural and ecological impacts in different regions, exacerbating the pressure on regional infrastructure design and water resources management10–13. In recent decades, the frequency and intensity of extreme precipitation in China have significantly increased, particularly in southeastern and northwestern China14–16. The Minjiang River Basin (MRB), located in the southeastern coastal region of China (Fig. 1a), experiences frequent extreme precipitation events due to its complex terrain and climate characteristics. Under the combined influences of weather system and topographic condition, extreme precipitation often triggers natural disasters such as floods, landslides, and debris flows, causing huge casualties and economic losses17,18.

Fig. 1.

Fig. 1

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Location of the study area (a) topographic features of the MRB. (b) WRF computational domain (D01-9 km, D02-3 km). The maps were created using ArcGIS Pro 3.0 software (https://www.esri.com/en-us/arcgis/products/arcgis-pro/overview).

Global Climate Models (GCMs) are widely used to study climate change on a global scale, encompassing past, present, and future climate scenarios. While GCMs can capture large-scale circulation features, their performance in characterizing extreme precipitation on regional scales is less than ideal, primarily due to low horizontal resolution and simplified physical parameters19. In recent years, Regional Climate Models (RCMs) have experienced rapid development. RCMs use the outputs from GCMs as lateral boundary conditions and employ dynamical downscaling to obtain more refined information20,21. RCMs can accurately describe small and medium-scale circulation and surface features, and effectively capture the local forcing, thus reflecting more complex physical processes22. Numerous studies indicated that increasing the resolution of climate models can significantly enhance the performance23–25. Seth and Giorgi were the first to use RCMs to simulate extreme climate events, analyzing the circulation mechanisms of droughts and floods in the central United States26. Subsequently, the research work on simulating and predicting extreme precipitation based on RCMs has been carried out27–31. Goubanova and Li studied the potential changes of extreme precipitation events around the Mediterranean Basin based on the Laboratoire de Météorologie Dynamique Zoom (LMDZ) model, and implied that the total precipitation would decrease32. Moreover, Coppola et al. and Nishant et al. also used different RCMs to study extreme precipitation events on small and medium-scales33,34. The results verified that RCMs have strong feasibility to simulate extreme precipitation events.

As a new generation of mesoscale numerical weather prediction model, the Weather Research and Forecasting model (WRF) is equipped with a comprehensive dynamical framework and physical parameterization schemes, which describes the land-atmosphere coupling processes in detail with higher spatial and temporal resolution. The WRF model designed to meet the needs of atmospheric research and operational forecasting has been widely adopted by many countries and organizations35,36. Bao et al. used the WRF model to assess the current and future precipitation changes in China37. It is considered that the WRF model can well describe the annual cycle and frequency of precipitation intensity and is also reliable for the spatial distribution of total precipitation and extreme precipitation. Yang et al., Gao et al. and Deng et al. employed the WRF model for ensemble forecasting of extreme precipitation events in different regions of China, respectively, revealing its applicability and potential in capturing extreme precipitation38–40. Toride et al. reproduced the extreme precipitation changes based on the WRF model in the Shasta Dam watershed of the United States over during 1851–201010. They discussed the impacts of changes in the intensity of extreme precipitation events on water resource management and sustainable development, emphasizing the importance of analyzing extreme precipitation trends on watershed scale.

Assessing the long-term trends of extreme precipitation in mountainous watersheds is crucial for understanding and mitigating the adverse impacts of natural disasters, particularly in regions where water resource management is heavily influenced by extreme weather events. Understanding these trends not only provides insights into the changing climate but also supports the development of effective disaster risk management strategies. Despite the importance of this issue, there is a notable gap in the current body of research. Studies that focus on the temporal and spatial variation of extreme precipitation in basins with complex topography are limited, especially when it comes to long-term simulations using high-resolution models like the WRF model. Most existing studies either focus on short-term simulations or regions with simpler topographic features, leaving a critical need for more detailed investigations in these challenging environments. This study aims to address this gap by conducting a comprehensive analysis of the spatio-temporal distribution and evolution patterns of extreme precipitation in the Minjiang River Basin (MRB) over the past 40 years. By utilizing high-resolution simulations, we aim to assess the model’s capability in capturing extreme precipitation events and to gain a deeper understanding of the physical processes driving these trends. Ultimately, this study will contribute to the scientific understanding of extreme precipitation dynamics in complex terrains and the practical application of climate models in disaster risk reduction and water resource management.

Data and methods

Model and experimental design

WRF version 4.3 was used in this study41. The simulations were integrated from January 1, 1981 to December 31, 2020. The first grid has a resolution of 9 km with a grid size of 100 × 90, while the second grid has a resolution of 3 km with a grid size of 142 × 130 (Fig. 1b). Meanwhile, the model was configured with 45 vertical levels and time step was set at 30s. There are numerous physical parameterization schemes available for the WRF model, and there is no optimal scheme combination that can be applied to all regions or events because of the different climate and underlying surface conditions in each region. As a result, based on previous sensitivity experiments in the MRB42, this study adopted the following parameterization schemes: New Tiedtke cumulus parameterization43, Purdue Lin microphysical scheme44, Dudhia shortwave radiation scheme45, Rapid Radiative Transfer Model longwave radiation scheme46, Noah land surface model47. In addition, when the model resolution is sufficiently high, certain convective processes can be explicitly represented48. Therefore, the cumulus scheme for the second grid was disabled. Many studies have indicated that land use and cover changes (LUCC) considerably influence the performance of the WRF model49–51. Hence, in order to ensure the accuracy of the results, this study replaced the LUCC data every ten years. The LUCC data were sourced from National Tibetan Plateau Data Center (http://data.tpdc.ac.cn/), with a spatial resolution reaching 100 m (Supplementary Figure S1).

Data

The initial and lateral boundary conditions of the WRF model were driven by the fifth-generation atmospheric reanalysis data (ERA5) from the European Centre for Medium-Range Weather Forecasts (ECWMF). ERA5 is available on regular latitude-longitude grids at 0.25°×0.25° resolution, with atmospheric parameters on 37 pressure levels. Compared with other reanalysis products, ERA5 has a more advanced 4DVAR assimilation system and higher spatio-temporal resolution52.

There are 30 meteorological stations conducting long-term consecutive measurements in the MRB (Supplementary Table S1). These data are used to analyze the spatio-temporal characteristics of extreme precipitation and to evaluate the performance of the WRF model. The selected stations adequately capture precipitation trends and exhibit no continuous interruptions of two weeks or more. Additionally, to ensure the authenticity and accuracy of the data, an error analysis and quality control were conducted on all datasets.

Methods

Extreme precipitation indices

The Extreme Precipitation indices are commonly used to assess extreme precipitation events53–55. The 12 extreme precipitation indices used in this study are sourced from the Expert Team on Climate Change Detection Monitoring and Indices (ETCCDMI). In order to accurately assess the extreme precipitation characteristics in the study area, this research modifies Rnnmm as both R1mm and R50mm (Supplementary Table S2).

According to different classification criteria, extreme precipitation indices can be divided into various ways. For example, Alexander et al. classified them based on different time scales into monthly extreme indices and annual extreme indices, and based on different thresholds, they can also be divided into absolute threshold indices and relative threshold indices56. Irannezhad et al. classified extreme precipitation indices into four categories: annual precipitation amount, intensity, frequency, and duration57. Considering the extreme precipitation characteristics in the MRB, this research categorizes extreme precipitation indices into three classes: (1) Intensity indices, including PRCPTOT, SDII, RX1day, RX5day, R95p, and R99p. (2) Frequency indices, including R1mm, R10mm, R20mm, R50mm. (3) Duration indices, including CWD and CDD.

Trend analysis

The Mann-Kendall (MK) trend test is widely used non-parametric statistical method in the field of hydrometeorology. However, the autocorrelation of hydrological and meteorological elements often makes certain variables with insignificant trend to become significant. Yue and Wang proposed the addition of pre-whitening processing before the MK test to enhance the reliability of the series trend58. Many studies indicated that the pre-whitening Mann-Kendall (PWMK) trend test is more reasonable than the MK trend test59–61. It provides a more accurate description of trend changes in hydrometeorological elements such as temperature, precipitation, and runoff. In this study, the PWMK trend test was used to calculate the trend changes in the extreme precipitation indices for both observational data and WRF model grid data. The pre-whitening procedure was applied by the following steps:

First, eliminating the linear trend of raw series.

graphic file with name M1.gif 1

where Inline graphic, Inline graphic and Inline graphic are the de-trended series, raw series value, and linear regression slope of the trend in the raw series at time t, respectively.

Second, removing the autocorrelation term from the de-trended series.

graphic file with name M5.gif 2

where Inline graphic is the lag-1 serial correlation coefficient of the de-trended series and Inline graphic is the de-trended and pre-whitened series, called the residual series.

Finally, we added the linear trend that was eliminated in the first step back to the de-trended or residual series.

graphic file with name M8.gif 3

where Inline graphic is the pre-whitening series.

Evaluation criteria

To quantitatively validate the ability of the WRF model, this study selected correlation coefficient (CC), Kling-Gupta efficiency (KGE), and percent bias (PBIAS) to evaluate the goodness of fit. Additionally, CC and root mean square error (RMSE) were chosen to assess the spatial average bias between observed and simulated data (Table 1).

Table 1.

Definition of evaluation criteria.

Metric Formula Optimal value Range
CC Inline graphic 1 (0, 1)
NSE Inline graphic 1 (-∞, 1)
KGE Inline graphic 1 (-∞, 1)
Pbias Inline graphic 0 (-∞, +∞)
RMSE Inline graphic 0 (0, +∞)
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Where Inline graphic presents hydrometeorological data at the Inline graphic station,Inline graphic presents data at the WRF grid point closest to the Inline graphic station, Inline graphic is the numbers of stations, Inline graphic presents the value of a specific moment in time, Inline graphic presents the correlation coefficient,Inline graphic presents the ratio of the mean of Inline graphic to Inline graphic, Inline graphic presents the ratio of the variance of Inline graphic to Inline graphic.

Results

Spatial distribution of extreme precipitation indices

Figure 2 illustrates the spatial distribution of observed and simulated extreme precipitation intensity indices in the MRB from 1981 to 2020. The observed annual total precipitation (OBS-PRCPTOT) decreases from northwestern to southeastern MRB, showing a significant gradient. The highest value, exceeding 1900 mm, is located at the junction of the Jianxi and Futun River Basins, while the lowest is less than 1600 mm in the downstream area. WRF-PRCPTOT and OBS-PRCPTOT exhibit good spatial consistency, but WRF overestimates precipitation, especially in the Jianxi and Shaxi River Basins, with maximum biases of 200–300 mm. On the contrary, WRF underestimates PRCPTOT in the downstream, with the minimum value of less than 1200 mm, and the biases ranging from 0 ~ 300 mm. The observed daily precipitation intensity (OBS-SDII) also shows a trend of transitioning from high values in the northwest to low values in the southeast. However, the difference is that the distribution range of the high value area of OBS-SDII is relatively small. WRF overestimates SDII, especially in the Shaxi River Basin and downstream MRB, where the maximum bias exceeds 3.5 mm·day⁻¹. The spatial distribution of observed maximum 1-day (OBS-RX1day) and 5-day (OBS-RX5day) precipitation is similar, with high values mainly along Mount Wuyi. OBS-RX1day ranges from 120 to 140 mm, and OBS-RX5day ranges from 220 to 265 mm. In comparison, the high value areas of WRF-RX1day and WRF-RX5day are more widely distributed and stronger. The biases are mainly concentrated in the northern of the Futunxi River Basin, the southern of the Shaxi River Basin and the downstream of the MRB, with the maximum bias exceeding 20 mm and 60 mm, respectively. Moreover, the high values of observed heavy precipitation (OBS-R95p) and extreme heavy precipitation (OBS-R99p) are both predominantly located near the Mount Wuyi, with values exceeding 900 mm and 325 mm, respectively. In comparation, WRF-R95p and WRF-R99p are significantly overestimated, with biases exceeding 120 mm and 70 mm, respectively, mainly distributed in the mountainous areas of Shaxi River Basin and the downstream of the MRB.

Fig. 2.

Fig. 2

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Spatial distribution of extreme precipitation intensity indices from observations and WRF, as well as the biases over the MRB during 1981–2020.

Overall, the extreme precipitation intensity gradually weakens from northwest to southeast, with high values mainly concentrated along Mount Wuyi. Meanwhile, WRF can capture the distribution of extreme precipitation intensity, but overestimates the value and extent of extreme precipitation, with the biases mainly distributed in the Shaxi basin and the complex mountainous areas of the downstream of the MRB (Mount Daiyun). The MRB is located in the coastal monsoon region of southeastern China, characterized by significant climate variability. The enhanced frontal precipitation in this area is attributed to the overestimation of the simulated low-level subtropical high pressure and the westerly trough, or due to a systemic bias of sea-land thermal difference62. Many research findings also confirmed that WRF generally overestimates the extreme precipitation intensity in the southeastern region of China39,63. Notably, WRF underestimates extreme precipitation in the estuarine areas, which contrasts with other basin regions.

The extreme precipitation frequency and duration indices are illustrated in Fig. 3 The wet days (OBS-R1mm) in the basin generally exceeds 100 days, with a high value center located in the downstream of the MRB, ranging between 130 and 160 days. However, WRF generally underestimates R1mm, with a smaller bias in the northern ranging from − 2 to 4 days, and a larger bias in the southern ranging from − 14 to −32 days. Moreover, WRF underestimates R1mm, with biases ranging from − 2 to 4 days in the north and − 14 to −32 days in the south. The distribution of heavy precipitation days (OBS-R10mm) is similar to R1mm, with most areas exceeding 50 days (40–65 days). The distribution of very heavy precipitation days (OBS-R20mm) shows high values in the west near Mount Wuyi (28–34 days). WRF-R20mm generally follows the same pattern but has biases of 3–6 days in the western Jianxi River Basin. Additionally, The observed extreme heavy precipitation days (OBS-R50mm) are concentrated near Mount Wuyi, with values exceeding 7 days, while WRF overestimates R50mm in the Shaxi River Basin and MRB downstream, with biases ranging from 2.4 to 3.0 days.

Fig. 3.

Fig. 3

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As in Fig. 2 but for extreme precipitation frequency and duration indices.

The observed consecutive wet days (OBS-CWD) generally exceed 8 days, and the highest value appears in the downstream of the MRB, more than 10 days, showing a distribution pattern of high values in the northwest and low values in the southeast. On the contrary, WRF-CWD gradually decreases from north to south, with high values appearing in the northern of the Jianxi River Basin, ranging from 10 to 11 days, and low values areas occurring in the MRB estuary, ranging from 5 to 6 days. The observed consecutive dry days (OBS-CDD) exhibit a spatial characteristic of low values in the north and high values in the south, ranging from 25 to 37 days. However, WRF overestimates CDD, with biases mainly concentrated in the downstream of the MRB, exceeding 14 days in maximum.

In summary, extreme precipitation in the MRB shows a spatial correlation, with high values concentrated along Mount Wuyi. Meanwhile, as the extreme precipitation intensity increases, WRF gradually transitions from underestimating to overestimating for the extreme precipitation frequency. Among them, the spatial distribution of WRF-20 mm is the most consistent with the reality. However, for duration indices, WRF exhibits large spatial biases, likely due to the nonlinear dynamics in complex terrains, which challenge the simulation of continuous wet and dry conditions64,65.

Taylor diagrams are presented in Supplementary Figure S2 to evaluates the performance of WRF for the extreme precipitation intensity, frequency, and duration. For intensity, PRCPTOT has the highest CC (0.90) and lowest RMSE (0.61), while SDII has the lowest CC (0.30) and highest RMSE (1.63). This indicates that WRF performs well for annual total precipitation but poorly for daily precipitation intensity. Among frequency indices, R20mm has the best performance (CC = 0.89, RMSE = 0.57), while R1mm and R50mm have CCs below 0.70. This suggests WRF overestimates extreme heavy precipitation while performing better for moderate and heavy rain. For CWD and CDD, WRF struggles with spatial distribution, showing low CC (0.52 and 0.42) and high RMSE (1.62 and 1.75).

Temporal variability of extreme precipitation indices

Figure 4; Table 2 illustrate the interannual variations and linear trends of the observed and simulated extreme precipitation indices in the MRB from 1981 to 2020. During this period, all the observed extreme precipitation intensity indices show an increasing trend. The correlation between the observed and simulated PRCPTOT is the strongest (CC of 0.97, KGE of 0.85), and the bias is the smallest (PBIAS of −1.45%), indicating that WRF can effectively capture the interannual variations of PRCPTOT. The observed PRCPTOT has a positive trend of 31.83 mm·10years−1, while the WRF results show a negative trend of −32.46 mm·10years−1. For SDII, the trends of observations and simulations are 0.37 mm·day−1·10years−1 and 0.44 mm·day−1·10years−1, respectively, showing good consistency in the time series (CC of 0.85, KGE of 0.80, PBIAS of 9.58%). The observed RX1day and RX5day show the same positive trend, with 3.92 mm·10years−1 and 2.45 mm·10years−1, respectively. The simulated RX1day and RX5day are 4.93 mm·10years−1 and 7.58 mm·10years−1, respectively. Compared with the observations, there are different degrees of overestimation, but CC and KGE are both around 0.8, showing a strong correlation. For R95p and R99p, the trend of simulations is highly consistent with that of the observations (CC > 0.85, KGE > 0.80). The observed and simulated R95p show a trend of increase with 25.63 mm·10years−1 and 28.35 mm·10years−1, and for R99p, they are 11.06 mm·10years−1 and 14.57 mm·10years−1, respectively. Overall, for the extreme precipitation intensity, WRF exhibits a good performance and strong correlation. In addition to PRCPTOT, the variation trends of simulated and observed intensity indices are consistent.

Fig. 4.

Fig. 4

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Interannual variation (left) and temporal linear trend (right) of extreme precipitation indices over the MRB during 1981–2020.

Table 2.

The evaluation criteria and variation rate of the observation (left) and WRF (right).

Category Index CC KGE PBIAS Variation rate
Intensity PRCPTOT 0.97 0.85 −1.45% 31.83/−32.46 (mm·10years−1)
SDII 0.85 0.80 9.58% 0.37/0.44 (mm·day−1·10year−1)
RX1day 0.79 0.75 16.75% 3.92/4.93 (mm·10 years−1)
RX5day 0.80 0.76 15.16% 2.45/7.58 (mm·10 years−1)
R95p 0.85 0.80 16.75% 25.63/28.35 (mm·10 years−1)
R99p 0.89 0.83 14.62% 11.06/14.57 (mm·10 years−1)
Frequency R1mm 0.93 0.83 −9.70% −1.29/−3.32 (mm·10 years−1)
R10mm 0.92 0.86 −6.29% 0.32/−1.13 (mm·10 years−1)
R20mm 0.94 0.89 6.47% 0.54/0.41 (mm·10 years−1)
R50mm 0.89 0.78 15.86% 0.54/0.59 (mm·10 years−1)
Duration CWD 0.74 0.42 −6.17% −0.22/−0.15 (mm·10 years−1)
CDD 0.86 0.65 −20.74% −0.34/−0.23 (mm·10 years−1)
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For the extreme precipitation frequency indices, the observations and simulations exhibit a high correlation, with CC mostly above 0.9 and KGE above 0.8. Specifically, R1mm of both observations and simulations show a decreasing trend, with − 1.29 mm·10years−1 and − 3.32 mm·10years−1, respectively, indicating a strong correlation in the time series (CC of 0.93, KGE of 0.83, PBIAS of −9.70%). For R10mm, the WRF results are close to those of R1mm (CC of 0.92, KGE of 0.86, PBIAS of −6.29%), but the observations and simulations show a opposite trend, with 0.32 days·10years−1 and − 1.13 days·10years−1, respectively. The performance of R20mm closely matches the observations, with CC of 0.94 and PBIAS of only 6.47%. Additionally, the trend of simulated R20mm is 0.41 days·10years−1, slightly lower than the observations of 0.54 days·10years−1. The correlation of R50mm is the lowest (CC of 0.89, KGE of 0.78), with the largest bias (PBIAS of 15.86%), but the trend is very close to observations, with 0.59 days·10years−1 and at 0.54 days·10years−1, respectively.

Both CWD and CDD show decreasing trends, with − 0.22 days·10years⁻¹ and − 0.34 days·10years⁻¹, respectively. The WRF results show similar declining trends, with − 0.15 days·10years⁻¹ for CWD and − 0.23 days·10years⁻¹ for CDD. CDD shows higher temporal correlation (CC = 0.86, KGE = 0.65) but a larger bias (PBIAS = −20.74%).In conclusion, WRF generally captures the interannual variations of all extreme precipitation indices in the MRB, with CC mostly above 0.80. Except for PRCPTOT and R10mm, WRF also accurately describes the trends of each index. In comparison, WRF tends to overestimate the variation rates of the extreme precipitation intensity indices (except PRCPTOT), while the extreme precipitation frequency (except R50mm) and duration indices exhibit the opposite trend.

Spatio-temporal evolution of extreme precipitation indices

Figures 5 and 6 show the PWMK trends of 12 extreme precipitation indices in the MRB from 1981 to 2020. For the intensity indices, OBS-PRCPTOT generally shows an increasing trend, with only 5 stations exhibiting a decreasing trend, mainly distributed in the downstream. WRF-PRCPTOT closely matches OBS-PRCPTOT in the northern MRB but shows overestimation and underestimation in the downstream. OBS-SDII exhibits an increasing trend across the basin, with seven stations reaching a 0.05 significance level, mainly in the northwestern MRB. WRF tends to overestimate SDII’s trend, with nine stations showing significance at 0.05. OBS-RX1day shows a decreasing trend at only five stations, with others increasing. WRF generally overestimates this increasing trend, especially in the central MRB. OBS-RX5day displays an increasing trend in the north and south but a decreasing trend in the center. WRF overestimates the increase in RX5day, with five stations showing significance. OBS-R95p shows an increasing trend, except for Gutian, with Tai’ning reaching significance. WRF-R95p overestimates the trend in the northwestern MRB, but in the downstream, it shows a decreasing trend in three stations. Compared with the observations, the simulated R99p shows a slight overestimation in the north and west of the basin, but generally performs well.

Fig. 5.

Fig. 5

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Spatial distribution of the PWMK test for 12 extreme precipitation intensity indices in the MRB during 1981–2020.

Fig. 6.

Fig. 6

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As in Fig. 5 but for extreme precipitation frequency and duration indices.

For the frequency indices, OBS-R1mm generally shows a decreasing trend except for Changle. WRF-R1mm shows consistent decline but overestimates the rate in the south, with 15 stations significant at 0.05. OBS-R10mm shows increasing trends in the north and decreasing in the south, with 19 stations increasing and 11 decreasing. However, WRF-R10mm overestimates the southern decline, with 24 stations showing a decline and six reaching significance. OBS-R20mm shows a general increasing trend in the north and south, with no significant trend except at Guangze station. The WRF results are opposite to the observations in the Shaxi and the downstream of the MRB, with 4 stations showing a significant decreasing trend. OBS-R50mm shows an increasing trend throughout the basin, with Jian’ou and Mingxi stations reaching significance. Compared with the observations, WRF-R50mm overestimates the increase in the western basin, with six stations showing significance, while in the downstream, it shows a decreasing trend in three stations.

For the duration indices, OBS-CWD and OBS-CDD show a decreasing trend, with 2 and 1 stations reaching a significance level of 0.05, respectively. Meanwhile, WRF can simulate the decreasing trends of CWD and CDD across the entire basin, although with varying degrees of biases.

Supplementary Table S3 summarizes the PWMK trends of 12 extreme precipitation indices at each station. Among them, PRCPTOT, SDII, RX1day, R95p, R99p, and R50mm exhibit an increasing trend at over 20 stations. The trend of SDII is most pronounced across the entire basin, with 7 stations reaching a significance level of 0.05. On the contrary, R1mm, CWD, and CDD show a decreasing trend at over 20 stations, with approximately 97% of the stations showing a negative trend for R1mm among 30 stations. Among the 12 indices, the results of R95p, R99p, and R50mm are closest to the observations, with a hit rate of 0.73. However, the performance of RX5day and R10mm is the poorest, with a hit rate of only 0.43.

In summary, the intensity indices show an upward trend in the MRB during 1981–2020, especially in the northwestern and western areas near Mount Wuyi. As for the frequency indices, the spatio-temporal evolution varies across different values. Specifically, across the entire basin, R1mm exhibits a decreasing trend, while R50mm showed an increasing trend. Meanwhile, the frequency of high intensity precipitation (R20mm, R50mm) significantly increases in the northern and western mountainous areas. Overall, WRF captures the spatio-temporal evolution patterns of various extreme precipitation indices, though it overestimates the increasing trend of intensity indices in the western and northern mountains and overestimates the decreasing trend of low-intensity frequency indices in the southern basin.

Discussion

In this study, the extreme precipitation intensity and frequency indices in the MRB from 1981 to 2020 show a positive trend (except R1mm), while the duration indices exhibit a negative trend, indicating that the extreme and sudden precipitation in the region increased and the persistence decreased. These findings are consistent with previous research results in southeastern China15,18,54.

We are particularly interested in the changes of extreme precipitation in small-scale complex terrain watersheds. The terrain in these areas is steep, and the confluence speed of rainstorm and flood is fast. It is easy to form a huge flood peak in a short time, which endangers the downstream urban plain area66. Overall, the WRF model generally shows wet biases in high-altitude areas like the Wuyi Mountains and dry biases in low-lying plains, such as the estuary region of the MRB. As precipitation intensity increases, the model shifts from underestimating to overestimating extreme events. For most extreme precipitation indices (SDII, RX1day, RX5day, R95p, R99p), overestimation occurs in mountainous regions, with high-intensity events (R50mm) following the same trend. Complex topographical features and the presence of intense weather systems pose significant challenges in the precise modeling of extreme precipitation events67–69. Compared to reality, the smoothing of complex terrain in the model may significantly reduce the terrain resistance encountered by air masses during ascent, weaken water vapor convergence at low altitudes, and result in excessive precipitation in mountainous areas70,71. Additionally, the simulation of evaporation and condensation processes in the WRF model may not be entirely accurate, particularly in areas with strong terrain-induced uplift, which may lead to an overestimation of atmospheric water vapor72. Numerous studies and evidence indicate a close relationship between monsoon, tropical cyclones, and extreme precipitation events73–77. However, reconstructing extreme precipitation caused by severe weather processes based on RCMs still presents certain limitations and uncertainties. Mandal et al. found that the WRF model provided a reasonable prediction of the spatial distribution of tropical cyclone precipitation but overestimated the intensity in the core regions of heavy rainfall, this overestimation may be significantly influenced by the vertical wind shear in the initial conditions78. Yang et al. used the WRF model to reconstruct East Asian summer monsoon precipitation and suggested that the overestimation of precipitation may further induce or amplify circulation biases at different scales, highlighting the critical role of precipitation feedback on the circulation and precipitation distribution38. The MRB has long been significantly impacted by the East Asian monsoon and tropical cyclones, the instantaneous and intense extreme precipitation events are mostly concentrated in the post-flood period (July to September) when the summer monsoon and tropical cyclones are active79, which is undoubtedly an important reason for the unsatisfactory model results.

There are numerous physical parameterization schemes in the WRF model, and the microphysics (MP) and cumulus (CU) schemes have a particularly significant impact on the accuracy of precipitation simulations80–83. Although we conducted comprehensive sensitivity tests and optimizations on the model’s MP (Purdue Lin microphysical scheme) and CU (New Tiedtke cumulus parameterization) schemes prior to this study to improve the accuracy of the simulation results, certain issues remain unavoidable because of the inherent limitations of each scheme. Nguyen-Xuan et al. found that New Tiedtke scheme over land produces excessive orographic precipitation, thus destroying its spatial pattern84. Compared to other CU schemes, the New Tiedtke scheme simulates significantly greater convective rainfall, with peak values notably higher than those of other schemes. Additionally, there is a certain deviation in the simulation of tropical cyclone positions using this scheme85. However, Xu et al. suggested that using the Purdue Lin scheme at a low resolution (3 km) constrains net condensation and moisture convergence, preventing accurate capture of localized weak convective precipitation86. This can provide a reference for explaining the model’s underestimation of low intensity precipitation indices (R1mm, CWD). Moreover, Yang et al. believe that even with optimized parameters, circulation biases still exist because of inappropriate radiation or planetary boundary layer (PBL) processes in the model36.

There is much evidence that more realistic land use data can improve simulation results49,87,88. It is worth emphasizing that although this study replaced the default land use data with high quality data closest to the study period, the simulated results still generally underestimated the extreme precipitation intensity and frequency in the estuarine area of the MRB, possibly due to the influences of urbanization processes (Supplementary Figure S1). Feng et al. suggested that changes of urban underlying surface characteristics not only directly affect urban temperature, but also have an important impact on precipitation89. Lin et al. found that urban land use changes significantly affect the atmospheric thermodynamic processes in the boundary layer, which ultimately change the spatio-temporal characteristics of precipitation90. Yang et al. proposed that urbanization enhances the thermal disturbance of temperature and surface pressure fields and strength the dynamic conditions during precipitation events91. For the WRF model, a spatial resolution of 3 km may not be sufficient to describe the complex microscale meteorological features within cities. Additionally, the processes such as atmospheric turbulence and radiation transfer within the urban areas may require more sophisticated parameterization schemes for accurate simulation92.

In general, the WRF model shows some potential in simulating extreme precipitation in complex terrain regions, yet this study still reveals some shortcomings. Given the complexity of extreme precipitation related to terrain effects, weather systems, and radiation schemes, among other dynamic and physical processes, further efforts are required to enhance accuracy. For instance, addressing the quality of boundary conditions through techniques like data assimilation, and conducting coupled simulation focusing on hydrological processes, urban climate characteristics, and dynamic responses of ecosystems. Additionally, due to the limitation in computational resources, our simulation experiments only employed one RCM. Therefore, future research should incorporate multiple RCMs and employ optimal ensemble methods to obtain more extensive and reliable information on future changes in extreme precipitation, ultimately facilitating climate change impact assessments and adaptation services.

Conclusions

In this study, we used the WRF model to simulate the distribution and variation of extreme precipitation in the MRB during 1981–2020 based on four different land use and land covers. The extreme precipitation indices were calculated based on both observations and simulations. The performance of the WRF model was evaluated from three aspects: spatial distribution, temporal variability, and spatio-temporal evolution. The important conclusions drawn from this study are as follows.

  1. Overall, WRF shows appropriate performance in capturing the spatial distribution of extreme precipitation indices. Among them, the results of extreme precipitation intensity and frequency indices are significantly better than that of duration indices, with the highest CC observed for PRCPTOT and R20mm, reaching 0.90 and 0.89, respectively. WRF generally overestimates the extreme precipitation intensity in the MRB, particularly in the complex mountainous regions of the Shaxi Basin and the downstream of the MRB, whereas it yields contrasting results for the flat terrain of the MRB estuary. For the extreme precipitation frequency, there is a certain relationship between the bias and the precipitation intensity, wherein high value events exhibit wet biases while low value events exhibit dry biases. Additionally, the results of CWD and CDD are relatively poor, with CC of only 0.52 and 0.42, respectively.

  2. In terms of the temporal variability, WRF generally captures the interannual variation trends of the 12 extreme precipitation indices, with CC mostly exceeding 0.8. PRCPTOT exhibits the highest CC of 0.97, while CWD shows the lowest CC of only 0.74. Except for PRCPTOT and R10mm, the observed and simulated linear trends of other indices are consistent. Compared with the observations, WRF overestimates the variation rate in the extreme precipitation intensity indices and underestimates the variation rate in the extreme precipitation frequency and duration index.

  3. WRF can basically reproduce the spatio-temporal evolution characteristics of extreme precipitation in the MRB. The results of the PWMK trend test show that the extreme precipitation intensity is on the rise, and WRF can capture the significant rising area. Across the entire basin, R1mm shows a gradual downward trend, while R50mm shows a gradual upward trend, and the simulated results are more extreme. In addition, for CWD and CDD, the results of observations and simulations show a general trend of decline.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary Material 1 (1,004.4KB, docx)

Acknowledgements

The operation of WRF model was supported by the High Performance Computing Center of Fujian Normal University.

Author contributions

Y.Z.: investigation, visualization, and writing—original draft. C.D. and W.X.: methodology, validation. Y.Z., L.J., C.J. and X.G.: visualization, supervision, and review. J.W., M.M. and J.P.: contributed to the revision of the manuscript. Y.C. and L.G.: Fund support. All authors reviewed and made substantial contributions to this work and approved it for publication.

Funding

Supported by the National Natural Science Foundation of China (Grant No. 42271030), Fujian Provincial Funds for Distinguished Young Scientists (Grant No. 2022J06018), the Scientific Project of Fujian Provincial Department of Science and Technology (Grant no. 2022Y0007) and “Young Eagle Plan” Top Talents of Fujian Province.

Data availability

The meteorological data were provided by Fujian Meteorological Observatory. ERA5 driving data were supported by the ECMWF public web server (https://cds.climate.copernicus.eu/). LUCC data set is provided by National Tibetan Plateau Data Center (http://data.tpdc.ac.cn/).

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Material 1 (1,004.4KB, docx)

Data Availability Statement

The meteorological data were provided by Fujian Meteorological Observatory. ERA5 driving data were supported by the ECMWF public web server (https://cds.climate.copernicus.eu/). LUCC data set is provided by National Tibetan Plateau Data Center (http://data.tpdc.ac.cn/).

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