Assessing rainfall erosivity changes over China through a Bayesian averaged ensemble of high-resolution climate models

Spatiotemporal variation in rainfall erosivity resulting from changes in rainfall characteristics due to climate change has implications for soil erosion in developing countries. To promote soil and water conservation planning, it is essential to understand past and future changes in rainfall erosivity and their implications on a national scale. In this study, we present an approach that uses a Bayesian model averaging (BMA) method to merge multiple regional climate models (RCMs), thereby improving the reliability of climate-induced rainfall erosivity projections. Our multi-climate model and multi-emission scenario approach utilize five RCMs and two Representative Concentration Pathways (RCP4.5 and RCP8.5) scenarios for the baseline period (1986–2005) and future periods (2071–2090) to characterize the spatiotemporal projection of rainfall erosivity and assess variations in China. Our results indicate that the two models outperform other models in reproducing the spatial distribution and annual cycle of rainfall erosivity in China. Moreover, we found an increasing trend in the annual rainfall erosivity from the baseline climate up to the RCMs for all models, with an average change in erosivity of approximately 10.9% and 14.6% under RCP4.5 and RCP8.5, respectively. Our BMA results showed an increase in the absolute value of rainfall erosivity by 463.3 and 677.0 MJ·mm·hm−2·h−1, respectively, in the South China red soil region and the Southwest China karst region under the RCP8.5 scenario. This increase indicates that climate warming will significantly enhance the potential erosion capacity of rainfall in these regions. Additionally, our study revealed that the Southwest China karst region and the Northwest China Loess Plateau region are more sensitive to radiation forcing. To mitigate the risk of soil erosion caused by climate change, it is necessary to consider changes in rainfall erosivity, local soil conditions, vegetation coverage, and other factors in different regions and take appropriate soil and water conservation measures.


Introduction
In the past decade, land-use change has led to a 2.5% increase in total soil erosion, surpassing the soil formation rate by 1 to 2 orders of magnitude (Montgomery 2007, Borrelli et al 2017).Despite efforts to mitigate soil degradation, soil erosion remains the primary cause of soil loss, resulting in decreased soil fertility and agricultural productivity, exacerbating poverty (Lee andHeo 2011, Amundson et al 2015).China is particularly affected, with an annual soil loss estimate of up to 3.3 billion tons and soil erosion areas accounting for about 90% of the impoverished population (Liang et al 2020).
Various factors, including soil type, soil water content, topography, and rainfall erosivity, influence the rate of soil erosion (Wischmeier and Smith 1958).In China, climate change-induced alterations in rainfall erosivity, attributed to changes in spatial and temporal rainfall patterns, have accelerated the overall rate of soil erosion (Yang and Lu 2015, Hoomehr et al 2016, Azari et al 2021).Climate projections suggest that a more intense hydrological cycle by 2070 could lead to a 30% to 66% increase in global water erosion, affecting 80% to 85% of the global land surface (Panagos et al 2022).However, while expected changes in rainfall erosivity have been studied in various regions, research on its impact in China has mainly focused on past variations, leaving a knowledge gap regarding the potential effects of climate change on regional rainfall erosivity.
Calculating rainfall erosivity involves a relatively simple algorithm due to the limitations of climate change models in accurately simulating rainfall parameters.Typically, global climate models (GCMs) or regional climate models (RCMs) are used with rainfall data under different climate change scenarios to estimate erosivity.In China, the commonly used algorithm by Zhang et al (2002), based on 71 representative stations, estimates monthly and annual rainfall erosivity using daily rainfall data.However, this model has been criticized for overestimating rainfall erosivity in certain regions (Xie et al 2016).To address this limitation, Xie et al (2016) proposed a new, more accurate and widely applicable model (Chen et al 2020).
In order to effectively address soil and water loss in China, it is crucial to accurately assess the projected rainfall erosivity under changing climatic conditions.Several national programs have been implemented to control soil erosion, but a reliable assessment is needed before implementing prevention and control measures on a larger scale (Xiao et al 2017, Li et al 2020, Li et al 2021).
This study aims to assess the potential impacts of climate change on rainfall erosivity at a national level by utilizing a selected ensemble of high-resolution regional climate models (RCMs).The hypothesis is that the application of arithmetic ensemble mean (AEM) and Bayesian model averaging (BMA) to RCM ensembles will enhance the reliability of rainfall erosivity projections influenced by climate change.A rainfall erosivity calculation model will be employed to determine the erosion potential based on daily rainfall data across different regions in China.The analysis will examine the spatial and temporal variations in rainfall erosivity under various Representative Concentration Pathways (RCPs) for the end of the 21st century.Furthermore, the study will investigate the underlying physical mechanisms driving the changes in rainfall erosivity, aiming to elucidate the relationship between climate warming and variations in erosivity.The comprehensive and robust assessment of rainfall erosivity change will provide valuable theoretical and technical support for soil and water loss prevention and control efforts in China.

Study area
In order to address the diverse impacts of rainfall erosivity on soil erosion across different regions in China, the Ministry of Water Resources proposed the National Soil and Water Conservation Regionalization (Trial Implementation) (Zhao et al 2013).This regionalization divides the study area into eight distinct soil and water conservation areas, taking into account factors such as soil erosion types, intensity, hazards, and local variations in soil erosion control measures.The purpose of this division is to identify vulnerable regions to rainfall erosivity and compare the distribution of rainfall erosivity among different sub-regions.The eight sub-regions are as follows: (I) Northeast China black soil region, (II) North China mountainous region, (III) Northwest China Loess Plateau region, (IV) North China sandstorm region, (V) South China red soil region, (VI) Southwest China purple soil region, (VII) Southwest China karst region, and (VIII) Qinghai-Tibet Plateau region, as illustrated in figure 1.This regionalization scheme enables a focused analysis of the specific challenges posed by rainfall erosivity in each sub-region, considering the unique soil types, complex terrain, and distinct precipitation patterns across China.By understanding the variations in rainfall erosivity distribution and vulnerability among these regions, targeted soil erosion control measures can be implemented to ensure effective soil and water conservation strategies.

Data
The present study aims to assess the impact of climate change on rainfall erosivity by analyzing historical data from 1986 to 2005 and projecting future scenarios from 2071 to 2090.Two emission scenarios, namely RCP4.5 and RCP8.5, were employed to represent different levels of greenhouse gas emissions.RCP4.5 reflects a stabilization scenario with a total radiative forcing of 4.5 W m −2 by 2100, while RCP8.5 represents a high emission scenario with a total radiative forcing of 8.5 W m −2 by the end of the 21st century.To fulfill the time series requirements for the historical and future periods, we selected five high-resolution Regional Climate Models (RCMs) from the Coordinated Regional Climate Downscaling Experiment (CORDEX).Table 1 provides detailed information on these models.In addition, we utilized daily precipitation data from the APHRODITE dataset, which covers a span of more than 50 years and has a horizontal resolution of 0.25°× 0.25°, to validate our model results.The study area was divided into eight soil and water conservation areas based on the National Soil and Water Conservation Regionalization proposed by the Ministry of Water Resources of the People's Republic of China.This division allows for a more focused analysis of rainfall erosivity patterns and variations across different regions.To capture a comprehensive range of changes in rainfall erosivity under increasing radiative forcing, we obtained climate simulations from four high-resolution climate models (0.5°× 0.5°) provided by CORDEX.Additionally, we included one model that ran continuously from 1969 to 2099.

Rainfall erosivity factors
Accurately estimating rainfall erosivity necessitates high-temporal-resolution rainfall data, which is often limited in availability.Consequently, methodologies have been developed to estimate rainfall erosivity using daily data.In China, the Xie model (Xie et al 2016) has emerged as a widely utilized method for calculating rainfall erosivity, owing to its superior performance compared to alternative models (Chen et al 2020).The calculation process of the R-factor from the Xie model is outlined as follows: where R d refers to the daily rainfall erosivity (MJ•mm•hm −2 •h −1 ), and P d represents the daily erosive rainfall value (mm).In this model, the daily erosive rainfall threshold was set to 10 mm.The parameter α was equal to 0.3937 in the wet season (May to September) and to 0.3101 in the cold season (October to April), and the parameter β was set to 1.7265.
BMA probabilistic prediction model can be expressed as: where p(f k |D) is the posterior probability of the sequence f k simulated by the model, that is, the probability that the model is optimal under the given data conditions.In fact, p(f k |D) is the weight of BMA w i , and the model with higher prediction accuracy is assigned more weight, and is the posterior distribution of the simulated value under the given model prediction f k and data D conditions.The mean value and variance of y are expressed as: The Expectation Maximization Algorithm is used to calculate the probability distribution parameters w i and σ i 2 of BMA simulation variables (Wang et al 2022)

Historical simulation
During the observation period from 1986 to 2005, the annual rainfall erosivity in China followed a decreasing trend from the southeast to the northwest, mirroring the pattern of annual precipitation (Zhu et  Figure 2 illustrates that the spatial pattern of annual mean rainfall erosivity simulated by RCMs differs from that of APHRODITE.Notably, CCLM overestimated rainfall erosivity over the Sichuan Basin and the eastern part of the Tibet Plateau, resulting in artificially high values.Conversely, HCLM accurately captured the spatial distribution of rainfall erosivity, particularly in the South China red soil region.The MCLM model provided an average rainfall erosivity estimate of 1229.9MJ•mm•hm −2 •h −1 , which closely aligned with the observations compared to other RCMs.The IDMI model exhibited scattered patterns of rainfall erosivity, with artificial highvalue centers in eastern China.The PRECIS model performed well in estimating erosivity in the Southwest China purple soil region and North China mountainous region, but underestimated erosivity in the South China red soil region and overestimated it in other regions.While RCMs generally captured the spatial distribution of rainfall erosivity in China, they tended to overestimate magnitudes in most areas, especially over the Qinghai-Tibet Plateau, due to interpolation uncertainty arising from a lack of rainfall stations in the region.The lower reaches of the Yarlung Zangbo River valley (29.61°N, 94.94°E) serve as the primary water vapor channel for the Tibet Plateau, facilitating the inflow of warm and moist air from the Indian Ocean, resulting in considerable rainfall erosivity over the southeast of the plateau.Finally, the AEM and BMA ensemble simulations of five RCMs were employed to enhance the robustness of climate system simulations.The AEM results revealed scattered artificial high-value areas in the southeast, predominantly influenced by the IDMI model.In contrast, the BMA ensemble simulations better captured the spatial pattern of rainfall erosivity.

Projections of rainfall erosivity
Figures 3 and 4 provide a visual representation of the projected changes in rainfall erosivity for RCMs under the RCP4.5 and RCP8.5 scenarios during the 2071-2090 period, relative to the baseline period.The results indicate that approximately half of mainland China's landmass is projected to experience an increase in rainfall erosivity ranging from 8.7% to 13.0% under the RCP4.5 scenario compared to the historical period.Specifically, CCLM simulates a substantial increase of approximately 927.2 MJ•mm•hm −2 •h −1 in rainfall erosivity for the South China red soil region, while also projecting a noticeable decrease in rainfall erosivity in the Southwest China purple soil region and karst region.HCLM projects the highest positive change in the South China red soil    3).This represents an increase of 9.9% and 10.9% compared to the historical period.The absolute difference between the R-factor derived from the 2090 projection and the factor from the baseline period indicates that climate change predominantly increases rainfall erosivity in most areas.It is crucial to pay extra attention to the more severe soil erosion in the South China red soil region and Southwest China karst region, which are particularly affected by the increased rainfall erosivity compared to other regions.Compared to the RCP4.5 scenario, the RCP8.5 scenario, which entails an additional 4.0 W m −2 radiative forcing, is projected to result in significantly higher rainfall erosivity across China, except for small areas in the Southwest China purple soil region.The analysis of RCMs indicates that under the RCP8.5 scenario, rainfall erosivity is expected to increase by 6.5% to 21.8% in China, with the largest increase predicted by IDMI and the

Discussion
Accurately predicting the future evolution of rainfall erosivity is crucial for effective soil conservation and land use planning.This information serves as a guide for implementing and managing soil conservation measures.
The Northeast China black soil region has gained national attention since 2000 due to its potential threat to China's commodity grain production and grain security (Li et al 2021).Unwise land use practices and harsh environmental changes have resulted in a significant reduction in soil depth, from 60-70cm in the 1950s to 20-30cm currently (Fang et al 2012).Despite the relatively small increase in rainfall erosivity within the region, it remains essential to strengthen soil and water conservation measures to prevent further deterioration.Climate warming has led to an uneven distribution of precipitation in northern China, resulting in more frequent droughts and extreme precipitation events (Zhu et al 2018, Zhang et al 2022).Prolonged droughts have exacerbated vegetation degradation and soil compaction, increasing the vulnerability of the soil to erosion during extreme precipitation events and intensifying soil and water loss.Strengthening comprehensive management of regional soil erosion is urgently needed to maintain the ecological integrity of the North China Plain and alleviate the water resource supply-demand imbalance downstream.The Loess Plateau is globally recognized as one of the most severely eroded regions, primarily due to human activities and its unique geographic features such as erodible loess soil and steep slopes (Zhao et al 2013).Rainfall erosivity is the primary driving force behind soil erosion in this area (Wen and Deng 2020).However, anthropogenic interventions have partially mitigated the adverse effects of increased rainfall erosivity (Guo et al 2019).Implementing appropriate erosion control measures can effectively minimize the risk of erosion (Jin et al 2021).
It is noteworthy that the greatest absolute increase in rainfall erosivity occurs in South China's red soil region.The region's undulating topography, characterized by interlacing mountains and hills, exacerbates the damage caused by high-intensity rainfall to surface soil through rapid runoff formation.To address soil erosion effectively, soil conservation measures should be targeted towards sloped farmlands and orchards, which are particularly susceptible to erosion (Li et al 2020).Furthermore, South China's red soil region is characterized by a high population density and rapid social and economic development, underscoring the need for appropriate adaptation and mitigation measures to ensure urban water and soil conservation (Li et al 2022).In the Southwest China karst region, severe soil erosion and rock desertification are prevalent due to excessive exploitation activities and karstification, coupled with the thin and easily erodible soil layer on karst landforms.Water erosion ranks as the second highest contributor to soil loss in China (Qin et al 2016).Despite substantial ecological restoration efforts by the Chinese government, the erosion risk in the Southwest China karst region is projected to increase in the future (Lai et al 2016).Consequently, it is essential to proactively formulate prevention measures to reduce soil erosion risk.
According to Sun et al (2022), although RCM simulations suggest a potential decrease in rainfall erosivity in the Southwest China purple soil region, climate change is still anticipated to increase seasonal droughts.These droughts have a detrimental impact on sloping farmlands, leading to reduced vegetation cover and increased exposure of land to raindrop impact and runoff, ultimately intensifying rainfall erosivity.Purple soil erosion in this region not only hinders the sustainable development of local agriculture but also poses a threat to the safe operation of the Three Gorges Project by contributing to a significant sediment load upstream.Conversely, climate change has minimal impact on changing rainfall erosivity in the North China sandstorm region, where soil erosion is predominantly caused by wind erosion.However, temperature and precipitation, influenced by climate change, are the primary factors affecting ecological vulnerability in this region, and improving these factors can help reduce erosion (Wu et al 2021).On the Qinghai-Tibet Plateau, rainfall erosivity increases with amplified precipitation, promoting vegetation restoration and growth, thereby enhancing the soil-protecting function of vegetation (Liu et al 2013).However, the central and eastern parts of the plateau are ecologically fragile and increasingly vulnerable to the impacts of climate change (Chen et al 2021).The significant increase in rainfall erosivity resulting from rising greenhouse gas concentrations poses a significant threat to maintaining ecological balance.
Figure 5 illustrates the seasonality of strong rainfall erosivity in the Southwest China purple soil region, which occurs predominantly from April to September, accounting for 79.4%-87.4% of the annual rainfall erosivity.While the annual distribution characteristics of rainfall erosivity simulated by CCLM and PRECIS remain consistent as radiative forcing increases, MCLM and IDMI simulations demonstrate a shift in the peak value of monthly rainfall erosivity to July under the RCP8.5 scenario, compared to June in the historical period and RCP4.5 scenario.
The relationship between extreme precipitation and temperature change has been increasingly explored in recent studies, employing the Clausius-Clapeyron (CC) relationship as a mechanism to explain the rise in extreme precipitation with climate warming.According to the CC relationship, the increased temperature raises the atmosphere's maximum water holding capacity.For every 1 °C increase in temperature, the atmospheric water holding capacity is estimated to rise by 6%-7% (Panthou et al 2014).Assuming other factors remain constant, precipitation intensity is directly influenced by the water content in the atmosphere.The ratio of precipitation intensity change to temperature increase is expected to follow the CC ratio.To investigate the mechanisms behind rainfall erosivity changes under climate change, this study explores the relationship between the 90th percentile of precipitation and temperature in each region (figure 6).Model simulations and observations both exhibit a peak structure in their corresponding relationship curves.Prior to reaching the peak temperature, rainfall intensity increases with rising temperatures, leading to a positive change in rainfall erosivity.Beyond the peak temperature, rainfall intensity decreases as temperature continues to rise.Notably, under the RCP8.5 scenario, the peak temperature is projected to shift to higher values, indicating that extreme rainfall will intensify with temperature warming.This heightened occurrence of extreme rainfall will elevate the potential for rainfall erosivity in each region (Duan et al 2021).The thermal mechanism plays a significant role in the development of extreme rainfall events, contributing to the projected future high levels of rainfall erosivity across China.
Assessing the impact of climate change on rainfall erosivity involves various sources of uncertainty, including model uncertainty and observational data uncertainty.To mitigate model uncertainty, employing an ensemble of regional climate models (RCMs) can be beneficial.The Bayesian Model Averaging (BMA) approach reveals that simulations from HCLM and PRECIS significantly contribute to accurately reproducing the spatial patterns of rainfall erosivity, while the impact of the other three simulations is minimal, indicated by their nearly zero BMA weights.This contradicts the assumption of the Average Ensemble Mean (AEM) approach, which assigns equal weights to each ensemble member, resulting in a significant deviation from the observed data.In contrast, the BMA approach assigns more weight to simulations that better replicate the historical climate.
Conventional rain gauges have limited capacity to capture the spatiotemporal variability of precipitation systems due to the uneven distribution of stations.This poses challenges for large-scale research, particularly in complex topographic regions.Gridded precipitation products, such as the APHRODITE dataset, offer an alternative data source with broad spatial coverage and high spatial-temporal resolution, making them more suitable for hydrological studies.APHRODITE, providing daily precipitation estimates at a high resolution of 0.25°for Monsoon Asia, is the most representative dataset in this regard.However, using APHRODITE as observations for comparison with RCMs simulation results introduces some uncertainties into the analysis, despite its extensive use and good performance in different Asian regions.
Recent studies have emphasized the limitations of simple algorithms for rainfall erosivity evaluation and highlighted the advantages of a field-based approach to water erosion assessment.While modeling cannot replace field measurement and on-site monitoring, it becomes indispensable and necessary for large-scale evaluations.The primary objective of this research is not to provide an exact value of soil erosion but to offer a comprehensive understanding of the potential future conditions of soil erosion.It lays the groundwork for future research, provides insights into potential mitigation measures, and informs decision-makers' planning processes.

Conclusion
This study utilizes an ensemble of high-resolution regional climate models (RCMs) to project rainfall erosivity under climate change, aiming to address soil and water loss issues and promote ecological remediation in China.The RCMs provide detailed information and effectively capture extreme rainfall events.Through reliable assessments and investigations of driving mechanisms, the study generates robust projections for the RCP4.5 and RCP8.5 scenarios at a national scale.
The findings reveal that the national multi-year mean rainfall erosivity from 1986 to 2005 is approximately 1010.8 MJ•mm•hm-2•h-1.Among the regions, the South China red soil region exhibits the highest annual mean rainfall erosivity, followed by the Southwest China purple soil region and Southwest China karst region, while the North China sandstorm region experiences the lowest erosivity.Notably, the HCLM and PRECIS models outperform the IDMI model in reproducing the spatial and temporal distributions of rainfall erosivity in China.The Bayesian Model Averaging (BMA) approach yields better results than the Average Ensemble Mean (AEM) approach.
Under both RCP4.5 and RCP8.5, all RCMs project an overall increase in rainfall erosivity across most regions.The greatest increase is projected for the South China red soil region and the Southwest China karst region.The simulations from CCLM and PRECIS indicate that climate change will not lead to seasonal variations in the annual distribution of rainfall erosivity.The study highlights the importance of implementing scientific prevention and management measures in different soil and water conservation areas to mitigate soil erosion risks.However, it is crucial to acknowledge limitations and uncertainties associated with data availability and model parameterization in this study.The calculation of rainfall erosivity only utilised a function related to rainfall amount, whereas climate change may affect rainfall erosion rates through changes in rainfall type or intensity.To address these challenges, future efforts should focus on adopting finer-resolution RCMs capable of realistic simulations of precipitation and other climatic variables.

Figure 1 .
Figure 1.The eight soil and water conservation areas used in the study over China.

Figure 6 .
Figure 6.Relationship between rainfall intensity and temperature warming over China from 5 RCMs under RCP8.5 (color lines) against APHRODITE for the baseline period (black line).

Table 1 .
(Madadgar and Moradkhani 2014)mulate and project rainfall erosivity.Bayesian model averaging (BMA) is an approach that combines the forecast densities predicted by different models and produces a new forecast PDF(Madadgar and Moradkhani 2014).Assume that y is the simulated value, D = [y 1 , y 2 , K, y T ] is the observations of the historical period, and f al 2018, Guo et al 2019).The erosivity exceeded 3500 MJ•mm•hm −2 •h −1 in the South China red soil region, while remaining below 1000 MJ•mm•hm −2 •h −1 in the Northeast China black soil region, Northwest China Loess Plateau region, North China sandstorm region, and Qinghai-Tibet Plateau region.The mean annual rainfall erosivity for China was estimated to be 1010.8MJ•mm•hm −2 •h −1 (table 2).These findings are consistent with previous studies (Guo et al 2019, Chen et al 2020).

Table 2 .
The regional mean rainfall erosivity (unit: MJ•mm•hm −2 •h −1 ) from the observation and RCMs for China and sub-regions.
region and Southwest China karst region, with the Southwest China purple soil region showing the lowest increase.MCLM projects positive changing trends, but the magnitude of change in rainfall erosivity varies the least among RCMs, with minimal change observed in the northwest.Conversely, IDMI overestimates rainfall erosivity for the baseline period and projects the largest change magnitude over China among all RCMs.By 2090, the South China red soil region, Southwest China purple soil region, and North China mountainous region exhibit the highest mean relative increase in rainfall erosivity, while the North China sandstorm region remains relatively stable.PRECIS projects a pronounced increase in rainfall erosivity in most parts of the South China red soil region, Southwest China purple soil region, and North China mountainous region.The AEM and BMA results reveal that under the RCP4.5 scenario, future rainfall erosivity over China is projected to be approximately 2674.0 MJ•mm•hm −2 •h −1 and 2068.3MJ•mm•hm −2 •h −1 , respectively (table

Table 3 .
(Zhu et al 2018)all erosivity (unit: MJ•mm•hm −2 •h −1 ) from RCMs and their ensemble means of China and sub-regions for 2071-2090 relative to 1986-2005 under two RCPs.According to the AEM and BMA RCMs ensemble results, rainfall erosivity is estimated to increase by 13.6% and 14.6%, respectively, compared to the baseline period under RCP8.5.The AEM reveals an absolute increase of 826.6 and 797.6 MJ•mm•hm −2 •h −1 in the Qinghai-Tibet Plateau and North China mountainous region, respectively.On the other hand, the BMA indicates that the South China red soil region and the Southwest China karst region will experience the largest absolute increase in rainfall erosivity, with values of 463.3 and 677.0 MJ•mm•hm −2 •h −1 , respectively.The comparison of results between the two RCPs suggests that changes in the Southwest China karst region and the Northwest China Loess Plateau region are particularly sensitive to the increased radiative forcing simulated by most models.The intensified warming under RCP8.5 may reduce the thermal contrast between the Asian landmass and neighboring oceans during winter, leading to weaker winter monsoons in northern sub-regions.This weakened winter monsoon prevents the influx of cold-dry air from high latitudes(Zhu et al 2018).