A Framework to Project Future Rainfall Scenarios: An Application to Shallow Landslide-Triggering Summer Rainfall in Wanzhou County China

Abstract

Fatal landslides are a widespread geohazard that have affected millions of people and have claimed the lives of thousands around the globe. A change in climate has significantly increased the frequency and magnitude of rainfall, which affect the susceptibility of slopes to shallow landslides. This paper presents a methodological framework to assess the future changes in extreme and seasonal rainfall magnitudes with climate model projections. This framework was applied to project summer rainfall over Wanzhou County, China, using an ensemble of four regional climate models (RCMs) from the East Asian domain of the Coordinated Downscaling Experiment (CORDEX) under the Phase 5 Coupled Intercomparison Modeling Project (CMIP5). The results find that extreme daily rainfall was projected to decrease in the mid-21st century, with an uncertainty measured by a coefficient of variation between 5% and 25%. The mean seasonal rainfall is projected to increase in the mid-21st century up to a factor of 1.4, and up to a factor of 1.8 in the late-21st century. The variation in the mid-21st century ranged from 10% to 35%, and from 30% to 50% in the late-21st century. This case study delivered a proof-of-concept for a methodological framework to derive shallow landslide-triggering rainfall scenarios under climate change conditions. The resulting spatially distributed climate change factors (CCFs) can be used to incorporate future rainfall scenarios in slope susceptibility models and climate impact assessments.

1. Introduction

Fatal landslides have affected millions of people and have claimed the lives of thousands around the globe [1]. Growing landslide frequency in a changing climate is expected with the increasing rainfall magnitudes and anthropogenic activities, which will destabilize sloped regions globally [2,3,4,5,6,7]. In order to conduct a quantitative analysis of the effect of changes in climate on landslide susceptibility, the projection of rainfall scenarios is essential for physically based models and susceptibility assessments [3,8,9]. It is foreseen that the initiation of shallow landslides will have a critical impact on changes in extreme rainfall and antecedent rainfall conditions [10,11,12,13,14,15,16,17,18].

Quantifying the evolution of rainfall variables as an input to physically based landslide models is a critical task. Studies have proposed frameworks and developed methods to assess slope stability under changing climate conditions. Initial assessment studies assess rainfall thresholds for slope susceptibility and incorporate dynamically downscaled climate models to estimate rainfall and typhoon events using extreme rainfall distributions [19,20]. The direct use of climate models as an input in impact models is hindered by uncertainties in the model processes that limit the representation of precipitation at a local scale [21,22]. The combined effect of these uncertainties leads to a bias between simulations and observations. This requires the post-processing of climate model outputs through a bias correction to be used for quantitative impact assessments [23].

The incorporation of bias correction methods to establish rainfall thresholds from climate model projections have been used to assess the triggering maximum 1-day rainfall and the antecedent rainfall conditions at durations varying between hours and months prior to a landslide [20,23,24]. One pertinent assumption in establishing thresholds from historical landslide inventories is that the temporal certainty of the recorded events is adequate to reconstruct the triggering rainfall conditions.

The limitation of landslide inventories is highlighted by the observed complex interactions of physical processes that govern the behavior of landslide susceptibility and add uncertainty in the predictions of thresholds [3,8,9]. Therefore, some studies have incorporated extreme rainfall projections from climate change models with physically based landslide susceptibility models to assess the impact on slope stability [25,26,27].

The role of antecedent rainfall as a determining factor for landslide initiation is recognized to significantly influence the rainfall thresholds of slope stability and results in physically based susceptibility models [8,10,11,12,13,14,15,16,17,18]. This reflects the primary role antecedent rainfall has on soil hydrological conditions that predispose shallow slope stability [10,17,18,28].

The consideration of antecedent conditions is widely used and a variety of approaches to incorporate its influence are utilized [29]. Indices have been established to capture the interaction between the rainfall with the predisposing hydromechanical conditions before an extreme rainfall event, and are widely used to establish better-informed thresholds in predicting slope stability [10,12,15,30]. The use of such indices requires detailed field data and models to capture the hydrological process that governs the movement between rainfall and recharge [13,14,30]. The incorporation of changing climate conditions with such indices requires the downscaling and correction of climate model outputs to serve as hydrological model inputs [27,31,32].

The duration by which antecedent conditions are considered to have a significant influence on stability can be determined as being 30 days. It has been shown that the 30-day antecedent conditions have a significant influence on the rainfall thresholds of slope failure [16,33], the recharge in a calibrated antecedent rainfall index [12,13,15], and the physically based seepage and stability model [17].

A gap in the existing frameworks and methods was observed in the incorporation of antecedent rainfall scenarios in susceptibility assessments from bias-corrected climate model projections. The projections of antecedent conditions on landslides provide significant information on the subsurface system and are critical to assessing susceptibility under climate change conditions. [3,10,11,12,13,14].

Incorporating changes in rainfall and associated parameters under changing climate conditions requires predictions of future susceptibility using physically based models [3]. This will give us better insight on the interaction between changes in rainfall and the physical processes governing slope stability [8,25]. It is essential to incorporate climate factor approaches and ensemble methods to reduce the uncertainty of rainfall projections [32,34,35]. The objective of this research is to establish a methodological framework to quantify landslide-triggering rainfall in the future with climate model projections and to measure the uncertainty in these projections. This framework integrates methods to establish present extreme and seasonal rainfall scenarios and to derive projections with bias-corrected climate change model outputs. Methods to quantify the performance of the derived present rainfall scenarios and the uncertainty in the ensemble of bias-corrected rainfall projections are presented in support of this framework. An application of this to a case study area over Wanzhou County, China, is presented to quantify the change in present rainfall conditions under the Representative Concentration Pathway 8.5 (RCP8.5) climate projections. The results and the identification of sources of uncertainties in this study aim to demonstrate a viable method to link climate model projections and quantitative slope susceptibility assessments.

2. Study Area

Wanzhou County, China, is located with the coordinates 30°24′25″ N, 107°52′22″ E to 31°14′58″ N, 108°53′25″ E. The 3457 km${}^2$ study area, in Figure 1, is located within the Three Gorges Reservoir, along the Yangtze River upstream of the Three Gorges Dam. The elevation in Wanzhou County ranges from 120 m to 1656 m asl, and, overall, the elevation of the northwest part is lower than the southeast part [36,37].

This region of China is categorized as a subtropical humid monsoon zone with a mean annual precipitation of 1191.3 mm. The precipitation in the area is characterized by 90% of the annual rainfall occurring between May and September. Summer rainfall can be characterized by short intense rainstorms with daily rainfall values exceeding 100 mm/day [38]. The lithology in Wanzhou County mainly comprises a Jurassic (J) system and a Triassic (T) system. The Jurassic system consists of mudstone, sandstone, siltstone, and shale. The Triassic system is primarily composed of limestone, claystone, sandstone, siltstone, and coal [36].

Frequent disastrous and complex landslide events in Wanzhou County have been the subject of research and susceptibility assessments in recent years due to its proximity to the Three Gorges Dam along the Yangtze River [39,40,41,42,43]. Heavy rainfall has been attributed as a significant trigger to the frequent landslides that have occurred [36,44,45].

A shallow landslide inventory created by the Wanzhou Institute of Geological Environment Monitoring, in Figure 1b, captures the spatial distribution of events within the Wanzhou County area from 1995–2005. Within this period, 186 shallow landslide events occurred across the study area. It was found that 146 of the shallow landslides in the area occurred between June and August.

The area of the shallow landslides varies from 50 m${}^2$ to 10${}^4$ m${}^2$, with a total area of approximately 0.4 km${}^2$. All of the landslides have a depth of less than 10 m, and volumes between 200 m${}^3$ to 10${}^5$ m${}^3$ [37]. Typical summer rainfall events that trigger shallow landslides are intense heavy rainfall over a short duration and continuous rainfall lasting for days [37,45]. As a consequence, the shallow landslides cause considerable damages and losses every summer in Wanzhou County [38].

Vertisols, Anthrosols, and Cambisols are the most common soil types in Wanzhou County, accounting for more than 75% of the total area in Figure 2. More than 80% of shallow landslides occurred in Vertisols and Anthrosols, whereas other soil types are of minor importance for landslide occurrence. The peak density of shallow landslides is also related to these two soil types.

Extensive assessments of climate change projection of rainfall and extreme events in the Upper Yangtze River Basin and across China have been conducted. An increase in the annual precipitation, frequency of wet days, and extreme rainfall by the end of the 21st century is projected in the region [48,49,50]. Other studies suggest a decrease in the precipitation rate and extremes by the middle of the 21st century [31,51].

Therefore, this study aimed to apply the framework to quantify the change between present and future rainfall scenarios for the summer season.

3. Materials and Methods

3.1. Methodological Framework

The methodological framework in Figure 3 outlines the process of performing a climate change analysis for extreme daily rainfall and mean seasonal rainfall at a regional scale. This framework takes input data from the observations to conduct a present rainfall analysis and regional climate model (RCM) simulations for a projected rainfall analysis. The resulting future rainfall scenarios utilize products from both analyses to describe the change in rainfall magnitude from the present. The final products of the framework outlined are future landslide-triggering rainfall scenarios. This can be obtained through the multiplication of the climate change factors (CCFs) to the present rainfall scenarios derived. While the framework represents pertinent variables and processes required to derive scenarios of rainfall in the future, the specific methods presented in this paper were selected based on the input data available for the study area.

3.2. Input Data

The China Meteorological Forcing Dataset (CMFD) was selected to analyze the present rainfall conditions of the study area [52]. These data have a temporal resolution of 3 h and a spatial resolution of 0.1°. They are derived from the integration of multi-satellite remote sensing products, reanalysis datasets, and rain gauge observations from 1979 to 2018.

In order to determine the change in rainfall magnitude under changing climate conditions, this study utilized RCM simulations from the Phase 5 Coupled Intercomparison Modeling Project (CMIP5) and the East Asian domain of the Coordinated Downscaling Experiment (CORDEX) [53,54]. A multi-model ensemble projection from RCM simulations at spatial resolutions of 0.22° was used in this study. The utilization of a multi-model ensemble aimed to limit uncertainties derived from the parametrization of individual climate models [55]. This research project considered an ensemble of 4 RCMs to pilot the methodological framework while still obtaining a reasonable projection [34]. The model outputs from REMO2015 [56] and RegCM4 [57] were selected based on their reasonable representation of the climate over China [31,58,59]. The combinations of the selected ensemble members are shown in

Table 1. Summary of ensemble members.

Ensemble Members	GCM Model	RCM Model
Member 1	HadGEM2-ES	REMO2015
Member 2	HadGEM2-ES	RegCM4
Member 3	MPI-ESM-LR	REMO2015
Member 4	MPI-ESM-MR	RegCM4

.

Two driving models providing boundary conditions for the RCM models were considered. The first was the HadGEM2-ES, developed by the United Kingdom’s Met Office Hadley Centre [60]. Two versions of the Max Planck Institute for Meteorology Earth System Model (MPI-ESM) were utilized in this study. The first was the MPI-ESM-MR, driving the RegCM4 outputs, and the MPI-ESM-LR, driving the REMO2015 outputs. The differences in configuration of the MPI-ESM models are in their grid configuration. The MPI-ESM-LR runs on a bipolar grid with a 1.5° horizontal resolution, whereas the MPI-ESM-MR runs on an “eddy-permitting” tripolar grid with 0.4° horizontal resolution [61].

The projection resulted from an equal weighing of ensemble members. This was implemented to reduce uncertainty in the climate projections that would otherwise be derived from assigning weights to ensemble members [35]. The climate model data from the RCMs considered in this research project belonged to the historical simulations and the projections of the RCP 8.5 scenario.

3.3. Present Rainfall Analysis

The methods for the present rainfall analysis mainly comprised frequency distribution modeling using extreme value statistics (EVS) and goodness-of-fit testing to derive and validate return period curves to represent extreme daily rainfall in the CMFD observations. The mean seasonal rainfall was computed by taking the mean daily rainfall between May and August to represent the antecedent rainfall conditions.

3.3.1. Extreme Daily Rainfall Analysis

The procedure for estimating the parameters of the Gumbel distributions was applied after extracting a time series of daily precipitation from each CMFD pixel within the study area. Three goodness-of-fit tests assessed the performance of the estimated distributions within a 95% confidence interval.

The application of extreme value statistics in this study area was implemented to determine the frequency distribution of extreme rainfall-triggering event rainfall. This study utilized the block maxima approach to derive the probability distribution functions of extreme daily rainfall from the daily precipitation measurements in CMFD dataset [62].

$$Mn=max\{P1,\dots ,Pn\}$$

(1)

where a sequence of n daily precipitation P variables was taken into consideration. The maximum values $Mn$ obtained from the blocks of the equation above were then utilized to obtain a probability distribution function. Although annual maxima are typically considered for hydrological applications, monthly maxima were used here to more precisely derive annual return levels [63,64].

The Gumbel probability distribution function was selected to obtain the return periods from the monthly maxima. An assessment of rainfall-induced complex landslides adopted the Gumbel distribution to model the frequency distribution of extreme daily rainfall at 10-day intervals derived from 50-year rainfall records within Wanzhou County [45]. The Gumbel distribution probability density function (PDF) $f(x)$ and cumulative density function (CDF) $F(x)$ are given in the following equations:

$$f(x)=(\frac{1}{\alpha })exp[-(\frac{x-\beta }{\alpha })-exp(-(-(\frac{x-\beta }{\alpha }))]$$

(2)

$$F(x)=exp[-exp(-(\frac{x-\beta }{\alpha }))]$$

(3)

where $\alpha$ is the scale parameter and $\beta$ is the location parameter. The relationship between the mean, $\mu$, location, and scale parameter is given:

$$\mu =\beta +0.5772\alpha$$

(4)

The extreme rainfall rates $R_T$ in mm/day given the recurrence period of T years were determined using the equation:

$$R_T=\mu -\alpha [ln(ln(\frac{T}{T-1}))]$$

(5)

The parameters for the Gumbel distributions were calculated by the maximum likelihood estimation (MLE) method implemented with the ’fitdistrplus’ R package [65].

3.3.2. Goodness-of-Fit Tests

The goodness-of-fit of the estimated Gumbel distributions through the Kolmogorov–Smirnov (KS) test, the Anderson–Darling (AD) test, and the Cramer–von Mises (CVM) criterion was evaluated at a confidence level of 95%.

The KS test statistic is the maximum vertical difference between the CDF of the modeled and empirical distributions. The KS test has been observed to be weaker in power when compared to other goodness-of-fit tests [66]. The AD test puts more weight on the performance of the tails of the cumulative distribution function, and is dependent on the distribution function taken into consideration. The CVM statistic measures the main squared difference between the empirical CDF and a fitted CDF. The KS, AD, and CVM tests were implemented through the ‘goftest’ R package [67]. The AD test is also observed to perform marginally better than the CVM test [66].

3.4. Projected Rainfall Analysis

This section presents the methodology developed to derive CCFs from the ensemble of bias-corrected RCM projections of extreme daily rainfall and mean seasonal rainfall.

3.4.1. Quantile Delta Mapping Bias Correction

The objective of bias correction is to remove systematic errors resulting from the different climate model configurations. Bias correction was performed on RCM outputs to extract the climate signals for extreme daily rainfall and mean seasonal rainfall. The bias-corrected rainfall was corrected against the reference period of 1979 to 2018. The dataset of the reference period consisted of simulations from the historical model results from 1980 to 2005, and the RCP 8.5 projections from 2006 to 2018. This process was used to derive scenarios for the mid-21st century and late-21st century scenarios.

A quantile delta mapping (QDM) bias correction method was implemented to preserve the changes in quantiles in the climate model projections [68,69]. The procedure for QDM follows the process of first detrending the simulated model projection through QM during a calibration period. The relative changes in quantiles between the calibration period and the projected period of interest were then derived from the ratio between the distribution of precipitation. This ratio of change is derived from the equation below:

$$\Delta (t)=\frac{x_{(m,p)}}{F_{m,c}^{-1}[F_{m,p}^{(t)}(x_{m,p}(t)]}$$

(6)

where $\Delta (t)$ is the factor of relevant change in precipitation for the period of interest t, $F_{m,c}^{-1}(t)$ is the inverse CDF derived from the model projections over the reference period, $F_{m,p}^{(t)}$ is the CDF derived from the model projections over the period of interest t, and $x_{m,p}(t)$ is the precipitation model projection over the period of interest t.

The bias-corrected precipitation is derived from the product between the factor of relative change and the detrended variable $\widehat{x}$, as shown in the equation:

$$x_{bc}(t)=\widehat{x}\Delta (t)$$

(7)

where $x_{bc}(t)$ is the bias-corrected precipitation time series for the period of interest t.

The objective of performing bias correction on RCM outputs was to correct the substantial systematic error, partly inherited from the GCM on the boundary conditions, and to obtain results to assess trends and climate signals. Bias correction was performed separately for daily rainfall and extreme daily rainfall.

The distributions of daily rainfall were corrected using a transfer function derived from the empirical cumulative distribution function of the observed daily rainfall. This approach reduces uncertainty derived from the fitting of an assumed frequency distribution model to the rainfall observations [69,70]. The bias correction of daily rainfall from May to August was used in order to compute the mean seasonal rainfall.

The application of bias correction to capture projected precipitation extremes considered limitations of the climate models to simulate the frequency and magnitude of such events on regional and local scales [71]. The conventional bias correction method using daily data proved to have a limited ability to capture extreme rainfall quantiles, thus requiring an independent bias correction for the application of extreme rainfall frequency analysis [72]. Though RCMs were found to over-predict the probability of extreme daily precipitation, it was found that results could be corrected to adequately represent the upper-tail distributions in observations [73].

The extreme daily rainfall utilized Gumbel distribution models as transfer functions. The Gumbel frequency distribution of extreme events has been used to represent extreme rainfall in the study area [45]. The magnitude of extreme daily rainfall was determined for different return periods with Equation (5) with the bias-corrected Gumbel fitting parameters for each grid point. The main limitation of the proposed QDM bias correction for extreme daily rainfall is the assumption that a Gumbel frequency distribution will remain adequate under future climate conditions.

3.4.2. Multi-Model Ensemble Projections

The multi-model ensemble projections considered were the most extreme scenario projections under RCP 8.5 conditions for mean seasonal rainfall and extreme daily rainfall. The scenarios are defined by the future periods in the mid-21st century from 2021–2060 and late-21st century from 2061–2100. The mean ensemble projections were reported as a CCF relative to the reference period of 1979 to 2018 (

Table 2. Definitions of climate change scenarios.

Scenario	Period (Years)	RCM Scenario Outputs
Reference	1979–2018	Historical + RCP 8.5
Mid-21st Century	2021–2060	RCP 8.5
Late-21st Century	2061–2100	RCP 8.5

).

In order to incorporate the trend of climate signals for extreme daily rainfall and mean seasonal rainfall, a CCF was computed. The derivation of change factors instead of directly applying downscaled RCM results reduced the uncertainty from the complex climate modeling chain [32]. The CCF represents the ratio of change in magnitude of rainfall in the future, given by Equation (8).

$$CC{F}_i=\frac{P_{F,BC}}{P_{H,BC}}$$

(8)

where $CC{F}_i$ is the climate change factor of or either the value of the mean seasonal rainfall, $CC{F}_{\mathrm{MSR}}$, or extreme daily rainfall, $CC{F}_{\mathrm{EDR},T}$, for a return period T. The derivation of the $CC{F}_{\mathrm{EDR},T}$ for extreme daily rainfall considers $P_{F,BC}$ as the magnitude of rainfall on the return period curve derived from the bias-corrected future scenario simulations corresponding to a return period T, and $P_{H,BC}$ as the magnitude of rainfall on the return period curve derived from the bias-corrected historical simulations corresponding to return period T. The climate change factor $CC{F}_{\mathrm{MSR}}$ for antecedent seasonal precipitation is computed by considering the mean seasonal rainfall. $P_{F,BC}$ is the the mean seasonal rainfall from bias-corrected future daily rainfall simulations, and $P_{H,BC}$ is mean seasonal rainfall derived from bias-corrected historical daily rainfall. A $CC{F}_{\mathrm{MSR}}$ value was derived for future scenarios defined in Table 2. The CCFs derived from the bias-corrected RCM results were then bi-linearly interpolated into a spatial resolution matching the CMFD data set grid points through the ‘akima’ package in R [74].

4. Results

4.1. Reconstruction of Triggering Rainfall Conditions

A 7-day uncertainty period was applied to find the maximum event rainfall and the 30-day antecedent rainfall for events that occurred from June to August of 1995–2005. The antecedent rainfall and EDR conditions corresponding to the shallow landslides recorded in the inventory for the period of 1995–2005 were reconstructed with the CMFD gridded precipitation dataset. A temporal uncertainty of 7 days prior to the recorded dates was incorporated by taking the maximum rainfall values within this time window [75].

The 2D density plot of reconstructed rainfall conditions in Figure 4 suggests that a significant number of the shallow landslides occurred with antecedent rainfall ranging from 3 mm/day to 6 mm/day, and the extreme daily rainfall (EDR) shows a cluster of events with values ranging from 10 mm/day to 30 mm/day, and a secondary grouping between 60 mm/day and 80 mm/day.

A comparison between the distribution of the reconstructed 30-day antecedent rainfall conditions of the inventory and all 30-day antecedent rainfall observations from all CMFD pixels within the study area is shown in Figure 5. The 30-day average rainfall is derived from CMFD observations across the study area for the months of May–July to represent all possible 30-day antecedent rainfall conditions from 1995 to 2005. The similarity between the medians and distributions of the two data sets is described in the plot of Figure 5. A Wilcoxon rank sum test on the medians of the 30-day antecedent rainfall data sets returned a p-value of 0.428. This indicates that the location of the medians of both distributions is statistically significant, within a 95% confidence interval.

Furthermore, a comparison of the distribution of the 30-day antecedent rainfall from May–July and May–August reveals identical distributions with similar medians in Figure 5. This indicates that the mean seasonal rainfall (MSR) from May to August can adequately represent the average antecedent rainfall conditions that were likely to have triggered shallow landslides from 1995 to 2005.

4.2. Extreme Daily Rainfall Scenarios

The EDR in this study is defined by the monthly maxima for the period of June to August of 1979–2018. The frequency distribution for each CMFD pixel in the area of interest was fit with a Gumbel mode; a summary of the parameters is presented in

Table 3. Summary of minimum, mean, and maximum Gumbel fit parameters.

Gumbel Fit Parameters	Minimum	Mean	Maximum
Scale $\alpha$	14.6	17.3	21.7
Beta $\beta$	29.4	32.9	36.9
Mean $\mu$	30.3	33.9	38.1
Standard Deviation $\sigma$	18.8	22.2	27.8

.

The goodness-of-fit statistical tests performed to validate the results of the Gumbel frequency distribution models are summarized in

Table 4. Summary of goodness-of-fit test statistics with p-values (in parenthesis).

Goodness-of-Fit Test	Minimum	Mean	Maximum
KS Test	0.029 $(0.39)$	0.052 $(0.86)$	0.082 $(1.00)$
AD Test	0.145 $(0.53)$	0.318 $(0.91)$	0.730 $(1.00)$
CVM Test	0.015 $(0.44)$	0.046 $(0.89)$	0.136 $(1.00)$

. The minimum, maximum, and mean test statistics and p-values across the spatially distributed pixels are summarized in Table 4. The results of the Gumbel distribution fitting to the EDR data across the area of interest provide an adequate model of the frequency distribution within a 95% confidence interval.

The resulting parameters of the validated Gumbel distributions were then utilized to estimate daily rainfall corresponding to return periods between 2 years and 200 years in Figure 6. The return curves derived from the Gumbel fittings indicate significant spatial variation in exposure to increased EDR magnitudes as the return period increases.

A comparison of the range of the Gumbel frequency distributions in Figure 6 for the study area and the reconstructed EDR in Figure 4 exhibits a limitation in the CMFD data set and the extreme value distribution in capturing the return period of the triggering-EDR event. The minimum EDR value captured by the extreme distribution is 40 mm/day, whereas a group of EDR values in the reconstruction of the inventory lies between 10 mm/day and 30 mm/day. This suggests that the antecedent rainfall and the MSR have a significant influence on triggering a majority of shallow landslides, with only a handful of landslides triggered by extreme rainfall events. These results reflect the incapability of spatiotemporal rainfall products in capturing rainfall patterns at the resolution necessary for reconstructing landslide-triggering EDR [76].

The spatial distribution of EDR magnitudes for the 10-year and 50-year return period scenarios are mapped in Figure 7. The center of Wanzhou County increases in EDR magnitude between the two return period scenarios. This area of risk is in the center of the study area, which lies within a valley between mountain ranges that reach peak heights of 1640 m on both sides, as shown in Figure 1. The location of this area suggests that an orographic enhancement of precipitation could influence low frequency, high magnitude EDR events during the summer season.

The projected climate change factors for EDR were obtained from the mean CCF of the EDR bias-corrected ensemble. The range of the ensemble mean $CC{F}_{\mathrm{EDR},T}$ values are between 0.9 and 1.2. A projected decrease below 1 for $CC{F}_{\mathrm{EDR},T}$ values was observed in the western region of Wanzhou County in the mid-21st century.

The first region covers a band in the western region of the study area and the extreme daily rainfall is expected to decrease, measured by the range of $CC{F}_{\mathrm{EDR},T}$ being between 0.9 and 1.0. The eastern region of the study area shows a consistent CCF between 1.0 and 1.2. An area in the southeast region of Wanzhou County has a CCF value projected to be below 1.0. This region reduces the area as the return period increases.

The spatial distribution of the projected $CC{F}_{\mathrm{EDR},T}$ values in the late-21st century projections in Figure 7 defines two characteristic regions. The first region predominantly covers the study area, with $CC{F}_{\mathrm{EDR},T}$ values between 1.2 and 1.4. The second region projects higher magnitudes of EDR, with $CC{F}_{\mathrm{EDR},T}$ values between 1.4 and 1.6. The central region of the Wanzhou County area and the northeast region shows a consistent pattern of ensemble $CC{F}_{\mathrm{EDR},T}$ projections ranging between 1.2 and 1.4 for EDR, whereas the southeastern region projects an increase in EDR by a factor of 1.4 to 1.6.

4.3. Mean Seasonal Rainfall Scenarios

The MSR was selected to represent the reference scenario that would describe the antecedent rainfall conditions with the potential to trigger landslides during the summer season. The MSR for the months of May to August for the years 1979 to 2018 range from 5.6 mm/day to 5.9 mm/day, as shown in Figure 8.

The projected MSR scenarios were obtained from the ensemble mean CCF from the bias-corrected daily rainfall. The $CC{F}_{\mathrm{MSR}}$ values for the ensemble projection of MSR in the mid-21st century range between 1.0 and 1.4, as shown in Figure 8. There are two distinct regions identified over the study area, with the western region projecting $CC{F}_{\mathrm{MSR}}$ values between 1.0 and 1.2. The values in the eastern region are projected to be between 1.2 and 1.4. In the projections for the late-21st century, the $CC{F}_{\mathrm{MSR}}$ values see an expanded range from 1.2 to 1.8. The increase in values can be identified through three regions. The increase in $CC{F}_{\mathrm{MSR}}$ occurs from west to east, with a narrow band in the southeast of the study area showing values between 1.6 and 1.8.

The ability of the reference scenario derived from the MSR to represent the distribution of the mean daily rainfall in the summer months was assessed by a comparison of the estimated density distributions in Figure 9. The mean daily rainfall of May, June, and August showed a close resemblance to the mean value in the MSR reference scenario. The deviation from the mean of the mean daily rainfall in July suggests a limited ability of the MSR to capture higher magnitude mean monthly rainfall values. Although there is a limitation in representing the distribution of July, the MSR scenario reasonably follows the distribution of rainfall in the summer months.

4.4. Bias Correction Performance

A three-fold cross-validation procedure was conducted to assess the performance of the bias-corrected daily rainfall results in comparison to the CMFD observations from May to August of 1979–2018 [77,78]. The performance of the bias correction was evaluated through the calculation root-mean-squared error (RMSE), summarized in

Table 5. Summary of minimum, mean, and maximum RMSE (mm) values for the bias-corrected daily rainfall from 1979–2018 for each ensemble member in Table 1.

Ensemble Members	Minimum	Mean	Maximum
Member 1	14.30	15.73	17.77
Member 2	14.37	15.79	17.32
Member 3	14.45	15.93	17.89
Member 4	14.33	15.75	17.26

.

The range of RMSE measurements across the study area for all ensemble members is from 14.30 mm to 17.89 mm. The analysis of the RMSE performance in the cross-validation presented provides no conclusive evidence, suggesting one ensemble member outperforms the other for the bias-correction procedure used in this study for daily rainfall.

The validation procedure for EDR was performed through the comparison of the ordered maximum monthly precipitation from the bias-corrected data set from May to August from 1979–2018. Figure 10 summarizes the distribution of RMSE, comparing the bias-corrected EDR versus the EDR derived from the raw RCM outputs across the study area.

The bias correction for EDR significantly reduced the RMSE versus the raw RCM EDR. The results of the comparison of RMSE on the ordered statistics suggest that the MPI-driven bias corrections outperform the HadGEM-driven outputs. This is supported by the interquartile range of the MPI models being between 4 mm/day and 8 mm/day, compared to the HadGEM outputs having a range of 5 mm/day to 10 mm/day. Furthermore, the outliers beyond the maximum whiskers are significantly fewer in number and lower in RMSE value for MPI-driven models when compared to HadGEM-driven models. The RMSE measurements suggest that the bias-corrected MPI-driven RCM models perform better than the HadGEM-driven RCM models in capturing extreme daily rainfall. The performance of the HadGEM-REMO bias correction is derived from the main limitation of the proposed QDM bias correction for EDR in the assumption that a Gumbel frequency distribution will remain adequate across the study area. The application of a mixture of distributions to be performed as a transfer function for bias correction outperforms a single distribution by allowing for a spatial variation of rainfall distributions in different grid cells [31].

4.5. Uncertainty in the Ensemble Projections

The uncertainty in the bias-corrected ensemble projections of future climate change scenarios in the mid-21st and late-21st centuries were assessed and measured using a coefficient of variation. This was calculated from the mean and standard deviation computed from the ensemble. The range of variation in $CC{F}_{\mathrm{EDR},T}$ under the projections for the mid-21st century scenarios is below 25%, as shown in Figure 11. There is an evident growth in uncertainty in the northern borders of the study area as the return period increases from 10 years to 50 years. The ensemble variation in this area is between 15% and 25%, with the majority of the study area remaining within the range of 10% to 15%.

The range of the variation in the late-21st century in Figure 11 is between 0% and 30%; similar to the range observed in the mid-21st century projections. A larger area of increased variation within was observed in the mid-21st century as the return period increased from 10 to 50 years, whereas a decrease in variation across the study area was observed in the late-21st century projections. This trend is particularly evident in the eastern region of the Wanzhou County area. The coefficient of variation of EDR is reduced between the 10-year and 50-year events, evident in the comparison of the southeastern region of the study area. This indicates less uncertainty in the projection of low frequency and high magnitude EDR events in the late-21st century.

The spatial distribution of the coefficient of variation for the MSR projections for the mid-21st century in Figure 11 ranges from 5% to 35%. The regions formed show an increasing trend of variation in the study area from the southwest corner to the northeast. The coefficients of variation of the projected $CC{F}_{\mathrm{MSR}}$ in the central region of the study area ranges from 20% to 25%. The highest variation is observed in the southeast corner, ranging from 25% to 35%. The variation in $CC{F}_{\mathrm{MSR}}$ for the late-21st century ensemble projections is significantly larger than the mid-21st century, with a range of 30% to 50%, as shown in Figure 11. The regional characteristics of the coefficient of variation in projected $CC{F}_{\mathrm{MSR}}$ show an increasing trend from the west to east. The variation in a majority of the Wanzhou County area is from 45% to 50%, thus representing significant uncertainty in the projected $CC{F}_{\mathrm{MSR}}$.

The significant variation in the far late-21st century projections can be attributed to uncertainty derived from the empirically derived transfer function utilized in the bias correction of daily rainfall. This is attributed to limitations in the ability to address large magnitude rainfall events and correct systematic bias. Bias corrections based on transfer functions derived from empirical cumulative density functions (CDFs) of the projections and the observations cannot provide a stable representation of the distributions in future climate projection [69,70]. These factors could magnify systematic biases in the extreme daily rainfall of the late-21st century climate model projections, leading to a significant variation of the ensemble projection.

5. Discussion

This section discusses items regarding the application of the framework to the Wanzhou County area. First, the limitations of the CMFD data in representing the present rainfall conditions. Second, a comparison of the resulting ensemble projections with other studies looking at trends over Wanzhou County. Finally, an analysis of sources of uncertainty derived from the bias correction methodology and ensemble model selection.

The present rainfall scenarios derived to represent the summer season are subject to the limitation of the CMFD data product in capturing actual ground conditions. The rainfall during this season is driven by the Asian summer monsoon, where extreme rainfall events are triggered by tropical cyclones. Unfavorable spatial and temporal resolutions have been a hindrance in capturing the rainfall intensities associated with this driving phenomenon [49]. The CMFD data product underestimated extreme rainfall and accumulated rainfall when measured to station-derived indices in the Qinghai-Tibet Plateau [79]. An assessment of gridded precipitation products found that the component rainfall products of the CMFD dataset were relatively consistent over the East Asian region [80]. The underestimation by the CMFD product compared to station rainfall measurements is attributed to the influence of the integration and interpolation of various rainfall products [52].

The ensemble projections of MSR and EDR scenarios resulted in independent trends for the mid-21st century and late-21st century. The RCP 8.5 pathway projections revealed significant variation among the four RCM ensemble members listed in Table 1. The mid-21st century MSR was predicted to increase by 20–40% relative to the reference scenario in this study. These projections follow a projected trend of increase in annual precipitation under the RCP 8.5 pathway [48]. The significant increase in MSR magnitude over the summer months can be attributed to an anticipated increase in wet days over the East Asian region [49]. This increase in total precipitation will lead to wet antecedent conditions and higher water tables, which will result in a more frequent attainment of critical water contents that will destabilize slopes [81]. An anticipated increase in shallow landslide activity in Southeast Asia, Central and South America, Southern Italy, and across the African continent is expected in response to climate change [3].

This study projected a decrease in EDR magnitude in the near future that follows projections of decreasing precipitation rates by 19.05–19.25 mm per decade by studies using a RegCM4 model at 25 km of horizontal resolution under the RCP8.5 scenario [31,58]. An analysis of six RegCM4 projections found that the decrease in extremes indices was not statistically significant, and was due to an underestimation of specific humidity and water vapor fluxes by the RCMs [51]. A significant increasing trend in maximum daily precipitation by the mid-21st century was projected to be 10.90% over the Yangtze River basin by an ensemble of five RCM models at a horizontal resolution of 50 km [48]. The comparison of this study’s results indicates the influence of model resolution and representations of atmospheric dynamics on climate projections.

This study projects an increase in both EDR and MSR in the late-21st century. The projections in this study are corroborated by an increase in extreme rainfall over China and an increase in summer season rainfall over the Yangtze River Basin by over 10% in relative changes between mid-21st century and late-21st century periods [51,69]. The projection from an ensemble of 30 CMIP5 models with the RCP8.5 pathway confirms an increase in extreme rainfall during the summer season in the late-21st century [49]. The reliability and certainty in the late-21st century projections are limited by the ability of the models to reproduce the Asian monsoon [50]. Therefore, the current systematic bias in CMIP5 models and low ability to capture extreme rainfall values is responsible for the altered magnitudes of EDR projections. This reflects the limits of the knowledge and understanding of climate systems by the climate modeling community [49].

The projections in this case study are limited by the bias correction methodology implemented to correct the RCM rainfall. The QDM bias correction method can amplify the increase in rainfall and substantially alter the magnitudes of the RCM climate signals for daily rainfall [69]. It has been found that climate variables in future projections change in higher-order moments [70]. Therefore, the applicability of empirically derived CDFs under future projections may lead to the amplification of extreme rainfall. This distortion of the bias-corrected rainfall is the main source of uncertainty in the MSR ensemble projections for the late-21st century.

The EDR projections are limited by the assumption that a Gumbel frequency distribution can adequately represent the distribution of extreme rainfall under future conditions. The tendency for the Gumbel distribution is to yield the smallest possible rainfall, thus returning the highest possible risk in comparison to other extreme value distributions [82]. The utilization of non-stationary generalized extreme value (GEV) distributions results in monthly resolved return levels and more precise estimations of return levels [63,64]. The introduction of a multi-distribution approach increases the robustness of the bias correction transfer functions in representing varying EDR distributions across the study area [31].

The bias-corrected results reflect the limitations inherent in the selection of GCM-RCM ensemble combinations. The variation in the ensemble CCFs suggests that a four-member ensemble is limited in producing converging projections for the late-21st century MSR. The limitations of climate model output responses to bias correction methods can be addressed with an expanded ensemble to decrease the uncertainty and create robust projections [69]. The coefficient of variations between ensemble members suggests another limitation in the building of an ensemble with equal weight and without performance selection criteria. The derivation of a reliable ensemble projection is dependent on the selection and configuration of its members [34,35,58,83,84]. Therefore, it is recommended that a wider ensemble of RCMs be considered through a selection procedure to assess the reliability of each member to be used to improve climate change projections.

6. Conclusions

This paper presented a framework to derive future landslide-triggering rainfall scenarios from climate model outputs. A methodology following the framework was demonstrated through its application to the Wanzhou County, China. This study derived projections of extreme and mean seasonal rainfall scenarios for the mid-21st century (2021–2060) and the late-21st century (2061–2100) from bias-corrected RCM projections.

The MSR projections over Wanzhou County increased in the mid-21st century, measured by a range of $CC{F}_{\mathrm{MSR}}$ between 1.0 and 1.4. The projected $CC{F}_{\mathrm{MSR}}$ in the late-21st century ranged between 1.2 and 1.8. It was found that the variation in $CC{F}_{\mathrm{MSR}}$ in the mid-21st century projections was between 10% and 35%. The uncertainty in the projections of the late-21st century ranged from 30% to 50%. The EDR ensemble projections indicated a decrease in the magnitude in the mid-21st century. The uncertainty in the ensemble projection for $CC{F}_{\mathrm{EDR},T}$ in mid-21st century and late-21st century scenarios was measured with a coefficient of variation between 5% and 25%.

The results of this case study delivered a proof-of-concept for a methodological framework to derive future rainfall scenarios under climate change conditions. The climate change factors (CCFs) derived for the mid-21st century and late-21st century scenarios in

Table 6. Climate change projections over Wanzhou County.

	Mid-21st Century	Late-21st Century
Climate Change Factors
Extreme Daily Rainfall	0.9–1.0	1.2–1.6
Mean Seasonal Rainfall	1.0–1.4	1.2–1.8
Coefficients of Variation
Extreme Daily Rainfall	5–25%	5–25%
Mean Seasonal Rainfall	10–35%	30–50%

can be applied as a multiplicative factor to the present rainfall-scenario-derived observation data sets. This study integrated the measurement of the performance of the bias correction and quantification of the model ensemble uncertainty in the presentation of the projections. The results of this framework can aid in the incorporation of future rainfall scenarios in incorporating the impact of climate change in future hazard assessments.