Bias Correction of Precipitation from Convection-Permitting Models at the Point Scale: A Case Study in Switzerland

doi:10.21203/rs.3.rs-4757565/v1

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Bias Correction of Precipitation from Convection-Permitting Models at the Point Scale: A Case Study in Switzerland

https://doi.org/10.21203/rs.3.rs-4757565/v1

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Convection-permitting models (CPMs) outperform coarser regional climate models in resolving convective processes and predicting short-duration, high-impact weather phenomena. Sub-daily rainfall data from CPMs are crucial for impact models, such as urban drainage systems, but bias correction is still needed for the accuracy in local scale. This study estimates biases and uncertainties in CPM simulations at hourly and daily intervals, testing quantile mapping (QM) for bias correction. Data from over 70 weather stations in Switzerland validated CPM outputs and correction methods using sub-hourly rainfall records. COSMO-CLM's 2.2 km simulations were used for historical and future scenarios. Classic QM and several advanced versions, including moving windows and spatial pooling, were tested. Validation focused on three aspects: (A) statistical distribution of precipitation, (B) historical rainfall indices, and (C) future changes in rainfall indices. CPM biases were assessed by (A) and (B), while QM impacts were evaluated by all three. Findings highlight CPM limitations, especially for sub-daily intervals, with wet biases in extreme percentiles up to 30–35 mm/hour. Biases varied with different precipitation patterns. While QM methods reduce biases, they can distort the climate change signal, particularly in hourly rainfall indices. Upgraded QM techniques, such as those using moving windows or spatial pooling, are recommended, though caution is needed with longer observation periods. Future work will examine seasonal precipitation impacts and use diverse CPM ensembles for more reliable simulations.

convection permitting models

precipitation

Switzerland

quantile mapping

bias correction

point scale

Convection-permitting models (CPMs) are climate models that simulate atmospheric processes at much higher spatial resolution than traditional climate models (Clark et al., 2016); Prein et al. (2015). Particularly for precipitation patterns, CPMs outperform coarser resolution regional climate models (RCMs) (Ban et al., 2021). By explicitly resolving convective processes such as thunderstorms, heavy rainfall, and local wind patterns, CPMs predict short-duration, high-impact weather phenomena (Schwartz, 2019; Woodhams et al., 2018). Their higher spatial resolution allows CPMs to more accurately capture interactions between topography and weather (Kendon et al., 2019; Prein et al., 2015), crucial for regions with complex terrains. CPMs enhance our understanding of climate variability and generate robust precipitation time series data for research on local-scale impacts of climate change (Cook et al., 2017; Kendon et al., 2019; Prein et al., 2015) Such high-resolution climate data are important for developing informed climate adaptation strategies in infrastructure design, urban heat and water management, renewable energy development, and transportation. The sub-daily rainfall data provided by CPMs is particularly useful for urban drainage applications (Cook et al., 2020; Cook et al., 2021; Rodriguez et al., 2024) due to the high-speed interactions between rainfall and runoff (Durrans et al., 1999).

However, CPMs exhibit biases in simulating certain weather or climate variables (Kendon et al., 2021; Kendon et al., 2014; Prein et al., 2015; Rybka, 2023). For instance, CPMs may inaccurately estimate the intensity of localized heavy rainfall events or fail to simulate convective storms precisely (Kendon et al., 2019; Prein et al., 2015). The complexity of processes like cloud formation and precipitation makes them inherently difficult to capture, leading to uncertainties in local rainfall simulations (Hewson & Titley, 2010; Jiang et al., 2018). The wet bias in hourly extreme precipitation intensity also remains apparent (Rybka, 2023).

Consequently, bias correction is still an essential step to enhance the reliability and usefulness of this high-resolution climate model data. Nevertheless, some studies have directly applied CPMs as input for climate impact models without bias correction or with simplified bias correction techniques. For instance, in a study incorporating a new rainwater harvesting module into the urban ecohydrological model Urban Tethys-Chloris (UT&C) across 28 cities in the USA, UT&C was driven by 4 km resolution convection-permitting simulations (Ziyan et al., 2023). However, the bias correction step was neglected in this study. Another work utilized 1.5 km RCM runs for the current climate and a potential future climate to drive a national gridded hydrological model - CLASSIC-GB (Kay et al., 2015) Precipitation data was converted from the 1.5 km RCM grid by proportionally distributing it to the smaller 1 km grid cells based on the area they cover. The author justified this by stating that the supposed improvements for hydrological modeling brought by bias-correction of input data are still in question. Some other works applied the simple bias corrections, such as the work of Archer et al (2024), who tested 2.2 km CPM precipitation data as input for a high-resolution hydrodynamic model (approximately 20 m resolution) to simulate rainfall-driven flood hazard events in the cities of Bristol and Bath, England. A simple adjustment technique was applied using channel bed elevations to produce the input rainfall data for their rainfall-driven flooding model. Or research using 5-km horizontal resolution WRF data as input for into the Soil and Water Assessment Tool (SWAT) model. The author only used spatial interpolation through the Thiessen polygon method to process the climate data as a preprocessing step (Lee et al., 2019) So far, very few studies have systematically examined potential biases across the distribution of rainfall data generated by CPMs and how these biases propagate into a range of climate indices, such as Total Precipitation and Max 1-Day Precipitation, which are relevant for water resources impact studies.

There might be a risk when the same bias correction is applied for all GCMs, RCMs, and CPMs. While bias correction techniques have been extensively studied for coarser-resolution climate models (Boé et al., 2007; Cannon et al., 2015; Jakob Themeßl et al., 2011; Switanek et al., 2017), their adaptation and applicability to CPMs, especially the sub-hourly simulations, have received comparatively little attention and remain uncertain. Velasquez et al (2020) proposed a new bias correction method tailored for the 2km resolution WRF model in Switzerland to take into account the orographic characteristics in the region (Velasquez et al., 2020). However, the validation stopped at daily rainfall time series since sub-daily precipitation was not included. Recently, the research of Ugolotti et al. (2023) quantified the impact of quantile mapping (QM) on the climate change signal (CCS) of the climate extremes derived from COSMO – CLM, a common CPM (Ugolotti et al., 2023). They also evaluated biological variables derived from a dynamic vegetation model using CPM as its input. However, this study focused on seasonal and annual climate indices and dynamic vegetation variables, without inclusion of daily or hourly variations of precipitation and temperature. Additionally, only one bias correction technique was tested in this study. Research is needed to develop and validate bias correction techniques for CPM outputs to ensure the reliability and consistency of long-term high-resolution climate projections and the accuracy of information from impact studies relying on high-resolution data.

Although bias correction methods exist (e.g., (Lenderink et al., 2007), (Schmidli et al., 2006), (Robert & Buishand, 2007), (Chen et al., 2013), Quantile Mapping (QM) (Sun et al., 2011; Wood et al., 2004) is one of the most widely used techniques by the impacts community due to its ease of use. QM adjusts the cumulative distribution functions of climate model data to match those of observed data at different quantiles, thus correcting biases across the entire distribution. Non-parametric QM, which corrects the empirical cumulative density distribution rather than using the theoretical cumulative distribution to fit the model simulation (parametric QM), is less prone to erroneous extrapolations from parametric methods (Cook et al., 2020; Velasquez et al., 2020), which can vary by region and season. However, bias correction techniques that are dependent on the robustness of the distribution, such as QM, are sensitive to the length of the calibration period (Berg et al., 2012). Yet due to the computational expense of high-resolution CPMs, simulations are often conducted for relatively short time periods, typically around 10 years for both past and future scenarios (Lucas-Picher et al., 2021). This limited sample size can inadequately represent climate variability and extremes, hindering not only our understanding of climate change impacts over longer periods, but also the robustness of empirical QM methods.

This short time span is particularly problematic due to the unpredictable dynamics of precipitation cells. Simulated rainfall patterns may not precisely match the location and time of observed precipitation cells. Pooling input from adjacent pixels or incorporating spatial information into QM can mitigate this issue. Kendon et al. (2008) tested the spatial pooling method, where daily precipitation data from neighboring grid cells are concatenated to form one long time series. The authors concluded that a 3x3 pooling can enhance the robustness of simulated changes in extreme precipitation (Kendon et al., 2008). Similarly, using a longer observational period may better capture the statistical characteristics of rainfall patterns and thus enhance the robustness of bias correction. (Wilks, 2011) demonstrated that longer time series data provide more stable estimates of statistical characteristics and reduce the influence of short-term variability. Additionally, longer observational records perhaps allow for a better representation of extreme events, aiding to accurately capture tail behavior and extreme values when correcting climate model outputs (Dessai et al., 2009). Alternatively, the moving window (MW) technique, which maps a transfer function to each time window of observed data, can be applied to better capture the temporal consistency within time series. Previous studies employing the MW approach used time windows ranging from 31 (Themeßl et al., 2012; Thrasher et al., 2012; Velasquez et al., 2020; Wilcke et al., 2013) to 91 days (Rajczak et al., 2016; Reiter et al., 2018; Van de Velde et al., 2020). Combining traditional empirical QM with the above "add-on" techniques can address both the shortcomings of daily and hourly CPM output and enhance the benefits of QM.

This study begins by quantifying biases in point-scale rainfall time series data generated by a CPM and then tests classical, empirical QM as well as its combination with a moving window, surrounding pixels, and longer periods of observation. Ultimately, we recommend the most suitable method for the specific needs of users. In this research, we focus on precipitation, the most complex variable to simulate for CPMs due to modeling challenges at high resolutions as well as the most important variable for many adaptation studies, including urban drainage applications. The objective of this paper has two folds:

To understand if CPM outputs require bias correction for use at the point scale and to identify the magnitudes of biases and uncertainties.
To improve the accuracy of CPM outputs using bias correction techniques, and to determine if the classic empirical QM is sufficient for bias correcting CPM output or if an upgraded version is recommended for various concerns of CPM output users.

The structure of this paper is as follows: Section 2 introduces the observational dataset and climate model used in this study, along with the validation scheme. Section 3 presents results on the evaluation of CPM simulations and the outputs of bias correction techniques. Section 4 discusses these results and Section 5 summarizes and concludes the paper.

In this study, we applied classical, non-parametric QM to bias-correct the output of a CPM (Section 2.1). This method assumes that mapped differences (biases) between simulated and observed baseline data can be transferred to bias-correct the simulated output of climate models (Voisin et al., 2010; Wood et al., 2002). The transfer function, constructed using information from the reference time frame only, is assumed to be stationary. It should be noted that this QM differs from Quantile Delta Mapping, which adds the difference between present and future simulations to the present observation (Cannon et al., 2015; Li et al., 2010; Wang & Chen, 2014) and thus does not assume a stationary transfer function. We chose empirical non-parametric QM for its simplicity and interpretability. In total, five QM methods were tested (Tab. 2): classical QM and four different combinations with the "add-on" techniques to address their potential impacts on various aspects of CPM output.

Table 1. Five quantile mapping techniques utilized in this study.

Acronym	Empirical quantile mapping	Moving window of 91 days	3 x 3 pixel pooling technique	10-year observed data record (2000-2009)	30-year observed data record (1990 to 2020)
QM	·
QM_MW	·	·		·
QM_9p	·		·	·
QM_30y	·				·
QM_MW-9p	·	·	·

2.1. CPM output

In this study, we used simulations of the convection-permitting COSMO-CLM (Consortium for Small-Scale Modeling in Climate Mode) (Rockel, 2008) from the Coordinated Regional Climate Downscaling Experiment (CORDEX) (Giorgi, 2009). COSMO-CLM is a non-hydrostatic model that employs fully compressible atmospheric equations, integrating sub-grid turbulence, convection, and parameterizations for grid-scale clouds and precipitation. TERRA-ML, a soil model introduced by (Doms, 2013), is utilized within COSMO-CLM to represent mass and heat exchanges between the surface and the atmosphere (Rockel, 2008). The simulations employ a horizontal grid spacing of approximately 0.0275° with a convection parameterization that is partially deactivated. Specifically, shallow convection remains parameterized, while deep convection is explicitly resolved (Lucas-Picher et al., 2021).

The lateral boundary conditions for the domain of this CPM, named ALP-3, come from the COSMO-CLM model at 12 km (EUR-11). The simulation in the reference period is the evaluation run (2000-2009, 1999 spin-up), driven by ERA-Interim reanalysis. To consider future projection of precipitation, the historical run (1996-2005, 1995 spin-up) and the future experiment (2090–2099; 2089 spin-up) driven by EC Earth Global Climate Models (GCMs) using the high-emissions scenario RCP 8.5 with the standard GCM-RCM nesting approach were utilized.

For the analysis, we aggregated the 6-minute COSMO simulation to a 30-minute interval to be compatible with the 10-minute observations from MeteoSwiss (also aggregated to 30-minutes). The 2.2 km horizontal spatial resolution grid cell containing the locations of each of the 74 stations (in Fig. 1; Section 2.2) were extracted to match the observed data. For the QM technique where 9 grid cells are pooled (see Section 2.2), values from the 8 adjacent pixels were also extracted to add more data to the distribution curves of the historical simulation.

2.2. Observational data and pre-processing

For this study, we utilized rainfall measurements provided by the Swiss automatic meteorological surface network (SwissMetNet, formerly ANETZ) (Fig. 1) at a temporal resolution of 10 minutes. It is important to note that the time duration covered by each station varies; the first measurement can commence from 1980, 1981, or later. The time slice window of the COSMO output hindcast simulation is 2000-2009. Therefore, for the observational data used for the QM technique that integrates 30 years of observed data, only the 64 stations that have at least 30 years of measurement data, spanning from 1990 to 2020, were selected. All values exceeding 9.6 mm in the 10-minute interval observed data were flagged as errors and truncated (personal communication with MeteoSwiss data provider, Nov, 2022). However, as noted by (Sevruk, 1985), the observations could still be biased due to deformation of the wind field by the rain gauge or losses due to evaporation and residual water at emptying. According to (Frei et al., 2008), who analyzed the heavy precipitation event of August 2005 in Switzerland, found that the relative uncertainties of point estimates based on the gauge network could reach 20-40%. It is important to acknowledge these potential biases when interpreting results.

To more effectively analyze the impacts of QM methods on different rainfall patterns, we employed Density-Based Spatial Clustering of Applications with Noise (DBSCAN) (Ester et al., 1996), a clustering algorithm used in machine learning and data mining. We grouped the 74 rain-gauge stations into 2 clusters based on differences in location (latitude and longitude), altitude, and the characteristics of each station’s rainfall pattern. These characteristics include: total annual rainfall, daily mean rainfall, hourly mean rainfall, monthly mean rainfall, annual maximum hourly rainfall, and annual number of wet days over a span of 30 years. Nineteen stations were assigned to the “Wetter” cluster (the rainier group), while the remaining stations were clustered into the “Drier cluster” (the less rainy group). The average annual total rainfall recorded for the whole Drier cluster accounts for 60% of the total rainfall recorded in the Wetter cluster (see Tab. 1). The clustering of stations exhibited strong correlations with annual rainfall (see Fig. 1) and displayed distinct differences in precipitation patterns between the Alpine and non-Alpine regions.

Table 2. Rainfall patterns of the two clusters of 74 rain-gauge network that were grouped using DBSCAN, presented with mean values and their corresponding standard deviations.

	Drier cluster	Wetter cluster
Hourly mean rainfall (mm)	8.44 (±0.96)	13.55 (±2.73)
Daily mean rainfall (mm)	2.79 (0.55)	4.67 (±1.14)
Monthly mean rainfall (mm)	84.83 (±16.7)	141.99 (±34.79)
Annual mean rainfall (mm)	944.06 (±188.13)	1582.37 (±387.81)
Annual hourly max rainfall (mm)	12.89 (±2.38)	17.51 (±3.69)
Annual number of wet days (days)	131.89 (±24.35)	145.93 (±35.42)

2.3. Validation method

A robust QM technique should not only represent the statistical distribution of daily and hourly rainfall, respect the annual indices estimated by observations in the reference period but also preserve the direction of change in future rainfall. Thus, the accuracy of the CPM outputs and the robustness of the QM methods were evaluated on the basis of (A) deviations across the full statistical distribution of precipitation, (B) annual rainfall indices estimated in the reference period, and (C) future projections of these indices. The latter criterion is used to determine if the QM method respects the direction of change, but not the accuracy of the CPM outputs.

Based on their representativeness and their usefulness for impacts studies, nine rainfall indices introduced by the Expert Team on Climate Change Detection and Indices (ETCCDI) (Karl et al., 1999) were selected for use in validation, as well as, the annual hourly mean intensity and the annual number of wet days (which are particularly interesting for urban drainage applications (Cook et al., 2021) )(Tab. 3). The thresholds to define wet days and wet hours are the same as previous studies – 1mm/day and 0.1mm/hour, respectively. To handle the drizzle effect, all values in CPM output below these thresholds are flagged and set to zero, following previous studies (Lafon et al., 2013; Velasquez et al., 2020). For the eleven precipitation indices, the bias is quantified as the mean absolute error (MAE) between indices computed by the observation and CPM output/QM output. The bias comparison considers both the mean and standard deviation of the annual indices over a 10-year period.

A robust framework to comprehensively and robustly validate bias correction methods of climate simulations is still lacking. According to (Maraun & Widmann, 2018), cross-validation should not be used to evaluate bias correction of free running climate simulations against observations. Further, thirty years of observational data are recommended to cover a sufficiently long period to capture a wide range of climate variability and extremes. Bias correction techniques that are mainly based on the robustness of the distributions like QM have been shown to be sensitive to the length of the calibration period (Berg et al., 2012; Lafon et al., 2013). Also, the leave-one-out verification introduces additional uncertainties due to the different lengths between the verification and calibration periods (Lafon et al., 2013; Velasquez et al., 2020). The internal climate variabilities, which are not the same between different time periods, can affect the robustness of bias correction techniques (Maraun et al., 2017; Maraun & Widmann, 2018). Therefore, in this study, the evaluation and validation periods are the same, and no independent cross-validation exercise is conducted, following several previous studies (Casanueva et al., 2016; Feigenwinter I, 2018).

Firstly, the full statistical distribution of rainfall was considered, and the five Quantile Mapping (QM) methods were assessed based on the bias of their outputs compared to observations. Only the 85th to the last percentiles were considered because precipitation is predominantly distributed from the middle 80th percentiles of both observations and simulation output (Kendon et al., 2012). Additionally, to evaluate the ability to accurately capture historical annual rainfall indices, the methods were ranked. The most effective QM method (rank of 1) would exhibit the greatest bias reduction compared to the uncorrected simulations (i.e., raw CPM output). To evaluate the effectives of the QM method to represent future projections, QM methods that reversed the signal in long-term precipitation patterns outlined by the CPM output were deemed unsuccessful. The optimal method was expected not only to preserve the direction of change but also avoid significant inflation or deflation of the climate change signal.

Table 3 Indices used for the validation in this study, including those from the Expert Team on Climate Change Detection and the two additional indices (in italics).

Purpose	Acronym	Definition	Units
Central tendency	SDII	Daily intensity	Mm
Central tendency	SHII	Hourly intensity	Mm
Frequency wet & dry spells	RW	Annual no. of wet days (daily intensity >1mm)	Days
	CDD	Maximum no. of consecutive dry days (daily intensity <1mm)	Days
	CWD	Maximum no. of consecutive wet days (daily intensity >1mm)	Days
Frequencies of extremes	R10mm	No. of days with precipitation >= 10mm/ day	Days
Proportion of extremes	R95T	Fraction of annual total precipitation due to events exceeding the 10 year 95^th percentile	%
Magnitudes of extremes	R95pTOT	Annual total precipitation due to events exceeding the 10 year 95^th percentile	Mm
	R1D	Maximum 1 day precipitation amount	Mm
	R5D	Maximum 5 day precipitation amount	Mm
Total rainfall	PRCPTOT	Total annual precipitation of wet days	Mm

3.1 Biases in uncorrected CPM output and corrected CPM output across the full statistical distribution of precipitation

Fig. 2 shows the bias of uncorrected CPM outputs for the historical period compared to the observations. This raw CPM data were aggregated to hourly and daily based on time stamps. Biases in the simulated rainfall from the CPM vary widely across quantile ranges and between weather station clusters. Uncorrected simulated daily precipitation data overestimate daily and hourly rainfall. This wet bias is particularly pronounced for extreme precipitation events (> 98th percentile) and for weather stations in the Wetter cluster (bias of up to 100mm/day). As such, the relative bias increases as the percentile decreases. The asymmetry in bias between quantile intervals becomes even more evident when considering hourly rainfall. Below the 98th quantile, the wet bias of the CPM does not exceed 1.5 mm/hour but reaches 35 mm/hour in the highest quantiles. Besides, Wetter cluster has a larger wet bias than Drier cluster, particularly in segments of the distribution lower than the 98^th percentile.

Fig. 3 illustrates a comparison of the outputs of the five QM methods to the uncorrected CPM output, focusing on the absolute bias of daily and hourly rainfall. All QM methods performed substantially better than the uncorrected CPM output up to a certain percentile. For daily rainfall, all(?) QM methods can remove the bias until the 97th percentile, equivalent to 21.7 mm/day in the observed data. Similarly, the hourly output from QMs performs well up to the 95th percentile, equivalent to 0.78 mm/hour in the observations. Interestingly, the QM methods transform the bias from a wet one to a dry one for daily precipitation at extreme values (98^th percentile and beyond). In terms of hourly rainfall, this wet bias remains in the last segment of the distribution, although the QMs strongly reduce the overestimations of the CPM output. Among the five QM techniques, QM_30y introduces dry biases in daily rainfall particularly in Drier cluster, while QM_MW and QM_MW-9p show slightly better performance than the others in the upper tail percentiles. However, it is not clear that any QM method outperforms the standard QM when considering hourly precipitation.

3.2. The annual historical precipitation indices

The uncorrected CPM outputs overestimate the mean of most indices, except for annual SHII, CDD, and R95T (Fig. 4). The mean values of biases from stations in each cluster show that the wet bias in the uncorrected CPM is substantial, reaching up to 400 mm for PRCPTOT and an excess of 20 days per year in the case of RW. For most indices, all the QM methods successfully reduce biases of the mean, but do not notably improve the extreme rainfall indices such as the R95T and R5D. The QM methods can, however, mitigate biases in RW, CWD, and the occurrence of extremes – R10mm. Yet the QM methods alter the direction of bias in several cases, including SHII, SDII, and extreme magnitude indicators such as total rainfall exceeding the R95pTOT, R1D and R5D. Moreover, the QMs tend to reduce the standard deviation (a measure of the dispersion in the set of annual indices), meaning that the distribution of each index over a 10-year period is reduced after bias correction.

Based on the biases shown in Fig. 4, the rankings are defined in Fig. 5. No QM method performed best at minimizing biases across all precipitation indices. Standard QM only outperformed other methods for PRCPTOT. The moving window approach most successfully reproduces patterns in the mean annual RW and CWD, as indicated by the lowest biases in the mean and variance in Fig. 4. Furthermore, the positive impact of the moving window is more profound in Drier cluster.

The benefit of using the 9-pixel approach is not as obvious as with the moving window. However, when combining both the 9-pixel and moving window methods, it becomes the best method to improve biases in the mean and variance of the extreme indicators such as CDD, R95pTOT, R1D, and R5D of the Wetter cluster. However, this favorable influence is less prominent in Drier cluster.

QM_30y showed the best results when reproducing R10mm in the Wetter cluster, but it is the least preferred method for the Drier cluster. Additionally, it demonstrates the highest occurrence of indices where the bias switches direction (e.g., from overestimation to underestimation). This observation could be linked to the dry bias in the Drier cluster depicted in the QM_30y results shown in Fig. 3.

3.3. Future projection of precipitation

Under the RCP8.5 scenario, precipitation frequency is projected to decrease while extreme intensity increases (Fig. 6), exacerbating dry conditions between intense rainstorms. COSMO simulations suggest a 2.5% to 7.5% decrease in PRCPTOT across Switzerland. Central tendency indices like SHII and SDII are expected to intensify. RW per year and CWD are anticipated to decline, prolonging dry spells with up to a 30% increase in CDD. Extreme events, such as R95T, R1D and R5D, will intensify, while the frequency of extreme precipitation events is projected to decrease by 4% to 13%. Additionally, changes in future rainfall vary between the different clusters of stations, with less rainy locations expected to experience a greater increase in extreme intensity (R95T, R1D and R5D) and hourly mean indicator – SDII compared to wetter areas. However, the decline in extreme precipitation frequency and observed decreases in total annual rainfall and maximum duration of wet spells are more pronounced in the rainier stations (Wetter cluster).

The impacts of QM methods on the CCS varied across indices and between the two groups of stations. Future projections of RW, CDD and R10mm were maintained well after bias correction. However, all QM methods failed to preserve the CCS of increased SHII. This recalls the negative influence of QM in capturing historical hourly mean precipitation shown in the previous section. For the stations in the Wetter cluster, all QM methods failed to respect the CCS for R5D, while in the case of the Drier cluster, no methods succeeded in preserving CWD, suggesting the sensitivity of extreme CCS to QM methods. Meanwhile, regarding the dispersion of annual indices, as indicated by the standard deviation, all five QM techniques were able to maintain their future increases.

Overall, the ranking results differ between the two clusters of stations and no QM method is clearly better than the others across all indices. Regarding the ability to maintain mean values of CCS, the standard QM method is not the best option in most cases. QM_MW-9p ranked first for many extreme indices, including R95pTOT for both groups of stations, CWD, and RW for the Wetter cluster, as well as R1D and R95T for Drier cluster. Furthermore, although QM_30y alters the direction of CCS in many cases, its positive impact in the less rainy cluster of stations can be observed from Fig. 7. QM_30y ranks the best in SDII, RW, CDD, and the frequency of extremes – such as R10mm in Drier cluster. When considering which method is the best to preserve StD of CCS of eleven indices, the moving window outperforms other methods in wetter cluster while QM_9p has the best performs in four over eleven indices.

The deficiencies of the CPM simulation are apparent in our results, with significant overestimation of hourly extreme precipitation intensities, consistent with prior studies (Kendon et al., 2012; Rybka, 2023). In Switzerland, where hourly rainfall thresholds for flash flood warnings range from 30 to 50 mm, CPMs' overestimation (up to 30-35 mm) requires bias correction and careful interpretation for climate change impact assessments. This overestimation can be attributed to the removal of outliers in the 10-minute interval measurements that were higher than 9.6mm, as mentioned in section 2.2 as a pre-processing step, while the outputs of CPM were directly applied in validation. Besides, CPMs exhibit a strong wet bias in total annual, and daily mean rainfall but underestimate mean hourly rainfall, indicating different biases across quantiles. These challenges highlight the need for further model refinement.

Additionally, CPMs show limitations in representing the diurnal cycle of convective precipitation and underestimating dry spell duration and frequency. They tend to overestimate annual indices like PRCPTOT, SDII, and annual RW due to their wet bias and underestimate the contribution of extreme rain to total annual rainfall. Accordingly, bias correction is essential before using CPM simulations for local climate impact studies.

The wet bias in CPM output is more pronounced in heavy rainfall regions and mountainous terrain (Wetter cluster), often overestimating heavy rainfall intensity and frequency (Ban et al., 2014; Kendon et al., 2012; Langhans et al., 2012; Prein et al., 2015; Sevruk, 1985). This overestimation, particularly in the Alps and Apennines during summer, is linked to increased vertical wind intensity at high altitudes (Barthlott & Hoose, 2015; Langhans et al., 2012; Vergara-Temprado et al., 2020). Therefore, Bias correction techniques should be tailored to local orographic characteristics and rainfall patterns (Velasquez et al., 2020)

Errors in CPM output arise from model deficiencies and other factors discussed in section 1. Besides the bias of driving data, discrepancies between the model and observed climate features regarding internal variability contribute to divergence from observations. Meanwhile, QM is an empirical and data-driven approach to bias correction. It does not take into account physical basics like dynamical downscaling, nor does it account for the bias of driving data or the internal variability of raw simulated data. Furthermore, the model biases and transform function are assumed to be temporally stationary. Nevertheless, these QM techniques are still worth investigating due to their prevalence in the impacts community.

Regarding the entire statistical distribution of precipitation, all QM outputs perform significantly better than uncorrected CPM output (Fig.3), until the 97th percentile and 95th percentile of daily and hourly precipitation, respectively. The biases in the uppermost percentiles remain after applying QMs. Empirical QM methods adjust simulated distribution quantiles to match observed ones, typically using a reference period. When a wet bias exists in extreme quantiles of model output, quantile mapping corrects by downward adjustment to match observations. Thus, previous overestimation of extreme rainfall in the model can become a dry bias after QM. This aligns with findings from (Themeßl et al., 2012), who noted QM's tendency to underestimate regional climate model extremes due to its methodological limitation of mapping to the calibration period's maximum.

For most rainfall indices, QM methods successfully reduce biases, particularly in indices representing daily and hourly mean rainfall. Our findings align with the assertion from (Lehner et al., 2021) that bias correction methods like QM have the capacity to statistically adjust the model's historical climate to accurately match observations. Also, the study by (Ugolotti et al., 2023) confirmed that their bias correction not only reduced the total amount of rainfall but also led to a better correspondence of the simulated and observed frequency of rainfall events. However, biases in indices of extreme rainfall, such as R95T, still remain. Additionally, QM methods alter the direction of bias in several cases, including SHII, SDII, and extreme magnitude indicators such as R95pTOT, R1D, and R5D. This pattern is likely linked with the transition from wet bias to dry bias with increasing percentiles (Fig.3).

For future projections involving atmospheric moisture variables like precipitation, preserving the relative change signal is vital to maintain physical scaling relationships with model-projected temperature changes, as demonstrated by the Clausius–Clapeyron equation (Clausius, 1834) . While empirical QM assumes stationarity in the relationship between model outputs and observations, implying constant statistical properties across different time periods or scenarios, this assumption may not always hold true in a changing climate context. Our findings suggest that QM has the potential to alter the magnitudes of climate change signals and even reverse the direction of projected changes (Fig. 6), consistent with prior research (Maraun & Widmann, 2018). Quantile trend-preserving methods like Quantile Delta Mapping show better preservation of raw signals across various indices and variables compared to standard QMs used in this study (Casanueva et al., 2020). However, their effectiveness depends heavily on the reference dataset used for calibration, making them more sensitive to observations, particularly regarding precipitation intensity, spells, and extreme indices (Casanueva et al., 2020). Therefore, the trade-off will hinge on the user's choice and preference.

Among the five QM methods tested here, the standard QM method is not the best option when considering the ability of QM to represent the annual indices in reference period and to respect the future projection of precipitation modeled by CPM. The moving window approach, whether applied independently (QM_MW) or combined with the 9-pixel method (QM_MQ-9p), excelled for both groups of weather stations. Moreover, both QM_MW and QM_MQ-9p ranked consistently among the two most performant QM methods for extreme precipitation indices, likely due to their ability to capture temporal patterns and persistence in extreme weather events. This effectiveness in capturing extremes is attributed to Switzerland's pronounced rainfall seasonality, influenced by its complex topography and proximity to moisture sources like the Mediterranean Sea and the European Alps (Frei & Schär, 2001; Schmidli & Frei, 2005; Sodemann & Zubler, 2010). Long-term records in Switzerland reveal winter and autumn trends in intense precipitation events, while spring and summer show fewer significant trends in heavy precipitation and spell-duration statistics, despite extreme events being most common in summer (Frei & Schär, 2001; Łupikasza, 2017; Schmidli & Frei, 2005).

Similarly, pooling input data from adjacent pixels (QM_9p) can enhance QM performance (Fig. 3) especially when combining with moving window. However, the positive impact of the spatial pooling method is not as significant as expected, possibly because using 8 surrounding pixels is still insufficient to capture extreme rainfall. Since the atmosphere is chaotic, extreme events might be shifted by more than 10 km in the outputs of CPM. Besides, the bias correction potential of QM_MW-9p on extreme indices is more pronounced for weather stations in the Wetter cluster than the Drier cluster. This implicitly suggests that combining surrounding pixels facilitates the representation of extreme weather values, especially for rainy mountainous regions like the Alpine. This could be due to the higher likelihood of simulated patterns from CPMs not precisely aligning with observed precipitation cells' location and timing in mountainous regions compared to low-elevation areas.

Interestingly, the QM_30y method, which boosts the sample size for QM by incorporating 30 instead of 10 years of observational data, performed worse than other QM methods (Fig.3). Fig.S1 in the Supplementary Information showed the statistical discrepancy between 10 years and 30 years of observational data in two groups of stations. For the same percentile ranges, 10 years of station data surpassed the dataset with 30 years. If the 10-year period includes one or more extreme events that contribute significantly to the overall precipitation total, this could result in higher precipitation amounts compared to the longer 30-year dataset. This discrepancy is particularly evident in the Drier cluster case, explaining the larger dry bias of QM_30y output in this group of stations when considering the statistical distribution of daily rainfall. This means that QM is sensitive to the time window of the calibration timeframe. The 30-year period may not accurately reflect the conditions experienced during the 10-year period. Therefore, using a longer time span of in situ data for quantile mapping requires extra caution.

Accordingly, our recommendations for the impacts community are to use QM with caution, always perform a validation step, and give more attention to extremes. The MW is beneficial for the standard QM, and the length of the time window should depend on the seasonality of local rainfall patterns. Additionally, combining QM with the surrounding pixel pooling technique is recommended, although the number of neighboring pixels included needs further investigation.

The objective of this research is twofold: firstly, to evaluate whether convection permitting model (CPM) output meets the standards for application at the point scale and assess the extent of biases present. Secondly, the study aims to investigate how implementing quantile mapping techniques enhances the accuracy of CPM simulation at the point scale, and recommend the most suitable quantile mapping method tailored to the specific concerns of CPM output users.

Our key finding is that the CPM evaluated in this study, the COSMO simulation at a 2.2 km resolution, still produces evident biases, particularly in sub-daily intervals. Wet biases reduce when quantile ranges increase, but a strong overestimation is observed in the most extreme percentiles of the distribution, which also varies depending on the location of stations. Biases are also evident when CPM reproduces annual historical rainfall indices, such as overestimation of total annual rainfall or underestimation of maximum duration dry spells. This underscores the need for bias correction when using CPM output at the point scale.

Overall, quantile mapping methods (QMs) can reduce biases in the comprehensive statistical distribution of precipitation throughout the reference period and most historical annual indices. However, the sensitivity of empirical QM to extreme rainfall and the time window of the calibration period were evident. Additionally, QMs can distort the climate change signal (CCS) produced by the COSMO simulation, with the most obvious negative impact seen in hourly mean rainfall. While performance of the different QM techniques varies by metric/rainfall property, upgraded versions of classical QM are recommended, such as QM combined with a moving window (applying QM locally within one or three-month period) or spatial pooling method (in this case, 8 surrounding pixels were included), although extra caution is advised when using longer periods of observation data.

While our testing was conducted within Switzerland, these recommendations can be extrapolated to regions with similar climate patterns. For example, regions where orographic lifting effects and vertical gradients result in more rainfall, such as the Alpine region, and areas with moderate precipitation because they are farther away from main moisture sources, like the Mediterranean Sea, similar to the non-Alpine region.

Our work has the potential for future improvement. The 10-year time frame of CPM output poses an obstacle when analyzing extreme distributions compared to a 30-year period. Future research could focus on more sophisticated extreme value analysis in CPM output and the impact of QMs on these extremes. Additionally, forthcoming research should consider the seasonal pattern of rainfall and its inter-annual variability of both historical indices and CCS. Also, expanding this study to an ensemble of CPMs is necessary to address the uncertainty inherent in using only one model, especially regarding future precipitation. Although this study primarily focuses on the impacts of QMs on CCS, it is important to note that fundamental climate model errors cannot be rectified through statistical postprocessing alone. Therefore, employing an ensemble of diverse CPMs will enhance the reliability of simulations concerning anticipated changes in precipitation in the future. Also, it would be good to test how these different techniques casqued down through models used in impacts studies such as urban drainage.

Acknowledgments

We acknowledge the World Climate Research Programme's Working Group on Regional Climate (https://cordex.org/) for producing and making available their model output. Further, we also thank the Center for Climate Systems Modeling (C2SM) for their storage capacities, data provision and support. We are also grateful for the computing resources provided by the CSCS- Swiss National Supercomputing Centre, Lugano.

Funding:

This work was supported by SNSF (Swiss National Science Foundation) (BETTER project -200021_204790).

Author Contributions

Trang Nguyen: Conceptualization, Methodology, Software, Writing. Lauren Cook: Supervision, Conceptualization, Resources, Reviewing and Editing. Andreas Dietzel: Supervision, Reviewing and Editing. Patricio Velasquez: Resources, reviewing.

Data availability

The bias corrected data that support the findings of this study are available from the corresponding author, Trang Nguyen and Lauren Cook, upon reasonable request.

The model simulations used in this study, set up by the CORDEX-FPS and initially presented by (Ban et al., 2021; Coppola et al., 2020; Pichelli et al., 2021) are provided as netCDF files on all ESGF (Earth System Grid Federation) index nodes worldwide (also see https://cordex.org/data-access/esgf/). Some simulations may still be underway at the time of publication as they are currently being CMORized. Should they be needed beforehand, an early version (not CMORized) can be requested from Ruth Lorenz ([email protected]).

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Bias Correction of Precipitation from Convection-Permitting Models at the Point Scale: A Case Study in Switzerland

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