Adaptation and Application of the large LAERTES-EU RCM Ensemble for Modeling Hydrological Extremes: A pilot study for the Rhine basin

. Enduring and extensive heavy precipitation associated with widespread river ﬂoods are among the main natural hazards affecting Central Europe. Since such events are characterized by long return periods, it is difﬁcult to adequately quantify their frequency and intensity solely based on the available observations of precipitation. Furthermore, long-term observations are rare, not homogeneous in space and time, and thus not suitable to run hydrological models (HMs) with respect to extremes. To overcome this issue, we make use of the recently introduced LAERTES-EU ( LA rge E nsemble of 5 R egional clima T e mod E l S imulations for EU rope) data set, which is an ensemble of regional climate model simulations providing over 12.000 (cid:58)(cid:58)(cid:58)(cid:58)(cid:58) 12,000 (cid:58) simulated years. LAERTES-EU is adapted for the use in an HM to calculate discharges for large river basins by applying a quantile mapping with a ﬁxed density function


Introduction
River (fluvial) floods are among the most disastrous and also costliest weather-related hazards in Central Europe (e.g., Alfieri et al., 2018).The damage caused by the devastating 2013 Elbe and Danube flood in Germany (e.g., Grams et al., 2014;Kelemen et al., 2016) has been estimated at 12 billion Euro (Merz et al., 2014).Major flood events along the main river networks are that a bias correction is important to simulate reasonable discharges.However, in other studies (e.g., Chen et al., 2018) the results were mixed.
Many studies have demonstrated the added value of a bias correction for precipitation without any linkage to hydrological applications (e.g., Dobler and Ahrens, 2008;Fang et al., 2015).Dobler and Ahrens (2008) compared different downscaling approaches for precipitation in Europe and South Asia as well as different bias correction methods (quantile mapping and local intensity scaling).The authors concluded that dynamical downscaling with an RCM in combination with a bias correction (quantile mapping with a gamma distribution) is most suitable to simulate precipitation in Europe.Fang et al. (2015) focused on the comparison of different bias correction methods and found that empirical quantile mapping and power transformation performed best for precipitation.However, they mentioned that the selection of an accurate correction method may be case sensitive.
The present study emanates from an interdisciplinary project aiming to quantify the flood risk for large European river basins using a model chain from meteorology over hydrology towards risk assessment.The novel RCM ensemble LAERTES-EU (LArge Ensemble of Regional climaTe modEl Simulations for EUrope), which was recently introduced by Ehmele et al. (2020), is now adapted and applied for hydrological applications.With this aim, daily precipitation amounts and daily mean 2-meter temperature are used as input data to drive an HM for discharge simulations.Ehmele et al. (2020) identified a positive bias in LAERTES-EU precipitation compared to observations, which would lead to an overestimation of the HM discharge response without a previous bias correction.We isolate ::::::: elaborate : the effects of the bias correction to both precipitation and discharge ::::::: statistics : and demonstrate the benefits of a data set like LAERTES-EU for hydrological applications such as the estimation of extreme discharges with high return periods and their statistical representation.We focus on the Rhine basin as a pilot area and address the following research questions: 1. Does the bias correction improve the representation of precipitation in LAERTES-EU adequately?
2. Is the applied HM capable of reproducing observed historical discharges?
3. Does the bias-corrected LAERTES-EU provide the potential to derive statistically robust estimates of flood return levels above 100 years?
This paper is structured as follows: The used data sets and the study area are introduced in Sect. 2. Section 3 contains the atmospheric part with the description and validation of the bias correction method.In Sect.4, the hydrological model is introduced and validated.In Sect.5, the benefit of a data set such as LAERTES-EU for hydrological modeling is demonstrated.
The last section (Sect.6) summarizes the results and provides the conclusions.

Data sets and study area
This study is based on the LAERTES-EU ensemble of RCM simulations (Ehmele et al., 2020), which is introduced in this section as well as different observational data sets used for calibration and validation of both the HM and the bias correction.

HYRAS
To estimate the added-value of the bias correction of precipitation, we consider the high-resolved (5×5 km 2 ) HYRAS (HYdrometeorological RASter) data set provided by the German Weather Service (DWD; Rauthe et al., 2013) as an independent data set.Aggregated to the RCM/E-OBS grid (25 km), HYRAS is used for the validation of the bias correction.In its original resolution, HYRAS is used for the calibration and validation of the HM.Note that HYRAS data are not homogeneous over time due to the changing number, location, and instrumentation of the observations.Furthermore, there is a certain bias in precipitation totals especially over complex terrain, where the number of observations is limited (e.g., Piani et al., 2010;Kunz, 2011;Berg et al., 2012).

Discharge observations
For the calibration of the rainfall-runoff model, daily mean values of runoff are required.We have selected 71 gauging stations in the Rhine basin, all of them having at least 20 years of continuous observations.The discharge data have various sources: the major part (40 gauging stations) is provided by the German Federal Institute of Hydrology3 , the rest is operated by the individual state ministries of environment from North Rhine-Westphalia4 , Rhineland-Palatinate5 , Baden-Wuerttemberg6 , Hesse7 , Bavaria8 , and Saarland9 .Two gauging station have been provided by the Swiss Federal Office for the Environment (FOEN).

Study area and time period
The focus in this study is on the Rhine river basin as a pilot area.The river Rhine has a length of about 1,200 km and a total basin size of approximately 185,000 km 2 . 10The annual mean discharge close to the estuary is 2,173 m 3 s −1 (Tockner et al., 2009;Hein et al., 2019).The source of the Rhine is located in the high Alpine Mountains.The basin is characterized by various terrain with mountains up to 4,000 m in the headwaters, rolling hills with elevations around 1,000 m and below in the middle part, and mostly flat lands in the northern part (Fig. 1a).Furthermore, the study area covers different precipitation climatologies.As shown for example by Ionita (2017), the mean annual precipitation exceeds more than 2,000 mm over a large area of the Rhine spring area.Due to the high elevation, a significant proportion falls as snow, especially in winter.As snow melt can be an important component for HMs (cf.Sect.4.1), the impact of the terrain is expected to be higher for the Alpine catchments than elsewhere.For the remaining study area, the annual precipitation amounts are generally below 1,000 mm (e.g., Tapia et al., 2015).
The Rhine basin is divided into 71 catchments associated with the same number of gauging stations (cf.Sect.2.2.3).Out of these 71 stations, we selected 6 for this study with various catchment size (Table 2 and Fig. 1b) to compare the observed and simulated discharges for past flood events.
The investigation period is limited by the given data sets.Using LAERTES-EU data blocks 2 and 4 and HYRAS, we focus on the period 1961-2006 for validation and calibration, which is covered by all :::::::::: precipitation : data sets.Regarding the statistical analysis, all available data are taken into account.

Bias Correction of Precipitation
In this section, we describe and validate the applied bias correction with respect to the statistical representation of precipitation within LAERTES-EU as the method itself has been validated by numerous previous studies (cf.below).Table 2. List of gauging stations (full name, used abbreviation (code), and associated river system, ::: and ::::: length :: L :: of ::: the ::: time ::::: series) : used for the validation of the hydrological model for selected historical flood events sorted by the upstream catchment size (A).(2020) showed that LAERTES-EU can produce a reasonable evolution of areal precipitation extremes over Central Europe and the Alpine region for the last century.Although a dry-day correction using E-OBS is already applied, there is still an offset between observations and LAERTES-EU for the considered yearly percentiles of spatial mean precipitation,

Code
indicating the need of further post-processing.As a positive bias in precipitation would result in overestimated discharges, a bias correction of LAERTES-EU is inevitable.
The review of Maraun (2016) or the study of Fang et al. (2015) provide a detailed overview of various bias correction methods.The selection of the most suitable method often depends on the application.Nevertheless, the gamma distribution seems to be most suitable in using the quantile method for correcting precipitation.For this study, we therefore use the gamma quantile mapping (GQM) technique with different correction functions for each month.The corrected precipitation amount can be calculated as follows (e.g., Gutjahr and Heinemann, 2013): where x is the precipitation of either the raw model (" raw "), or the bias corrected model (" corr "); m denotes the month, while d is the day within month m.F is the cumulative density function of the gamma distribution, and F −1 its inverse with (" obs ") referring to the observations.
The ::::: applied : bias correction aims to improve the intensity of daily precipitation considering each month separately to account for seasonality.Building F both for observed and simulated precipitation, the probability of the model intensities is adjusted to those of the observations.Using a parameterized density function instead of an empirical approach allows to retain the heavy tail of the model distribution to a high degree, which represents the unknown and not yet observed range of intensities.The correction factors for the gamma distributions were defined separately for each data block and month.Therefore, all members within a data block are first concatenated and treated as a single data set to which in a second step a gamma distribution is fitted.We did not correct the individual members independently as such an approach would force all members to the target (observed) distribution which would result in a reduced ensemble spread and thus, an underestimated natural internal climate variability (Chen et al., 2019).

Validation of bias-corrected precipitation
The bias of the corrected and uncorrected LAERTES-EU data block 2 ::::::: ensemble ::::: mean : is shown in Fig. 2. For the uncorrected precipitation, a positive bias is visible within almost the entire Rhine basin compared to E-OBS and HYRAS (Fig. 2a,c).
The annual cycle of spatially averaged monthly mean precipitation sums (Fig. 4) shows maxima in summer and winter (in agreement with, e.g., Bosshard et al., 2014).Compared to E-OBS and HYRAS, which show similar values, the course of the annual cycle was already well captured in the uncorrected LAERTES-EU data block 2 but with an enhanced amplitude.
However, there is a distinct positive bias for all months.Without bias correction, LAERTES-EU data block 4 fails to capture the summer maximum.Instead, a local maximum of precipitation is observed during the spring month.After correcting, the bias is significantly reduced preserving the annual cycle of precipitation.For LAERTES-EU data block 4, the bias correction leads to a stronger reduction in winter and an increase in summer.
From the presented results we conclude that the bias correction provides a clear added value for precipitation fields, distributions, and the annual cycle.

Hydrological modeling
In this section, we first introduce the used HM.The ability of the HM to simulate extreme discharges is tested by (a) a comparison of observed and simulated discharges in general and (b) for a number of selected historical Rhine river floods.
The one used here is based on the HBV-IWS model (He et al., 2011) and has been adapted for spatially distributed input data.It consists of four main routines: (i) snow melt and snow accumulation; (ii) soil moisture and effective precipitation; (iii) evapotranspiration (ET); and (iv) runoff response.A triangular weighting function is used to simulate surface routing delays.Finally, the Muskingum routing method (Cunge, 1969) is used to route the flow from upstream to downstream.The 235 model parameters are calibrated towards observations for each catchment, respectively (He et al., 2011).The model runs at a daily time step with 5 km grid spacing and requires inputs of daily precipitation, temperature and ET.Since ET is not directly provided by LAERTES-EU, it is calculated from the mean daily temperature following the approach of Oudin et al. (2005).The model was calibrated and validated using the time series of the 71 gauging stations (cf.Sect.2.2.3).:::::::: Therefore, ::: the ::::::::::: investigation In this study, the Nash-Sutcliffe model efficiency coefficient (NSE, Eq. 2; Nash and Sutcliffe, 1970) is used for calibrating :::::::: validating the HBV model.The NSE is a measure of how the simulated discharges match with the observed ones for ::::: during the validation period.Possible values range between (−∞; 1] with higher values representing a better match.NSE = 1 represents a perfect match between the observation and simulation.It ::: The ::::: NSE is defined by: with the observed discharge Q i,obs at gauge i, the corresponding simulated discharge Q i,mod , the mean of all observations Q obs , and the total number of considered observations N .If NSE = 1, the model in the mean is assumed to be unbiased (numerator/sum of deviations equal zero), in case of NSE = 0, the predictive skill of the model is as good as the mean of the observations (Krause et al., 2005;McCuen et al., 2006).
The NSE for the 71 individual catchments of the Rhine basin (cf.Sect.2.3) is shown in Figure 5 for HYRAS (Fig. 5a), and E-OBS (Fig. 5b) as HM forcing.In both cases the NSE shows a good general agreement between the observed and simulated discharges.In fact, only a few of the smaller catchments have a lower NSE.Nevertheless, it also illustrates a better match for HYRAS, which has a higher spatial resolution.As LAERTES-EU is bias-corrected towards E-OBS (due to its spatial availability for entire Europe), we expect the discharge errors caused by the HM to be in the same order, even assuming a perfect precipitation input.

Historical flood events
Additionally to the overall performance in the previous section, we analyse :::::: analyze in detail three major Rhine river flood events :::::: within :: the ::::::::: validation ::::: period: March 1988, December 1993, and January 1995.The time series of simulated and observed discharges are shown exemplary for the Emmerich (EMME) station (cf.Table 2) in Fig. 6.The results for the other gauging stations can be found in the supplemental material (Fig. S2-S6).For those selected case studies, the model is capable to identify flood peaks in terms of timing and intensity.One limitation of the model is to capture significant day-to-day variations in discharge (BETZ, GROL, and ROCK for January 1995), which would require a higher temporal resolution of the HM than daily time steps.A second limitation is the overestimation of flood peaks at EMME of 10-20%, which is likely due to the relatively simple flood wave routing procedure.

Added value of bias-corrected LAERTES-EU for HM forcing
In the previous section we have provided evidence that the used HM is capable to simulate realistic discharges on a daily basis for different (sub-) catchment extensions.However, the results indicate that a proper representation of input precipitation is beneficial due to the high model sensitivity.We now analyze in how far LAERTES-EU can provide a stochastic data set to represent the statistical properties of observed river discharges.
As LAERTES-EU (both uncorrected and bias corrected) includes simulated precipitation data for thousands of years, we can calculate discharges for different return periods (RPs) from a sorted series of the yearly maximums using the plotting positions approach of Weibull (Makkonen, 2006).For the historical discharges, we have just about 50 years of measured discharges, and 68 (34) years of simulated discharges based on E-OBS (HYRAS).To estimate higher return periods, we need to make assumptions on the underlying distribution of discharge extremes.Although various distributions are used in hydrology, we mainly use a Weibull distribution fitted by the L-moments method (Hosking, 1990) in this study.To illustrate the uncertainty in the distribution selection, we also use Gamma and Gumbel distributions for the observed discharges.
2. The applied HM can reproduce historical flood events in terms of peak discharge and timing.Nevertheless, the results are case sensitive and depend on the catchment size and related terrain characteristics.Moreover, the results demonstrate the necessity of a proper representation of the forcing data.Regarding (1), we provide evidence that the applied bias correction works properly across the whole model chain.The positive precipitation bias of LAERTES-EU (Ehmele et al., 2020) is reduced to a large degree.The statistical distributions like IPCs and the annual cycle are now in good agreement with the E-OBS reference data.The applied methodology of adaptive correction functions (depending on data block, month) has many advantages.For example, it enables the consideration of different bias magnitudes across the year, with a stronger adjustment during winter months.Treating a LAERTES-EU data block as a single data set, the internal variability of the single members within a data block is partly conserved.Furthermore, the approach retains the heavy tail of the distribution representing the not yet observed range of values, as can be expected from such a long data set.However, the quality of the bias correction strongly depends on the reference data set and is therefore limited to the quality of observations.Given Regarding (2), we have applied the HM to historical flooding events (three cases for the Rhine) using observations as forcing.
We provide evidence that the HM can reproduce these events properly in terms of timing and peak discharge.Deviations to observed discharges can be attributed to some limitations of the used data sets and HM, like the relatively coarse spatial resolution and the daily time step.The former has mainly a significant impact in mountainous terrain or for small catchments while the latter mainly affects the flood wave propagation and timing.Nevertheless, a timing error is identified in a few cases and magnitude deviations can be further post-processed.
Regarding (3), the quality of the discharge simulations strongly depends on the catchment size.For the entire basins or large catchments, the bias correction clearly has an added value, given that the estimated discharge return periods are remarkably close to the observations which were extrapolated for high return periods using several distribution functions.The uncorrected data leads to a general overestimation of discharges.For smaller catchments, the results are more mixed.In cases where E-OBS driven simulations show low discharges, the simulations after bias correction also show an underestimation.This behavior can be explained with the stronger sensitivity of the smaller catchments to small-scale and/or convective phenomena as well as sub-daily effects (e.g., Seibert and Auerswald, 2020).Due to the limited length of observations ::::::::::: observational :::::: records, the estimated return values for high return periods show a high uncertainty.From a statistical point of view, the large amount of data of LAERTES-EU should enable more robust estimates in that context :: at :::: least ::: for :::: large :::: and ::::::: medium :::: size ::::::::: catchments ::: as :::: seen :: in ::: the :::::::: estimated ::::: return :::::: periods ::: for ::::::: selected :::::::: historical ::::: flood ::::: events.
The resulting methodology and obtained discharge data can be used to develop probabilistic catastrophe models and risk assessments.This can be performed not only for single catchments but on national and pan-European scales, combining the extreme value statistics from multiple river basins.In particular, adaptations and applications of the presented methodology are ongoing for several large Central European river basins such as the Danube, Elbe, Oder, or Vistula basin.Regarding hydrology, some recalibration of the HM set up to further improve the model performance in these basins is ongoing.For instance, the results can be post-processed (scaled) for further impact modeling using a quantile-quantile mapping technique.
This calibration step will fix the underestimation of peak discharge values while maintaining the large spatial and temporal variability of simulated floods from LAERTES-EU.Regarding the atmospheric part, LAERTES-EU will be used in a follow-up study investigating the relation between the spatial variability of precipitation over Europe and teleconnection patterns.Further applications of LAERTES-EU can include a statistical and/or combined statistical-dynamical downscaling towards higher resolutions to improve both precipitation and discharge representation, especially over mountain ranges.Other extensions could be the evaluation of other variables/hazards and the investigation of so-called compound events, i.e., simultaneously occurring multiple hazards (e.g., Zscheischler et al., 2018;Raymond et al., 2020).The analysis can also be extended by considering climate projection scenarios (e.g., RCP4.5/RCP8.5;Jacob et al., 2014) to estimate possible changes in the frequency, intensity, and extension of hydrometeorological extremes in the 21 st century.

Figure 1 .
Figure 1.Maps of the Rhine basin with (a) the elevation (in meters above mean sea level; basin marked with red contour) and (b) overview of the location (triangles) and associated catchments (colored shading) of gauging stations that were chosen for model validation.

Figure 3 .
Figure 3. Intensity-probability-curve (IPC) of daily rainfall totals within the Rhine basin for LAERTES-EU data blocks 2 and 4, HYRAS, and E-OBS.For LAERTES-EU, the IPCs for the original data set (uncorr) and the bias corrected (BC) data set are shown.

Figure 4 .
Figure 4. Annual cycle of the spatially averaged mean monthly precipitation sum [in mm] based on LAERTES-EU data block 2 and 4 for uncorrected model data (uncorr), bias-corrected data (BC), E-OBS, and HYRAS.

Figure 6 .
Figure 6.Time series of simulated and observed discharges (black) at the Emmerich station (EMME) for the flood events (a) March 1988, (b) December 1993, and (c) January 1995.The simulations are forced with HYRAS (red), and E-OBS (yellow), respectively.

Table 1 .
Ehmele et al. (2020)ensemble LAERTES-EU with the classification into data blocks, the underlying forcing data, the covered time period, and the number of members and simulation years.TableadaptedfromEhmele et al. (2020).