Compound climate extremes such as co-occurring drought and heat or compound precipitation and wind extremes can have a substantial impact on the natural environment and human systems that often exceeds the impact caused by a single extreme . Over recent years a number of compound extremes have been investigated. For instance, several studies have analysed the dependence between storm surge and heavy precipitation or extreme runoff to estimate the risk of compound flooding in coastal areas. Compound droughts and heatwaves have been studied for different regions and varying temporal scales . The occurrence rate of compound precipitation and wind extremes has been estimated for the Mediterranean region , Europe , and at the global scale . Other studies have investigated the co-occurrence of hot days and hot nights or the co-occurrence rate of heavy precipitation and snowmelt to estimate the risk of rain-on-snow events . Such a quantification of the occurrence rate of compound extremes is important for assessing the risk of associated impacts today and in the future. Most of the above studies identify compound extremes by thresholding the contributing variables to quantify the occurrence of compound extremes and changes associated with climate change. However, the dependence structure in the tails is only rarely investigated. Due to the rarity of compound extremes, a large number of samples is required to obtain robust estimates, making it difficult to rely solely on observational data .

Large ensemble simulations offer an opportunity to estimate future changes in the occurrence of compound events without running into data limitations . However, such simulations need to be interpreted with care as it is often largely unknown how well the employed models represent observed compound events , and differences might be large between models. Climate models are regularly evaluated based on their ability to represent well-known processes in the climate system and predominantly univariate comparisons with key climate variables , though some multivariate metrics have been explored . Yet little is known about the ability of climate models to capture observed occurrence rates of compound extremes , a challenging task for two primary reasons. First, due to their rarity, a robust quantification of the likelihood of compound extremes requires large amounts of data, thus making it difficult to establish a “ground truth” for many applications. Second, suitable metrics for evaluating multivariate extremes have not been widely tested and applied in a climate context. Such metrics, however, are essential to assess how well models represent compound events, in particular to assess future risks . When observational data are scarce, process-based model simulations and reanalysis data can be employed to extend or replace purely observational datasets.

To date, model–data comparisons related to compound extremes have been conducted to a very limited extent, often relying on simplifying assumptions and typically confined to precipitation and temperature. For instance, a high likelihood of compound hot and dry summers has been linked to a strongly negative correlation between summer temperature and precipitation . While there is generally good agreement with respect to this correlation between climate models and observation-based datasets in the Northern Hemisphere, there is strong disagreement in the Southern Hemisphere, for which the models show a much stronger dependence. This finding may suggest that climate models overestimate dependence between summer temperature and precipitation. However, this discrepancy may also be related to the way gridded observation-based datasets are assembled. In particular, for locations without an active measurement station nearby, the mean seasonal cycle is often used to fill gaps in the observational networks e.g.. This approach reduces the strength of co-variability between temperature and precipitation in poorly sampled regions, which are mostly in the Southern Hemisphere. Thus, assessing the ability of climate models to represent compound events may reveal underappreciated limitations in gridded observation-based datasets. We are not aware of studies so far that have evaluated the dependence between precipitation and wind speed.

In this study we focus on compound precipitation and wind extremes, which can have severe socio-economic impacts including human fatalities, impaired critical infrastructure, and economical damage . We investigate differences in the occurrence of compound precipitation and wind extremes for different datasets over a region in central Europe including the Alps. To this end, we introduce a new measure that assesses dissimilarity between the tails of bivariate distributions. We study an experimental design with two factors. The first factor is the type of boundary conditions in a high-resolution regional weather model, either from reanalysis or a global circulation model. The second factor corresponds to the effect of different climate forcing between today and the future under a high-emission scenario. Our object of study under this design is the dependence between heavy precipitation and strong wind in winter over central Europe. In addition, comparisons with a state-of-the-art reanalysis product are implemented.

We use daily precipitation sums and daily maximum wind speed in the extended winter (November–March) from one reanalysis product and three model simulations over a period of 20 years. The employed reanalysis product is ERA5 from which we use data for the period 1980 to 1999 CE. This reanalysis is generated with an updated numerical weather prediction model and data assimilation system compared to the prior product ERA-Interim and integrates additional data sources. The data are available at a resolution of roughly 30 km (spectral resolution of T639), with 137 vertical levels and hourly output.

The three simulations are performed with the Weather Research and Forecasting (WRF) model which is forced with boundary conditions from (i) ERA-Interim (ERAI-WRF), (ii) a period of free-running global climate simulations for the present day (CESM-WRF), and (iii) a period covering the end of the 21st century under Representative Concentration Pathway 8.5 (CESM-WRF-fut, a high-emission scenario). The global climate simulation is performed with the Community Earth System Model (CESM) for the period 850 to 2100 CE. Details on the setting are described in and . In this study we use the period 1980 to 1999 CE as the present day and 2080 to 2099 CE as the future.

The periods of the global simulations and the ERA-Interim period (1980 to 1999 CE) are dynamically downscaled with WRF in version 3.5. WRF is vertically discretized in 40 terrain-following η-coordinate levels. The horizontal resolutions of the four two-way nested domains (Fig. ) are 54, 18, 6, and 2 km. The innermost domain covers the box [4.75∘E,15.25∘E]×[43.25∘N,48.75∘N] and is exclusively used in this study. The setup is described in more detail in and . Important for this a study is that the convection parameterization is disabled for the simulations at 6 and 2 km resolution; at these scales the model is convection-permitting. This is an important step in improving the simulation of precipitation, though some problems still remain . For adequately simulating wind, the setting of the planetary boundary layer parameterization is key. We use a modified version of the fully non-local scheme developed by , which specifically treats effects of the unresolved orography . For the ERAI-WRF simulation we allow analysis nudging of wind, temperature, and humidity above the planetary boundary layer in order to stay close to the large-scale behaviour of the reanalysis data . For the two simulations driven by CESM, nudging is omitted to allow the regional model to correct potential systematic biases of the CESM (e.g. a zonal atmospheric circulation that is too strong in the mid-latitudes; ). The WRF output is provided in hourly resolution.

We remap the original hourly data to a common regularly spaced grid with 0.25∘ spatial resolution using conservative remapping and subsequently compute daily precipitation sums and daily wind speed maxima. The 0.25∘ spatial resolution was chosen as it is closest to the original resolution of the ERA5 reanalysis data. Note, however, that all WRF simulations are run at a much higher convection-resolving resolution. The explicit resolution of convection and a much higher resolution of the topography may result in a more accurate representation of the dependence between precipitation and wind extremes in the simulations than in ERA5. We further note that mean wind speed in ERA5 generally decreases with elevation (Fig. a), which is the opposite of the expected behaviour for the response of wind speed to elevation from observations and what is modelled by WRF (Fig. b). The discrepancy in mountainous regions between reanalysis data and observations with respect to wind speed is also evident in other reanalysis datasets such as ERA-Interim , which is the predecessor of ERA5. In contrast, WRF has been shown to also simulate wind speed reasonably well in mountainous terrain . For these reasons – WRF better resolves cloud processes, topography, and wind speed, while ERA5 misrepresents the wind speed gradient with elevation – we use ERAI-WRF as the reference for all analyses.

We first present a simple correlation analysis based on the Spearman's rank correlation coefficient. Daily precipitation sums and maximum wind speed are generally strongly correlated in winter in most areas of the study domain except in the northwest of Italy (Fig. ). All model simulations show a relatively consistent pattern, whereas ERA5 shows negative correlations at the southern slopes of the Alps along the northwestern Italian border (Fig. b). Most correlations are significant (α=0.05).

When considering only the dependence in the tails based on χ and including a spatial and temporal neighbourhood, the spatial patterns look quite different (Fig. ). The WRF simulations show a highly heterogeneous picture with strong local variations, generally strong dependence over most parts of the Alps and close to the Adriatic coast, and weak dependence otherwise (Fig. a, c, d). Overall, ERAI-WRF shows slightly higher tail dependence compared to the WRF simulations driven by CESM. In contrast to the WRF simulations, in ERA5 tail dependence varies rather smoothly in space, with higher values in northeastern Italy and along the eastern border of France (Fig. b).

The block sizes that attain the maximum tail dependence χ for precipitation and wind extremes for each pixel are shown in Fig. . On average for 75 % of the pixels, the maximum is attained with no temporal lag (blue in Fig. ). In contrast, there seems to be a shift in space, as maxima tend to co-occur in neighbouring grid points: block sizes with larger than minimal (0.25∘) spatial extent occur on average in 60 % of all locations (lighter colours in Fig. ). This means that extremes in daily precipitation sums and wind extremes tend to occur on the same day but potentially not at exactly the same location; they occur with some distance apart. In particular in the south of the Alps but also in some regions north of the Alps, this distance is 1.75∘, or about 100–200 km (very light colours in Fig. ). The strongest agreement of the dependence patterns is between CESM-WRF and CESM-WRF-fut, which agree for half of the locations in the maximizing block size. In contrast, the agreement is 29 % between ERAI-WRF and ERA5 and 39 % between ERAI-WRF and CESM-WRF. Note that grid points at the boundaries cannot attain maxima with block sizes larger than one grid point as no data values are available outside the study domain.

The tails between winter daily precipitation sums and wind speed maxima show a significantly different dependence structure between ERAI-WRF and CESM-WRF in 46 % of all grid points, mostly in Switzerland and in the north of the study domain but also in many regions in northern Italy (Fig. a). The percentage of grid points with significantly different tail behaviour is slightly higher for the comparison of ERAI-WRF and ERA5 (49 %), though in this case most of the differences occur in grid points located along a wide diagonal band from the southwest to the northeast through the entire study domain (Fig. b). Interestingly, the comparison of ERAI-WRF with CESM-WRF-fut results in only 36 % of pixels with significantly different tail behaviour (Fig. c). Thus, CESM-WRF-fut agrees better with ERAI-WRF with respect to the tail behaviour than CESM-WRF and ERAI-WRF. Finally, only 18 % of pixels show significantly different tail behaviour when comparing CESM-WRF and CESM-WRF-fut (Fig. d), indicating the pair with the largest number of grid points at which no significant difference in the tail behaviour could be found. The numbers of grid points with significantly different tail behaviour depend somewhat on the threshold u and generally decrease with increasing extremeness (that is, increasing u), but the differences between the different pairwise comparisons remain similar (Table ). In particular, the differences between ERAI-WRF and CESM-WRF and between ERAI-WRF and CESM-WRF-fut are generally larger than the differences between CESM-WRF and CESM-WRF-fut, indicating that the main finding, namely that boundary conditions in WRF appear to be the key factor in explaining differences in the dependence behaviour between wind and precipitation extremes, is robust for different parameter values of the difference measure.

We have introduced a new metric for comparing tail dependence structures between wind and precipitation extremes in reanalysis data and weather model simulations. In our WRF simulations, the type of boundary conditions, either ERAI or CESM, appears to have a stronger effect on the coupling between high wind and heavy precipitation than the change in external forcing (present-day and future) in CESM (Fig. ). This suggests that the studied dependence structures between the tails of precipitation sums and wind speed maxima in winter are a rather robust feature of the combination of models (boundary conditions plus a high-resolution weather model) and thus also somewhat determined by the boundary conditions. In consequence this also means that here we are probably detecting rather stable dynamical features that are largely independent of strong external forcing such as (much) higher mean temperatures. Because the model setting determines the dependence structure, sampling uncertainties in this dependence, for instance to robustly assess risks under future climate conditions, would require a range of different climate and weather model combinations.

The employed block maxima approach (Fig. ) has the effect that precipitation and wind extremes are considered together even if they might occur some distance apart in either time or space. This is to ensure that extremes in wind and precipitation are considered together if they emerge from the same atmospheric processes (e.g. föhn). At the same time, the block maxima approach can help diagnose why datasets differ in their tail dependence structure of precipitation and wind extremes, for instance if the spatio-temporal blocks for which extremes are attained differ strongly.

Regarding the optimal spatial and temporal lags between wind and precipitation extremes there is generally good agreement that along the southern slopes of the Alps the dependence is maximized for precipitation and wind extremes occurring on the same day and up to 1.75∘ apart (lightest blue in Fig. ), which could be related to föhn events that lead to heavy precipitation north of the mountain range and extreme winds on the southern slopes or vice versa. Indeed, heavy precipitation events on the Alpine southern side are often related to high moisture transport ahead of cold fronts that is associated with moderate winds that are not as strong as potential föhn gusts on the Alpine northern side .

Most heavy precipitation events in the investigation domain in winter are associated with extratropical cyclones. Within extratropical cyclones, wind speed maxima and precipitation maxima are often linked to fronts and conveyor belts , and this may result in co-located extremes. However, important modulations of both extreme wind and precipitation patterns by the local complex orography are to be expected , and such local föhn effects, channelling effects, flow blocking, and many more might be captured by the high-resolution WRF simulations but not in ERA5.

Overall, ERA5 shows quite a different behaviour for the Spearman's rank correlation (Fig. ) and simple tail dependence χ (Fig. ) compared to the high-resolution weather model simulations. Spatial patterns are much smoother, probably related to the much coarser spatial resolution (30 km compared to the original 2 km in the WRF simulations). Furthermore, wind speeds over high mountains are unrealistic, as they decrease with height rather than increase (Fig. ). These limitations render ERA5 unsuitable as a benchmark for the tail dependence between precipitation and wind extremes in the Alpine area with its complex orography. Presently, homogenized gridded wind observations of good quality are not available for this region. Therefore, driving a well-calibrated high-resolution weather model with observation-based boundary conditions is currently the best benchmark to study compound wind and precipitation extremes.

We would like to note that in our setup ERAI-WRF is nudged to the driving reanalysis ERA-Interim. The reason for this is that the simulation should stay close to the large-scale behaviour of the reanalysis data. As mentioned in the Data section, we only use wind, temperature, and humidity above the planetary boundary layer and the nudging is not strong. Nevertheless, the behaviour of extremes might be changed due to the modification of the dynamical equations to some extent, but we think that this effect is minor. Furthermore, precipitation is not nudged.

Evaluating how well models represent tail dependencies may help select those models that are fit for purpose regarding the analysis of compound events for a range of different event types . In particular, when the interest lies in the simulation of impacts, the approach may help decide when multivariate bias adjustment approaches would need to be employed , as univariate bias adjustment might increase biases in impacts that depend on multiple correlated drivers .

Evaluating the ability of climate models to represent the likelihood of compound climate extremes is important for well-informed climate risk assessments. In this study we investigated differences in the tail behaviour of precipitation and wind extremes in winter between different weather model simulations and a reanalysis dataset for a region in central Europe. Employing a new metric to measure differences in the tail behaviour of bivariate distributions, we found that simulations of the same model pair with different external forcing conditions (climate change conditions) differ less than simulations for present-day conditions with different boundary data. Our results further suggest that reanalysis data are not suitable as a benchmark for the analysis of compound precipitation and wind extremes over complex terrain such as the Alps. Overall, differences between model simulations (different boundary conditions and weather and/or climate models) can be substantial. Our results suggest that climate impact modelling needs to take uncertainties related to the simulation of compound extremes into account to provide robust risk assessments for today and the future.