Abstract

An extreme-value analysis of projected changes in heavy precipitation is carried out for an ensemble of eight high-resolution regional climate model simulations over the European domain. The consideration of several regional climate models that are forced by different global models allows for an assessment of the robustness of the results in terms of intersimulation agreement. The extreme-value statistical method is based on a model that includes time-dependent parameters. Summer and winter are examined separately. This allows for identifying and sharpening the understanding of physical processes inducing the changes in precipitation characteristics. Thermodynamic aspects of changes in heavy precipitation are discussed. Variables that are related to the process of precipitation formation, such as precipitable water and cloud liquid water, are examined. In this context, the scaling of changes in heavy precipitation and other thermodynamic quantities with changes in temperature is explored. The validity of a Clausius–Clapeyron scaling of heavy precipitation is assessed on regional scales. Significant regional and seasonal differences in trends of heavy precipitation and only a limited validity of the Clausius–Clapeyron scaling are found. In winter, enhanced moisture transport and storm-track intensity lead to an increase in heavy precipitation, especially over the northern parts of the European continent. In summer, the increase of precipitable water is less than that required to maintain the same probability for saturation over southern Europe, which results in negative trends of heavy precipitation in these regions.

1. Introduction

Among the consequences that may result from warmer climatic conditions, changes in extreme events can have the most devastating effects locally. Heavy precipitation events are critical particularly because they can cause floods in riverine areas and landslides in mountainous regions. Such hazards can result in enormous losses of infrastructure, ecosystems, or human lives. A detailed exploration of the causes of heavy precipitation and possible changes in heavy precipitation characteristics is therefore important.

Causes for changes in heavy precipitation can broadly be classified as being of a dynamic or thermodynamic nature (Emori and Brown 2005; Muller et al. 2011). Dynamic causes refer to changes in the atmospheric circulation while thermodynamic causes encompass changes in temperature and atmospheric moisture content. Yet, the separation is not clear-cut and overlapping is possible. Changes in atmospheric stability and convective activity, for instance, are related to thermodynamic characteristics of the boundary layer and induce alterations in the dynamics of the atmosphere.

A starting point for the discussion of thermodynamic aspects of changes in heavy precipitation is the Clausius–Clapeyron equation (Allen and Ingram 2002; Pall et al. 2007; Allan and Soden 2008; Trenberth 2011). It describes the temperature dependence of the saturation water vapor pressure and implies about a 7% change in the water-holding capacity of the atmosphere per kelvin temperature change, assuming constant relative humidity. Since heavy precipitation events are likely to occur when all the moisture in a volume of air is effectively precipitated out, this suggests a similar scaling of heavy precipitation with temperature. However, several issues remain. For instance, there is a widespread decrease in surface relative humidity over land in global warming simulations (O’Gorman and Muller 2010; Sherwood et al. 2010). Moreover, warming and moistening does not take place uniformly over the troposphere (Soden et al. 2005) under changing greenhouse gas concentrations. This can have an effect on the static stability of the atmosphere and subsequently on the frequency and intensity of convective activity (Del Genio et al. 2007; Frierson 2008; O’Gorman and Schneider 2009). Furthermore, the temperature increase over land significantly outpaces changes over the ocean in global warming simulations, especially in the Northern Hemisphere summer. This may lead to a drying of arid land areas (Mariotti et al. 2008). In general, the availability of moisture can be limited over land, which has an impact on precipitation formation, although the link between soil moisture and precipitation is not straightforward (Hohenegger et al. 2009). In Europe, the increased amount of convective precipitation that falls over wet compared to dry soils is not necessarily steered directly by the local amount of evaporation. Instead, convective precipitation over land might be driven by the buildup of a shallow boundary layer in which heat and moisture are accumulated and provide a source of convective instability through a high concentration of low-level moist entropy (Schär et al. 1999).

Dynamic causes for heavy precipitation are often intertwined with thermodynamic effects. For instance, strong convective activity can occur in the warm cores of baroclinic eddies (Korty and Schneider 2007). Changes in atmospheric circulations also imply changes in horizontal temperature gradients and moisture convergence (Held and Soden 2006). The weakening of convective activity can have both local causes as well as causes related to changes in water vapor mass flux and wind stress due to alterations in the large-scale flow. For example, a poleward expansion of the Hadley cell implies a strengthening of subsidence in certain subtropical regions like the Mediterranean (Lu et al. 2007; Frierson et al. 2007; Lionello et al. 2008) and a shift in midlatitude storm tracks (Ulbrich et al. 2008; Bengtsson et al. 2009). Related may be changes in modes of variability like the North Atlantic Oscillation (Gerber and Vallis 2009). Moreover, changes in the meridional temperature gradient due to polar amplification can affect the moisture dynamics of the atmosphere (Boutle et al. 2010). In Europe, for the formation of precipitation, the influence of local evaporation versus moisture advection into a region is more dominant in summer when convective effects are more pronounced in relation to large-scale transports (Frei et al. 1998).

The discussion so far suggests that causes for changes in heavy precipitation can be quite different regionally and seasonally (Berg et al. 2009). In the present study, an ensemble of high-resolution regional climate model (RCM) simulations is used to estimate changes of heavy precipitation in a warming climate and to investigate causes for these changes. Limited-area models have been shown to reproduce well the statistics of heavy precipitation on a daily time scale (Frei et al. 2003; Semmler and Jacob 2004; Frei et al. 2006; Hohenegger et al. 2008; Hanel and Buishand 2010).

Extreme-value statistics represent an appropriate tool to analyze the occurrence rate of extreme weather events (Coles 2001; Embrechts et al. 1997) and have been applied in hydrology, meteorology, and climatology for many years (Buishand 1989; Katz 1999; Katz et al. 2002; Naveau et al. 2005). Based on an extreme-value analysis including time-dependent parameters, seasonal characteristics of trends in heavy precipitation events over Europe are examined under climate change conditions. Also, a discussion of changes in variables that govern precipitation formation is provided. The focus of this study is the understanding of the interplay between trends in heavy precipitation and changes in related physical processes as simulated by high-resolution climate models.

The structure is as follows. Section 2 gives an overview of the climate model simulations that are analyzed. A description of the extreme-value statistical techniques that are applied is provided in section 3. In section 4, the results of the statistical analysis of trends in heavy precipitation events over Europe are presented. Additionally, we relate the trends in heavy precipitation to changes in other variables that govern precipitation formation, with a focus on the Clausius–Clapeyron relation. Finally, in section 5, a discussion of the results is given and the conclusions summarize the findings.

2. Climate model simulations

The regional climate model simulations analyzed in this study were performed in the ENSEMBLES project, which was part of the Sixth Framework Programme (FP6) by the European Union. The domain covers the whole European area with a spatial resolution of about 25 km. The period 1961–2099 was simulated with anthropogenic forcing because of the emission of greenhouse gases and sulfate aerosols as defined by the Special Report on Emissions Scenarios (SRES) A1B emission scenario (Nakicenovic and Swart 2000).

An overview of the models considered in the present work is given in Table 1. The RCMs are RACMO (Lenderink et al. 2003) run by the Royal Netherlands Meteorological Institute (KNMI), RCA (Kjellström et al. 2005) run by the Swedish Meteorological and Hydrological Institute (SMHI) and the Community Climate Change Consortium for Ireland (C4I), HadRM3 (Collins et al. 2006) run by the Hadley Centre, CLM (Böhm et al. 2006) run by the Swiss Federal Institute of Technology Zurich (ETHZ), and REMO (Jacob 2001) run by the Max Planck Institute for Meteorology (MPI-M).

Table 1.

Climate model simulations considered in the present work. Regional climate models: Regional Model (REMO), Climate version of “Lokal-Modell” (CLM), Hadley Centre Regional Model version 3 (HadRM3), Regional Atmospheric Climate Model (RACMO), and Rossby Centre Regional Atmospheric Climate Model (RCA). Driving global climate models: ECHAM version 5/Max Planck Institute Ocean Model (ECHAM5/MPI-OM), third climate configuration of the Met Office Unified Model (HadCM3), Institute Pierre Simon Laplace Climate Model (IPSL), and Bergen Climate Model (BCM).

Climate model simulations considered in the present work. Regional climate models: Regional Model (REMO), Climate version of “Lokal-Modell” (CLM), Hadley Centre Regional Model version 3 (HadRM3), Regional Atmospheric Climate Model (RACMO), and Rossby Centre Regional Atmospheric Climate Model (RCA). Driving global climate models: ECHAM version 5/Max Planck Institute Ocean Model (ECHAM5/MPI-OM), third climate configuration of the Met Office Unified Model (HadCM3), Institute Pierre Simon Laplace Climate Model (IPSL), and Bergen Climate Model (BCM).
Climate model simulations considered in the present work. Regional climate models: Regional Model (REMO), Climate version of “Lokal-Modell” (CLM), Hadley Centre Regional Model version 3 (HadRM3), Regional Atmospheric Climate Model (RACMO), and Rossby Centre Regional Atmospheric Climate Model (RCA). Driving global climate models: ECHAM version 5/Max Planck Institute Ocean Model (ECHAM5/MPI-OM), third climate configuration of the Met Office Unified Model (HadCM3), Institute Pierre Simon Laplace Climate Model (IPSL), and Bergen Climate Model (BCM).

The RCMs are driven by different global general circulation models (GCMs) at their lateral boundaries. In the case of HadCM3, two versions are used: HadCM3Q0 is the standard model version and HadCM3Q16 is a version with higher sensitivity to climatic variability that was obtained by changing some of the model parameters. A detailed description of the modifications can be found in Collins et al. (2006). Also shown in Table 1 are the convection parameterizations of the regional climate models. For reasons of clarity, only a subset of simulations from the ENSEMBLES project is considered in the present work. The simulations are selected because they cover simulations from the same RCMs driven by different GCMs as well as simulations with the same GCMs driving different RCMs. Also, all main convection parameterization schemes are covered. Yet, this selection is not exhaustive and the results will to some extent depend on the chosen models, their parameterization schemes, and the dynamics of the driving global models. Nevertheless, the range of the chosen combinations is expected to show which climatic trends in heavy precipitation over Europe are robust with respect to the selection of the RCM and the driving GCM. In this context, robustness is defined as the agreement of the majority of simulations on the trend in a specific region.

In the present work, no validation of the regional climate models is performed since this is not the aim of this study. In the framework of the ENSEMBLES project, the regional climate model simulations analyzed in this study have been validated against observations with respect to temperature, precipitation, geopotential height, and cloud fraction (Kjellström et al. 2010; Lenderink 2010; Lorenz and Jacob 2010; Sanchez-Gomez et al. 2009; Christensen et al. 2010). For an attempt to validate the regional climate model REMO over Germany with regard to trends in heavy precipitation events, the reader is referred to Tomassini and Jacob (2009).

3. Extreme-value analysis

The focus of this study is trends in heavy daily precipitation totals. The density of precipitation events decreases toward the upper tail of the distribution. Extreme-value theory tackles the problem to estimate the distribution of rare events. In the present work, the Poisson point process approach is used. The occurrence of exceedances over a high threshold u (i.e., heavy precipitation events in the context of the present paper) is modeled by a Poisson process. The parameters of the Poisson point process likelihood correspond to the parameters of the generalized extreme value (GEV) distribution for block maxima. Thereby, the Poisson point process approach is connected to the traditional extreme-value theory [this connection is described in more detail in Tomassini and Jacob (2009; see also Embrechts et al. 1997; Coles 2001)]. One advantage of the Poisson point process is the independence of the scale parameter σ on the choice of the threshold u. Also, covariates can be introduced immediately. As the aim is to analyze the climatic trends of heavy precipitation, time is introduced as a covariate here; the statistical model is then a nonhomogeneous Poisson point process.

Let Xi be a series of independent and identically distributed random variables. If the threshold u is sufficiently large, a sequence of point processes converges on regions (0, 1) × [u, ) for any z > u to a Poisson point process with intensity Λ on A = [t1, t2] × (z, ), where

 
formula

Let Tj be the time of the jth exceedance and the value of the jth exceedance of the threshold u, j = 1, … , nu, with nu being the number of exceedances. The interval [0, T] spans the whole time period. It can be shown that the likelihood function of the Poisson process (for each grid box separately) is given by

 
formula

where a+ = a if a > 0 and zero otherwise. Similar to Smith (2003), the temporal dependence of the location parameter μt and the scale parameter σt is chosen as

 
formula

where μ0, σ0, β1, and β2 are constants. The shape parameter ξ is assumed to be constant in time. It characterizes the tail of the heavy precipitation distribution. Positive values of ξ imply a heavy tail that is associated with the Fréchet family. In contrast, negative values of ξ imply a bounded tail associated with the Weibull family and values very close to zero indicate exponential tail behavior.

For the present work the threshold u is defined to be the 95% quantile of the time series of daily precipitation totals for each grid point and for each simulation of the ensemble separately. Considering the findings by R. L. Smith (1999, unpublished manuscript), the choice of this threshold is reasonable since this analysis focuses on the investigation of climatic trends of heavy, 24-h precipitation events and not on return periods of very extreme events at the far end of the distribution tails. A validation of this threshold choice applying W statistics has been carried out by Tomassini and Jacob (2009). The 95% quantile is constant in time and is estimated empirically for the whole time period from 1961 to 2099, including days without precipitation. All grid boxes for which the 95% quantile is smaller than 0.5 mm of precipitation are excluded from the analysis.

The Poisson point process model assumes the threshold exceedances to be independent. Therefore, declustering is applied to the data in advance. In this analysis, heavy precipitation events are assumed to be dependent (belonging to the same precipitation front) when they are separated by, at most, one day. This is reasonable for precipitation because strong events occur mostly in highly dynamic meteorological situations, passing a location quickly, or as convective events, which are rather short-lived with time scales of no more than a day. Accordingly, declustering is applied as follows. Two threshold exceedances are considered to belong to the same cluster if no more than one day lies in between them, except if at this day in between no precipitation has occurred. Each one of these clusters is then treated as one heavy precipitation event and the maximum of the exceedances within each cluster is considered the corresponding precipitation amount (Davison and Smith 1990). Inspection of the data has shown that the declustered time series do not feature temporal autocorrelation any longer, which justifies this method.

Maximum likelihood parameter estimation is carried out for μ0, σ0, β1, β2, and ξ by minimizing the negative log-likelihood. The integral in (2) is approximated numerically. For more details the reader is referred to Tomassini and Jacob (2009).

From the estimated parameters of the inhomogeneous Poisson point process, high quantiles of the distribution of the data can be calculated in the following way:

 
formula

with , m pointing to the m-observational return value [equivalent to the (100 − m−1)% quantile], and ζu being the probability that the threshold is exceeded.

For this analysis, the statistical computing language R (R Development Core Team 2011) is used, with the packages POT (Ribatet 2011) and ismev (Coles and Stephenson 2011) in particular.

4. Results

a. Trends in heavy precipitation over Europe

The statistical analysis is carried out separately for summer [June–August (JJA)] and winter [December–February (DJF)]. In the following, the focus will mainly be on trends in the 99.9% quantile of total daily precipitation for winter and summer over the time period from 1961 to 2099. The 99.9% quantile corresponds to a value of m = 1000, that is, an event that occurs once in 1000 observations, including days without precipitation. In the present study this occurs one time in about 11 seasons.

1) Winter

Figure 1 shows the relative linear trend of the 99.9% quantile of daily winter precipitation for the eight-member ensemble of RCM simulations. With high consistency, the RCMs project a generally positive trend in northern Europe, which is strongest over northern Scandinavia. Nevertheless, along the Atlantic coast of Norway, where the average precipitation is known to be high, heavy precipitation is projected to decrease or remain constant, depending on the driving GCM. In southern Europe, particularly on the Iberian Peninsula and around the Mediterranean Sea, the RCMs suggest no change in heavy precipitation or even a decrease. In general, the increase of heavy precipitation is found to be stronger over the continents than over the oceans, consistent with the pattern of temperature changes.

Fig. 1.

Relative trends of the 99.9% quantile of daily winter precipitation.

Fig. 1.

Relative trends of the 99.9% quantile of daily winter precipitation.

Figure 2 shows the number of models that agree on an increase in the 99.9% quantile of daily winter precipitation. The large-scale pattern of heavy precipitation changes is found to be broadly consistent across the models. Inconsistencies occur mainly over the Alpine ridge, the Pyrenees, and along the western coast of Norway. Furthermore, the simulations do not match well in a rather narrow transition zone between positive and negative trends, located over the Mediterranean region.

Fig. 2.

Number of models that agree on a positive relative trend of the 99.9% quantile of daily winter precipitation. The number 8 indicates that all simulations agree on a positive trend; 0 indicates that all simulations agree on a negative trend.

Fig. 2.

Number of models that agree on a positive relative trend of the 99.9% quantile of daily winter precipitation. The number 8 indicates that all simulations agree on a positive trend; 0 indicates that all simulations agree on a negative trend.

Figure 1 indicates that the regional climate models are strongly determined by the large-scale forcing provided by the driving global climate models. The group of three ECHAM5/MPI-OM-driven RCMs as well as the group of three HadCM3-forced regional models show very similar patterns of change. In the simulation of C4I, the regional climate model RCA is driven by a high-sensitivity version of HadCM3. The zonal band of large trends over the continent becomes more pronounced and covers parts of the Atlantic as well. It also shows quite a pronounced decrease of heavy precipitation over the Alpine ridge and the Pyrenees, and an increase south of the Alps. The ECHAM5/MPI-OM-driven simulations do not show clear trends in central Europe, including the mountainous areas.

The pattern of change in the 99.9% quantile corresponds to the trend pattern in the location parameter μ (Fig. 3), which is essentially commensurate with the mean of the heavy precipitation distribution. The trend of μ gives indications about a shift in the distribution of precipitation events. Strong increases stretch from the northwest to the northeast of the continent, while in the southern Mediterranean, pronounced decreases can be observed. Generally, the areas where the location parameters show negative trends exhibit a somewhat larger extent than for the 99.9% quantiles. This indicates that in southern regions, an increase in variance plays a decisive role for the sign of trends in the quantiles. The behavior of the scale parameter σ tends to confirm this interpretation (Fig. 4).

Fig. 3.

Relative trends of the location parameter μ for winter.

Fig. 3.

Relative trends of the location parameter μ for winter.

Fig. 4.

Relative trends of the scale parameter σ for winter.

Fig. 4.

Relative trends of the scale parameter σ for winter.

The scale parameter σ is essentially analogous to the variance of the heavy precipitation distribution and indicates changes in the day-to-day variability of the intensity of precipitation events. Trends in σ are not very distinct in any of the climate model simulations. The strong north–south gradient in trends as prevalent for the location parameter μ and for the quantiles is not present for σ. Also, in the very southern part of Europe, where μ is projected to decrease markedly, the scale parameter remains essentially constant. The regional climate model simulation that is driven by the high-sensitivity version of HadCM3 shows a clearer positive trend in σ in most areas, including the Mediterranean. When seen as part of the changes in the 99.9% quantile, the trends in σ seem to damp the strong trends in μ partly, especially where the changes in μ are negative. Small changes in σ can obviously play a large role for changes of the 99.9% quantile.

Figure 5 shows the values of the shape parameter ξ to be mostly close to zero. The largest positive values occur over the Mediterranean coastlines, and largest negative values over Scandinavia, except over the Atlantic coast of Norway. The different simulations are surprisingly consistent in this respect. Over the Alps, however, the estimates show some ambiguity among the various models. The values of ξ in climate model simulations are to some extent dependent on the resolution. Increased resolution tends to lead to higher values in ξ (Tomassini and Jacob 2009).

Fig. 5.

Estimated shape parameter ξ for winter.

Fig. 5.

Estimated shape parameter ξ for winter.

2) Summer

Figure 6 shows the relative trend of the 99.9% quantile of daily summer precipitation for all the regional climate model simulations. As mentioned in section 3, grid boxes for which the 95% quantile of daily precipitation is smaller than 0.5 mm are excluded from the analysis. They appear as white areas in the figures.

Fig. 6.

Relative trends of the 99.9% quantile of daily summer precipitation.

Fig. 6.

Relative trends of the 99.9% quantile of daily summer precipitation.

The simulations show a slight positive trend in heavy precipitation over northern Europe, whereas negative values occur in the south. In the transition zone between positive and negative trends and over the Mediterranean Sea, the agreement between the simulations is low (Fig. 7). In the regions with stronger positive and negative changes, the simulations show high consistency. The magnitude of the changes differs, especially for the decrease in heavy precipitation over southern Europe (Fig. 6). Whereas in the ECHAM5/MPI-OM-driven simulations and the RCA simulation driven by HadCM3Q16, a sharp border is prevalent between negative and positive trends at the latitude of the British Channel in the west and at the latitude of the Alps farther east, the pattern is less distinct in the other simulations. All models project positive trends in some regions in the Mediterranean and Alpine area, but they are not consistent in location.

Fig. 7.

As in Fig. 2, but for summer precipitation. Gray areas denote grid boxes for which the 95% quantile of daily precipitation is smaller than 0.5 mm in at least one simulation. These grid boxes are excluded from the analysis.

Fig. 7.

As in Fig. 2, but for summer precipitation. Gray areas denote grid boxes for which the 95% quantile of daily precipitation is smaller than 0.5 mm in at least one simulation. These grid boxes are excluded from the analysis.

Similar to the situation in winter, the trends in the location parameter μ show patterns that resemble the trends in the 99.9% quantiles (Fig. 8), but substantially amplified in relative terms. In Scandinavia a strong increase is projected, while in the Mediterranean region, France, and eastern Europe the location parameter shifts to smaller values. The RCM simulations are consistent with respect to the geographical pattern. Trends in the scale parameter σ exhibit a somewhat clearer north–south gradient than in winter, with a negative sign in many regions in the south. Yet, the changes are not large in relative terms (Fig. 9). In comparison to winter, the trends in the scale parameter σ in summer show a pattern that is more similar to the pattern of changes in the 99.9% quantiles. This indicates that changes in the variability of heavy precipitation events play a larger role in summer.

Fig. 8.

As in Fig. 3, but for summer.

Fig. 8.

As in Fig. 3, but for summer.

Fig. 9.

As in Fig. 4, but for summer.

Fig. 9.

As in Fig. 4, but for summer.

The values of the shape parameter ξ (not shown) are essentially positive in summer and larger than in winter. Positive values of ξ imply heavy tails, which means that even the far tail of the distribution holds some mass. Higher values of ξ thus indicate an increasing impact of changes in σ on changes in the 99.9% quantiles. The highest values of around 0.5 are obtained over the Mediterranean Sea. Over continental Europe the values of ξ range in general between 0 and 0.35. In the northern parts of the domain, including Scandinavia, ξ takes values close to zero, and no systematic differences can be found between land and sea areas.

b. Heavy precipitation and the Clausius–Clapeyron relation

The Clausius–Clapeyron relation suggests the increase of precipitable water to be about 7% K−1 of warming, assuming that relative humidity remains constant. This relation is examined on regional scales, dividing the relative linear trend of precipitable water by the linear trend of 2-m temperature at each model grid point. Cloud liquid water and heavy precipitation trends are treated likewise. This gives the first idea of how closely the processes of cloud and precipitation formation follow the Clausius–Clapeyron scaling on regional scales. For this section, four simulations of the ensemble are selected for reasons of brevity. Nevertheless, the chosen simulations represent a large range within the ensemble, since different RCMs, different driving GCMs, and different convective parameterization schemes are covered (see Table 1). The results show that the driving global climate models play an important role in heavy precipitation trends in the RCM simulations. To analyze the influence of the large-scale forcing on the Clausius–Clapeyron scaling, two RCM simulations driven by ECHAM5/MPI-OM and two driven by HadCM3 are selected. Linear trends of all variables are estimated for the time period from 1961 to 2099.

On a regional scale, the analyzed RCM simulations suggest some variation in the trends of precipitable water per kelvin temperature increase over Europe (Fig. 10). In all simulations, the changes are strongest over the Atlantic Ocean, where they take values up to 18% K−1. Over land in winter, the changes range from 8% to 12% K−1 in the west and from 6% to 8% K−1 in the east. However, the spatial variability is to a large extent due to regional differences in the amplitude of the temperature increase. In absolute terms, the trend in precipitable water in winter is rather uniform over the whole domain in all simulations. In summer, the increase in precipitable water per kelvin is distinctly smaller in southern Europe—with values between 0% and 6% K−1—compared to northern parts of the continent. As a consequence, relative humidity markedly decreases by up to −4% K−1 in these regions (not shown). The strong contrast between land and ocean in the precipitable water trends in summer over southern Europe indicates that atmospheric water vapor is limited by the local availability of water.

Fig. 10.

Relative trends of the precipitable water in % K−1 temperature change for (left) winter and (right) summer.

Fig. 10.

Relative trends of the precipitable water in % K−1 temperature change for (left) winter and (right) summer.

The relation between the trends of cloud liquid water and temperature depends to a considerable extent on the driving GCM (Fig. 11). In winter, the ECHAM5/MPI-OM-driven RCMs show weak positive and negative changes around the Mediterranean, and give values from 4% to 10% K−1 over the landmasses farther north. Over the Atlantic Ocean, an increase of up to 18% K−1 is suggested. This is again related to the small absolute temperature increase of only about 1 K in this area over the whole time period. The RCA simulation driven by the high-sensitivity global model HadCM3Q16 shows values of more than 18% K−1 over a large band ranging from Iceland southeastward over northern and central Europe to the Black Sea. The trends in cloud liquid water in winter correspond closely to the changes in heavy precipitation (Fig. 12), although there is an offset between the two variables. While heavy precipitation changes by around 5% K−1 over land, the trends in cloud liquid water are considerably stronger.

Fig. 11.

As in Fig. 10, but for cloud liquid water.

Fig. 11.

As in Fig. 10, but for cloud liquid water.

Fig. 12.

As in Fig. 10, but for the 99.9% quantile of daily precipitation.

Fig. 12.

As in Fig. 10, but for the 99.9% quantile of daily precipitation.

In summer, cloud liquid water increases with temperature in northern Europe and decreases in southern Europe, again in qualitative agreement with the changes in heavy precipitation (Fig. 12). This feature is robust across all four simulations. Nevertheless, the magnitude of the trends differs between the RCMs. The HadRM3 simulation exhibits negative trends over the complete European landmass except Scandinavia, whereas the other simulations show a relatively clear line between positive trends in the north and negative trends in the south. Areas of positive and negative trends match well for cloud liquid water and heavy precipitation, only the amplitude of the pattern is more pronounced in the case of cloud liquid water.

To better quantify the relationships between the trends in precipitable water, cloud liquid water, and heavy precipitation per kelvin of warming, we investigate whether a threshold exists for precipitable water and cloud liquid water changes below which heavy precipitation decreases in the regional climate model simulations. Figure 13 shows conditional density diagrams for the summer season. Only land points are considered. The graphics show the probabilities of heavy precipitation trends being positive or negative, given a certain value of precipitable water or cloud liquid water. The black areas denote the conditional densities for negative trends, the gray areas for positive trends.

Fig. 13.

Conditional density of (left) precipitable water and (right) cloud liquid water on positive values (gray) and negative values (black) of changes in the 99.9% quantile of precipitation (P99.9) K−1 of warming for summer. Only land points are considered.

Fig. 13.

Conditional density of (left) precipitable water and (right) cloud liquid water on positive values (gray) and negative values (black) of changes in the 99.9% quantile of precipitation (P99.9) K−1 of warming for summer. Only land points are considered.

For changes in precipitable water, a threshold below which at least 80% of the changes in heavy precipitation are negative is found to be 5%–7% K−1, depending on the simulation. All four simulations show a gradual decrease in the probability of negative heavy precipitation trends occurring with increasing magnitudes of changes in precipitable water per kelvin temperature increase.

Negative changes in heavy precipitation are found to concur with negative changes in cloud liquid water. One can find a value from −5% to −2.5% K−1 for cloud liquid water change as the threshold below which 80% of the changes in heavy precipitation are negative. As for precipitable water changes, the driving global model has some influence on the shape of the conditional distribution. In the HadCM3-driven simulations, the density decreases more rapidly toward zero, whereas it changes more gradually for the ECHAM5/MPI-OM-driven simulations.

We exemplify the scaling behavior of trends in heavy precipitation with changes in precipitable water and cloud liquid water in more detail for two selected regions: Scandinavia (55°–70°N, 5°–30°E), possessing a rather wet and oceanic climate, and eastern Europe (44°–55°N, 16°–30°E), being characterized by dryer continental conditions. The regions are selected based on the definitions by Christensen and Christensen (2007) and again only land points are taken into account. Scatterplots of the changes of the 99.9% quantiles versus changes in precipitable water and cloud liquid water are shown in Fig. 14 for Scandinavia in winter, and in Fig. 15 for eastern Europe in summer. All trends are scaled by the respective change in near-surface temperature.

Fig. 14.

Scatterplots of the pointwise changes of heavy precipitation vs (left) precipitable water and (right) cloud liquid water over Scandinavia in winter. The regression is shown as solid gray line and the dashed lines show the intercept of the regression line with the x axis at the point of zero changes in heavy precipitation.

Fig. 14.

Scatterplots of the pointwise changes of heavy precipitation vs (left) precipitable water and (right) cloud liquid water over Scandinavia in winter. The regression is shown as solid gray line and the dashed lines show the intercept of the regression line with the x axis at the point of zero changes in heavy precipitation.

Fig. 15.

As in Fig. 14, but for eastern Europe in summer.

Fig. 15.

As in Fig. 14, but for eastern Europe in summer.

For the winter months in Scandinavia (Fig. 14, lhs), the changes in heavy precipitation show hardly any dependence on the changes in precipitable water, except for the RCA simulation driven by the high-sensitivity global model HadCM3Q16. In the other simulations, the change of precipitable water is rather uniform with a mean value of 7%–8.8% K−1. Distinctly stronger correlations from 0.53 to 0.81 are found between the changes in heavy precipitation and cloud liquid water (Fig. 14, rhs). The dashed lines in Fig. 14 point to the offsets between the changes of cloud liquid water and heavy precipitation. They essentially scatter around zero, indicating that in winter the qualitative behavior of trends in heavy precipitation is closely connected to changes in cloud liquid water.

In the summer months in eastern Europe (Fig. 15), correlations of changes in heavy precipitation with changes in precipitable water and cloud liquid water are similar and range between 0.46 in the RCA simulation driven by ECHAM5 and 0.84 in the RCA simulation driven by HadCM3Q16. This suggests that the regional water budget governs both precipitable water and cloud liquid water. An increase of about 7% K−1 in precipitable water is needed to maintain the level of heavy precipitation (dashed lines in Fig. 15, lhs). The decrease in relative humidity caused by moisture-availability limitations affects all variables. Cloud liquid water scales quite closely with heavy precipitation, although the slope of the regression line in Fig. 15 (rhs) proves to be clearly smaller than 1: changes of 5% K−1 in cloud liquid water correspond to trends of 1%–2% K−1 in heavy precipitation. Qualitatively similar behavior can be observed in other regions in southern Europe as well.

5. Discussion and conclusions

An extreme-value analysis of projected changes in heavy precipitation in an ensemble of eight high-resolution regional climate model simulations over the European domain is presented. In general, the different models agree well on the qualitative nature of the trends. The results show robust trends for heavy precipitation over many parts of Europe in a warming climate. In winter, the changes are positive over most of the European continent, with changes of up to 30% in high quantiles over northern Europe. A north–south gradient in the trends can be observed, and in the most southern parts of Europe they are close to zero or even negative. In summer, despite strong increases in near-surface temperatures, negative trends in heavy precipitation occur over a large area that extends from central to southern Europe. These negative trends can reach up to −30% in regions like Spain, southern France, southern Italy, or Greece. In northern Europe, changes in heavy precipitation are positive also in summer.

The changes in the extreme-value distributions mainly originate from shifts in the location parameter. For some parts of southern Europe in summer, negative trends in the location parameter contrast with positive changes in the scale parameter, suggesting a general decrease in heavy precipitation in conjunction with increased variability. However, these areas are not widespread, and negative trends in the location parameter generally are accompanied by negative trends in the scale parameter.

In other studies on Europe, similar results for changes in heavy precipitation were found with different RCM–GCM combinations (e.g., Durman et al. 2001; Frei et al. 2006). Because of the parameterization of processes at scales below the resolution of the RCMs, such as convection, radiation, land surface processes, and cloud microphysics, RCMs have limitations, which can lead to model uncertainties. The convective parameterization scheme can particularly be an issue for summer precipitation and on subdaily time scales (Lenderink and van Meijgaard 2008). Also, in summer the simulation of soil moisture can highly affect changes in temperature and precipitation via the alteration of changes in evapotranspiration (Seneviratne et al. 2010). In the present study, the RCM results for heavy precipitation changes are found to be to some extent influenced by the large-scale patterns of their driving GCMs. Despite the limitations, the robustness of the results found in this analysis from an ensemble of various RCMs with different driving GCMs and different parameterization schemes gives confidence in the pattern of heavy precipitation changes.

The changes in the 99.9% quantile of daily precipitation totals, precipitable water, and cloud liquid water are divided by temperature changes to test the Clausius–Clapeyron scaling for these variables. Precipitable water is expected to change with temperature by 7% K−1 following the Clausius–Clapeyron relation, assuming that relative humidity remains constant. Since heavy precipitation events are likely to occur when effectively all the moisture in a volume of air is precipitated out, this suggests a similar scaling of heavy precipitation with temperature.

In winter, the change in precipitable water is rather uniform in absolute terms. The scaled pattern mostly reflects the differences in temperature trends over the domain. Over the European continent, changes are close to the Clausius–Clapeyron relation (i.e., 7% K−1). Although qualitatively the situation is not very different for cloud liquid water, the spatial pattern of changes in cloud liquid water better correlates with changes in heavy precipitation per kelvin temperature increase. The scaling factor is about 2–4, that is, a change of 1% K−1 in heavy precipitation corresponds to a change of 2%–4% K−1 in cloud liquid water.

This suggests that overall in winter, the large-scale dynamics play a decisive role. Patterns of trends in moisture-related variables reflect changes in storm-track densities and storm intensities (Bengtsson et al. 2006). Thereby, changes in precipitable water do not relate to changes in cloud condensate and precipitation in an immediate and straightforward way. Alterations in dynamical processes that lead to the formation of clouds and rainfall are not governed by the amount of precipitable water alone. Other aspects like changes in meridional temperature gradients or static stability contribute to the mechanism.

The most robust sub-Clausius–Clapeyron behavior in precipitable water is found over the southern European landmasses in summer. This leads to decreases of relative humidity of about −4% K−1 in these regions. The distinct differences between changes over land and ocean indicate that moisture is limited by the local availability of water, which can evaporate from the soil or vegetation (Seneviratne et al. 2010). Humidity changes in the atmospheric boundary layer can affect cloud and precipitation formation (Hohenegger et al. 2009). Accordingly, cloud liquid water decreases over southern Europe in summer. Both cloud liquid water and precipitable water show a qualitatively similar scaling behavior with regard to heavy precipitation. Ultimately, the changes in the local hydrological cycle and the moist static stability in the region are also an expression of alterations in the large-scale circulation and indicate a poleward extension of the Hadley cell and increased subsidence over the Mediterranean area (Lu et al. 2007; Frierson et al. 2007; Mariotti et al. 2008).

In many regions of Europe, the results of this study question the role of precipitable water as a governing factor for changes in heavy precipitation. It is shown that the trends in heavy precipitation are smaller than that predicted by the Clausius–Clapeyron relation. Moreover, in the midlatitudes, processes of cloud and precipitation formation also depend on dynamical aspects such as local moisture convergence, changes in moist static stability, and baroclinic storm activity. A more complete picture of the physical mechanisms determining changes in heavy precipitation over Europe can only be gained by also considering these dynamical aspects.

Acknowledgments

The ENSEMBLES data used in this work were provided by the EU FP6 Integrated Project ENSEMBLES, whose support is gratefully acknowledged. The authors would like to kindly thank Bjorn Stevens, Cathy Hohenegger, and Daniela Jacob for helpful discussions and three anonymous reviewers for their valuable comments and suggestions that greatly helped to improve the article.

REFERENCES

REFERENCES
Allan
,
R. P.
, and
B. J.
Soden
,
2008
:
Atmospheric warming and the amplification of precipitation extremes
.
Science
,
321
,
1481
1484
.
Allen
,
M. R.
, and
W. J.
Ingram
,
2002
:
Constraints on future changes in climate and the hydrological cycle
.
Nature
,
419
,
224
232
.
Bengtsson
,
L.
,
K.
Hodges
, and
E.
Roeckner
,
2006
:
Storm tracks and climate change
.
J. Climate
,
19
,
3518
3543
.
Bengtsson
,
L.
,
K.
Hodges
, and
N.
Keenlyside
,
2009
:
Will extratropical storms intensify in a warmer climate?
J. Climate
,
22
,
2276
2301
.
Berg
,
P.
,
J. O.
Haerter
,
P.
Thejll
,
C.
Piani
,
S.
Hagemann
, and
J. H.
Christensen
,
2009
:
Seasonal characteristics of the relationship between daily precipitation intensity and surface temperature
.
J. Geophys. Res.
,
114
,
D18102
,
doi:10.1029/2009JD012008
.
Böhm
,
U.
,
M.
Kücken
,
W.
Ahrens
,
A.
Block
,
D.
Hauffe
,
K.
Keuler
,
B.
Rockel
, and
A.
Will
,
2006
:
CLM - The climate version of LM: Brief description and long-term applications. COSMO Newsletter, No. 6, 225–235
.
Boutle
,
I. A.
,
S. E.
Belcher
, and
R. S.
Plant
,
2010
:
Moisture transport in mid-latitude cyclones
.
Quart. J. Roy. Meteor. Soc.
,
136
,
1
15
.
Buishand
,
T. A.
,
1989
:
Statistics of extremes in climatology
.
Stat. Neerl.
,
43
,
1
30
,
doi:10.1111/j.1467-9574.1989.tb01244.x
.
Christensen
,
H.
,
E.
Kjellström
,
F.
Giorgi
,
G.
Lenderink
, and
M.
Rummukainen
,
2010
:
Weight assignment in regional climate models
.
Climate Res.
,
44
,
179
194
.
Christensen
,
J. H.
, and
O. B.
Christensen
,
2007
:
A summary of the prudence model projections of changes in European climate by the end of this century
.
Climatic Change
,
81
,
7
30
.
Coles
,
S.
,
2001
:
An Introduction to Statistical Modeling of Extreme Values. Springer, 208 pp
.
Coles
,
S.
, and
A.
Stephenson
, cited
2011
:
Ismev: An Introduction to Statistical Modeling of Extreme Values. R package version 1.36. [Available online at http://CRAN.R-project.org/package=ismev.]
Collins
,
M.
,
B. B. B.
Booth
,
G. R.
Harris
,
J. M.
Murphy
,
D. M. H.
Sexton
, and
M. J.
Webb
,
2006
:
Towards quantifying uncertainty in transient climate change
.
Climate Dyn.
,
27
,
127
147
.
Davison
,
A. C.
, and
R. L.
Smith
,
1990
:
Models for exceedances over high thresholds
.
J. Roy. Stat. Soc.,
B52
,
393
442
.
Del Genio
,
A. D.
,
M.-S.
Yao
, and
J.
Jonas
,
2007
:
Will moist convection be stronger in a warmer climate?
Geophys. Res. Lett.
,
34
,
L16703
,
doi:10.1029/2007GL030525
.
Durman
,
C. F.
,
J. M.
Gregory
,
D. C.
Hassell
,
R. G.
Jones
, and
J. M.
Murphy
,
2001
:
A comparison of extreme European daily precipitation simulated by a global and a regional climate model for present and future climates
.
Quart. J. Roy. Meteor. Soc.
,
127
,
1005
1015
,
doi:10.1002/qj.49712757316
.
Embrechts
,
P.
,
C.
Klüppelberg
, and
T.
Mikosch
,
1997
:
Modelling Extremal Events for Insurance and Finance. Springer, 645 pp
.
Emori
,
S.
, and
S. J.
Brown
,
2005
:
Dynamic and thermodynamic changes in mean and extreme precipitation under changed climate
.
Geophys. Res. Lett.
,
32
,
L17706
,
doi:10.1029/2005GL023272
.
Frei
,
C.
,
C.
Schär
,
D.
Lüthi
, and
H. C.
Davies
,
1998
:
Heavy precipitation processes in a warmer climate
.
Geophys. Res. Lett.
,
25
,
1431
1434
.
Frei
,
C.
,
J. H.
Christensen
,
M.
Déqué
,
D.
Jacob
,
R. G.
Jones
, and
P. L.
Vidale
,
2003
:
Daily precipitation statistics in regional climate models: Evaluation and intercomparison for the European Alps
.
J. Geophys. Res.
,
108
,
4124
,
doi:10.1029/2002JD002287
.
Frei
,
C.
,
R.
Schöll
,
S.
Fukutome
,
J.
Schmidli
, and
P. L.
Vidale
,
2006
:
Future change of precipitation extremes in Europe: Intercomparison of scenarios from regional climate models
.
J. Geophys. Res.
,
111
,
D06105
,
doi:10.1029/2005JD005965
.
Frierson
,
D. M. W.
,
2008
:
Midlatitude static stability in simple and comprehensive general circulation models
.
J. Atmos. Sci.
,
65
,
1049
1062
.
Frierson
,
D. M. W.
,
J.
Lu
, and
G.
Chen
,
2007
:
Width of the Hadley cell in simple and comprehensive general circulation models
.
Geophys. Res. Lett.
,
34
,
L18804
,
doi:10.1029/2007GL031115
.
Gerber
,
E. P.
, and
G. K.
Vallis
,
2009
:
On the zonal structure of the North Atlantic Oscillation and annular modes
.
J. Atmos. Sci.
,
66
,
332
352
.
Hanel
,
M.
, and
T. A.
Buishand
,
2010
:
On the value of hourly precipitation extremes in regional climate model simulations
.
J. Hydrol.
,
393
(
3–4
),
265
273
,
doi:10.1016/j.jhydrol.2010.08.024
.
Held
,
I. M.
, and
B. J.
Soden
,
2006
:
Robust responses of the hydrological cycle to global warming
.
J. Climate
,
19
,
5686
5699
.
Hohenegger
,
C.
,
A.
Walser
,
W.
Langhans
, and
C.
Schär
,
2008
:
Cloud-resolving ensemble simulations of the August 2005 Alpine flood
.
Quart. J. Roy. Meteor. Soc.
,
134
,
889
904
.
Hohenegger
,
C.
,
P.
Brockhaus
,
C. S.
Bretherton
, and
C.
Schär
,
2009
:
The soil moisture–precipitation feedback in simulations with explicit and parameterized convection
.
J. Climate
,
22
,
5003
5020
.
Jacob
,
D.
,
2001
:
A note to the simulation of the annual and inter-annual variability of the water budget over the Baltic Sea drainage basin
.
Meteor. Atmos. Phys.
,
77
,
61
73
.
Katz
,
R. W.
,
1999
:
Extreme value theory for precipitation: Sensitivity analysis for climate change
.
Adv. Water Res.
,
23
,
133
139
.
Katz
,
R. W.
,
M. B.
Parlange
, and
P.
Naveau
,
2002
:
Statistics of extremes in hydrology
.
Adv. Water Res.
,
25
,
1287
1304
.
Kjellström
,
E.
, and
Coauthors
,
2005
:
A 140-year simulation of European climate with the new version of the Rossby Centre regional atmospheric climate model (RCA3). SMHI Tech. Rep. 108, 54 pp
.
Kjellström
,
E.
,
F.
Boberg
,
M.
Castro
,
H.
Christensen
,
G.
Nikulin
, and
E.
Sánchez
,
2010
:
Daily and monthly temperature and precipitation statistics as performance indicators for regional climate models
.
Climate Res.
,
44
,
135
150
.
Korty
,
R. L.
, and
T.
Schneider
,
2007
:
A climatology of the tropospheric thermal stratification using saturation potential vorticity
.
J. Climate
,
20
,
5977
5991
.
Lenderink
,
G.
,
2010
:
Exploring metrics of extreme daily precipitation in a large ensemble of regional climate model simulations
.
Climate Res.
,
44
,
151
166
.
Lenderink
,
G.
, and
E.
van Meijgaard
,
2008
:
Increase in hourly precipitation extremes beyond expectations from temperature changes
.
Nat. Geosci.
,
1
,
511
514
.
Lenderink
,
G.
,
B.
van den Hurk
,
E.
van Meijgaard
,
A.
van Ulden
, and
J.
Cuijpers
,
2003
:
Simulation of present-day climate in RACMO2: First results and model developments. KNMI Tech. Rep. 252, 24 pp
.
Lionello
,
P.
,
U.
Boldrin
, and
F.
Giorgi
,
2008
:
Future changes in cyclone climatology over Europe as inferred from a regional climate model simulation
.
Climate Dyn.
,
30
,
657
671
.
Lorenz
,
P.
, and
D.
Jacob
,
2010
:
Validation of temperature trends in the ENSEMBLES regional climate model runs driven by ERA40
.
Climate Res.
,
44
,
167
177
.
Lu
,
J.
,
G. A.
Vecchi
, and
T.
Reichler
,
2007
:
Expansion of the Hadley cell under global warming
.
Geophys. Res. Lett.
,
34
,
L06805
,
doi:10.1029/2006GL028443
.
Mariotti
,
A.
,
N.
Zeng
,
J.-H.
Yoon
,
V.
Artale
,
A.
Navarra
,
P.
Alpert
, and
L. Z. X.
Li
,
2008
:
Mediterranean water cycle changes: Transition to drier 21st century conditions in observations and CMIP3 simulations
.
Environ. Res. Lett.
,
3
,
044001
,
doi:10.1088/1748-9326/3/4/044001
.
Muller
,
C. J.
,
P.
O’Gorman
, and
L. E.
Back
,
2011
:
Intensification of precipitation extremes with warming in a cloud-resolving model
.
J. Climate
,
24
,
2784
2800
.
Nakicenovic
,
N.
, and
R.
Swart
, Eds.,
2000
:
Special Report on Emissions Scenarios. Cambridge University Press, 599 pp
.
Naveau
,
P.
,
M.
Nogaj
,
C.
Ammann
,
P.
Yiou
,
D.
Cooley
, and
V.
Jomelli
,
2005
:
Statistical methods for the analysis of climate extremes
.
C. R. Geosci.
,
337
,
1013
1022
,
doi:10.1016/j.crte.2005.04.015
.
O’Gorman
,
P. A.
, and
T.
Schneider
,
2009
:
The physical basis for increases in precipitation extremes in simulations of 21st-century climate change
.
Proc. Natl. Acad. Sci. USA
,
106
,
14 773
14 777
.
O’Gorman
,
P. A.
, and
C. J.
Muller
,
2010
:
How closely do changes in surface and column water vapor follow Clausius–Clapeyron scaling in climate change simulations?
Environ. Res. Lett.
,
5
,
025207
,
doi:10.1088/1748-9326/5/2/025207
.
Pall
,
P.
,
M. R.
Allen
, and
D. A.
Stone
,
2007
:
Testing the Clausius-Clapeyron constraint on changes in extreme precipitation under CO2 warming
.
Climate Dyn.
,
28
,
351
363
.
R Development Core Team
, cited
2011
:
The R Project for Statistical Computing. [Available online at http://www.r-project.org/.]
Ribatet
,
M.
, cited
2011
:
POT: Generalized Pareto distribution and peaks over threshold. R package version 1.1-1. [Available online at http://CRAN.R-project.org/package=POT.]
Sanchez-Gomez
,
E.
,
S.
Somot
, and
M.
Déqué
,
2009
:
Ability of an ensemble of regional climate models to reproduce weather regimes over Europe-Atlantic during the period 1961-2000
.
Climate Dyn.
,
33
,
723
736
.
Schär
,
C.
,
D.
Lüthi
,
U.
Beyerle
, and
E.
Heise
,
1999
:
The soil–precipitation feedback: A process study with a regional climate model
.
J. Climate
,
12
,
722
741
.
Semmler
,
T.
, and
D.
Jacob
,
2004
:
Modeling extreme precipitation events - A climate change simulation for Europe
.
Global Planet. Change
,
44
,
119
127
.
Seneviratne
,
S. I.
,
T.
Corti
,
E. L.
Davin
,
M.
Hirschi
,
E. B.
Jaeger
,
I.
Lehner
,
B.
Orlowsky
, and
A. J.
Teuling
,
2010
:
Investigating soil moisture–climate interactions in a changing climate: A review
.
Earth-Sci. Rev.
,
99
(
3–4
),
125
161
,
doi:10.1016/j.earscirev.2010.02.004
.
Sherwood
,
S. C.
,
W.
Ingram
,
Y.
Tsushima
,
M.
Satoh
,
M.
Roberts
,
P. L.
Vidale
, and
P. A.
O’Gorman
,
2010
:
Relative humidity changes in a warmer climate
.
J. Geophys. Res.
,
115
,
D09104
,
doi:10.1029/2009JD012585
.
Smith
,
R. L.
,
2003
:
Statistics of extremes, with applications in environment, insurance and finance. Extreme Values in Finance, Telecommunications and the Environment, B. Finkenstadt and H. Rootzen, Eds., Chapman and Hall/CRC Press, 1–78
.
Soden
,
B. J.
,
D. L.
Jackson
,
V.
Ramaswamy
,
M. D.
Schwarzkopf
, and
X.
Huang
,
2005
:
The radiative signature of upper tropospheric moistening
.
Science
,
310
,
841
844
.
Tomassini
,
L.
, and
D.
Jacob
,
2009
:
Spatial analysis of trends in extreme precipitation events in high-resolution climate model results and observations for Germany
.
J. Geophys. Res.
,
114
,
D12113
,
doi:10.1029/2008JD010652
.
Trenberth
,
K.
,
2011
:
Changes in precipitation with climate change
.
Climate Res.
,
47
,
123
138
.
Ulbrich
,
U.
,
J. G.
Pinto
,
H.
Kupfer
,
C.
Leckebusch
,
T.
Spangehl
, and
M.
Reyers
,
2008
:
Changing Northern Hemisphere storm tracks in an ensemble of IPCC climate change simulations
.
J. Climate
,
21
,
1669
1679
.