The deterministic description of the subgrid-scale land–atmosphere interaction in regional climate model (RCM) simulations is changed by using stochastic soil and vegetation parameterizations. For this, the land–atmosphere interaction parameterized in a land surface model (LSM) is perturbed stochastically by adding a random value to the input parameters using a random number generator. In this way, a stochastic ensemble is created that represents the impact of the uncertainties in these subgrid-scale processes on the resolved scale circulation. In a first step, stochastic stand-alone simulations with the VEG3D LSM are performed to identify sensitive model parameters. Afterward, VEG3D is coupled to the Consortium for Small-Scale Modeling–Climate Limited-Area Modeling (COSMO-CLM) RCM and stochastically perturbed simulations driven by ERA-Interim (2001–10) are performed for the Coordinated Downscaling Experiment–European Domain (EURO-CORDEX) at a horizontal resolution of 0.22°. The simulation results reveal that the impact of stochastically varied soil and vegetation parameterizations on the simulated climate conditions differs regionally. In central Europe the impact on the mean temperature and precipitation characteristics is very weak. In southern Europe and North Africa, however, the resolved scale circulation is very sensitive to the local soil water conditions. Furthermore, it is demonstrated that the use of stochastic soil and vegetation parameterizations considerably improves the variability of monthly rainfall sums all over Europe by improving the representation of the land–atmosphere interaction in the stochastic ensemble on a daily basis. In particular, inland rainfall during summer is simulated much better.
In regional climate models (RCMs) dynamical processes in the atmosphere are described by partial differential equations that are discretized on a numerical grid. However, physical processes evolving on small spatial and temporal scales, such as the land–atmosphere interaction or convection, are not resolved on that grid scale. For this reason, physical parameterizations are used to calculate these subgrid-scale processes and to supply them as quantities that can be used in the partial differential equations.
Based on the resolved scale circulation, such parameterizations simulate deterministically subgrid-scale processes and their feedback effects on the resolved scale circulation. Apart from the deterministic solution of these parameterization schemes, however, a variety of additional subgrid states are possible, which are consistent with the resolved scale input (Palmer 2001) but not captured in the RCMs. Thus, the large variability of the subgrid-scale processes and their feedback effects on the regional climate conditions are not represented well by RCM simulations.
In this context, one of the most important subgrid-scale components influencing the climate conditions on the regional scale is the land–atmosphere interaction. The properties of soil and vegetation affect the regional climate by controlling exchange and partitioning of turbulent heat and water vapor fluxes between the surface and the atmosphere and determining the radiation budget at the surface [e.g., summarized in Seneviratne et al. (2010) and McPherson (2007)]. A realistic description of the land–atmosphere interaction in an RCM is essential to properly simulate regional climate conditions.
Within an RCM these interactions are parameterized in a land surface model (LSM). An example of such a parameterization in an LSM is the unsaturated flow of water through the soil, which is described by the Richards equation. According to this equation, the soil water content depends on the hydraulic conductivity and the soil matric potential. These quantities depend on the soil type and must be parameterized. Another example is the exchange of turbulent heat fluxes between the surface and the atmosphere, based on the assumption of a logarithmic wind profile within the Prandtl layer, which is described by the Monin–Obukhov similarity theory (e.g., Stull 2012). In this context, the wind profile depends on the roughness length and the displacement height, which have to be specified for different land-use types.
In most cases, such parameter values are derived from point data or laboratory measurements. Hence, they are not valid everywhere and only partly reflect natural conditions. Furthermore, small-scale characteristics of soil and vegetation in an RCM are averaged over a grid cell, as a result of which important features of the land surface due to spatial variability sometimes are not represented in these mean parameter values. This means that parameterizations of subgrid-scale soil and vegetation processes always cause a certain degree of uncertainty (Mölders 2005).
In the literature, many methods are described to account for subgrid-scale uncertainties. Especially in numerical weather prediction, much work was done to handle this problem, an example being the use of multimodel (Hagedorn et al. 2005) or multiphysics ensembles (Stensrud et al. 2000). In a multimodel ensemble, the model uncertainties of an RCM as a whole are considered by performing simulations with different RCMs. In a multiphysics ensemble, different parameterizations for the same physical process are applied in simulations with one RCM to account for the parameterization error. The problem of these approaches, however, lies in the fact that it is very difficult to determine whether the ensemble spread is based on a systematic bias of the single ensemble members or whether it really reflects natural variability.
Another possibility to deal with subgrid-scale uncertainties in RCM simulations is to use stochastic parameterizations (Berner et al. 2011; Bowler et al. 2008; Doblas-Reyes et al. 2009; Palmer et al. 2009; Plant and Craig 2008; Stainforth et al. 2005). In this case, the subgrid-scale processes and, consequently, their feedback effects on the regional climate conditions are stochastically perturbed by introducing a random term in the parameterizations, such that the parameter values are varied within a sensible range. This is done using a random number generator (Buizza et al. 1999). In this way, a stochastic ensemble representing the impact of the uncertainties in the subgrid-scale processes on the simulated resolved scale circulation is created. Because of the random variation of the deterministic parameterizations in this approach, the stochastic ensemble is expected to capture the large variability of the subgrid-scale processes, which might improve the simulation of their feedbacks on the regional climate conditions (Berner et al. 2011). For this reason, such an approach is applied for the land–atmosphere coupling in the present study.
The aim of this paper is to investigate the influence of stochastic subgrid-scale soil and vegetation parameterizations on the simulated regional climate conditions. In a first step, stochastically perturbed stand-alone simulations with the VEG3D LSM (Braun and Schädler 2005) are performed to identify sensitive model parameters. In a second step, VEG3D is coupled to the Consortium for Small-Scale Modeling–Climate Limited-Area Modeling (COSMO-CLM; also referred to as CCLM) RCM (Rockel et al. 2008). For coupling VEG3D to CCLM, the Ocean Atmosphere Sea Ice Soil, version 3, Model Coupling Toolkit (OASIS3-MCT) software is used (Valcke et al. 2015). With this coupled model system, an ensemble of stochastically perturbed simulations is created and analyzed. These simulations represent the impact of the subgrid-scale soil and vegetation processes on the regional climate. Finally, this stochastic ensemble’s capability of improving the simulation of regional climate conditions in Europe is studied.
a. Models used
In this study, CCLM (with COSMO, version 5.0, and CLM, version 7), the climate version of the three-dimensional nonhydrostatic weather forecast model COSMO (Doms et al. 2011; Baldauf et al. 2011) of the German Weather Service (DWD), is used to perform coupled climate simulations. In CCLM the hydro-thermodynamical equations describing compressible motions in a moist atmosphere are solved numerically. For this, the equations are discretized on an Arakawa-C grid (Arakawa and Lamb 1977) based on rotated geographical coordinates. In the vertical direction a terrain-following height coordinate is used. For numerical integration, a Runge–Kutta scheme is applied using the time splitting method by Wicker and Skamarock (2002). The resulting prognostic variables are the temperature, pressure perturbation, the horizontal and vertical wind components, and the specific humidity, as well as the cloud water/ice content and the specific water content of rain and snow.
To describe subgrid-scale processes in the CCLM, the following physical parameterizations are utilized: the radiative transfer scheme by Ritter and Geleyn (1992), the Tiedtke parameterization of convection (Tiedtke 1989), and the turbulence scheme of Raschendorfer (2001) using a level 2.5 closure for turbulent kinetic energy (TKE) as prognostic variable (Mellor and Yamada 1982). A reduced version of a one-moment cloud microphysics scheme by Seifert and Beheng (2001) is also implemented. All physical parameterizations used in CCLM as well as the dynamics and numerics are described in detail in Doms et al. (2011).
Within an RCM, the soil–vegetation–atmosphere interactions are parameterized in an LSM. The LSM calculates the reaction of the soil and vegetation to the atmospheric input (wind, temperature, pressure, incoming shortwave and longwave radiation, and precipitation). Transport of heat and water from the surface to the deep soil and vice versa is solved numerically. Based on the resulting soil conditions, the turbulent heat fluxes between the surface and the atmosphere are calculated, thus providing a lower boundary condition to the RCM.
For this study, VEG3D is used as LSM and replaces the multilayer (ML) version of the DWD soil model TERRA (TERRA-ML; Schrodin and Heise 2002), the standard LSM implemented in CCLM. VEG3D is a multilayer LSM developed by Schädler (1990) based on a model designed by Deardorff (1978). Further developments were performed at Karlsruhe Institute of Technology (KIT) by Lenz (1996), Grabe (2002), Braun (2005), and Meissner (2008). The performance of VEG3D was evaluated in several studies, for example, by Braun and Schädler (2005) and Kohler et al. (2012).
VEG3D solves the heat conduction equation for temperature and the Richards equation for soil water by using finite-difference methods. Ten nonequidistant soil layers are used, the bottom being located at a depth of 15.0 m. Heat conductivity depends on the presence of water and is parameterized after Johansen (1977) for different soil types. The hydraulic conductivity of an unsaturated soil is parameterized using an approach of Van Genuchten (1980). The top boundary conditions for VEG3D are calculated by the atmospheric part of CCLM. As lower boundary conditions, a gravitational flow for soil water and a climatic value for temperature are applied.
If vegetation is present, the radiation and turbulent heat fluxes between the soil surface and the atmosphere are obtained via a massless vegetation layer implemented in VEG3D. This layer has its own canopy temperature and specific humidity derived iteratively from the canopy’s energy balance. Based on these quantities, vertical turbulent mixing is parameterized using the Monin–Obukhov similarity theory (Stull 2012) as a function of the gradients between the surface, the canopy, and the lowest atmospheric level.
VEG3D is coupled to CCLM via the OASIS3-MCT coupling software developed by the Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS) in Toulouse, France (Valcke et al. 2015). In the climate modeling community, the OASIS coupler is software that is widely used to couple different parts of the climate system, such as atmosphere, ocean, soil, and vegetation, in one model system (Valcke 2013). Thus, the major task of the coupler is the exchange and, if necessary, the interpolation of coupling fields between CCLM and VEG3D.
This study uses Ocean Atmosphere Sea Ice Soil, version 3, Model Coupling Toolkit. This model version is a combination of the OASIS3 coupler and the MCT developed by the Argonne National Laboratory, United States (Larson et al. 2005). OASIS3-MCT works as a library linked to both models. Communication between all model components is accomplished via the Message Passing Interface (MPI) library. The exchange of the coupling fields between CCLM and VEG3D is managed within the unified OASIS interface in CCLM (Will et al. 2017).
b. Experimental setup
In this study, VEG3D simulations are performed using stochastic soil and vegetation parameterizations. The first step consists of stand-alone simulations with the LSM, where all relevant soil and vegetation parameters are randomly varied to identify sensitive model parameters (section 3). This means that only the input parameters loaded from lookup tables into the LSM are stochastically perturbed. Subsequently, VEG3D is coupled to CCLM via OASIS3-MCT and a stochastic ensemble is created by perturbing these sensitive VEG3D parameters in coupled simulations to investigate the impact of the subgrid-scale land–atmosphere interaction on regional climate simulations. The model domain used for the coupled CCLM–VEG3D simulations comprises the entire European continent, the Mediterranean Sea, North Africa, and the eastern part of the North Atlantic (Fig. 1) and is identical to the Coordinated Downscaling Experiment–European Domain (EURO-CORDEX; Jacob et al. 2014). The horizontal grid spacing is 0.22° and the model domain comprises 232 × 226 grid points. In the vertical direction the atmosphere is discretized in 40 levels. A time step of 150 s is used. All simulations were performed for the decade 2001–10 driven by ERA-Interim (Dee et al. 2011) at the lateral boundaries and at the lower boundary over sea. To be able to initialize all simulations with balanced soil conditions, soil moisture and temperature values were used as initial conditions, which were produced by a transient VEG3D stand-alone run (1955–2010) driven by the European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis of the twentieth century (ERA-20C; Poli et al. 2013). To evaluate the simulation results, field means of several regions according to the Prediction of Regional Scenarios and Uncertainties for Defining European Climate Change Risks and Effects (PRUDENCE) project (Christensen and Christensen 2007) were analyzed (Iberian Peninsula, central Europe). The influence of subgrid-scale land–atmosphere interaction on the mean characteristics of temperature and precipitation in Europe is investigated by comparing the ensemble results with a reference run using the original lookup table parameters (section 4). In section 5, the ability of this stochastic ensemble to improve the simulation of regional rainfall conditions in Europe is studied by comparing its results with E-OBS (Haylock et al. 2008).
c. Creating stochastic parameterizations
In stochastic parameterizations, specific model parameters are randomly varied to create a stochastic ensemble that represents their impact on the regional climate conditions. To be able to build up the stochastic ensemble in a meaningful way, sensitive model parameters need to be identified in a first step. For this, a sensitivity analysis is performed, where all parameter values related to soil and vegetation processes in VEG3D are varied systematically at the beginning of a simulation. Note that only the input parameters contained in lookup tables are stochastically perturbed. The parameterization itself, including its mathematical formulation, is not changed.
In general, a parameter is an average value derived from several point observations or laboratory measurements to represent the mean physical characteristics of the soil and vegetation types under consideration. But because of the large variability of physical properties within single soil and vegetation types (Gutmann and Small 2007), the spread around the mean values can be very large. A parameter value consequently contains a certain degree of uncertainty, which is represented by its standard deviation (Mölders 2005). These uncertainties can be taken into account by stochastically perturbing the input parameter values depending on their standard deviations. In the case of the relevant soil parameters, uniformly distributed random numbers are produced using a random number generator. Afterward, these numbers are transformed to normally distributed numbers, which provide a consistent range for stochastic perturbation of the mean parameter values. Information about the standard deviations of these soil parameters is obtained from Cosby et al. (1984). The uncertainties of vegetation parameters are only given in maximum and minimum values (Dorman and Sellers 1989; Garratt 1993; Henderson-Sellers 1993), which approximate the range for perturbation. As information about the standard deviations of vegetation parameters is lacking, the input parameters are varied by using uniformly distributed random numbers. To prevent inconsistencies in the description of vegetation in the LSM, identical random numbers are used for the leaf area index and the fractional plant cover of a grid box. These parameters are derived from Global Land Cover 2000 (GLC2000; Bartholomé and Belward 2005).
During a simulation, some of these stochastically perturbed variables may change because they contain time-dependent arguments. The plant cover values are kept within the range of 0.05–0.975, while the leaf area index is not allowed to drop below 0.5 (Table 1). Moreover, several soil variables, such as the hydraulic soil conductivity or the matric potential, are not constant. These quantities depend on the amount of soil water and vary within a simulation. To describe these variations, the input parameters are defined in the lookup table for saturated soil conditions and are further processed within the LSM to the actual values for the hydraulic soil conductivity and the matric potential.
Of all soil and vegetation parameters in VEG3D, the albedo has a special position. Within the LSM, a vegetation albedo is defined for each land-use type as a soil albedo depending on soil type and soil water content. However, CCLM does not distinguish between these two albedo types, which is why a weighted average of the albedos is passed on to CCLM. Both the vegetation and the soil albedo parameters in the lookup table are perturbed using different random numbers.
This sensitivity study was made by performing 1D stand-alone simulations with VEG3D for the Falkenberg test site (Neisser et al. 2002) for the year 2008. The Falkenberg observation site is an open grassland site located southeast of Berlin that is managed by the DWD’s Lindenberg Observatory. Regular measurements of soil temperature, soil water content, and turbulent heat fluxes are provided by the DWD and can be used for the validation of the model runs. Another advantage of this 1D stand-alone simulation is the short run time for a 1-yr run, allowing for a fast identification of all sensitive VEG3D model parameters. Subsequently, the identified sensitive VEG3D parameters were varied in coupled CCLM–VEG3D simulations to investigate the impact of the uncertainties in soil and vegetation parameterizations on regional climate simulation results.
3. Identification of sensitive parameters
Within the framework of the sensitivity studies, only one parameter value from the lookup table was changed in each simulation at the beginning of the stand-alone run using the random number generator. For each randomly varied model parameter, 10 simulations were performed.
Figure 2 shows the deviations of these simulations from a reference run in which no parameter values were changed, with the water content at a depth of 54 cm (Fig. 2a), the soil temperature at the same depth (Fig. 2b), as well as latent (Fig. 2c) and sensible (Fig. 2d) heat fluxes at the surface. In each box plot, the deviations of all 10 stochastic simulations of one perturbed parameter to the reference run are summarized. The simulation results for hydraulic soil conductivity (hydc), matric potential (pot), heat capacity (cap), albedo (alb), leaf area index (lai), fractional plant cover of a grid box (pcov), stomatal resistance (sto), and displacement height (disp) are shown.
The turbulent heat fluxes as well as the temperature are sensitive to vegetation-related parameters, such as displacement height, stomatal resistance, plant cover, and leaf area index (Figs. 2b–d). Also, the albedo, which consists of the vegetation albedo and the soil albedo, affects these quantities considerably. Varying the soil parameters, hydraulic conductivity, matric potential, and heat capacity has little impact on the temperature or surface fluxes. However, the former two parameters strongly affect the soil water content (Fig. 2a). According to these results, the set of sensitive parameters chosen for the stochastic parameterizations comprises the leaf area index, plant cover, stomatal conductance, displacement height, soil/vegetation albedo, and hydraulic soil conductivity. The range in which these parameters are varied is summarized in Table 1 for the two land-use classes of grassland and deciduous forest.
Our stochastic ensemble built up of this parameter set comprises 60 simulations (10 stochastic simulations for each of the six chosen parameters). For stand-alone simulations and their short run times, such an ensemble size does not cause any problems. But in coupled CCLM–VEG3D simulations, computational costs would be prohibitive. For this reason, we tried to reduce the ensemble size in a second study. For this, all six sensitive VEG3D parameters were perturbed at the same time. As in the first study, random numbers were generated separately for each parameter and then applied to the input table. In Fig. 3, 10 (mul1) and 20 (mul2) of these multiperturbed simulations are summarized and compared to the single-perturbed runs, consisting of 10 stochastic simulations for each of the six sensitive parameters. It is found that already 10 multiperturbed simulations create a larger ensemble spread than the 6 × 10 single-perturbed simulations for the soil water content, soil temperature, and turbulent heat fluxes. The 20 multiperturbed simulations only slightly increase the ensemble spread compared to the 10 multiperturbed runs for the turbulent heat fluxes. For the water content, the spread is shifted, but not increased. For the temperature, no wider spread can be observed. Considering these small effects on the ensemble spread, doubling of the computing times is not justified. Hence, a multiperturbation approach comprising 10 ensemble members was applied in the following coupled stochastic simulations. Thus, the computational costs are kept within reasonable limits.
4. Coupled CCLM–VEG3D runs
In a first step, a coupled CCLM–VEG3D simulation with no varied parameter values was performed to create a reference run for validation. Then, 10 stochastic simulations were made using the multiperturbation approach for all six sensitive VEG3D parameters. At the beginning of each simulation, all sensitive parameters were perturbed by perturbing input variables using random numbers specific of each parameter and each grid point. Thus, a stochastic ensemble was created, representing the impact of the uncertainties in the subgrid-scale soil and vegetation parameterizations in VEG3D on the simulated resolved scale circulation. In this section the influence of these soil and vegetation parameterizations on the mean regional characteristics of temperature and precipitation is investigated by comparing the mean monthly values of the stochastic ensemble with the results of the reference run. Figure 4 shows the mean monthly 2-m temperatures and the mean monthly precipitation sums over the decade 2001–10 for the Iberian Peninsula (Fig. 4, left) and central Europe (Fig. 4, right). The reference run is drawn in red, the stochastic ensemble spread in light blue, and the E-OBS in black.
Only a small ensemble spread for the mean monthly precipitation sums can be observed in both domains. For the mean monthly 2-m temperatures, the stochastic ensemble spread is almost negligible. In central Europe, for example, no differences in the simulated mean 2-m temperatures between the 10 stochastic simulations and the reference are evident. In all simulations, CCLM slightly underestimates the observed 2-m temperatures over the whole year. Consequently, the influence of stochastic parameterizations in VEG3D on the mean CCLM simulation results is very small. Hence, random changes in subgrid-scale soil and vegetation processes do not change the mean regional characteristics of temperature and precipitation over central Europe.
Despite the small ensemble spread, a systematic deviation in the mean 2-m temperatures and the mean precipitation sums between the stochastic simulations and the reference run can be observed for the Iberian Peninsula during summer. In the stochastic ensemble, the mean 2-m temperatures in summer are systematically lower than in the reference run, enhancing the observed cold bias in CCLM all over the year. At the same time, summer rainfall in all 10 stochastic simulations is increased compared to the unperturbed CCLM–VEG3D run, thus improving the agreement with the observations. The lower 2-m temperatures in summer in the stochastic ensemble are not restricted to the Iberian Peninsula. They can also be observed all over southern Europe and especially in North Africa, as is illustrated (Fig. 5a) and explained in Fig. 5.
In Fig. 5 the differences between the stochastic VEG3D ensemble and the CCLM–VEG3D reference run for several climate quantities over the whole model domain are presented for July. The lower 2-m temperatures in the southern regions in all stochastic ensemble members are caused by higher latent heat fluxes in the same areas compared to the reference run (Fig. 5b). Because of the reduced near-surface temperatures and the increased evapotranspiration rates, cooler and moister air develops in the runs of the stochastic ensemble over North Africa (Fig. 5c). Subsequently, this cooler and moister air mass is transported by the anticyclonal boundary layer flow from over North Africa to southern Europe, represented by the wind field in 850 hPa in Fig. 5c. As a result, the amount of rainfall over the Iberian Peninsula is increased in all members of the stochastic ensemble compared to the reference run and agreement with observations is better (Fig. 5f).
This systematic deviation between the stochastically perturbed runs and the unperturbed simulation can be explained by differences in the availability of water for evapotranspiration. During summer, the latent heat fluxes in southern Europe and especially in North Africa are limited by the availability of soil water for evapotranspiration. Figure 5e shows the mean latent heat fluxes over the period 2001–10 for the Iberian Peninsula. The reference run again is drawn in red, the stochastic ensemble in light blue. With increasing solar radiation during summer, the latent heat fluxes continuously increase in the reference run as well as in the stochastic ensemble simulations. But starting in June, the latent heat fluxes suddenly decrease in the reference run, while the fluxes in the stochastic simulations remain on a higher level. As enough energy is available for evapotranspiration during this time, a lack of soil water in the reference run is supposed to cause the observed decrease of latent heat, whereas soil water still can be evapotranspired in the stochastic ensemble. This surplus of soil water in North Africa and the Iberian Peninsula in the stochastic ensemble runs is illustrated in Fig. 5d.
Between the unperturbed simulation and the stochastically perturbed runs, all boundary conditions (lateral and SST forcing) are the same. These systematic differences in simulated temperature and precipitation are thus assumed to be caused by differences in the land–atmosphere coupling, which are produced by the random parameter perturbation itself. In the stochastic CCLM–VEG3D simulations, one of the perturbed parameter values in the lookup table is the hydraulic conductivity of a saturated soil (section 3). Because of the random parameter variation, the effective hydraulic conductivity calculated in the LSM is increased in 50% of the grid cells and decreased in the other 50%. An increase of the effective hydraulic conductivity means an increase of soil water available for evapotranspiration in regions with limited soil water due to an increased upward transport of water from deeper soil layers in 50% of the grid cells. In the other 50%, by contrast, lower values for the hydraulic conductivity do not affect the evapotranspiration rates in such areas, because water availability already is the limiting factor in these grid cells. That is why the evapotranspiration rates in these dry areas are increased in stochastic simulations. This nonlinear behavior of hydraulic conductivity produces asymmetric evapotranspiration rates, resulting in moister soils near the surface in arid areas. This effect is shown in Fig. 5d. All over North Africa and the southern parts of Spain, higher soil water contents at a depth of 1 m can be observed during July in the stochastic ensemble simulations. The resulting systematic increase of latent heat fluxes in these areas during summer (Fig. 5e) then causes the differences in the summer precipitation described above. Over the rest of Europe, where soil water is not the limiting factor, only noise in the differences of soil water content can be detected. The differences in latent heat fluxes and in the summer precipitation sums are negligible. To check this mechanism, an additional stochastic CCLM–VEG3D simulation with unperturbed hydraulic conductivity values was performed. In this run, no significant differences to the reference run were observed in terms of mean summer rainfall on the Iberian Peninsula (Fig. 5f).
This unexpected behavior of the stochastic ensemble shows how sensitive the mean precipitation characteristics in southern Europe are to the local soil water content. Consequently, changes in the soil water regime, especially in North Africa, can considerably affect rainfall amounts on the Iberian Peninsula in summer.
5. Ensemble performance
In this section, we study the question of whether the stochastic ensemble has the potential to improve the simulation of the rainfall characteristics in Europe. In other words, we want to find out whether stochastic soil and vegetation parameterizations have an added value compared to unperturbed simulations or not.
For this, the stochastic ensemble mean for all monthly precipitation sums between 2001 and 2010 is compared to all monthly precipitation sums of the reference run. In this case, all monthly sums over the period are validated, not only the mean conditions as in section 4. To quantify the added value, a skill score is used. It is defined as the ratio of the mean-square error (MSE) of the stochastic ensemble mean and the mean-square error of the reference run compared to E-OBS:
The reddish colors in Fig. 6 show the areas where the stochastic ensemble mean has an added value compared to the reference run for the monthly precipitation sums in summer (Fig. 6a) and in winter (Fig. 6b) between 2001 and 2010. The blue colors indicate the regions where the stochastic ensemble mean has no added value or even less skill.
In both seasons all over Europe, the reddish colors dominate and a considerable added value of the stochastic ensemble mean for the monthly precipitation sums is evident. The added value of the ensemble mean can be explained by a better representation of single rainfall events on a daily basis within the stochastic ensemble. As described in section 3, soil and vegetation parameters are randomly varied in the stochastic VEG3D parameterizations. As a consequence, deviating land surface conditions are calculated in each ensemble member. Hence, the stochastic ensemble includes possible land surface states that are different from the deterministic solution of the reference run. As found in several studies, the prevailing land surface conditions are an important trigger for the development of precipitation events, especially convective rainfall (Pal and Eltahir 2001; Pielke et al. 1991, 1997; Schär et al. 1999). Consequently, rainfall in the stochastic ensemble can develop at various places or move on different tracks across the model domain. For this reason, more grid cells are affected by rain within the ensemble mean than in the reference run. Between 2001 and 2010, the number of grid cells in which rain is detected within one day (event) is increased by about 14.2% for the ensemble mean. As a result, the hit rate for correctly simulated events is also increased and the number of missed events is decreased (Table 2). This increases the correlation of the simulated rainfall events in the stochastic ensemble mean to the observed events in contrast to the reference run (Fig. 7). Thus, the random factor in the formation of rain, especially in the development of convection, is better captured in the stochastic ensemble mean than in the reference run.
However, both the ensemble mean and the reference run overestimate the total number of grid cells with rainfall events (Table 2), and hence also the precipitation sums in these cells. But in contrast to the reference run, this precipitation bias is reduced within the ensemble mean. By averaging the precipitation sums of each ensemble member, the rainfall amounts occurring during false alarms are reduced, which is why the mean-square error relative to the observations is reduced to 17.27 mm compared to 22.06 mm of the reference run. In combination with the higher correlation coefficients, the lower MSE values of the stochastic ensemble mean for the daily precipitation sums causes the increased skill score values on a monthly base, as is illustrated in Fig. 6.
This effect is particularly dominant in the summer season (Fig. 6a). During this time, a marked added value of the stochastic ensemble mean can be observed all over Europe. The only exceptions are the southern parts of the Iberian Peninsula and North Africa. In these regions no added value exists, although the area-averaged precipitation sums are improved (Fig. 4). In winter the added value is not as evident as in summer, but still exists (Fig. 6b). The higher skill score values in summer compared to winter can be explained by the stronger influence of the land–atmosphere interaction on the rainfall development, especially for convective events, in contrast to the large-scale circulation.
Additionally, the added value in the coastal regions of Scandinavia, the British Isles, and the Iberian Peninsula is not as pronounced as in the inner parts of the continent. This is not surprising, since the lower boundary conditions over the sea remain the same in all simulations performed. While climate conditions in coastal areas depend on the unmodified ocean state, continental climate is strongly influenced by the stochastically perturbed interactions between soil, vegetation, and atmosphere. For this reason, the improved description of subgrid-scale land–atmosphere interaction in the stochastic ensemble affects the development of rainfall within the continent more strongly than near the sea and thus systematically improves the continental simulation results.
6. Discussion and conclusions
In this study, stochastic soil and vegetation parameterizations were implemented in the coupled CCLM–VEG3D model system to improve the description of subgrid-scale land–atmosphere interaction in regional climate simulations. Sensitive VEG3D model parameters identified using stand-alone simulations were stochastically perturbed for each soil column in CCLM–VEG3D simulations for Europe, thus creating a stochastic ensemble that represents the impact of these unresolved interactions on the resolved scale circulation. The ability of this stochastic ensemble to improve simulation of the regional climate was investigated by comparing the ensemble mean with an unperturbed simulation.
Analysis revealed that the impact of stochastically varied soil and vegetation parameters on the mean temperature and precipitation characteristics in central Europe is very weak. For both near-surface temperatures as well as precipitation sums, only a small ensemble spread is created. For the Iberian Peninsula, however, a systematic deviation between all stochastic ensemble members and the reference run was observed. Because of an increase of the hydraulic conductivity in 50% of the grid boxes by stochastic modeling, the amount of soil water available for evapotranspiration is systematically increased during summer. This results in enhanced latent heat fluxes in the stochastic simulations. Near-surface temperatures drop in North Africa and southern Spain. Consequently, a cooler and moister air mass evolves and is transported by the anticyclonal boundary layer flow from North Africa to the Iberian Peninsula, which increases the precipitation sums in summer. In southern Europe and North Africa, the resolved scale circulation consequently is very sensitive to the local soil water conditions.
In the stochastic ensemble, the area-averaged 2-m temperatures are worse than in the reference run, while the area-averaged precipitation sums are improved. This improvement of one atmospheric variable and deterioration of another one can often be observed in regional climate simulations and are mentioned in several publications (e.g., Hackenbruch et al. 2016). In such a case, the RCM is not entirely able to adequately reproduce physical processes in the atmosphere and their interactions for a certain a region. Changing or improving one process does not necessarily improve all the other processes involved. This is also reflected by the lack of added value of the stochastic ensemble for the spatial distribution of rainfall on the Iberian Peninsula.
Because of the lack of observational datasets, soil moisture is a quantity that is very difficult to determine, especially for deep soils. Consequently, soil initialization in climate models is always subjected to considerable uncertainties (Khodayar et al. 2015). To minimize the associated error, a spinup is performed to initialize the RCMs with equilibrium soil conditions. But these equilibrium states are model dependent, as a result of which each LSM produces its own soil water conditions, which affect the mean regional climate in different ways. Hence, an adequate simulation of the summer climate conditions is a challenging task in sensitive regions, such as the Iberian Peninsula. One way to solve this problem is to perform ensemble simulations using different LSMs and different initial soil conditions to account for all these uncertainties (Stensrud et al. 2000). Such an approach is strongly recommended for this region.
Furthermore, it was demonstrated that the simulation of monthly rainfall over Europe could be improved considerably by using stochastic soil and vegetation parameterizations in RCM simulations. Although the mean precipitation characteristics are not changed, higher skill score values for the monthly precipitation sums are reached for the stochastic ensemble mean. By adding a random factor to these subgrid-scale processes, representation of the land–atmosphere interaction is improved on a daily basis in the stochastic ensemble. Simulation results improved in particular during summer in the more continental parts of Europe, because of the strong coupling of the local land–atmosphere interaction to the regional development of convective rainfall.
In regional climate modeling, very high-resolution simulations are usually performed to better resolve subgrid-scale processes, but these simulations are computationally very expensive and can presently be realized for small domain sizes only (Prein et al. 2015). Still, the results of this study revealed that stochastic parameterizations in mesoscale RCM simulations already improve the description of the small-scale land–atmosphere interaction. This means that simulation results can be improved for a much larger domain in a way similar to very high-resolution simulations. Stochastic parameterization thus represents one possibility to avoid such time-consuming and computer-resource-consuming high-resolution simulations.
We acknowledge funding by the Federal Ministry of Education and Research in Germany (BMBF) under the MiKlip II research program (FKZ: 01LP1518A).