“Fast physics” (called every advection time step): The land surface scheme TERRA provides vertical profiles of prognostic soil temperature, water, and ice for up to nine surface tiles (up to three different land use tiles, three snow tiles, and three water tiles). Recent developments include a new resistance-based formulation of bare soil evaporation and a new technique for computing the surface temperature, the so-called skin temperature . Both developments improve the prediction of the 2 m temperature, for instance, and other surface variables . The effects of urban structures at the land surface are described by the urban model TERRA_URB , which was ported from the COSMO model to ICON in the framework of the COSMO Consortium's Priority Project CITTÀ . The freshwater lake model FLake and a sea ice scheme derived from FLake provide prognostic surface temperatures over lakes and sea ice, respectively. The turbulent transfer and diffusion schemes of ICON are based on the Mellor-Yamada level-2 scheme, using a prognostic equation for turbulent kinetic energy . The turbulent transfer, i.e., the computation of transfer coefficients and with that of surface turbulent heat fluxes, is done on every surface tile. The grid-scale precipitation scheme accounts for precipitation formation over the ice phase, using the hydrometeor categories of cloud water, cloud ice, rainwater, and snow .

“Slow physics” (called at lower frequency): The shortwave and longwave radiation are computed with “ecRad”, the radiation scheme of the European Centre for Medium-Range Weather Forecasts (ECMWF), as introduced by . Its implementation in ICON is described by . The Tiedtke-Bechtold scheme for shallow and deep convection was adopted from ECMWF's Integrated Forecasting System (IFS) model. The grid-scale effects by the sub-grid scale orography (SSO) are described by IFS's SSO scheme , and grid-scale effects by the non-orographic gravity-wave drag are based on . Cloud cover is represented by a diagnostic scheme using a quadratic distribution function of total water (sum of water vapour and cloud water) for liquid clouds, and an analogous equation for ice clouds, also taking convective anvils into account.

The distribution of the incoming short-wave radiation between the components of the surface energy budget can be tuned by specifying scaling parameters. The sensitivities of the modelled climate with respect to the most important of these parameters have been tested during parameter optimisation in this study, however, near surface temperature biases remained and therefore, additional tuning parameters were introduced: the soil-moisture dependent tuning of the surface albedo and a factor on the minimum stomata resistance attributed to each land-use type given by external data (GLOBCOVER). These new parameters are part of the official ICON release now.

The portion of incoming solar energy absorbed at the surface depends on the surface albedo. Therefore, the albedo strongly influences the heating of the soil. In ICON-CLM, we prescribe monthly MODIS surface albedo at the land surface. This encompasses the vegetation type and the bare soil albedo. A new parameter tune_albedo_wso (with its values abbreviated to taw) was introduced, correcting the albedo for very dry soils with taw1 and very wet ones with taw2 for the soil types sand, sandy loam, loam, and loamy clay (soil types 3–6 in TERRA). The idea behind this tuning is that wetter soils are darker and, thus, less reflective. The albedo α is corrected by αc, dependent on soil moisture in the top soil layer wsotop, whose thickness Δzsotop is set to 10 mm in the parameterisation. The albedo for the near-infrared (nir), visible (vis), and ultraviolet (uv) wavelength bands αi,0 is corrected as follows: 1αi(wsotop)=max⁡[αi,0⋅(1+αvis,c(wsotop)/αvis,0),αi,min⁡] with i∈{nir, vis, uv}, αni,min⁡=0.08, αvis,min=0.05, αuv,min⁡ = 0.02, αi,0: uncorrected albedo.

The limit values αi,min⁡ used in the ICON model remained unchanged. The albedo correction of the visible band αvis,c is introduced for dry (taw1) and wet (taw2) soils with a smooth transition between the soil moisture wso,dtop (dry limit) and wso,wtop (wet limit) in the following way: αvis,c(wsotop)=taw1ifwsotop≤wso,dtoptaw2ifwsotop≥wso,wtoptaw2+(taw1-taw2)sin⁡2[π(wsotop+3wso,wtop-4wso,dtop)2(wso,wtop-wso,dtop)]otherwise We use the soil moisture limit values wso,dtop=0.001m=∧0.1⋅Δzsotop and wso,wtop=0.002m=∧0.2⋅Δzsotop.

Using αvis,c(wsotop), the corrected albedos αvis, αnir, and αuv are determined via Eq. (). The correction is done only for the vegetation-free part of each tile. At the end of the albedo routine, the values are aggregated over all tiles.

The most important tuning parameters for further fine-tuning the surface energy budget by affecting the turbulent heat fluxes are the resistances to the fluxes in the laminar boundary layer: rlam_heat, cr_bsmin, rat_lam, rat_sea, rsmin_fac. In addition to the parameters already available in the model, the parameter rsmin_fac has been introduced in order to have the opportunity of tuning the latent and sensible fluxes independently over water and over land. Table  gives an overview of the impacts of the resistance parameters on the heat fluxes and surface types.

The main resistance parameter that scales both fluxes over land and water surfaces is rlam_heat. The parameter rat_sea is scaling the resistance of the fluxes over water. Here, the latent heat flux is equal to potential evaporation. The resistances and their scaling factors for vegetation, the land-use class-dependent evaporation/stomata resistance for plants are tunable by adjusting rsmin_fac. cr_bsmin is the tunable minimal bare soil resistance for evaporation. rat_lam influences the latent heat flux over land only.

All namelist parameters used are listed with a short description in Table .

The ICON model includes three parameterisations that contribute to the simulated cloud cover. These encompass grid-scale cloud cover, subgrid-scale cloud cover from convection parametrisation, and subgrid-scale cloud cover from stratus or stratocumulus shallow clouds. The grid-scale cloud cover occurs when the grid-box relative humidity (rh) reaches 100 %. In this case, the cloud cover is automatically set to one, and the microphysics parameterisation is initiated, potentially producing precipitation. When rh is below 100 %, the grid-scale cloud cover remains zero. When the grid box rh is below 100 % but the stratification is unstable, the convection parameterisation is activated, and the cloud cover is estimated from the cloud water detained into the anvil . This cloud cover aims to describe shallow or penetrative cumulus, which may produce light to medium precipitation. The third cloud cover parameterisation is the subgrid-scale cloud cover of stratus or stratocumulus shallow clouds . When the grid-box mean rh is slightly below 100 % and subgrid-scale turbulent fluctuations are large enough, the grid box may contain small clouds (with rh of 100 %) and cloud-free areas with rh below 100 %. The turbulent fluctuations are parametrised using a top-hat total water distribution with a fixed half-width, which is around 5 % of the total water, which means that the water content varies uniformly within a narrow range around the mean value. This leads to a quadratic dependence of the subgrid-scale cloud cover on the total water.

The subgrid-scale cloud cover parametrisation due to turbulence is regarded as most uncertain, and therefore several parameters of the scheme are introduced as tuning parameters in ICON. The parameter tune_box_liq determines the half-width of the top-hat total water distribution. The parameter tune_box_liq_asy is a scaling factor that determines the asymmetry term of the cloud cover for over- and undersaturation. The quadratic increase of cloud cover from 0 to 1 ranges between rhi and rhf, where 2rhi=100⋅(1-2⋅tune_box_liq⋅tune_box_liq_asy),rhf=100⋅(1+2⋅tune_box_liq).

In practice, since rh is not allowed to exceed 100 %, the cloud cover is cut off and does not reach 1 at rh=100%. With higher tune_box_liq or tune_box_liq_asy, the quadratic increase of cloud cover starts at lower rhi, resulting in higher cloud cover. However, the increase of tune_box_liq_asy leads to the increase of cloud cover for the entire range between rhi and rh=100%, while the increase of tune_box_liq does not change the value of the cloud cover at rh=100%. Therefore, a higher sensitivity is expected to tune_box_liq_asy in comparison to tune_box_liq. Practically, the increase of cloud cover at lower rh is reflected in larger areas covered by partial cloudiness.

Finally, the scaling parameter allow_overcast determines the steepness of the parabolic function. Its decrease increases the steepness, preserving rhi. As a result, a lower allow_overcast results in a higher cloud cover, especially at rh close to 100 %. This increase is reflected in the appearance of local spots with full overcast.

We used the ICON namelist parameter allow_overcast with a newly introduced monthly dependency. This change was inspired by the identification of monthly variations in model errors through a detailed analysis of test simulations. Technically, we simulated in monthly chunks and passed the appropriate monthly value to the namelist. It is defined for the month m as the mean value ao with added user-defined deviations from the mean aoac, scaled with a tunable amplitude aoa: 3allow_overcast[m]=ao+aoa⋅aoac[m].

Since this parameterisation does not include precipitation production, the described parameters affect the simulated radiation transfer through the clouds only. Therefore, their tuning is useful for correcting global radiation biases related to uncertainties in subgrid-scale cloud cover.

The ICON-CLM model domain for this study is the EURO-CORDEX region. The horizontal grid resolution is R13B5 in ICON terminology, which equals a mesh size of 12.14 km (Fig. S1 in the Supplement). Vertically, a hybrid height-based terrain-following coordinate Smooth LEvel VErtical (SLEVE) coordinate; is used with 60 layers up to a model top of 23.5 km. We use a model time step for advection of 100 s. In this study, ICON-CLM is driven by 3-hourly ERA5 reanalysis data . In previous tests , it became obvious that an upper-boundary nudging towards the ERA5 data was beneficial for the European model domain due to the very large extension of the domain: The centre points of the western and the eastern boundaries are more than 7000 km apart. During the transition between summer and winter, high and low-pressure systems develop and travel across Europe at a high frequency. The nudging communicates these developments to the regional model and avoids strong boundary effects. It is applied above a height of 10.5 km to the horizontal wind components and additionally to the density and the virtual potential temperature using pressure, temperature, and specific humidity of ERA5. The nudging coefficient is maximum (i.e., =1) at the uppermost level and decreases to <0.5 in the third model layer from the top (full level height of 18.87 km), <0.25 in the fifth (at 16.34 km height), and <0.1 in the ninth (14.06 km).

At the ocean surface, ICON-CLM is using interpolated sea surface temperatures and sea ice fraction from ERA5. All boundary data are updated every three hours.

The ICON model provides different functionalities for the temporal aggregation of output variables and for vertical interpolation. We use the aggregation typical for climate variables and the interpolation to pressure levels and levels of constant height above mean sea level. ICON-CLM is running in a scripting framework or workflow engine, the so-called Starter Package for ICON-CLM Experiments SPICE,. The workflow consists of a parallel pre-processing of the lateral boundary conditions, the ICON-CLM simulation itself, post-processing, and archiving. The post-processing includes the interpolation of model output from the R13B5 ICON grid to the rotated EUR-12 grid and the generation of time series, the interpolation to constant heights above ground, and the calculation of typical climate variables like potential evapotranspiration, which are not directly diagnosed within ICON.

The reference simulation is the experiment C2I101 reference configuration for experiments listed in Table . It is using the general setup as described in Sect.  and the physical parameterisations as described in Sect. , apart from the urban parametrisation TERRA_URB. As external parameters, GLOBE orography data , FAO soil types , land-use data from GLOBCOVER2009 , monthly varying Tegen aerosols , and MODIS surface albedo for different wavelength bands were used. Spectral solar irradiance and ozone data Global and regional Earth-system Monitoring using Satellite and in-situ data project (GEMS) climatology merged with data by the project “Monitoring Atmospheric Composition and Climate” (MACC), were prescribed as in the default NWP setup for global applications. These settings constitute the reference configuration (Fig. , stage 1g) for all experiments conducted in the definition phase of a new reference, where we mainly tested the external datasets, existing alternative parametrisations, and a group of parameters. Table  provides an overview of the tested parameters along with their descriptions, while Table  details the specific modifications applied in each experiment, identified by IDs ranging from C2I101 to C2I130. Here, all simulations were conducted for the period 1979–1984, with the period 1980–1984 used for model evaluation and shown in the figures with seasonal means. The initial year served as a spin-up period to allow the system to reach a quasi-equilibrium state (Table ). An alternative initialisation with soil moisture from a longer spin-up experiment is available among the sensitivity experiments.

The new reference was defined as (C2I200/C2I200c) according to the tuning strategy (Fig. , stage 2g), using new settings as for example, transient aerosols (cf. Sect.  and Table  for more details). For the tuning process, a second time period, 2002–2008, was used (experiment IDs C2I2**c). The period from 2003 to 2008 was used for the evaluation and tuning, and the figures refer to the seasonal means obtained from this period. This second period was added to increase the number of available observational data, as sufficient satellite data are not available in earlier times. Optimised LiMMo configurations were tested in experiments C2I291c and C2I294c (cf. tuning strategy step 4f). The ICON namelist parameters and the simulation acronyms are written in the manuscript with font typewriter.

Since the tuning initiative took place at the same time as the development of the ICON source code, the model version was changed several times during the process (see Table ).

The settings for the transient forcing of aerosol and ozone and the time-dependent insolation were gradually adopted from the ICON setup for coupled global climate projections, ICON-XPP, ; see experiments C2I105, C2I118, C2I119 (Table ) for a description of the respective ICON settings. The implementations were adopted from a predecessor of ICON-XPP, called ICON-ESM , which are in turn very similar to those in the atmospheric part of the general circulation model by the Max-Planck-Institute, ECHAM-6 . The main development had to be invested into the treatment of the input parameters provided by these climatologies, which required adaptations in the radiation interface for ecRad. For the aerosols, the input of the transient “Max Planck Aerosol Climatology Version 2” (MACv2) of is implemented, with the option to use the simple plume scheme MACv2-SP of . Only the simple plume scheme includes the option to account for different aerosol concentrations in dependence on the respective climate scenario. As the optimised setup described in this article will also be used to downscale GCM simulations for different scenarios, the simple plume scheme must be used. Additionally, a transient climatology for volcanic aerosols can be read. For ozone, the CMIP6 dataset was made available. Moreover, an option to switch on time-dependent spectral solar irradiance as recommended for CMIP6 is available.

Due to the switch from the Tegen aerosol climatology to the transient MACv2-SP climatology, the aerosol-microphysics coupling as used in NWP is not applicable anymore. Therefore, the use of an external MODIS climatology of cloud droplet number concentration (CDNC) was implemented for ICON-XPP, which is tested in C2I241 (see Table ). The current implementation uses a non-transient, but monthly varying climatology of and was adjusted with a satellite-based CDNC retrieval by and as used in ECMWF's IFS model. To account for the scenario-dependence of aerosols and, with that, of CDNCs, we implemented a scaling factor that can be derived from the implementation of the simple plume scheme . This implementation is not tested for the periods considered here, but will be used for the production of RCM scenarios.

The meta-model framework has two distinctive features: first, a linear regression emulator, and second, gradient-based optimisation of meta-model parameters to minimise the error norm between the emulator and the observations.

Unlike previous studies, which mainly utilised quadratic regression , the LiMMo concept has successfully proven that linear approximation possesses decent approximation quality for multi-year monthly mean values, requiring only a linear number of simulations (for N parameters, the number of simulations required for training is O(N)). Contrary to this, the quadratic regression requires O(N2) simulations, because one has to conduct one new simulation with every two parameters disturbed simultaneously to approximate the interaction terms. This imposes a significant limitation on the number of parameters available for tuning.

The linear regression REG(p) defined in the following equation is a function of the model parameters p and approximates ICON-CLM variables. The regression yields monthly mean values, which correspond to the climatological monthly means (average December, January, etc.): 4REGi,j,k,n(p)=MODrefi,j,k,n+∑m(pm-pmref)⋅Ki,j,k,nm.

Here, REGi,j,k,n is the 2D regression result ((i,j) are spatial indices, k is the number of the climatological month, and n is the index of the model variable), MODrefi,j,k,n is the model output for the reference simulation, pm and pmref are the test parameter and reference parameter values for the parameter with index m (corresponding to MODref), and Ki,j,k,nm is the tendency tensor of the parameter pm. The tendency tensor is assembled explicitly as the linear combination of simulations (see Table , column “signal”), divided by the parameter increment (see Table , columns “test value” and “ref value”). Note that the regression in Eq. () is constructed to be exact for the reference parameter values.

To start the experiments with the meta-model, we select the error norm function ERR(p), which sets the distance between meta-model (Eq. ) and observational data. We give the details of the error norm function in the following section (Sect. ). Mathematically, the aim of the meta-model tuning is to find the vector of model parameters p that would minimise the ERR(p).

For the linear regression approximation with a spatial RMSE-based error norm, the target minimisation function ERR(p) is a smooth, convex, scaled Euclidean norm function of the model parameters. This function is known to have only one global minimum. Consequently, the initial parameter values have no impact on the outcome, and the optimisation process always converges to the global minimum. However, this minimum may be on the boundary of the constrained region for certain parameters. This, however, should not be the case for physically consistent parameters and physically meaningful parameter ranges of parameter values admitted. Section  will show that this was not the case for the parameters optimised in this study.

In previous studies devoted to objective calibration e.g.,, Monte Carlo sampling was utilised for this purpose. The general problem of this approach is the exponentially growing complexity with the dimensionality of the parameter space N, which in practice limits N. In previous studies, N was limited to 7–8 parameters.

In the LiMMo framework, the Monte Carlo method is applied to binary parameters (logical and integer value parameters). The number of these parameters can be significantly higher due to the very fast solution of the linear model. Thus, more sophisticated methods are not necessary to solve this type of problem within a few hours.

For real number parameters, the LiMMo framework suggests the implementation of gradient-based optimisation. This method searches for the next value of the parameter vector pn→pn+1 in the direction opposite to the gradient of the error norm in the parameter space ∂ERR(p)/∂p, until the increment of the error norm function becomes less than a given threshold ERR(pn+1)-ERR(pn)<ε. As proposed by , the limited-memory Broyden-Fletcher-Goldfarb-Shanno method with box constraints fits really well to the purpose and the convex nature of the problem. This method requires an initial guess and the minimum and maximum parameter values pmmin and pmmax to set up the box constraints. The search process is restricted to the defined hyper-rectangle, which ensures that the final result is physically meaningful. The complexity of gradient descent increases linearly with the dimensionality of the parameter space. In practice, an optimisation with 15–20 parameters is in the order of a few minutes only.

We successfully built a regression meta-model with over 15 parameters and ran multiple optimisation loops (see Sect. ). As a result, we obtained several parameter sets derived from LiMMo as final contenders for the new, optimised ICON-CLM configuration.

In the LiMMo framework, the error norm (single number) between the model output and observational data is calculated using the Root Mean Square Error (RMSE). The observational data are first interpolated onto the model's output grid. Then, multi-year monthly averages were computed for both the model output and the observational time series.

To compute the error norm, we consider the horizontal model outputs MODi,j,k,n for the variables vn. The indices i and j represent the spatial coordinates on the horizontal grid, while k indicates the month. The observational data OBSi,j,k,n are stored in the same multi-year monthly mean manner on the model grid.

The spatially aggregated Root Mean Square Error, RMSEk,n, for each month and variable is given by 5RMSEk,n=1Nx⋅Ny∑i,jMODi,j,k,n-OBSi,j,k,n2, where Nx⋅Ny denotes the number of grid points on the horizontal plane of the simulation domain, excluding the boundary relaxation zones. For each variable and month, the intrinsic variability σk,n is defined as the RMSE between some reference and its disturbance simulation. In our case, the disturbance is achieved by shifting the initial conditions back by one month: 6σk,n=1Nx⋅Ny∑i,jMODrefi,j,k,n-MODdisi,j,k,n2. The error ERRn for each variable is calculated as the time-averaged RMSE normalised by the intrinsic variability, defining the dimensionless signal-to-noise type measure of model prediction quality with respect to observations: 7ERRn=1Nt∑kRMSEk,nσk,n, where Nt=12 represents the number of months. Finally, the total error norm, ERR, is defined as the weighted sum of the errors for each variable, which determines the aggregated quality of the model simulation for all the prognostic variables that have been considered: 8ERR=∑ncn⋅ERRn,∑ncn=1. The weights cn are chosen by the user to reflect the relative importance of each variable, directly controlled by the optimisation aim (Fig. (1d); see Sect. ). The aim of LiMMo tuning is to minimise this error norm (Eq. ) with respect to the model parameters.

For the significance tests and Score Points of evidence (ScoPi) we followed the approach introduced by . The ScoPi is calculated point-by-point, considering the 3-daily means or sums, respectively, of the given variables (Table ). Given that the ERA5 data, used as boundary conditions for the conducted experiments, are “realistic” reanalysis data, we assume that the model can adequately capture the variability of a given variable at synoptic time scales within a single grid cell. This enables, on the one hand, having a time series long enough for testing the robustness of the employed metrics using Monte-Carlo approaches. On the other hand, it allows for making the variables more Gaussian through averaging: this then allows for the application of estimators such as the RMSE, which are better suited for normally distributed data . For CERES cloud cover, monthly mean values are considered instead of 3-daily means, representing the original temporal resolution of the CERES data set. When applying the LiMMo, monthly mean values of the variables are used.

The ScoPi score is described in detail by . It is dependent on the shares of grid points in a model sub-region, presenting a significant improvement or worsening in a metric for a variable with respect to the reference run. If the share of grid points in a model region with a strong (not only moderate) significance Fss is larger than 0.5, the score is enlarged by 0.5 as given in Eq. , Fms denotes the shares with moderate significance. 10ScoPi=Fss+0.5⋅sign(Fss)if Fss>0.5Fmsotherwise The great advantage of the ScoPi score is its inherent standardisation for different types of variables. The values always range between -1.5 and 1.5. Therefore, the ScoPi score can be aggregated over different types of variables and metrics. The inspection of these values allows us to gain a comprehensive understanding of the reasons for possible improvement/worsening in the model performance for a given configuration. The ScoPi score is computed for each PRUDENCE region (see Fig. S1), for different metrics m, seasons s, and various atmospheric variables v. If the share of significant grid points in a sub-region is too small (lower than 0.4), the ScoPi score is not accounted for when aggregated. In this case, it is assumed that there is no noticeable large-scale change in the model results with respect to the reference. The aggregation with respect to a specific PRUDENCE region is done by calculating the sum over the ScoPi values for all seasons, metrics, and variables (Eq. ). For integrating over several variables, different weights cv are considered per variable, as given in Table . The resulting value is referred to as ScoPi_region. 11ScoPiregion(r)=∑v,m,scvScoPiv,m,s(r)1|ScoPiv,m,s(r)|>0.4, where 1|ScoPiv,m,s(r)|>0.4 is the indicator function giving 1 for ScoPis larger/smaller than 0.4/-0.4 and 0 elsewhere.

The threshold of 0.4 ensures that the majority of the locations in a specific region and for a specific model configuration show a significant improvement/worsening compared to the reference experiment. For instance, if at least 40 % of the grid points show significantly improved performance for simulation B with respect to reference A, the ScoPi score is 0.4, although 60 % of the grid points show no significant changes. The same is true if 60 % of the grid points show significant improvement and 20 % significant worsening.

ScoPi_simulation is defined as a weighted sum across all PRUDENCE regions, incorporating additional regional weighting factors (Eq. ). Each PRUDENCE region is assigned a specific weight, based either on its area or its distance from mid-Europe (domain A4 in Fig. S1). The corresponding weights are listed in Table . 12ScoPisimulation=∑rcr⋅ScoPiregion(r), To calculate a ScoPi_simulation, it is a prerequisite that each contributing region is analysed with the same set of metrics and variables. Therefore, it is not possible to summarise regions' results for different variables, i.e., temperatures for land points of PRUDENCE regions and latent heat fluxes of sea points.

The ScoPi is calculated in a first place considering the mean BIAS against observations for all of the given variables. Then, it is also applied to the other metrics mentioned above. When applying the error metric “linear correlation”, we used the method proposed by and described in as a significance test for the differences between two simulations. Tests with several metrics done by revealed that the ranking between the tested simulations remains stable in relation to the reference: the higher the ScoPi score, the better the overall performance of the tested simulation.

To quantitatively compare the impact of different parameter changes on model results and to help in the selection of parameters, which are worth considering for further tuning, we introduce the sensitivity measure SENSn,mseas for variable vn on the change of parameter pm for a specific season (seas). Each sensitivity experiment simulates the change of only one parameter from the reference value pmref by an increment of Δpm. The definition of the sensitivity measure is comparable to the definition of the error norm with respect to observations (Eq. ): 13SENSn,mseas=1Nseas⋅∑k∈seas1σk,n⋅1Nx⋅Ny⋅∑i,jMODi,j,k,npm=pmref+Δpm-MODi,j,k,npm=pmref2, where Nseas is the number of months in a specific season, σk,n is the intrinsic variability of variable vn for the month number k (Eq. ), Nx,Ny are the number of grid points along the domain axes, MODi,j,k,n is the ICON-CLM model output temporally averaged to monthly mean values for several years (i,j – spatial indices, k is the index of month, n is the index of model variable).

In addition, we applied a grid point mask to the model quantities before calculating the sensitivities, using only the grid points with available observations (E-OBS for all variables except hfls_o, and HOAPS for hfls_o). This shows the sensitivity only for the relevant part of the model domain.

Within a physically meaningful range of parameters, the sensitivity can be treated as a signal-to-noise ratio. The signal is the RMS difference between the model outputs for the reference configuration and the configuration with the parameter disturbed. The noise is the intrinsic variability of the model. Therefore, statistically significant changes yield a sensitivity value greater than 1. We consider the model to be “sensitive” to a parameter change for SENSseas values above 2.

External parameters are static or monthly varying fields prescribed “externally” to the model and describe the physical properties of the environment. We replaced data sets of lower quality and/or resolution with those of higher quality and/or resolution. In the following, we discuss the impact of the parameter modification on model results. Where the simulation quality is discussed, we use E-OBS data as an observational reference. The sensitivities of the model to changes of the external parameters in winter and summer (see average values in Fig. ) are large for soil type (“Avg” sens: DJF = 2.6, JJA = 2.6) and orography data (“Avg” sens: DJF = 2.0, JJA = 1.4), and minor for natural and anthropogenic aerosol (“Avg” sens: DJF = 1.2, JJA = 1.8), and aerosol-cloud-feedback (“Avg” sens: DJF = 0.8, JJA = 1.1). The summer tasmin is thereby the most sensitive variable. A configuration with the higher-quality external parameters is used later on as a new reference, C2I250c, for the parameter tuning.

For the soil type distribution sensitivity experiment, we replaced the default FAO soil dataset by the Harmonised World Soil Data Base version 2.0 HWSD v2.0; , see Fig. a and b. The HWSD v2.0 data have a much smaller typical length scale (4 to 7 km) in comparison with FAO (10 to 50 km) and show a higher frequency of sandy loam than loam soil types (Fig.  c).

Figure  shows the impact of the systematic shift to more “sandy loam” soils on tas, hfss, and hfls in summer. Additionally, Fig. S2 gives the surface air pressure and the relation of sensible to latent heat flux (Bowen ratio). The shift increases the daily maximum temperature tasmax in central to eastern Europe and tasmin over the southern Iberian Peninsula and in northern Africa by up to 1 K. The change in tasmin is highly correlated with the Bowen ratio, in particular in regions with low hfls. The change in tasmax is strongly correlated with the absolute sensible heat flux hfss, in particular in central to eastern Europe and the Hungarian basin. Here we find a small change in the Bowen ratio since the latent heat flux is relatively high in these regions. Approximately, we find a change of temperature with forcing dT/dF≃0.1 Km2W-1.

A similar effect we found in Morocco and Algeria for soil types change from loam to loamy clay in the north. Consistently herewith, in areas of the Mediterranean region, where loamy clay is changed to loam (Adriatic coast, Po valley, Greece, and Turkey), we found the opposite in summer: an increase of hfls and a decrease of Bowen ratio. Interestingly, the same effect is found in regions of a change from loamy clay to clay (Sicily). In these regions, the loamy clay holds more plant-available water than clay and loam during the summer. While clay has a high total water holding capacity, a significant portion of that water is held very tightly and is hardly available for plant transpiration. The loamy soils are already dry in summer since the water evaporated and/or drained in previous months.

A similar phenomenon can be found for the shift from sand or loam to sandy loam in the region of northern Germany, Denmark, and Poland. Here, “sandy loam” exhibits the highest hfls.

Using the updated model orography data set is accompanied by applying a set of revised tuning parameters for the sub-grid scale orography scheme (see settings of C2I206 in Table ). Figure a shows the z0 of the GLOBE dataset based orography, while Fig. b indicates a strong increase in z0 over Sweden and north-eastern Russia when using orography data based on the Multi-Error-Removed Improved Terrain Digital elevation model (MERIT). The main effect is a reduction of sfcWind (10 m wind speed) (Fig. ) by 0.5 to 1.0 ms-1 on average due to a combined effect of subgrid-scale orography scheme and the direct effect of increased surface roughness, this means a reduction of the model bias compared to E-OBS (Fig. ). The changes of subgrid slopes by using MERIT orography do not affect the sfcWind.

The reduction in sfcWind over Africa can be attributed to the adjustment of the tuning parameter values of the gravity wave and subgrid-scale orography scheme (see C2I206 and C2I200 in Table ). As there is a lack of observational data in this area, it remains unclear whether this change represents an improvement or not.

For CMIP6-CORDEX, it is recommended even mandatory for EURO-CORDEX, to use transient anthropogenic aerosols. Thus, as the reference experiment was set up with the standard Tegen aerosols used for NWP, which are constant in time (with a mean annual cycle), the impact of the transient aerosols prescribed by the MACv2-SP climatology was tested. The Tegen climatology is representative for the early to mid-90s, which is a period when anthropogenic emissions over Europe are already reduced compared to the 80s, for which the experiments were conducted. Thus, the transient MACv2-SP climatology contains realistically higher Aerosol optical depth (AOD) values for the 80s.

The sensitivity of the climatology for AOD and related meteorological quantities is largest in summer (Fig. ). The respective sensitivity for winter is shown in Fig. S4. In summer, the differences in AOD (Fig. a) are strongly correlated with rsds differences (Fig. b). There is nearly no impact on clt (Fig. f). AOD is increased and shortwave radiation is reduced over Europe by approximately 10 Wm-2. Consistently, a cooling of tasmax by 0.5 K is found in Europe.

In northern Africa and the eastern Mediterranean, the AOD signal is highly correlated with rsds but neither with tasmin nor with tasmax (Fig. c and d). The latter are highly correlated with the downwelling longwave radiation rlds increase of 10 to 20 Wm-2 (Fig. e). Increased rlds can partly be explained by increased cloud cover at night. However, the cloud cover difference is small and cannot be detected below 500 hPa, so the effect on thermal radiation is minor. clearly shows a warming due to direct radiative effects of the MACv2 aerosol over northern Africa and Arabia. The explanation is that the “mineral dust aerosol particles in those regions are relatively large, elevated (off the ground) and absorbing”. With that, mineral dust can “contribute to a significant greenhouse effect”. However, it is debatable if MACv2 overestimates the increase of longwave radiation as it neglects the natural variability of mineral dust both in terms of variability of particle sizes and mineralogical composition, which can have a considerable influence e.g.and the references therein.

In winter, the impact of AOD on rsds is much weaker in Europe than in summer. A weak cooling is found in southern and eastern Europe in tasmax and tasmin (Fig. S4).

However, for the new treatment of the indirect aerosol effect (aerosol-cloud-fb, icpl_aero_gscp=3), we only found a mean sensitivity of (“Avg” sens: DJF = 0.8, JJA = 1.1). The values are similar for all variables. Thus, the impact is not significant.

In this section, we discuss ICON-CLM sensitivities to parameter changes of surface and subsurface processes (see Tables  and ). Those parameters that do not exhibit a signal-to-noise ratio (i.e., sensitivity) significantly higher than one are introduced only shortly hereafter, but the results of the tests are neither shown nor further discussed.

The change of the scaling factor of minimum resistance to plant transpiration rsmin_fac from 1.0 to 1.2 exhibits a mean sensitivity of (“Avg” sens: DJF = 0.7, JJA = 1.0).

We tested the increase of bare soil minimum resistance to turbulent fluxes cr_bsmin in (C2I111–C2I200) from 110 to 150 sm-1. The results are similar to those found for rsmin_fac increase and exhibit a mean sensitivity of (“Avg” sens: DJF = 0.9, JJA = 1.1).

The factor rat_lam is scaling the resistance to turbulent latent heat flux over land in comparison with that over ocean surfaces. For the change from 1.0 to 0.8, we found a sensitivity for clt of (“clt” sens: DJF = 2.1, JJA = 2.2) and (“Avg” sens: DJF = 1.2, JJA = 1.5). Due to the definition of the signal as a linear combination of four simulations (see Table ), the noise level is twice the noise level used for the definition of the sensitivity in Table . Considering the higher noise level of rat_lam test results, the results can be regarded as not significant.

A change of the parameter value for itype_z0 from 2 to 3 results in an increase of surface roughness z0 in mountainous regions. For itype_z0=2, z0 is determined from land-cover-related roughness considering tile-specific land use class. For itype_z0=3, additionally, the subgrid-scale orography is considered. We found a mean sensitivity of (“Avg” sens: DJF = 3.0, JJA = 2.5) resulting from high sensitivities of mean sea level pressure psl and wind speed ws. The impact of the change on tas, pr_amount, and sfcWind is shown in Fig. . A systematic effect is found for the wind speed, which is reduced in mountainous regions. Additionally, the effects on psl and the turbulent fluxes hfls and hfss are shown in Fig. S5. The impact on psl is up to 0.3 hPa and thus negligible. In winter, the hfls is increased and hfss is decreased slightly in mountainous regions. In summer, the hfss is systematically decreased by up to 10 Wm-2 in mountainous regions in the Mediterranean while causing a decrease in tas by up to 0.5 K.

The parameter is the scaling factor of turbulent heat flux resistance at the surface (see also Table ). For the change of the scaling factor of resistance to turbulent heat fluxes rlam_heat from 10 to 6.25, we found a sensitivity for hfls_o (“hfls_o” sens: DJF = 7.0, JJA = 5.7) and (“Avg” sens: DJF = 1.9, JJA = 1.6) on average. The decrease of rlam_heat leads to a strong increase of hfls_o over the Mediterranean Sea and the Atlantic Ocean in winter. In summer, the effect is reduced in the Atlantic but remains high in the Mediterranean Sea (Fig.  left).

The impact on tas, pr_amount, and rlds is shown in Fig. S6. We found an increase of tas over the entire domain by 0.3 K in winter and not in summer. This occurs, since the two effects of increased latent heat flux on the cloud cover, as later discussed in detail in Sect. , result in a winter increase of long wave downward radiation rlds due to an increase of low cloud cover. In summer, the reduction of short wave and increase in long wave are small and similar.

The scaling factor of resistance to turbulent heat fluxes over the sea surface rat_sea is reducing the resistance over water in comparison with land surfaces. We found high sensitivities for hfls_o of (“hfls_o” sens: DJF = 4.5, JJA = 4.0) and (“Avg” sens: DJF = 1.4, JJA = 1.2) on average, which is similar to rlam_heat. Figure , right, shows the impact of increased resistance on hfls, which is spatially very similar distributed to the effect of reduced rlam_heat. The impact on tas, pr_amount and rlds is shown in Fig. S7 as for rlam_heat.

The albedo correction, now as a modification of the official ICON release source code available (Sect. ), for dry soils (tune_albedo_wso(1)=0.1) is changing the albedo by up to 0.1 if the upper soil layer is dry. For tas we found a sensitivity of (“tas” sens: DJF = 3.5, JJA = 3.8) and of (“Avg” sens: DJF = 3.1, JJA = 2.6) on average. Figure  shows a decrease of tasmin, tasmax in summer of 0.5 to 1.5 K in the Mediterranean due to an increase of short wave outgoing radiation flux at the surface rsus of 10 to 20 Wm-2. Additionally, Fig. S8 shows a slight decrease of pr_amount and hfls in JJA in central to northern Europe due to increased rsus, which is an indirect effect.

The albedo correction for wet soils (tune_albedo_wso(2)=-0.1) is changing the albedo by up to -0.1 if the upper soil layer is wet. It exhibits a very weakly significant impact on the reflected solar radiation in the southern part of the domain in summer and no significant impact on the other surface energy budget components, nor on tas.

The new parameterisation of horizontal transport of subsurface water due to gravitation itype_hydmod=1 shows high sensitivities for summer tasmax (“tasmax” sens: DJF = 1.3, JJA = 5.3), for latent heat flux over land hfls_l and (“hfls_l” sens: DJF = 2.3, JJA = 3.7) and (“Avg” sens: DJF = 1.2, JJA = 2.7) on average. The impact on tas, pr_amount and hfls is shown in Fig. S9. It exhibits a warming over mountains and a cooling in water down-flow regions due to a decrease/increase in hfls, e.g., in the Alpine region and the Po valley, respectively, and in particular in the dry summer season. This is consistent with the physical expectation as the lateral redistribution of water results in a changed evaporative fraction affected by surface and subsurface heterogeneities and orography.

In northern Africa, there is an increase of hfls of 3 to 5 Wm-2. We hypothesise that this is due to the reduced vertical gravitation flux in this parameterisation.

Unfortunately, this parameterisation was not included in the officially released model version used for configuration optimisation in this study, so it was not considered further.

The frequency of calling of the convection, radiation, subgrid-scale orography drag, and gravity wave drag parameterisations might have a systematic impact on the simulation results if the time increment DT is too large. However, the computing time is increasing with decreasing DT. This test investigated the opportunity of larger DT values. The sensitivity found for DT_PHY is for sfcWind (“ws” sens: DJF = 27, JJA = 8.3) and (“Avg” sens: DJF = 5.1, JJA = 1.9) on average. The dependency of the solution on the time step (see Fig. S10) indicates the need for the shorter time step. Consistently herewith, the analysis of the results showed that the longer time step corrupts the development of gravity waves, so the larger DT is not used.

For the change of minimum turbulent transport coefficients for heat and momentum tkhmin,tkmmin we found a sensitivity for tasmin of (“tasmin” sens: DJF = 2.2, JJA = 2.3) and (“Avg” sens: DJF = 1.5, JJA = 1.3) on average. Reducing the minimum vertical transport reduces the mixing in a stable atmosphere. Stable conditions occur particularly in winter and at night. This reduces the sensible heat flux at the surface, thereby increasing cooling during the night. In cloudy conditions, it helps to dissolve the low cloud cover, which exists over too long time spans otherwise.

Figure S11 shows the impact of the reduction of the parameter values on tasmin, hfss, and clt. We find a reduction to tasmin by 1 K in winter and 0.5 in summer, and no significant impact on precipitation. In winter, the downward positive sensible heat flux hfss is reduced by 2 Wm-2 in stable stratification, in particular in snow-covered regions and in the desert. In summer, this effect is weaker. The cloud cover and the longwave downward radiation are slightly increased, but do not have a dominant impact on the near-surface temperature. However, the overall effect decreases the simulation quality, and thus, these parameter value changes have not been considered in the new reference, and they are not used as optimisation parameters.

The stochastic shallow convection scheme (lstoch_sde=.true.) aims at parameterising the shallow convection in simulations resolving deep convection, i.e., at horizontal grid sizes smaller than 20 km. It has to be used together with setting both lrestune_off and lmflimiter_off to “True”. The parameter sensitivity for pr_amount of (“pr_amount” sens: DJF = 3.8, JJA = 2.0), for hfls_l of (“hfls_l” sens: DJF = 3.1, JJA = 2.6) and (“Avg” sens: DJF = 2.1, JJA = 2.0) on average.

Figure shows the impact on tas, pr_amount, and rsds. The pr_amount in winter is strongly decreased due to flow disturbances at the inflow boundary, at coastlines, and at some of the mountain chains, in particular when the wind speeds are high. The precipitation is increased inland, indicating a potentially strong relation to sea breeze circulations. In summer, mainly the mountainous pr_amount is increased by enhanced shallow convection. Herewith, rsds is consistently reduced by 5 to 10 Wm-2 over large parts of the domain in summer.

An unexpected effect is the reduction in tas in the north-east of the domain. A more detailed inspection revealed a reduction of rlds due to increased mixing.

The parameterisations of precipitation and cloud cover diagnostics described in Sect.  have a direct impact on the irradiance at the surface rsds and rlds. The most important ICON parameters are considered in this study.

The 1-moment scheme (mass; inwp_gscp=1) with two categories of ice (cloud ice, snow) is tested with new ice nucleation (inwp_gscp=3). We tested it together with recommended configuration settings (see C2I108 in Table ). Overall, we found high sensitivity on inwp_gscp change (“Avg” sens: DJF = 4.0, JJA = 6.0) and especially high values for rsds (“rsds” sens: DJF = 9.7, JJA = 10.2).

As shown in Fig. S12, the new ice nucleation generates much higher pr_amount at the eastern outflow boundary and in mountainous regions in summer. The strong increase in rsds values in winter in the Mediterranean (up to 15 Wm-2) and over the North Atlantic and northern Europe (up to 40 Wm-2) in winter leads to an increase in tas of up to 0.8 K in winter and 1 K in summer in the corresponding regions. Additionally, we found a distinct reduction of tas in the north-eastern part of the domain in winter, where the pr_amount is not systematically influenced. This indicates an increase in cloud base height, resulting in reduced rlds. Due to the reduction of the overall simulation quality, the scheme tested is not used in the new 12 km grid reference (see also Fig. ).

The subgrid-scale cloud cover scheme is a parameterisation of the cloud cover due to vertical mixing processes (convection, turbulence) if the rh is below 100 %. Here, the impact of the scheme, already available in the COSMO model (inwp_cldcover=3), is investigated in comparison with the reference (inwp_cldcover=1) cloud cover diagnostics. The latter is used in the radiation scheme and has no direct impact on precipitation. We found a sensitivity for clt of (“clt” sens: DJF = 6.9, JJA = 6.1) and (“Avg” sens: DJF = 2.2, JJA = 2.6) on average.

The impact on tas, rsds, and rlds is shown in Fig. . We found a rsds change of -3 and -5 Wm-2 in winter and summer, respectively, due to increased cloud cover, together with an rlds increase of up to 10 and 6 Wm-2 in winter and summer, respectively. This resulted in an increase in radiative forcing and an increase in tas over North Europe by up to 1 K in winter and over land in summer by approximately 0.3 K.

The results in radiation components show an increase in clt and a reduction of the cloud bottom height, in particular in winter, and the relevance of the diagnostic cloud cover for tuning of the surface forcing.

The process-specific subgrid-scale cloud cover diagnostics and their tuning parameters (allow_overcast, tune_box_liq, tune_box_liq_asy and others, see Sect. ), were introduced for the new scheme in ICON (inwp_cldcover=1); they are not available for the old scheme from the COSMO model (inwp_cldcover=3). This study, therefore, uses the latest tuning options of the new subgrid-scale cloud cover scheme.

The shape factor allow_overcast of the quadratic dependence of subgrid-scale cloud cover on rh is a parameter of the cloud cover scheme itype_cldcover=1. We found a sensitivity for clt of (“clt” sens: DJF = 3.3, JJA = 4.0) and (“Avg” sens: DJF = 1.7, JJA = 2.6) on average.

As mentioned in Sect. , smaller values of allow_overcast result in higher subgrid-scale cloud cover. Figure shows the sensitivity of reducing allow_overcast from 1.0 to 0.9.

Figure c and f show an increase of total cloud cover, in particular in summer and over the sea, where the cloudiness is mainly partial. During winter, a decrease in rsds (Fig. S13) is found over land in central and southern Europe, and an increase of 3 Wm-2 in downward longwave radiation over northern and central Europe, which results in an increase of up to 0.5 K in tas in snow-covered regions.

While over the Mediterranean and southern Europe, the radiative forcing effect is close to zero, over northern Europe, the daily mean tas (Fig. ) is increased by up to 0.5 K and tasmin by up to 1 K. During winter, the sunshine duration is short in northern Europe. Consequently, the prevailing effect is an increase in the long-wave radiation absorbed by the surface (see Fig. S13).

The increase in clt can be explained by frequent cyclonic synoptic situations leading to overcast (total cloud cover of 1). In these situations, a reduction of allow_overcast can lead to an increase of clt at additional model levels, in particular for low clouds, reducing the bottom cloud height and making the existing cloudy layer optically more opaque. However, it can not lead to an increase in the clt greater than 1. This argument may explain the low sensitivity of the clt to the change in allow_overcast in northern Europe in winter, an increase of rlds, and a strong increase of tas, in particular in snow-covered regions.

Figure shows that the increase in clt in summer is much higher than in winter, resulting in a rsds reduction of 20 Wm-2 in summer and of 10 Wm-2 in winter and over the entire northern part of the domain and in relatively small changes in rlds (see Fig. S13). Figure d consistently shows a reduction in tas of about 0.3 to 0.5 K in particular during the day. This is shown by the reduction of tasmax of up to 1 K.

An inflow boundary effect can be found in pr_amount in winter and summer (Fig. b and e). Since the cloud cover diagnostics are not used in the microphysics scheme, this effect is probably caused by a feedback of reduced reflected shortwave radiation on precipitable water.

The increase of the range of relative humidity tune_box_liq around 100 % from 0.05 to 0.07, within which the cloud cover is increasing from 0 to 1 (see Eq. ), exhibits the highest sensitivity for clt (DJF = 2.1, JJA = 2.6). The mean sensitivities “Avg” are (DJF = 1.2, JJA = 1.7). This increases the subgrid-scale cloud cover and reduces rsds.

The effect of increasing tune_box_liq is very similar to that of reducing allow_overcast to 0.9 but weaker, in particular in summer. While the effect of reducing allow_overcast is reflected in the appearance of full overcast areas, strongly influencing insolation, the effect of increasing tune_box_liq is reflected in a slight increase of partial cloudiness areas (see Figs. c and f) with a weaker effect on insolation and thus on tas (see Figs. a and Fig. d). For comparison, Fig. S14 shows tasmax, rsds and rlds in winter and summer.

For the scaling factor determining the asymmetry term of the cloud cover for over- and undersaturation tune_box_liq_asy, we found a sensitivity for clt of (“clt” sens: DJF = 3.5, JJA = 4.3) and (“Avg” sens: DJF = 1.5, JJA = 2.3) on average.

The effect of increasing tune_box_liq_asy is very similar to that of reducing allow_overcast and increasing tune_box_liq. There is an increase in clt (see Fig. ) and a reduction of rsds (see Fig. S15, center). As expected (see Sect. ), the effect of increasing tune_box_liq_asy is stronger than the effect of increasing tune_box_liq, leading to a larger increase of partial cloudiness. The comparison of the results shown in Figs. , S13, , and S15 show that the effects of decreasing allow_overcast and increasing tune_box_liq_asy are of similar magnitude in tas, rsds and rlds. However, the spatial structures are different and accumulate to significantly different patterns in tas, tasmax and tasmin.

The task of expert tuning is to find an optimised model configuration based on the test simulation results for the tuning parameters and values given in Table . The procedure applied was as follows. Each expert was invited to suggest an Expert configuration. After discussion of all Expert configurations based on a comparison of the model bias, parameter sensitivities and configuration changes suggested, ten of the Expert configurations have been simulated and evaluated using the test simulation and evaluation procedure. The configurations C2I266c to C2I272c given in Table  are five of these configurations. New Expert configurations were suggested, aiming at further optimising the best configuration found, which was C2I268c. The configurations C2I277c to C2I280c are four of the final configurations simulated and evaluated. However, the improvements found have not been significant, so that C2I268c was identified as the optimised Expert configuration. It yielded the highest ScoPi values in comparison with the reference C2I200c and did not include any extreme namelist parameter values.

The configuration of C2I268c is using a combination of three test simulations for individual parameters: allow_overcast=0.9 (see Figs.  and S13), rlam_heat=6.25 (see Fig. S6), tune_albedo_wso=(0.1,-0.1) (see Fig. S8). Reducing allow_overcast directly increases the low cloud cover and thus decreases the rsds in winter in mid to southern Europe by 3 Wm-2 (in winter the cloud cover is already high) and in summer in northern to mid Europe by 12 Wm-2. It increases the incoming long wave radiation as well, in particular in northern Europe in winter by 5 Wm-2, resulting in a warming in northern to mid Europe in DJF by 0.3 K. In summer, the increase of cloud cover and the resulting reduction of rsds is dominating the reduction in tas. This is combined with the heat flux resistance parameter rlam_heat reduction by 30 %. The latter increases hfls and hfss over water in winter and summer (see Fig. a and c for hfls). The dominating effect is an increased low cloud cover and the associated increase of incoming long wave radiation and tas in the entire domain in winter (Fig. S6c and a). In summer, the change in rsds and tas is close to zero. These two parameter changes reduce rsds and increase tas in winter in northern Europe. The third important change is that of the albedo. The dry soil albedo increase is decreasing the absorption of rsds in the Mediterranean, in particular in summer, resulting in a summer cooling. The wet soil albedo decrease has no significant impact on the results.

An intercomparison of the Expert configurations given in Table  shows that most of the configurations C2I266c to C2I272c are using albedo tuning for dry/wet soils. The result of C2I271c was the only one not showing a clear reduction of the summer warm bias in northern Africa and the eastern Mediterranean. This justified the albedo tuning. The configuration C2I266c is the only one using tune_box_liq and tune_box_liq_asy instead of allow_overcast together with different values for other parameters than in C2I268c. These values for other parameters together with allow_overcast=0.9 can be found in C2I267c and C2I272c.

The main differences between C2I272c and C2I268c are the values for rlam_heat=5 instead of 6.25 and rat_sea=0.7 instead of 0.8. An inspection of the evaluation results for C2I268c (see Figs. S16 and S19) and C2I272c reveals very similar summer and winter tas and winter rsds biases. The rsds summer values are slightly higher in C2I272c.

The evaluation of C2I266c and C2I272c (Fig. ) indicates a slightly smaller bias in winter rsds in C2I266c. In summer, the biases for the Iberian Peninsula and northern Africa are similar. In C2I266c, a strong decrease of rsds is found in the central to eastern part of the domain. This indicates that the increase of tune_box_liq and tune_box_liq_asy by 40 % and 25 %, respectively, is generating too high cloud cover in some subregions of the domain.

The results of C2I266c to C2I272c lead to the selection of C2I268c as the new reference for further expert tuning. The configurations C2I277c to C2I280c comprise different annual cycles (aoac[m]) added to the allow_overcast mean value, as well as scaling factors for latent heat flux over land rat_lam and/or for minimum plant transpiration resistance rsmin_fac. These are used to further reduce the cold bias in tasmax (see Fig. S18), the positive bias of rsds in winter and the complex positive/negative bias in summer (see Fig. S19). However, the small improvements achieved did not justify using questionable parameter settings like the annual cycle aoac or strong deviations from parameter values used in operational NWP (rsmin_fac=1.5, rat_lam=1.2).

A final evaluation of additional model variables for the Expert configurations revealed a strong overestimation of the latent heat flux over water by C2I268c and by the other Expert configurations in comparison with the reference C2I200c (see Fig. ).

The discussion demonstrates typical potential and drawbacks of expert tuning. On the one hand, it enables a definition of a new configuration by the combination of a small number of test simulation results and a small number of model variables very efficiently. On the other hand, two important drawbacks can be highlighted. First, model variables, which are not in the focus of interest, are typically neglected. Second, optimal parameter values cannot be determined, they can only be estimated. To find the optimal values, many more simulations would be necessary to consider cross-dependencies of parameterisations.

This section provides the settings used to configure the LiMMo framework. For detailed information on the LiMMo method, please refer to Sect. .

We selected the following list of parameters for the LiMMo tuning (check Table  to see the description of parameters): allow_overcast parameters ao and aoa, tune_albedo_wso(1), tune_albedo_wso(2), rlam_heat, rat_sea, rat_lam, rsmin_fac, tune_box_liq, and tune_box_liq_asy. Most of these parameters show high sensitivity (see Fig. ), while tune_albedo_wso(2) signal is very weak. We decided to keep the latter under consideration for consistency, although we do not expect it to significantly affect the results.

As reference simulation, which defines the shift tensor of regression approximation (see Eq. ), we used C2I250c (see Table ), since it provides acceptable quality while incorporating the most up-to-date external data sets that we would like to use in the end. Moreover, C2I250c is the simulation of the revised reference configuration (see Sect.  and compare Fig. 2g).

To define the error norm that is minimised by the gradient method, we have tested two sets of weights for the model quantities, presented in Table . These weights are applied to define the quality measure of the configuration (error norm), given in Eq. (), and have the unit sum. The main difference between the two sets of weights is the reduced weight of hfls_o in the second case. The residual 0.05 was added to rsds. As we will demonstrate later, this seemingly small adjustment has a strong impact on the LiMMo optimised configuration obtained.

As mentioned in Sect. , the optimisation process (gradient descent) is restricted to the parameter space limited by MIN and MAX boundaries for each parameter. These values, along with the initial guess, are listed in Table . These values were chosen after extensive consultations with ICON developers and experienced users, to ensure the physical consistency of the optimised parameter values. In Table , we also present the resulting values for the two sets of weights from Table .

In Fig.  we present the ScoPi scores for the revised reference simulation (C2I250c), the simulation (C2I268c) using the expert tuning, and the simulations C2I291c and C2I294c) using the LiMMo optimised configuration. The score is a measure of increase/decrease of the simulation quality with respect to the reference simulation C2I200c. The scores for the (land) PRUDENCE regions are shown in Fig.  on the left, and the scores for the water sub-regions considering lhfl_o are shown on the right.

The ScoPi of the revised reference C2I250c suggests that the changes in external data sets and updates in model versions do not influence the mean model quality but have impacts on the regional distribution of the biases for the land quantities only.

The expert and LiMMo tuned configurations reveal relatively high positive ScoPi values, indicating significant improvements in simulation quality. The best performing simulation for the land quantities is the expert tuned configuration C2I268c (11.5 points), followed by the LiMMo tuned configuration C2I294c with low weight for hfls_o (9 points) and C2I291c with high weight for hfls_o (7 points). The improvements are found for all PRUDENCE regions with the weakest ScoPis over the Iberian Peninsula.

The LiMMo tunings C2I291c and C2I294c do not achieve the same model quality as expert tuning C2I268c with respect to ScoPi over land (Fig. , left). This, however, is not showing that the expert tuning outperforms LiMMo tuning. It shows that the additional constraint of LiMMo tuning, the reduction of the bias of latent heat flux bias over water (hfls_o is reducing the quality over land, as shown by ScoPi considering land points only. However, the analysis of hfls_o-based ScoPi reveals the weak performance in simulating latent heat flux with C2I268c and C2I294c.

Figure  shows the time mean spatial RMSE with respect to observations and all variables considered in the LiMMo optimisation separately for the winter (a), the summer (b) and for all months (c). The values are normalised by the RMSE of C2I200c and shown as percentages. The intrinsic uncertainties of the model (see Eq.  and Table ) are given as vertical whiskers. This allows to assess the statistical significance of the tuning.

First, we could not find a significant change in precipitation RMSE for any of the optimised configurations (see Fig. c for pr_amount). The changes of pr_amount in both winter and summer RMSE are also below the level of significance (see Fig. a and b for pr_amount). This can be explained by the relatively low sensitivity of pr_amount to parameter changes considered (see Fig. , column pr_amount). The initial configuration C2I200c has decent precipitation quality because a similar configuration is used for NWP. Therefore, the precipitation quality of the optimised configurations can be regarded as satisfactory.

Second, the expert optimised configuration C2I268c shows statistically significant improvement of RMSE for tas and tasmax in winter and summer. The LiMMo optimised configuration C2I294c (low weight of hfls_o, see Table ) also reduces the RMSE significantly for tas in winter and for tasmax in summer. The second LiMMo configuration C2I291c (high weight of hfls_o, see Table ) exhibits a different result. In winter, the tasmax RMSE is significantly increased. In summer, it is significantly reduced. For tasmin, the opposite holds – there is a slight decrease in winter and a significant increase in summer. The slightly reduced quality (5 %–10 % higher RMSE in comparison with C2I294c) of summer tasmin and winter tasmax affects climatologically relevant quantities like the number of tropical nights and frost days. This can be accepted for regional climate applications, considering the significant improvement in winter tasmin and summer tasmax, improving the quality of winter cold nights and summer hot days. It allows for keeping or even improving the predictability of cold events in winter and heat waves in summer, which are usually of the main interest for the risk assessments.

Third, Fig.  shows significant and strong differences in rsds and hfls_o (for optimised configuration with respect to C2I200c). The results are similar for C2I200c and C2I250c. Thus, updating the external parameters has a minor impact on these quantities. A large and significant decrease of up to 30 % in rsds RMSE was found for the expert (C2I268c) and LiMMo-optimised (C2I291c, C2I294c) configurations with 30 % to 35 % in winter for all three and about 15 % to 20 % in summer for the LiMMo configurations only.

Fourth, the rsds RMSE reductions in C2I268c and C2I294c are accompanied by a significant and strong increase of the hfls_o RMSE (30 % to 40 % in winter and 10 % to 20 % in summer). The C2I291c configuration, however, is the only one showing a significant and strong reduction of hfls_o RSME in both seasons (∼ 17 % in winter and ∼ 7 % in summer).

In the current section, we show the seasonally averaged 2-dimensional bias plots for the most significant changes identified in the RMSE analysis (see Fig.  in Sect. ).

First, we compare the 2-dimensional biases of summer tasmin and winter tasmax for configurations C2I200c, C2I250c, and C2I291c in the Fig.  to ensure that there are no severe violations of the model quality by the configuration changes in these quantities. The update of the external data sets leads to an overall positive temperature shift in summer tasmin (Fig. b vs. a). The LiMMo tuning slightly reduces the summer tasmin bias, especially in central Europe and northern Africa (Fig. c vs b), but the bias still remains overall positive and larger than in the original setup (Fig. c vs. a). The positive temperature shift is visible for winter tasmax as well (Fig. e vs. d), slightly reducing the negative bias. However, the LiMMo tuning reverses this improvement, leading to a slightly stronger negative bias (Fig. f vs. d). This degradation is mainly confined to the northern African region. Overall, the quality of the summer tasmin and winter tasmax can be regarded as similar in C2I291c and C2I200c, especially for the target region of central Europe.

Second, in Fig.  we present the summer rsds and winter hfls_o biases for C2I200c, C2I268c, and C2I291c. The LiMMo parameter tuning clearly reduces the positive rsds bias over central and western Europe while slightly increasing it in Eastern Europe (Fig. c vs. a). The expert tuning results in an enhanced negative bias over central and eastern Europe (Fig. b vs. a), while slightly reducing the positive bias in Western Europe. Along with the ambiguous performance for rsds, we observe a strong degradation of winter hfls_o of 10 Wm-2 in the Expert configuration C2I268c (Fig. e vs. d). The LiMMo configuration C2I291c provides clearly reduced bias in the Atlantic and Mediterranean (Fig. f vs. d). A comprehensive analysis of seasonal 2D biases for tas, tasmin, tasmax, rsds, hfls_o, pr_amount and psl is provided in the supplementary materials (see Sect. S5).