The study analyzes the impact of coupling hydrological processes to the regional atmospheric modeling system WRF with respect to water and energy exchange at the land-surface–atmospheric-boundary-layer interface. The lateral flow of infiltration excess, as well as river inflow and routing, are addressed by the WRF-Hydro extension. Several parameters of WRF-Hydro influence the land surface water redistribution and thus the hydrographs and require therefore thorough calibration.

To finally come up with a fully coupled WRF-Hydro setup, several intermediate steps are required that involve different components of the modeling system. As outlined in Fig.  we build a modeling chain with the items WRF-Hydro standalone (WRF-H_SA), WRF standalone (WRF_SA), and WRF-Hydro fully coupled (WRF-H_FC). WRF-H_SA refers to the hydrologically extended land surface model that is not coupled to an atmospheric model and gets its driving data from gridded (pseudo-)observations. WRF standalone (WRF_SA) is the classic version of WRF that has no hydrological extension and that is driven by data from a global circulation model. WRF-H_FC extends WRF_SA with the hydrological implementations of WRF-H_SA.

Of the eight driving variables required by WRF-H_SA, only interpolated precipitation is available from observations with adequate coverage. Thus, the remaining input variables (temperature, humidity, wind, and radiation) are taken from a preceding standalone WRF (WRF-ARW 3.7; Advanced Research WRF) simulation.

The modeling chain encompasses the following four steps: (1) a classic standalone WRF run (1 April 2015–31 October 2016) with standard land surface model (LSM) parameters to derive the driving variables required by (2) the standalone WRF-Hydro simulations (WRF-H_SA; 1 April–31 July 2015 and 15 April 2016–31 October 2016) that also ingest hourly gridded observed precipitation Radar-Online-Aneichung – RADOLAN – of the German weather service – DWD;, (3) a fully coupled WRF-Hydro simulation (WRF-H_FC; 15 April 2016–31 October 2016) using calibrated parameters from WRF-H_SA, and (4) a rerun of the classic standalone WRF (WRF_SA; 15 April 2016–31 October 2016) with the same parameter set obtained from WRF-H_SA. Finally, this leads to a commensurable set of simulations, coupled vs. uncoupled. Consequently, WRF_SA does not represent an optimized setup of a classic WRF standalone model. Therefore, it is possible that with other parameter combinations for WRF_SA even better performance could be achieved. However, tuning WRF_SA is not easily possible because it does not feature the simulation of discharge and other point observations are sparse and represent different scales. They are thus only suitable for the evaluation of simulation results.

The computational demand was about 0.021 million core hours for the WRF_SA simulations, 0.32 million core hours for the WRF-H_SA calibration runs, and 0.042 million core hours for WRF-H_FC on a 2.3 GHz Intel Haswell system.

Figure visualizes the domain and nesting configuration for the WRF_SA and WRF-H_FC simulations.

A telescoping configuration with three nests is employed. The horizontal resolutions are 15 by 15, 3 by 3, and 1 by 1 km for domains 1, 2, and 3, respectively. The finest domain extends from the city of Munich in the northeast to the mountain valleys of Inn and Lech in the southwest. For all domains, the number of vertical levels is 51. The model top is defined at 10 hPa. The WRF-H_SA and WRF-H_FC simulations cover the period 15 April to 31 October 2016 including a half month for model spin-up. The starting date corresponds to snow-free conditions for most of domain 3. The spin-up strategy avoids the uncertain simulation of the snow storage dynamics for the winter season. For the surface variables in WRF-Hydro, we consider a 15 d spin-up to be sufficient. The initial (15 April 2016) soil moisture fields for both WRF_SA and WRF-H_FC are taken from the last WRF-H_SA simulation time step (31 October 2016). We assume that this 6-month spin-up period is sufficient to come up with reasonable starting conditions for a commensurable set of simulations. The model runs are performed continuously with none of the variables being reinitialized in between. Lateral surface water flow processes (i.e., overland and channel routing) in WRF-H_SA and WRF-H_FC are computed on a 100 by 100 m grid with the extent being identical to that of domain 3. The integration time steps for the atmospheric part (WRF including the Noah-Multiparametrization – Noah-MP – LSM) are 60, 12, and 4 s for domains 1, 2, and 3, respectively. The hydrological routines are called at hourly intervals.

The WRF physics parameterization for the selected domains is listed in Table . Cumulus parameterization is only activated for the outermost domain 1, while explicit convection is chosen for the finer grids (domains 2 and 3), according to .

For uncoupled and coupled simulations, Noah-MP is used as the land surface model. For Noah-MP the selected configuration deviates from the default setup as follows: the Community Land Model (CLM) method is selected for stomatal-resistance computation, the method is used to determine infiltration and drainage (similar to the classic Noah LSM), the two-stream radiation transfer applied to the vegetated fraction (option 3) is chosen, and the dynamic vegetation option is enabled.

The static data are adopted from the standard WRF geographic dataset. The land cover for domains 1 and 2 is based on USGS (United States Geological Survey) classification and includes lakes. For the innermost domain the land cover information is based on the CORINE Land Cover dataset of the European Union, reclassified according to the USGS classes. The elevation data for the 100 m grid are derived from the Advanced Spaceborne Thermal Emission and Reflection Radiometer global digital elevation model (ASTER GDEM, version 2).

Noah-MP provides different options for the computation of groundwater discharge and surface runoff (infiltration excess), but only WRF-Hydro enables the simulation of lateral hydrological processes such as the overland routing of surface runoff and channel (discharge) routing. A short description of the most relevant model details for this study is provided below. Further information about technical features and standard model physics options are given in , while Sect.  describes the specific improvements made to the original model in order to fit with the specific features of the complex topography of this study area.

In the WRF-Hydro modeling system only subsurface and surface overland flow routing are allowed to directly affect atmosphere dynamics (i.e., only these processes are fully coupled). After every LSM loop, a subgrid disaggregation loop is run prior to the routing of saturated subsurface and surface water, in order to achieve the desired spatial refinement (from 1 km to 100 m) for the two-state-variable infiltration excess and soil moisture content. At this stage, linear subgrid weighting factors are assigned for preserving the subgrid soil moisture and infiltration excess spatial variability structures from one model time step to the next. Then, subsurface lateral flow is calculated, using the method suggested by and within the Distributed Hydrology Soil Vegetation Model (DHSVM). The water table depth is calculated according to the depth of the top of the highest (i.e., nearest to the surface) saturated layer. Finally, overland flow routing also accounts for the possible exfiltration from fully saturated grid cells and is achieved through a fully unsteady, explicit, finite-difference, diffusive-wave approach similar to that of and . In this study the steepest descent method is used with a time step of 6 s. After the execution of the routing schemes, the fine-grid values are aggregated back to the native land surface model grid.

Concerning the one-way coupled processes modeled in the WRF-Hydro system (i.e., no feedback with the atmosphere), in this study, the channel flow and baseflow modules are used. Specifically, channel flow routing is performed through an explicit, one-dimensional, variable-time-stepping diffusive-wave formulation. Overland flow discharging into the stream channel occurs when the ponded water depth of specific grid cells, assigned to a predefined stream channel network, exceeds a fixed retention depth. The channel network has a trapezoidal geometry, depending on the Strahler stream order functions. Currently no overbank flow is simulated. Baseflow to the stream network is represented through a simple bucket model which uses an exponential equation to achieve the bucket discharge as a function of a conceptual water depth in the bucket. Several baseflow subbasins (i.e., several conceptual buckets) can be specified within a watershed, but since an empirical equation is used, its parameters need to be estimated for each of the subbasins. The baseflow model is linked to WRF-Hydro through the deep-drainage discharge from the land surface soil column. The estimated baseflow discharged from the bucket model is then combined with the lateral inflow from overland flow and is input directly into the stream network as a part of the stream inflow. The total subbasin baseflow flux to the stream network is equally distributed among all channel pixels within the subbasin.

The reservoir module (retention of channel flow in lakes and reservoirs) is disabled for the simulations of this study because only one gauge (Ach-OBH) would be slightly affected by a 7.66 km2 lake (Staffelsee), but the number of calibration parameters and thus calibration runs would considerably increase. Since the lake evaporation is explicitly considered by the Noah-MP land surface model, we do not assume any impact on the land-surface–boundary-layer exchange by this simplification.

The model, as applied in this study, differs from the version 3 of WRF-Hydro with respect to soil layer representation and model time steps. Large parts of the modeling domain and the considered river catchments exhibit mountainous terrain with steep slopes covered by shallow soil layers. Here, the model's general assumption of 2 m soil thickness (or depth to bedrock) does not hold true, as it may lead to an overestimated retention of infiltrating water. Therefore, in this study, the soil layer definition is changed from a domain uniform to a grid-point-based representation, and soil layer thicknesses are set to the Noah-MP standard (0.1, 0.3, 0.6, and 1 m) distribution for hillslopes below 50 % and to more shallow values (0.05, 0.05, 0.1, and 0.1 m) for all slopes >50 %. The 50 % threshold leads to a realistic discriminability of valley bottoms and hillslopes. In addition, the infiltration (REFKDT) and percolation (SLOPE) parameter implementation is changed from domain-wide uniform values to subcatchment-wise distributed (lumped) values. Another important change is made with respect to the time step configuration of WRF-H_SA and WRF-H_FC simulations. As pointed out in , differing intervals used for the temporal integration of the Noah LSM lead to inconsistent amounts for the soil water fluxes. The issue is caused by numeric effects when time steps become very small (1 km WRF requires about 4 s) in fully coupled WRF-Hydro simulations with high resolutions. To eliminate the problem and to make all simulations comparable, the hydrology part (subgrid) in WRF-H_FC is only called at an hourly time step, similar to that of WRF-H_SA. In WRF-H_FC the flux variables of domain 3 are therefore cumulated in between the (hourly) calls of the hydrological routines, and on the other hand, the overland routing output (surface head) is returned to domain 3, equally distributed over the LSM time steps (4 s). The subsurface routing option for saturated soil layers is deactivated in this study, as full saturation rarely takes place in the region and because the module would require extending the calibration by two more parameters.

Atmospheric boundary conditions for the outer domain of the WRF_SA and the WRF-H_FC simulations are derived from the ERA (ECMWF – European Centre for Medium-Range Weather Forecasts – Reanalysis) Interim reanalysis with 0.75∘ horizontal grid spacing, 37 pressure levels from 1000 to 1 hPa, and 6 h temporal resolution. Forcing data for WRF-H_SA are taken from the standard WRF simulation output for domain 3. The variables comprise near-surface air temperature, humidity, wind, surface pressure, and short- and longwave downward radiation. Since precipitation from WRF simulation is typically biased and dislocated, an observational product of the German weather service RADOLAN; is used for substitution. It combines gauge and rain radar information and is available with an hourly time step and 1 km2 resolution.

Different approaches for the calibration of the WRF_SA model have been followed in previous works, all of which were based on the comparison of the observed hydrographs. adopted a stepwise approach, where the parameters controlling the total water volume were first calibrated (namely, the infiltration factor, REFKDT, and the surface retention depth, RETDEPRT), followed by the parameters controlling the hydrograph shape (namely, the surface roughness, OVROUGHRT, and the channel Manning roughness, MANN). , , , and followed a similar approach. Specifically, the latter added in the first calibration step the parameter that governs deep drainage (SLOPE) and in the second step the saturated soil lateral conductivity and the bucket outflow exponent (EXPON). Furthermore, to refine calibration they introduced an automated procedure based on the Parameter Estimation and Uncertainty Analysis software PEST;. mainly focused on the REFKDT and, secondarily, on the MANN parameters. Finally, proposed a satellite-based approach for arid (bare-soil) regions aimed at calibrating topographic slope, saturated hydraulic conductivity, and infiltration parameters, based on physical soil properties and not depending on observed runoff.

Calibrating a complex hydrological model with a large number of parameters by means of only river discharge can be very problematic, particularly because of the known problem of equifinality . Several approaches are adopted to reduce or control this problem, particularly challenging for the emerging fully distributed paradigm in hydrology , either constraining the parameter set by means of various strategies e.g., and/or incorporating different observations than discharge in the calibration process e.g.,. A fully coupled atmospheric–hydrological approach further increases the degrees of freedom of the model, making the issue even more complex. In this study, while the calibration of the hydrological model is performed offline, accounting only for discharges from several cross-river sections, the effect of the resulting parameter set is evaluated considering soil, surface (both in terms of vegetation and hydrology), and atmosphere compartments all together with their reciprocal interactions. Further research will focus on a more thorough analysis of equifinality issues in two-way coupled hydrometeorological models. After several preliminary runs, where the model sensitivity to all the parameters involved in literature calibration procedures is tested, the WRF-H_SA model calibration also follows a two-step approach but in a different sense with respect to . First, the Latin-Hypercube–One-factor-At-a-Time LH-OAT; method is used to determine the sensitivity of a set of eight selected parameters on subbasin river discharge but also to obtain a starting configuration for the automated parameter optimization. The first step includes some iterations to find an optimal threshold value for the delineation of shallow soils on the steep mountain slopes and deeper soils in the plains (see also Sect. ). In the next step, seven sensitive parameters are optimized for the six different subbasin outlets (Fig. b) using PEST . Table  gives an overview of the parameters and their relevance.

The calibration procedure is adopted for the different subcatchments in cascade, starting from upstream (i.e., parameters are first calibrated for Am-OAG, Ach-OBN, and Rt-RST, then for Am-PEI and Ach-OBH, and, finally, for Am-WM; see Fig. b). For LH_OAT the goodness of fit is determined using the volumetric efficiency VE;: 1VE=1-∑|Qobs-Qsim|∑Qobs, where QObs and Qsim denote the observed and simulated discharge in m3 s-1 and NSE is the Nash–Sutcliffe efficiency. PEST optimization relies on an objective function given by the sum of squared deviations between model-generated streamflow and observations. Table  lists the subcatchment-wise calibrated parameters. The optimum slope gradient for the delineation of shallow and deep soil regions is found to be 50 % (22.5∘). Accounting for the shallow mountain slopes considerably improves the hydrographs for Am-OAG and Am-PEI, as it increases underestimated peaks and decreases overestimated retention. A comparison of the respective hydrographs and performance measures for calibration and the validation period is shown in Figs. S1 and S2 in the Supplement. Since the study focuses on land–atmosphere exchange, and river routing has no feedback to the LSM, the channel parameters (geometry and Manning roughness coefficient) are not further optimized with respect to peak timing.

The calibration period length of 3.5 months (15 April–31 July 2015, including 14 d of spin-up) is selected as a compromise between the number of model runs (about 2000, which relates to about 0.32 million core hours for WRF-H_SA), which are required during hypercube sampling and PEST optimization, and the available computational resources.

The hydrographs for the calibration and validation periods of the WRF-H_SA runs are presented in Figs.  and . The final parameter sets and goodness-of-fit measures are listed in Table .

For all subcatchments, reasonable configurations could be determined. However, for the three Ammer subcatchments (OAG, PEI, and WM), it was required to add constant baseflow rates of 2, 4.71, and 5.13 m3 s-1 to the simulated hydrographs, respectively. Adding constant baseflow is justified by the fact that due to the glacial processes of the last ice age, large storage bodies, which dip reversely with the surface elevation, were formed in the mountain valleys by overdeepening . Further downstream, towards the opening of the valley, where the aquicludes reach towards the surface, springs are abundant. The channel inflow from such long-term storage cannot be realized by WRF-Hydro's conceptual bucket scheme. It would require the implementation of a more sophisticated groundwater model. The underestimation of long-term baseflow by the model has no influence on the land-surface–atmosphere exchange, as there is no interaction of the channel routing with the LSM. The amounts for constant baseflow are derived manually after the PEST parameter optimization so that the recession curves of the simulations agree well with the observations. For the Ach and Rott subcatchments channel, baseflow is related to shallow aquifers with shorter residence times which should be solely captured by the model.

Focusing on the values of the calibrated parameters, it can be observed that the surface infiltration parameter REFKDT, as compared to the standard settings in WRF and Noah-MP (e.g., nominal range of 0.5–5.0, according to ; 0.1–0.4, according to ), is rather low (therefore allowing lower infiltration) for all subcatchments except Ach-OBH. The associated LSM surface runoff scaling parameter REFDK is globally set to 2×10-6, as smaller values would have decreased infiltration to even smaller amounts. Also, the percolation parameter SLOPE was mainly reduced as compared to the standard values (0.1–1.0, according to Niu et al., 2011b), meaning that a relatively limited portion of former infiltration excess water is needed to be transferred to the bucket storage to assure good performance for the simulated baseflow. As for the surface overland roughness scaling factors, they generally remarkably increase the standard value of 1.0, contributing to the increase of the hydrograph's lag time and the relative reduction of the peak discharge. The retention depth scaling factors, instead, are much closer to the standard value of 1, varying slowly both the total volumes of the hydrographs and the lag time of the initial response of the catchment to rainfall. The bucket scheme parameters should be evaluated considering their mutual influence on the model exponential equation. In general, the higher the ZMAX value is, the slower the response time of the bucket is, and the higher the COEFF value is, the higher the potential contribution of the bucket model to the total runoff is. From this point of view, the most reactive subcatchment is Am-PEI. In this subcatchment, REFKDT is rather small, and therefore the contribution by the bucket needs to be quicker also because of the rather large subcatchment site. However, this bucket's behavior cannot be appreciated by looking at the hydrographs in Fig.  both because in the simulations the values of the bucket storage height are never close to ZMAX and because the resulting discharge in the graph also depends on the contribution of the upstream catchment Am-OAG. During the PEST automated calibration, some parameters hit a boundary limit of the calibration range, which was previously set starting from the results obtained with the LH-OAT method. For example, the optimized ZMAX values hit the lower boundary for the three upstream catchments. In such cases the constraints were relaxed, allowing the parameters to exceed the previous limits, but if negligible or even null improvements were found, we preferred to come back to the previous borders. Finally, it is noteworthy to highlight that, since the study focuses on land–atmosphere exchange and river routing has no feedback to the LSM, the channel parameters (geometry and roughness coefficient) are not further optimized concerning peak timing.

The calibration performed in the spring and summer of 2015 is validated over the period 1 May–31 October 2016 (Fig. ). The performance statistics for the validation period are comparable to those of the calibration period, and in the cases of Ach-OBN, Am-OAG, and Rt-RST they even improved. For Ach-OBH, as expected due to the disabling of the reservoir option, the buffering effect of the lake cannot be reproduced by the model, thus leading to an overestimation of most of the peak values. However, with respect to the overall discharge in the Ammer catchment, these cutoff peaks are rather small. The performance for Am-WM is lower for both 2015 and 2016, as it aggregates the mismatches of all the upstream subcatchments.

The results of the calibration are in line with other hydrological modeling studies for the Ammer catchment. implemented TOPMODEL Topographical Model; into a SVAT (soil–vegetation–atmosphere transfer) model framework and yielded an NSE of 0.92 for a 1-year simulation on a daily basis for the gauge Fischen (near Am-WM). achieved NSE performances of 0.2 (Am-OAG), 0.42 (Am-PEI), 0.75 (Am-WM), 0.68 (Ach-OBN), and 0.18 (Ach-OBH), using WaSiM-ETH Water Balance Simulation Model; for the year 2001. obtained an NSE of 0.91 with the WRF-Hydro standalone model for Am-PEI, for a 3-month simulation of a major flood event in 2005.

The commonly favored lumped calibration of WRF-Hydro seems to be rather limited, concerning the transferability of parameter sets among subcatchments and with respect to the numerical efficiency for automated calibration. Especially for complex terrain, e.g., as presented by this study, the distribution of discharge gauges does not agree with landscape units. Therefore, the lumped-parameter sets have to unify quite diverse subcatchment conditions which may lead to unrealistic spatial representations of the physical properties they represent. Thus, for further studies, it is recommended to find parameter sets that are bound to landscape characteristics, such as relief, land cover type, and soil features e.g.,, which also contribute to reduce the equifinality problem .

The evaluation of WRF_SA and WRF-H_FC simulations with measurements from the TERENO Pre-Alpine Observatory focuses on the radiation input, its partitioning into water, and energy fluxes at the land surface and on the near-surface atmospheric and subsurface states. Figure  shows the mean diurnal cycles of simulated and observed downward surface shortwave radiation for three TERENO Pre-Alpine Observatory sites for the period June to October 2016.

For all locations, the simulations overestimate radiation from sunrise to sunset with similar magnitude. While correlations for the hourly values are high (r2 for DE-Fen of 0.76, DE-RbW of 0.73, and DE-Gwg of 0.66), the mean errors (MEs in W m-2 for DE-Fen of 61, DE-RbW of 57, and DE-Gwg of 78) reveal considerable bias. Also the mean absolute errors show substantial scatter (MAEs in W m-2 for DE-Fen of 89, DE-RbW of 91, and DE-Gwg of 107). The overestimation of summer shortwave radiation for central Europe with WRF has also been documented by other studies and is usually related to underestimated cloud cover, especially in the mid troposphere, where convection is active . The increased bias for DE-Gwg could be related to local shading due to topography in this narrow Alpine valley and because of higher convective activity in this mountain region. The comparison of the WRF_SA and WRF-H_FC simulations does not yield considerable differences.

The results for downward longwave radiation are given in Fig. .

The negative biases for the different locations (ME in W m-2 for DE-Fen of -14, DE-RbW of -4, and DE-Gwg of -21) correspond with the above-suggested cloud cover underestimation. With -1 % to -6 %, the relative deviations are rather small. Again, the differences between the standalone and coupled models are nominal. A similar overestimation is obtained for total absorbed shortwave radiation (Table S1 in the Supplement). Thus, for the TERENO Pre-Alpine Observatory locations it can be stated that shortwave radiation input to the land surface is overestimated by 33 % to 56 % by both the standalone and coupled models.

The diurnal cycles of latent- and sensible-heat fluxes are presented in Figs.  and for three different grassland sites. Converted evapotranspiration rates are plotted alongside in Fig. . The analysis is split by month from June to October 2016 to provide insight about the temporal variations. The observations comprise data from flux towers and lysimeters. Their spread can be seen as a measure of uncertainty. The measurements for the flux tower at DE-RbW are missing from 25 September to the end of October.

The coupled WRF-H_FC simulation exhibits increased latent- and decreased sensible-heat fluxes for the DE-Fen and DE-RbW sites, whereas WRF_SA and WRF-H_FC are very similar for the Alpine valley location (DE-Gwg). In the case of sensible-heat flux, the hydrologically enhanced model (WRF-H_FC) outperforms or is equal to the standalone simulation (WRF_SA). For latent heat and evapotranspiration, the mean diurnal fluxes are overestimated for DE-Fen for June to August by either both models or the coupled run. A constant positive bias is also found for DE-Gwg (except for October). Tables  and list the performance measures for observations of latent and sensible heat vs. the flux tower for the period June to October 2016; Table  provides the measures for data of evapotranspiration vs. the lysimeter.

For latent heat and likewise evaporation, correlation improves considerably for DE-Fen and DE-RbW with the coupled model, but ME and MAE deteriorate for DE-Fen and DE-Gwg. An overall improvement for WRF-H_FC with respect to the observations is only obtained for DE-RbW. In general, the simulations are in better agreement with the flux-tower data than with those of the lysimeters. This could be related to the difference in spatial support of the measurements. For sensible heat, the coupled run yields improved performance for DE-Fen and DE-RbW and is also in good agreement with the observations at DE-Gwg.

Ground heat flux (Fig. S3) is overestimated by the models from about 2 h after sunrise until noon. From afternoon till dawn, both simulations overestimate the upward (land-to-atmosphere) radiative flux. WRF_SA and WRF-H_FC differ slightly for ground heat fluxes, with WRF-H_FC showing slightly increased performance with respect to the observations (Table S2).

The diurnal course of 2 m air temperature (Fig. S4) is similar for uncoupled and coupled model for June and October for all stations. The mountain peak stations (Kol and LaS) and the alpine valley station (DE-Gwg) are hardly sensitive to coupling. Prominent deviations between WRF_SA and WRF-H_FC occur for July to September at the foreland stations (DE-Fen, DE-RbW, and Ber). Here, the coupled simulations between 06:00 and 18:00 UTC agree better with the observations. Nighttime values are generally overestimated by both models, and coupling does not have an influence. The mean errors improve between 0.34 and 0.6 K for the foreland and between 0.11 and 0.25 K for the mountain stations, whereas correlation remains identical. A slight improvement with coupling is also obtained for the MAE values (Table S3).

Figure  provides the monthly diurnal cycles for the 2 m mixing ratio. The model comparison reveals higher values for the coupled model run, especially during sunshine hours (06:00–18:00 UTC). Also prominent is a peak in 2 m moisture around 17:00 UTC for both models that is not as pronounced in the observations.

For July to August, the coupled simulation resembles the observations better for the morning rise in moisture concentration, but towards the afternoon, the constant rise exceeds the measurements. According to the performance measures in Table , the correlation increases considerably with the WRF-H_FC configuration for the DE-Fen and DE-RbW sites. Also ME and MAE are reduced. For DE-Gwg the findings are similar; however the magnitudes are lower.

Altogether, it can be stated that the hydrologically enhanced setup (i.e., WRF-H_FC) leads to an improved representation of 2 m temperature and mixing ratio.

Observed and simulated soil moisture for the DE-Fen site are presented in Fig. .

The gray ribbons depict the 25th to the 75th percentiles of a wireless soil moisture sensor network that consists of 55 profiles with measurements at 5, 20, and 50 cm depth SoilNet; further details are available at. Obviously, simulations and observation show a considerable offset, and also the temporal variations are much smoother for the model. The discrepancies in the soil moisture time series are largely attributable to the difference in saturation water content. The LSM assumes loam for the DE-Fen site (and almost for the entire area of domain 3) with a maximum volumetric soil moisture content of 44 %, whereas in reality the region consists of sandy-to-silty loams and also peaty areas where the maximum soil moisture ranges between 50 % and 80 %. With WRF-H_FC the soil moisture values are about 8 %–10 % higher than with WRF_SA. Also the decline differs between the two with WRF_SA leading to a much dryer scenario for the summer months. That is where WRF-H_FC-simulated latent-heat flux and evapotranspiration largely outperform. Altogether, for DE-Fen, the decline predicted by WRF-H_FC seems more realistic with respect to the observations. This is also confirmed by the mostly improved statistical measures (Table ). The representation of soil moisture in LSMs is a general challenge. Soil parameters and water content are often tuned to unrealistic values for the sake of obtaining a good matching of the surface exchange fluxes with observations . The recent publications of global and continental high-resolution soil hydraulic datasets like, e.g., are helpful to improve and unify soil moisture representations in those models. However, these datasets, with their underlying water retention models e.g.,, are not supported by the Noah LSMs, and an implementation would be out of the scope of this study.

Figure  visualizes the monthly water budgets for the six different subcatchments for WRF_SA, WRF-H_FC, and WRF-H_SA (standalone WRF-Hydro) simulations, according to the water balance equation P=E+RSF+RUG+ΔSsoil, where P is precipitation, E is evapotranspiration, RSF and RUG are surface and subsurface runoff, and ΔSsoil is soil storage variation.

Deviations in subcatchment-aggregated precipitation are small for WRF_SA and WRF-H_FC. P in WRF-H_SA, which originates from the gridded observation product (RADOLAN), differs for most of the months and regions. WRF_SA and WRF-H_FC overestimate P for the mountainous regions (Am-OAG and Am-PEI) for May and June. For the other subcatchments the months of June to August are mainly underestimated. September and October are well resembled for Rt-RST. For the others, October sums are overestimated. For evapotranspiration E an increasing tendency can be seen from WRF_SA via WRF-H_FC to WRF-H_SA. An underestimated P in WRF_SA and WRF-H_FC results in a decreased E. For the Am-OAG subcatchment, the overestimation in P is transferred to surface and subsurface runoff. This is likely because of the soil moisture in the mountain region is generally higher and E is rather energy limited and therefore cannot increase considerably. Moreover, slopes are steeper, and soil thickness is reduced so that percolation takes place quickly. The variation in soil volumetric water content is irregular among models and for the different months. This indicates a nonlinear feedback for the land–atmosphere interaction. Soil infiltration generally increases with the hydrologically enhanced models; however, the amounts for WRF-H_FC and WRF-H_SA vary according to P. Storage depletion (negative values) does not exhibit any tendency among the different models. Surface runoff (infiltration excess) with WRF_SA is 50 % (for some of the subcatchments more than 100 %) higher than with WRF-H_FC and WRF-H_SA. Conversely, groundwater recharge (soil drainage) increases for the hydrologically enhanced models. Again, differences between WRF-H_FC and WRF-H_SA are due to the individual precipitation amounts. On a monthly scale, changes of the canopy water storage compensate (not shown). The water budget residuals, caused by the subgrid aggregation and disaggregation and by other numerical artifacts, can reach up to 31 mm for WRF-H_FC at Rt-RST in September, but in the mean they are 5.6 mm. Altogether, the coupling with hydrology leads to increased infiltration and slightly increased E but almost no changes in P. A reason for this could be that the distance of the displacement between precipitation generation and falling locations is generally much larger than the one covered by the domain boundaries in this study .

Table  lists the performance measures for the discharge simulated with the fully coupled model (hydrographs available in the Fig. S3) with baseflow-shifted simulations (compare Table , WRF-H_SA calibration) denoted by sh. Nash–Sutcliffe efficiency (NSE) values are poor for all stations; Kling–Gupta efficiency KGE'; values lie between 0.07 and 0.39 with a general performance gain for the baseflow-shifted time series. For all subcatchments except Am-OAG, negative MEs are observed, with values ranging from -22.6 to 2.98 mm per month. For the three Ammer gauges (OAG, PEI, and WM), adding the baseflow shifting leads to an improved baseline of the hydrographs and volumetric efficiency but also to considerable overestimation of the cumulated sums. If the non-shifted MEs for Q are compared with those of P, it turns out that for some of the subcatchments (Am-WM, Ach-OBH, and Rt-RST), the deviations are of a similar amount as precipitation bias. The poor performance of the fully coupled simulation to predict hourly discharge can be clearly mapped to the model's difficulty in reproducing the timing and positioning of precipitation.

Figure  shows the time series of root mean square deviations (RMSDs) of the spatial variograms for the WRF_SA and WRF-H_FC simulations subdivided by the four soil layers in the model. The variograms were computed using 10 equidistant lags of 1 km from 1 to 10 km. The RMSDs were computed for the six different subcatchments; for the Ach, Ammer, and Rott catchments; and for the full domain. For the calculation, the subregions were masked so that the adjacent areas and lakes did not impact the results. The analysis reveals that the structural differences between the two models have their maximum in late summer and fall. Surprisingly, layer 3 gives the strongest variations in spatial patterns. The changes for layers 1 and 2 are not so pronounced. The cause for this might be that the thinner top layers are strongly influenced by precipitation and infiltration processes, and thus the spatial patterns are shaped accordingly. Due to its larger thickness, layer 3 reacts more sluggishly. Thus deviations are more persistent. Layer 4 is even thicker but shows only slight variations over time. It is likely that the free-drainage boundary condition has a regulatory effect here. Also the withdrawal of water for plant transpiration is partly reduced, as only forest land cover classes have roots in this layer per definition. Am-OAG depicts a special case as soil layers are considerably thinner for the steep mountain slopes (see Sect. ). Thus, response times are short, and the routing of infiltration excess water is quickly propagated through all layers. The variability for the united Ach, Ammer, and Rott catchments is less pronounced than seen for the smaller entities, but still the maximums are from late summer to fall, and layer 3 is affected most.