The mesoscale hydrological model is a grid-based, spatially distributed hydrological model driven by daily precipitation, temperature, and potential evapotranspiration (PET). It accounts for major hydrological processes such as snow generation and snowmelt, canopy interception, soil infiltration, ET, deep percolation, baseflow generation, and surface runoff routing. The open-source model code repository is available and is under active development and maintenance (https://git.ufz.de/mhm/mhm, last access: 5 October 2022). The model uses three distinct levels to organize the modeling procedures: level 0 (L0) for input data of the sub-grid physical basin characteristics, level 1 (L1) for the realization of the integrated hydrological processes, and level 2 (L2) for the specification of meteorological forcing inputs. An unique component of mHM is the multiscale parameter regionalization (MPR) technique that allows for the seamless inference of the spatial variability of the required model parameters on various modeling scales. One of the distinguishing aspects of the MPR approach compared to other regionalization techniques is to deliver a quasi scale-invariant model performance across modeling scales and to improve the transferability of model parameters to ungauged basins . The model was applied and evaluated in multiple climatological regions, including Europe , West Africa , India , and the conterminous United States . Within the MPR technique, the subgrid physical basin characteristics at L0 are linked to model parameters through transfer functions and a set of global parameters and are subsequently upscaled to generate effective parameters at L1. The aggregation is based on a set of upscaling rules (e.g., arithmetic or harmonic mean) following flux conservation schemes .

A general overview on the model processes and parameterization can be obtained from and . Only the SM component of mHM is described here, due to its relevance for this study. The incoming precipitation and snowmelt are partitioned into root-zone SM and runoff components, depending on the degree of soil saturation, using a power function similar to the well-known HBV model . The degree of non-linearity depends on the underlying vegetation and soil characteristics following the MPR framework . The evapotranspiration from soil layers is estimated as a fraction of the potential evapotranspiration depending on the SM stress and the fraction of vegetation roots present in each layer . The moisture stress function depends on the specification of soil-water content at a permanent wilting point as well as at critical and saturation levels, which are determined using a set of pedo-transfer functions estimated within the MPR framework .

The new setup GDM-v2-2021, as used in the GDM version 2, includes several changes to the previous model setup GDM-v1-2016. The main features of the two mHM setups that are used in the analysis are described in Table . While the GDM-v1-2016 uses mHM version 5.6, mHM was updated to version 5.10 (see https://github.com/mhm-ufz, last access: 5 October 2022) in GDM-v2-2021. The implemented changes in mHM did not change the hydrological process representations related to SM that were used in the simulations here. Between the setups GDM-v1-2016 and GDM-v2-2021, the projection system was changed from the projected coordinate system Gauss–Krueger 4 (EPSG:31468) to the World Geodetic coordinate system (EPSG:4326). While the size of the grid cells in the GDM-v1-2016 setup was fixed at 4 km × 4 km (L1 level), the grid cell size in the GDM-v2-2021 setup is measured in degrees. As such, the grid cell size varies with latitude, with grid cell width in an east–west direction decreasing from 1.23 km at 47.25∘ N latitude (south of Germany) to 0.98 km at 55.5∘ N latitude (north of Germany) and with a constant grid cell length of 1.7 km in a north–south direction.

Soil texture (sand and clay fraction) and mineral bulk density are derived from national digital soil maps provided by the BGR (Federal Institute for Geosciences and Natural Resources). The BUEK200 dataset used in the GDM-v2-2021 setup substantially increased the mapping resolution compared to the BUEK1000 dataset used in the GDM-v1-2016 setup (scale 1:1000000 to 1:200000). At the time of the creation of this study, the database version of BUEK200 was v0.5. Figure  shows the depth-averaged clay contents for an exemplary region in Central Germany, where SM observations that were used in the analysis are located. The soil map used for the study (BUEK) is the standardized basic soil mapping for Germany. It shows the distribution and association of soils and their properties in Germany. The map content is classified according to soil regions and soil landscapes. For each map unit, a soil series is given, composed of an index soil (dominant soil) and accompanying soils. For modeling, the soil properties of the index soil within the spatial mapping unit were used to derive the model parameters.

The soil depths in mHM are discretized into an upper soil layer at depth 0–25 cm, including a top layer at depth 0–5 cm, and the remaining depth of the soil profile. In the GDM-v2-2021 setup, an additional layer at 25–60 cm was added due to stakeholder feedback, mainly from the agricultural sector. The tillage depth is set to 30 cm in both model setups. The land use datasets used in the model setups GDM-v1-2016 and GDM-v2-2021 were CORINE and GLOBCOVER , respectively. Hydrogeological input data that define the aquifer properties and govern the baseflow recession rates were derived from the HUEK200 database for GDM-v1-2016 and the GLIM database for GDM-v2-2021 . Digital elevation models were derived from and , respectively.

The SM observations used to conduct the model evaluations were gathered from the environmental observation networks TERENO and FLUXNET FLUXNET2015 Dataset; as well as from the Cunnersdorf site operated by the DWD. In total, SM data from 40 locations were compiled and processed for the analysis (see Fig. ). Although it is not feasible to establish an evenly distributed grid of SM measurements on a national level , the available locations cover a wide range of climatic and vegetation conditions in Germany.

In total, we analyzed 46 measurements from 24 grassland sites, 9 crop sites, 6 forest sites, and 1 site containing a forest clearing. Four of the sites have multiple measurement methods available, which allowed for the comparison of the evaluations between the measurement methods at single sites. The elevation ranges from 4 to 1252 ma.m.s.l., and the long-term yearly precipitation sums range from below 500 mm to more than 1500 mm. Time series lengths of the observations are between 2.8 and 17.8 years with a median (mean) of 6.5 (6.7) years. A detailed overview of the location characteristics is shown in Table .

The data is comprised of four different SM measurement methods. SM observations from 7 FLUXNET and 16 TERENO sites in Germany, based on several vertically distributed sensors within one soil profile, were used (in the following abbreviated SPM). The sensor depths are described in Table . SPM sites used from TERENO-Northeast Observatory are further described in and . SM data from lysimeters are available for four sites from the TERENO-SOILCan lysimeter network at the Bad Lauchstädt experimental site and the TERENO Pre-Alpine Observatory (PAO) . Lysimeters are large vessels containing an undisturbed soil column to allow gravimetric measurements. Since the lysimeter vessels are closed at the bottom, water tension is adjusted to reference measurements at the same depth in the undisturbed soil close to the lysimeter . In the lysimeters, SM is measured by single sensors in multiple depths. At each SOILCan-site, multiple lysimeters are organized in hexagons . The number of lysimeters per site are described in Table .

For 3 of the 40 sites (Am Grossen Bruch, Hohes Holz, and Wüstebach), spatially distributed measurements (SDM) of SM are available. Multiple sensors are installed in a spatial grid at different depths, covering an area of some hundreds of square meters. For the locations Hohes Holz and Am Grossen Bruch, 39 and 20 profiles with sensors at multiple depths were used, respectively (depths varied slightly between profiles depending on soil property changes). Therefore, they are not denoted explicitly. For the Wüstebach site, 51 profiles with two sensors each at 5, 20, and 50 cm depth were used . The Wüstebach SM measurement network is described in detail in .

SM observations derived from cosmic-ray neutron sensing (CRNS) stations were used from 17 sites (see Table ) of the TERENO observatories . The soil albedo component of cosmic-ray neutrons is particularly prone to changes of SM . However, since neutrons are sensitive to all pools of hydrogen, the measured neutron signal is also affected by biomass , intercepted water , and snow and therefore requires a correction of the measured signal in this respect. In this study, periods of snow cover have been excluded from the CRNS data. SM from CRNS data has been calculated by standard methods and aggregated to daily time steps. This leads to typical statistical uncertainties of less than 3 vol.% .

All SM data were checked according to their flagging conventions for doubtful or low-quality values. In some cases, doubtful data was removed manually after personal communication from site maintainers (e.g., some sites from the TERENO PAO lysimeter sites showed doubtful data after frost in early 2017). The available SM data in the respective depths, as noted in Table 2, were aggregated to weighted vertical averages according to the soil discretization depths in mHM (0–25, 25–60 and 0–60 cm). Highest weights were allocated when the sensor depth was located in the center of the soil depth range and when weights linearly decreased towards the edges of the soil depth range. The spatial mean values were calculated for the SDM measurements based on the available sensors.

Since the computation of SM drought indices, including the estimation of SM probability distributions by kernel density estimates, is hampered for the available observed data due to the limited length of observed SM data (< 10 years for most locations), the analysis here is based on a comparison of observed to simulated SM e.g.,. It is widely known that absolute SM values cannot be adequately determined by a regional model (partly due to the spatial heterogeneity), yet the hydrological model typically captures the temporal dynamics well . As drought is defined by the deviation from normal conditions, SM anomalies were calculated. To preserve the units of volumetric SM (mmmm-1) and the original range of SM dynamics, standardization by dividing standard deviation was not undertaken in this study. The anomalies are calculated in two ways. First, the mean of all values in each SM time series is subtracted: 1θ(anom)i,k=θi,k-θ‾.

Secondly, the multi-year mean for each day of the year is subtracted to deseasonalize the anomalies. The removal of the annual average cycle of SM is necessary for the subsequent drought classification based on percentile thresholds, as described in the next section. 2θ(deseas-anom)i,k=θi,k-θ‾i,

where i is the calendar day of the year (DOY 1,…,365) and k is the year. To reduce uncertainty in the mean resulting from heterogeneous and small sample sizes, for each i, a moving window with 15 d on each side of the day was used to increase the sample size, and the multi-year mean of each i was calculated based on the mean of 500 randomly drawn bootstrap samples. Since there are some data gaps in the observed data (see Table  for data availability), the simulated data was masked to the available observed data to allow a comparable calculation of SM seasonality. Leap days were removed before calculating the deseasonalized anomalies.

The evaluation of observed against simulated SM is based on the Spearman rank correlation coefficient (R). The Spearman rank correlation coefficient is a non-parametric measure to quantify the strength of the monotonic relationship between two variables. The correlations are calculated on whole data records as well as on sub-periods (months, seasons, and vegetative active period) to investigate the seasonal variability in the performance metrics. Paired Wilcoxon signed rank tests were conducted to identify significant changes between the model setups.

Here, 1.2 km × 1.2 km simulations in two soil layers (GDM-v2-2021) are compared to SM observations using four different measurement methods: cosmic-ray neutron sensing (CRNS), spatially distributed measurements (SDM), single profile measurements (SPM), and lysimeter (LYSI). SM anomalies as well as deseasonalized SM anomalies are used.

Figure  shows the results for three selected locations that contain both CRNS and SDM measurements for the six-year period 2014–2019. In general, the SM anomalies and deseasonalized data agree well, with a small reduction of correlations for the deseasonalized data. Furthermore, observations and simulations agree well both in the uppermost soil layer (0–25 cm) and in the deeper layer (25–60 cm depth). The correlation strength between simulations and observations from different measurement techniques is similar for the sites Am Grossen Bruch and Hohes Holz but deviates more for the Wüstebach site. It is worth noting that different spatial scales are mapped by those measurements. While the SPM (not included here) represents point information, the SDM and CRNS cover an area less than 0.1 km2, and the mHM simulations cover an area of ≈ 1.44 km2. In general, the day-to-day variability is lower in simulations than in observations. At the forest sites Wüstebach and Hohes Holz, the day-to-day variability in the CRNS data is higher than in SDM. Several environmental factors other than SM can influence the CRNS signals (see Methods). While the changing biomass might have a low impact on the signal, it can introduce a (constant) systematic bias. Since only anomalies are analyzed here, the impact of such bias on this (comparative) anomaly analysis should be minimal. Intercepted water on leaves and in the litter layer can be particularly challenging to quantify, especially in forested stations such as Hohes Holz or Wüstebach . It might lead to stronger dynamics in the CRNS signal during and shortly after rain events in comparison to the model output or other observation methods. Additionally, partial deforestation in 2013 at the Wüstebach site modified SM flows, resulting in a stronger response to rainfall . Nevertheless, there is no general tendency for lower correlations at forest sites than at crop and grassland sites (see Fig. ). Crop sites show slightly lower correlations than grassland sites, which is expected, since anthropogenic activities (e.g., crop rotation) are not represented in mHM. Correlations display no clear tendency across the range of elevation and precipitation regimes. In general, Fig.  reveals that the model performance does not systematically depend on site conditions. Moreover, no systematic relationship between correlations and the length of the time series can be found (see Fig. d).

Monthly Spearman correlation coefficients for all locations and measurement methods at 0–25 cm depth are shown in Fig. . The correlation coefficients show an apparent clear seasonal variation, with the highest values in summer and autumn months and the lowest values in winter. The highest median correlation is detected in August (0.87), while the lowest median correlation is found in January (0.37). The spread of the correlation coefficients within the different locations is largest in winter months, with some locations having correlations close to 1.0, while in February and March, some locations with CRNS, SPM, and LYSI measurements show correlations below zero. The intra-annual variation of performance metrics was similar to the findings of , who extensively evaluated simulated SM from four different hydrological models (Noah, Mosaic, SAC, VIC) in the North American Land Data Assimilation System phase 2 (NLDAS-2) dataset, which is used for drought monitoring in the United States and similarly observed generally higher correlations in summer and lower correlations in winter. The lower correlations observed in winter could be related to higher uncertainties in simulations and observations with respect to frozen soils and snow cover. The sensor quality of SDM, SPM, and LYSI in winter can be reduced during frost days. In particular, SPM and LYSI measurements can be affected by sensor failures, as they rely only on a few sensors compared to the spatially distributed measurements (SDM) with a larger number of sensors. Appendix Fig.  shows correlations between simulated SM, CRNS, and SDM. Low correlations between simulations and observations are accompanied by low correlations between the measurement methods, especially in winter. In a climate impact study investigating low flows over Europe, it could be shown that uncertainty due to the selection of the hydrological model dominates the overall uncertainty, including the meteorological drivers in snow-dominated areas . Furthermore, the mHM does not contain a full energy balance model, which limits the description of soil frost depths.

Observations using different SM measurement methods display considerably different correlations. The SPM generally vary more, with large variation in winter and the presence of low-performance outliers in summer months. CRNS measurements show a consistently high performance in summer months but notably low correlations in winter (especially January). As snow days were removed from the time series in the CRNS measurements, the anomaly calculation from the remaining data was impacted by a smaller sample size. Another reason for the lower correlations observed might be due to the variable penetration depth of CRNS, which ranges between 15 to 70 cm depending on SM . This could introduce systematic and temporally variable errors and affect the correlation between observed and simulated soil water content . Comparison to the mHM top soil (0–25 cm) layer is assumed to remain a good compromise, since the soil water distribution is rather homogeneous between 0 and 25 cm under wet conditions. Under dry conditions, the footprint is deeper and more heterogenous, but the highest sensitivity is in the upper soil layers (exponential sensitivity). The SDM measurements show the most consistent performance across all months, with the exception of May, as illustrated in Fig. a. All measurement methods at these sites show a drop in correlations to the SM simulations in May and June, while the observations have higher correlations between each other (see also Fig. ). This points to deficiencies in the model, which may be related to the static vegetation module in mHM, which does not include processes such as possible early onset of the growing season and consequent earlier depletion of the soil water storage. Moreover, lower correlations of deseasonalized anomalies in May are detected, especially at forest locations (median of 0.63 over all forest locations). The timing of leaf unfolding in trees, usually between late April to May , is subject to annual fluctuations and affects evaporation from the soil and therefore SM dynamics. Figure b depicts the SPM data from FLUXNET and TERENO – which cover the time periods 1997–2014 and 2011–2019, respectively – separately. The seasonal variation of the correlations is in good agreement among both monitoring networks and time periods. The performance at TERENO sites is generally higher than at the FLUXNET sites, possibly due to a larger number of sensors installed along the soil depth in the TERENO sites, which may improve the vertical averaging of SM (see Table ).

The Spearman correlation coefficients for each season and soil depth are depicted in Fig. . Note that, here, only locations that have SM data in all depths were considered, and CRNS data were excluded, as its varying penetration depth does not allow a consistent depth-wise evaluation. This leads to a smaller sample size of locations (n = 26). Figure  shows that the median correlation is lower for the deeper SM simulations for all seasons, except for winter. In spring, the lower depth also shows the strongest negative difference to the upper depth in comparison to summer and autumn (spring Δ-0.19, summer Δ-0.12, fall Δ-0.02). The correlations vary more in the 25–60 cm depth between locations in all seasons, with more outliers of very low correlations observed. Since the mHM was conceptualized for dominant processes at the large scale (mesoscale), not all processes that are important at the local scale are currently accounted for (e.g., species-specific root water uptake, lateral flow, or groundwater–soil water interaction). For instance, showed that, for the distributed SM measurements at the Wüstebach catchment, SM dynamics in the topsoil (5–50 cm depth) are influenced by groundwater. Processes of capillary rise are not modeled in mHM; hence, it is expected that agreement to simulated SM by mHM at sites with groundwater influence is lower compared to groundwater-distant sites. This effect should increase with depth due to increasing groundwater influence, which could explain the lower correlations in the 25–60 cm depth. SPM sites might be more affected by this than SDM, in which these effects can be averaged out. Identification of groundwater characteristics at each measurement site was, however, out of scope for this study.

The SDM outperform SPM and LYSI, with higher-than-average correlation values, especially for the 25–60 cm depth, which underlines the assumption that the local characteristics of single sensors – e.g., groundwater influence and the resulting spatial variability of SM – are averaged out over a larger area and generally supports the closer-scale match of SDM measurements and the 1.2 km × 1.2 km simulation grid cells. It has to be noted that the SPM at the same sites as the SDM also show comparable high correlation values (for an overview of the locations, see Table ).

In the following, the comparison between observations and the two model setups GDM-v1-2016 and GDM-v2-2021 (i.e., GDM version 1 and 2) as well as drought metrics between the two simulation setups are shown and discussed. Table  shows the median values of the Spearman correlation coefficients for selected sub-periods (seasons, vegetative active period April–October) and for the full year. Considering the observed SM data from all locations and measurement methods, the median correlations between the two simulation setups increase slightly by +0.05 in GDM-v2-2021. On a seasonal scale, the results show a small decrease in the correlations in spring (Δ-0.03) and summer (Δ-0.01) but a significant increase of correlations in fall (Δ+0.07) and winter (Δ+0.12) in the new model setup. Several of the changes in the model setup may provide explanations for the improved model agreement to observed SM dynamics in fall and winter. The higher modeling resolution of the 1 km runs may better resolve the sub-grid variability of cold-season-related processes, such as snow accumulation, that improve the simulated SM dynamics. In addition, the finer spatial soil texture representation possibly contributes to an improved model representation of soil wetting and drying – e.g., especially during saturated conditions in the cold season. When analyzing the metric over the vegetative and non-vegetative active period (defined as April–October and November–March, respectively), the increase in median correlations is +0.03 and +0.10, respectively. Median correlations using CRNS and SPM measurements support the overall findings. In general, the results show that the CRNS yields higher median correlations than the SPM measurements for both model setups, except for spring. While the median correlation in winter increased by +0.17 between GDM-v1-2016 and GDM-v2-2021 for CRNS, there is only a small increase of +0.03 in correlation for SPM. Similar results showing an overall increase in simulation performance were found by . In their study, the EMCWF operational and re-analysis SM product using the hydrological model H-TESSEL was improved due to changes in the soil hydrology in the model and an increase of model resolution. They concluded that a better representation of soil texture might obtain further improvements. Furthermore, found moderate improvements in the agreement of SM simulations compared to observations through implementing updated soil texture information.

Spearman rank correlations between simulated and observed deseasonalized SM anomalies that fall below the 20th percentile in the observed SM time series are shown in Fig.  to specifically analyze the dry anomaly spectrum. It is important to emphasize that we do not aim to estimate drought periods here, as its solid calculation requires a much longer time series. The drought estimation is performed using histograms for every grid cell and day of the year (see method Sect. 2.4.1). Consequently, estimating robust percentiles requires time series lengths of minimum 30 years – this means that the time series length of the observational data is considered insufficient. Figure a shows a median correlation of 0.61 over all observations in the GDM-v2-2021 setup. The performance in the two model setups remains similar. However, the comparison between the measurements with a larger spatial footprint (SDM, CRNS) and point-scale measurements (SPM, LYSI) shows that the agreement between simulations and the larger footprint observations increased towards the high resolution setup, but the median agreement to the point-scale SM measurement decreased. In general, the measurements with a larger spatial footprint display higher agreement to the simulations. Due to the varying day-to-day variability of SM between the SM observation types and the simulations, in Fig. b, an additional statistical smoothing was applied by calculating a running 30 d mean on the daily SM time series before subtraction of the seasonal SM cycle. This approach is similar to the SM preprocessing for the SMI, as proposed in . Figure b shows that, when smoothing is applied, the agreement between observations and simulations during dry periods can be substantially improved to a median correlation of 0.7 over all observations in the GDM-v2-2021 setup (≈ 1 km resolution). In particular, the agreement between the point-scale measurements and simulations is increased to a median correlation of 0.63 in both model setups.

Next, we contrast the drought characteristics based on the two model setups to assess the differences in drought ranking and the spatial structure of drought events. Annual drought intensities aggregated over Germany based on the daily SMI using simulated SM from 1952–2020 are presented in Fig.  and are grid-based for the last decade in Fig. . Figure  shows only marginal differences between the model setups, which are slightly more prominent in the top soil compared to the total soil column. The model setups largely agree on the three years with the most intensive droughts. The ranking in the top soil during the vegetative active period differs slightly due to the similar drought intensities in the years 1959, 1976, and 2003. The drought years are more pronounced with respect to drought intensities in the GDM-v2-2021 setup in the top soil, but in contrast, the average drought area is estimated to be larger in the GDM-v1-2016 setup in those years. Generally, the classification of drought years aggregated over Germany results in similar estimates using the different operational drought monitor setups.

To assess regional differences in drought characteristics between the model setups, Fig.  shows the drought intensity maps in the vegetative active period for 2011–2020. Drought intensities are more spatially diverse in the GDM-v2-2021 setup, stemming from the higher granularity of the GDM-v2-2021 setup, which includes higher-resolution soil information and less smooth patterns than the GDM-v1-2016. Nevertheless, the general patterns are similar between the two setups. Regionally, large differences can be seen (e.g., the drought intensities in the Swabian and Franconian Jura regions are more pronounced than the neighboring areas in the GDM-v1-2016 setup – see years 2017 and 2019 for the total soil). Additionally, the differences in drought intensities are more pronounced in the total soil column in the last decade, which can be explained by multi-annual, cumulative effects. The current total soil drought lasts, in many regions, for at least three years. In Fig. , the variance between grid cells for drought intensities during the vegetative active period are shown as semi-variograms. In general, the spatial variance is larger in the total soil than top soil. The GDM-v2-2021 setup shows a generally larger spatial variance between grid cells in the top soil and a larger increase with distance (see Fig. a). The spatial variance in the total soil is lower at smaller distances in the GDM-v1-2016 setup but slightly higher at larger distances. Figure b, showing semi-variance normalized by distance, demonstrates that, in the GDM-v2-2021 setup, the distance-normalized variance of drought intensities is increased, especially at small spatial scales in both the top and total soil, indicating larger local differences in response to drought intensities. These findings are in line with , who investigated the influence of different soil databases on resulting hydrologic fluxes. They reported that the higher variability of soil properties in the finer soil database generally resulted in simulations with more variability in (extreme) hydrologic responses.

We would like to highlight that, in our study, several changes besides changing the underlying soil dataset were implemented between the operational model setups, as described in Sect. 2.2. The changes, such as the land use and geology datasets, influence the hydrological simulations, yet they play a minor role for the SM simulations compared to the change in the soil dataset. The SM simulations are not influenced by the geological dataset, because no direct feedback from the saturated aquifer to the SM reservoir is implemented in mHM. To demonstrate the different role of the change in SM dynamics related to the specific soil and land use datasets, temporal correlations between SM from separated model runs fixing all model settings (L1 ≈ 1.2 km × 1.2 km resolution, default mHM parameters), only changing the soil dataset (BUEK200 – BUEK1000), and, in a separate step, only changing the land use dataset (CORINE – GLOBCOVER) are shown in Fig. . The change of the soil dataset has a much larger impact on the SM simulations compared to the change of the land use dataset in these specific model setups. The CORINE and GLOBCOVER land use datasets both already have high horizontal resolutions (≈ 100 and 300 m, respectively). The differences between the land use datasets mostly lie in the subgrid scale of the mHM hydrological modeling resolution and have a minor effect on the upscaled hydrological response at the L1 level (here ≈ 1.2 km × 1.2 km).