1. Introduction
Numerical atmospheric models generally consider terrestrial hydrological processes as only being vertical, in order to estimate the surface heat fluxes for constraining the atmospheric lower boundary condition. This is, for example, the case for the Weather Research and Forecasting (WRF) Model (Skamarock and Klemp 2008) coupled with the Noah land surface model (LSM; Chen and Dudhia 2001). In this approach, the lateral redistribution of soil moisture according to the topography and groundwater depth is, however, neglected. To relax this constraint and better represent soil moisture spatial variability, coupled atmospheric–hydrological models have been developed in recent years (e.g., Maxwell et al. 2007, 2011; Anyah et al. 2008; Gochis et al. 2015; Rahman et al. 2015; Wagner et al. 2016; Larsen et al. 2016).
The initiation and development of moist convection is sensitive to thermally induced wind circulations originating from the spatial variability in surface heat fluxes (e.g., Pielke 2001). Soil moisture heterogeneities can generate such circulations (e.g., Chen and Avissar 1994; Cheng and Cotton 2004; Taylor et al. 2007; Rieck et al. 2014). Coupling the Advanced Regional Prediction System (ARPS; Xue et al. 2000) with a three-dimensional and variably saturated groundwater flow model (ParFlow; Jones and Woodward 2001) for an idealized case study, Maxwell et al. (2007) found a shallow water table–induced circulation that impacted the location of convective cells after a 36-h run. Coupling WRF with the Hydrological Modeling System (HMS; Yu et al. 2006), Wagner et al. (2016) investigated groundwater effects on surface and atmospheric variables in a catchment of southeast China for an 8-yr period. Comparing WRF and WRF-HMS precipitation results, basin-averaged differences were minor, although spatial redistribution on the order of ±5% occurred. Rahman et al. (2015) simulated two convective events in western Germany with the Terrestrial System Modeling Platform (TerrSysMP; Shrestha et al. 2014), a version of the COSMO model coupled with ParFlow. They performed ensemble simulations based on perturbed initial conditions, with and without groundwater coupling. Their ensemble mean results supported the fact that groundwater dynamics noticeably affects soil moisture, surface fluxes, convective initiation, and the precipitation amounts. Recently, Larsen et al. (2016) brought evidence that including groundwater feedbacks in an atmospheric model can reduce the difference between simulated and observed seasonal precipitation, at least in the case of a river basin in Denmark.
Senatore et al. (2015) applied WRF and its hydrologically enhanced version, that is, WRF-Hydro (Gochis et al. 2015), to a catchment in southern Italy for a 3-yr period. Senatore et al. (2015) concluded that the lateral redistribution of soil moisture additionally resolved in WRF-Hydro reduced surface runoff and increased soil moisture amounts and drainage. However, the change in precipitation between WRF and WRF-Hydro was modest due to strong oceanic and orographic forcing in their study region. Differences between WRF and WRF-Hydro seasonal precipitation were also small in the case of a steep catchment at the foothills of Mount Kenya, East Africa (Kerandi et al. 2018). In West Africa, Arnault et al. (2016) found that the impact of overland flow and runoff–infiltration partitioning on precipitation was scale dependent, that is, much more noticeable in a 100 × 100 km2 domain, but not in a 500 × 2500 km2 domain. WRF-Hydro also produced daily discharge moderately close to observations according to the Nash–Sutcliffe model efficiency coefficient (NSE; Nash and Sutcliffe 1970): 0.27 in the case of Senatore et al. (2015), 0.43 in the case of Arnault et al. (2016), and 0.02 in the case of Kerandi et al. (2018).
The above studies show that the representation of terrestrial water flow indeed impacts the surface fluxes and planetary boundary layer (PBL) dynamics, thus potentially influencing precipitation. The representation of PBL dynamics in atmospheric models, through turbulence parameterization, also influences precipitation. However, it is unknown if the uncertainty in the representation of terrestrial water flow increases the precipitation spread originating from PBL scheme uncertainty.
This study addresses the precipitation sensitivity to the uncertainty in the representation of terrestrial water flow for central Europe during the warm season April–October 2008. An ensemble of WRF and WRF-Hydro simulations is performed based on various turbulence parameterization schemes and a varied runoff–infiltration partitioning parameter. The uncertainty in the representation of terrestrial water flow is accounted for by comparing simulations with a varied runoff–infiltration partitioning parameter and by comparing WRF and WRF-Hydro simulations. The first objective of this study is to assess the respective impacts of the uncertainties in turbulence parameterization and terrestrial water flow representation on precipitation. The second objective is to assess if these impacts depend on the weather regime (e.g., Barthlott et al. 2011; Keil et al. 2014) or the spatial variability in surface fluxes (e.g., Pielke 2001). The third objective is to assess the skill of the WRF and WRF-Hydro simulations in reproducing observed daily precipitation, as well as observed daily discharge for WRF-Hydro. The method to address these objectives, including the models used, the ensemble strategy, the observational validation dataset, and quantitative metrics, is detailed in section 2. Results are given in section 3, and a summary and perspective are finally provided in section 4.
2. Method
a. Modeling approach: WRF and WRF-Hydro setups
The WRF Model (Skamarock and Klemp 2008) and the hydrologically enhanced version of WRF, that is, WRF-Hydro (Gochis et al. 2015), are used to simulate the regional land–atmosphere system over central Europe and investigate the impact of terrestrial water flow representation uncertainty on precipitation. The simulation period is from 1 January to 31 October 2008, with the first three months being considered for spinup time. Initial and lateral boundary conditions of the regional model are provided by the 6-hourly operational analyses (OP) at 0.125° resolution from the European Centre for Medium-Range Weather Forecasts (ECMWF).
In both WRF and WRF-Hydro setups the equations of atmospheric motion are solved at a time step of 10 s on a rotated grid of 0.025° (2.8 km) horizontal resolution centered over central Europe and slightly larger than that used in the Consortium for Small Scale Modeling (COSMO-DE) setup (Baldauf et al. 2011; Gebhardt et al. 2011) (see Fig. 1a). The topography is derived from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) global digital elevation model (GDEM; NASA 2015). The vertical coordinate is a terrain-following hybrid pressure coordinate (Skamarock and Klemp 2008), with 50 vertical levels and a pressure top at 10 hPa. Subgrid processes additionally parameterized are the longwave and shortwave radiative fluxes [Mlawer et al. (1997) and Dudhia (1989), respectively], cloud microphysics (Hong and Lim 2006), atmospheric turbulence, and surface heat and moisture fluxes as follows.
(a) Terrain elevation (m MSL) of the 2.8-km-resolution WRF domain. The height scale is given by the colored bar to the right. The curved black lines delineate the coast and the political boundaries. (b) As in (a), but for the routing grid at 280-m resolution coupled with the WRF domain in the WRF-Hydro setup. The thin black lines show river channels with a Strahler stream order above 4. The bold black lines delineate the river basins considered in this study, labeled with numbers 1–5. Each of these basins is also named by the juxtaposition of its river and outlet name, as 1) Rhine–Koeln, 2) Weser–Liebenau, 3) Elbe–Neu Darchau, 4) Danube–Kienstock, and 5) Inn–Passau. The area covered by these five river basins is called area A. It is noted that the Inn–Passau river basin is part of the Danube–Kienstock river basin.
Citation: Journal of Hydrometeorology 19, 6; 10.1175/JHM-D-17-0042.1
Three different PBL schemes are considered for the parameterization of turbulence: the Asymmetrical Convective Model version 2 (ACM2) scheme of Pleim (2007), the Mellor–Yamada–Janjić (MYJ) scheme of Janjić (1994), and the Yonsei University (YSU) scheme of Hong et al. (2006). This is to generate the model ensemble detailed in section 2b. These three particular PBL schemes have already been considered for evaluating turbulence parameterization uncertainty in WRF ensembles (e.g., García-Díez et al. 2013).
Surface fluxes are calculated with the Noah LSM predicting soil temperature and soil moisture in a 2-m-depth, four-layer column and taking into account vegetation effects (Chen and Dudhia 2001). Albedo, vegetation fraction, and leaf area index (LAI) are taken from satellite-derived climatology (Csiszar and Gutman 1999; Gutman and Ignatov 1998; Kumar et al. 2014), whereas other land surface and soil parameters are assigned for each land category and soil texture from the GlobCover2009 land cover map (Arino et al. 2012) and the Harmonized World Soil Database (HWSD; FAO/IIASA/ISRIC/ISS-CAS/JRC 2012), respectively. It is noted that the conversion table of Smiatek (2014) is used to translate GlobCover2009 and HWSD original classes into WRF Preprocessing System indexes.
In the WRF-Hydro setup, which also includes the Noah LSM as in the WRF setup, the atmospheric grid at 2.8-km resolution (Fig. 1a) is coupled with a terrestrial subgrid at 280-m resolution including a river network (Fig. 1b) in order to route surface water WS overland, soil moisture in the subsurface, and stream water in the river channels (Gochis et al. 2015). The time step to resolve these terrestrial processes is set to 10 s, as for the atmospheric processes. Technically, WS and soil moisture are conservatively disaggregated on the terrestrial subgrid, routed, and aggregated back to the atmospheric grid each time step. The topography of the terrestrial subgrid is derived from the ASTER dataset. The river network is obtained with ArcGIS software using the Catchment Characterization and Modeling version 2.1 (CCM2) database (de Jager and Vogt 2010). It is emphasized that this WRF-Hydro setup allows for reinfiltration, that is, WS infiltrating at a later time step eventually at a different grid point, and exfiltration, that is, WS originating from water excess in a fully saturated soil column. The WS reaching a river channel grid point in the terrestrial subgrid is finally removed from the land and added to the water in the river channel. The part of WS contributing to the river flow stands for the surface runoff RS [Eq. (2)] in the WRF-Hydro setup and is added to the model outputs (as in Arnault et al. 2016). This allows us to define a WRF-Hydro-derived terrestrial water budget equation as in Eq. (2), in which the storage term ΔS also includes the surface water change ΔWS.
In the WRF-Hydro setup, the river water volume is routed on a pixel-by-pixel basis using a diffusive wave formulation allowing for backwater effects. Channel parameters, including the initial river head, bottom width, and side slope of the river channel, and Manning’s channel roughness coefficient are prescribed as functions of Strahler stream order (Strahler 1957). In comparison to other WRF-Hydro studies (e.g., Yucel et al. 2015; Arnault et al. 2016; Kerandi et al. 2018), the Manning coefficients used here have been decreased for calibration purposes, ranging from 0.35 at the order 1 to 0.03 at the order 8. Otherwise, the further channel parameters are default. The WRF-Hydro model could also be further calibrated with respect to discharge, by tuning land surface and soil parameters such as, among others, the stomatal resistance, surface roughness, and the soil’s hydraulic conductivity, which are currently assigned as a function of land category and soil texture. However, this study focuses only on the runoff–infiltration partitioning parameter as it plays the key role for surface water retention and subsequent redistribution by the lateral routing components of WRF-Hydro. Investigating the impact of further parameters would be beyond the scope of this article.
Surface variables, including those in the budget equation [Eq. (2)], are stored at an hourly interval, as well as the geopotential heights at 500 hPa and the convective available potential energy (CAPE). For WRF-Hydro, terms of Eq. (3) are additionally saved on the terrestrial subgrid at a daily interval.
b. Ensemble strategy
There is a potential link between terrestrial water flow, soil moisture, surface fluxes, PBL dynamics, and precipitation (e.g., Chen and Avissar 1994; Cheng and Cotton 2004; Taylor et al. 2007; Maxwell et al. 2007; Rieck et al. 2014; Senatore et al. 2015; Rahman et al. 2015; Arnault et al. 2016; Wagner et al. 2016; Larsen et al. 2016; Kerandi et al. 2018). A comparison between the respective effects of terrestrial water flow and PBL dynamics uncertainty could provide further insight on the precipitation sensitivity to terrestrial water flow.
Accordingly, the following WRF/WRF-Hydro ensemble is constructed in order to allow for a comparison between turbulence and terrestrial water flow uncertainty effects. The WRF and WRF-Hydro setups of section 2a are run for the three PBL schemes, ACM2, MYJ, and YSU, and for two values of k [Eq. (1)], that is, k = 1 and k = 3, with 3 being the default value. The two values for k represent the terrestrial water flow uncertainty in the vertical, the two models, WRF and WRF-Hydro, represent the contribution of lateral flow to terrestrial water flow uncertainty, and the three PBL schemes represent the turbulence parameterization uncertainty. This makes an ensemble (ENS) of 12 members: six WRF members and six WRF-Hydro members. Figure 2 provides a conceptual view of ENS. The ensemble subsets of the members using the PBL scheme X are called ENS(X), where X stands for ACM2, MYJ, or YSU. The ensemble subsets of the members using k = 1 and k = 3 are called ENS(k = 1) and ENS(k = 3), respectively, whereas those of the WRF and WRF-Hydro members are called ENS(WRF) and ENS(Hydro), respectively.
Conceptual view of the members of the ensemble ENS presented in section 2b. Each member is named according to the model used [WRF (W) or WRF-Hydro (H)], the PBL scheme used [ACM2 (A), MYJ (M), or YSU (Y)], and the value of the parameter k (1 or 3). The links between the members, colored in red, blue, and green, represent the three groups of ensemble subsets used for the computation of the normalized precipitation spreads SPBL, Sk, and SHydro, respectively (see section 2e).
Citation: Journal of Hydrometeorology 19, 6; 10.1175/JHM-D-17-0042.1
A so-called control ensemble, similar to ENS except for the initial time, is generated, in order to evaluate the magnitude of random noise in the model results. Here, we arbitrarily choose to initialize this control ensemble on 2 January 2008.
c. Validation datasets
Precipitation ensemble results are validated with the E-OBS gridded precipitation product PEOBS from the European Climate Assessment and Dataset project (Haylock et al. 2008). The PEOBS product is available daily on a grid at 0.25° resolution. As remarked by Haylock et al. (2008), PEOBS is the product of an interpolation method that has been designed to facilitate the comparison with regional climate models at the same spatial scale.
Daily discharge QGRDC from the Global Runoff Data Center (GRDC 2013) is also considered in this study for validating the results from the WRF-Hydro hydrological extension. The selected stations are Koeln, Liebenau, Neu Darchau, Kienstock, and Passau, located at the rivers Rhine, Weser, Elbe, Danube, and Inn, respectively (see Fig. 1b). The covered basin areas are referred to as Rhine–Koeln (144 × 103 km2), Weser–Liebenau (20 × 103 km2), Elbe–Neu Darchau (131 × 103 km2), Danube–Kienstock (96 × 103 km2), and Inn–Passau (28 × 103 km2), respectively. The total area covered by these five river basins has a size of about 625 km × 625 km and is named area A. This set of river basins has been chosen as it covers a large part of central Europe, that is, area A (Fig. 1b), and allows us to test WRF-Hydro for different catchment sizes in various hydrological environments: a mixed high–low mountainous region (Rhine–Koeln, Danube–Kienstock, Inn–Passau) and low mountainous region (Weser–Liebenau, Elbe–Neu Darchau).
d. Continuous ranked probability score
It is noted that the unit of the CRPS is identical with that of daily precipitation, which in our case is millimeters per day. One could decide to normalize the CRPS [Eq. (4)] by the observed daily precipitation in order to have a dimensionless score. However, such a normalized CRPS would be improper as it would favor forecast distributions that unduly emphasize low precipitation events, and therefore become misleading (Lerch et al. 2017).
e. Normalized ensemble spread
f. Weather regime dependence
In regional atmospheric modeling, internal processes uncertainty preferentially affects precipitation during weak synoptic forcing episodes (e.g., Stensrud et al. 2000; Keil et al. 2014). The question here is, if the precipitation sensitivity to the uncertainty in the representation of terrestrial water flow also depends on the level of synoptic forcing.
Parameter 
In this study the weather regime dependence is tested for the contribution of the terrestrial water flow representation uncertainty to the normalized ensemble spread of daily precipitation. As in Keil et al. (2014), hourly CAPE and P are convolved with a Gaussian kernel of half-width size of 56 km before computing an hourly value for 
g. Surface flux spatial variability dependence
As for 
The fact that HENS is computed in a similar manner as 
3. Results
a. Model validation
In this section the performance of the ensemble and ensemble subsets (section 2b) in reproducing the synoptic dynamics from the input ECMWF OP, and the observational products PEOBS and QGRDC (section 2c), is investigated.
1) Synoptic-scale dynamics
Synoptic dynamics is assessed here with the geopotential heights at 500 hPa called Z500, as usually done in midlatitude meteorology (e.g., Holton 2004). Figure 3a displays the 6-hourly evolution of the area A–averaged Z500 from the ECMWF OP, that is, Z500ECMWF, and from the ENS members, that is, Z500ENS. It shows that Z500ENS remains close to Z500ECMWF, and that there is not much variation between ENS members. This is confirmed by the 6-hourly evolution of the spatial root-mean-square error (RMSE) between these two quantities, with values between 5 and 30 m (Fig. 3b). The small spread of Z500ENS at the 6-h time scale suggests that the simulation domain (Fig. 1a) is small enough that the boundary conditions effectively control the synoptic-scale dynamics of the solution in the interior of the domain.
(a) The 6-hourly time series of the geopotential height Z500 at 500 hPa spatially averaged in area A (see Fig. 1b), from the ECMWF operational analyses (Z500ECMWF, black line) and from the ENS members (Z500ENS, red line). The range in the red line represents the spread between the ENS members’ results. The x axis gives the time (days) from 1 Apr to 31 Oct 2008, and the y axis gives the height (m). (b) As in (a), but for the spatial RMSE between Z500ECMWF and Z500ENS.
Citation: Journal of Hydrometeorology 19, 6; 10.1175/JHM-D-17-0042.1
2) Mean precipitation
The mean precipitation of the ensemble PENS, as well as that of the ensemble subsets PENS(ACM2), PENS(MYJ), PENS(YSU), PENS(k=1), and PENS(Hydro), are averaged for the simulation period April–October 2008 and are compared with the observation PEOBS in Fig. 4. Averaged PEOBS is above 3 mm day−1 in the southern high mountainous region of area A, and below 3 mm day−1 in the lower regions to the north. This spatial distribution is qualitatively reproduced by PENS (cf. Figs. 4a and 4b), although with a mean overestimation of 23%. This overestimation is mainly distributed in the southeastern half of area A, and particularly in the upper Elbe River basin, where the difference-to-observation value reaches 100% (Fig. 4c).
(a) Average precipitation P (mm day−1) for the period April–October 2008 in area A (see Fig. 1b), derived from the mean of the ENS members. The scale is given by the colored bar to the right of the panel. (b) As in (a), but from the observational dataset E-OBS. (c) As in (a), but for the normalized difference (%) between ENS derived and observed P. (d)–(h) As in (c), but between the ENS(ACM2), ENS(MYJ), ENS(YSU), ENS(k = 1), ENS(Hydro), and ENS member means, respectively. See section 2b for details about the subscripts. All plotted data in this figure are resampled at a resolution 10 times that of WRF, that is, 28 km, in order to facilitate the comparison between modeled and observed quantities.
Citation: Journal of Hydrometeorology 19, 6; 10.1175/JHM-D-17-0042.1
YSU mainly increases the average precipitation, while ACM2 mainly decreases it and MYJ has a mixed effect (Figs. 4d–f). However, these PBL effects are much smaller than the difference to PEOBS (cf. color scales in Figs. 4c and Figs. 4d–f). The change in average precipitation for the period April–October 2008 induced by modifications in the representation of terrestrial water flow ranges from −5% to +5% (Figs. 4g,h), which is comparable to that obtained by Wagner et al. (2016). However, this is smaller than the change induced by the PBL scheme, that is, ranging from −20% to +20%.
3) Daily precipitation
The skill of the ENS members in reproducing daily PEOBS is assessed with the continuous ranked probability score CRPSENS defined in section 2d [Eq. (6)] and displayed in Fig. 5a. In average for the period April–October 2008, CRPSENS is above 2 mm day−1 in the southern high mountainous region of area A and below 2 mm day−1 in the lower regions to the north. This pattern is similar to that of the ensemble mean precipitation PENS (cf. Figs. 4b and 5a), so that the lowest ensemble skill is associated with the highest precipitation, mainly in the high mountainous region. On average over the entire area A, CRPSENS is about 1.5 mm day−1 (Table 1).
(a) As in Fig. 4, but for the CRPS (mm day−1) [Eq. (6)] of the whole ensemble ENS averaged for the period April–October 2008. (b)–(l) As in (a), but for the normalized difference (%) between the CRPS of ensemble subsets and CRPSENS. The data displayed in each panel are spatially averaged in area A and arranged in Table 1.
Citation: Journal of Hydrometeorology 19, 6; 10.1175/JHM-D-17-0042.1
The first row shows the CRPS (mm day−1) [Eq. (6)] of the whole ensemble ENS, averaged in area A (see Fig. 1b) and for the period April–October 2008. The remaining rows show the difference (%) between the CRPS of each ensemble subset and CRPSENS. The ensemble subset ENS(Hydro, k = 1) giving the lowest averaged CRPS is bolded. The values provided in this table are derived from the data displayed in Fig. 5.
The ability of each PBL scheme to improve the ensemble skill is investigated and is shown in Figs. 5b–d, displaying the respective relative differences between CRPSENS(ACM2), CRPSENS(MYJ), CRPSENS(YSU), and CRPSENS. All three of the PBL ensemble subsets have a CRPS that is substantially higher than CRPSENS. This indicates that even the best PBL subensemble is inferior to the ensemble containing all three PBL schemes in terms of probabilistic skill. Overconfidence is known to penalize the probabilistic skill of an ensemble (e.g., Weigel et al. 2008). Accordingly, each PBL ensemble subset appears to be overconfident, and the full ensemble reduces this overconfidence.
The impact of the other ensemble subsets on the CRPS, that is, ENS(WRF, k = 1), ENS(WRF, k = 3), ENS(Hydro, k = 1), ENS(Hydro, k = 3), is investigated in Figs. 5e–h. These panels show that each of these ensemble subsets has a CRPS slightly smaller than that of ENS. This means that an ensemble subset considering the three PBL schemes, but only one value for k, and only one model, that is, WRF or WRF-Hydro, has a better skill than the full ensemble itself. Accordingly, following Weigel et al. (2008), considering only one option for the representation of terrestrial water flow reduces the overconfidence of the ensemble. Table 1 further shows that the ensemble subset using WRF-Hydro and k = 1, that is, ENS(Hydro, k = 1), exhibits the lowest CRPS, with an induced area-average diminution of −5.5%.
The robustness of this result is assessed in a bootstrap approach by computing the CRPS based on 100 randomly selected days instead of the full period April–October 2008. Reconducting this random evaluation one thousand times, it is found that ENS(Hydro, k = 1) exhibits the lowest mean CRPS in 90% of the cases. This suggests that the skill of a WRF ensemble can be improved by considering several atmospheric turbulence parameterization options, but only one best option for the terrestrial water flow representation, which in this case is WRF-Hydro with k = 1.
4) Basin-averaged results
Basin-averaged daily time series of PENS in the river basins Rhine–Koeln, Weser–Liebenau, Elbe–Neu Darchau, Danube–Kienstock, and Inn–Passau are close to those of PEOBS (Fig. 6), with a correlation coefficient r between 0.67 and 0.91 and a mean difference-to-observation value between +12% and +39% (Table 2). This is in agreement with the precipitation overestimation discussed in section 3a(2) (see Fig. 4c). The timing of the daily peaks is generally well captured, and there is not much difference in terms of daily variation among ENS members’ basin-averaged precipitation time series (see range of the red lines in Fig. 6).
Daily time series of precipitation P (mm day−1) from E-OBS (black line) and from the ENS members (red line), spatially averaged in the river basins shown in Fig. 1b: (a) Rhine–Koeln (1), (b) Weser–Liebenau (2), (c) Elbe–Neu Darchau (3), (d) Danube–Kienstock (4), and (e) Inn–Passau (5). The range in the red line comes from the spread between the ENS members’ results. Statistics related to these time series are provided in Table 2.
Citation: Journal of Hydrometeorology 19, 6; 10.1175/JHM-D-17-0042.1
Statistics between simulated and observed basin-averaged daily times series of P and Q shown in Figs. 6 and 7 sorted by basins. For P the range of the correlation coefficient r and bias (%) originating from the ENS members is indicated; for Q it is the range of the NSE, which is indicated.
WRF-Hydro produces daily time series of discharge QENS(Hydro) moderately close to that observed at the outlets of the five selected river basins (Fig. 7), with a mean difference to observations between −39% and +17% and an NSE value ( Nash and Sutcliffe 1970) generally above 0.3 (Table 2). This is comparable to what has previously been obtained with WRF-Hydro (e.g., Yucel et al. 2015; Senatore et al. 2015; Arnault et al. 2016; Kerandi et al. 2018), but noticeably lower to what is usually obtained with traditional “uncoupled” hydrological models in part because the meteorological forcing is prescribed in this latter case (e.g., Newman et al. 2015; Zink et al. 2017). Indeed, the quality of the WRF-Hydro discharge not only depends on the simulated amount of basin-averaged precipitation (Fig. 6), but also on the spatial distribution of simulated precipitation within the basin, which is challenging for an atmospheric model. It is also acknowledged that the discrepancies between simulated and observed discharge in Fig. 7 may also be related to 1) distributed parameters not properly calibrated for this particular application, such as the unsaturated hydraulic conductivity, surface roughness or stomatal resistance, and 2) the relatively short 3-month spinup time considered in this study for snow and soil moisture in deeper soil layers to reach equilibrium. Still, it is of high interest to assess how well the coupled WRF-Hydro modeling system is able to reproduce observed streamflow at respective gauge locations.
As in Fig. 6, but for specific discharge Q (mm day−1) from GRDC and from the ENS(Hydro) members at the outlet of the river basins shown in Fig. 1b: (a) Koeln (1), (b) Liebenau (2), (c) Neu Darchau (3), (d) Kienstock (4), and (e) Passau (5).
Citation: Journal of Hydrometeorology 19, 6; 10.1175/JHM-D-17-0042.1
The best discharge result is obtained for Elbe–Neu Darchau, that is, NSE > 0.8, with a peak in late April 2008 probably related to snowmelt, and a slow descent afterward (Fig. 7c). The Weser–Liebenau’s discharge has a similar temporal variation, although in this case QENS(Hydro) largely underestimates the baseflow contribution from June to October 2008 (Fig. 7b). NSE is accordingly smaller, with values above 0.39. This could be related to a relatively large contribution of soil water older than 3 months in the case of the Weser–Liebenau discharge, which would require a longer spinup time in order to be properly taken into account. Danube–Kienstock and Inn–Passau’s discharge displays many more peaks, which makes hydrological modeling in these basins more challenging. Parts of these two river basins are located in a high mountainous region where fast surface runoff generation during a storm event is more likely to occur. Peaks simulated in QENS(Hydro) are still relatively close to those in QGRDC (see Figs. 7d,e), as deduced by a NSE above 0.3. Finally, concerning the discharge of Rhine–Koeln, QENS(Hydro) displays such peaks as well, in relation to an upper catchment area also in the high mountainous region. However, these peaks are not in QGRDC, with this last one also displaying a higher base flow (see Fig. 7a). These discrepancies are confirmed by relatively low NSEs, between 0.0 and 0.39 (Table 2), and could be related to the fact that the storing influence of lakes is not taken into account in WRF-Hydro, as it is known that Lake Constance and the lakes of the Swiss Alps in the Upper Rhine attenuate the flood peaks in the Lower Rhine (e.g., Lohre et al. 2003; Bronstert et al. 2007). Such a smoothing is not seen in the case of the Danube–Kienstock and Inn–Passau discharge, which is potentially explained by the fact that these two basins do not have a lake as big as Lake Constance.
b. Relative impact of terrestrial water flow representation on land surface variables
In coupled hydrological models, the consideration of terrestrial water flow primarily modifies the distribution of soil moisture and surface fluxes (Maxwell et al. 2007; Senatore et al. 2015; Rahman et al. 2015; Arnault et al. 2016; Wagner et al. 2016; Larsen et al. 2016; Kerandi et al. 2018). In the following, this impact is discussed with the terrestrial water budget [Eq. (2)] and river water budget [Eq. (3)]. Figure 8a displays daily time series of the terms of Eq. (2) spatially averaged in area A (see Fig. 1b) and derived from the mean of ENS members. It shows that ΔS and RS mainly follow the daily variations of P, whereas E and RG have a much smoother temporal variation. The differential daily time series between the mean of ENS(k = 1) [ENS(Hydro)] and ENS members are displayed in Fig. 8b (Fig. 8c) and summed in Table 3. Figures 8b and 8c show that daily changes in ΔS mainly counterbalance those in RS. Parameters E and RG are not much affected on the daily scale, but noticeable changes in the total sums are found (see Table 3). The increase of ΔS is associated with an increase of E, RG, and P, whereas the decrease of ΔS is associated with a decrease of E, RG, and P. However, the impact of modified terrestrial water flow representation on the average precipitation in area A is small: ±2 mm over 631 mm for the considered time period, which is about ±0.3% (Table 3).
(a) Daily time series of the terms (mm day−1) of the soil water budget [Eq. (2)], that is, precipitation P, surface evaporation/sublimation E, surface runoff RS, ground runoff RG, and soil water storage ΔS, spatially averaged in area A (see Fig. 1b) and derived from the ENS members mean. (b) As in (a), but from the difference between ENS(k = 1) and ENS member mean. (c) As in (a), but from the difference between ENS(Hydro) and ENS member mean. Temporal sums of the displayed data are provided in Table 3.
Citation: Journal of Hydrometeorology 19, 6; 10.1175/JHM-D-17-0042.1
Temporal sums for the period April–October 2008 of the terms of the terrestrial water budget [Eq. (2)] spatially averaged in area A and displayed in Fig. 8, averaged for all the ensemble members in the first row. The second and third rows show the difference between ensemble subsets and the whole ensemble. The values are in millimeters.
The robustness of the above result is assessed by comparing with the control ensemble result. In the control ensemble the total sum of precipitation is increased by about 0.25%, which gives the magnitude of random noise. The change in precipitation induced by modifying the representation of terrestrial water flow is slightly larger than this random noise. According to a standard t test, the change is significant only at the p > 0.1 level. This confirms that the terrestrial water flow uncertainty has a reduced and barely significant impact on the total sum of precipitation in area A. In the control ensemble, we find that modifying the representation of terrestrial water flows induces a change in ΔS, E, RG, and P of the same sign and with a similar amplitude as in Table 3 (not shown). In terms of physical processes, this suggests that some of the water evaporating from the surface in area A falls back in area A as precipitation, so that changing the amount of surface evaporation by decreasing surface infiltration or enabling lateral terrestrial water flow would have a direct effect on the amount of precipitation.
Figure 9a displays daily time series of the terms of Eq. (3) spatially averaged in area A (see Fig. 1b) and derived from the mean of ENS(Hydro) members. It shows the contributions of RS and RG to daily discharge generation in area A. Isolated peaks in simulated Q are mainly related to RS. The river water storage term ΔWR acts as a buffer and smooths the Q isolated peaks with respect to those of RS. This smoothing can be further calibrated with the Manning roughness coefficients, which are currently specified as a function of stream order.
(a) As in Fig. 8a, but for the terms of the river water budget [Eq. (3)], that is, river discharge Q, surface runoff RS, ground runoff RG, and river water storage ΔWR, derived from the ENS(Hydro) member mean. (b) As in (a), but from the difference between ENS(Hydro, k = 1) and ENS(Hydro) member mean. Temporal sums of the displayed data are provided in Table 4.
Citation: Journal of Hydrometeorology 19, 6; 10.1175/JHM-D-17-0042.1
Decreasing k to 1 slightly increases RS, although the associated increase in Q is partly counterbalanced by a smaller decrease in RG (Fig. 9b, Table 4). However, the impact of decreasing k on the area-average discharge is small: +2 mm over 182 mm for the considered time period, which is about +1.1% (Table 4). As a side note, this is a noticeable difference with West Africa, where Arnault et al. (2016) found that the amount of simulated discharge was tightly related to the value of k.
c. Relative impact of terrestrial water flow representation on precipitation
The impact of terrestrial water flow representation is further discussed with the normalized ensemble spreads of daily precipitation SENS, SPBL, Sk, and SHydro (see section 2e), displayed in Fig. 10 as averaged maps for the period April–October 2008. Parameter SENS is generally between 0.5 and 0.8 in the central and northern parts of area A but is below 0.5 in the southern part in association with a strong orographic forcing on precipitation there.
(a) As in Fig. 4, but for the normalized spread of daily precipitation SENS [Eq. (7)] averaged for the period April–October 2008 and computed and displayed at the original resolution of WRF, that is, 2.8 km. (b)–(d) As in (a), but for the normalized difference (%) between the normalized spreads SPBL, Sk, and SHydro from groups of ensemble subsets [Eq. (8), Fig. 2] and SENS.
Citation: Journal of Hydrometeorology 19, 6; 10.1175/JHM-D-17-0042.1
Parameter SPBL is generally slightly lower than SENS (Fig. 10b), with an area-average difference of about 5%. In comparison, Sk and SHydro are much lower (see Figs. 10c,d), with an area-average difference of about 40%–50%. This shows that the uncertainty in the modeled atmospheric turbulence is largely dominating the full ensemble spread SENS and that the averaged contribution of the terrestrial water flows representation uncertainty to this variability is 5%. The reduced spread between the ensemble members using the same PBL scheme is in accordance with the fact each of the PBL ensemble subsets ENS(ACM2), ENS(MYJ), and ENS(YSU) is overconfident in comparison to the full ensemble ENS and that ENS is overconfident in comparison to each of the ensemble subsets that consider only one terrestrial water flow option, as discussed in section 3a(3).
Parameter SENS is much closer to SPBL in the southern part of area A, suggesting that a strong orographic forcing inhibits the impact of terrestrial water flow representation uncertainty on precipitation. The largest impact occurs in the central and northern parts, where SENS locally exceeds SPBL by 5%–20% (Fig. 10b). Accordingly, the uncertainty in the representation of terrestrial water flow preferentially affects precipitation in regions with moderate topography. The next sections investigate if the sensitivity of precipitation to terrestrial water flow uncertainty varies from day to day, potentially in relation with the weather regime and surface flux spatial variability.
d. Role of weather regime
The weather regime dependence of SPBL, Sk, and SHydro is investigated with the daily convective adjustment time scale averaged for the ENS members in area A, referred as 
(a) Scatterplot between daily values of the convective adjustment time scale 
Citation: Journal of Hydrometeorology 19, 6; 10.1175/JHM-D-17-0042.1
The red bold plus signs in Fig. 11 indicate the days when area-average SENS exceeds area-average SPBL by more than 20%. These are the days when the precipitation sensitivity to the uncertainty in the representation of terrestrial water flow is most noticeable. According to the red bold plus signs in these scatterplots, these days are mostly associated with a weak synoptically forced weather regime (
e. Role of surface flux spatial variability
The surface flux spatial variability dependence of SPBL, Sk, and SHydro is investigated with the surface flux spatial heterogeneity averaged for the ENS members, referred as HENS (section 2g). Figure 11b displays the scatterplot between daily values of HENS and SPBL. The correlation is close to that obtained in previous section, with a R2 of 0.40. A similar correlation is obtained for Sk and SHydro (not shown). This means that internal processes uncertainty preferentially affects precipitation when surface flux spatial variability is high. The fact that the coefficient of determination in Fig. 11a is close to that in Fig. 11b further suggests that surface flux spatial variability is as important as the weather regime to explain the precipitation ensemble spread driven by model physics.
As in Fig. 11a, the red bold plus signs in Fig. 11b indicate the days when area-average SENS exceeds area-average SPBL by more than 20%. It is noted that these days are associated with relatively large values of HENS, that is, above 0.15 mm day−1 km−1, whereas the total range of HENS values spreads from 0 to 0.4 mm day−1 km−1. This result suggests that, in central Europe, the uncertainty in the representation of terrestrial water flow most noticeably affects precipitation preferentially when surface flux spatial variability is high.
4. Summary and perspective
This study addressed the precipitation sensitivity to the uncertainty in the representation of terrestrial water flow in central Europe. For this purpose, an ensemble of WRF and WRF-Hydro simulations was generated for the period April–October 2008, using the COSMO-DE grid at 2.8-km resolution and ECMWF operational analyses as forcing data, taking into account turbulence uncertainty with three PBL parameterization (ACM2, MYJ, or YSU schemes), and vertical water flow representation uncertainty with two values for the runoff–infiltration partitioning parameter k, that is, 1 and 3. The contribution of lateral flow to the uncertainty in the representation of terrestrial water flow was considered by comparing the WRF and WRF-Hydro simulations.
Enabling lateral terrestrial water flow in WRF-Hydro generally increased soil moisture, surface evaporation, and precipitation in the study region, whereas these variables were generally decreased by reducing the runoff–infiltration partitioning parameter. However, a similar precipitation change was found by changing the initial time of the ensemble, which confirmed that the total sum of precipitation in the study region was not much affected by terrestrial water flow uncertainty. The fact that the change in surface evaporation and precipitation were in phase, both in the ensemble and in the control ensemble, is thought to be related to regional precipitation recycling.
The impact of these terrestrial water flow effects on precipitation was evaluated with the normalized ensemble spread. The full ensemble spread was largely dominated by the uncertainty in the modeled atmospheric turbulence. On average for April–October 2008, the difference between the full and turbulence-uncertainty-driven ensemble spread was about 5%, which was considered to be the averaged effect of terrestrial water flow representation uncertainty. This averaged effect was found to be inhibited over steep terrain, but enhanced in regions where topography is moderate. Special attention was drawn to the days when the normalized ensemble spread of the full ensemble was about 20% higher than that originating from turbulence parameterization uncertainty. These particular days were associated with relatively high values of the convective adjustment time scale and surface flux spatial variability. It was therefore concluded that the uncertainty in the representation of terrestrial water flow is more likely to noticeably affect precipitation when the weather regime is weakly synoptically forced and surface flux spatial variability is high. As 1) the additional description of lateral terrestrial water flow noticeably increases the normalized ensemble spread in certain conditions and 2) the WRF-Hydro coupled modeling system allows us to describe this lateral flow at a moderate computational cost, we argue that WRF-Hydro is suitable for ensemble forecasting.
Further focus of the study was on assessing the skill of ensemble members in reproducing the E-OBS daily precipitation product. Spatially averaged daily time series of E-OBS precipitation in five large river basins in central Europe were approximately well reproduced, with a correlation coefficient above 0.67. Precipitation was on average overestimated between +12% and +39%. As for the normalized ensemble spread, modifying the representation of terrestrial water flow had much less impact on the average precipitation amount than the choice of the PBL scheme. The ensemble skill in reproducing E-OBS daily precipitation was further evaluated with the CRPS. The ensemble subset considering the three PBL schemes, but only the WRF-Hydro model and the value of 1 for k provided the lowest CRPS (highest ensemble skill). The decrease of probabilistic skill, or increase of confidence, for the ensemble subsets considering several terrestrial water flow options is coherent with the reduced ensemble spread induced by the terrestrial water flow uncertainty. Future studies should investigate if for other years and/or other regions the skill of a WRF ensemble is also improved by considering several atmospheric turbulence parameterization options, but only one best option for the representation of terrestrial water flow.
Finally, the WRF-Hydro ensemble driven by ECMWF operational analyses showed diverse skills in reproducing streamflow in large European river basins, with NSE ranging from 0 to 0.91. Future research with WRF-Hydro could also focus on an enhanced calibration of the various distributed land surface and soil parameters and the use of multiyear spinup to investigate the potential of further improvement in reproducing streamflow.
Acknowledgments
This research is part of the subproject “A5-The role of soil moisture and surface- and subsurface water flows on predictability of convection” of the Transregional Collaborative Research Center SFB/TRR 165 “Waves To Weather” funded by the German Science Foundation (DFG). ECMWF operational analyses were obtained within the framework of a special project at the ECMWF. WRF and WRF-Hydro simulations were performed on the computational resource ForHLR I funded by the Ministry of Science, Research and the Arts Baden-Württemberg and DFG (Deutsche Forschungsgemeinschaft). We acknowledge the P-EOBS dataset from the ECA&D project (http://www.ecad.eu) and the Q-GRDC dataset from the Global Runoff Data Center (http://www.bafg.de/GRDC/EN/Home/homepage_node.html). Special thanks go to Christian Barthlott for providing COSMO static input data; George Craig, Stephan Rasp, Michael Riemer, and Lotte Bierdel for fruitful discussions about skill scores; Gerhard Smiatek, Dominikus Heinzeller, Christof Lorenz, Patrick Laux, Thomas de Couet, Carsten Maas, Hartmut Häfner, and Christoph Sörgel for the logistic and computer support; and two reviewers for helping to clarify the manuscript.
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