Impact of river water levels on the simulation of stream–aquifer exchanges over the Upper Rhine alluvial aquifer (France/Germany)

Regional alluvial aquifers are characterized by strong interactions between groundwater and surface water (Winter 1999; Woessner 2000; Sanford 2002; Sophocleous 2002; Thierion et al. 2012; Sun et al. 2016). Groundwater feeds rivers during dry periods, while rivers contribute to the recharge of aquifers under conditions of high water level that are associated with large precipitation or snowmelt. These stream–aquifer exchanges make the alluvial hydrosystem vulnerable to pollution by anthropogenic sources. Upward capillary fluxes from shallow groundwater into the unsaturated soil column is also suspected to impact regional climate by modifying the water and energy exchanges between the ground surface and atmosphere, in particular by increasing evapotranspiration (Koster and Suarez 2001; Yeh and Eltahir 2005; Vergnes et al. 2014; Fan 2015; Döll et al. 2016). Therefore, the understanding of these interactions is essential for effective management of water resources as well as for estimating the impacts of anthropogenic activities or climate change.

Stream–aquifer exchanges are complex processes depending on climatic, hydrogeological, and geomorphological conditions (Winter 1999; Sophocleous 2002; Rupp et al. 2008). Their simulation usually requires the use of coupled surface-water/groundwater hydrological models. In general, a two-dimensional (2D) hydrogeological model is coupled to a hydrological model or a hydraulic model. Stream–aquifer exchanges can be represented either through a physically based approach considering the hyporheic zone as a continuum interface, or by using a conductance model (Kollet and Maxwell 2006; Rushton 2007; Flipo et al. 2014). A conductance model computes the flux as the product between a transfer coefficient, depending on the riverbed characteristics, with the hydraulic head gradient between the river and the aquifer—for example, Sun et al. (2016) used the Soil and Water Assessment Tool (SWAT) semi-distributed model to study river water and groundwater exchange in an alluvial plain by using a new module based on conductance. In contrast, Kollet and Maxwell (2006) used an integrated surface-water/groundwater flow model that directly couples the governing equations of overland flow and variably saturated groundwater flow, thereby avoiding the need to define a transfer coefficient. The conductance model is commonly used at regional scale due to its good results with respect to the lower computational burden and the limited number of parameters involved, although the increase of computational capacity tends to make the physically based approach more feasible (Kollet and Maxwell 2006).

A lot of research has been carried out on the determination of the transfer coefficient (Rushton 2007; Fan et al. 2007). Indeed, this parameter represents control of the quantity of water that flows between the stream and the aquifer, and depends on several parameters such as the riverbed permeability or the temperature. Conversely, only a few studies have focused on the representation of the water level of rivers, yet it is a parameter of crucial importance in coupled models—for example, a spurious estimation of the river level may lead to surface-water bodies in the model that do not match their observed position and extent (Käser et al. 2014). Moreover, strong biases between observed and simulated piezometric heads or river water levels can also occur, particularly in alluvial plains where the water table is close to the surface. Even if the representation of river levels is taken into account in some hydrological models (Graham and Butts 2005; Doble et al. 2012, 2014; Zhang and Ross 2015; Thiéry 2015), its influence on the simulated stream–aquifer exchanges and groundwater flooding in regional hydrological modeling is still unclear.

The representation of river levels in coupled hydrogeologic-hydrologic models mainly depends on the way the topography and the river geometry are defined, and on the type of hydrological routing model that is used. In the case where the temporal variability of the river level is neglected, the river level is commonly derived from a digital elevation model (DEM). DEMs give access to the topography at regional scale using either airborne or remote-sensing techniques. In hydrological modeling, they are widely used to delineate watershed boundaries and stream networks. However, they are also associated with systematic errors related to the stream channel geometry (Orlandini and Rosso 1998; Paiva et al. 2011; Brasington et al. 2012; Käser et al. 2014), the presence of vegetation (Kellndorfer et al. 2004), surface-water effects (Schumann et al. 2008) and random noise inherent to the measurement device (Rabus et al. 2003; Sun et al. 2003; Farr et al. 2007; Javernick et al. 2014). These errors typically result in unrealistic slopes along the drainage network and cause unrealistic “pits” (lows) and “dams” (high; Käser et al. 2014). The random noise can influence the simulated stream–aquifer exchanges; therefore, some methods have been proposed to deal with this problem—for example, Paiva et al. (2011) used a low-pass filter for removing the vegetation effect and random noise from the DEM. Moreover, DEMs do not always capture the fine-scale morphological features that are important for certain hydrological processes—for example, breaks-in-slope from weirs and dams of the stream surface are generally associated with the largest errors in DEMs, while they are major drivers of hyporheic exchanges (Heritage et al. 2009; Schäppi et al. 2010; Käser et al. 2014). Lastly, a study conducted by Saleh et al. (2011) over the Oise River catchment in France showed that using fixed river levels in a coupled surface-subsurface hydrological model at a daily time step not only leads to biased assessments of stream–aquifer exchanges, but also to biased estimates of the near river piezometric head distributions.

Taking into account the temporal variability of river levels appears to be essential to improve both stream–aquifer exchanges and near-river piezometric heads. The fluctuations of river levels are commonly simulated either by using a variable velocity algorithm in a hydrological routing model (Saleh et al. 2011; Dai et al. 2015; Häfliger et al. 2015) or by using a hydrodynamic model based on the Saint-Venant equations (Thompson et al. 2004; Saleh et al. 2013; Barthel and Banzhaf 2016). Simulating variable river levels makes the representation of the river geometry essential for studying both flood inundation and stream–aquifer exchanges—for example, any deviation from a vertical representation of banks will increase the area of exchange during a stream flow event (Doble et al. 2012). However, the coarseness of the model resolution and the complexity of the stream channel morphology lead the modelers to use simplified hypotheses that raise new problems in representing these processes—for example, river geometry is often represented as a rectangular cross-section (Käser et al. 2014). In such cases, the unknown parameters refer to the width, the banks, and the bed of the river. At the regional scale, these parameters are often defined through simple geomorphological laws based on available observed datasets (Arora and Boer 1999; Decharme et al. 2008; Vergnes et al. 2014), which are not always appropriate to the geomorphological and climatic context. Moreover, the elevation of the riverbed is often derived from a DEM and therefore shares the associated uncertainties—as an example, Thierion et al. (2012) suggested that the use of spatially homogeneous riverbed parameters leads to smoother spatial variations of the simulated stream–aquifer exchanges along the river network compared to the observed ones.

In this context, the aim of this paper is to quantify how the representation of river levels affects the stream–aquifer exchanges and the groundwater floods in the context of an alluvial aquifer. This study focuses on the Upper Rhine Graben alluvial aquifer known for its strong stream–aquifer interactions (Trémolières et al. 1993) using the hydro(geo)logical modeling platform Eau-Dyssée. This model was first used by Thierion et al. (2012) on the Upper Rhine Graben using fixed river water levels and it is proposed here to use this modeling framework to compare different representations of the river levels in Eau-Dyssée.

All the results shown in this section refer to the whole period of simulation that spans from 1 July 1986 to 31 July 2003. Figures 4 and 5 show the spatial distribution of the biases and the RMSE respectively between the observed and simulated piezometric heads for the four simulations at each of the 190 piezometers. In all, 60% of the PHY piezometric heads range between −1 and 1 m in terms of bias, while 84% have a RMSE score below 1 m (Fig. 4). This percentage decreases to 38.4 and 74% respectively with the PSRTM simulation. This difference is due both to the underestimation of the piezometric heads located in the eastern border of the aquifer and to the overestimation in the south-eastern part of the domain. VMAN and VRC exhibit about 55 and 54% of piezometric heads ranging between −1 and 1 m in terms of bias respectively. These percentages are slightly deteriorated compared to PHY, due to a more pronounced positive bias occurring along the Rhine River when using fluctuating river levels. However, about 84% of the simulated piezometric heads have a RMSE score below 1 m with both VMAN and VRC, which is the same percentage as for the PHY prescribed-values simulation (Fig. 5), which can be explained by the gain obtained with the river fluctuating levels in terms of amplitudes that compensate the more pronounced mean biases. At least, negative and positive biases are present in the south-western and south-eastern part of the aquifer respectively for all the simulations, especially for PSRTM (Fig. 4). These positive biases can be attributed to the uncertainties inherent to the SRTM topographic data as discussed later.

Figure 6 compares the observed and simulated piezometric heads in terms of correlation at each of the 190 selected piezometers. The correlation coefficient corresponds here to the covariance of the simulated and observed piezometric heads divided by the product of their standard deviation. The PHY simulation is given as the reference simulation. Each simulation is then compared to PHY in terms of correlation differences. No significant pattern can be found for PHY, except that the scores are slightly deteriorated near the Rhine River. The PRSTM simulation generally gives poorer results than PHY; however, the VRC and VMAN simulations improve the scores, especially along the Rhine River. In particular, the VMAN simulation gives better correlations in the southern part along the Rhine River; thus, 17% of the scores are improved with VRC and 35% with VMAN.

In Fig. 7, the spatial impact of the river level fluctuations on the distribution of piezometric heads is characterized at each aquifer cell by calculating the temporal mean absolute differences (MAD) between the piezometric heads with and without taking into account water level fluctuations:where H_fix(t_i) (m) is the simulated piezometric head at a given time using a constant river water level corresponding to the PHY simulation, H_var(t_i) (m) is the simulated piezometric head using variable river levels and N is the number of time steps.

The spatial distribution of MAD varies from a few centimeters to more than 1 m. A strong pattern appears at the main confluences between the Rhine River and its tributaries, while the main impact is located along the Rhine River; moreover, the impact of the fluctuating river levels with VMAN concerns a wider area than with VRC.

Figure 8 shows the spatial distribution of biases between the observed and simulated river levels for all the simulations at each of the 37 available gauging stations. In all, 62% (11%) of the PHY (PSRTM) biases range between −1 and 1 m and 19% (60%) are greater than 1 m, which shows that PSRTM strongly overestimates the river levels, whereas 41% (51%) of the VRC (VMAN) biases range between −1 and 1 m, which shows that VMAN better reproduces the mean river levels than VRC. The VRC and VMAN simulations tend to overestimate river levels in the northern part of the aquifer. As previously shown in Fig. 6 for the piezometric heads, Fig. 9 shows the correlation coefficient for PHY and the differences of correlation between PSRTM and PHY, VRC and PHY, and VMAN and PHY. The median correlation coefficients are equal to 0.63, 0.62, 0.66 and 0.68 for PHY, PSRTM, VRC and VMAN respectively. Altogether, 80% of the simulated piezometers have a correlation coefficient greater than 0.42 for PHY, 0.43 for PSRTM, 0.46 for VRC and 0.51 for VMAN. The correlations given in Fig. 9 show that VMAN reproduces the river levels slightly better than VRC. These results agree with the previous comparison of piezometric heads (see Fig. 5); however, they should be treated with caution considering the small number of river level measurements compared to the number of piezometers.

Figure 10a,b focuses on the Ill and the Rhine rivers, respectively, by giving the profiles of the annual mean river levels and the stream–aquifer exchanges estimated by each simulation. Table 1 gives the repartition of the stream–aquifer exchanges between the positive (infiltration toward the aquifer) and negative (aquifer feeding the river) fluxes for both rivers and for each simulation. The PSRTM river level is unrealistic and noisy and hence gives strong variations of the stream surface for both the rivers. These errors lead in turn to noisy stream–aquifer exchanges characterized by strong and unrealistic peaks in the signal. The profiles of the other simulations are smoother due to the moving average filter with a 1.8-km window size applied to the elevation of the river surface. For the Ill River, the profile of the VRC river level is generally higher than VMAN and results in a decrease of the recharge to the aquifer; thus, the VRC stream–aquifer exchange curve is lower than the VMAN curve in Fig. 10a. Upstream, the river exclusively feeds the aquifer (negative flux), while closer to the outlet, the river mostly feeds the aquifer. For the Rhine River, the profiles of the river levels simulated with PHY, VRC and VMAN reflect the channelized shape of the river and its numerous dams. As a consequence, the stream–aquifer exchanges are negative all along the Rhine River, except sometimes in the neighborhood of the dams.

Figure 11 gives the spatial distribution of the mean water-table depths as well as the delineation of the observed wetlands from the RAMSAR and Natura 2000 datasets. The red color corresponds to the simulated groundwater overflow, that is, where the simulated piezometric head is equal to or above the topography. A visual overview reveals that the observed and simulated groundwater overflow agree relatively well for all the simulations except for PSRTM. This is especially the case along the Rhine River. Groundwater flooding is overestimated over the western part of the alluvial plain. To complete these results, the accumulated distribution of the mean water-table depths located over the observed wetlands are plotted in Fig. 12 for each simulation. Wetlands in this area are expected to correspond to areas where groundwater overflows; that is, negative values in Fig. 12. The more the curve is shifted toward the right, the more the simulation agrees with the observed wetlands. The PHY, VMAN and VRC simulations outperform the PSRTM simulation. These results show the importance of representing a more realistic topography when simulating groundwater flooding. The VMAN and VRC simulations give slightly better results than the PHY simulation.

The results presented in this study confirm the importance of a good representation of the river water level in a context of alluvial plains (Käser et al. 2014). Two kinds of improvement were shown to be useful: (1) a finer description of the river topography, and (2) a temporal variation of the river water level. Indeed, a spurious estimation of the river level leads to strong biases in the simulation of the piezometric heads and unrealistic stream–aquifer exchanges. Such spurious estimations are linked to the error regarding specifying the elevation of the river level or its riverbed, due to the noise inherent in the satellite-based DEM used for defining the channel topography (Sun et al. 2003; Kellndorfer et al. 2004; Schumann et al. 2008; Paiva et al. 2011; Käser et al. 2014). In the case of a conductance model, which is commonly employed in regional hydrogeological models, these noises strongly affect the sign of the hydraulic head gradient between the river and the aquifer. In this case, this leads to strong unrealistic negative (the rivers feeds the aquifer) or positive (the aquifer feeds the rivers) peaks, as shown in Fig. 10. Since the stream–aquifer exchanges represent about 80% of the total recharge over the Upper Rhine aquifer (Thierion et al. 2012), these topographic errors can be the source of strong biases when simulating groundwater.

In order to avoid these errors, two corrections were applied. First, a low-pass filter was applied in order to obtain a continuous downstream slope along the drainage network (Paiva et al. 2011; Käser et al. 2014). This helps to suppress the unrealistic peaks of stream–aquifer exchanges and, in turn, to reduce the biases between the observed and simulated piezometric heads. Secondly, a fine-tuned river level was chosen along the Rhine River. This new river level takes into account the numerous dams built along the Rhine River and therefore allows one to simulate more realistic stream–aquifer exchanges. Indeed, the Rhine River has been strongly channelized in order to avoid groundwater flood inundation. As a consequence, the infiltration through the bottom of the Rhine riverbed became the main process for feeding the groundwater stream (Trémolières et al. 1993). The simulated stream–aquifer exchanges should be negative all along the Rhine River. In this study, this is the case for all the simulations in Fig. 10 except the PSRTM simulation. Moreover, the corrected topography allows one to improve the strong positive biases of piezometric heads simulated with PSRTM and located over the southeastern part of the aquifer. These improvements are only due to a lower river level defined for PHY on the first tributary of the Rhine shown in green in Fig. 13 and illustrate the importance of choosing a well-defined river water level in regional hydrogeological modeling.

The fluctuations of the river levels affect the simulation of the piezometric heads. Whatever the method used (rating curves or Manning’s formula), the comparison between observed and simulated piezometric heads is improved with respect to the simulations with fixed river levels (Fig. 5) and shows the relevance of the geomorphological relationships based on observations that are proposed in this study to determine the elevation of the riverbed (Eq. 8). Nevertheless, the Manning formula seems to give better results than the rating curves. Indeed, the correlations computed for the piezometric heads and the river levels are better with VMAN than with VRC; moreover, the fluctuating river levels of VMAN have a more pronounced effect on the piezometric heads than VRC (Fig. 7). These differences are mostly due to the fact that the rating curves cannot be defined for all the river cells because of the lack of observations for some rivers or tributaries (see Fig. 2). Conversely, the computation of the fluctuating river levels is possible on all the cells with the Manning formula; however, the Manning formula seems to overestimate the simulation of the river water levels, in particular for the Rhine River (see Fig. 10). Such behavior can be attributed to the uncertainties remaining on the hypothesis for defining the cross section of the river and the geomorphological parameters (width, elevation of the riverbed, slope and Manning’s coefficient). Moreover, the Rhine River is strongly anthropized and the river discharge is influenced by the numerous dams, thresholds, and human withdrawals—for example for supplying the needs of nuclear plants.

The fluctuating river water levels also affect the simulation of the surface-water/groundwater interactions. The recharge from the river to the aquifer is slightly increased (see Table 1). Moreover, the agreement between the observed wetlands and the simulated groundwater overflows appear to be better. These elements confirm the relevance of the corrections applied to the topography as well as the new geomorphological relationship describing the elevation of the riverbed. This study also points out the need for data to better estimate the river levels at regional scale, both for parameterizing the models and evaluating the simulated hydrological variables. Such need could be fulfilled by the future Surface Water and Ocean Topography satellite mission, which will provide estimations of land surface water with a spatial resolution of about 50–100 m (Häfliger et al. 2015; Biancamaria et al. 2016).