In this paper, a Reynolds-averaged Navier-Stokes (RANS) equations solver, interFoam of OpenFOAM®, is validated for wave interactions with a dike, including a promenade and vertical wall, on a shallow foreshore. Such a coastal defence system is comprised of both an impermeable dike and a beach in front of it, forming the shallow foreshore depth at the dike toe. This case necessitates the simulation of several processes simultaneously: wave propagation, wave breaking over the beach slope, and wave interactions with the sea dike, consisting of wave overtopping, bore interactions on the promenade, and bore impacts on the dike-mounted vertical wall at the end of the promenade (storm wall or building). The validation is done using rare large-scale experimental data. Model performance and pattern statistics are employed to quantify the ability of the numerical model to reproduce the experimental data. In the evaluation method, a repeated test is used to estimate the experimental uncertainty. The solver interFoam is shown to generally have a very good model performance rating. A detailed analysis of the complex processes preceding the impacts on the vertical wall proves that a correct reproduction of the horizontal impact force and pressures is highly dependent on the accuracy of reproducing the bore interactions.

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Growing energy demand has increased interest in marine renewable energy resources, i.e. wave energy which is harvested through Wave Energy Converter (WEC) Arrays.
However, the wave energy industry is currently at a significant juncture in its development, facing a number of challenges which require that research re-focuses on a holistic techno-economic perspective, where economics consider the full life-cycle costs of the technology. It also requires development of WECs suitable for niche markets, because in Europe there are inequalities regarding wave energy resources, wave energy companies, national programmes and investments. As a result, in Europe there are leading and non-leading countries in wave energy technology. The sector also needs to increase confidence of potential investors by reducing (non-)technological risks. This can be achieved through an interdisciplinary approach by involving engineers, economists, environmental scientists, legislation, governmental bodies and policy experts. Consequently, the wave energy sector needs to receive the necessary attention compared to other more advanced and commercial ocean energy technologies (e.g. offshore wind).
The formation of the first open pan-European Network on an interdisciplinary approach will contribute to largescale WEC Array deployment by dealing with the current bottlenecks. The WECANet European COST Action, introduced in September 2018 and presented in this paper, aims at a collaborative and inclusive approach, as it provides a strong networking platform that also creates the space for dialogue between all stakeholders in wave energy. An important characteristic of the Action is that participation is open to all parties interested and active in the development of wave energy. Previous activities organised by WECANet core group members have resulted in a number of joint European projects and scientific publications. WECANet’s main target is the equal research, training, networking, collaboration and funding opportunities for all researchers and professionals, regardless of age, gender and country in order to obtain understanding in the main challenges governing the development of the wave energy sector.@en

In this work, internal wave generation techniques are developed in an open source non-hydrostatic wave model (SimulatingWAves till SHore, SWASH) for accurate generation of regular and irregular long-crested waves. Two different internal wave generation techniques are examined: a source term addition method where additional surface elevation is added to the calculated surface elevation in a specific location in the domain and a spatially distributed source functionwhere a spatially distributed mass is added in the continuity equation. These internal wave generation techniques in combination with numerical wave absorbing sponge layers are proposed as an alternative to the weakly reflective wave generation boundary to avoid re-reflections in case of dispersive and directional waves. The implemented techniques are validated against analytical solutions and experimental data including water surface elevations, orbital velocities, frequency spectra and wave heights. The numerical results show a very good agreement with the analytical solution and the experimental data indicating that SWASH with the addition of the proposed internal wave generation technique can be used to study coastal areas and wave energy converter (WEC) farms even under highly dispersive and directional waves without any spurious reflection from the wave generator.@en

Estimation of wave overtopping over the crest of coastal structures is crucial to design effective and cost efficient countermeasures against storms. Semi-empirical formulas are often used for wave overtopping assessment, but they are not always applicable for complex structures which exist in reality (e.g. a storm wall on a dike in a shallow or very shallow foreshore). Detailed numerical models such as Eulerian and Lagrangian RANS models have potential to simulate overtopping of complex coastal structures with good accuracy. However such models require significant computational resources. The use of such models is often not feasible for the design of coastal structures, which often requires multiple iterations and model runs over a reasonably long period of time (e.g. wave trains with 1000 individual waves). In this paper we investigated the applicability of the simplified depth integrated wave transformation model SWASH for wave overtopping estimation of impermeable coastal structures in shallow foreshores. The validation results demonstrate the capability of SWASH to predict mean wave overtopping discharge with good accuracy compared to results from four different overtopping experimental campaigns (comprising 124 individual cases). The overall performance of SWASH to estimate mean wave overtopping discharge is as accurate as those obtained by semi-empirical equations in literature. However, in order to obtain accurate mean wave overtopping discharge with the SWASH model, the incident wave properties at the toe of the dike need to be accurately reproduced. For cases where this is not possible, a correction method is proposed in this paper. Detailed validation of the instantaneous wave overtopping also shows a good agreement with physical model data. In one example, a single, intensive overtopping event was not well resolved by the SWASH model and the instantaneous wave overtopping was under-predicted. However, this did not contribute significantly to the mean wave overtopping discharge. An additional advantage of the SWASH model is that specific coastal structure geometries can be modelled in SWASH if they are not covered by semi-empirical equations. Even in a case with rapidly varied flow (e.g. vertical wall on a dike) the model shows sufficient robustness. In this paper the details on the SWASH model configuration and post processing methods are outlined to enable the reader to reproduce reliable wave overtopping estimation over impermeable coastal structures in shallow foreshores.

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Subsurface flow and storage dynamics at hillslope scale are difficult to ascertain, often in part due to a lack of sufficient high-resolution measurements and an incomplete understanding of boundary conditions, soil properties, and other environmental aspects. A continuous and extreme rainfall experiment on an artificial hillslope at Biosphere 2's Landscape Evolution Observatory (LEO) resulted in saturation excess overland flow and gully erosion in the convergent hillslope area. An array of 496 soil moisture sensors revealed a two-step saturation process. First, the downward movement of the wetting front brought soils to a relatively constant but still unsaturated moisture content. Second, soils were brought to saturated conditions from below in response to rising water tables. Convergent areas responded faster than upslope areas, due to contributions from lateral subsurface flow driven by the topography of the bottom boundary, which is comparable to impermeable bedrock in natural environments. This led to the formation of a groundwater ridge in the convergent area, triggering saturation excess runoff generation. This unique experiment demonstrates, at very high spatial and temporal resolution, the role of convergence on subsurface storage and flow dynamics. The results bring into question the representation of saturation excess overland flow in conceptual rainfall-runoff models and land-surface models, since flow is gravity-driven in many of these models and upper layers cannot become saturated from below. The results also provide a baseline to study the role of the coevolution of ecological and hydrological processes in determining landscape water dynamics during future experiments in LEO.

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Based on a literature overview, this paper summarizes the impact and legacy of the contributions of Wilfried Brutsaert and Jean-Yves Parlange (Cornell University) with respect to the current state-of-the-art understanding in hydraulic groundwater theory. Forming the basis of many applications in catchment hydrology, ranging from drought flow analysis to surface water-groundwater interactions, hydraulic groundwater theory simplifies the description of water flow in unconfined riparian and perched aquifers through assumptions attributed to Dupuit and Forchheimer. Boussinesq (1877) derived a general equation to study flow dynamics of unconfined aquifers in uniformly sloping hillslopes, resulting in a remarkably accurate and applicable family of results, though often challenging to solve due to its nonlinear form. Under certain conditions, the Boussinesq equation can be solved analytically allowing compact representation of soil and geomorphological controls on unconfined aquifer storage and release dynamics. The Boussinesq equation has been extended to account for flow divergence/convergence as well as for nonuniform bedrock slope (concave/convex). The extended Boussinesq equation has been favorably compared to numerical solutions of the three-dimensional Richards equation, confirming its validity under certain geometric conditions. Analytical solutions of the linearized original and extended Boussinesq equations led to the formulation of similarity indices for baseflow recession analysis, including scaling rules, to predict the moments of baseflow response. Validation of theoretical recession parameters on real-world streamflow data is complicated due to limited measurement accuracy, changing boundary conditions, and the strong coupling between the saturated aquifer with the overlying unsaturated zone. However, recent advances are shown to have mitigated several of these issues. The extended Boussinesq equation has been successfully applied to represent baseflow dynamics in catchment-scale hydrological models, and it is currently considered to represent lateral redistribution of groundwater in land surface schemes applied in global circulation models. From the review, it is clear that Wilfried Brutsaert and Jean-Yves Parlange stimulated a body of research that has led to several fundamental discoveries and practical applications with important contributions in hydrological modeling.

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Because of global warming, the hydrologic behavior of the Rhine basin is expected to shift from a combined snowmelt-and rainfall-driven regime to a more rainfall-dominated regime. Previous impact assessments have indicated that this leads, on average, to increasing streamflow by ~30% in winter and spring and decreasing streamflow by a similar value in summer. In this study, high-resolution (0.088°) regional climate scenarios conducted with the regional climate model REMO (REgional MOdel) for the Rhine basin are used to force a macroscale hydrological model. These climate scenarios are based on model output from the ECHAM5-Max Planck Institute Ocean Model (MPI-OM) global climate model, which is in turn forced by three Special Report on Emissions Scenarios (SRES) emission scenarios: A2, A1B, and B1. The Variable Infiltration Capacity model (VIC; version 4.0.5) is used to examine changes in streamflow at various locations throughout the Rhine basin. Average streamflow, peak flows, low flows, and several water balance terms are evaluated for both the first and second half of the twenty-first century. The results reveal a distinct contrast between those periods. The first half is dominated by increased precipitation, causing increased streamflow throughout the year. During the second half of the century, a streamflow increase in winter/spring and a decrease in summer is found, similar to previous studies. This is caused by 1) temperature and evapotranspiration, which are considerably higher during the second half of the century; 2) decreased precipitation in summer; and 3) an earlier start of the snowmelt season. Magnitudes of peak flows increase during both periods, and the magnitudes of streamflow droughts increase only during the second half of the century.@en

Understanding the long-term (interannual-decadal) variability of water availability in river basins is paramount for water resources management. Here, the authors analyze time series of simulated terrestrial water storage components, observed precipitation, and discharge spanning 74 yr in the Colorado River basin and relate them to climate indices that describe variability of sea surface temperature and sea level pressure in the tropical and extratropical Pacific. El Niño-Southern Oscillation (ENSO) indices in winter [January-March (JFM)] are related to winter precipitation as well as to soil moisture and discharge in the lower Colorado River basin. The low-frequency mode of the Pacific decadal oscillation (PDO) appears to be strongly correlated with deep soil moisture. During the negative PDO phase, saturated storage anomalies tend to be negative and the "amplitudes" (mean absolute anomalies) of shallow soil moisture, snow, and discharge are slightly lower compared to periods of positive PDO phases. Predicting interannual variability, therefore, strongly depends on the capability of predicting PDO regime shifts. If indeed a shift to a cool PDO phase occurred in the mid-1990s, as data suggest, the current dry conditions in the Colorado River basin may persist.@en

The hydrological regime of the Rhine basin is expected to shift from a combined snowmelt-rainfall regime to a more rainfall-dominated regime because of climate change, leading to more extreme flood peaks and low flows. Land use changes may reinforce the effects of this shift through urbanization or may counteract them through, for example, afforestation. In this study, we investigate the effect of projected land use change scenarios on river discharge. Sensitivity of mean and extreme discharge in the Rhine basin to land use changes is investigated at various spatial scales. The variable infiltration capacity (VIC) (version 4.0.5) model is used for hydrological modeling forced by a high-resolution atmospheric data set spanning the period 1993-2003. The model is modified to allow for bare soil evaporation and canopy evapotranspiration simultaneously in sparsely vegetated areas, as this is more appropriate for simulating seasonal effects. All projected land use change scenarios lead to an increase in streamflow. The magnitude of the increase, however, varies among subbasins of different scales from about 2% in the upstream part of the Rhine (about 60,000 km₂) to about 30% in the Lahn basin (about 7000 km₂). Streamflow at the basin outlet proved rather insensitive to land use changes because over the entire basin affected areas are relatively small. Moreover, projected land use changes (urbanization and conversion of cropland into (semi)natural land or forest) have opposite effects. At smaller scales, however, the effects can be considerable.

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Hillslopes have complex three-dimensional shapes that are characterized by their plan shape, profile curvature of surface and bedrock, and soil depth. To investigate the stability of complex hillslopes (with different slope curvatures and plan shapes), we combine the hillslopestorage Boussinesq (HSB) model with the infinite slope stability method. The HSB model is based on the continuity and Darcy equations expressed in terms of storage along the hillslope. Solutions of the HSB equation account explicitly for plan shape by introducing the hillslope width function and for profile curvature through the bedrock slope angle and the hillslope soil depth function. The presented model is composed of three parts: a topography model conceptualizing three-dimensional soil mantled landscapes, a dynamic hydrology model for shallow subsurface flow and water table depth (HSB model) and an infinite slope stability method based on the Mohr-Coulomb failure law. The resulting hillslope-storage Boussinesq stability model (HSB-SM) is able to simulate rain-induced shallow landsliding on hillslopes with non-constant bedrock slope and non-parallel plan shape. We apply the model to nine characteristic hillslope types with three different profile curvatures (concave, straight, convex) and three different plan shapes (convergent, parallel, divergent). In the presented model, the unsaturated storage has been calculated based on the unit head gradient assumption. To relax this assumption and to investigate the effect of neglecting the variations of unsaturated storage on the assessment of slope stability in the transient case, we also combine a coupled model of saturated and unsaturated storage and the infinite slope stability method. The results show that the variations of the unsaturated zone storage do not play a critical role in hillslope stability. Therefore, it can be concluded that the presented dynamic slope stability model (HSB-SM) can be used safely for slope stability analysis on complex hillslopes. Our results show that after a certain period of rainfall the convergent hillslopes with concave and straight profiles become unstable more quickly than others, whilst divergent convex hillslopes remain stable (even after intense rainfall). In addition, the relation between subsurface flow and hillslope stability has been investigated. Our analyses show that the minimum safety factor (FS) occurs when the rate of subsurface flow is a maximum. In fact, by increasing the subsurface flow, stability decreases for all hillslope shapes.

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This paper presents a steady-state analytical hillslope stability model to study the role of topography on rain-induced shallow landslides. We combine a bivariate continuous function of the topographic surface, a steady-state hydrological model of hillslope saturated storage, and the infinite slope stability assumption to investigate the interplay between terrain characteristics, saturated storage within hillslopes and soil mechanics. We demonstrate the model by examining the stability of nine characteristic hillslope types (landform elements) with three different profile curvatures (concave, straight and convex) and three different plan shapes (convergent, parallel and divergent). For each hillslope type, the steady-state saturated storage corresponding to given recharge rates is computed for three different average bedrock slope angles. On the basis of the infinite slope stability method, the factor of safety (FS) along the hillslopes is determined. Our results demonstrate that in the steep slopes, the least stable situation occurs in hillslopes with convergent plan shapes and concave length profiles, while the convex ones are more stable. In addition to testing our method for nine characteristic hillslope types, a general relationship between plan shape and profile curvature of landform elements and the factor of safety is derived for a pre-defined hillslope length scale. Our results show that slope stability increases when profile curvature changes from concave to convex. In terms of plan shapes, changing from convergent to divergent, slope stability increases for all length profiles. However, we find that the effect of plan shape is more pronounced for convex length profiles. Overall, we demonstrate that, in addition to bedrock slope, hillslope shape as represented by plan shape and profile curvature is an important control on hillslope stability.

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Recently, D'Odorico and Fagherazzi (2003) proposed "A probabilistic model of rainfall-triggered shallow landslides in hollows" (Water Resour. Res., 39, 2003). Their model describes the long-term evolution of colluvial deposits through a probabilistic soil mass balance at a point. Further building blocks of the model are: an infinite-slope stability analysis; a steady-state kinematic wave model (KW) of hollow groundwater hydrology; and a statistical model relating intensity, duration, and frequency of extreme precipitation. Here we extend the work of D'Odorico and Fagherazzi (2003) by incorporating a more realistic description of hollow hydrology (hillslope storage Boussinesq model, HSB) such that this model can also be applied to more gentle slopes and hollows with different plan shapes. We show that results obtained using the KW and HSB models are significantly different as in the KW model the diffusion term is ignored. We generalize our results by examining the stability of several hollow types with different plan shapes (different convergence degree). For each hollow type, the minimum value of the landslide-triggering saturated depth corresponding to the triggering precipitation (critical recharge rate) is computed for steep and gentle hollows. Long term analysis of shallow landslides by the presented model illustrates that all hollows show a quite different behavior from the stability view point. In hollows with more convergence, landslide occurrence is limited by the supply of deposits (supply limited regime) or rainfall events (event limited regime) while hollows with low convergence degree are unconditionally stable regardless of the soil thickness or rainfall intensity. Overall, our results show that in addition to the effect of slope angle, plan shape (convergence degree) also controls the subsurface flow and this process affects the probability distribution of landslide occurrence in different hollows. Finally, we conclude that incorporating a more realistic description of hollow hydrology (instead of the KW model) in landslide probability models is necessary, especially for hollows with high convergence degree which are more susceptible to landsliding.@en

Recently, we presented a steady-state analytical hillslope stability model to study rain-induced shallow land-slides. This model is based on kinematic wave dynamics of saturated subsurface storage and the infinite slope stability assumption. Here we apply the model to investigate the effect of neglecting the unsaturated storage on the assessment of slope stability in the steady-state hydrology. For that purpose we extend the hydrological model to compute the soil pore pressure distribution over the entire flow domain. We also apply this model for hillslopes with non-constant soil depth to compare the stability of different hillslopes and to find the critical slip surface in hillslopes with different geometric characteristics. In order to do this, we incorporate more complex approaches to compute slope stability (Janbu's non-circular method and Bishop's simplified method) in the steady-state analytical hillslope stability model. We compare the safety factor (FS) derived from the infinite slope stability method and the more complex approach for two cases: with and without the soil moisture profile in the unsaturated zone. We apply this extended hillslope stability model to nine characteristic hillslope types with three different profile curvatures (concave, straight, convex) and three different plan shapes (convergent, parallel, divergent). Overall, we find that unsaturated zone storage does not play a critical role in determining the factor of safety for shallow and deep land-slides. As a result, the effect of the unsaturated zone storage on slope stability can be neglected in the steady-state hydrology and one can assume the same bulk specific weight below and above the water table. We find that steep slopes with concave profile and convergent plan shape have the least stability. We also demonstrate that in hillslopes with non-constant soil depth (possible deep landslides), the ones with convex profiles and convergent plan shapes have slip surfaces with the minimum safety factor near the outlet region. In general, when plan shape changes from divergent to convergent, stability decreases for all length profiles. Finally, we show that the applied slope stability methods and steady-state hydrology model based on the relative saturated storage can be used safely to investigate the relation between hillslope geometry and hillslope stability.

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Characterization of the space-time variability of soil moisture is important for land surface and climate studies. Here we develop an analytical model to investigate how, at the dry-end of the soil moisture range, the main characteristics of the soil moisture field (spatial mean and variability, steady state distribution) depend on the intermittent character of low intensity rain storms. Our model is in good agreement with data from the recent National Airborne Field Experiment (NAFE'06) held in the semiarid Australian Murrumbidgee catchment. We find a positive linear relationship between mean soil moisture and its associated variability, and a strong dependency of the temporal soil moisture distribution to the amount and structure of precipitation.

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We investigate the role of interannual climate variability on spatial soil moisture variability dynamics for a field site in Louvain-la-Neuve, Belgium. Observations were made during 3 years under intermediate (1999), wet (2000), and extremely dry conditions (2003). Soil moisture variability dynamics are simulated with a comprehensive model for the period 1989-2003. The results show that climate variability induces non-uniqueness and two distinct hysteresis modes in the yearly relation between the spatial mean soil moisture and its variability. We demonstrate that the direction of hysteresis is related to a yearly climate index that does not require soil moisture observations.

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Experiments have shown that plants can compensate for water stress in the upper, more densely rooted, soil layers by increasing the water uptake from deeper layers. By adapting root water uptake to water availability, plants are able to extend the period of unstressed transpiration. This strategy conflicts with the approach in many land surface schemes, where plant water uptake is treated as a static process. Here we derive expressions for the typical drydown trajectories of evapotranspiration and soil moisture for both strategies. We show that the maximum difference in evapotranspiration between the two strategies during drydown can exceed 50%. This in turn leads to a difference in root zone soil moisture of up to 25%. The results stress the importance of incorporating realistic root water uptake concepts in land surface schemes.@en

Root zone soil moisture is a key variable in many land surface hydrology models. Often, however, there is a mismatch in the spatial scales at which models simulate soil moisture and at which soil moisture is observed. This complicates model validation. The increased availability of detailed datasets on space-time variability of root-zone soil moisture allows for a posteriori analysis of the uncertainties in the relation between point-scale observations and the spatial mean. In this paper we analyze three comprehensive datasets from three different regions. We identify different strategies to select observation sites. For instance, sites can be located randomly or according to the rank stability concept. For each strategy, we present methods to quantify the uncertainty that is associated with this strategy. In general there is a large correspondence between the different datasets with respect to the relative uncertainties for the different strategies. For all datasets, the uncertainty can be strongly reduced if some information is available that relates soil moisture content at that site to the spatial mean. However this works best if the space-time dynamics of the soil moisture field are known. Selection of the site closest to the spatial mean on a single random date only leads to minor reduction of the uncertainty with respect to the spatial mean over seasonal timescales. Since soil moisture variability is the result of a complex interaction between soil, vegetation, and landscape characteristics, the soil moisture field will be correlated with some of these characteristics. Using available information, we show that the correlation with leaf area index or a wetness coefficient alone is insufficient to predict if a site is representative for the spatial mean soil moisture content.@en

[1] The matter of the efficient and parsimonious parameterization of hillslope subsurface flow remains an important issue in catchment hydrological studies (Brutsaert, 1995). Insights into the influence of the shape and hydraulic characteristics of hillslopes is required to further our understanding and our ability to model catchment hydrological processes. Recently, Troch et al. (2003) introduced the hillslope-storage Boussinesq (HSB) equation to describe subsurface flow and saturation along geometrically complex hillslopes. The HSB equation can be linearized and further reduced to an advection-diffusion equation for subsurface flow in hillslopes with constant bedrock slopes and exponential width functions. This paper presents a dimensional analysis of the latter equation in order to study the moments of the characteristic response function (CRF), corresponding to the free drainage of this type of hillslope. These moments, in a dimensionless form, can be expressed as functions of a similarity parameter, hereafter called the hillslope Péclet number, and a group of dimensionless numbers accounting for the effects of the boundary and initial conditions. The analytical expressions for the first four central CRF moments are derived for two types of initial conditions. The analysis of their respective influences shows that the hillslope Péclet number is an efficient similarity parameter to describe the hillslope subsurface flow response. Moreover, comparison between the CRF moments predicted by means of our similarity analysis and empirical moments derived from outflow measurements for different types of laboratory hillslopes shows good agreement.@en

It has recently been suggested that the bimodality in warm season soil moisture observations in Illinois is evidence of a soil moisture-precipitation feedback. Other studies however provide little evidence for a strong feedback in this region. Here we show that seasonality in the meteorological conditions in combination with the nonlinearity of the soil moisture response alone can induce this bimodality. The existence of preferred wet and dry soil moisture states may have implications for the understanding and modeling of soil moisture dynamics in mid-latitude regions.

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Recently, Troch et al. [10] introduced the hillslope-storage Boussinesq (hsB) equation to describe subsurface flow and saturation along complex hillslopes. They demonstrated that numerical solutions of the hsB equation account explicitly for plan shape of the hillslope, by introducing the hillslope width function, and for profile curvature through bedrock angle and the hillslope soil depth function (see also Paniconi et al. [7] and Hilberts et al. [4]). This paper presents an analytical solution of the linearized hsB equation applicable to hillslopes with constant bedrock slope and exponential width functions. Then, the first four moments of the impulse response function (travel time distribution) of such hillslopes are derived using the Laplace transform of the partial differential equation describing the groundwater flow. These moments are explicitly related to the hydraulic (porosity, conductivity) and geometric (bedrock slope, width function, and soil depth) parameters of a hillslope. The zeroth moment can obviously be interpreted as the total outflow volume, and the (normalized) first moment as the mean response time of the hillslope. The second, third, and fourth moments have interpretations in terms of the relative width, asymmetry, and peakedness, respectively, of the hydrograph. The paper examines the effect of the geometric properties of hillslopes on the travel time distribution in a dimensionless context.@en