[1] Hillslope response to rainfall remains one of the central problems of catchment hydrology. Flow processes in a one-dimensional sloping aquifer can be described by Boussinesq's hydraulic groundwater theory. Most hillslopes, however, have complex three-dimensional shapes that are characterized by their plan shape, profile curvature of surface and bedrock, and the soil depth. Field studies and numerical simulation have shown that these attributes are the most significant topographic controls on subsurface flow and saturation along hillslopes. In this paper the Boussinesq equation is reformulated in terms of soil water storage rather than water table height. The continuity and Darcy equations formulated in terms of storage along the hillslope lead to the hillslope-storage Boussinesq (HSB) equation for subsurface flow. Solutions of the HSB equation account explicitly for plan shape of the hillslope by introducing the hillslope width function and for profile curvature through the bedrock slope angle and the hillslope soil depth function. We investigate the behavior of the HSB model for different hillslope types (uniform, convergent, and divergent) and different slope angles under free drainage conditions after partial initial saturation (drainage scenario) and under constant rainfall recharge conditions (recharge scenario). The HSB equation is solved by means of numerical integration of the partial differential equation. We find that convergent hillslopes drain much more slowly compared to divergent hillslopes. The accumulation of moisture storage near the outlet of convergent hillslopes results in bell-shaped hydrographs. In contrast, the fast draining divergent hillslopes produce highly peaked hydrographs. In order to investigate the relative importance of the different terms in the HSB equation, several simplified nonlinear and linearized versions are derived, for instance, by recognizing that the width function of a hillslope generally shows smooth transition along the flow direction or by introducing a fitting parameter to account for average storage along the hillslope. The dynamic response of these reduced versions of the HSB equation under free drainage conditions depend strongly on hillslope shape and bedrock slope angle. For flat slopes (of the order of 5%), only the simplified nonlinear HSB equation is able to capture the dynamics of subsurface flow along complex hillslopes. In contrast, for steep slopes (of the order of 30%), we see that all the reduced versions show very similar results compared to the full version. It can be concluded that the complex derivative terms of width with respect to flow distance play a less dominant role with increasing slope angle. Comparison with the hillslope-storage kinematic wave model of Troch et al. [2002] shows that the diffusive drainage terms of the HSB model become less important for the fast draining divergent hillslopes. These results VOL. 39, NO. 11, 1316, doi:10.1029/2002WR001728, 2003 have important implications for the use of simplified versions of the H...

[1] The Boussinesq equation for subsurface flow in an idealized sloping aquifer of unit width has recently been extended to hillslopes of arbitrary geometry by incorporating the hillslope width function w(x) into the governing equation, where x is the flow distance along the length of the hillslope [Troch et al., 2003]. Introduction of a source/sink term N allows simulation of storm-interstorm sequences in addition to drainage processes, while a function S c (x) representing the maximum subsurface water storage can be used to account for surface saturation response in variable source areas activated by the saturation excess mechanism of runoff generation. The model can thus simulate subsurface flow and storage dynamics for nonidealized (more realistic) hillslope configurations. In this paper we assess the behavior of this relatively simple, one-dimensional model in a series of intercomparison tests with a fully three-dimensional Richards equation model. Special attention is given to the discretization and setup of the boundary and initial conditions for seven representative hillslopes of uniform, convergent, and divergent plan shape. Drainage and recharge experiments are conducted on these hillslopes for both gentle (5%) and steep (30%) bedrock slope angles. The treatment and influence of the drainable porosity parameter are also considered, and for the uniform (idealized) hillslope case the impact of the unsaturated zone is examined by running simulations for different capillary fringe heights. In general terms, the intercomparison results show that the hillslope-storage Boussinesq model is able to capture the broad shapes of the storage and outflow profiles for all of the hillslope configurations. In specific terms, agreement with the Richards equation results varies according to the scenario being simulated. The best matches in outflow hydrographs were obtained for the drainage experiments, suggesting a greater influence of the unsaturated zone under recharge conditions due to transmission of water throughout the hillslope. In the spatiotemporal water table response a better match was observed for convergent than divergent hillslopes, and the bedrock slope angle was not found to greatly influence the quality of the agreement between the two models. On the basis of the intercomparison experiments we make some suggestions for further development and testing of the hillslope-storage model.

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Abstract. 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. The limited spatial support of observations combined with the large spatial variability of the soil moisture field 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, and we present methods for quantifying the uncertainty that is associated with each 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 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.

Successful dispersal of freshwater sponges depends on the formation of dormant sponge bodies (gemmules) under adverse conditions. Gemmule formation allows the sponge to overcome critical environmental conditions, for example, desiccation or freezing, and to re-establish as a fully developed sponge when conditions are more favorable. A key process in sponge development from hatched gemmules is the construction of the silica skeleton. Silica spicules form the structural support for the three-dimensional filtration system the sponge uses to filter food particles from ambient water. We studied the effect of different hypergravity forces (1, 2.5, 5, 10, and 20 × g for 48 h)—as measure for environmental stress—on the ability of developing sponges to set-up their spiculous skeleton. Additionally, we assessed whether the addition of nutrients (i.e., dissolved 13C- and 15N-labeled amino acids) compensates for this stress. Our results show that freshwater sponges can withstand prolonged periods of hypergravity exposure and successfully set-up their skeleton, even after 48 h under 20 × g. Developing sponges were found to take up and assimilate dissolved food before forming a functional filtering system. However, fed and non-fed sponges showed no differences in skeleton formation and relative surface area growth, suggesting that the gemmules’ intrinsic energy fulfills the processes of skeleton construction. Additionally, non-fed sponges formed oscula significantly more often than fed sponges, especially under higher g-forces. This suggests that the eventual formation of a filtration system might be stimulated by food deprivation and environmentally stressful conditions. These findings indicate that the process of spiculous skeleton formation is energy-efficient and highly resilient. The uptake of dissolved food substances by freshwater sponges may contribute to the cycling of dissolved organic matter in freshwater ecosystems where sponges are abundant.