hydrology of catchments should not be neglected. Bronstert and Plate (1997), Nakayama and

Watanabe (2006) and Sharratt et al. (1999) stated that an accurate forecast of runoff production, both qualitatively and quantitatively, of catchments or hillslopes can only be achieved, if the specific influence of micro-topography in hydrological models is being accounted for.

So far, several modeling studies have addressed the effects of micro-topography on hydrological processes. More conceptual modeling approaches were used in Dunne et al. (1991) to simulate overland flow and infiltration processes for a uniform sinusoidal micro-topography. Spatially-explicit, physically-based approaches focusing on representing overland flow by solving the two dimensional depth-averaged dynamic wave equations were used in Esteves et al. (2000), Fiedler and Ramirez (2000) and Antoine et al. (2009). Spatially-explicit, physically-based and integrated models, which are capable of simultaneously representing surface and subsurface flow processes were used in Qu and Duffy (2007) and Frei et al. (2010). Each of the aforementioned studies represented micro-topography at the plot scale using different geostistical approaches to represent micro-micro-topography like Kriging interpolation (Weiler and Naef, 2003), Gaussian methods (Antoine et al., 2009), a combination of fractal and Markov-Gaussian processes (Abedini et al., 2006) or Markov Chain models of transitions probabilities (Frei et al., 2010). Especially the representation of micro-topographical effects in fully integrated models, were the governing partial differential equations (PDEs) for the overland and subsurface flow domains are solved simultaneously, has proven to be computationally extremely demanding. Frei et al. (2010) for example reported excessively long simulation runtimes of almost two month for solving a yearly modeling scenario. The high effort, necessary to represent micro-topography in spatially-explicit hydrological models, restricts the application to small scales. However, to reduce the computational and numerical complexity and in order to account for micro-topography beyond the plot scale in regional or watershed models, which is necessary for an accurate prediction of runoff production (Bronstert and Plate, 1997, Nakayama and Watanabe, 2006, Sharratt et al., 1999), a new approach in representing micro-topography in numerical flow models is required.

In this study, we want to introduce an approach were micro-topography and its influence on surface and subsurface flow, in numerical flow models, can be represented more efficiently. For that purpose, the study exemplarily uses the synthetic hydrological/biogeochemical wetland model established in Frei et al. (2010) and Frei et al. (in press) as a test case scenario. Frei et al. (2010) investigated surface runoff generation during rainfall events of variable intensity for a small synthetic wetland section with hummocky topography using a fully integrated surface/subsurface flow model. In a second study, Frei et al. (in press) used a coupled hydrological/biogeochemical model to show, that the micro-topographic controlled interactions between fast surface flow and slower matrix flow, can result in quite complex subsurface flow patterns which are responsible for the formation of local

STUDY 3 applying this new approach to models presented in Frei et al. (2010) and Frei et al. (in press), we want to show that important hydrological controls, induced by surface micro-topography, principally can be mimicked by using a, planar model with a lower grid resolution and superimposed, spatially distributed rill storage height variations. Rill storage is a commonly used concept in numerical flow models to account for retention of surface flow due to vegetation or small scale surface properties (Therrien et al., 2008). As part of this study, two plot scale (10m x 20m) flow models with different spatial resolutions, simulating surface and subsurface flow interactions for a common hydrological year, were set up using the rill storage concept to represent micro-topography. The models with planar surfaces and superimposed rill storage height variations are compared to a model, which uses a highly resolved three-dimensional DEM for representation of micro-topography and a planar reference case without rill storage height variations. Specifically we want to show that the introduced rill-storage concept is basically able to (1) mimic the dynamics and spatial patterns of surface flow generation (micro-channeling effects); (2) accurately represent typical subsurface flow patterns and residence time distributions; (3) represent important biogeochemical patterns that are induced by micro-topography (hot spot formation). Findings from this study may help modelers to better account for micro-topography in numerical flow models because the rill storage concept offers possibilities where high model grid resolutions can be circumvented which results in significantly reduced computation times.

STUDY 3

2 Materials and Methods

This study combines numerical flow modeling for integrated simulation of surface and sub-surface flow processes with geostatisitcal indicator simulations to define zones of variable rill storage height to represent surface micro-topography. For the characterization of sub-surface flow patterns, particle tracking was used. Results of the numerical flow model were coupled to a biogeochemical model based on the sequential stream tube approach described in Frei et al. (in press). Detailed information about the numerical flow code, the applied geostatistical approaches and the concept of coupling subsurface hydrology and biogeochemistry are given in Frei et al. (2010) and Frei et al. (in press) and are only briefly summarized in this section.

2.1 Surface/Subsurface Flow Simulations

Surface and subsurface hydrology was simulated for a hypothetical section of a riparian wetland representing a field site in the Lehstenbach experimental catchment in south eastern Germany (Gerstberger, 2001). The numerical code HydroGeoSphere (Therrien et al., 2008), subsequently referred to as HGS, was used to simulate surface and subsurface hydrology. HGS is a fully integrated numerical surface-subsurface flow model, which is increasingly used within the hydrologic/hydrogeologic community. Variably saturated flow in porous media is simulated by solving the Richards Equation in three dimensions. Overland, flow in two dimensions, is implemented using the diffusion wave approximation to the depth averaged dynamic wave equations (Therrien et al., 2008). Coupling of the surface and sub-surface domains is implemented via the conductance concept assuming that the exchange flux depends on the gradient across a coupling interface, the thickness of the interface (coupling length), its relative permeability and the vertical saturated hydraulic conductivity (Therrien et al., 2008). Governing equations for variably saturated subsurface and surface flow are solved simultaneously via a control volume, finite element approach (Therrien et al., 2008). As part of this study, four different flow models were set up using HGS (a summary is given in Table 1):

(1) The micro-topography model, as presented in Frei et al. (2010), uses a geostatisitcally generated DEM representing highly resolved micro-topographical structures (hollow and hummocks). The model was generated for a 10m x 20m domain using a regular finite element grid with an uniform grid spacing of 0.1m in X, Y and Z. The micro-topography model was used as a reference to test the rill storage concept against a model with a highly resolved DEM.

(2) A planar reference model was set up using an identical grid resolution compared to the micro-topography model, but here the model was set up using a planar, inclined surface to represent runoff generation and flow conditions without micro-topographical structures and rill storage height

STUDY 3 (3) The highly resolved, planar model with superficial rill storage height variations (p-rs-high) uses a planar, inclined surface with superimposed, spatially distributed rill storage height variations. This model uses the same grid resolution as the micro-topography model.

(4) The low grid resolution planar model with rill storage height variations (p-rs-low) has a much coarser numerical grid and in contrast to the other models uses irregular finite elements. Average grid spacing was reduced from 0.1 m to 0.4 m leading to a ten fold reduced number of computational nodes (210,000 compared to 20,878).

Table 1: Characteristics of the different flow models used in this study. All models expect for the p-rs-low model use a regular finite element mesh (regular) with 210,000 computational nodes and constant grid spacing of 0.1 m. The p-rs-low model uses an irregular finite element mesh (irregular) with an average grid spacing of 0.4 m and 20,878 computational nodes.

surface type spatial

resolution grid spacing

nodes

reference planar, inclined surface 21m x 10m

x 2m 0.1m (regular) 210,000

STUDY 3