3.3 Subsurface Residence Times Distribution

Fractal scaling and power law distributed residence times have been shown to be a common characteristic of many hydrologic systems, which is partly caused by the effects of topography at various scales. Power law distributed residence times were reported for subsurface flow processes over a wide range of scales, from streambeds (10⁰m) up to the continental scale (10⁶ m) (Kollet and Maxwell, 2008b). Compared to other common distribution models for residence times, like exponential or advection/dispersion models, the power law distribution has a long tail reflecting very long sub-surface residence times. Figure 6 shows the estimated subsurface residence times for the four different flow models. The subsurface residence times, estimated for the micro-topography model, can be well approximated with a power law distribution (R²=0.9188). Subsurface residence times for the planar reference model apparently follow a different kind of distribution as indicated by the worse approximation with the power law distribution (R²=0.6377). Similar as observed for small scale in-channel bedforms (Cardenas, 2008), the hummocky topography of riparian wetlands and its effect on subsurface flow processes, leads to power law scaling of residence times. By replacing the three- dimensional micro-topography with distributed rill storage height zones, subsurface residence times remain power law distributed as indicated by the good fit of the p-rs-high model (R²=0.9002). Slopes of the fitted distributions for the micro-topography and the p-rs-high model (A=-1.1849 and -1.1729) lie within the range of reported values (between -1.088 and 1.28) for hydrological systems showing fractal behaviour (Haggerty et al., 2002, Cardenas, 2008). However, compared to the micro-topography model, smallest subsurface residence times (0-20 days) are underrepresented in the distribution of the p-rs-high model and maximum observed subsurface residence times are higher (5,700 days compared to 7,200 days). For the p-rs-low model, residence times still show a very good fit to a power law distribution (R²=0.87) but seem to be shifted towards higher residence times as indicated by the slightly flatter linear slope (A=-0.8671), which might be explained by the reduced grid resolution where only 1,898 individual subsurface flow path lines were evaluated (one path line per surface node) compared to 21,000 path lines for the p-rs-high model.

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Figure 6: Estimated subsurface residence time distributions for the different flow models. Residence times estimated for the micro-topography model and the rill storage height models show a good fit (R²) to a power law distribution (red line as shown using a double logarithmic scale). The fitting parameters represent the linear slope (A) and the center distance to the x-axis (B). Residence time distribution estimated for the planar reference do not follow a power law distribution as indicated by the bad fit.

3.4 Biogeochemical Process Patterns

For a hummocky wetland, Frei et al. (in press) showed that local biogeochemical hot spots, for specific redox-sensitive processes, are generated because of the complex subsurface flow patterns and the non-uniform exposure to different hydrological and biogeochemical boundary conditions.

Formation of local hot spots formation for the micro-topography model is shown in Figure 7. Hot spots for reduction processes (e.g. de-nitrification, sulfate or iron reduction) are preferentially generated below hummock structures because here, infiltrating water is rich in oxidized species (e.g.

nitrate, sulfate or iron(III)) which are being depleted under anaerobic conditions (Frei et al., in press).

Below depressions, reduction processes are inactive because the upwelling water is already in a reduced condition which means that no oxidized species are available for reduction processes.

However, upwelling water is rich in reduced species like sulfide or iron(II) and below depressions, these reduced species may get in contact with atmospheric oxygen. This is the reason why local hot

STUDY 3 spots for oxidation processes are generated below depressions (Frei et al., in press). Small scale variations of activation and inactivation of redox-sensitive processes in Frei et al. (in press) are directly related to the superficial micro-topography.

Figure 7: Cross sections showing the formation of biogeochemical hot spots as a result of the complex flow path distribution and the non-uniform exposure to different hydrological and biogeochemical boundary conditions. Results exemplarily show the results of the coupled hydrological/biogeochemical simulations described in Frei et al. (in press) for iron reduction. The micro-topography model and the rill storage height models show spatially pronounced hot spots in the subsurface, where the planar reference shows a more homogenous distribution of biogeochemical activity.

As shown before, if spatially distributed rill storage zones are superimposed on top of a planar surface, subsurface flow patterns can be generated, which are very similar to those observed for the micro-topography model. By applying the same streamtube approach as presented in Frei et al. (in press) to represent biogeochemistry, results show that for a planar surface with rill-storage height variations similar biogeochemical patterns can be generated (Figure 7) compared to the micro-topography model. For the p-rs-high model, hot spots for sulfate reduction are correctly generated below infiltration areas (hummocks) hot spots for oxidation processes (not shown) below upwelling areas (depressions). By reducing the grid resolution, it is still possible to generate typical hot spot

STUDY 3 in the p-rs-low model compared to the micro-topography or the p-rs-high models. For the p-rs-low model particle tracking simulations are only based on 1,898 individual flow paths (one particle per surface node) instead of 21,000 flow paths for the more highly resolved p-rs-high and micro-topography models, which will results in more diffuse hot spots in these model as compared to the models using a higher grid resolution.

3.5 Simulation Runtimes

All simulations were performed using the non-parallel version of HGS, running on a modern multi-core workstation. Due to the high grid resolution and the integrated simulation of surface and subsurface flow, the computational efficiency for the original micro-topography model is very low.

Especially for stress periods where surface flow is generated, converging time steps become extremely small, which clearly affects the overall model performance. For a yearly scenario with variable rainfall inputs, the micro-topography model needs up to 48 days to be solved (Table 2 according to Frei et al., 2010). By using the same grid resolution while replacing the three- dimensional micro-topography with superficial rill storage height variations (p-rs-high), computation time can be reduced by a factor of almost two (Table 2). If superficial rill storage height variations are used together with a ten times reduced grid resolution (p-rs-low), computation time for solving the yearly scenario drop below one day.

Table 2: Computation times to solve a yearly scenario with variable rainfall inputs for the different models with micro-topography, spatially distributed rill storage height variations (p-rs-high/p-rs-low) and the planar reference.

simulation period [days]

computation time (real time) [days]

micro-topography 365 48

planar reference 365 23

p-rs-high 365 25

p-rs-low 365 0.63

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