A physically-based numerical model of catchment water flow to evaluate dominant controls of residence time distribution

Abstract:

Abstract

The residence time distribution (RTD) of water within catchments is a tool to describe catchment-scale transport and mixing. To better understand dominant controls of RTDs and their time-invariant behavior we use a fully coupled three-dimensional numerical model of surface and subsurface flow. We carefully calibrate the model to the data-rich Schäfertal catchment in Central Germany and use this model as a base case for numerical experiments. Here we present first results of systematical variations of the model domain's bottom geometry and groundwater recharge rates. RTDs are derived on basis of post processing particle tracking algorithm. Results reveal a shift between unimodal and bimodal RTDs depending on the model volume and substantial drifts of water ages with changing groundwater recharge. Further numerical experiments will evaluate RTDs in the interplay between catchment's structural properties and dynamic climatic forcing.

Introduction

The residence time distribution (RTD) of water is a fundamental characteristic of catchments. Its investigation has improved the general understanding of many hydrological and biochemical processes, such as the characterization of catchments discharge behavior, the old water paradox and temporal variations in water quality. While the hydrological response observed in the hydrograph alone is not fully suitable to unveil the catchment subsurface complexity and dominant processes, the catchment RTD is fully integrating this complexity.

The distribution of water and solutes inside the catchment is strongly influenced by intermittent rainfall and evapotranspiration forcing. Consequently, RTDs are characterized by non-stationarity (Botter, Bertuzzo, and Rinaldo, 2011; Rinaldo et al., 2011, van der Velde et al. 2010). Recent studies take this non-stationary behavior into account and relate RTDs of water in the catchment discharge and evapotranspiration to the water age distribution in the remaining storage (Botter, Bertuzzo, and Rinaldo, 2011; van der Velde et al., 2012). Both studies are thus proposing conceptual frameworks for catchment-scale mixing processes. There is a lack of methods to directly measure or derive time-variant RTDs in discharge as well as in the evapotranspiration flux. Therefore, numerical models of water flow are a possible tool to study major controls of catchment mixing and water age within storage, evapotranspiration and discharge.

In this study we aimed to use a coupled surface-subsurface numerical model (HydroGeoSphere; Brunner and Simmons, 2012) of the small Schäfertal headwater catchment in Central Germany. RTDs of discharge and evapotranspiration as well as age distribution of the storage are derived from the calculated velocity fields within the subsurface domain. Potential controls, such as rainfall forcing, evapotranspiration, land use and soil heterogeneity are systematically evaluated within numerical experiments taking the calibrated Schäfertal model as a base case. This manuscript will focus on the modelling approach and the evaluation of residence times on basis of particle tracking. As an example we systematically vary depth and shape of the lower boundary of the model domain. Additionally, we connect the domains with variable groundwater recharge rates under steady state and transient conditions and evaluate the corresponding RTDs.

Material & Methods

Our research area is a first order, low mountain headwater catchment (ca. 1.60 km²) within the Harz Mountains, Germany (Borchardt, 1982). The well-instrumented Schaefertal catchment provide a long time series of hydrological and meteorological information, which can be used to setup and validate our hydrological model (Reinstorf et al., 2010). Contrary, the groundwater flow field and subsurface structure are less known. The site is intensively influenced by agricultural land use and exhibits strong seasonal dynamics of water flow and hydrochemistry due to snowmelt processes (Ollesch et al., 2010). The modeling was performed using HydroGeoSphere (Brunner and Simmons 2012), a coupled surface and subsurface model, which solves the three-dimensional Richards Equation for variable saturated soils and a modified Saint Venant equation for two-dimensional surface water flow. The Open Source software Paraview (Ahrens et al., 2005) and R (R Core Team, 2012) was chosen as post processing tools to perform and analyze forward particle tracking algorithms under steady state and transient conditions.

Since the shape and depth of the lower domain bottom in the model domain is highly unknown we systematically evaluated the effect of different scenarios on the resulting residence time distribution. Ten depth and geometry scenarios of the domain bottom were created (5 horizontal bottom geometries - constant base and 5 variable bottom geometries - parallel to surface topography; both minimum depths ranging from 2 m to 50 m). The geometry scenarios were combined with fifteen steady state simulations for different groundwater recharge rate scenarios (0.1 mm up to 15 mm per day). At this very first stage, the model's internal structure was discretized by two different homogenous layers (averaged catchment representation) parallel to the input digital elevation model (2x2 m). Furthermore, a statistical analysis on RTDs was performed for each combination. Later model setups will incorporate a recently developed heterogeneous soil representation, evapotranspiration and transient simulations. 

Results

The derived RTDs spans particle ages from hours to several years showing complex shapes depending on model domain geometry and groundwater recharge rate. As a consequence unimodal or bimodal behavior can be observed. Model results indicate a strong influence of the chosen model geometry on the RTDs. In cases of horizontal domain boundaries with large model volumes, RTDs are characterized by bimodal behavior, indicating that two distinct main pathways (short and long) dominate within this catchment. The shallower the horizontal bottom geometry the shorter are the particle paths without losing the bimodal behavior. Variable bottom geometry setups with small model volumes result in unimodal RTDs with a significant shorter mean residence time. Higher recharge rates results in a shift to the younger ages. At the same time the variance of the observed particle ages increase.

Conclusions

The first result of this study stresses the time-invariant behavior of RTDs by strong shifts of residence times with changing recharge rates. Moreover the result indicates the need of a realistic subsurface characterization. We believe that, within this framework of systematical variations of catchment characteristics in the physically based numerical model we are able to better understand catchment mixing and water age distributions. This approach can therefore be a valuable tool to identify and investigate catchment behavior in the interplay between catchment's structural properties and dynamic climatic forcing.

References

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