A novel physical eco-hydrological model for preferential flow challenging observational and modeling concepts

Abstract:

1 Introduction

On the one hand we find many models bound to discharge as prominent target variable (which is also a very prominent hydrological observable) and only few model concepts with highly resolved soil moisture distribution (which is also much more problematic to measure). On the other hand the challenge to understand how pore-scale processes integrate into an eco-hydrological response regarding soil moisture dynamics, ecological feedbacks or residence time distribution is unsolved. Hence the broadly discussed scale issue is extended by observational limitations.

From a modeling perspective one major reason for the proposal of an alternative approach is the conceptual mismatch of either the need for explicit definition of macropore structures in representative elementary volume (REV) models, or inadequately lumped considerations in dual-porosity approaches.

From the perspective of experimental concept development and hydrological understanding we quest for appropriate and parsimonious use of gathered data for simulations on a physical basis. Moreover, the model shall serve as virtual reality to explore hypotheses in more detail.

We present a Lagrangian model approach for preferential flow at the plot and hillslope scale. It is bridging and extending classical hydrological process models, dual domain concepts and stochastic approaches rigorously based on scale- and process-aware observables and explicit hypotheses. Special regard is given to the lessons learned for preferential flow modeling and observation at the plot scale and to some exemplary model applications.

2 Model

2.1 A Novel Plot Scale Model Concept

The model consists of a macropore domain as representative 1D structures and a soil matrix domain spanned as 2D continuum with a cyclic vertical boundary hosting the macropores. The topologically explicit definition of the domains is based on observed macropore density (multi-tracer sprinkling experiments) and accounts for skewed soil moisture distributions and macropore-matrix interaction. Figure 1 illustrates this.

Central in the model is the Lagrangian representation of water as particles, which move diffusively in the 2D matrix domain and advectively through the 1D macropores. The water particles are constant in mass and may move freely across all domains.

Through this setup we disentangle and bridge advective and dispersive domains:

Diffusive flux is represented as 2D random walk on the matrix domain. It includes a dynamic dispersion term after Uffink et al. (1990, 2012) and Kitanidis (1994) to account for diffusivity as self-dependent property and the resulting non-static random walk field. It is parameterized by van Genuchten parameters established from laboratory analysis of the water retention properties of undisturbed 250 ml soil core samples.

Advective flux can take place in the macropore domain. It is parameterized based on the depth distribution of tracer recovery using a cumulative curve method (Leibundgut et al., 2011). By employing this approach we assume an asymptotic preferential flow field for the experiment, which ranges near the capacity of the macropore network (high rainfall amount, not too high intensity) while macropore matrix interaction is minimal (relatively high soil moisture or assumed to be negligible). The network’s density and capacity is derived from dye tracer images or 3D time-lapse GPR surveys during the sprinkler experiment.

2.2 Macropore-Matrix Interaction

One central aspect is macropore-matrix-interaction, which modifies the preferential flow asymptote. Friction control of the fast transport through tortuosity and network configuration and the dissipation of the potential energy is implicitly captured in such a distribution of advective velocity, which we regard as stochastic stream tubes (Jury and Roth 1990).

The interaction is treated as hypothesis, which can be tested with the model. One approach we explored and present is computing the dissipation of the potential advective momentum of a particle by its experienced drag from the matrix domain depending on its matrix head.

3 Scale- and Process-Aware Observations

Deeply connected to the model development is the quest for appropriate parameters. It is well known that site properties are dynamic, that point measurements underlie local heterogeneity and organization, and that suitable effective model parameters substantially deviate from measurements.

We approach this issue by increased awareness for the processes: Advective processes like preferential flow take place under conditions far from well mixed and in connected structures. Thus they can be best observed at high resolution and through integral breakthrough to capture a large spectrum of the residence distribution curve.
For diffusive processes like matrix head driven soil moisture redistribution the assumption of well mixed conditions is adequate. Hence they can be observed with measurements of integration volumes like soil moisture and matrix head measurements.

Moreover, environmental properties underlie uncertainty and often skewed distributions. E.g. for macropore networks the model needs to rely on distributions and representative realizations. Through this the information gain through more and better data and the adjoined different process representations can be analyzed, since they are no stiff prerequisite to run the model.

4 Results and Discussion

4.1 Random Walk as Equivalent for the Richards Equation

We compared a 1D Richards equation with a 1D random walk solution. Figure 2 presents the results from a simulation with a wetted Loess soil without any structural domain. Although the method needs further exploration of its numerical and theoretical stability in a wide range of cases, these results are used as validation of the approach.

4.2 Model Results and Validation

We present two current test cases of the model. The first is a synthetic case of an unrealistically intense storm of 200 mm in 1.3 hours, which illustrates the capabilities of the model: Fast flow of the advective phase and diffusive lateral redistribution (Figure 3).

The second test is a comparison against the performed sprinkler experiment where we clearly see deficits regarding macropore matrix interaction when only governed through a random walk dissipation approach (Figure 4).

4.3 Need for Explicit Topology in the Advective Case

From the beginning we aimed at a parsimonious model. However, the current version is far from simplistic. This is basically due to the fact, that when including an advective transport macropore-matrix interaction and lateral redistribution must be considered. Else the fast phase with 3 to 5 times higher velocities will simply rush through the domain, leaving the slow phase untouched.

The linked dual domain concept needs an explicit positioning a) to allow for lateral redistribution (if one macropore will lead to high infiltration at a certain depth also the conditions for other macropores will change) and b) to represent lateral moisture distribution in order to switch back to a well suited and highly efficient 1D Eulerian Richards solver in case of lateral equilibrium and no advection.

4.4 Further Development of Hydrological Observations

At the current stage, the model domain can be set up based on dye tracer and/or GPR data from sprinkler experiments. Although this is already a decent data basis, experimental results considerably depended on the used methods.

The model unveils critical points like macropore-matrix interaction or the strong ties between observational technology and model conceptualization. We will discuss the model’s capabilities as virtual reality to develop new concepts and observation strategies.

 

 

References

Jury, W. A. and Roth, K.: Transfer functions and solute movement through soil, Birkhauser. 1990.

Kitanidis, P.: Particle-tracking equations for the solution of the advection-dispersion equation with variable coefficients, Water Resources Research, 30, 1994.

Leibundgut, C., Maloszewski, P. and Külls, C.: Tracers in Hydrology, Wiley. 2011.

Uffink, G.: Analysis of Dispersion by the Random Walk Method, 1–158 pp. Proefschrift, Technische Universiteit Delft, 6 February. 1990.

Uffink, G., Elfeki, A., Dekking, M., Bruining, J. and Kraaikamp, C.: Understanding the Non-Gaussian Nature of Linear Reactive Solute Transport in 1D and 2D, Transport in Porous Media, 91(2), 547–571, 2012.