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Institut für Wasserbau - IWS

Selected Topics and International Network Lectures

16:00 Uhr
Dr. rer. nat. Insa Neuweiler
Leiterin Jungwissenschaftlergruppe: Effective Soil Parameters for Infiltration Processes, Institut für Wasserbau, Uni Stuttgart

Influence of connected structures on upscaled models for flow and transport in the unsaturated zone

Flow velocity of water in the unsaturated zone is described by the Richards equation. Transport of solutes, such as agrochemicals, in the vadose zone is mostly described by an advection-dispersion equation. Soil is in reality highly heterogeneous, so the hydraulic parameters vary in space and their detailed structure is unknown. Heterogeneity of hydraulic soil parameters has a strong influence on flow and transport processes. As an example, it determines dispersion of solute concentration. As water and mass fluxes usually have to be predicted on length scales much larger than the typical length scales of heterogeneities, flow and transport models have to be upscaled to predict spatial averages of state variables (water content or solute concentration). Upscaled models for flow and transport in aquifers are quite well established. In the unsaturated zone, where variances of hydraulic parameters can be extremely high, assumptions such as smoothly varying, moderately heterogeneous hydraulic parameter fields can often not be made to derive upscaled models.

Heterogeneity of soil is usually captured by modeling hydraulic parameters as correlated random fields. These fields are mostly directly or indirectly assumed to be multi-Gaussian. This implies that no information is used upon whether a certain parameter range is spatially connected or forms isolated clusters. However, connectivity has been found to have a strong influence on parameters of upscaled flow models, in particular if the variance of parameters is high.

In this presentation, the influence of connected structures of heterogeneous hydraulic parameter fields on upscaled flow and solute transport models in the vadose zone will be discussed. Upscaled models are derived using homogenization theory. The models are analyzed for different configurations of connected and isolated parameter ranges and for different parameter contrasts. Homogenization theory is based on an expansion of the flow- and transport equation in terms of the ratio between typical large length scale (for example the medium size) and typical small length scale (for example the length scale of a macroscopic representative elementary volume). By analyzing different parameter contrasts, quantified in terms of the expansion parameter, it can be demonstrated that, for example, the occurrence of non-equilibrium effects in the upscaled model depends crucially on the information about connectivity of different parameter ranges. Besides the type of upscaled model, also the effective model parameters depend on this type of information and can deviate significantly from effective parameters derived under the assumption that parameter fields are multi-Gaussian.