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 advectiondispersion 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 multiGaussian. 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 nonequilibrium
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 multiGaussian.
