November 23, 2010
|| Dr. Peter Lehmann
Soil and Terrestrial Environmental Physics (STEP), Institute of Terrestial Ecosystems (ITES), ETH Zurich
||Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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Flow and transport processes in the vadose zone ('shallow' region below ground surface and above water-table) are controlled by spatial arrangement and connectivity of structures at various scales (for example water-filled pores or wet sub-regions). Percolation theory provides a framework to quantify connectivity and its effect on media properties and is hence a 'natural' approach to analyze processes in the vadose zone. Percolation theory is based on the assumption that structural elements are randomly distributed in space. With increasing fraction of structural elements, clusters are formed and build eventually a connected structure when a value denoted as percolation threshold is exceeded. After a short introduction in percolation theory, various examples of a percolation threshold and its relevance for porous media properties will be presented in this seminar.We will start with the concept of air-entry value, a characteristic capillary pressure related to pronounced drop of water saturation in the soil water characteristics (capillary pressure/saturation relationship). For small samples (when effects of gravity can be neglected), the air-entry value equals the percolation threshold of the air phase with air spanning the entire sample. Based on geometrical analysis of imaged porous media, the air-entry value can be related to the mode of pore size distribution (pore size defined by spheres inserted into imaged pore space). Elements of this characteristic pore size form a so-called critical path, defining air-entrance and permeability of a porous medium. At larger scales (when gravity becomes relevant) the air-entry value has an additional significance related to the dynamics of fronts (interface between water saturated and partially air-filled zones). In course of air invasion during evaporation or drainage, the capillary pressure at the front equals to the air-entry value. This can be shown with concept of 'gradient percolation' taking into account depth-dependent percolation rules. While the air-entry value defines air entrance in large pores, another critical pore size exists that characterizes the loss of liquid phase continuity due to air invasion in small voids. This percolation threshold of the liquid phase limits range of capillary flow and hence hydraulic conductivity. By applying rules of percolation theory we will predict hydraulic conductivity as a function of water content and penetration depth of drying fronts.The lecture will be closed with examples from catchment scale hydrology, focusing on subsurface flow after heavy rainfall events. Here, percolation theory is used to predict hillslope properties based on the fraction of wet sub-regions within a catchment. As soon as these regions connect, a fast drainage pathway emerges and subsurface flow at bottom of hillslope occurs.