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Accueil du site → Doctorat → États-Unis → 1998 → A low-dimensional dynamical model of hillslope soil moisture, with application to a semiarid field site

Pennsylvania State University (1998)

A low-dimensional dynamical model of hillslope soil moisture, with application to a semiarid field site

Brandes, David

Titre : A low-dimensional dynamical model of hillslope soil moisture, with application to a semiarid field site

Auteur : Brandes, David

Université de soutenance : Pennsylvania State University

Grade : Doctor of Philosophy (PhD) 1998

The validity of a low-dimensional, integral-balance model of hillslope soil moisture is explored through dynamical systems theory, numerical experiments with Richards’ equation, and spatio-temporal modal analysis. The practical utility of the low-dimensional modeling approach is then demonstrated by simulation of soil moisture dynamics at a semiarid field site. A stability analysis of the existing two-state variable model (Duffy, 1996) is conducted to assess the key parameters and terms controlling hillslope dynamics. Results show that the form of the steady-state moisture relation determines the stability and degree of damping of model solutions. The condition for instability is shown to be nonphysical for homogeneous hillslopes ; however, lightly-damped equilibria are expected for high precipitation rates. The dynamic response of the model is then examined by comparing model phase portraits to numerical simulations of Richards’ equation. Results indicate that the two-state variable model is insufficiently constrained. A constrained reformulation of the model is proposed, based on conservation of the hillslope pore volume. Phase portraits of the constrained model are consistent with simulations of Richards’ equation. A series of numerical experiments of model hillslopes is then conducted to assess the effect of stratified, trending, and macropore soil heterogeneity on the integral storage-flux relations of the model. The resulting storage-flux relations are similar to those of the homogeneous soils, but are generally higher order. This indicates that heterogeneity will not necessarily add dimensions to the system. Dimensionality of the forced homogeneous hillslope system is investigated by modal analysis of numerically-generated soil moisture time series. For short forcing periods (relative to the hillslope response time), the system has a dimension of approximately one, and behaves essentially linearly. For forcing periods on the order of the hillslope response time, two to three additional modes are required to represent the coupled soil moisture and water table nonlinear dynamics. Finally, an integral-balance model forced by temperature and precipitation is developed for an experimental hillslope site at Los Alamos National Laboratory, New Mexico. The model successfully simulates spatially-averaged soil moisture and interflow data, using parameter values derived from field data and numerical modeling of the site.

Mots clés : Hydrology, Soil moisture, Hillslope, Semiarid, Earth sciences

Accès au document : Proquest Dissertations & Theses

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