Roy W. Koch

Date of Award


Document Type


Degree Name

Doctor of Philosophy (Ph.D.) in Systems Science / Civil Engineering


Systems Science

Physical Description

4, xv, 203 leaves: ill. 28 cm.


Soil moisture -- Mathematical models, Watersheds -- Mathematical models, Hydrologic models




The object of current efforts at investigating catchment response is to derive a physically based stochastic model of the watershed. Recent studies have, however, indicated that a limiting factor in deriving such models is the dependence of hydrologic response on initial soil moisture. The dependence affects the distributions and moments of the hydrological processes being investigated. A stochastic model of soil moisture dynamics is developed in the form of a pair of stochastic differential equations (SDE's) of the Ito type. The sources of stochasticity are linked to the random inputs of rainfall and evapotranspiration (ET). One of the SDE's describes the "surplus" case, in which sufficient infiltration always occurs to allow for moisture depletion by the processes of drainage through and ET out of the root zone. The other SDE represents the "deficit" case, in which lack of adequate moisture leads only to an ET-controlled depletion process. Sample functions and moments of moisture evolution are obtained from the SDE's. From the general model of soil moisture, a specific model of initial soil moisture (the moisture at the beginning of a rainstorm event) is developed and its moments are derived. Furthermore, the probability distribution of initial moisture is postulated to permit the assessment of how initial moisture affects the estimation of hydrologic response. The moisture dynamics model reveals that the stochastic properties of moisture ae sensitive to initial conditions in the watershed only for less permeable soils under the "surplus" state but are practically insensitive to such conditions for more permeable soils. The stochastic properties are also less sensitive to initial conditions for all soil types whenever under the "deficit" state. These results suggest that hydrologic processes, such as precipitation excess and infiltration, depend on initial moisture only in regions where the soils are generally less permeable and where the climate tends to sustain a "wet" environment, whereas in arid or semi-arid regions, such processes would not depend on initial moisture. These conclusions imply that, in arid regions, an effective value of initial moisture such as the mean can be used to estimate the properties of the hydrologic processes, whereas in "wet" environments, more accurate values of the properties must be "weighted" based on the probability distribution of initial soil moisture.


Portland State University. Systems Science Ph. D. Program.

Persistent Identifier