Simplifications to the depth-integrated soil water transport equation lead to an Ito stochastic differential equation where the evaporation is related to the stored water by the nonlinear soil water diffusivity function. From the derived equation the diffusivity function was estimated from daily stored water measurements obtained at the field scale using nonlinear filtering theory for a period of 100 days.Comparisons with daily evaporation measured with a sensitive 50-ton lysimeter indicated that the proposed method may be used to determine soil water diffusivity functions at the field scale under natural conditions when applied water and evaporation are the primary controlling physical mechanisms in the hydrologic budget.
INTRODUCTION
Approximate solutions to the nonlinear diffusion equation have been demonstrated to be in good agreement with measurements obtained from laboratory column experiments of drying soils [Gardner and Hillel, 1962; Gardner andGardner, 1969]. In nature, however, the simple initial and boundary conditions which can be imposed in laboratory column studies seldom exist. In addition, other variables play a role in the field such as redistribution of water during evaporation, random precipitation, hysteresis, salinity, temperature, and nonuniform initial soil moisture profiles [e.g., Black et al., 19i59; Jury et al., 1978; Lima et al., 1990; Dane and Klute, 1977]. Major complications also arise due to the natural variation of soil properties in the field [e.g., Nielsen et al., 1973; Biggar and Nielsen, 1976]. In this study we investigate the applicability of an approximate solution to the nonlinear desorptive diffusion equation proposed by Gardner [ 1962] to compute evaporation as well as to determine a field diffusivity function from stored water observations and applied water events in the natural environment. There are, of course, a large number of physical transport mechanisms which are not explicitly accounted for in the drying soil model, so that the simplifying assumptions are assumed to generate a sequence of noise disturbances to the transient flow model system [Zielinski, 1991; Shumway, 1988]. Further, an inherent difficulty in field studies is that averaging observations at various spatial locations results in an additional nonstationary noise component that needs to be accounted for when determining the evaporation or the diffusivity function using stored water measurements [White, 1988; Schmugge et al., 1980]. Due to the uncertainties in the model of the physical system, as well as the spatial variability of observations in the field, application of a nonlinear filtering theory is suitable since the two sources of uncertainty can be accounted for in both the evaporation as well as the diffusivity calculation [
