A 2-STATE INTEGRAL-BALANCE MODEL FOR SOIL-MOISTURE AND GROUNDWATER DYNAMICS IN COMPLEX TERRAIN

A dynamical model is devised for a hydrologic system where unsaturated and saturated storage serve as the principal control on rainfall-runo ff and where complex topography, drainage area, and variable depth of moisture penetration describe the flow geometry, The model is formed b y direct integration of the local conservation equation with respect t o the partial volumes occupied by unsaturated and saturated moisture s torage, respectively. This yields an ''integral-balance'' model in jus t two state variables. The relationship of the dynamical model to fiel d data in complex terrain is found through a joint probability density for terrain features. This serves as a ''volume'' weighting function to construct conditional averages for the state variables and fluxes o ver a specified range of terrain features. The scale of averaging coul d range from hillslopes to river basins. Two examples of the joint pro bability of terrain features (altitude and aspect) are demonstrated fo r Valley, Ridge, and Appalachian Plateau digital elevation models. The strategy of a dynamical model formed by conditional averages of state variables with respect to terrain features is proposed as a way of si mplifying the dynamics while preserving the natural spatial and tempor al scales contributing to runoff response. The parametric form of the storage-flux or constitutive relationships for the proposed model is d etermined from numerical experiments in a simple hillslope flow geomet ry. The results show that a competitive relation exists between unsatu rated and saturated storage except for the lowest precipitation rates. Saturation overland flow is proposed to be a storage-feedback relatio n. Solutions to the integral-balance model are presented in terms of t he phase portrait, which represents all possible solution trajectories in state-space. The timing and magnitude of peaks in the runoff hydro graph from pulse-type input events demonstrate quick flow from near-st ream saturated storage, saturation overland flow including rejected ra infall (storage-feedback), and late-time infiltration from upslope sub surface flow.