## Soil Hydrologic Model (SHM)

A theoretical partial differential equation for unsaturated flow (referred to as the diffusion equation or Richards equation) was derived to describe the vertical moisture flow by combining Darcy's Law with the continuity equation (Swartzendruber, 1969). The Richard's equation is solved using the Crank-Nicholson numerical scheme (Press at al., 1986; Capehart and Carlson, 1994) and a finite difference scheme of forward in time andbackward in space.
SHM receives information from HMS about the available water depth on each grid node at each time step during the simulation. The available water depth is the summation of precipitation and water routed from neighboring grids through kinematic wave approach in THM. The infiltration and evaporation are treated as either sources or sinks in Richards equation rather than incorporated into the upper boundary condition of soil profile. The amount of infiltration and evaporation is distributed over top layers while ET is extracted from the entire root zone according to a weighted function which depends on vegetation type and height. The procedure for the calculation of evaporation on a bare soil and ET on the vegetation canopy follows the Penman-Monteith method (Monteith, 1981). The Green-Ampt technique of infiltration calculation was implemented in SHM (Chow et al., 1988). After computations in SHM, it passes calculated ET back to HMS for the water budget calculation for next time step. The modified SHM offers us the potential to simultaneously run multi-storm simulation with mesoscale model (MM). It could provide the spatial distributed soil moisture content to MM in each time step during the simulation. For more detailed information about the processes in SHM, reader should refer to Capehart and Calson (1994) and other sources.