EQUIVALENT STEADY SOIL-MOISTURE PROFILE AND THE TIME COMPRESSION APPROXIMATION IN WATER-BALANCE MODELING

The definition of preevent soil moisture profile and time compression analysis are critical components in water balance models that are base d on realistic infiltration/exfiltration relations and include profile redistribution of vadose zone moisture. In this paper, detailed analy sis of these two fundamental components of water balance modeling is p resented. Numerical integration of the governing equations for liquid moisture flow in the unsaturated zone is used in simulations designed to illustrate the role of temporal variability in the system. The simu lations consist of forcing the surface of a one-dimensional soil colum n, bounded at its based by a fixed water table, with the output of a s tochastic event-based model of precipitation and potential evaporation . The simulations are run until (and beyond when) an equilibrium condi tion is reached between the long-term mean values of surface and botto m fluxes. For situations with a deep water table, two distinct zones d evelop: a near-surface, highly unsteady zone, and a deeper, quasi-stea dy zone. The equivalent steady moisture profile, i.e., the steady prof ile corresponding to the mean of the simulated column flow, is found t o reasonably approximate the temporal mean, mean prestorm, and mean po ststorm moisture profiles, particularly in the deeper zone. In the upp er zone the equivalent steady profile forms a biased estimate of the t emporal mean. The bias is shown, through perturbation analysis, to lea d to overestimation of the wetness of the mean moisture profile. For s hallow water tables the distinction between the two zones collapses. I n this case both the equivalent steady profile and the mean profile ar e close to the hydrostatic profile. The simulations are also used to t est the utility of the time compression approximation (TCA) in modelin g surface fluxes under temporally variable initial conditions. We demo nstrate that the use of the mean prestorm and poststorm event moisture profiles as initial conditions for the infiltration and exfiltration flux capacities does not produce major bias in TCA-predicted surface f luxes. In this sense the TCA behaves as a linear operator. Furthermore , we demonstrate that the estimation of these mean initial condition p rofiles by the equivalent steady state soil moisture profile is an ade quate approximation for determining mean land surface response to even t-based atmospheric forcing.