Downward water flow through sloping layers in the vadose zone: time-dependence and effect of slope length

Abstract

We develop a 2-D numerical model to simulate both steady-state and transient downward water flow through sloping layers in the vadose zone with a deep water table. The horizontal flow component obtained with the 2-D numerical model varies with position along the slope, but was nearly the same as the 1-D analytical solution once beyond a few meters from blocked vertical boundaries at the upper or lower end of the slope. Under time-variable precipitation, both the time delay and the peak magnitude of the response deep within the profile are not simply proportional or in one-to-one correspondence to the strength of each rainfall event, but rather depend on the initial moisture status in the profile as well as the previous rainfall events. An interesting phenomenon for the transient case is that the horizontal flow component reversed direction to upslope during the time of heavy rain. This is due to the flow pattern near the upper surface boundary (a sloping wetting front), and is a consequence of the sloping geometry. Previous studies (Warrick et al., 1996) have shown that multidimensional steady-state water flow through a sloping interface can essentially be solved by a one-dimensional analytical solution for an infinite long slope. The simulations suggest that a 1-D numerical analysis should also be valid for 2-D transient flow cases, if the slope is of sufficient length and the point of evaluation is sufficiently far from the beginning or end of the slope.