Subsurface water distribution from furrows described by moment analyses

Moment analysis techniques are applied to describe the spatial and temporal subsurface wetting patterns resulting from furrow infiltration and redistribution. These techniques are adapted from previous work with drip irrigation. The water added is considered as a "plume" with the zeroth moment representing the total volume of water applied to the domain. The first moments lead to the location of the center of the plume, and the second moments relate to the amount of spreading about the mean position. Using moments, any fraction of the applied water and its spatial extent, defined by an ellipse, can be related to a "probability" curve. Remarkably, the probability curves are, for practical purposes, identical for all times and for all of the soils considered in this study. The same observation was made in relation to the distribution of water under a dripper. The consistency of the probability relationships can be exploited to pinpoint the distribution of irrigation water under a furrow in a compact and physically meaningful way. This approach is tested with numerically generated data for infiltration from furrows in three contrasting soils. The general conclusion is that moment analysis allows a straightforward, physically meaningful description of the general pattern of moisture distribution. Potential applications of the results of moment analyses include improved irrigation management, formulation of the infiltration and redistribution process from a furrow in a neural network setting, and parameter estimation of the soil hydraulic properties.