Subsurface water distribution from drip irrigation described by moment analyses

Moment analysis techniques are used to describe spatial and temporal subsurface wetting patterns resulting from drip emitters. The water added is considered a "plume'' with the zeroth moment representing the total volume of water applied. 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. We tested this approach with numerically generated data for infiltration from surface and buried line and point sources in three contrasting soils. Ellipses ( in two dimensions) or ellipsoids ( in three dimensions) can be depicted about the center of the plume. Any fraction of water added can be related to a "probability'' curve relating the size of the ellipse ( or ellipsoid) that contains that amount of water. Remarkably, the probability curves are identical for all times and all of the contrasting soils. The consistency of the probability relationships can be exploited to pinpoint the extent of subsurface water for any fraction of the volume added. The new method can be immediately applied to the vital question of how many sensors are needed and where to install them to capture the overall water distribution under drip irrigation. For example, better agreement with the "exact'' solution occurs with increasing the number of observation points from 6 to 9 and no significant improvement when increasing from 9 to 16. The method can also be applied to parameter estimation of soil hydraulic properties, which we uniquely reproduced for generated data.