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. DESIGNING drip irrigation systems involves selection of an appropriate combination of emitter discharge rate and spacing between emitters for any given set of soil, crop, and climatic conditions, as well as understanding the wetted zone pattern around the emitter (Bresler, 1978; Lubana andNarda, 2001).Water distribution is affected by many factors, including soil hydraulic characteristics, initial conditions, emitter discharge rate, application frequency, root characteristics, evaporation, and transpiration. A traditional way to visualize spatial and temporal soil water distributions includes determination of the water content at points around the emitter and drawing contours between these points. Practical information includes estimation of the position and shape of thewetted volume (Dasberg andOr, 1999). Previous investigators have used descriptions of the extent of wetting, including the surface wetted diameter, wetted depth, and wetted volume (Ben-Asher et al., 1986; Schwartzman and Zur, 1986; Angelakis et al., 1993; Chu, 1994; Zur, 1996; Dasberg and Or, 1999; Hammami et al., 2002; Thorburn et al., 2003; Cook et al., 2003). The volume of the wetted soil represents the amount of soil water stored in the root zone. The domain of interest should be consistent with the anticipated depth of the root system, while its width is associated with the spacing between emitters and lines (Zur, 1996). A comprehensive method of characterizing spatial– temporal distributions is through moment analyses. This approach is widely used to describe solute transport in the vadose zone (e.g., Barry and Sposito, 1990; Toride and Leij, 1996; Srivastava et al., 2002). With respect to water, Yeh et al. (2005) and Ye et al. (2005) calculated the zeroth, first, and second moments of a three-dimensional water content plume and defined an ellipsoid that described the average shape and orientation of the plume for each observation period. This led to snapshots of the observed water content plume under transient flow conditions, which was used to derive a three-dimensional effective hydraulic conductivity tensor. The objective of this study was to implement moment analyses to describe subsurface water distribution resulting from drip irrigation and to test this approach with numerically generated data. This includes infiltration for both line and point sources in contrasting soils. The considerable advantages gained by the moment analyses over alternatives is detailed.