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Stochastic analysis of soil water monitoring for drip irrigation management in heterogeneous soils

Many drip irrigation management schemes rely on frequent monitoring of soil water content and matric potential, using various sensors (e.g., tensiometers or time domain reflectometry probes). The soil water information is used either for irrigation scheduling or for adjusting schedules based on evapotranspiration measurements. Spatial variations in soil properties induce variations in wetting patterns about the drippers, which complicate the acquisition and interpretation of information on soil water status. The objective of this study was to quantify the effects of mild spatial variation in soil hydraulic properties on wetting patterns and the consequences on soil water sensor placement and interpretation. The soil hydraulic properties (saturated hydraulic conductivity, K s , and the exponent α of the exponential unsaturated hydraulic conductivity function) were considered as random space functions. Small perturbation expansions were applied to analytical solutions of steady state flow from point sources. The resulting analytical expressions relate the variability of K s and α to the expected variability in soil water pressure head (h) and relative saturation (S) about a point source. Comparisons of the analytical predictions with Monte Carlo simulations (for surface and buried sources) resulted in excellent agreement for coefficients of variation of In(K s ) and α ≤ 0.3. The expressions may be used as first approximations to define regions with small uncertainty that may be most suitable for soil water monitoring and control in drip-irrigated fields. Another application is for determining the minimum number of sensors needed to obtain estimates with a prescribed estimation error. The derived spatial covariance functions of S and h may be used to identify regions in the field with different wetting patterns or simply to interpolate measurements to unmeasured portions of the field.