Abstract

A method for determining soil hydraulic parameters based on periodic point source solutions of the linearized Richards equation is proposed. Closed-form solutions were derived for buried and surface point sources with a sinusoidally varying flux. These solutions describe the dependence of the matric flux potential (MFP) amplitude and phase shift on the distance from the point sources, frequency of source flux alternations, and soil hydraulic parameters. The Fourier series representation of square waves was used to extend the point source solutions for sinusoidally varying flux to square-wave cyclic inputs of water with a 50% duty cycle—a preferable operating mode for field experiments. Close to the sources, the amplitudes and shape of MFP waves from a step input were more pronounced than those from a sinusoidal input, but the difference diminished as distance increased. The proposed method involves recording the pressure head variations with a continuously reading tensiometer installed below a pressure-compensating emitter controlled by an irrigation computer. Among 16 cyclic step-input irrigation tests, one series involved pressure-head measurements at a single depth and varied water-pulse durations; the second involved pressure-head measurements at various depths with a fixed water-pulse duration. The soil saturated hydraulic conductivity, the coefficient α of Gardner’s conductivity model, and the coefficient k of the linearized unsteady-flow equation were estimated by matching the periodic solution for cyclic step inputs to the measured pressure-head data with a two-step inversion procedure: an amplitude-shift (AS) estimation procedure followed by the Levenberg–Marquardt (LM) optimization algorithm. The AS procedure was effective, and the LM optimization yielded only minor improvements. Our main findings are: (i) the periodic solution for step inputs yields reasonably good predictions of pressure-head variations measured at various depths below an emitter for different periods of water application; and (ii) the proposed point-source method seems to yield consistent and reliable estimates of the three soil hydraulic parameters.

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