R. Haverkamp

Three-dimensional analysis of infiltration from the disc infiltrometer: 2. Physically based infiltration equation

In situ measurement of soil hydraulic properties may be achieved by analyzing the unconfined efflux from disc tension infiltrometers, once consistent infiltration equations can be derived. In this paper an analytical, three-dimensional infiltration equation is developed, based on the use of parameters with sound physical meaning and adjustable for varying initial and boundary conditions. The equation is valid over the entire time range. For practical purposes, a simplified solution is also derived. The full and simplified equations give excellent agreement with published experimental results and are particularly useful for determining soil hydraulic properties through application of inverse procedures.

Physics of water repellent soils

Although it is generally well known that water repellent soils have distinct preferential flow patterns, the physics of this phenomenon is not well understood. In this paper, we show that water repellency affects the soil water contact angle and this, in turn, has a distinct effect on the constitutive relationships during imbibing. Using these constitutive relationships, unstable flow theory developed for coarse grained soils can be used to predict the shape and water content distribution for water repellent soils. A practical result of this paper is that with a basic experimental setup, we can characterize the imbibing front behavior by measuring the water entry pressure and the imbibing soil characteristic curve from the same heat treated soil. q 2000 Elsevier Science B.V. All rights reserved.

Infiltration under ponded conditions: 3. A predictive equation based on physical parameters.

We derived a new infiltration equation that takes into account the possibility of an infinite diffusivity near saturation. Using the example of two soils (clay and coarse sand), we showed that this new infiltration equation has a sound physical basis. In particular, all parameters used are true soil properties that are constant with time and independent of the water depth imposed as a surface boundary condition. Compared with analytical, numerical, and experimental results, the equation shows a great precision (σ2 < 5.10-3 cm2) at all times. The present law introduces a significant improvement over the law obtained in part 1 of this series dealing with ponded infiltration by introducing the physical effect of an infinite diffusivity at saturation.

Parameter constraints on closed-form soilwater relationships

Abstract The constraints on the different fitting parameters used in the water retention equation, h(θ), and hydraulic conductivity, K(θ), are analyzed using the infiltration equation as a testing tool. The following characteristic equations are considered: those of Gardner; Brooks and Corey; Brutsaert; Van Genuchten subject to both Mualems and Burdines condition; Van Genuchten combined with Brooks and Corey; and Fujita. It is shown that most combinations of h(θ) and K(θ) or K(h) break down, when tested over the large range of soil types encountered in field situations. For clay soils, especially, the best-fit parameter values often become inconsistent with the infiltration theory. The best combination is the Van Genuchten equation for h(θ) with the Burdine condition m = 1 − 2 n and the Brooks and Corey equation for K(θ). This combination satisfies the infiltration condition for all soil types, even when applied to the two extreme cases used by Green and Ampt and Talsma and Parlange. The interdependence of h(θ) and K(θ) parameters is discussed.

INFILTRATION UNDER PONDED CONDITIONS: 1. OPTIMAL ANALYTICAL SOLUTION AND COMPARISON WITH EXPERIMENTAL OBSERVATIONS

Under ponded infiltration the cumulative infiltration is a function of soil properties, initial conditions, and water layer thickness above the soil surface. For arbitrary soil properties and arbitrary dependence of water layer thickness on time but uniform initial water content, an optimization technique predicts the cumulative infiltration from the integration of an ordinary differential equation. If the thickness of the water layer is constant with time, a fully analytical result is obtained. Careful experimental observations carried out in the laboratory illustrate the validity and accuracy of the result.

Error Analysis In Estimating Soil Water Content From Neutron Probe Measurements: 1. Local Standpoint

We present a variance analysis for quantifying the different sources of errors induced on volumetric water content measurements and calculation of soil water storage with the use of a neutron moisture meter in one single access tube. For comparative purposes, we apply the analysis to field data obtained with two different probes. In each case the calibration curve is established by measuring simultaneously and independently neutron count rates and corresponding water contents. Two different approaches are considered, i.e. the unbiased treatment and the biased treatment. The unbiased treatment differs from the biased by its correction for measurement errors using the leastsquare technique. For the site under consideration, we show that the calibration component is the major contribution to the total variance associated with an individual water content estimation. The use of the unbiased statistical treatment notably decreases the total variance. In cases where the calibration curve is established very accurately, the instrument component can be reduced by increasing the number of count replications at each sampling point or the counting time or both. The loss of precision due to using neutron count rate ratios instead of simple count rates is negligible if several count replications are made in a standard medium or if the counting time is long enough. We show that the rule of integration of water content profiles in order to calculate water storage has a great importance: the use of Simpsons rule drastically decreases the associated variance as compared with the classical trapezoidal method.

INFILTRATION UNDER PONDED CONDITIONS: 2. INFILTRATION EQUATIONS TESTED FOR PARAMETER TIME-DEPENDENCE AND PREDICTIVE USE1

We analyzed six different infiltration equations—those of Kostiakov (1932), Horton (1940), Mezencev (1948), Green and Ampt (1911), Philip (19576) and Par-lange et al. (1985)—for precision, parameter time-dependence, and applicability for predictive use. The tests were carried out by comparison with reference solutions, i.e., analytical, experimental, or numerical for two different head conditions at the soil surface. The results show that all the infiltration equations but those of Kostiakov and Horton, satisfy sufficiently well the imposed precision criterion. Only one model, however, the Parlange infiltration equation, has the advantage of using parameters that are constant in time and independent of the number of data points chosen for their evaluation procedure. The parameters entering into the other algebraic infiltration equations have to be considered as fitting parameters without physical significance and representative only of the experiment for which they are determined.

Application of a simple soil-water hysteresis model.

Abstract A simple hysteresis model is reformulated on the basis of the Brooks and Corey equation for the relationship between soil-water content and matric potential. In principle, the method requires the knowledge of a drying curve (boundary or primary) to predict the wetting boundary and all scanning curves. Experimental observations used recently to assess a variety of soil-water hysteresis models show that the present model is simple, accurate and general.

A distributed physical approach for surface-subsurface water transport modeling in agricultural watersheds

Abstract Surface cover and soil type have a major influence upon groundwater recharge and groundwater quality in agricultural watersheds. However, several hydrological models focus on simulating groundwater recharge without including the influence of agricultural practices and soil characteristics. In this study, ANSWERS, a distributed parameters surface nonpoint source model has been modified to include the simulation of water transport in the vadose and saturated zones. This model takes into account the spatial and temporal variability of crop cover and management practices, and the spatial variability of soil type and rainfall distribution. It is physically based and uses parameters that can be easily determined from readily available soil and plant information. It has been validated at multiple scales: local scale, field scale and watershed scale. At the local and field scale, it predicts accurately drainage below the root zone and evapotranspiration on different type of soil cover. At the watershed scale, it reproduces well the piezometric levels and trends of variation.

Infiltration under ponded conditions: 4. An explicit predictive infiltration formula

An approximation to an implicit infiltration formula presented earlier in this series is developed. At worst, the relative error of the approximation is always less than 1%, and it is much better than that for most cases. The approximation becomes more accurate in both the short- and long-term limits as it becomes exact in each case. Application of the new formula is demonstrated using both laboratory and numerical experiments.