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The objective of the present work is to investigate the flux&ndash, concentration (F(&Theta, )) relation, where &Theta, is the normalized soil volumetric water content for the case of one-dimensional horizontal flow, subject to constant concentration conditions. More specifically, the possibility of describing F(&Theta, ) by an equation of the form F(&Theta, ) = 1 &minus, (1 &minus, &Theta, )p+1 is examined. Parameter p is estimated from curve-fitting of the experimentally obtained &lambda, (&Theta, ) data to an analytic expression of the form (1 &minus, )p where &lambda, is the well-known Boltzmann transformation &lambda, = xt&minus, 0.5 (x = distance, t = time). The results show that the equation of (1 &minus, )p form can satisfactorily describe the &lambda, ) relation for the four porous media tested. The proposed F(&Theta, ) function was compared with the limiting F(&Theta, ) function for linear and Green&ndash, Ampt soils and to the actual F(&Theta, ) function. From the results, it was shown that the proposed F(&Theta, ) function gave reasonably accurate results in all cases. Moreover, the analytical expression of the soil water diffusivity (D(&Theta, )) function, as it was obtained by using the equation for &lambda, ) of the form (1 &minus, )p, appears to be very close to the experimental D(&Theta, ) data (root mean square error (RMSE) = 0.593 m2min&minus, 1).

Water infiltration in soil is a complex process that still requires appreciation of interactions among three phases (soil particles, water and air) to enable accurate estimation of water transport rates. To simulate this process, the Green&ndash, Ampt (GA) model and the Modified Green-Ampt (MGA) model introduced in the paper &ldquo, A new method to estimate soil water infiltration based on a modified Green&ndash, Ampt model&rdquo, have been widely used. The GA model is based on the hypothesis that the advance of the wetting front in soil under matric suction can be treated as a rectangular piston flow that is instantaneously transformed after passage of the infiltration front, and the MGA model does not contain the influence of pore size change. This cannot accurately reflect the soil moisture change process from unsaturation to saturation. Due to soil stratification and other inhomogeneity, predictions produced with these models often differ widely from observations. To quickly obtain the soil moisture distribution after passage of the wetting front for horizontal infiltration, an improved modified Green&ndash, Ampt (IMGA) model is presented, which estimates the soil moisture profile along a horizontal column in a piecewise manner with three functions. A logarithmic function is used to describe the gradual soil saturation process in the transmission zone, and two linear functions are used to represent the wetting zone. The algorithm of the IMGA model for estimating the water infiltration rate and cumulative infiltration is configured. To verify the effectiveness of IMGA model, a lab model test was performed, and a numerical model was built to solve the horizontal one-dimensional Richards equation using the finite&ndash, element method. The results show that the IMGA model is more accurate than the GA and MGA models. The horizontal soil moisture profiles obtained by the IMGA model are closer to the measured data than the numerical simulation results. The relative errors of the MGA and IMGA models decrease with an increase in infiltration time, whereas that of the GA model first decreases and then increases with infiltration time. The primary novelty of this study is nonlinear description of soil moisture content distribution, and derivation of unit transfer coefficient.