Investigation of β parameter used in Haverkamp 1D-analytical infiltration equation

For heterogeneous soils, accurate water modeling in unsaturated soil conditions is a very important prerequisite since activation of macropore during the flow process is directly linked to the bulk saturation of the soil matrix. Indeed, macropores activate and begin to infiltrate when they receive the runoff from saturated matrices. To this point, the accurate estimation of the matrix hydraulic properties is of uttermost importance. We then focus on the accuracy of estimates for hydraulic parameters, by fitting to the well-know Haverkamp 1D analytical infiltration equation, that is widely used for Beerkan type infiltration. This equation involves an infiltration constant called β that is fixed to a by-default value of 0.6. This value is considered for relatively dry condition and for all type of soils, including fine matrices (silt, clay, etc.) but also coarse soils which are prone to preferential flows. However, the values of β have already been questioned by several authors. In this study, we performed a numerical study to investigate the value of β. Several cumulative infiltrations were numerically generated and fitted to Haverkamp’s model to derive the parameter β. This was then plotted as a function of initial water content and the type of soil. We proved that β is not constant. Especially for lower permeable soils, previous studies point that β value must be over 1 which is in contradiction with the domain of definition of β and the usual ranges considered for this parameter. Therefore, using β equal to 0.6 leads to an overestimation of Ks, leading to an overestimation of the soil capability to infiltrate and the prediction of the water budget. Numerical investigations of β show that this parameter is also a function of the degree of saturation. As defined by Haverkamp (1994), it varies from 1 for dry soil conditions to zero for saturated conditions. The hypothesis of the constancy of β allows easy integration of Richards 1D equation, leading to the formulation proposed by Haverkamp et al. However, it conducts for low permeable of soils to overestimate Ks. In this study, we demonstrate that the use of the adequate function for describing β in function to the degree saturation and the soil type improves significantly the accuracy of Haverkamp’s model.