Soil-dependent β and γ shape parameters of the Haverkamp infiltration model for 3D infiltration flow

Estimating of soil sorptivity ((Figure presented.)) and saturated hydraulic conductivity ((Figure presented.)) parameters by field infiltration tests are widespread due to the ease of the experimental protocol and data treatment. The analytical equation proposed by Haverkamp et al. (1994) allows the modelling of the cumulative infiltration process, from which the hydraulic parameters can be estimated. This model depends on both initial and final values of the soil hydraulic conductivity, initial soil sorptivity, the volumetric water content increase ((Figure presented.)) and two infiltration constants, the so-called (Figure presented.) and (Figure presented.) parameters. However, to reduce the number of unknown variables when inverting experimental data, constant parameters such as (Figure presented.) and (Figure presented.) are usually prefixed to 0.6 and 0.75, respectively. In this study, the values of these constants are investigated using numerical infiltration curves for different soil types and initial soil water contents for the van Genuchten-Mualem (vGM) soil hydraulic model. Our new approach considers the long-time expansions of the Haverkamp model, the exact soil properties such as (Figure presented.), (Figure presented.) and initial soil moisture to derive the value of the (Figure presented.) and (Figure presented.) parameters for each specific case. We then generated numerically cumulative infiltration curves using Hydrus-3D software and fitted the long-time expansions to derive the value of the (Figure presented.) and (Figure presented.) parameters. The results show that these parameters are influenced by the initial soil water content and the soil type. However, for initially dry soil conditions, some prefixed values can be proposed instead of the currently used values. If an accurate estimate of (Figure presented.) and (Figure presented.) is the case, then for coarse-textured soils such as sand and loamy sand, we propose the use of 0.9 for both constants. For the remaining soils, the value of 0.75 can be retained for (Figure presented.). For (Figure presented.) constant, 0.75 and 1.5 values can be considered for, intermediate permeable soils (sandy loam and loam) and low permeable soils (silty loam and silt), respectively. We clarify that the results are based on using the vGM model to describe the hydraulic functions of the soil and that the results may differ, and the assumptions may change for other models.