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

• Published in: Hydrological processes Vol. 37; no. 6
• Main Authors: Yilmaz, D., Lassabatere, L., Moret‐Fernandez, D., Rahmati, M., Angulo‐Jaramillo, R., Latorre, B.
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.06.2023; Wiley Subscription Services, Inc; Wiley
• Subjects: Agricultural sciences; Beerkan infiltration; Constants; Earth Sciences; Haverkamp model; Hydraulic conductivity; Hydraulic models; Hydraulics; Hydrology; Hydrus‐3D synthetic soils; Infiltration; Life Sciences; Loam; Mathematical models; Modelling; Moisture content; Moisture effects; Parameters; Sand; Sandy loam; Sandy soils; saturated hydraulic conductivity; Sciences of the Universe; Silt loam; Soil conditions; Soil conductivity; Soil moisture; Soil permeability; Soil properties; soil sorptivity; Soil study; Soil texture; Soil types; Soil water; steady‐state; Three dimensional flow; Three dimensional models; Water content; Beerkan infiltration; saturated hydraulic conductivity; soil sorptivity; steady-state; Haverkamp model; Hydrus-3D synthetic soils
• ISSN: 0885-6087; 1099-1085
• DOI: 10.1002/hyp.14928

Estimating of soil sorptivity (S) and saturated hydraulic conductivity (Ks) 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 (∆θ) and two infiltration constants, the so‐called β and γ parameters. However, to reduce the number of unknown variables when inverting experimental data, constant parameters such as β and γ 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 S, Ks and initial soil moisture to derive the value of the β and γ 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 β and γ 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 S and Ks 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 γ. For β 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. The contours of the objective error functions for soil sorptivity, S, and soil saturated hydraulic conductivity, Ks, show a valley meaning of infinite possible values for shape parameters. Crossing of each valley allows to retrieve the optimum values of β and γ for accurate estimates of S and Ks.