A scaling procedure for straightforward computation of sorptivity

Abstract. Sorptivity is a parameter of primary importance in the study of unsaturated flow in soils. This hydraulic parameter is required to model water infiltration into vertical soil profiles. Sorptivity can be directly estimated from the soil hydraulic functions (water retention and hydraulic conductivity curves), using the integral formulation of Parlange (1975). However, calculating sorptivity in this manner requires the prior determination of the soil hydraulic diffusivity and its numerical integration between initial and final saturation degrees, which may be difficult in some situations (e.g., coarse soil with diffusivity functions that are quasi-infinite close to saturation). In this paper, we present a procedure to compute sorptivity using a scaling parameter, cp, that corresponds to the sorptivity of a unit soil (i.e., unit values for all parameters and zero residual water content) that is utterly dry at the initial state and saturated at the final state. The cp parameter was computed numerically and analytically for five hydraulic models: delta (i.e., Green and Ampt), Brooks and Corey, van Genuchten–Mualem, van Genuchten–Burdine, and Kosugi. Based on the results, we proposed brand new analytical expressions for some of the models and validated previous formulations for the other models. We also tabulated the output values so that they can easily be used to determine the actual sorptivity value for any case. At the same time, our numerical results showed that the relation between cp and the hydraulic shape parameters strongly depends on the chosen model. These results highlight the need for careful selection of the proper model for the description of the water retention and hydraulic conductivity functions when estimating sorptivity.

[1]  D. Deneele,et al.  Hydrodynamic Characterization of Basic Oxygen Furnace Slag through an Adapted BEST Method , 2010 .

[2]  M. Iovino,et al.  Beerkan Estimation of Soil Transfer parameters (BEST) across soils and scales , 2019, Journal of Hydrology.

[3]  Y. Mualem.  A New Model for Predicting the Hydraulic Conductivity , 1976 .

[4]  B. Minasny,et al.  SORPTIVITY OF SOILS , 2012 .

[5]  M. Iovino,et al.  Comparing Alternative Algorithms to Analyze the Beerkan Infiltration Experiment , 2014 .

[6]  J. Parlange,et al.  On Solving the Flow Equation in Unsaturated Soils by Optimization: Horizontal Infiltration , 1975 .

[7]  Randel Haverkamp,et al.  Parameter constraints on closed-form soilwater relationships , 1992 .

[8]  J. Philip,et al.  THE THEORY OF INFILTRATION: 4. SORPTIVITY AND ALGEBRAIC INFILTRATION EQUATIONS , 1957 .

[9]  R. Carsel,et al.  Developing joint probability distributions of soil water retention characteristics , 1988 .

[10]  R. Haverkamp,et al.  Use of scaled forms of the infiltration equation for the estimation of unsaturated soil hydraulic properties (the Beerkan method) , 2005 .

[11]  K. Kosugi.  Lognormal Distribution Model for Unsaturated Soil Hydraulic Properties , 1996 .

[12]  Rafael Angulo-Jaramillo,et al.  New Analytical Model for Cumulative Infiltration into Dual‐Permeability Soils , 2014 .

[13]  B. Mohanty,et al.  Reduction of Feasible Parameter Space of the Inverted Soil Hydraulic Parameter Sets for Kosugi Model , 2013 .

[14]  J. Fernández-Gálvez,et al.  Deriving physical and unique bimodal soil Kosugi hydraulic parameters from inverse modelling , 2021, Advances in Water Resources.

[15]  P. Broadbridge,et al.  The Green–Ampt limit with reference to infiltration coefficients , 2012 .

[16]  J. Fernández-Gálvez,et al.  A general Beerkan Estimation of Soil Transfer parameters method predicting hydraulic parameters of any unimodal water retention and hydraulic conductivity curves: Application to the Kosugi soil hydraulic model without using particle size distribution data , 2019, Advances in Water Resources.

[17]  M. Iovino,et al.  BEST‐2K Method for Characterizing Dual‐Permeability Unsaturated Soils with Ponded and Tension Infiltrometers , 2019, Vadose Zone Journal.

[18]  Isabelle Braud,et al.  Beerkan Estimation of Soil Transfer Parameters through Infiltration Experiments—BEST , 2006 .

[19]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[20]  R. Haverkamp,et al.  Soil water retention. I. Introduction of a shape index , 2005 .

[21]  Isabelle Braud,et al.  Assessment of an efficient numerical solution of the 1D Richards' equation on bare soil , 2006 .

[22]  J. Hopmans,et al.  Prediction of Unsaturated Relative Hydraulic Conductivity from Kosugi's Water Retention Function , 2013 .

[23]  M. V. Genuchten,et al.  Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone , 2003 .

[24]  Hydraulic Properties of Rocks , 2010 .

[25]  R. Haverkamp,et al.  Numerical evaluation of a set of analytical infiltration equations , 2009 .

[26]  R. H. Brooks,et al.  Hydraulic properties of porous media , 1963 .

[27]  Jan W. Hopmans,et al.  Scaling Water Retention Curves for Soils with Lognormal Pore-Size Distribution , 1998 .

[28]  J. Parlange,et al.  Calculating parameters for infiltration equations from soil hydraulic functions , 1996 .