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Soil Physics

Soil Water Retention

II. Derivation and Application of Shape Index

^a Laboratoire d'Etude des Transferts en Hydrologie et Environnement, LTHE (UMR 5564, CNRS, INPG, UJF, IRD), BP 53X, 38041, Grenoble, Cedex 9, France
^b Instituto Mexicano de Tecnología del Agua (IMTA), Paseo Cuauhnáhuac 8532, Col. Progresso 62550 Jiutepec, Morelos, Mexico
^c CSIRO Land and Water, Indooroopilly, Qld. 4067, Australia

^* Corresponding author (haverkamp{at}hydrowide.com)

The concept of a shape index was introduced in Part I to characterize the water retention curve. A potential problem with the parameterization of retention data is the interdependency of parameter values and their conversion to other parametric models. In this Part II the shape index is used to derive formulae for the conversion between: (i) hydraulic parameters of the Brooks-Corey (BC) and van Genuchten (vG) equations, (ii) parameter sets with and without the constraint that the residual water content _r = 0, and (iii) vG-shape parameters with different constraints. The dependency of hydraulic parameters on the optimization strategy and the applicability of conversion equations were investigated with 660 retention curves from the GRIZZLY database. The BC-shape parameter and the vG-shape factor mn are poorly correlated for larger and mn (overall r² = 0.96 for _r = 0). Instead of the commonly used equality = mn, conversion based on the shape indices P_BC and P_vG is more accurate (r² = 0.99). The shape index is also convenient to accurately predict shape parameters for different constraining scenarios involving _r and m = 1 – k/n. The values for _r and the shape parameters and mn are not unique. They are positively correlated to maintain the same soil water capacity for a particular soil. For the optimization of parameters, we recommend constraining _r. Accurate optimization of retention data, in particular the shape parameters, is possible by constraining _r to a non-zero value inferred from the shape index.

Abbreviations: BC, Brooks-Corey Model • RMSE, root mean square error • vG, van Genuchten Model

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