Application of the Groenevelt-Grant soil water retention model to predict the hydraulic conductivity

作者：Grant C D^*; Groenevelt P H; Robinson N I

来源：Australian Journal of Soil Research, 2010, 48(5): 447-458.

DOI：10.1071/SR09198

• incomplete gamma function

We outline several formulations of the Groenevelt-Grant water retention model of 2004 to show how it can be anchored at different points. The model is highly flexible and easy to perform multiple differentiations and integrations on. Among many possible formulations of the model we choose one anchored solely at the saturated water content, theta(s), to facilitate comparison with the van Genuchten model of 1980 and to obtain a hydraulic conductivity function through analytical integration:
theta(h) = theta(s) - k(1){exp[-(k(0)/h)](n)},
where, k(0), k(1), and n are fitting parameters. We divided this formulation by qs to obtain the relative water content, theta(r)( h), and inverted the function to produce a form required for integration, namely:
11/h beta(theta(r)) - 1/k(0)(beta)(-ln(theta(s)/k(1)(1 -theta(r)))(beta/n)
in which the parameter beta is introduced to accommodate both the 'Burdine' and 'Mualem' models.
The integrals are identified as incomplete gamma functions and are distinctly different from the incomplete beta functions embodied in the van Genuchten-Mualem models. Rijtema's data from 1969 for 20 Dutch soils are used to demonstrate the procedures involved. The water retention curves produced by our Groenevelt-Grant model are virtually indistinguishable from those produced by the van Genuchten model. Relative hydraulic conductivities produced by our Mualem and Burdine models produced closer estimates of Rijtema's measured values than those produced by the van Genuchten-Mualem model for 19 of his 20 soils. This work provides an alternative to the widely used van Genuchten-Mualem approach and represents a preamble for the, as yet unsatisfactory, treatment of the tortuosity component of the unsaturated hydraulic conductivity function.

• 出版日期2010