CUBIC APPROXIMATION OF HYDRAULIC-PROPERTIES FOR SIMULATIONS OF UNSATURATED FLOW

An adequate description of soil hydraulic properties is critical to modeling unsaturated flow. However, flexible descriptions based on the functions normally used may increase simulation times. This disadvantage can be overcome by using piecewise cubic approximation of such descriptions based on a table of function and derivative values. A further advantage of this technique is that the Kirchhoff transform variable can be approximated in the same way, even when it cannot be obtained analytically. Results for simulated infiltration into an aggregated soil indicated that hydraulic properties over the entire matric potential range could be approximated using 8-12 points without causing significant errors in simulations, whether the Kirchhoff transform was used or not. Run times using the original van Genuchten functions were 40% or 280% greater, depending on whether an incomplete beta function was used. The cubic approximation method thus allows more flexible use of the popular van Genuchten hydraulic property functions, since these involve incomplete beta functions unless unsatisfactory restrictions are placed on their parameters.