1-, 2- and 3-dimensional modeling of water movement in the unsaturated soil matrix using a fuzzy approach

Abstract

Modeling water movement in the unsaturated soil matrix is usually based on the numerical solution of the Richards equation. This approach requires much computational effort, therefore practical 2- or 3-dimensional applications are extremely rare. The purpose of this paper is to describe a computationally efficient and simple method. It is based on a transformation of the unsaturated Darcy law to a fuzzy rule system. The rule system is combined with the continuity equation yielding a fuzzy rule-based model for simulating the unsaturated flow. Basic definitions of fuzzy logic are given and the concept of the unsaturated flow model is outlined. The presented model performs well compared with a semi-analytical model and a 2-dimensional, numerical model. Furthermore the model has been incorporated into a physically-based and distributed, hydrological model. Model simulations for different types of hydrological situations show that the fuzzy rule-based approach is especially suitable for real-life applications.