An Extension of the Talbot–Ogden Hydrology Model to an Affine Multi-dimensional Moisture Content Domain

The Talbot–Ogden hydrology model provides a fast mass conservative method to compute infiltration in unsaturated soils. As a replacement for a model based on Richards equation, it separates the groundwater movement into infiltration and redistribution for every time step. The typical feature making this method fast is the discretization of the moisture content domain rather than the spatial one. The Talbot-Ogden model rapidly determines how well ground water and aquifers are recharged only. Hence, it differs from models based on advanced reservoir modeling that are uniformly far more expensive computationally since they determine where the water moves in space instead, a completely different and more complex problem. According to the pore-size distribution curve for many soils, this paper extends the one dimensional moisture content domain into a two dimensional one by keeping the vertical spatial axis. The proposed extension can describe any pore-size or porosity distribution as an important soil feature. Based on this extension, infiltration and redistribution are restudied. The unconditional conservation of mass in the Talbot–Ogden model is inherited in this extended model. A numerical example is given for the extended model.