For all spatial scales, from pore through local and field, to a watershed, interaction of the land surface with the atmosphere will be one of the crucial topics in hydrology and environmental sciences over the forthcoming years. The recent lack of water in many parts of the world shows that there is an urgent need to assess our knowledge on the soil moisture dynamics. The difficulty of parameterization of soil hydrological processes lies not only in the nonlinearity of the unsaturated flow equation but also in the mismatch between the scales of measurements and the scale of model predictions. Most standard measurements of soil physical parameters provide information only at the local scale and highlight the underlying variability in soil hydrological characteristics. The efficiency of soil characteristic parameterization for the field scale depends on the clear definition of the functional relationships and parameters to be measured, and on the development of possible methods for the determination of soil characteristics with a realistic use time and effort. The soil’s hydraulic properties that affect the flow behavior can be expressed by a soil water retention curve that describes the relation between volumetric water content, θ(L3L3), and soil water pressure, h(L), plus the relation between volumetric water content and hydraulic conductivity, K(L/T). In the next section, the determination of soil hydraulic parameters is first discussed for local and field scale. Then, we show how the pore-scale processes can be linked to soil hydraulic properties. These properties are then used in some of the modern methods that use integral and superposition solutions of Richards’ equation for infiltration and water flow problems for both stable and preferential types of flows. Finally, some practical aspects for watersheds are discussed to highlight the difficulties encountered when large-scale predictions are needed.
Physics‐informed neural networks with monotonicity constraints for Richardson‐Richards equation: Estimation of constitutive relationships and soil water flux density from volumetric water content measurements
