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Abstract Hydrologic predictability suffers from a lack of a comprehensive theory of stormflow generation. This is particularly true in situations where soil hydraulics dominate partitioning of rainfall into runoff and soil moisture. For this reason most hydrologic models use simplified methods to calculate infiltration. To model infiltration processes, rigorous hydrologic models often numerically solve some form of the Richardson/Richards Equation (RRE); the partial differential equation that describes the variation of water content over time at a point in unsaturated porous media in response to rainfall, plant water uptake, or groundwater table dynamics. Solving the RRE is one of the most challenging problems in hydrologic prediction because of the highly nonlinear dependence of hydraulic conductivity and capillarity on water content, plus numerical solver convergence challenges associated with steep gradients in water content or discontinuous media properties such as soil layering and tillage/compaction. One common method used to reduce computational effort and improve RRE solution robustness involves the use of a coarse spatial discretization of the soil. However, coarse discritizations can violate the Representative Elementary Volume (REV) assumption and can smooth heterogeneities, leading to inaccurate solutions. This presentation reviews a Lagrangian reinterpretation of the RRE called the Soil Moisture Velocity Equation (SMVE) which was first published in 2017 by Fred’s research team. The one-dimensional vertical solution of the SMVE employs a finite water content discretization of the soil, which is advantageous because it avoids the need to discretize the soil in space. The SMVE advection-like term can be solved as an ordinary differential equation using standard numerical methods. The SMVE solution simulates infiltration in layered soils as well as the effects of groundwater on infiltration. It does this with guaranteed mass conservation, and without the computational expense and numerical reliability issues that can impede RRE solutions. Compared to an appropriately applied RRE solution, the SMVE solution exhibits less than five percent difference in calculated infiltration over multi-month simulations. This presentation derives the SMVE from the RRE, and gives examples showing the advantages of this transformative new infiltration modeling tool. It compares solutions of the SMVE against HYDRUS-1D and analytical solutions. The presentation concludes by showing positive results obtained with the newest development using the technique, a continuous Green & Ampt infiltration solution that is valid for layered soils in arid and semi-arid regions.
Bio Dr. Fred L Ogden is Chief Scientist for Water Prediction with the NOAA National Weather Service. From 2006-2017 he served as a Professor in the Department of Civil and Architectural Engineering, University of Wyoming. Fred's primary interest is hydrological model development and predictability. Together with students, he has published widely cited papers in tropical hydrology, hydrometeorology, vadose zone modeling, appropriate use of models, and hydraulics & hydrologic engineering. Several of Dr. Ogden’s papers with collaborators and students have received recognition for having made significant contributions to challenges as diverse as groundwater protection, sediment control at riverside intakes, applications of remotely sensed evapotranspiration, and simulation of soil moisture dynamics. He is a recipient of the Collingwood Prize and the Arid Lands Hydraulic Engineering award, both from the American Society of Civil Engineers.