Improved Infiltration Model Formulations for Application in Watershed Models

Objective:

The NWM is applicable to the entire CONUS and involves runoff computations at hundreds of thousands of points. There is a need to utilize an effecient method for computing runoff. The Richards equation is the premiere formulation for modeling infiltration, however, the computation time is prohibitive. The LGARTO formiulation is an alternative to the solution to the Richards equation and provides solutions that are one or two orders of magnitude faster while also guaranteeing solution convergence and mass balance integrity. The objectives of the research are: (1) Formulate an extension to the LGARTO model that accounts for preferential flow of water coupled to the flow in the soil matrix, (2) Implement a sophisticated numerical method in LGARTO, (3) Test the extended model formulations using numerical solutions to the Richards equation, (4) Construct a hydrologic model based on LGARTO, which will be compared against the National Water Model (version 3) across a variety of environments, and a limited subset of SacSMA-modeled small NCRFC catchments, thereby determining the utility of a parsimonious analog of the Richards equation in the context of a lumped hydrologic model.

Approach:

The infiltration/runoff amount from rainfall or snowmelt events on the landscape can be assessed most accurately by utilizing numerical solutions to the Richards equation. The challenge though is that the Richards equations is highly nonlinear and numerical solutions to the equation require significant computing time. In some instances the numerical solutions do not converge. A longstanding viable alternative to the Richards equation for cases of single infiltration events is a formulation based on the Green and Ampt equation. Recent developments have revised the Green-Ampt formulation to allow for sequential infiltration events including moisture redistribution, evapotranspiration, and interaction with a shallow water table. The new formulation, LGARTO, is already implemented in the NWM. This formulation already shows significant computational advantages over numerical solutions to the Richards equation. A limitation of the current LGARTO model is needed to account for preferential flow processes that are observed to occur in soils. The approach to address this need is to develop a parallel LGARTO model for flow in soil macropores and interacts dynamically with the LGARTO solution for flow in the soil matrix. The dynamic interaction is handled by implementing the well-known formulation developed by Gerke and van Genuchten (1993) for Richards equation solvers. The new LGARTO formulation will be tested for accuracy and computational advantage by comparing solutions to the equivalent Richards equation solvers. The new formulation will also be tested within the context of the NWM to determine prediction accuracy for observed stream discharge.

Impact:

Abstract:

Infiltration of rainfall or snowmelt water is an important part of the hydrologic cycle and directly affects the occurrence of flood events as well as the recharge of soil profiles and underlying groundwater. The NWM has the infiltration process as part of the model's capability to forecast daily hydrology and to predict flooding and drought events. The prediction of infiltration can be conducted with empirical methods, or more preferably with equations based on physics. One physics-based equation is the Richards equation. The solution to this equation is challenging and demands too much time relative to other hydrologic processes simulated by the NWM. An alternative to the Richards equation is the reasonable approximation represented by the Green-Ampt (GA) type of infiltration equation. A solution for the GA formulation has been developed (LGARTO; Layered Green Ampt with Redistribution and Talbot-Ogden) and implemented in the NWM, and it is found to be much faster computationally in comparison to the Richards equation solution. A current need for the LGARTO formulation is the ability to account for preferential flow since many soils have preferential flow features such as soil cracks, decayed root channels, and channels formed by soil fauna. The current project will involve the development of a dual-permeability formulation for the LGARTO model, and test this model for accuracy of predictions, and evaluate its computational efficiency relative to the solution by the dual-permeability formulation of the Richards equation.

The outcomes of this research will be the developed dual-permeability LGARTO model and comparison testing of the model to the dual-permeability Richards equation formulation. Based on current tests with the model there is a clear computational advantage to implementing this infiltration formulations in the NWM. The formulation provides essentially the same results as numerical solutions to the Richards equation while requiring a small fraction of the computational time to achieve such results.