At a point infiltration models for calculating runoff

Refer to Chapter 5 of the Rainfall Runoff Processes Workbook

The rate at which water moves into the soil is the infiltration rate.  This rate depends on the soil moisture content, the distribution of soil moisture content in the soil, and the amount of incoming precipitation water at the soil surface. The maximum rate that soil can absorb water is the infiltration capacity.  Any excess surface water input that does not infiltrate, collects on the ground surface and contributes to runoff as overland flow. 

Richards equation combining conservation of mass and Darcy's equation expressed with moisture content or pressure head as the independent variable.

Richards equation can be used to solve for pressure head, or equivalently moisture content during infiltration or drainage of a soil profile assuming a specific form for the soil moisture characteristic curves.  Except for special cases numerical solutions are required using codes such as Hydrus 1-D.

Even though the complexity of solving Richard's equation can be overcome with modern computational methods the practical limits on quantifying soil properties limit extensive use of Richard's equation solutions.  Simplified at a point parameterizations for calculation of infiltration are still used.  There are three at-a-point infiltration models presented in this section:  Green-Ampt, Horton, and Philips.  Using these models one can calculate runoff at a point, given a time series of surface water input and soil conditions.  There are three cases to be considered throughout the time series:  (1) excess surface water ponds on the surface throughout the interval; (2) there is no ponding throughout the interval; and (3) ponding begins at some time during the interval.  The output of the models is the runoff amount generated from excess surface water input; the cumulative infiltrated depth of water is the state variable for the models. 

An important concept that emerges from the Green-Ampt model is that infiltration capacity during a storm decreases as a function of cumulative infiltrated depth.  This provides for a decrease in infiltration capacity and increase in runoff ratio with time, consistent with empirical observations.  In the Green-Ampt model, infiltration capacity is modeled as a function of cumulative infiltration depth, whereas the Horton and Philips infiltration models calculate infiltration capacity as a function of time. 

The three infiltration models presented are three of the most popular from a number of at a point infiltration models used in hydrology.  However, if one does not have enough soils data to attempt to represent the physics of infiltration using the above models, empirical and index methods may be used.

The flowchart and examples in the workbook, Excel spreadsheets and animated solution are designed to guide you through the procedure for solving these at a point infiltration models for time varying precipitation input.  After working through these you should be able to calculate runoff using one of the at-a-point infiltration models presented.