Modeling rainfall run-off responses and antecedent moisture effects using principles of system identification

Robert Czachorski, OHM Advisors


Rainfall-runoff dynamics of surface water, combined sewer, and separate sewer systems can be highly impacted by antecedent moisture conditions, or the relative wetness or dryness of the system. Accurately simulating these dynamics is critical for developing predictive models of systems that are sensitive to antecedent moisture. This paper presents the results of 25 years of work formulating, applying and refining a hydrologic model that addresses the impacts of antecedent moisture conditions on the rainfall-runoff process. The development, process and equations of the model are presented. The model was derived using the principles of system identification from the field of aerospace control systems to find the simplest mathematical model that accurately describes the relationship between system inputs and the flow output. Developing and testing the model was done primarily from observations in the Midwest U.S. where both preceding rainfall and seasonal hydrologic conditions impact antecedent moisture dynamics. For these systems, the model described here is perhaps the most parsimonious that can accurately simulate these dynamics. This provides several advantages to the modeler, including ease of use, fewer parameters to calibrate, ability to quickly identify optimal parameters, and ease to represent in a numerical computer routine. Physical interpretation of the model structure and parameters is possible, providing the modeler with useful insights into the physical processes driving the rainfall-runoff dynamics.

The paper contains the following major components:

  • An overview of antecedent moisture effects on rainfall-runoff systems.
  • An introduction to system identification and the parsimony principle.
  • The step-by-step process that shows the buildup of the model development.
  • The detailed model equations.
  • Some commentary on the use, applications and physical interpretation of the model.

The model was initially developed between 1995 and 2000. It has been updated and applied to hundreds of systems and presented in several papers over the years. Until now, the details of the model, including the equations, have been held as a trade secret by H2Ometrics. With this paper, we are releasing the equations and model process into the public domain. The publication of this paper will be accompanied by a series of spreadsheets that show the model computations and a series of tutorial videos that show how the model works.

 Click here to download a static PDF version of the presentation.

 Click here to watch recorded presentation on YouTube.

Permanent link: