Modeling Rainfall–Runoff Responses and Antecedent Moisture Effects Using Principles of System Identification

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 U.S. Midwest. 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 of representation 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.