Modeling Rainfall Runoff Responses with Antecedent Moisture Effects

Introduction
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.

Rainfall-runoff systems are prevalent throughout the natural and built environment, and include surface runoff, stormwater systems, combined sewer systems, and separate sanitary sewer systems. Modeling of these systems is performed for applications like flood control, combined sewer overflow control, and separate sanitary sewer overflow control. Billions of dollars in capital improvements are designed each year based on the outcomes and accuracy of models. The purpose of a model is to simulate unobserved conditions from a mathematical description of the system based on past system performance. In that respect, for a model to be useful, it must be capable of making accurate predictions of future events.

Overview
This paper presents applications for modeling rainfall runoff responses with an antecedent moisture model. 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.

Details of the model, its development, and the equations, including a description of system identification and the parsimony principle. - Commentary on the use, applications and physical interpretation of the model. - Processes for application of the model including calibration, validation, continuous simulation, frequency analysis and design. 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 recently, the details of the model, including the equations have been held as a trade secret. The equations and model process were recently released 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.

Model Development Antecedent moisture conditions, or the relative wetness or dryness of a system, can have a tremendous impact on rainfall-runoff dynamics. The magnitude of the runoff (flow) from rainfall can be affected by how wet the drainage area is from prior conditions. Wetter conditions can produce more runoff, and drier conditions can produce less runoff. Wetness conditions can be affected by a multitude of hydrologic conditions that include items such as prior rainfall, depression storage, air temperature, evaporation, evapotranspiration, solar radiation, soil types, and many other factors. Hydrologic systems can exhibit a wide variation in their response to antecedent moisture conditions. The impact could be as small as initial depression storage on an impervious surface that only affects runoff by a small percentage, or it could be as large as varying wetness conditions in a separate sanitary sewer system that change inflow and infiltration volumes by an order of magnate or more. Understanding the relative impact of antecedent moisture on these systems is critical for engineering design and system operations. These effects can be critically important for developing accurate predictive models of systems that are sensitive to these effects. The importance of accurately accounting for antecedent moisture effects has been covered extensively in the literature. Simulating the rainfall-runoff dynamics of such systems requires the use of an accurate continuous model that is developed to simulate many storms that may occur over a wide range of antecedent moisture conditions. Compared to single event simulation, a continuous simulation can more correctly represent antecedent conditions by incorporating processes of both dry weather periods and wet weather periods. The characteristics of the system identification approach and parsimony are well suited for developing models to simulate rainfall runoff responses and antecedent moisture effects. These principles have been applied to develop the model for simulating the rainfall runoff responses and antecedent moisture effects described in this paper. The development, process and equations of the model will be reviewed

Applications
The paper will cover applications of the model for system design, including:
- Spreadsheet companion to the equations.
- Data requirements and observation data content for developing a model.
- Diurnal flow filtering from total flow signal in sewer applications.
- Calibration and validation processes.
- Model performance quantification through a rigorous accuracy of fit process
- Long-term continuous simulation and frequency analysis for system design.
- System benchmarking under identically simulated antecedent moisture conditions using the model.