Benchmarking Sewer RDII Models

Introduction: Rainfall-Runoff models predict the flow response to an arbitrary time series of rainfall data falling over a catchment and are critical to modeling sewer collection systems. Many methods exist to model overland flow for storm and combined systems (or inflow in sanitary systems), and they are relatively successful. Infiltration, water that enters the sewer under the surface through defective infrastructure, is a key concern in sanitary systems. Due to soil interactions, modeling the rainfall-runoff relationship for infiltration is more difficult and generally less accurate with existing methods. One issue with existing methods is the effect of antecedent moisture. Antecedent moisture plays some effect in overland runoff, where wet conditions before a storm can result in higher flow responses, but it is the observation of the authors that it can have a much larger effect in modeling infiltration. This sensitivity to antecedent moisture, or 'antecedent moisture dependence', means that the observed flow response at some sewer sites for a 2-inch rain event is much more than double the response to a 1-inch rain event. The sensitivity of antecedent moisture dependence varies widely from site to site due to a mostly unknown set of factors. Modeling infiltration at sites with high antecedent moisture dependence is a challenge using existing methods. Currently the RTK Unit Hydrograph method is the most widely used hydrologic model of inflow and infiltration. The RTK method assumes a linear flow response to rainfall which. In order to improve model performance, initial abstraction parameters and seasonally-varying parameters are sometimes used. The Groundwater Infiltration Module (GIM) in Infoworks ICM is another widely used method. The GIM has a conceptual model with a physical basis of 'soil store' and 'ground store' reservoirs that infiltrate into the sewer, and it can model increasing infiltration with increasing wetness. The Antecedent Moisture Model (AMM) was developed and used by Robert Czachorski for nearly two decades, but only recently were the equations released into the public domain. AMM is an empirically-calibrated method, similar to the RTK Unit Hydrograph method, but whereas RTK assumes a fixed capture coefficient (or percent capture), AMM can model variability in the capture coefficient as a function of antecedent moisture and season. Purpose: Almost no prior work has focused on comparing different models quantitatively. It is common for SWMM users to use the RTK method, Infoworks ICM users to use the GIM model, and Mike+ users to use the NAM method without understanding the other models available. Testing of the models against each other would be beneficial to guide modelers toward selection of a model (or model software). Having standard benchmark tests will also guide the development of emerging models (like AMM). This talk will first lay out 6 criteria of a good model, then suggest benchmark tests to measure performance against the 3 quantitative criteria. It will then present the results and finally discuss implications for model selection and model calibration. Methodology: Eleven long-term meter sites from 6 different states across the country, along with corresponding rain gauge data, were used for model calibration. This data represents a truly diverse set of high-quality flow metering data comprising 975 separate rain events. Eight different RDII models (and model flavors) were identified for testing. A genetic algorithm was used to auto-calibrate each model to the flow meter data. Each model was calibrated to each of the 11 datasets to compare performance. Three separate tests were performed to evaluate each model for accuracy, the ability to extrapolate, and the ability to calibrate well to short data periods. Conclusions: The current study highlights the variety of models that exist to represent RDII but which make quite varied assumptions and each have strengths and weaknesses. Models were benchmarked on several metrics encompassing the goodness of fit, tendency to overfit, performance when extrapolating to larger events than observed in the calibration data, and accuracy of calibration after calibrating to a short data period. No model performed best in every test, and there is somewhat of an inherent tradeoff: models with higher complexity tend to fit the data better but with increased risk of overfitting. This is the first study of its kind to quantitatively compare performance of multiple RDII models across a sufficient dataset of meter data. The findings are practical to practitioners when selecting models for calibration and when calibrating those models. This study also provides a dataset and framework for benchmarking of other or new models in future study.