In the past when the computers and modeling software were too slow for continuous long-term simulations, an event-by-event model calibration and verification approach was used to meet specific model accuracy criteria. Event-based model calibration consists of adjusting model input parameters, such as roughness, imperviousness, soil permeability, etc., until the difference between the modeled and observed event quantities is within acceptable accuracy criteria. Model verification consisted of running the calibrated model with one or more independent events to verify the accuracy of the calibrated model. The accuracy is defined as the percent difference between observed and modeled quantities (e.g., depth, flow volume, flow rate). If model validation does not produce accurate results, the model calibration is refined further. Model calibration and verification steps are repeated several times (usually 10 to 20 times) until satisfactory results are obtained. Generally, event-based model calibration and verification is laborious and expensive. Furthermore, larger wet weather events generally used in the event-based calibration and validation can bias the model results to extreme conditions.
With the availability of long-term continuous flow meter and rainfall data and faster computers, models can now be calibrated to a long-term flow record spanning from few months to several years. The practice of model calibration for large and complex regional systems is evolving over the years away from the two-step calibration and verification process to a single-step continuous calibration process.
There are a variety of statistical measures that may be used to measure the goodness-of-fit between a measured and a modeled hydrograph. Statistical measures such as Integral Square Error (ISE), Nash-Sutcliffe Efficiency (NSE), and coefficient of determination (R2) can be used as a single, non-subjective, statistical measure of calibration and validation. Certain modeling software (e.g., PCSWMM) has integrated tools (objective functions) for computing such statistical measures. Continuous calibration using such software reduces labor hours as no cumbersome spreadsheet pre-processing of rainfall data (event selection) or post-processing of model results (for calculating % difference in depth, flow, and volume) is required outside the model. Model can be considered calibrated when the statistical criteria are met. Rather than calibrating and validating the model to few observed events, calibrating to the entire observation period can be accomplished. Continuous calibration can ensure that there is no overall or seasonal bias in the simulations and that over-simulation and under-simulation of individual storms balance out over the course of the long-term simulation. Best of all, because the model is calibrated to the entire observation period, there is no need to verify the model with independent events. In fact, when all observed events have already been used in calibration, no events are left for verification.
This paper will provide information and comparison of various statistical measures that can be used in continuous calibration. Examples will be provided from the Metropolitan Sewer District of Greater Cincinnati (MSDGC) SWMM model which is one of the largest SWMM model in the world. MSGDC provides sewerage collection and treatment services to approximately 230,000 residential and commercial users in Hamilton County, Ohio. It serves an area covering approximately 290 square miles through approximately 3,000 miles of sanitary and combined sewers, seven major wastewater treatment plants, three package treatment plants, and more than 120 pump stations. The treatment system has a dry weather capacity of 200 MGD. The largest Mill Creek plant has a wet weather capacity of 440 MGD. The paper will describe MSDGC’s massive ongoing 15-year model calibration and verification work and how the model is being used for the planning and design of CSO/SSO Consent Decree projects. Challenges and lessons learned will be shared.