An Analytical Stochastic Approach for Evaluating the Performance of Combined Sewer Overflow Tanks

Abstract Storm water detention tanks are widely used for the control of combined sewer overflows. Conventional continuous simulation and recently developed analytical probabilistic models have been used for analyzing the hydrologic operation of storm water detention tanks. These analyses are necessary in order to accurately estimate the runoff capture efficiency of a given control system or the required storage capacity for achieving a desired runoff capture efficiency. The analytical probabilistic models still have the shortcomings of making simplifying assumptions about the initial storage conditions of a detention tank. Developed in this study is a new stochastic analysis method which can provide similar results as provided by continuous simulations and overcome some of the shortcomings of the previously developed analytical probabilistic models. This stochastic analysis method uses closed‐form analytical equations to estimate the runoff capture efficiency and required storage capacity. Results from these analytical equations are validated by comparing with continuous simulation results and close agreements are observed. These analytical equations are therefore proposed as a computationally efficient alternative for analyzing the hydrologic performance of combined sewer overflow tanks. Plain Language Summary Storm water detention tanks are widely used for the control of combined sewer overflows. Conventional continuous simulation and recently developed analytical probabilistic models can be used for analyzing their hydrologic operations. Continuous simulations are time consuming to perform and require a large amount of input data. Analytical probabilistic models still have the shortcoming of making simplifying assumptions about the initial storage conditions of a detention tank. A new analytical stochastic model is developed in this study which eliminates the shortcomings of both the continuous simulation and analytical probabilistic approaches. The new analytical stochastic model uses closed‐form equations to directly estimate the system performance statistics. It can thus be used as a convenient tool for the planning, design, and operation of combined sewer overflow tanks. Key Points A new analytical stochastic approach was developed to evaluate the hydrologic performance of combined sewer overflow tanks Results of the proposed approach compare well with conventional continuous simulation results The proposed approach can be used as a convenient tool for the planning, design, and operation of combined sewer overflow tanks