Stochastic Approaches for Estimating the Performance of Low Impact Development Practices

Abstract

To reduce the impacts of urbanization on the natural hydrologic cycle, low impact development (LID) practices have been increasingly implemented worldwide. This thesis aims at improving the existing analytical models and developing new sets of analytical equations to quantify the performance statistics of structural LID practices. As a starting point, the previously developed analytical probabilistic approach is extended for developing an event-based probabilistic model of infiltration facilities, which is based on the exponential probability distributions of rainfall characteristics and the mathematical representation of the hydrologic processes involved in the operation of infiltration facilities. Analytical equations for the determination of their overflow frequency and stormwater capture efficiency are obtained. To better understand the antecedent condition and avoid using any simplifying assumptions about it, an analytical stochastic approach is then proposed for the analysis of rainwater harvesting (RWH) systems and permeable pavement systems (PPSs). Using this approach, the forward stochastic differential equations that relate the probabilities of the moisture state involved in the operation of RWH systems and PPSs are established. The steady-state probability distributions of moisture contents are then analytically solved from these stochastic differential equations. Based on these steady-state probability distributions, the stormwater capture and water saving efficiencies of RWH systems are analytically derived. Applying the stochastic approach together with the analytical probabilistic approach to study the operation of PPSs, analytical equations that can be used for evaluating the stormwater capture efficiency of PPSs are also obtained. Verifications of all the analytical solutions are made for a wide range of cases located in different climate regions by comparison with continuous simulations. It is demonstrated that the analytical equations presented in this thesis provide an easy-to-use tool with higher accuracy and wider application range for the planning and design of LIDs, which is much needed given the increasing implementations of LIDs.