Reachability Analysis as a Design Tool for Stormwater Systems

Effective stormwater management requires systems that operate safely and deliver improved environmental outcomes in a cost-effective manner. However, current design practices typically evaluate performance assuming that a given system starts empty and operates independently from nearby stormwater infrastructure. There is a conspicuous need for more realistic design-phase indicators of performance that consider a larger set of initial conditions and the effects of coupled dynamics. To this end, we apply a control-theoretic method, called reachability analysis, to produce a more objective measure of system robustness. We seek two primary contributions in this work. First, we demonstrate how the application of reachability analysis to a dynamic model of a stormwater network can characterize the set of initial conditions from which every element in the network can avoid overflowing under a given surface runoff signal of finite duration. This is, to the authors' knowledge, the first published application of reachability analysis to stormwater systems. Our second contribution is to offer an interpretation of the outcomes of the proposed reachability analysis as a measure of system robustness that can provide useful information when making critical design decisions. We illustrate the effectiveness of this method in revealing the trade-offs of particular design choices relative to a desired level of robustness.