Reachability Analysis as a Design Tool for Stormwater Systems: Towards Planning in the Presence of Stochastic Surface Runoff

Stormwater infrastructure is required to safely manage uncertain precipitation events of varying intensity, while protecting natural ecosystems, under restricted financial budgets. In practice, candidate designs for stormwater detention or retention systems are commonly evaluated assuming that a given system operates independently from nearby systems and is initially empty prior to an extreme storm event. In recent work, we demonstrate the use of a control-theoretic method, called reachability analysis, to provide a more realistic design-phase indicator of system performance [1]. In particular, reachability analysis predicts the response of a dynamically-coupled stormwater storage network to a deterministic storm event under a wide range of initial conditions simultaneously [1]. The outcomes of this analysis can be viewed as measures of system robustness that inform the evaluation of safety-critical design choices [1]. Here we discuss how to extend the recent work to incorporate the stochastic nature of surface runoff. We represent surface runoff as a random disturbance to a dynamic system model of a stormwater storage network. Using a probability distribution of surface runoff derived from a Monte Carlo method, we apply an existing algorithm [2] for stochastic reachability analysis to the problem of designing robust stormwater storage systems. We discuss particular advantages and disadvantages of using stochastic reachability analysis, deterministic reachability analysis, or random sampling to assess system robustness.