Hydrodynamic flows during heavy rain events: Scalable algorithmic methods for simulation and sensitivity analysis

Abstract. We present significant progress for scalable and fine-grained computation of large flooding events. As a first step, we describe (I) breakthroughs for simulating time-dependent, high-resolution runoff in large-scale heavy-rain scenarios, based on two algorithmic speedup techniques. The first is (a) a flow-based subdivision technique of the terrain that enables independent, parallel simulation of different regions, while ensuring consistency of the overall simulation. The second is (b) a feature-based algorithmic grid refinement technique. Using this refinement, runtimes for high-resolution hydrodynamic simulations are reduced by 85–90% compared to uniform 1m grids, which can result in better than real-time performance for realistic inputs in medium-sized regions. In combination with state-of-the-art commercial software and powerful computing devices, these techniques make it possible to carry out simulations for large-scale scenarios that were previously infeasible due to memory requirements, and provide considerable speedup for medium- or small-scale scenarios.

Combining both techniques, the time-dependent runoff during a five-hour heavy-rain event at 1 m output resolution for an area of 370 km² in the mountainous Harz region (i.e., for 370,000,000 terrain points with considerable elevation differences and ensuing dynamic flows) can be simulated within three days; without our techniques, such a simulation would not even be possible due to the unmanageable memory requirements.

This progress enables us to demonstrate how to address a second challenge: How can we deal with the instability of precipitation events, which are notoriously difficult to predict with good accuracy? We use our new computational capabilities to conduct (II) a large-scale, multifaceted sensitivity analysis, providing insights into different scenarios for possible time-dependent runoff and flooding when varying the input precipitation for our study area. This makes it possible to identify both regions of stability (for which the outcomes are largely unchanged under input variations) as well as critically unstable locations (for which the outcome may change significantly under input variations). In particular the latter is of crucial value for effective disaster mitigation: Knowing where relatively small changes in the input can make a huge difference in the outcome is invaluable when deciding where to invest limited resources with the greatest impact. We demonstrate the viability of this approach by identifying such a critical location for our study area.