Analytical modeling of the hydrologic response under moving rainstorms: Storm–catchment interaction and resonance

• We propose an analytical framework to explore rainstorm-catchment interactions.
• Resonance conditions depend on the relative size between storm and basin.
• For a Dirac storm complete resonance conditions may arise for any storm direction.
• Partial resonance conditions arise for storms moving downstream along main channel.
• Resonance conditions depend on basin geomorphic and kinematic features.

SummaryIn this study, we propose a simple yet broad analytical framework for analyzing the hydrological response of a catchment under moving rainstorms; the method can be used as a tool to explore the main relevant features of the storm-catchment interactions. We analyze the response of the basin to an excess rain field (rain contributing to direct runoff), which is assumed to be variable in space and time; catchment response is supposed to be characterized by the time-invariant distribution of the travel time of water particles within the basin. We use the framework developed herein to investigate the conditions that enhance peak flow, leading to the so-called resonance effect, in terms of storm size, direction and velocity. Our results show how resonance conditions depend on the relative size of the rainstorm with respect to basin size. In particular, for storm sizes much smaller than the dimension of the catchment, a complete resonance effect occurs for infinite combinations of the direction and speed of the moving rainstorm. On the contrary, when storm size is much larger than the basin size, the flood peak tends to be independent on rainstorm movement. In the intermediate conditions a partial resonance effect emerges as a consequence of both the superposition of rainfall contributes in time and the increased flow response of the basin; the latter is a result of the larger rainfall volume injected over time. For illustration purposes, we present and discuss a case study based on the open-book idealized catchment.