Numerical simulation of the shallow water equations coupled with a precipitation system driven by random forcing

Townsend, Philip James Andrew (2018) Numerical simulation of the shallow water equations coupled with a precipitation system driven by random forcing. Doctoral thesis (PhD), University of Sussex.

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Abstract

Quantification of flood risk and flood inundation requires accurate numerical simulations, both in terms of the mathematical theory that underpins the methods used and the manner in which the meteorological phenomena that cause flooding are coupled to such systems. Through our research, we have demonstrated how rainfall and infiltration effects can be incorporated into existing flood models in a rigorous and mathematically consistent manner; this approach departs from preceding methods, which neglect terms representing such phenomena in the conservation or balancing of momentum. We demonstrate how the omission of these terms means the solution derived from such models cannot a priori be assumed to be the correct one, which is in contrast to solutions from the extended system we have developed which respect the energetic consistency of the problem.
The second issue we address is determining how we can model these meteorological phenomena that lead to flooding, with a specific interest in how existing observation data from rain gauges can be incorporated into our modelling approach. To capture the random nature of the precipitation, we use stochastic processes to model the complex meteorological interactions, and demonstrate how an accurate representation of the precipitation can be built. Given the specific industrial applications we have mind in regards to flood modelling and prediction, there will be a high computational cost associated with any such simulations, and so we consider techniques which can be used to reduce the computational cost whilst maintaining the accuracy of our solutions. Having such an accurate flood model, coupled with a stochastic weather model designed for efficient computational modelling, will enable us to make useful predictions on how future climate change and weather patterns will impact flood risk and flood damage.

Item Type: Thesis (Doctoral)
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: G Geography. Anthropology. Recreation > GB Physical geography > GB0651 Hydrology. Water (Ground and surface waters)
Q Science > QA Mathematics > QA0297 Numerical analysis
Q Science > QC Physics > QC0851 Meteorology. Climatology Including the earth's atmosphere > QC0980 Climatology and weather
Depositing User: Library Cataloguing
Date Deposited: 16 Jul 2018 13:12
Last Modified: 16 Jul 2018 13:13
URI: http://sro.sussex.ac.uk/id/eprint/77216

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