Mathematical modelling of debris flows and mudslides incurring from extreme rainfall events. The case of the Madeira Island flash-floods in 2010

Daniel Conde, Rui M. L. Ferreira, Rodrigo Proença Oliveira

Tuesday 30 june 2015

14:05 - 14:20h at South America (level 0)

Themes: (T) Flood risk management and adaptation, (ST) Flood risk assessment

Parallel session: 6J. Floodrisk - Assessment

On the 20th February of 2010 a torrential rainfall struck the Atlantic Island of Madeira, Portugal, resulting in violent floods and mudslides that claimed a death toll of nearly 50 lives and damage costs rising up to €1.5 Million. At the capital city of Funchal, to where three main streams converge, an overwhelming flash-flood was responsible for nearly half of the total victims. The combination of a continued and heavy runoff with multiple mudslides resulted in debris-flow fronts that propagated downstream while carrying very high concentrations of solid material. These two-phase solid-fluid flows were responsible for most of the infrastructural damage across the island, due to their significantly increased mass and momentum. The aim of the present modelling work is to validate a recently developed 2DH model for torrential flows with the data of the event of 20th February of 2010. The numerical tool, STAV-2D (CEHIDRO - IST), is based on a finite-volume method using a flux-splitting technique featuring a reviewed Roe-Riemann solver, with appropriate source-term formulations to ensure full conservativeness. STAV-2D also features specific formulations for simulating the interaction of debris-flows with natural mobile beds composed of poorly sorted sediment mixtures and has been validated with both theoretical solutions and laboratory data. The modelling of the existing natural and built environment is fully explicit. All buildings, streets and channels are accurately represented within the mesh geometry. Such detail is relevant for the reliability of the validation using field data, since the major sedimentary deposits within the urban meshwork of Funchal were identified and characterized in terms of volume and grain size distribution during the aftermath of the 20th February of 2010 event. Indeed, the measure of the quality of the numerical results is the agreement between simulated and estimated volume of deposited sediment and between estimated and modelled grain-size distribution of the deposits. The formulations expressing closures for flow resistance and flow-bed interaction and their parameters are discussed. The simulation tool resulting from this modelling effort is expected to help the establishment of new methodologies and parameters for hydraulic design and hazard assessment in the Island of Madeira.