A methodology to estimate probability of occurrence of floods using principal component analysis

Abstract:

Flood events and debris flows are characterized by a very rapid response of basins to precipitation, often resulting in loss of life and property damage. Complex topography with steep slopes and narrow valleys increase the likelihood of having these events. An early warning system (EWS) is a tool that allows anticipating a hazardous event, which in turns provides time for an early response to reduce negative impacts. These EWS’s can rely on very powerful and computer-demanding models to predict flow discharges and inundation zones, which require data typically unavailable. Instead, simpler EWS´s based on a statistical analysis of observed hydro-meteorological data could be a good alternative. In this work we propose a methodology for estimating the probability of exceedance of maximum flowdischarges using principal components analysis (PCA). In the method we first perform a spatio-temporal cross-correlation analysis between extreme flows data and daily meteorological records for the last 15 days prior to the day of the flood event. We then use PCA to create synthetic variables which are representative of the meteorological variables associated with the flood event (i.e. cumulative rainfall and minimum temperature). Finally, we developed a model to explain the probability of exceedance using the principal components. The methodology was applied to a basin in the foothill area of Santiago, Chile, for which all the extreme events between 1970 and 2013 were analyzed.Results show that elevation rather than distance or location within the contributing basin is what mainly explains the statistical correlation between meteorologicalrecords and flood events. Two principal components were found that explain more than 90% of the total variance of the accumulated rainfalls and minimum temperatures. One component was formed with cumulative rainfall from 3 to 15 days prior to the event, whereas the other one was formed with the minimum temperatures for the last 2 days preceding the event. Finally, a simple model relating the probability of exceedance of flood with the two principal components was successfully implemented (i.e. with values of R²>0.7).