A multivariate model for flood forecasting of lake levels

Abstract

A new multivariate flood forecast model for lake levels has been developed. The model is based on the concept of the projection theorem, to obtain the projection of lakes flood levels on total rainfall forecasted or observed at nearby rainfall gauges. A comprehensive analysis of 20 historical and significant rainfall events on Lake Wakatipu and Lake Wanaka in the South Island of New Zealand has been carried out to detect the best time series and functions to be used for this projection. The study showed that linear relationships exist between total lake rise and total rainfalls observed at available rain gauges. In addition, during flood events, linear relationship can be utilised to represent the function between observed cumulative rainfall and cumulative lake rise at 10 hours (Lake Wakatipu) and 7 hours (Lake Wanaka) of lead time. Analysis of relationships between lake rise and alternative options for available rainfall sites resulted in the choice of rainfall sites for the best forecast model. Parameter estimation of a multivariate model which includes both Lake Wakatipu and Lake Wanaka flood levels and the selected rainfall sites was carried out by using the projection equations of orthonormal sets. The derived model was applied to two observed events which were not included in the calibration process. The new model has performed well in forecasting flood levels of both lakes. Keywords: flood forecast, flood modelling, rainfall-runoff, lake level, projection theorem, Hilbert space.