A multivariate model for flood forecasting of lake levels

Abstract

A new multivariate model for fl ood forecasting of lake levels has been developed and applied to Lake Wakatipu and Lake Wanaka in the South Island of New Zealand. The model is based on the concept of the projection theorem to derive the optimum projection of the increase in lake levels on the driving factors for this increase. The driving factors that have been considered in this research are observed rainfall at sites in the catchment area or close to it, stream fl ows from rivers draining this rainfall in the region and outfl ows from the lakes. About 22 years of observed rainfall, river fl ows, lake outfl ows and lake levels have been investigated to select 23 signifi cant events for model calibration and 2 events for model validation. A lag of 10 hours (Lake Wakatipu) and a lag of 7 hours (Lake Wanaka) between cumulative lake rise and cumulative rainfalls have been verifi ed to improve the modelling process and have been utilized in the multivariate model. The analysis of the fi tted parameters for the multivariate model has resulted in the removal of some sites from the model due to their insignifi cant contribution or their being on odd with the realistic physical hydrological process. The projection theorem for orthonormal sets in the Hilbert space has been applied to the statistical characteristics of the data to estimate the optimum parameters of the multivariate model. Two multivariate models have been developed in this research. The fi rst multivariate model is for the long-term forecast of the rise of lake levels based on the forecasted rainfalls at selected rainfall sites in the catchment. The second multivariate model was derived based on the physical process of the hydrologic budget of a catchment and can be used for forecasted lake rise during the fl ood event based on rainfalls and stream fl ows gauged in the catchment areas of the lakes, in addition to the lake outfl ows.