Author(s)

M. MOHSSEN & M. GOLDSMITH

Abstract

A new concept for flood modelling of lake levels has been introduced, analysed, and tested for Lake Wakatipu in the South Island of New Zealand. Lake level response to significant rainfall events is substantially different from rivers. Lakes usually have enormous storage to absorb the peak of the flood event, and their outflows are dependent on their level rather than the inflows. The new concept is based on carrying out a lagged correlation analysis between hourly data for the cumulative rainfall and the total rise of the lake level in order to determine the lagged time series of total lake rise which will provide the best projection for its forecast onto the cumulative rainfall. The focus has been to carry out this analysis on hourly data during significant rainfall events which resulted in significant lake rise. In return, the time frame for such analysis is usually several hours or few days, as is the case for Lake Wakatipu. Thus, some variables which are usually considered for lake analysis, such as evapotranspiration, can be negligible compared with the huge amount of rain causing the flood event. Based on the best lagged correlation, three models have been derived to forecast flood levels of Lake Wakatipu. Correlation analysis of lagged correlations showed that a lag of 11 hours results in the highest correlation between cumulative rainfall and total rise of Lake Wakatipu level, while 14 hours produced the highest correlation between cumulative rainfall and total lake inflows. All three models utilised these optimum lagged hours for the best projection of total lake rise/inflow. The first model is a lag-11 non-linear regression model, while the second model is a lag-11 linear regression model, and the third one is a lag-14 comprehensive hourly mass balance model. The results of model testing showed that the simple linear regression model produced the best forecasts, while the more sophisticated complete mass balance model, in general, was not as good, and the non-linear regression model (while having the highest determination coefficient) was the least performing.

Keywords

flood forecast, flood modelling, lagged correlations, lake level, projection theorem, rainfall-runoff, regression analysis