A Multivariate Model for Flood Forecasting of Lake Levels

A Multivariate Model for Flood Forecasting of Lake Levels

M. Mohssen 

Department of Environmental Management, Faculty of Environment, Society and Design, Lincoln University, Lincoln 7647, New Zealand

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A new multivariate model for flood 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 flows from rivers draining this rainfall in the region and outflows from the lakes. About 22 years of observed rainfall, river flows, lake outflows and lake levels have been investigated to select 23 significant 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 verified to improve the modelling process and have been utilized in the multivariate model. The analysis of the fitted parameters for the multivariate model has resulted in the removal of some sites from the model due to their insignificant contribution or their being on odd with the realistic physical hydrological process. The projection theorem for ortho-normal 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 first 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 flood event based on rainfalls and stream flows gauged in the catchment areas of the lakes, in addition to the lake outflows.


Lake level, fl ood forecast, fl ood modelling, Hilburt Space, lagged-correlations, projection theorem, rainfall-runoff, regression analysis


[1] Bye, P. & Horner, M., Easter 1998 Floods Report by the Independent Review Team to the Board of the Environmental Agency, Vol. 1, Environmental Agency: Bristol, 1998.

[2] Demeritt D., Cloke, H., Pappenberger, F., Thielen, J., Bartholmes, J. & Ramoset, M.-H. Ensemble predictions and perceptions of risk, uncertainty, and error in flood forecast-ing. Environmental Hazards, 7, pp. 115–127, 2007. doi: http://dx.doi.org/10.1016/j. envhaz.2007.05.001

[3] Jowitt, P.W., A conceptual system model of rainfall-runoff on the Haast River. Journal of Hydrology, New Zealand, 38(1), pp. 121–144, 1999.

[4] Moore, R. et al., Forecasting for flood warning. C.R. Geoscience, 337, pp. 203–217, 2005. doi: http://dx.doi.org/10.1016/j.crte.2004.10.017

[5] Vaziri, M., Predicting Caspian Sea surface water level by ANN and ARIMA models. Journal of Waterway, Port, Coastal. Ocean Engineering, 123(4), pp. 158–162, 1997. doi: http://dx.doi.org/10.1061/(ASCE)0733-950X(1997)123:4(158)

[6] Tiwari, M.K. & Chatterjee, C., Development of an accurate and reliable hourly flood fore-casting model using wavelet–bootstrap–ANN (WBANN) hybrid approach. Journal of Hydrology, 394, pp. 458–470, 2010. doi: http://dx.doi.org/10.1016/j.jhydrol.2010.10.001

[7] Chen, S.H., Lin, Y.H., Chang, L.C. & Chang, F.J., The strategy of building a flood forecast model by neuro-fuzzy network. Journal of Hydrological Processes, 20(7), pp. 1525–1540, 2006. doi: http://dx.doi.org/10.1002/hyp.5942

[8] Kisi, O., et al., Forecasting daily lake levels using artificial intelligence approaches. Com-puters & Geosciences, [7], 2011. doi: http://dx.doi.org/10.1016/j.cageo.2011.08.027

[9] Talebizadeh, M. & Moridnejad, A., Uncertainty analysis for the forecast of lake level fluctuations using ensembles of ANN and ANFIS models. Expert Systems with Appli-cations, 38, pp. 4126–4135, 2010. doi: http://dx.doi.org/10.1016/j.eswa.2010.09.075

[10] Ondimu, S. & Murase, H., Reservoir level forecasting using neural networks: Lake Naivasha. Biosystems Engineering, 96(1), pp. 135–138, 2007. doi: http://dx.doi.org/ 10.1016/j.biosystemseng.2006.09.003

[11] Ozgur Kisi, O., Shiri, J. & Nikoofar, F., Forecasting daily lake levels using artificial intelligence approaches. Computers & Geosciences, 41, pp. 169–180, 2012. doi: http:// dx.doi.org/10.1016/j.cageo.2011.08.027

[12] McSaveney, E., Floods - New Zealand’s Number One Hazard, TeAra - The Encyclope-dia of New Zealand, updated 2-Mar-09, 2009

[13] Mohssen, M. & Goldsmith, M., Flood forecasting of lake levels: A new concept. International Journal of Safety and Security Engineering, 1(4), pp. 363–375, 2011. doi: http://dx.doi.org/10.2495/SAFE-V1-N4-363-375

[14] Brockwell, P.J. & Davis, R.A., Time Series: Theory and Methods, Springer-Verlag: New York Inc., pp. 46–51, 1991.