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high efficiency in optimization of reservoir operation can be achieved, as shown in [11]. However, it is worth mentioning that the representation of the KL expansion is specific to inflow distribution. Different inflow ensembles i.e., the ESP may result in different KL expansion form in which the parameter of M may vary from case to case. 5. CONCULUSIONS The ensemble inflow and its associated uncertainty can be modeled by a KL representation with only three terms, meaning three variables. This result in a high efficiency in modeling the propagation and optimal control of the inflow uncertainty in reservoir operation, comparing to Monte Carlo method which normally sampling thousand times in each optimization routine. ACKNOWLEGEMENT The authors thank National Natural Science Foundation of Hubei Province (2017CFB613) and open funding of Hunan Provincial Key Laboratory of Key Technology on Hydropower Development(PKLHD201705). The authors would also like to thank Prof. Nathan Gibson and Dr. Veronika Vasylkivska for providing the Matlab code for the Karhunen-Loeve expansion. REFERENCES [1] KIM, S., LIMON, R. A., et al. Integrating Ensemble Forecasts of Precipitation and Streamflow into Decision Support for Reservoir Operations in North Central Texas. In AGU Fall Meeting Abstracts, 2016, Feb. [2] KosambiD. D., Statistics in function space, J. Indian Math. Soc. (N.S.) 7 (1943), 76–88. [3] Karhunen K.K, On linear methods in probability and statistics, Ann. Acad. Sci. Fennicae. Ser. A. I. Math.-Phys., 1947, No. 37, 1–79. [4] Williams, M. M. R. (2015). Numerical solution of the Karhunen–Loeve integral equation with examples based on various kernels derived from the Nataf procedure. Annals of Nuclear Energy, 76, 19-26. [5] XIU, D. (2010). Numerical methods for stochastic computations: a spectral method approach. Princeton University Press, 2010. [6] Narayanan, M. V., King, M. A., Soares, E. J., Byrne, C. L., Pretorius, P. H., &Wernick, M. N. (1999). Application of the Karhunen-Loeve transform to 4D 176