Stochastic modeling of the Van Lake monthly level fluctuations in Turkey

Planning, design, construction and operation of lakeshore structures require information about the future likely extremes of the lake levels at a given risk percentage. Alternative future likely synthetic sequences can be numerically generated provided that the underlying generating mechanism of the lake level fluctuation phenomenon is identified. Simple linear and periodic nonlinear models are used for modeling the deterministic part in the lake level records. Linear trend is eliminated from the original lake level historic data by regression line technique. The nonlinear part needs two stages for its identification. First Fourier series is applied to model interannual periodicities in the lake level fluctuation series and then monthly standardization procedure is applied for seasonal periodic nonlinear component modeling. A second order Markov model is found suitable for the remaining stochastic parts. The application of the methodology is presented for the Lake Van monthly level data in eastern Turkey. Suitable models are identified and their parameters are estimated for trend, periodic and stochastic parts. Likely, synthetic lake levels are generated by the stochastic model and hence lake level extreme values are depicted for the next 2, 6, 12, 24, 60 and 120 months with risk calculations. Such risk calculations take into account the stochastic characteristics of the lake level fluctuations only. The deterministic parts as linear trends and periodicities are added to the stochastic extreme events for the actual simulation of the lake levels. The model presented in this paper is not for time prediction of future lake levels but rather for the simulation of possible equally likely extreme lake level value occurrences over any desired future period.