A reliable linear method for modeling lake level fluctuations

Accurate forecasting of lake level time series (LLTS) is an important but challenging problem with major economic, social and environmental implications. However, in recent years, the level of uncertainty in the existing LLTS forecast methods has increased significantly due to climate change, therefore, the need to develop more accurate models. The main research question for this study is whether it is necessary to use nonlinear methods in LLTS modeling or if linear methods can produce as accurate and reliable forecast tools. We introduce a new linear-based forecast method for LLTS using spectral analysis, seasonal standardization, and stochastic terms. The application of the new LLTS forecast method is tested on two case study Lakes, including the Van Lake, in Turkey and the Michigan-Huron Lake, in North America. A two-step preprocessing techniques based on standardization and differencing was used for the Van Lake, and spectral analysis and differencing was employed for the Michigan-Huron Lake. We then compared the accuracy and uncertainty of the proposed linear method with an artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) methods. The uncertainty of the new linear LLTS forecast model was +/- 0.00455 and +/- 0.00264 for the Van Lake and the Michigan-Huron Lake, respectively, compared to +/- 0.00625 and +/- 0.00766 for the ANN and the ANFIS (respectively) at the Van Lake and +/- 0.00312 and +/- 0.00319 for the ANN and the ANFIS (respectively) at the Michigan-Huron Lake.