A generalized linear stochastic model for lake level prediction

Endorheic lakes are one of the most important factors of an environment. Regarding their morphology, these lakes, in particular saline lakes, are much more sensitive and can either benefit or pose a threat to their surroundings. Thus, constant monitoring of such lakes' water level, modeling and analyzing them for future planning and management policies is vitally important. We proposed a generalized linear stochastic model (GLSM) for forecasting the weekly and monthly Urmia lake water levels, the sixth-largest saltwater lake on Earth. In this methodology, three approaches are defined to pre-process data. The first approach is merely based on the differencing method, while the second and third are a one-step (the combination of de-trending with standardization and spectral analysis) and two-step (the combination of the 2nd approach with normalization transform) preprocessing, respectively. A thorough comparison of the GLSM results with eminence nonlinear AI models (Adaptive Neuro-Fuzzy Inference Systems, ANFIS, Multilayer Perceptron, MLP, Gene Expression Programming, GEP, Support Vector Machine with Firefly algorithm, SVM-FFA, and Artificial Neural Networks ANN) showed that by using an appropriate method that delivers accurate information of the entailing terms in time series, it is possible to model Urmia lake level with acceptable precision. Concisely, the GSLM with coefficients of determination (R²) 99.957% and root mean squared error (RMSE) of 2.121% outperformed the SVM-FFA with R² 99.59%, RMSE 3.27%, ANN with R² 99.56%, RMSE 3.3%, ANFIS with R² 98.9%, RMSE 4.3%, GP with R² 99.89%, RMSE 3.47%, GEP with R² 94.75%, RMSE 4.15% for forecasting weekly time series. In forecasting monthly time series, the GLSM method with R² 99.517% and RMSE 6.91% also outperformed GEP R² 91.95%, RMSE 15.3%, ANFIS R² 92.85%, RMSE 47.55% models. Consequently, GSLM proved that by applying proper comprehensible linear techniques promising results can be obtained rather than using sophisticated AI methods.