Coupling a hybrid CNN-LSTM deep learning model with a Boundary Corrected Maximal Overlap Discrete Wavelet Transform for multiscale Lake water level forecasting

Developing accurate lake water level (WL) forecasting models is important for flood control, shoreline maintenance and sustainable water resources planning and management. In this study, improved accuracy of forecasts (up to three months) of Lake Michigan and Lake Ontario WLs was achieved by coupling Boundary Corrected (BC) Maximal Overlap Discrete Wavelet Transform (MODWT) data preprocessing, with a hybrid Convolutional Neural Network (CNN) Long-Short Term Memory (LSTM) deep learning (DL) model. Hybrid DL-based model performance was compared to that of BC-MODWT machine learning (ML) [e.g., Random Forest (RF) and Support Vector Regression (SVR)] models. For each lake, all models were calibrated using 70% of the monthly WL (in meters) data series (January 1918 to February 1988), with the remaining 30% (March 1988 to December 2018) serving for validation. In both standalone and wavelet-machine learning models, a hybrid correlation-based feature selection (CFS)-particle swarm optimization (PSO) search method served to select input variables among candidate WL lags of up to twelve months, whereas for the CNN-LSTM DL models, input variable selection was carried out automatically by the CNN structure. For the MODWT-based ML and DL models, input time series were decomposed using a BC-MODWT approach. Scaling coefficients were developed through several mother wavelet approaches (i.e., Haar, Daubechies, Symlets, Fejer-Korovkin and Coiflets) with different filter lengths (up to twelve) and decomposition levels (up to seven). Model performance was evaluated using several visual and statistical metrics, including the correlation coefficient, r; the root mean standard error, RMSE; and Willmot's Index, WI. The CNN-LSTM DL model outperformed the standalone SVR and RF models. For all time horizons, coupled MODWT-based CNN-LSTM models outperformed standalone and hybrid models in WL forecasting. Not all wavelet family/filter length/decomposition combinations improved standalone models; however, the proposed BC-MODWT-CNN-LSTM model implementing the Haar mother wavelet (for Lake Michigan - one-month ahead: r = 0.994, RMSE = 0.04 m, WI = 0.996; two-months ahead: r = 0.979, RMSE = 0.07 m, WI = 0.989; threemonths ahead: r = 0.957, RMSE = 0.102 m, WI = 0.976; for Lake Ontario - one-month ahead: r = 0.956, RMSE = 0.082 m, WI = 0.978; two-months ahead: r = 0.864, RMSE = 0.141, WI = 0.912; three-months ahead: r = 0.755, RMSE = 0.182 m, WI = 0.841) outperformed standalone ML and BC-MODWT-ML-based models. Accordingly, the BC-MODWT-CNN-LSTM model can be viewed as a potentially useful approach to increase the accuracy of lake WL forecasts.