Deep signals: enhancing bottom temperature predictions in Norway’s Mjøsa Lake Through VMD- and EMD-Boosted machine learning models

In this study, we benchmark various machine learning techniques against a synthetic but physically based reference time series (model-simulated (ERA5-Land/FLake) bottom-temperature series) and assess whether decomposition methods (VMD and EMD) improve forecast accuracy using Support Vector Machine (SVM), Multi-Layer Perceptron (MLP), Random Forest (RF), Gaussian Process Regression (GPR), and Long Short-Term Memory (LSTM) with the monthly average data of Mjøsa, the largest lake in Norway, between 1950 and 2024 from the ERA5-Land FLake model. A total of 70% of the dataset was used for training and 30% was reserved for testing. To assess the performance several metrics, correlation coefficient (r), Nash–Sutcliffe efficiency (NSE), Kling–Gupta efficiency (KGE), Performance Index (PI), RMSE-based RSR, and Root Mean Square Error (RMSE) were used. The results revealed that without decomposition, the GPR-M03 combination outperforms other models (with scores r = 0.9662, NSE = 0.9186, KGE = 0.8786, PI = 0.0231, RSR = 0.2848, and RMSE = 0.2000). Considering decomposition cases, when VMD is applied, the SVM-VMD-M03 combination achieved better results compared to other models (with scores r = 0.9859, NSE = 0.9717, KGE = 0.9755, PI = 0.0135, RSR = 0.1679, and RMSE = 0.1179). Conversely, with decomposition cases, when EMD applied, LSTM-EMD-M03 is explored as the more effective combination than others (with scores r = 0.9562, NSE = 0.9008, KGE = 0.9315, PI = 0.0256, RSR = 0.2978, and RMSE = 0.3143). The results demonstrate that GPR and SVM, coupled with VMD, yield high correlation (e.g., r ≈ 0.986) and low RMSE (~0.12), indicating the ability to reproduce FLake dynamics rather than as accurate predictions of measured bottom temperature.