Daily water level forecasting with limited data using cluster- and season-based transfer learning.

The coupling of clustering or classification with deep learning presents an appealing knowledge-guided approach for hydrological prediction. However, applying such an approach to short-term water level forecasting with limited data may result in inadequately populated samples in each cluster for model development. In this study, we developed a framework by combining transfer learning and either seasonal classification or fuzzy C-means (FCM) clustering to tackle this problem. We applied this framework to daily water level prediction at the Lechang Gorge in China. Initially, we explored various combinations of missing data treatment, independent variables, internal parameters, and hyperparameters to pre-train the base Long Short-Term Memory (LSTM) model. The optimally pre-trained model exhibited no significant systematic prediction error (bias = -0.003 m) and achieved an R-value of 0.943, an NSE of 0.457, and an RMSE of 0.889 m for validation. Subsequently, we fine-tuned the pre-trained models using data from four seasons (post-dry, early-flood, post-flood, and early-dry) and two seasons (flood and dry), as well as using cluster data through FCM clustering with either precipitation or water level data. Compared to pre-trained models, the optimally fine-tuned models based on seasonal classification tended to outperform in dry-related periods but underperformed in flood-related seasons. The optimally fine-tuned model based on FCM clustering using precipitation outperformed the baseline in almost all clusters, achieving an RMSE of 0.412 m (a 6.2% improvement) during validation. Overall, transfer learning helps to overcome the limitations of small data by enabling the model to learn from a broader dataset and then adapt to specific conditions within each cluster. This method also enhances the interpretation and helps to identify directions for further improvement of river forecasting models.