Operational stream water temperature forecasting with a temporal fusion transformer model

Stream water temperatures influence aquatic biodiversity, agriculture, tourism, electricity production, and water quality. Therefore, stakeholders would benefit from an operational forecasting service that would support timely action. Deep Learning methods are well-suited for this task as they can provide probabilistic forecasts at individual stations of a monitoring network. Here we train and evaluate several state-of-the-art models using 10 years of data from 55 stations across Switzerland. Static features (e.g. station coordinates, catchment mean elevation, area, and glacierized fraction), time indices, meteorological and/or hydrological observations from the past 64 days, and their ensemble forecasts for the following 32 days are included as predictors in the models to estimate daily maximum water temperature for the next 32 days. We find that the Temporal Fusion Transformer (TFT) model performs best for all lead times with a cumulative rank probability score (CRPS) of 0.73 ºC averaged over all stations, lead times and 90 forecasts distributed over 1 full year. The TFT is followed by the Recurrent Neural Network (CRPS = 0.77 ºC), Neural Hierarchical Interpolation for Time Series (CRPS = 0.80 ºC), and Multi-layer Perceptron (CRPS = 0.85 ºC). All models outperform the benchmark ARX model. When factoring out the uncertainty stemming from the meteorological ensemble forecasts by using observations instead, the TFT improves to a CRPS of 0.43 ºC, and it remains the best of all models. In addition, the TFT model identifies air temperature and time of the year as the most relevant predictors. Furthermore, its attention feature suggests a dominant response to more recent information in the summer, and to information from the previous month during spring and autumn. Currently, daily maximum water temperature probabilistic forecasts are produced twice per week and made available at https://drought.ch/de/allgemeine-lage/wassertemperatur/fliessgewaesser-1-1.html.