Time Distributed Deep Learning Models for Purely Exogenous Forecasting: Application to Water Table Depth Predictions Using Weather Image Time Series

Matteo Salis, Abdourrahmane M. Atto, Stefano Ferraris, Rosa Meo,
Time Distributed Deep Learning Models for Purely Exogenous Forecasting: Application to Water Table Depth Predictions Using Weather Image Time Series,
Environmental Modelling & Software,
Volume 193,
2025,
106568,
ISSN 1364-8152,
https://doi.org/10.1016/j.envsoft.2025.106568.
(https://www.sciencedirect.com/science/article/pii/S136481522500252X)
Abstract: Deep Learning (DL) models have revealed to be very effective in hydrology, especially in handling spatially distributed data (e.g. raster data). We have proposed two different DL models to predict the water table depth in the Grana-Maira catchment (Piedmont, IT) using only exogenous weather image time series. Both the models are made of a first Time Distributed Convolutional Neural Network (TDC) which encodes the images into hidden vectors. The first model, TDC-LSTM uses then a Sequential Module based on an LSTM layer to learn temporal relations and output the predictions. The second model, TDC-UnPWaveNet uses instead a new version of the WaveNet architecture, adapted for handling output of different length and completely shifted in the future to the input. Both models have shown remarkable results focusing on different learnable information: TDC-LSTM has focused more on bias while the TDC-UnPWaveNet more on the temporal dynamics maximizing correlation ρ, achieving mean BIAS (and standard deviation) −0.18(0.05), −0.25(0.19) and ρ 0.93(0.03), 0.96(0.01) respectively over all the sensors.
Keywords: Deep Learning; Image time series; CNN; LSTM; WaveNet; Groundwater resources; Water table depth