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

Groundwater resources are one of the most relevant elements in the water cycle, therefore developing models to accurately predict them is a pivotal task in the sustainable resource management framework. Deep Learning (DL) models have been revealed to be very effective in hydrology, especially by feeding spatially distributed data (e.g. raster data). In many regions, hydrological measurements are difficult to obtain regularly or periodically in time, and in some cases, the last available data are not up to date. Reversely, weather data, which significantly impacts water resources, are usually more available and with higher quality. More specifically, we have proposed two different DL models to predict the water table depth in the Grana-Maira catchment (Piemonte, IT) using only exogenous weather image time series. To deal with the image time series, both models are made of a first Time Distributed Convolutional Neural Network (TDC) which encodes the image available at each time step into a vectorial representation. 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 here to output a sequence shorter and completely shifted in the future with respect to the input one. To this aim, and to deal with the different sequence lengths in the UnPWaveNet, we have designed a new Channel Distributed layer, that acts like a Time Distributed one but on the channel dimension, i.e. applying the same set of operations to each channel of the input. TDC-LSTM and TDC-UnPWaveNet have shown both remarkable results. However, the two models have focused on different learnable information: TDC-LSTM has focused more on lowering the bias, while TDC-UnPWaveNet has focused more on the temporal dynamics, maximizing correlation, and KGE.