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

arXiv: https://arxiv.org/abs/2409.13284 · HTML: https://mlsanity.com/paper/2409.13284/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 93 references that are in the map.
- First posted on arXiv 20 Sep 2024.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Temporal Convolutional Networks for Action Segmentation and Detection](https://mlsanity.com/paper/1611.05267/) (2016)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [Efficient Object Localization Using Convolutional Networks](https://mlsanity.com/paper/1411.4280/) (2014)
- [Deep Learning for Precipitation Nowcasting: A Benchmark and A New Model](https://mlsanity.com/paper/1706.03458/) (2017)
- [Conditional Time Series Forecasting with Convolutional Neural Networks](https://mlsanity.com/paper/1703.04691/) (2017)
- [Convolutional Sequence to Sequence Model for Human Dynamics](https://mlsanity.com/paper/1805.00655/) (2018)
- [Temporally Distributed Networks for Fast Video Semantic Segmentation](https://mlsanity.com/paper/2004.01800/) (2020)
- [A trans-disciplinary review of deep learning research for water resources scientists](https://mlsanity.com/paper/1712.02162/) (2017)
- [STConvS2S: Spatiotemporal Convolutional Sequence to Sequence Network for Weather Forecasting](https://mlsanity.com/paper/1912.00134/) (2019)
- [Investigating Temporal Convolutional Neural Networks for Satellite Image Time Series Classification: A survey](https://mlsanity.com/paper/2204.08461/) (2022)

## Abstract (arXiv)

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.