Wavelet gated multiformer for groundwater time series forecasting

Abstract

Developing accurate models for groundwater control is paramount for planning and managing life-sustaining resources (water) from aquifer reservoirs. Significant progress has been made toward designing and employing deep-forecasting models to tackle the challenge of multivariate time-series forecasting. However, most models were initially taught only to optimize natural language processing and computer vision tasks. We propose the Wavelet Gated Multiformer, which combines the strength of a vanilla Transformer with the Wavelet Crossformer that employs inner wavelet cross-correlation blocks. The self-attention mechanism (Transformer) computes the relationship between inner time-series points, while the cross-correlation finds trending periodicity patterns. The multi-headed encoder is channeled through a mixing gate (linear combination) of sub-encoders (Transformer and Wavelet Crossformer) that output trending signatures to the decoder. This process improved the model’s predictive capabilities, reducing Mean Absolute Error by 31.26 % compared to the second-best performing transformer-like models evaluated. We have also used the Multifractal Detrended Cross-Correlation Heatmaps (MF-DCCHM) to extract cyclical trends from pairs of stations across multifractal regimes by denoising the pair of signals with Daubechies wavelets. Our dataset was obtained from a network of eight wells for groundwater monitoring in Brazilian aquifers, six rainfall stations, eleven river flow stations, and three weather stations with atmospheric pressure, temperature, and humidity sensors.

Explaining the Mechanism of Multiscale Groundwater Drought Events: A New Perspective From Interpretable Deep Learning Model

“…The empirical method is typically suited for investigating large-scale regions, as the uncertainties associated with regional climate in smaller catchments and the complexities of the confluence process make empirical evaluation challenging. Consequently, methods that analyze time series of GWLs, such as water table fluctuation method (Bloomfield et al, 2015;Boumis et al, 2022) and wavelets analysis (Serravalle Reis Rodrigues et al, 2023), can identify underlying temporal patterns and correlations in the data, thereby assisting in the assessing and warning of groundwater drought events in specific (Gullacher et al, 2023). Another strategy for assessing groundwater drought involves analyzing different types of drought indicators to understand how they propagate to groundwater droughts.…”