A wavelet-assisted deep learning approach for simulating groundwater levels affected by low-frequency variability.

Groundwater level (GWL) simulations allow the generation of reconstructions for exploring the past temporal variability of groundwater resources or provide the means for generating projections under climate change on decadal scales. In this context, analyzing GWLs affected by low-frequency variations is crucial. In this study, we assess the capabilities of three deep learning (DL) models (long short-term memory (LSTM), gated recurrent unit (GRU), and bidirectional LSTM (BiLSTM)) in simulating three types of GWLs affected by varying low-frequency behavior: inertial (dominated by low-frequency), annual (dominated by annual cyclicity) and mixed (in which both annual and low-frequency variations have high amplitude). We also tested if maximal overlap discrete wavelet transform pre-processing (MODWT) of input variables helps to better identify the frequency content most relevant for the models (MODWT-DL models). Only external variables (i.e., precipitation, air temperature as raw data, and effective precipitation (EP)) were used as input. Results indicate that for inertial-type GWLs, MODWT-DL models with raw data were notably more accurate than standalone models. However, DL models performed well for annual-type GWLs, while using EP as input, with MODWT-DL models exhibiting only minor improvements. Using raw data as input improved MODWT-DL models compared to standalone models; nevertheless, all models using EP performed better for annual-type GWLs. For mixed-type GWLs, while using EP as input, MODWT-DL models performed well, with substantial improvements over standalone models. Using raw data as input, improvement of MODWT-DL models is marginal compared to that of standalone models; nevertheless, they perform better than standalone models with EP. The Shapley Additive exPlanations (SHAP) approach used to interpret models highlighted that they preferentially learned from low-frequency in precipitation data to achieve the best simulations for inertial and mixed GWLs. This study showed that MODWT-based input pre-processing is highly suitable to better simulate low-frequency varying GWLs.