Implementing augmented deep Machine learning for effective shallow water table management and forecasting

Abstract

This study addresses the gap in understanding and forecasting shallow water table depth (WTD), a critical factor in groundwater resource management and agricultural productivity. Despite the importance of accurately forecasting WTD for sustainable water resource management, current methods frequently struggle to capture the complexities and dynamics of WTD fluctuations. In response, this research, which was conducted in Québec, Canada, leverages machine learning techniques—namely, extreme learning machines (ELMs) and long short-term memory (LSTM) networks, augmented by the Holt-Winters (HW) state-space method—to develop a comprehensive analysis and forecasting approach for shallow WTD. The datasets were recorded by 8 sensors with hourly temporal resolutions from June to September, covering the growing season. The objective was to increase forecast accuracy by employing a detailed structural analysis of WTD time series data, selecting appropriate forecast steps, and fine-tuning model inputs through statistical tests and model-agnostic interpretation methods. The performance was evaluated via various metrics, including the correlation coefficient (R), root mean square error (RMSE), mean absolute relative error (MARE), and Theil’s U accuracy and quality coefficients, across short- to long-term forecasts (1-, 12-, 24-, 48-, and 72-hour ahead). Integration of HW with the ELM and LSTM models markedly improved the forecasting capabilities, particularly for the LSTM model, which achieved high accuracy of R = 0.988 for 1-hour forecasts and low error rates (RMSE = 0.648 cm, MARE = 0.007, UI = 0.005, and UII = 0.010), although accuracy decreased for longer forecast horizons, resulting in the lowest accuracy for 72-hour forecasts, with R = 0.638, RMSE = 4.550 cm, MARE = 0.051, UI = 0.036, and UII = 0.071. Similarly, the ELM model showed promising results in short-term forecasts when coupled with HW (R = 0.988, RMSE = 0.676 cm, MARE = 0.007, UI = 0.005, and UII = 0.010) but experienced a decrease in performance accuracy over more extended forecast periods (R = 0.707, RMSE = 5.559 cm, MARE = 0.053, UI = 0.045, and UII = 0.089). Although the ELM model presented a negligible strong correlation in some forecast steps, the LSTM model offered consistently higher forecast accuracy and quality across all assessed horizons. The study demonstrates the superiority of the LSTM model in consistently providing more accurate forecasts, highlighting the importance of integrating HW to capture complex temporal patterns in hydrological forecasting. This advancement in forecasting WTD has substantial implications for enhancing groundwater resource management and agricultural decision-making, significantly contributing to sustainable water resource utilization and supporting agricultural productivity through informed data-driven practices.