Enhancing groundwater predictions by incorporating response lag effects in machine learning models

Water shortage has emerged as a worldwide issue in recent decades, mostly caused by the depletion of freshwater resources resulting from the combined impact of human activity and climate change. Groundwater is a crucial freshwater resource that plays a vital role in promoting sustainable societal development and preserving the ecological equilibrium of the environment (Sun et al. 2023). The North China Plain, which is a significant region for grain and cotton production in China, possesses a mere 1.7% of the country's water resources. As a result, more than 70% of the extracted groundwater is utilized for agricultural irrigation (Zhang et al. 2013b; Wang et al. 2023b). Overexploitation of water resources beyond their sustainable limit leads to various issues, including the deterioration of ecosystems and the decline of biodiversity (Foster et al. 2004; Wang et al. 2023a). Hence, accurately forecasting the fluctuating patterns of groundwater is crucial for effectively managing and optimally utilizing groundwater resources (Zhang et al. 2019).

An essential focus and problem in groundwater predictions have always been to scientifically comprehend the influence of different driving variables on groundwater levels (Eshtawi et al. 2015). However, the factors that affect the groundwater system are intricate. The climate is the main factor responsible for fluctuations in groundwater levels, providing the main source of recharge to groundwater and affecting the processes of groundwater (Wang et al. 2018; Di Nunno & Granata 2020). As a result, groundwater changes display cyclical and seasonal patterns that resemble the climate (Yan et al. 2018). Zhang et al. (2013a) stated that alterations in rainfall play a significant role in causing abnormalities in the flow of groundwater. Lubczynski (2011) observed that evapotranspiration (ET) decreases the overall recharge of groundwater, limiting the flow of groundwater and the replenishment of groundwater resources. Nazarieh et al. (2018) determined that the disparity between the infiltration caused by precipitation (P) and irrigation, and the ET, is equivalent to the quantity of water that seeps into the lower layers of soil. These findings suggest that climate change has a significant effect on the replenishment of groundwater, mainly through changes in P and ET.

Integrating influence factors into the prediction model has been a prominent topic in previous studies, aiming to accurately understand the fluctuating patterns of groundwater (Zhang et al. 2017). In the field of hydrometeorological science, machine learning models have been widely applied in related statistics and predictions (Podgorski & Berg 2020), groundwater potential prediction (Naghibi et al. 2016), and groundwater storage prediction (Chen et al. 2019). Azizi et al. (2024) employed artificial neural networks to forecast future groundwater levels in the Sahneh Plain by analyzing temperature and P, thereby uncovering patterns of change. Di Nunno & Granata (2020) assessed the impact of rainfall and ET on the forecast of groundwater levels and validated the dependability of the NARX-BR network. Gong et al. (2016) compared the accuracy of the model by analyzing various hydrologic data, including P, temperature, and lake level, using different combinations. These studies largely rely on factors that change in real time with groundwater levels, with little consideration given to the delayed response of groundwater to these factors.

While P and ET are commonly used by scholars to forecast groundwater levels, their effects on infiltration can cause a significant delay in groundwater recharge (De Vries & Simmers 2002). Previous research has indeed verified the existence of a substantial delay in the relationship between groundwater levels and meteorological (MET) factors (Wang 2011; Qi et al. 2015; Niu et al. 2023). Furthermore, this lag effect demonstrates spatial diversity. However, most current studies on predicting groundwater levels do not consider the delayed impact of climate influences on groundwater levels, which might lead to decreased accuracy.

This study aims to improve the accuracy of groundwater level predictions by incorporating the lag effect of climate on groundwater levels and utilizing the random forest (RF) model and the SHapley Additive exPlanation (SHAP) technique. Due to the cyclical variation of groundwater levels throughout the year in Hebei Province, which is largely influenced by seasonal irrigation (Tsuchihara et al. 2023), we treat the month as a separate variable to capture this trend. We incorporate the delayed impact of climatic elements on groundwater levels by utilizing P, ET, and time as independent variables, while the groundwater level serves as the dependent variable. We create a forecast model using the RF model, a well-utilized method in hydrological research (Mital et al. 2020; Diniz et al. 2021; Rao et al. 2022), to assess the importance of incorporating the lag effect into groundwater estimates. Ultimately, we employ the SHAP technique to assess the significance and efficacy of each factor in relation to changes in groundwater levels, both before and after considering the lag effect.

Over the past few years, a significant number of groundwater observation wells have been set up in the research region. These wells have been classified into two categories: shallow and deep groundwater sites, depending on their average water level in relation to the first impermeable layer. Specifically, the groundwater levels were measured relative to the sea level. The groundwater level data collected for this study covers the time period from 2018 to 2022, with measurements taken every 4 h. Following a quality assessment, stations displaying extended aberrant records were excluded, while those with small irregularities were rectified. A total of 972 shallow and 885 deep groundwater sites were ultimately chosen in Hebei Province. Subsequently, the monthly mean groundwater level was computed for each location to acquire the monthly groundwater level data of Hebei Province.

The P data are obtained from the Integrated Surface Hourly (ISH) dataset provided by the National Oceanic and Atmospheric Administration (NOAA). This study utilized daily P data from all stations across China and employed the inverse distance weighting method to interpolate nationwide daily P raster data. The data pertaining to the study area in Hebei Province were obtained by applying a mask, with a spatial resolution of 1 km.

The ERA5 reanalysis package, offered by the European Centre for Medium-Range Meteorological Forecasts (ECMWF), encompasses a comprehensive dataset of global climate and MET information spanning 80 years (Hersbach et al. 2023). This study aggregated data at four-hour intervals and retrieved data using a mask specific to Hebei Province. Subsequently, the data underwent spatial downsampling using the cubic spline interpolation technique, yielding monthly ET data for Hebei Province spanning from 2018 to 2022, with a geographical resolution of 1 km.

In this formula, n is the number of samples of and ⁠. k represents the corresponding lag time, with months. When ⁠, it indicates no lag, meaning that the groundwater level and MET data are synchronized. The cross-correlation coefficient ranges from −1 to 1, with values closer to an absolute value of 1 suggesting a higher degree of correlation. For this investigation, sites that have a lag cross-correlation coefficient higher than 0.5 are regarded as having notable lag effects (Niu et al. 2023).

As the lag threshold increased from 0.1 to 0.5, the proportion of significant lag sites decreased significantly. For rainfall, the proportion dropped from 98.1 to 15.1%, while for evapotranspiration, it decreased from 86.3 to 19.1%. Under low threshold conditions, although a large amount of lag information is retained, the analysis results lack distinction and exhibit poor robustness. When the lag threshold approaches 0.5, the two lag ratio curves tend to level off, indicating that the proportion of significant lag sites becomes less sensitive to threshold changes, resulting in more stable outcomes.

The RF model has been extensively utilized in hydrometeorological science for statistical analysis and forecasting purposes, including groundwater potential prediction and storage prediction. The algorithm, proposed by Breiman (2001), is an ensemble learning technique specifically developed to address classification and regression problems. It combines predictions from multiple decision tree models to improve accuracy and consistency through methods such as voting or averaging. By using different subsets of data, the process generates a range of models, and their predictions are combined to provide the final output (Cao et al. 2023). RF is effective at handling high-dimensional data. It introduces randomness in the selection of both samples and features and can also assess the importance of different variables. These features provide RF with a distinctive advantage in its algorithm (Adhikary & Dash 2017).

In this study, SHAP was used to interpret the importance and effects of factors in the groundwater level prediction model, thereby evaluating the role of groundwater response lags in water level prediction. The kernel SHAP explainer from the SHAP library in Python was employed to perform this analysis.

Shallow groundwater in the study area experiences an average delay of 4.55 months compared to P, as shown in Figure 5(a), and an average delay of 9.21 months compared to ET, as shown in Figure 5(c). Locations with extended latency periods are still concentrated in proximity to areas where excessive extraction occurs, where sites in the northern agricultural and grassland regions experience shorter latency periods. These areas generally exhibit high soil permeability and dense organic layers, facilitating the rapid absorption and storage of P. This enables water to swiftly enter into the groundwater layer. In addition, the presence of a large amount of vegetation enhances the permeability of the soil by means of its root system, which speeds up the processes of water penetration and ET. As a result, the time it takes for groundwater levels to respond to MET conditions is reduced.

Deep groundwater, being situated at greater depths in the geological layers and having a less direct link to surface water, exhibits a slower reaction to changes in P and ET compared to shallow systems as shown in Figure 5(e)–5(h). The majority of deep groundwater lag sites are located in the impermeable regions of southeastern Hebei, which coincide with places where deep groundwater is being excessively extracted. Excessive extraction reduces the levels of deep groundwater, lengthening the channels through which water flows and increasing the time it takes for water to seep into the earth. This intensifies the effects of P and ET. Human activities also modify hydrological conditions, diminishing the immediate reaction of groundwater. The replenishment of deep groundwater occurs, on average, 5.91 months after P and 9.63 months after ET. The sites with shorter ET lag times are primarily located in the grassland and woodland regions of northern Hebei. These places experience less human involvement and have more fractured rocks, which enable faster contact between groundwater and the surface.

The sites experiencing substantial latency are primarily located in central and southern Hebei Province, as well as the northern mountainous forest regions (Figure 6). Human extraction activities have altered the hydrological processes in the shallow overexploited areas. This disruption of the normal management of groundwater systems has led to a slower infiltration process and more noticeable delays in response. Furthermore, forested areas possess dense soil and vegetation cover, which can retain water effectively in their root systems and soil layers. As a result, the impacts of P and ET are delayed in reaching the groundwater system, leading to noticeable lag effects.

P and ET lag sites are more extensively spread than MET lag sites, which are located primarily in the eastern and southeastern boundaries of Hebei. This could be attributed to the elevated levels of yearly P and ET in these areas. In order to assess the predictive accuracy of models that take into account lag effects, both real-time and lag parameters are utilized as independent variables for sites that experience substantial delays.

This study uses RF to build two prediction models in order to assess the influence of lag effects on prediction accuracy. In the model that takes into account the delayed impacts of groundwater, the groundwater level is utilized as the dependent variable. The independent variables include the observation period (measured in months) and the P and ET that occurred before each measurement, corresponding to the lag durations at each location. The model, which does not take into account lag effects, utilizes synchronous temporal components of each site's groundwater level as explanatory variables. Both models utilize data from the time period of 2018–2021 as the training set and take the data at different locations for each month of 2022 as the validation set. After training the models with the optimal parameters, their performance is presented in Table 1 for both the validation and test set.

The RF model, which takes into account the lag effects of MET elements, demonstrates superior accuracy on the test set. A detailed percentage improvement comparison is provided in Table 2, which highlights that R² improves by 3.37% for shallow groundwater and 3.87% for deep groundwater. Meanwhile, MAE is reduced by 34.78 and 36.58%, respectively, and RMSE decreases by 27.45 and 8.91%, respectively.

In contrast, sites that show weak improvement in accuracy are primarily found in the forested mountainous regions of Hebei Province. The vegetation coverage in these places is extensive, and variations in groundwater level are mostly driven by direct natural P, resulting in less substantial delayed effects. Hence, incorporating lag effects into the model does not substantially enhance accuracy. In addition, the hydrological conditions in mountainous forest areas remain steady due to low human activity, resulting in predictable fluctuations in groundwater levels. This high prediction accuracy is achieved even without considering lag effects.

The significance of P and ET is more prominent for deep groundwater compared to shallow groundwater. Upon careful consideration of lag effects, it is evident that P exerts the greatest influence on groundwater levels. Deep groundwater is less impacted by human activities and possesses a more stable hydrogeological system, resulting in MET elements playing a more substantial role in influencing deep groundwater. ET primarily takes place in the soil surface and the vegetation layer. Deep groundwater, which is located at larger depths compared to shallow groundwater, is essentially unaffected by surface water supplies. Hence, ET exerts a diminished influence on deep groundwater. On the other hand, P is crucial for supplying water to deep groundwater, which significantly influences fluctuations in deep groundwater levels.

Upon taking lag effects into account, the temporal scatter points exhibit a uniform distribution around the center axis, suggesting a minimal influence on groundwater levels and diminished overall significance. This demonstrates that the model efficiently mitigates noise originating from the time variable and more accurately captures MET influences. The distribution of P points is predominantly located on the positive axis, signifying a favorable influence on groundwater levels. This is because higher amounts of P result in greater water infiltration and the subsequent recharge of groundwater. Similarly, the concentration of ET points in the negative zone suggests that higher ET leads to increased water loss and a reduction in groundwater levels. This is consistent with actual situations in the real world, indicating that taking into account lag effects offer a more precise explanation of how factors affect groundwater levels.

Utilizing P and ET data from Hebei Province from 2018 to 2022, this study thoroughly examines the delayed impacts of shallow and deep groundwater in relation to MET variables and their influence on the accuracy of model predictions. Initially, we evaluate these delayed impacts by the calculation of time-lag correlation coefficients. In this study, we employ a RF model and incorporate SHAP analysis to uncover the alterations in feature importance and the influence of different explanatory variables on fluctuations in groundwater levels. These changes are observed both before and after considering the impacts of lag. In order to enhance the precision of groundwater fluctuations modeling, we incorporate the influence of irrigation into the model, given that irrigation exhibits seasonal variations. Using P, ET, and time as input variables, the RF model is constructed to incorporate the lag effects of these elements, with groundwater level as the output variable. Our study utilizes SHAP analysis to assess the correlation and efficacy of each element in connection to changes in groundwater level, taking into account the lag effects.

The average lag time for shallow groundwater in response to P and ET is 4.55 and 9.21 months, respectively. P exhibits a positive correlation with groundwater levels, meaning that higher levels of P lead to an increase in groundwater levels. On the other hand, ET shows a negative correlation, indicating that higher levels of ET resulted in a decrease in groundwater levels. In the study area, sites with significant lag effects, accounting for 15.08% in shallow groundwater and 19.06% in deep groundwater, are mainly concentrated in regions experiencing intensive groundwater overextraction. These areas are characterized by slower recharge rates and longer response times, particularly for deep aquifers, which amplifies the lag effects. The sites are primarily located in the non-porous regions of central and southern Hebei, which coincide with areas where excessive extraction occurs. The lag reactions of deep groundwater are more evident due to their weaker links to surface water. The average lag periods for P and ET are 5.91 and 9.63 months, respectively. Significant lag effects were predominantly observed in the southeastern parts of the study area, where deep groundwater overextraction occurs, likely due to the slower recharge rates of deep aquifers. In contrast, lag effects were less pronounced in the northwestern agriculture and grassland regions, where shallow groundwater systems dominate and respond more quickly to external influences. These findings suggest that extraction depth may play a critical role in influencing lag effects, with broader implications for managing groundwater resources in overextracted regions and understanding lag effects in aquifer systems under similar conditions globally.

Two prediction models are built using RF before and after taking into account lag effects. For 2022, the average R² for predicting shallow groundwater, accounting for lag effects, is 0.983, whereas, for deep groundwater, it is 0.966, indicating a strong predictive capability. Upon comparison, it is shown that taking into account lag effects greatly enhanced the accuracy of predictions. Specifically, R² increased by 0.23, 0.13, and 0.19 average for the MET, P, and ET lag sites, respectively, compared to models that did not account for lag effects. The majority of accuracy enhancements are observed in overextracted locations in shallow groundwater, suggesting that a more thorough consideration of lag effects provides a more accurate representation of the intricate infiltration processes in these regions. By incorporating lag effects, projections based on time series and spatial distribution provide a more accurate representation of groundwater level changes in Hebei Province.

The SHAP results reveal that, in the shallow groundwater model, the significance of P and ET substantially increases when lag effects are taken into account, and conversely, the relevance of the month reduces. When it comes to deep groundwater, all elements are more significant compared to shallow groundwater, with P being the most relevant factor. Geographically, areas where groundwater levels are significantly affected by time are mainly found in flat areas, where MET factors play a more significant role in areas with excessive groundwater extraction. This makes groundwater levels more responsive to rainfall and ET, emphasizing the susceptibility of these systems to MET factors. Upon taking lag responses into account, the relationship between each factor and groundwater levels underwent a shift. By taking into account lag effects, the noise caused by the time variable in groundwater predictions is minimized, and the influence of MET elements is more properly represented. This approach provides a more realistic representation of the impact of each component on groundwater levels.

Due to the complexity of groundwater systems, which vary significantly across different regions, this study aims to provide a framework for lag effect analysis and groundwater level prediction. For groundwater in different regions influenced by various factors, the factors of lag effect are recommended to be chosen according to specific conditions, for example, soil type, geological structure, hydrological conditions, P patterns, and human activities. The framework in this study can be adapted to the specific geographical, climatic, and hydrological conditions, and here, we only presented a case study in a semi-arid area.

Moreover, sustainable groundwater management must not only focus on the immediate availability of water but also consider long-term trends and lag effects. Studies show that groundwater levels exhibit delayed responses to P and evapotranspiration, especially in overexploited areas. In regions such as the southern-central impermeable zones of Hebei Province, which suffer from groundwater overexploitation, measures are urgently needed to mitigate this issue. Incorporating lag effects into predictive models can provide more accurate analyses of groundwater dynamics, helping decision-makers identify potential risks associated with groundwater fluctuations and avoid resource depletion due to overextraction.

This work was supported by the Innovative Training Project for College Students (Grant No. 202310319128Y), the National Natural Science Foundation of China (Grant No. 42201020), and Hebei Province Science and Technology Program for Water Resources (Grant No. 2023-12).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.