Optimizing groundwater management to prevent drawdown and sustain agricultural production using machine learning model

doi:10.21203/rs.3.rs-4614420/v1

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Optimizing groundwater management to prevent drawdown and sustain agricultural production using machine learning model

https://doi.org/10.21203/rs.3.rs-4614420/v1

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This study presents a comprehensive analysis of groundwater level prediction and management using an extreme gradient boosting (XGB) model, optimized through Bayesian techniques. To address the challenge of unavailable accurate pumping volume data in high-density agricultural well areas, our approach leverages well power consumption as a key feature for the machine learning model. This innovative method enables accurate groundwater level predictions based on precipitation and power consumption data. To mitigate significant groundwater level declines during drought periods, the developed XGB model offers flexible design scenarios with varying degrees of groundwater extraction reduction. This capability allows for rapid predictions of groundwater levels, providing decision-makers with a powerful tool to adapt to hydrological uncertainties caused by future climate change. The results of model testing present that the increases in groundwater levels with a 25% reduction in power consumption range from 0.45 to 0.79 m during the wet season and from 0.45 to 0.99 m during the dry season. Interestingly, as the percentage of power consumption reduction increases, the elevations in groundwater levels do not increase proportionally, indicating that the non-linear characteristics among the interactions of precipitation, pumping behaviors, and groundwater level variations. In all three scenarios, the increases in groundwater levels during the dry season are significantly greater than those during the wet season. This implies that appropriate reductions in pumping volumes during drought periods can effectively prevent sharp groundwater level drawdowns. Furthermore, the XGB model plays a crucial role in formulating groundwater extraction reduction policies and agricultural fallow subsidy programs. When considering the opportunity cost of agricultural labor, the subsidies for the first and second crop periods meet only 30% and 59% of the economic profit, respectively. This economic shortfall is a major barrier to the adoption of fallowing practices by farmers during droughts. Therefore, it is crucial to enhance these subsidies to make fallowing a more viable and attractive option for farmers. In conclusion, while predictive modeling offers a robust tool for groundwater management and policy decision-making, there is a clear need for improved economic incentives and integrated management strategies.

Earth and environmental sciences/Hydrology

Earth and environmental sciences/Environmental social sciences/Climate-change adaptation

Groundwater level prediction

Extreme gradient boosting

Drought

Agricultural economic

Groundwater is the largest and one of the most important sources of freshwater, and it supports a major part of the domestic and irrigation needs of many nations¹. However, the increase in groundwater extraction and continued climate change have played significant roles in the groundwater level decline². Extreme climatic conditions such as droughts and anthropogenic activities, such as rapid population growth, industrial development, the expansion of agricultural activities, and other domestic uses, have escalated the demand for groundwater, highly influencing groundwater levels³. A decrease in the groundwater level can trigger serious environmental consequences, such as groundwater quality deterioration, ecosystem degradation, reduced agricultural production, land subsidence, and seawater intrusion^4,5. Moreover, agricultural irrigation is critical for crop production and food security worldwide. For regions with intensive agricultural development, the increasing demand for water resources, coupled with the effects of climate change, has led to water scarcity issues and competition among different sectors. Therefore, the sustainable use of groundwater is essential for water resource conservation and food security.

Accurately predicting groundwater levels is a significant challenge in managing aquifer systems, especially in regions where surface water is scarce⁶. There are two main categories of models for groundwater prediction: physically descriptive models and data-driven empirical models⁷. Physical models typically require extensive datasets covering parameters such as the water content, hydraulic conductivity, precipitation, volume of groundwater extraction, and soil properties, as well as information about human activities, such as dam construction^8,9. These models also require precise information on the properties of aquifers to account for subsurface variability¹⁰. However, implementing physical models is challenging due to the immense need for accurate data, which are often limited due to cost and time constraints^11,12. Although physical models are historically important, they have limitations. They require large amounts of data and can take a long time to construct, particularly for complex hydrogeological systems. Furthermore, the nonlinear behavior of subsurface systems and their responses to climatic variables can complicate modeling, given the large datasets required to achieve high accuracy.

As alternatives, data-driven empirical models have gained traction, as an in-depth representation of some system properties is unnecessary¹³. Machine learning algorithms use advanced mathematics to identify optimal functions based on the available data and support tasks such as prediction, classification, and anomaly detection. Machine learning algorithms excel at identifying intricate patterns in data, making them an excellent choice for groundwater level prediction¹³. In the last two decades, artificial neural networks (ANNs) have become popular algorithms, followed by support vector machines (SVMs) and adaptive network-based fuzzy inference systems (ANFISs)^14,15. However, the main drawback of these algorithms is that they are computationally intensive, and training is time consuming, especially for large datasets. Despite their good performance in modeling groundwater levels, ANNs can get stuck at local minima and be affected by overfitting during model training. In addition, their inability to compute missing values and address data correlations can lead to complex simulations with long calibration times¹⁶. SVMs are sensitive to the choice of kernel function and parameters and struggle with noisy data. Moreover, it is challenging to determine suitable numbers of fuzzy sets and rules when applying ANFISs¹⁷.

Decision tree-based models, notably extreme gradient boosting (XGB), are appealing alternatives to ANNs¹⁸. These models are particularly advantageous for small datasets and offer various benefits. Unlike ANNs, decision trees provide more interpretable results. They allow for flexible model development, accommodating data with varying complexities and levels of accuracy. Decision trees can effectively model nonlinear relationships without requiring prior statistical assumptions, data transformations, or outlier elimination. These algorithms are valuable for both classification and regression tasks in supervised learning. Decision trees recursively partition the training data across input variables and fit simple functions to each partition. However, decision tree models are sensitive to data size and quality, potentially leading to overfitting. To address this issue, ensemble decision trees combine multiple weak learners to form a robust model. Boosting and bagging are two key techniques in ensemble modeling. Bagging involves training homogeneous weak learners in parallel using bootstrap subsets of the original dataset and combining their results to reduce model variance. Boosting can be used to train weak learners sequentially in an adaptive manner, with a focus on challenging samples that can reduce model bias. These techniques have inspired various machine learning algorithms. For instance, random forests (RFs), which are based on bagging, have become prominent for classification and regression across various fields. Additionally, algorithms such as AdaBoost and the gradient boosting machine (GBM) implement boosting. GBM algorithms, such as the light gradient boosting machine (LightGBM) and extreme gradient boosting (XGB), excel at capturing the complex nonlinear relationships among variables. XGB, in particular, is renowned for its exceptional performance and is highly recommended for predicting natural phenomena. In summary, decision tree-based models, especially XGB, are attractive alternatives to ANNs. XGB models provide interpretable results, are well suited for small datasets, and have demonstrated remarkable performance and versatility in various practical applications^19–21.

The application of XGB for groundwater level prediction remains relatively unexplored, despite recent reports of remarkable performance and accuracy. Table 1 shows that previous studies employed XGB for various purposes, ranging from small- to large-scale applications. These applications encompass irrigation pumping and planning, investigating the demands of growing populations, assessing hydrogeological interactions, and exploring drought mitigation strategies. The spatial scope, including the study area and the number of monitored groundwater wells, largely depends on the specific research objectives. The temporal scales of datasets are primarily determined based on data availability and the objectives of groundwater level prediction. One critical concern in groundwater level prediction using machine learning is the collection of sufficient input features. Table 1 highlights that the most employed model inputs include observed groundwater level, precipitation, evapotranspiration, and temperature records, as previously noted by¹⁴. Groundwater levels in aquifer systems are predominantly monitored via observation wells, providing critical insights into how hydrological influences affect recharge, storage, and discharge. Previous studies have consistently underscored the significance of the relationships among groundwater levels, rainfall, and groundwater utilization by growing populations^22–24. Groundwater discharge is frequently characterized by the pumping rate^25–27. However, assessments of dynamic groundwater pumping in the field are often challenging due to substantial infrastructure costs, particularly in areas with intensive irrigation. As a practical alternative, many machine learning models can be used to estimate total groundwater pumping over a season or year, as a proxy for groundwater discharge. Notably, in regions where electric motors power most irrigation wells, electricity consumption has become a reliable indicator of groundwater pumping rates^28,29.

Table 1

Previous studies of the application of XGB model on groundwater level prediction
Purpose of previous study	Temporal scale	Spatial scale of study area	Input parameters	Performance of model testing
To assess geological-geomechanical properties on groundwater level changes (Kenda et al., 2018)	Daily	518 stations	Groundwater information Weather data Pump sensor data	R² = 0.644 RMSE = 0.0211 cm
To improve Real-time irrigational planning (Brédy et al., 2020)	Hourly	~ 0.18 km² with 3 monitoring wells	Groundwater level Precipitation Evapotranspiration	R² = 0.73–0.83 RMSE = 2.66–3.59 cm (for P1 well)
To keep water sustainability and drought mitigation (Hussein et al., 2020)	Monthly	Global	7 features sets from satellite images	R² = 0.6165 RMSE = 5.544–6.145 m
To predict groundwater level in highly populated towns (Osman et al., 2021)	Daily	1429.1 km² with 5 monitoring wells	Groundwater level Precipitation Temperature Evaporation	R² = 0.11–0.92 RMSE = 0.137–0.448m
To predict groundwater level dynamics across a tropical peatland (Hikouei et al. (2023)	Monthly	453 km² with 292 dipwells	Groundwater level Precipitation Evapotranspiration Surface heights Distance to the canal	R² = 0.995 RMSE = 0.101 m
To assess the geo-environmental for sustainable groundwater restoration (Mahammad et al., 2023)	Seasonal	3200 km² with 30 monitoring wells	Precipitation Population growth Use of groundwater	R= -0.72–0.9 RMSE = 4.73–0.52m

From a macroscopic perspective, the primary motivation behind groundwater level prediction is the anticipation of drought events increasing in frequency in the context of continued climate change. The escalating stress of surface water scarcity has led to the overexploitation of groundwater, resulting in heightened pumping costs, diminished base flow, saltwater intrusion, and land subsidence³⁰. However, curbing intensive irrigation pumping could lead to notable losses, spanning agricultural economics and food security. Consequently, addressing the mitigation of irrigation practices and assessing the socioeconomic implications of groundwater management are imperative tasks^31–33. Hence, the objective of this study is to establish a groundwater level prediction model using data related to groundwater dynamics, electricity consumption by pumping wells, and precipitation as inputs for the XGBoost (XGB) algorithm. The developed model can be applied to assess the impact of reducing groundwater usage for irrigation on crop yields and fallowing subsidies.

2.1 Study area

Yun-Lin County, which is situated in the southern region of the Choushui River alluvial fan in southwestern Taiwan, spans an extensive area of approximately 1,291 km² and serves as a crucial hub for rice production (Fig. 1(a)). The formation of this alluvial fan was influenced by the Choushui River, which flows from the Central Mountains before diverging to create a triangular alluvial fan characterized by fine-grained sediment enriched in organic carbon. Hydrogeologically, the Choushui River alluvial fan is primarily categorized into apex-fan and apron-fan areas. Due to inadequate surface water resources and rapid direct runoff within the apron fan area, a considerable volume of groundwater has been extracted to serve as a reliable source of irrigation water for agricultural cultivation. Intensive pumping activities have led to a significant decline in groundwater levels and subsequent land subsidence. The Global Navigation Satellite System (GNSS) has been used by the Water Resources Agency in Taiwan to identify areas with land subsidence rates exceeding 3 and 5 cm/year, raising concerns about the safety of public transportation infrastructure.

In this study, a groundwater monitoring well located at the center of a land subsidence area and adjacent to the Taiwan High-Speed Rail network is selected as the target for groundwater level prediction. This groundwater monitoring well, situated in an apex-fan area, was completed in gravel and sand, constituting an unconfined aquifer. In the apron fan areas, geological formations consist of interlayered sequences, including marine and nonmarine sequences. The nonmarine sequences, comprising coarse sediment ranging from medium sand to highly permeable gravel, constitute the most significant aquifer units. According to geological investigations by the Water Resources Agency in Taiwan, the depths of the main aquifers at these monitoring wells range from 7–12 m, 65–102 m, and 121–146 m, respectively (Fig. 1(b)).

Rainfall infiltration serves as the primary recharge source for the shallowest aquifer. Based on measurements by the Central Weather Administration in Taiwan, the average annual rainfall at the meteorological station in this study from 2007 to 2023 totaled 1323 mm, with a noticeable difference between the wet (May–October) and dry (November–April) seasons, with values of 1155.3 mm/year and 168.1 mm/year, respectively. Notably, approximately 87.3% of the annual rainfall occurs during the wet season, highlighting the reliance on groundwater resources for irrigation during the dry season. Figure 1(c) illustrates the distribution of pumping wells around the monitoring wells. Within a 2.5-km radius surrounding the groundwater monitoring wells in the study area, a total of 2,894 pumping wells were identified. These wells cover an agricultural land area of 1,520 hectares, with approximately 1,030 hectares dedicated to rice cultivation.

2.2 Data preparation and model features

An extensive dataset spanning over 20 years of groundwater level monitoring data and rainfall measurements was established to provide a robust foundation for assessing temporal variations in groundwater resources. Notably, the numerous pumping wells have a notable effect on the aquifer system. The power consumption of each individual pumping well within a 2.5 km radius of the monitoring wells was utilized as a model feature in replace of the pumping volume. The groundwater level, rainfall, and power consumption data for pumping wells spanning from July 2007 to June 2023 were sourced from the Water Resources Agency, the Central Weather Administration, and Taiwan Power Company, respectively. Since power consumption data are available monthly, hourly groundwater level data and rainfall records were respectively averaged and summed to establish monthly datasets.

In this study, pumping wells were categorized based on their registered water usage rights into agricultural, industrial, domestic, public, and other classes. Notably, within the agricultural water usage class, five types of irrigation practices, five types of livestock farming, and an aquaculture practice are identified (Table 2). The depth, motor power, and diameter of the pumping wells were obtained to explore the pumping well characteristics. Based on the classes of pumping wells illustrated in Fig. 2(a), 1,061 pumping wells are dedicated to single-crop rice cultivation, while 684 pumping wells are used for double-crop farming, together accounting for 60% of all pumping wells. Another significant purpose of groundwater abstraction is dryland farming, with 909 pumping wells allocated for this purpose, constituting 31.4% of the total. Hence, these three purposes represent the primary types of groundwater discharge from the aquifer. Although the remaining classes of pumping wells represent only 8.6% of the total, their power consumption must still be considered due to the potential impact of flow rate on groundwater levels, which cannot be overlooked. Furthermore, the characteristics of most pumping wells exhibit consistency, as evidenced by several factors. Approximately 79.5% of the wells reach a depth of at least 50 meters below the ground, while 85.1% of the wells feature pumping motors with a horsepower rating between 2 and 5 HP. Additionally, the diameter of the well tube for 87% of the wells falls within the range of 2 to 5 inches (Fig. 2(b)-(d)). Despite the use of conversion factor for estimating the pumping volume at each well, which refers to the volume of groundwater abstracted per unit power consumed, uncertainties arise due to variations in hydrogeological conditions and well characteristics³⁴. Considering that the power consumption of a single well is directly proportional to the pumping volume, utilizing consumed power as the input for machine learning models is preferable to using the estimated groundwater volume, even in numerical transport models.

Table 2

Groundwater usage category and the average power consumption of pumping wells in each category
Groundwater usage		Abbreviation	Power consumption of pumping well
Groundwater usage		Abbreviation	Average ± Standard deviation	Minimum–maximum
Agricultural water use
	Irrigation-Single crop rice	AWU-IP1	114,135.3 ± 55,483.4	25,750–278,451
	Irrigation-Double crop rice	AWU-IP2	66,322.8 ± 29,167.1	19,353–153,966
	Irrigation-Dryland	AWU-ID	68,537.7 ± 23,036.2	26,958–144,872
	Irrigation-Greenhouse	AWU-IG	612 ± 414.4	95–2,732
	Irrigation-Other	AWU-IO	53,411.7 ± 12,792	27,002–88,647
	Livestock-Cow	AWU-LC	239.3 ± 122.9	23–547
	Livestock-Swine	AWU-LS	7,714 ± 3,227.8	2,385–16,233
	Livestock-Fowl	AWU-LF	2,914 ± 2,199.1	602–10,214
	Livestock-Duck	AWU-LD	145.6 ± 100.8	5–581
	Livestock-Other	AWU-LO	30.3 ± 28.8	0–170
	Aquaculture-Freshwater	AWU-AF	4,375.9 ± 1,412.1	919–8,913
Industrial water use		IWU	1,418.8 ± 510.3	591–2,843
Domestic/public water supply		DPWS	4,313.3 ± 2,067.6	1,245–7,048
Other uses		OU	20,241.3 ± 6,525.2	8,362–49,923

Upon collection of raw data regarding the electrical power consumed by each pumping well, it was observed that some wells were either constructed after 2007 or abandoned before 2023. As a result, the categorization of pumping wells based on their purpose became imperative. The power consumption values within the same categories were aggregated to preserve the raw data rather than removing the data. In summary, the features of the prediction model included the monthly power consumption for 14 categories of pumping wells, along with the previously mentioned groundwater level and rainfall data.

2.3 Development of the extreme gradient boosting model

Extreme gradient boosting (XGB) is a supervised machine learning method that was introduced by³⁵, and it employs a recursive partitioning procedure. In XGB, trees are sequentially and stagewise grown by fitting decision trees to training data subsets, applying a loss function to the residuals of the preceding tree, and combining the loss function and the results of the previous tree to construct the subsequent tree. The utilization of the second partial derivatives of the loss function enables XGB to effectively minimize loss, resulting in high accuracy. The ultimate prediction of XGB is derived from the weighted contribution of all the decision trees used. XGB is highly efficient in supervised learning tasks as an ensemble learning technique in the realm of gradient boosting machines. Its implementation extends to both classification and regression applications, offering notable advantages such as high execution speed and compatibility with out-of-core computations. The prediction accuracy of this model is assessed through metrics such as deviation and model variation³⁶. Given that $\:D=\left\{\left({x}_{i},{y}_{i}\right)\right\}$ is considered a dataset with n samples and m features, the prediction value is generated using the following equations (Eqs. (1) and (2)):

$$\:\widehat{{y}_{i}}=\sum\:_{k=1}^{k}{f}_{k}\left({x}_{i}\right),\:{f}_{k}ϵ\phi\:$$

$$\:\phi\:=\left\{f\left(x\right)={w}_{s}\left(x\right)\right\}(s:\:{R}^{m}\to\:T,\:{w}_{s},\:ϵ{R}^{T})$$

where $\:{x}_{i}$ represents one sample, $\:{f}_{k}\left({x}_{i}\right)$ represents the prediction score, φ is the set of regression trees, $\:f\left(x\right)$ is each tree, s is a structural parameter, w is the leaf weight, T is the number of leaves per tree, k is the number of trees used to obtain the ensemble results, and $\:\widehat{{y}_{i}}$ is the predicted output. Further details on XGBoost (XGB) theory can be found in the works of^35–37.

The XGB algorithm and model performance were implemented using the scikit-learn library in the Anaconda python distribution (version 2020.07). The dataset consisted of 192 monthly measurements for each variable, such as the groundwater level, rainfall, and the power consumption of pumping wells. The first 174 monthly measurements were adopted for model training to obtain the best-fit model and optimal hyperparameters. The remaining 18 monthly records were used for model testing. For the training dataset, the 'TimeSeriesSplit' function from the scikit-learn library was used to perform cross-validation of the time series data. The dataset was divided into 10 consecutive subsets, with each subset serving as a validation set once and the rest serving as the training set to validate the stability of model training.

Hyperparameter settings significantly influence the performance of machine learning models, and improper selection can lead to poorly performing models. Traditionally, hyperparameters are chosen through trial-and-error, grid search, random search, or heuristic optimization algorithms^38,39. Bayesian optimization is a state-of-the-art approach for the global and local optimization of hyperparameters and efficiently searches through a hyperparameter space to find the optimal set of values for the XGB model^40,41. This approach is characterized by broader applicability than other methods, such as the grid search and random search methods, and has been widely used in numerous machine learning algorithms. In this study, Bayesian optimization was implemented for hyperparameter selection via cross-validation for the training data. The Gaussian process prior and expected improvement were adopted as bases of the prior and acquisition functions, respectively, for optimizing the hyperparameters⁴⁰. In this method, the objective function is continuously updated by adding sample points, and cross-validation is used to select the combination of hyperparameters that yields the highest average score for the model. The objective function of Bayesian optimization is shown in Eq. 3.

$$\:{X}^{\left(*\right)}=arg\text{min}\:{X}_{x\in\:S}f\left(X\right)$$

where $\:{X}^{\left(*\right)}\:$ denotes the optimal hyperparameter combination, S denotes the candidate set of x, and $\:f\left(X\right)$ is the objective function.

Tree-based machine learning models such as XGB prioritize features based on their importance⁴². XGB estimates feature importance, aiding in the evaluation of the predictive power of input variables. It also provides contribution scores to assess variable significance. Importance is determined based on relevance (squared) and the number of selections in splitting, with weights assigned based on the contribution to model improvement and averaged over all trees⁴³. The XGB scale variable sums to 100 across all trees, with high values for individual trees indicating strong impacts on the results⁴⁴. This method provides a comprehensive assessment of variable contributions. Model performance was evaluated using the following statistical criteria: root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) (Eqs. 4–6)

$$\:RMSE=\sqrt{\frac{{\sum\:}_{i=1}^{N}{({y}_{i}-\widehat{{y}_{i}})}^{2}}{N}}$$

$$\:MAE=\frac{1}{N}{\sum\:}_{i=1}^{N}\left|{y}_{i}-\widehat{{y}_{i}}\right|$$

$$\:{R}^{2}=1-\frac{{\sum\:}_{i=1}^{N}{({y}_{i}-\widehat{{y}_{i}})}^{2}}{{\sum\:}_{i=1}^{N}{y}_{i}^{2}-\frac{\sum\:_{i=1}^{N}{\widehat{{y}_{i}}}^{2}}{N}}$$

2.4 Application of the XGB model for adapting to groundwater level decline

A well-developed prediction model is necessary to fully consider the impacts of pumping on groundwater level variations. The model can be used to develop strategies to reduce groundwater pumping and implement policies such as agricultural fallowing in response to significant declines in groundwater levels. Furthermore, establishing a threshold groundwater level is essential for evaluating the extent to which groundwater pumping needs to be restricted in the future to ensure the safety of groundwater resources. The exceedance probability, an indicator used in the current groundwater level management strategy in Taiwan, has also been widely utilized in previous studies regarding the management of groundwater resources during periods of drought^45–47. This indicator can be estimated from historical groundwater level data using the Weibull distribution⁴⁸. Exceedance probabilities of > 85%, > 25% and < 25% correspond to the safe level, the lower limit of exceedance, and the extremely low limit of exceedance, respectively. Based on the predicted groundwater levels under various rainfall conditions, adjustments in the XGB model can be made to reduce power consumption of pumping wells by certain proportions. This approach can be used to determine the optimal quantities of groundwater pumping and fallowing, aimed at maintaining groundwater levels above the lower limit of exceedance. Additionally, the economic profitability of agricultural crop production, particularly rice production, can be calculated to evaluate the cost of conserving groundwater resources in the future in periods with limited rainfall.

3.1 Dynamics of groundwater level, power consumption, and precipitation

The analysis of rainfall data revealed that precipitation is predominantly concentrated in the wet season and is primarily influenced by monsoon and typhoon events (Fig. 3). The average annual rainfall recorded during the period from 2007 to 2022 was 1549.1 ± 397.9 mm. The lowest annual rainfall levels were observed in 2011 and 2020 at 928.5 mm and 1058 mm, respectively. Furthermore, the average rainfall during the dry season was 248.5 ± 142.9 mm, which significantly increased to 1296.6 ± 369.3 mm during the wet season. The reliance on groundwater as a reliable irrigation water resource is reflected in the variation in groundwater levels. The seasonal cycling of groundwater indicates that the increase in groundwater levels each year follows the significant rainfall in the wet season (Fig. 3). The average groundwater level during the wet season (-3.92 ± 3.2 m with a range of -15.01 to -1.35 m) was significantly greater than that during the dry season (-4.75 ± 3.28 m with a range of -13.29 to 1.53 m) (t test, p value < 0.05). The substantial disparity in rainfall between dry and wet years, as well as between seasons, contributed to the uncertainty surrounding the availability of natural water for agricultural irrigation purposes. Notably, the groundwater levels reached their lowest point during the dry season in 2020, which was attributed to the severe drought resulting from the low rainfall in 2020. These conditions persisted into the wet season of 2021. An increase in water scarcity has led to the construction of more groundwater pumping wells, a trend expected to continue with climate change.

Table 2 outlines the abbreviations for each groundwater usage category and provides the average power consumption of pumping wells in each category. Rice and rainfed crops are the predominant crops in the study area, resulting in higher power consumption for agricultural irrigation than for other purposes. Notably, the average power consumption for the “other” class is significant, as some groundwater users may not specify a particular crop during water rights registration, resulting in classification into this category. The wide ranges of consumed power imply that groundwater abstraction amounts can significantly vary among different months and years. The trend of the monthly variation in power consumption indicates that the period from February to June corresponds to the highest groundwater demand, especially for single-crop, double-crop, and dryland farming (Fig. 4). The utilization of groundwater for livestock, aquaculture, industry, and domestic purposes shows no significant cyclic variation. In addition, the water consumption for swine cultivation and domestic use slightly increased after 2014 due to increases in the livestock market price and municipal development, respectively, resulting in stress on the water supply and increased groundwater pumping.

3.2 Performance of the XGB model for groundwater level prediction

To develop the groundwater level prediction model, the hyperparameters were determined using Bayesian optimization, a commonly employed approach⁴⁹. Table 3 provides details of the search intervals of the XGB model. According to the results of 10-folds model training and validation, the RMSE, MAE, and R² values are 0.001–0.978, 0-0.807, and 0.901-1, respectively, for model training and 0.804–2.597, 0.626–2.233, and 0.781–0.852, respectively, for model validation. Figure 5 presents the validation results of the groundwater level prediction from January 2022 to June 2023. The consistent variations between the monitored and predicted groundwater levels indicate that the developed model effectively captures the trends in groundwater levels using power consumption and rainfall data, which are critical factors to consider. The predicted groundwater levels during wet season well fitted with the monitored groundwater levels. However, during the dry season, the predicted groundwater levels were slightly higher than the monitored levels. Due to a prolonged drought from late 2021 until the monsoon season of 2023 in Taiwan (Fig. 3), the limited precipitation encouraged the practice of fallowing policies. Nonetheless, the sharp decrease in groundwater levels from December 2022 may be attributed to unregistered pumping, as the decrease in power consumption from registered pumping wells was significant (Fig. 4).

Table 3

Definitions, search intervals, and best-fit of hyperparameters in XGB model
Hyper-parameters	Definition	Search interval	Best fitted
learning_rate	The rate at which the model learns pattern in training data	0.0001–0.1	0.003
n_estimators	The maximum number of trees generated	1,000–50,000	50000
max_depth	Maximum depth of tree	1–10	10
min_child_weight	The sum of the minimum weights of each leaf	1–5	1
gamma	Minimum loss reduction needed for further leaf node partition	0–0.5	0
subsample	Subsample ratio of the training instances	0.3–0.9	0.3
colsample_bytree	Column sampling rate	0.3–0.9	0.5911
scale_pos_weight	Balance positive and negative weights to address class imbalance	1–10	3
reg_alpha	L1 Regularization parameters	0.001–10	0.0126
reg_lambda	L2 Regularization parameters	0.001–10	0.0013
base_score	The initial prediction score of all instances	0.3–0.7	0.3798

Among the 10-fold model training and validation processes, the subset with the lowest RMSE and MAE is considered the best-fit model, with the corresponding hyperparameters shown in Table 3. For this best-fit model, the RMSE, MAE, and R² values are 0.002, 0.00, and 0.999, respectively, for model training, and 0.804, 0.626, and 0.818, respectively, for model validation. These impressive results, achieved using only precipitation and power consumption data for groundwater level prediction, support the utilization of the hyperparameter values for further predictions with the XGB model. In terms of predictions of groundwater variations, the XGB model consistently outperformed other machine learning algorithms in both the training and validation stages, primarily due to its superior calibration capability, as indicated by the RMSE and MAE^24,50. The XGB algorithm integrates a regularization term to control model complexity and is adaptable to various types of base classifiers. After each computational iteration, the weights of the leaf nodes are adjusted by a reduction factor, mitigating the influence of individual classifiers and promoting a more balanced and effective learning process³⁵. Moreover, the Bayesian optimization approach employed in this study utilizes Bayes' theorem to determine the minimum and maximum values of the objective function. In each iteration, information from previous calculations is leveraged to optimize subsequent steps, creating an efficient search process⁵¹. ⁵²highlighted a notable advantage of Bayesian optimization, which is the automatic estimation of model parameters in coupled machine learning models.

The selection of input features plays a crucial role in ensuring the stability and robustness of prediction models⁵³. Feature importance analysis provides insights into the contribution of each variable to the target value. In this study, the importance of the input variables for groundwater level prediction was automatically estimated by using the trained models (Fig. 6). The results revealed that AWU-IP2 had the most significant impact on the prediction, with the highest relative importance (0.409) in the model, followed by AWU-IP1 (0.078) and AWU-ID (0.072). Groundwater pumping for rice cultivation, the primary agricultural activity in the study area, accounts for the highest electricity consumption. Additionally, due to the implementation of water-saving policies by the Taiwanese government, a considerable portion of farmland is now used to grow rainfed crops.

Moreover, the average power consumptions of AWU-IP1, AWU-IP2, AWU-ID, and AWU-IO are significantly higher than those of other groundwater usage purposes (Table 2). However, the feature importance of these four purposes does not follow the order of power consumption. The groundwater abstraction for paddy rice and dry farming is highly correlated with seasonal variations in precipitation and groundwater levels (Fig. 4), making AWU-IP1, AWU-IP2, and AWU-ID the top three in feature importance. In contrast, there is no significant variation in the power consumption of AWU-IO, resulting in its lower feature importance. Therefore, the XGB model can clearly reflect the impact of seasonal pumping behavior on groundwater level changes. Water usage purposes with high power consumption and significant differences between wet and dry seasons will predominantly control the rise and fall of groundwater levels. Conversely, water usage purposes with stable power consumption act like baseline data, having little impact on groundwater level changes.

The high density of pumping wells underscores the urgency of addressing the over-extraction of groundwater to mitigate adverse impacts on both agricultural practices and infrastructure safety. Theoretically, halting pumping activities has emerged as the most viable strategy for preventing further exacerbation of land subsidence. However, this course of action poses a significant challenge, as it directly impacts the self-sufficiency of rice production in Taiwan. Therefore, there is an urgent need for the development of a groundwater level prediction model to help optimize management. This model must achieve a balance by reducing irrigation pumping, subsequently facilitating the recovery of land subsidence while simultaneously maintaining essential crop production.

3.3 Impacts of reducing pumping from environmental and agroeconomic perspectives

The primary objective of this study is to utilize a well-trained groundwater level prediction model to assess the impact of reducing groundwater pumping from both environmental and socioeconomic perspectives. The groundwater level fluctuations of the best-fit model from January 2022 to June 2023 revealed that the monthly groundwater levels between August 2022 and March 2023 consistently fell below the lower limit level and even dipped below the extremely low level (Fig. 7). Local farmers often rely on groundwater extraction during the second crop period to mitigate the risks associated with unpredictable rainfall patterns during the monsoon season and typhoon events. Additionally, substantial groundwater abstraction occurs at the beginning of each year to flood paddy fields in preparation for the first crop period. To evaluate the effectiveness of reducing groundwater pumping to maintain groundwater levels, we considered scenarios where 25%, 50%, and 75% of paddy fields adhere to the government's fallowing recommendations, resulting in corresponding reductions in power consumption. Figure 7 presents the groundwater level predictions for these varied reduction percentages. The increases in groundwater levels with a 25% reduction in power consumption range from 0.45 to 0.79 m during the wet season and from 0.45 to 0.99 m during the dry season. As the percentage of power consumption reduction increases, the elevations in groundwater levels do not increase proportionally. A 50% reduction in power consumption results in groundwater level increases ranging from 0.68 to 1.6 m in the wet season and from 1.07 to 1.96 m in the dry season. A 75% reduction leads to increases ranging from 0.68 to 1.98 m in the wet season and from 1.05 to 3.11 m in the dry season. In all three scenarios, the increases in groundwater levels during the dry season are significantly greater than those during the wet season. This implies that appropriate reductions in pumping volumes during drought periods can effectively prevent sharp groundwater level drawdowns. In this study, a 50% reduction in power consumption maintains monthly groundwater levels within safe level. Over the past few decades, the implementation of fallowing policies has been a common strategy for coping with the shortage of irrigation water during drought periods. While fallow practices have aided in groundwater maintenance and prevented rapid drawdown and potential land subsidence, they have also led to significant economic losses in agricultural cultivation. In addition, determining the appropriate area for fallowing poses a significant challenge for local governments due to the need to balance rice production self-sufficiency with fallow subsidies³¹. Water management policies often entail trade-offs between economic and sustainability objectives^32,33. From an agricultural economic perspective, farmers are likely to opt for the option that offers the best financial return, whether it be rice prices or fallow subsidies, which complicates the promotion of fallowing policies during drought periods⁵⁴.

While the benefits of reducing groundwater pumping to prevent declines in groundwater levels are widely recognized among residents, the willingness to adhere to fallowing policies largely hinges on the incentives provided. In our study area, we aimed to estimate the economic profitability of rice production under fallow conditions. Economic profit serves as a crucial indicator for assessing firms' economic value and aids in decision-making processes^55,56. It is essential to distinguish between accounting profits and economic profits. Accounting profit represents a firm's net income or revenue minus explicit costs, while economic profit represents opportunity costs, including both explicit and implicit costs⁵⁵. Accounting profit is a firm's net income or revenue minus expenses (total explicit costs). Economic profit is the total revenue minus opportunity costs (total explicit costs and total implicit costs) from all inputs. The formula for calculating the accounting profit is as follows.

$\:{\pi\:}_{a}$ = total revenue - total explicit costs (7)

where π_a is the accounting profit. The total revenue is the average grain yield per hectare of rice multiplied by the average price. Total production costs (explicit costs) include direct costs (seedling fees, material fees, pesticides and other medicines, fertilizer fees, wages, and water purchase fees) and indirect costs (farmhouse fees, farm tool fees, land rent, and capital interest).

To assess the economic profit of rice production, we need to consider both explicit costs (production costs) and implicit costs (opportunity costs), which encompass labor income from nonagricultural activities, nonagricultural land rent, and capital interest. When the opportunity cost of agricultural labor exceeds zero, the economic profit (π_e) calculation involves subtracting the total explicit and implicit costs from the total revenue (Eq. 8).

$\:{\pi\:}_{e}$ = Total revenue - (total explicit costs + total implicit costs) (8)

In cases in which the opportunity cost of agricultural labor equals zero, signifying that farmers cannot find work outside the agricultural sector, the economic profit ($\:{\pi\:}_{\widehat{e}}$) must be adjusted to account for self-employed wages (Eq. 9).

$$\:{\pi\:}_{\widehat{e}}=\:{\pi\:}_{e}+\:\text{s}\text{e}\text{l}\text{f}-\text{e}\text{m}\text{p}\text{l}\text{o}\text{y}\text{e}\text{d}\:\text{w}\text{a}\text{g}\text{e}\text{s}$$

According to the Ministry of Agriculture's annual report on rice production and cost analysis in 2022, the economic profitability per hectare in our study area was determined, as outlined in Table 4. While the fallow subsidies during the second crop period may barely offsets the opportunity cost when agricultural laborers can find work outside the sector, it remains insufficient for the first crop period. Consequently, when the opportunity cost of agricultural labor is zero, fallowing subsidies for the first and second crop periods only reach 30% and 59% of the economic profit, respectively. This is the main reason why it is challenging to promote fallowing policies during drought periods to sustain groundwater levels within safe limits.

Table 4

Economic profitability per hectare of rice cultivation in this study area
		1st crop	2nd crop
Direct costs (A)
	Seedling fees	423.8	403.1
	Material fees	1.3	3.4
	Pesticides and other medicines	458.6	485.8
	Fertilizer fees	534.7	483.1
	Wages	2189.4	2354.9
	Water purchase fees	200.4	65.5
Indirect costs (B)
	Farmhouse fees	22.6	13.8
	Farm tool fees	2.7	1.6
	Land rent	814.1	613.7
	Capital interest	5.2	5.6
Total production costs (A + B)		4652.8	4430.5
Average grain yield of rice (kg/ha)		7686.0	6564.0
Average price per kg		0.8	0.8
Total revenue (C)		5867.0	5141.8
Accounting profit (1) = (C)-(A + B)		1214.1	711.3
Assumed land rent (2)		524.1	336.9
Assumed capital interest (3)		5.2	5.6
Self-employed Wages (4)		394.5	347.0
When opportunity cost of agricultural labor is > 0, Economic profit = (1)+(2)+(3)		1743.4	1053.8
Fallowing subsidy		1037.1	1176.8
When opportunity cost of agricultural labor is 0, Economic profit = (1)+(2)+(3)+(4)		2138.0	1400.9
Fallowing subsidy		642.6	829.7

To encourage farmers to participate in fallowing, it is crucial to increase fallow subsidies. This approach not only incentivizes farmers to reduce groundwater usage but also mitigates the economic losses associated with fallowing. Enhanced subsidies could ensure that groundwater levels are maintained within safe limits during droughts, thereby balancing agricultural productivity with sustainable water management practices. Wit the predictive capabilities of this model, it provides policymakers with a flexible and efficient approach to determine the optimal percentage of fallow land. By incorporating data-driven insights, policymakers can tailor their strategies to maximize the benefits of groundwater conservation while minimizing economic repercussions in the agricultural sector.

This study has effectively demonstrated the application of an XGB-based model to predict groundwater levels and evaluate the impacts of reduced groundwater pumping from both environmental and socioeconomic perspectives. The model, optimized through Bayesian techniques, has shown high predictive accuracy, evidenced by the strong alignment between observed and predicted groundwater levels. This validates the use of precipitation and power consumption data as significant predictors in the model. The analysis of groundwater level fluctuations from January 2022 to June 2023 revealed that strategic reductions in groundwater pumping can substantially mitigate groundwater depletion. Specifically, a varied percentages reduction in groundwater extraction resulted in different groundwater level increases to safe level in the wet and dry seasons. This suggests that appropriate management of groundwater resources, through reduced pumping, can help maintain groundwater levels within safe limits, thereby reducing the risk of over-extraction during drought periods.

However, the economic implications of such conservation strategies present significant challenges. The current fallowing subsidies are insufficient, covering only a fraction of the economic profits from rice cultivation. When considering the opportunity cost of agricultural labor, the subsidies for the first and second crop periods meet only 30% and 59% of the economic profit, respectively. This economic shortfall is a major barrier to the adoption of fallowing practices by farmers during droughts. Therefore, it is crucial to enhance these subsidies to make fallowing a more viable and attractive option for farmers. In conclusion, while predictive modeling offers a robust tool for groundwater management and policy decision-making, there is a clear need for improved economic incentives and integrated management strategies. Future research should aim to refine these models further by incorporating additional variables and conducting long-term studies to evaluate the cumulative effects of groundwater management policies on agricultural output and ecosystem health. Through such efforts, sustainable agricultural practices can be promoted, ensuring the long-term availability and health of groundwater resources.

Declaration of Interests

The authors declare no competing interests.

Author Contributions

Conceptualization, S.W.W, Y.Y.C. and T.W.P.; Methodology, Y.H.K., Y.Y.C., and S.H.H.; Writing – Original Draft, S.W.W. and Y.H.K.; Writing – Review & Editing, M.K. and L.C.C.; Funding Acquisition, S.W.W. and L.C.C.; Resources, Y.Y.C. and S.H.H.; Supervision, M.K. and L.C.C.

Acknowledgments

The authors wish to express their appreciation to the National Science and Technology Council, Taiwan (R.O.C.) for their financial support under Grant Numbers NSTC 112-2625-M-032-003.

Data availability statement

Data are available on request from the authors.

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The Authors declare no Competing Financial or Non-Financial Interests.

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Optimizing groundwater management to prevent drawdown and sustain agricultural production using machine learning model

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Abstract

Figures

1. Introduction

2. Materials and methods

2.1 Study area

2.2 Data preparation and model features

2.3 Development of the extreme gradient boosting model

2.4 Application of the XGB model for adapting to groundwater level decline

3. Results and discussion

3.1 Dynamics of groundwater level, power consumption, and precipitation

3.2 Performance of the XGB model for groundwater level prediction

3.3 Impacts of reducing pumping from environmental and agroeconomic perspectives

Conclusion

Declarations

Declaration of Interests

Author Contributions

Acknowledgments

Data availability statement

References

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