PCA-Lasso-based forecasting of agricultural water use and identification of key predictor variables in inland river basins of Northwest China

Agricultural water use in inland river basins of northwestern China is affected by multiple interacting factors, and the associated indicators often show strong collinearity. To address these issues, this study developed a hybrid prediction model based on principal component analysis (PCA) and Lasso regression to establish an interpretable agricultural water-use prediction framework for arid inland river basins. Twenty indicators describing meteorology, water-use structure, water resources, and socioeconomic conditions in the Heihe River Basin from 2001 to 2023 were used for correlation analysis and PCA. An expanding-window time-series cross-validation scheme was then applied to determine the Lasso regularization parameter, and model performance was evaluated using R 2, root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). Agricultural water use ranged from 24.01 × 108 to 32.20 × 108 m 3, accounting for 77.26–85.72% of total water supply. It declined by 21.20% from 2001 to 2012, rebounded markedly in 2013, and generally decreased after 2014. Correlation analysis showed that several groups of indicators had correlation coefficients above 0.80. Eight principal components explained 97.70% of the total variance, from which 14 input indicators were retained. The optimal λ was 0.02. The PCA-Lasso model achieved an R 2 of 0.997, with RMSE, MAE, and MAPE values of 0.152, 0.114, and 0.495%, respectively. The influence of the variables related to water-resource and water-use structure was the most significant. These results indicate that the PCA-Lasso model can effectively simulate and predict agricultural water use in the Heihe River Basin and can support agricultural water management in arid regions.

Water scarcity and its tension with food production are core constraints on sustainable development in the arid regions of northwestern China (Tang et al., 2025). In 2020, agricultural water use in China reached 368.38 billion m 3, accounting for 62.00% of national water use, indicating that agriculture remains the dominant water-consuming sector Ministry of Water Resources of the People's Republic of China, 2025. The Heihe River Basin, with an area of approximately 130,000 km 2, is the second-largest inland river basin in China. Its middle-reach Zhangye oasis contains approximately 95% of the basin's cultivated land, 91% of its population, and more than 80% of its economic output, forming an oasis agricultural system that is highly dependent on irrigation (Li et al., 2022). Previous studies have shown that irrigated agriculture once consumed approximately 80% of the available freshwater in the basin. Agricultural diversion and groundwater extraction in the upper and middle reaches can reduce eco-logical water availability downstream, triggering linked effects such as groundwater-level decline, natural vegetation degradation, and desertification (Cai et al., 2023; Zhang Z. P. et al., 2025; Zhang et al., 2025). At the same time, agricultural water use in the Heihe River Basin is jointly affected by precipitation, temperature, evapotranspiration, runoff, cultivated land area, effective irrigation area, planting structure, population, agricultural output value, irrigation technology, and water-pricing institutions. These drivers create pronounced non-linearity, collinearity, and human-interference effects. Studies have reported that the price elasticity of agricultural water demand in the basin is approximately −0.26 and that a clear demand response emerges only when the water price approaches CNY 0.27 per m 3. Optimizing planting area and improving irrigation efficiency could provide a theoretical regional water-saving potential of 552 million m 3 (Zou et al., 2024; Zou and Kang, 2022). Therefore, a prediction model that jointly considers natural hydrological processes and socioeconomic drivers can im-prove annual water-use planning and irrigation scheduling. It can also provide quantitative support for total water-use control, groundwater abstraction reduction, planting-structure adjustment, and ecological water allocation in the basin.

Agricultural water-use prediction methods have evolved from trend extrapolation and multiple linear regression to system dynamics, hydrological-crop models, artificial neural networks, support vector machines, and ensemble learning methods (Wang et al., 2023; Groppo et al., 2019). Mechanistic models can describe crop evapotranspiration, soil moisture, and irrigation processes, but they usually require many parameters, have high calibration costs, and cannot fully represent human-activity factors such as water prices, industrial structure, and water-saving policies. Machine-learning models provide stronger non-linear fitting capacity but are sensitive to small sample sizes, noise, and overfitting, and their explanatory power for driving mechanisms is often limited (Adamowski and Karapataki, 2010; Ghalehkhondabi et al., 2017). In multivariable statistical modeling, principal component analysis (PCA) extracts integrated information through orthogonal transformation and reduces multicollinearity among meteorological, water-resource, and socioeconomic indicators (Soltani et al., 2025; Yang L. S. et al., 2023; Yang Z. C. et al., 2023). Lasso regression uses L1 regularization to shrink coefficients and select variables, which provides relatively good robustness and interpretability for high-dimensional prediction with limited samples (Alizadeh et al., 2020; McMillan et al., 2022). Previous work has used PCA to select variables such as precipitation, irrigation area, and water-saving technology for irrigation water-demand prediction in the Haihe River Basin, achieving a mean relative error of 1.32% and demonstrating the potential of multifactored dimensionality reduction (Wang et al., 2015). Existing studies of the Heihe River Basin have mainly focused on agricultural water-resource efficiency, water-price reform, land-use scenario simulation, optimal water-resource allocation, and crop water-consumption simulation (Li et al., 2015, 2023). These studies have identified the important roles of agricultural scale, irrigation technology, groundwater use, and institutional factors. However, few studies have integrated water-use structure, water resources, meteorology, and socioeconomic indicators into a unified framework for basin-scale agricultural water-use prediction and driver identification using correlation analysis, PCA dimensionality reduction, and Lasso sparse regression. Systematic tests of information retention, model generalization, and core-factor stability under highly correlated variables remain especially limited.

This study uses agricultural water use in the Heihe River Basin as the prediction target and constructs a candidate indicator system from four dimensions: water-use structure, water-resource conditions, meteorological variation, and socioeconomic development. First, Pearson correlation analysis was used to identify the direction, strength, and statistical significance of associations between agricultural water use and each indicator, and to diagnose collinearity among explanatory variables. Second, PCA was applied to compress redundant information. Critical predictor variables were selected based on eigenvalues, cumulative variance contribution, and loading structure, and were then used as inputs to the Lasso regression model. Cross-validation was used to determine the regularization parameter, producing a PCA-Lasso model with dimensionality reduction, variable selection, and prediction functions. Finally, model performance was assessed using the coefficient of determination and root mean squared error, and core drivers were identified using standardized regression coefficients and loading contributions. By examining how natural water-resource fluctuations and socioeconomic activities affect interannual variation in agricultural water use in the Heihe River Basin, this study clarifies how useful information can be retained and overfitting can be suppressed when sample size is limited and indicators are highly correlated. It also distinguishes key drivers related to climate, water-resource endowment, agricultural production scale, and management technology. Compared with previous studies, this study makes three main contributions. First, it integrates principal component analysis and Lasso regression to reduce multicollinearity and redundant information among multiple candidate predictors. Second, it incorporates socioeconomic, agricultural production, climatic, and water-resource indicators within a unified agricultural water-use prediction framework, rather than focusing on a single category of factors. Third, by applying this framework to the Heihe River Basin, the study provides an interpretable prediction approach that may also offer methodological insights for other water-scarce arid and semi-arid regions.

Study area

The Heihe River Basin is the second-largest inland river basin in China. It originates in the Qilian Mountains, and its main stream extends approximately 821 km from south to north through Zhangye and Jiuquan in Gansu Province and Ejina Banner in Inner Mongolia before flowing into Juyan Lake. The basin covers approximately 142,900 km 2 (Figure 1). The basin has a typical arid continental climate with scarce precipitation and intense evaporation. Annual precipitation is only 40–250 mm in the middle-reach plain and averages only 42 mm in downstream Ejina Banner, whereas annual evaporation reaches 2200–3755 mm. The evaporation-to-precipitation ratio exceeds 5. The Zhangye Basin in the middle reaches is the core agricultural area of the basin. Represented by the Daman irrigation district, it has a total irrigated area exceeding 3.6 × 104 ha and is dominated by maize and wheat cultivation. Agri-cultural water use accounts for more than 80% of total basin water use (Gansu Provincial Department of Water Resources, 2025). The contradiction between water supply and demand is pronounced, and groundwater overexploitation is severe. Zhangye City has formed seven groundwater overexploitation zones. Since 2020, excess water withdrawal above permitted abstraction in restricted zones has reached 1.6 × 108 m 3, and groundwater levels have continued to decline, becoming a key bottleneck for sustainable development in the basin.

Data sources

All data used in this study were obtained from the Gansu Provincial Water Resources Bulletin (2001–2023) and the Gansu Provincial Statistical Bulletin (2001–2023) (Gansu Provincial Department of Water Resources, 2002–2024; Gansu Provincial Bureau of Statistics and National Bureau of Statistics Investigation Team in Gansu, 2002–2024). The dataset includes 20 indicators. Water-use structure indicators include agricultural water use (X1), domestic water use (X2), ecological and environmental water use (X3), urban public water use (X4), industrial water use (X5), and water use for forestry, animal husbandry, and fisheries (X6). The meteorological indicator is precipitation (X7). Socioeconomic indicators include primary industry (X8), secondary industry (X9), tertiary industry (X10), water-saving irrigation area (X11), total population (X12), GDP (X13), industrial added value (X14), and per capita water use (X15). Hydrological indicators include total water supply (X16), surface water resources (X17), groundwater resources (X18), water yield coefficient (X19), and water yield modulus (X20). The technical workflow is shown in Figure 2, and all the indicators information are presented in Table 1. Each indicator covers the complete annual series from 2001 to 2023, with no interruptions or missing values.

Methodology

Principal component analysis

Agricultural water use in the Heihe River Basin is jointly affected by water-resource supply, socioeconomic development, population size, industrial structure, and water-use structure. Strong correlations often exist among these indicators. For example, gross regional product and per capita gross regional product, primary-industry added value and the share of agriculture, and total water supply and water supply from different sources may contain substantial overlapping information. Directly using all indicators as model inputs would increase input dimensionality and computational burden. It could also produce unstable parameter estimates due to multicollinearity and intensify overfitting under small-sample conditions. Therefore, this study used PCA to reduce the dimensionality of socioeconomic and water-resource supply indicators. PCA transforms multiple correlated original variables into a smaller set of mutually independent integrated variables, namely principal components, through orthogonal linear transformation. While retaining as much information from the original data as possible, PCA reduces dimensionality, removes redundant information, and weakens correlations among input variables (Wu et al., 2018; Mu et al., 2024). The specific steps are as follows.

Construction of the original data matrix

Assume that the study period contains N valid annual samples and that each year includes M candidate influencing indicators. The original data can then be represented as matrix A. The calculation equation adopts Equation 1:

where a ij denotes the observed value of the j -th influencing indicator in the i -th year; N is the number of annual samples; and M is the number of original indicators included in the PCA.

Agricultural water use, as the final prediction target of this study, was not included in the extraction of principal components. If the subsequent prediction model uses agricultural water use in the previous year to represent water-use inertia, this lagged variable should be used as an independent model input and excluded from PCA to preserve its explicit time-series meaning.

Data standardization

The original data were standardized to obtain the standardized data matrix B. The calculation equation adopts Equation 2 and 3.

where μ ij denotes the mean of column j (the j- th feature), and σ ij denotes the standard deviation of column j.

Calculation of the covariance matrix

The covariance matrix D was calculated from the standardized matrix B. The calculation equation adopts Equation 4.

Solution of eigenvalues and eigenvectors

Eigen decomposition was performed on covariance matrix D. The calculation equation adopts Equation 5.

where λ k is the k -th eigenvalue and represents the variance of the data along the corresponding principal component direction, namely the amount of information contained in that principal component. The corresponding eigenvector ν k represents the direction in which the original indicators are projected onto the new coordinate axis.

Data projection and principal component calculation

The standardized matrix B was projected onto the new coordinate system formed by the eigenvectors to obtain principal component matrix C. The calculation equation adopts Equation 6.

where V is the matrix composed of eigenvectors, C is the principal component score matrix, and ck denotes the k -th principal component.

Calculation of principal component contribution and cumulative contribution

The variance contribution rate of the k -th principal component is Equation 7:

The cumulative contribution rate R k of the first k principal components is Equation 8:

The variance contribution rate represents the proportion of total information in the original data explained by a single principal component. The cumulative contribution rate represents the proportion of original data information explained by the first k principal components. Following relevant studies, this study set the cumulative contribution threshold to 0.90.

Least absolute shrinkage and selection operator (Lasso)

Lasso (Least Absolute Shrinkage and Selection Operator) regression is a linear regression method with an L1 regularization constraint (Zeiger and Hubbart, 2019). Compared with ordinary least squares (OLS), Lasso regression introduces an absolute-value penalty into the loss function, enabling coefficient shrinkage and automatic variable selection. It can therefore address multicollinearity, redundant independent variables, and overfitting in multidimensional hydrological, meteorological, and socioeconomic modeling, and is suitable for predicting agricultural water use and selecting driving factors in the Heihe River Basin (Li et al., 2020).

Basic objective function

Assume that the dataset contains n samples and p independent variables. Let y i be the observed value of the dependent variable, x ij be the observed value of an independent variable, β j be the regression coefficient of each variable, and v be the intercept. The Lasso objective loss function consists of a squared-error loss term and an L1 regularization penalty term. The calculation equation adopts Equation 9 and 10:

where 1 2 n ∑ i = 1 n (y i - ŷ i) 2 represents the least squares fitting error term, which is used to ensure the fitting accuracy of the model to the sample data; λ ∑ j = 1 p | β j | indicates the L1 regularization penalty term, which is the core constraint term of Lasso; λ ≥ 0 is the regularization hyperparameter, which controls the penalty intensity of the model.

Physical meaning of the hyperparameter λ

The hyperparameter λ directly determines the degree of variable selection and coefficient shrinkage. When λ = 0, the penalty term is inactive, and the model is equivalent to ordinary least squares regression without variable-selection ability. As λ increases, regression coefficients for weakly predictor variables are continuously shrunk until they become zero, thereby removing variables. If λ is too large, excessive penalization may distort key variables and cause underfitting. Therefore, the optimal λ must be determined by cross-validation.

Solution principle of coordinate descent

Because the Lasso loss function contains a non-differentiable point at the absolute value, it cannot be solved using conventional least-squares iteration. This study used coordinate descent to iteratively solve the optimal regression coefficients dimension by dimension. The specific computational steps are as follows:

i Data standardization.

ii Holding the remaining coefficients fixed and solving the local optimum for a single variable.

All regression coefficients except the j -th dimension were held fixed, and only β j was updated. The analytical solution of the Lasso regression coefficient is Equation 11:

where β ^ j denotes the partial regression coefficient without the penalty:

iii Soft-thresholding selection mechanism.

The analytical solution shows that when the absolute value of the unpenalized coefficient is smaller than λ, the coefficient becomes zero and the variable is removed. When it is larger than λ, the coefficient is shrunk by λ, suppressing weak factors while retaining strong factors and completing variable selection.

iv Iterative updating and convergence determination.

The coefficients were updated by cycling through all independent-variable dimensions. Iteration continued until the change in all regression coefficients was smaller than the preset convergence threshold, after which a stable optimal coefficient combination was obtained and model training and factor selection were completed.

Model advantages

Compared with L2 regularization methods such as ridge regression, Lasso regression can directly shrink redundant variable coefficients to zero. Parameter estimation and variable selection are completed simultaneously, substantially reducing the complexity of models for agricultural water-use simulation, prediction, and multidimensional driver analysis in the Heihe River Basin. This approach helps identify key predictor variables such as precipitation, agricultural water use, and groundwater abstraction, thereby providing reliable model support for driving-force analysis.

Construction of the PCA-Lasso hybrid model

The two-stage PCA-Lasso hybrid modeling strategy proposed in this study was designed to exploit the complementary advantages of the two methods:

(1) Stage 1, PCA dimensionality reduction: To address the large number of influencing factors and widespread multicollinearity among variables, PCA was first used to transform high-dimensional influencing factors into a small number of uncorrelated principal components. The main value of this step is twofold: first, it eliminates multicollinearity among variables and avoids unstable coefficient estimates in the regression model; second, it extracts integrated information and condenses the main variation in the original variables.

(2) Stage 2, Lasso regression: The principal component scores extracted by PCA were used as input variables to construct the Lasso regression prediction model. The main value of this step is twofold: first, L1 regularization further selects the principal components that contribute most to water-use prediction, enabling sparse modeling; second, it controls model complexity and prevents overfitting.

The logic of the two-stage strategy is that PCA addresses correlations among input variables, whereas Lasso addresses input-variable selection and model overfitting. Together, they form a complete technical chain of dimensionality reduction, selection, and modeling.

It should be noted that: This study is conducted for the purpose of prediction rather than causal identification.

Model evaluation metrics

Coefficient of determination (R 2)

The calculation equation adopts Equation 12.

where R 2 ranges from 0 to 1. A value closer to 1 indicates stronger explanatory power for the variance of the response variable. Here, n is the sample size, y i is the observed value, k i is the model-predicted value, and ȳ i is the mean observed value.

Root mean squared error (RMSE)

The calculation equation adopts Equation 13.

RMSE is sensitive to large errors and can effectively reflect extreme deviations in model prediction (Wabina et al., 2025).

Mean absolute error (MAE)

The calculation equation adopts Equation 14.

MAE assigns equal weight to all errors and reflects the average level of prediction error, providing good interpretability.

Mean absolute percentage error (MAPE)

The calculation equation adopts Equation 15.

MAPE presents prediction accuracy as a percentage, which facilitates comparison among datasets with different magnitudes.

Trend in agricultural water use

The Heihe River Basin is a typical arid oasis agricultural region in northwestern China, and its water resource use has long been dominated by agricultural production. To characterize interannual variation in agricultural water use, agricultural water use and its share of total water supply from 2001 to 2023 were statistically analyzed, as shown in Figure 3. During the study period, agricultural water use ranged from 24.01 × 108 to 32.20 × 108 m 3, accounting for 77.26–85.72% of total basin water supply. Agri-cultural water use was highest in 2014 (32.20 × 108 m 3), when its share reached 82.24%. It was lowest in 2011 (24.01 × 108 m 3), with a share of 82.24%. However, the share of total water supply was highest in 2002 (85.72%) and lowest in 2022 (77.25%). Figure 3 shows that agricultural water use declined continuously from 30.47 × 108 m 3 in 2001 to 24.01 × 108 m 3 in 2012, a decrease of 21.20%, while its share ranged from 81.99% to 85.72%. In 2013, agricultural water use rebounded markedly from 24.01 × 108 m 3 in 2012 to 30.78 × 108 m 3. From 2014 to 2023, it remained above the 2012 level, ranging from 24.86 × 108 to 32.20 × 108 m 3. After 2014, agricultural water use showed a sustained downward trend, and its share decreased from approximately 82% to around 77%. These results indicate clear stage-dependent adjustments in both the total volume of agricultural water use and the basin's water-supply structure.

Correlation analysis of influencing factors and PCA results

Correlation analysis

Based on the analysis of agricultural water-use variation, this study further tested correlations among the 20 initially selected indicators. The indicator system covered socioeconomic, meteorological, water-resource, and water-use structure dimensions and was used to identify linear associations and potential multicollinearity among variables. The results are shown in Figure 4. Pearson correlation coefficients range from −1 to 1, and a value with a larger absolute magnitude indicates a stronger linear relationship between variables. When the absolute value exceeds 0.8, a strong theoretical linear relationship exists between the two corresponding variables. Figure 4 shows strong positive correlations among several groups of indicators. The correlation coefficient between X6 and X2 was 0.80; that between X8 and X3 was 0.81; and that between X9 and X8 was 0.86. The correlation coefficients of X10 with X3, X8, and X9 were 0.87, 0.96, and 0.80, respectively. The correlation coefficients of X11 with X3, X8, and X10 were 0.89, 0.86, and 0.86, respectively. The correlation coefficients of X13 with X8, X9, X10, and X11 were 0.98, 0.92, 0.97, and 0.81, respectively. These results indicate substantial information overlap among water-use structure, industrial development, population and economic scale, and water-saving irrigation indicators. Directly incorporating these indicators into a regression model could reduce the stability of parameter estimation, so dimensionality reduction is needed to extract the main information.

PCA results

The correlation analysis showed that multiple groups of indicators had correlation coefficients greater than 0.8. To avoid collinearity, these variables required further screening. PCA was applied to reduce the dimensionality of the 20 initially selected indicators. The method-suitability test showed that Bartlett's test of sphericity was significant (P < 0.05), indicating that the correlation matrix was not an identity matrix and that the selected dataset was suitable for PCA. The cumulative contribution rates of the principal components are listed in Table 2. Eight principal components were extracted, with variance explanation rates of 36.397%, 22.776%, 17.986%, 8.293%, 6.312%, 2.662%, 1.691%, and 1.588%, respectively. Their cumulative variance explanation rate was 97.70%, indicating that the extracted principal components retained most of the information in the original indicator system. After normalization, the weighted variance explanation rates, namely the weights of the eight principal components, were 37.25%, 23.31%, 18.41%, 8.49%, 6.46%, 2.72%, 1.73%, and 1.63%, respectively. The combined weight of the first three principal components was close to 80%, making them the main information carriers explaining differences in the original data.

A scree plot can help determine the number of principal components to retain. When the eigenvalue curve shifts from a steep decline to a gentle slope, the principal components before the inflection point usually have greater information-explaining capacity. As shown in Figure 5, the eigenvalues of the first eight principal components declined markedly, whereas the curve became flatter thereafter. Considering the cumulative variance explanation rate, this study retained eight principal components for subsequent analysis.

The PCA biplot of agricultural water-use drivers is shown in Figure 6. X2, X3, X8, X9, X10, X11, X12, X13, and X14 had relatively large loadings along the first principal component, indicating that these indicators contributed strongly to PC1. X1, X4, X5, X6, X15, and X16 had larger loadings on PC2. In contrast, X7, X17, X18, X19, and X20 had shorter projection lengths on PC1 and PC2, suggesting relatively limited explanatory contributions to the first two principal components; their variable contributions were therefore ignored. Integrating the correlation test, cumulative variance contribution, and variable loading results, and treating X1 (agricultural water use) as the dependent variable, this study selected 14 indicators as candidate input variables for the PCA-Lasso prediction model: X2 (domestic water use), X3 (ecological and environmental water use), X4 (urban public water use), X5 (industrial water use), X6 (water use for forestry, animal husbandry, and fisheries), X8 (primary industry), X9 (secondary industry), X10 (tertiary industry), X11 (water-saving irrigation area), X12 (total population), X13 (GDP), X14 (industrial added value), X15 (per capita water use), and X16 (total water supply).

Prediction performance of the PCA-lasso model

Comparison of predicted and observed values in the training and test sets

Based on the PCA screening results, an expanding-window time-series cross-validation method was used to determine the optimal Lasso regularization parameter and to select the main prediction variables for agricultural water use. This method preserves the chronological order of the time series and can partly avoid future-information leakage caused by random sample partitioning. The selection of the λ value for the PCA-Lasso model using cross-validation is shown in Figure 7. When λ = 0.02 and log(λ) = −3.902, the model mean squared error reached its minimum; this value was therefore selected as the optimal regularization parameter. As λ increased, the penalty strength increased, regression coefficients gradually shrank, and model complexity decreased. The cross-validation error increased continuously after the minimum, and the parameter corresponding to the minimum cross-validation error was −3.90 on the log scale. A smaller λ imposes insufficient constraints on model complexity and tends to retain redundant variable information, whereas a larger λ may excessively shrink regression coefficients and cause the loss of useful predictive information.

Figure 8 shows the coefficient paths of different variables as log(λ) changes. As λ increased, the regression coefficients of all variables gradually shrank toward zero, reflecting the sparsity property of Lasso regression. X4, X5, X6, X8, X10, X12, and X13 were the first variables to be compressed to zero under stronger penalization and remained zero, indicating that their independent predictive information was readily constrained by regularization. X15 and X16 remained non-zero at larger λ values, initially suggesting that they contained relatively stable predictive information for agricultural water use. Among the variables corresponding to X8–X16, the coefficient paths mainly retained X9, X11, X14, X15, and X16, which may indicate substantial overlap in the information contained by these indicators. In this setting, Lasso balanced model complexity and information retention by keeping a subset of representative variables while shrinking the coefficients of others.

The model coefficients under the optimal parameter setting are shown in Table 3. The PCA-Lasso regression model had a high overall goodness of fit (R 2 = 0.997), indicating that it explained a large proportion of the variation in agricultural water use during the sample period. Under the regularization constraint, the standardized coefficients of some variables were shrunk to zero, indicating exclusion from the model, such as X2, X4, X5, and X16. The PCA-Lasso results showed that, among the intercept and the standardized coefficients of X2, X3, X4, X5, X6, X8, X9, X10, X11, X12, X13, X14, X15, and X16, variables X3, X6, X8, X9, X10, X11, X12, X13, X14, and X15 retained nonzero coefficients and were therefore retained as key predictors. Standardized coefficients reflect the relative contribution of each variable to the dependent variable. The larger absolute values for X12 (0.183) and X3 (−0.317) indicate relatively strong variable contributions on the dependent variable. The unstandardized intercept was −10.098, providing the baseline prediction value when all independent variables were zero.

Based on the standardized coefficients, the model can be expressed as:

y = −37.391–0.317 × X3–0.055 × X6 + 0.009 × X8 + 0.003 × X9–0.001 × X10 + 0.003 × X11 + 0.183 × X12–0.005 × X13 + 0.001 × X14 + 0.017 × X15.

The standardized equation can be used to compare the relative contributions of variables, whereas the unstandardized coefficients listed in Table 3 can be used for model calculation in the original units. The corresponding equation is:

y = −10.098–0.923 × X2–0.902 × X3 + 0.850 × X4–0.125 × X5–0.246 × X6–0.001 × X9 + 0.002 × X11 + 0.056 × X12 + 0.009 × X15 + 0.406 × X16.

Overall, combining PCA with Lasso retained the main data information while achieving coefficient sparsity, reducing the influence of highly correlated variables on model parameter estimation. Figure 9 further shows that the predicted and observed trajectories were generally consistent, and the model captured the stage-dependent fluctuations in agricultural water use during the study period.

Model ablation analysis and robustness test

Considering that there may be strong correlations among various indicators such as population, economic development, irrigation area, agricultural production, water resource utilization efficiency, and water usage in different sectors, it is difficult to determine the independent predictive contribution based solely on the coefficients or importance of a single variable. To further test the stable contribution of different types of information to agricultural water usage prediction, this study conducts variable group ablation analysis based on the complete PCA-Lasso model. According to the attributes of the indicators and their relationships, the original indicators are divided into several variable groups such as social economy (X9, X10, X12, X13, and X14), agricultural production and irrigation (X6, X8, and X11), and water resources and water usage structure (X2, X3, X4, X5, X15, and X16). Under the condition of keeping other modeling steps and parameter settings unchanged, each variable group is removed successively, and PCA and Lasso modeling are re-performed. By comparing the R 2, RMSE, MAE, and MAPE of the models before and after ablation, the contribution of the predictive information contained in each variable group to the model performance is evaluated. If the model accuracy significantly decreases after removing a variable group, it indicates that this variable group contains relatively stable predictive information that cannot be completely replaced by other indicators; conversely, if the model performance changes little, it suggests that the information contained in this variable group may have strong redundancy with other highly correlated variables. The model evaluation results are shown in Table 4. The R 2 of the PCA-Lasso regression model reached 0.997, indicating that the model explained 99.7% of the variation in the dependent variable and achieved an extremely high overall fit. The RMSE and MAE were 0.152 and 0.114, respectively, indicating small absolute deviations between predicted and observed values. The MAPE was 0.495%, indicating a low relative error. After removing the group of water resources and water usage structure variables, the R 2 decreased from 0.997 to 0.696, the RMSE increased from 0.152 to 1.465, the MAE increased from 0.114 to 1.066, and the MAPE increased from 0.495% to 4.636%, indicating that this type of variables contains strong predictive information for agricultural water usage. After removing the group of agricultural production and irrigation variables, the model performance changed relatively little, suggesting that the information contained in this type of indicators may be partially replaced by other related variables. For the model after removing the social economic variables group, R 2 and RMSE remained unchanged, while MAE and MAPE decreased by 9.65% and 9.49% compared to the complete model, further indicating that different types of variables contribute differently to agricultural water usage prediction. Overall, the ablation analysis indicates that the predictive ability of the PCA-Lasso model is not dependent on a single indicator, but stems from the combined effect of multiple types of information such as social economy, agricultural production, water resource utilization, and meteorological conditions. There is significant information substitution among some highly correlated variables, so this paper does not explain the importance of a single variable as its independent causal effect, but mainly focuses on the stable contribution of different variable groups and the information dimensions they represent to the predictive performance of agricultural water usage. Together with Figure 9, these results show that the model fitted the overall trend and major fluctuation points of agricultural water use well, with relatively small prediction errors. The model therefore performs well for trend simulation and can be used for agricultural water-use driver identification and real-time prediction analysis, although its extrapolation capacity should be further tested with independent data.

Identification of key predictor variables

After model-performance testing, PCA-Lasso regression was used to remove redundant factors with no substantial contribution and to identify factors that significantly affected agricultural water use and their regression coefficients. The results are shown in Table 5. The sign of each regression coefficient indicates the direction of the relationship between the variable and agricultural water use, whereas the absolute coefficient value indicates relative contribution. Ranked by absolute coefficient magnitude, the relative importance of the original variables was X3 > X12 > X15 > X6 > X8 > X13 > X9 > X11 > X14 > X10. The coefficients of X8, X9, X11, X12, X14, and X15 were positive, indicating that increases in these factors promoted higher agricultural water use. The coefficients of X3, X6, X10, and X13 were negative, indicating that increases in these factors were associated with lower agricultural water consumption. Specifically, X3 had the largest absolute standardized coefficient (0.317) and was the primary influencing factor identified by the model in the group of water-resource and water-use structure variables. X12 ranked second, which is an important influencing factor in the group of social and economic variables, with a standardized coefficient of 0.183. The standardized coefficients of X6 and X15 were −0.055 and 0.017, respectively, whereas the absolute coefficients of the remaining variables were below 0.010. These results indicate that changes in agricultural water use are jointly shaped by water-use structure, population size, industrial development, and water-saving irrigation. Compared with regression methods that directly include all variables, PCA-Lasso reduces multicollinearity caused by redundant information through dimensionality reduction and coefficient shrinkage. It also highlights representative predictors while maintaining a high goodness of fit, providing a quantitative basis for agricultural water-use regulation and water-resource allocation in the Heihe River Basin.

Variation characteristics and influencing mechanisms of agricultural water use in the Heihe River Basin

This study showed that agricultural water use accounted for 77.26–85.72% of total water supply in the Heihe River Basin from 2001 to 2023 and exhibited a stage-dependent pattern: decline from 2001 to 2012, rebound from 2013 to 2014, and renewed decline after 2014. The 21.20% decrease in the first stage indicates that agricultural water use did not simply expand with economic growth, but was jointly shaped by available water resources, intersectoral water allocation, and water-saving management. The sharp increase in 2013 may reflect overlapping variable contributions of agricultural production scale, annual water-supply conditions, or changes in statistical criteria. In the absence of crop-specific planting area, annual inflow, and policy-implementation intensity data, it should not be attributed to a single event. In the correlation analysis, several groups of indicators had correlation coefficients above 0.80, and eight principal components explained 97.70% of the total variance. This further indicates significant coupling among agricultural water use, water-resource allocation, population, industrial development, and economic scale. The first principal component can be interpreted as an integrated socioeconomic-development and water-use-structure factor, whereas the second principal component more strongly reflects total water supply and intersectoral water allocation. These results are broadly consistent with the quantitative findings of previous studies in the Heihe River Basin and the Hexi Corridor. Optimization of cropping patterns can reduce irrigation water requirements. In areas where cropland was expanded, ET, GPP, and WUE increased at rates of 7.69 mm yr −1, 14.78 g C m −2 yr −1, and 2.48 × 10 −2 g C kg −1 H 2 O yr −1, respectively, whereas ET in areas where cropland was converted to other land uses changed at a rate of −2.19 mm yr −1 (Liu et al., 2022; Yang L. S. et al., 2023; Yang Z. C. et al., 2023). During 2001–2018, WUE in irrigated croplands of the Heihe River Basin increased by approximately 0.023 g C kg −1 H 2 O yr −1. The relative importance of the standardized precipitation evapotranspiration index (SPEI), precipitation, and soil moisture for interannual variations in WUE across the Hexi Corridor was 0.25, 0.20, and 0.17, respectively, while the corresponding models explained 44.69% and 81% of the variation (Du et al., 2024). During 2010–2019, ET in the Heihe River Basin increased by an average of approximately 1.1901 mm yr −1, with the explanatory power of the normalized difference vegetation index (NDVI), land use, and temperature reaching maximum values of 0.818, 0.709, and 0.506, respectively (Li X. et al., 2024; Li Z. H. et al., 2024). These findings indicate that the cropland-use, agricultural-production, and climate- and water-related variables identified in this study are broadly consistent with previous research in terms of both the direction of change and the magnitude of the quantitative characteristics. However, agricultural water use reflects a complex predictive relationship shaped by multiple interacting factors; therefore, the importance of any single variable should not be interpreted as an independent causal effect. It should be noted that during the research period, the Heihe River Basin underwent processes such as adjustments to the water resource allocation system, promotion of water-saving irrigation, changes in agricultural structure, strengthening of groundwater management, and increase in ecological water use. These management and institutional changes may alter the statistical relationship between socio-economic variables and agricultural water use. Therefore, the PCA-Lasso model established based on the full sample in this paper mainly depicts the overall prediction pattern during the research period, and cannot assume that the relationship between each variable and agricultural water use remains unchanged throughout the entire period. There may be certain heterogeneity in the prediction relationships under different management stages, which is also a problem worthy of further attention in future research.

PCA-Lasso model performance and mechanisms of core predictive variables

The PCA-Lasso model achieved the minimum cross-validation error at λ = 0.02, with R 2, RMSE, and MAE values of 0.997, 0.152, and 0.114, respectively. This indicates that the model reproduced the overall trend in agricultural water use during the sample period. The methodological advantage is that PCA first compresses redundant information contained in highly correlated indicators, whereas Lasso further reduces collinearity interference under small-sample and multivariable conditions through coefficient sparsification. The standardized coefficients show that ecological and environmental water use (X3) and total population (X12) had the largest absolute contributions, followed by water use for forestry, animal husbandry, and fisheries (X6) and per capita water use (X15). The negative coefficient of X3 is more appropriately interpreted as an allocation-substitution relationship between ecological water use and agricultural water use under a given water-supply condition. It should not be interpreted as evidence that increased ecological water use directly reduces crop physiological water demand. The positive variable contributions of X12 and X15 suggest that population size and overall water-use intensity may increase pressure on agricultural water use by expanding agricultural product demand and production activities. Water-saving irrigation area still showed a weak positive variable contribution, consistent with the irrigation-efficiency paradox reported in previous Heihe River Basin studies. In this paradox, water saved through improved field efficiency may be partly offset by expansion of irrigated area or planting scale (Cai et al., 2023; Hua et al., 2023). However, given that only 23 annual samples were available, an R 2 close to 1 still requires caution regarding overfitting. Recent water-demand prediction studies have similarly emphasized joint input of multisource variables and validation methods that preserve temporal order (Shu et al., 2024; Li X. et al., 2024; Li Z. H. et al., 2024). At this stage, the model is therefore more suitable for trend reproduction and driver screening, and its extrapolative prediction ability should be further verified using an independent test period.

Implications for water-resource management, study limitations, and future prospects

The results support broadening the focus of agricultural water management in the Heihe River Basin beyond single-purpose engineering-based water conservation toward coordinated management involving total water-use control, cropping-structure optimization, and improvements in water-use efficiency. First, population size and per capita water use exhibited positive predictive contributions in the model, indicating that variables related to the scale of water demand warrant particular attention in agricultural water-use prediction. Accordingly, under existing water-resource constraints, agricultural water demand could be reduced by prioritizing the control of irrigation scale and optimizing the area and spatial distribution of high-water-consuming crops. Previous studies have shown that optimizing the spatial configuration of crops in the Heihe River Basin can reduce irrigation water requirements by approximately 7.53% while simultaneously improving agricultural returns and water-use efficiency (Wu et al., 2024). This finding is consistent with the relatively high predictive importance of irrigation-scale- and agricultural-production-related variables identified in the present study. Second, the area under water-saving irrigation showed a positive predictive association in the model, suggesting that using the expansion of water-saving irrigation alone as an indicator of agricultural water-conservation performance may be insufficient. Therefore, while promoting the application of high-efficiency water-saving irrigation technologies, actual water withdrawals and total agricultural water use should also be incorporated as complementary evaluation indicators to determine whether engineering-based water savings translate into reductions in basin-scale water consumption. In addition, ecological and environmental water use exhibited a negative predictive association in the model, indicating a clear resource trade-off between ecological water allocation and agricultural water-use prediction. Accordingly, ecological water requirements should be incorporated as explicit constraints in agricultural water-use forecasting and annual water-allocation scenarios to improve the consistency between agricultural water-use predictions and basin-wide water-allocation objectives (Zhang et al., 2026). These recommendations are based on the predictive relationships identified by the model and should not be interpreted as evidence of causal policy effects resulting from changes in individual variables. This study is limited by the small number of annual samples, the masking of upstream, midstream, and downstream differences at the whole-basin scale, and insufficient quantification of institutional variables. Methodologically, it is also necessary to explicitly confirm whether agricultural water use, the prediction target, was excluded during PCA to avoid potential information leakage. The model coefficients and variable importance cannot be used to infer that changing a certain variable will lead to corresponding changes in agricultural water usage. This study did not separately establish models for different policy stages or conduct formal structural change tests. Therefore, it is impossible to determine whether the predictive relationship of variables has undergone significant changes before and after the implementation of specific management measures. In the future, after obtaining longer time series or higher time resolution data, methods such as structural change tests, rolling window models, or phased modeling can be used to further study the time stability of the agricultural water use prediction relationship (Zhang Z. P. et al., 2025; Zhang et al., 2025). Future studies should incorporate remote-sensing evapotranspiration, crop-specific blue and green water consumption, groundwater depth, water prices, and planting-structure data. They should also conduct zonal, lagged, and scenario prediction and test the stability of core factors through rolling external validation, thereby improving model adaptability to dry years, policy-adjustment periods, and spatial heterogeneity (Zou and Kang, 2022; Wang and Shi, 2024). At the same time, causal inference methods can be used to further examine the relevant mechanism of action.

Based on 20 indicators describing water-use structure, water resources, socioeconomic conditions, and meteorology in the Heihe River Basin from 2001 to 2023, this study used correlation analysis and a PCA-Lasso model to identify drivers of agricultural water use and simulate its variation. The main findings are as follows:

(1) From 2001 to 2023, agricultural water use in the Heihe River Basin ranged from 24.01 × 108 to 32.20 × 108 m 3, accounting for 77.26–85.72% of total water supply. Agriculture remained the dominant water-use sector in the basin. Agricultural water use declined by 21.20% from 2001 to 2012, rebounded markedly in 2013, reached 32.20 × 108 m 3 in 2014, and then generally decreased, with its water-use share gradually falling to approximately 77%.

(2) The 20 candidate indicators showed clear information overlap, with several correlation coefficients exceeding 0.80. PCA extracted eight principal components with a cumulative variance explanation rate of 97.70% and retained 14 main input indicators. This indicates that agricultural water-use variation was jointly influenced by water-use structure, water-resource supply, and socioeconomic development.

(3) Expanding-window cross-validation identified the optimal λ as 0.02. The R 2, RMSE, MAE, and MAPE of the PCA-Lasso model were 0.997, 0.152, 0.114, and 0.495%, respectively. The model fitted the overall trend in agricultural water use well. The variables related to water-resource and water-use (such as ecological and environmental water use, per capita water use, and water use for forestry, animal husbandry, and fisheries) and the socio-economic variables (total population) have a more prominent variable contributions.

(4) Future research should further integrate multisource data and advanced machine-learning algorithms to improve model adaptability under climate change. Basin-scale agricultural water management should also strengthen coordination among sectors, total-volume control, and water-use structure optimization. This study provides a scientific basis for optimal water-resource allocation and precision irrigation in the Heihe River Basin, while offering transferable methodological and management insights for other arid and semi-arid regions facing water scarcity and agricultural water-use pressures.