Shandong province is the main critical grain-producing area in China, characterized by maize is one of the main grain crops in the province. The experiment was conducted at the Agricultural Water Resource Efficient Use Experimental Site of Ludong University (37.54° N, 121.39° E) in the province. The elevation of the site is 47.8 m. The region experiences a warm temperate continental monsoon climate, with mean annual temperature ranging from 11.8°C to 13.0°C, and annual precipitation varying between 651.9 mm and 722.2 mm (mainly occurring in July and August) (Yantai Meteorological Bureau, 2023). The soil is loam, with pH value of 6.5–7.0, organic matter content ranging from 1.5% to 2.5%, organic C content between 1.0% and 1.5%, and nitrogen content ranging from 0.05% to 0.15% (Chen et al., 2019). The maximum field water holding capacity of the soil is about 22% (Zhang et al., 2021).

The summer maize cultivar “Jinhai No. 5” was sown in pots on 11 June 2023 and harvested on 27 September 2023. We conducted drought experiments during four different growth stages of maize: Jointing Stage (JS), Tasseling Stage (TS), Flowering Stage (FS), Grain Filling Stage (GFS). During each drought period, the soil moisture of control treatment was maintained at 60%–70% of the maximum field capacity, while the drought treatment was maintained at 40%–50% of the maximum field capacity. Each treatment was replicated in three pots, resulting in a total of 15 potted plants (4 drought-period treatments × 3 replicates + 1 control treatment × 3 replicates) (Figure 1). The pots used for the maize were plastic containers weighing 1.4 kg, with an upper diameter of 43 cm, a bottom diameter of 26 cm, and a height of 24 cm (Figure 1). Each pots was filled with a mixture of 20 kg of soil from the site and 5 g of “Sackoff” compound fertilizer (total nutrient content of 51.0%). Soil moisture of all treatments was monitored and maintained daily between 17:00 and 18:00 by weighting the pots. During watering, the pots were placed on an electronic scale to ensure precise control of water application, allowing for accurate adjustments as necessary.

SR rates were measured using the Photosynthesis-Fluorescence System (LI-6400XT, LI-COR Biosciences, Lincoln, NE, United States) equipped with the 6400–09 SR Chamber. The SR measurement collar was installed in each pot to a depth of 3 cm and 2 cm above the soil surface, with a measurement surface area of 80 cm². There was a 24-hour waiting period between the placement of the ring and the first SR monitoring. The T s was measured using the soil temperature sensor (equipped with LI-6400-09) during SR measurements, with the sensor inserted near the SR measurement point at a depth of 5–10 cm. SR and T s were measured simultaneously for all pots to ensure consistency across the experiment.

To estimate the dependence of seasonal variations in SR on T s , the relationship was fitted using an exponential equation (Equation 1): S R = k e a T s (1) Where the unit of SR is μmol·m⁻²·s⁻¹, the unit of T s is ◦C, and k and a are constants (Davidson et al., 1998; Knohl et al., 2008). The temperature sensitivity of SR, represented by Q₁₀, which indicates the increase in SR for every 10°C rise in temperature, was calculated using Equation 2: Q 10 = e 10 a (2)

Hyperspectral data for summer maize were collected using a spectrometer (ASD FieldSpec HandHeld2) between 11:00 a.m. and 1:00 p.m. under clear skies with minimal wind to ensure consistency. The spectrometer was calibrated with a standard reference panel to approximate 100% reflectance. During each measurement, the spectrometer was held 10–15 cm above the maize canopy, with ten readings averaged. In this study, spectral data from 350 to 910 nm were used (Table 1). For example, wavelengths of 680 nm and 800 nm were used to calculate Normalized Difference Vegetation Index (NDVI), while 705 nm and 750 nm were used to calculate NDVI₇₀₅ (Table 1). These hyperspectral vegetation indices are important indicators of plant health, biomass, and stress levels, providing critical information for monitoring crop conditions. They help assess photosynthetic activity and water content of vegetation, both of which are essential for evaluating crop performance and SR dynamics. Triangular parameters, such as edge amplitudes and areas (e.g., blue, yellow, red edges), are often used to represent spectral shifts related to changes in vegetation physiology, including pigment concentration, stress response, and overall growth status (Table 1).

Figure 2 showed the importance of input features in both the XGBoost and MLR models, along with their contributions to simulating SR. In the XGBoost model (Figure 2A), the feature T s was the most significant factor, suggesting that soil temperature T s had the largest influence on SR predictions for summer maize. Other important features included the red edge position ( λ r ) and red trough reflectance ( R r ). In contrast, the MLR model (Figure 2B), which was optimized using the AIC (AIC = −68.3913), revealed that the Ratio Vegetation Index (RVI) had the greatest impact. This finding suggests that specific vegetation indices played a critical explanatory role in the MLR model’s simulation of SR. Additional features, such as the NDVI and the Photochemical Reflectance Index (PRI), also had significant effects on the MLR model’s performance.

The XGBoost model significantly outperformed the MLR model in estimating SR for summer maize throughout the whole growth season (Figure 3A). The XGBoost model achieved a higher R ² value (R ² = 0.9298), indicating a stronger ability to explain variance, and a lower RMSE (RMSE = 0.2887), demonstrating lower prediction error. The fitted curve for the XGBoost model closely aligned with the 1:1 line, with data points clustered around it, suggesting that the XGBoost model accurately simulated SR across both high and low values. In contrast, the MLR model’s fitted curve deviated more from the 1:1 line, with data points showing greater scatter. The MLR model tended to overestimate lower SR values and underestimate higher SR values.

In the comparative analysis of model errors, the residual distributions of the XGBoost and MLR models exhibited significant differences (Figure 3B). The error of the XGBoost model was smaller and more concentrated, with residuals primarily ranging between −1 and 1, and a median close to 0, indicating that XGBoost demonstrated higher accuracy and stability in its prediction of SR rate. In contrast, the error range of the MLR model was broader, spanning from −2 to 2, with notably higher variability in the residuals. The boxplot of the MLR model displayed a wider interquartile range and pronounced lower outliers, suggesting that this model yielded larger errors for certain data points and lacked stability in its predictions.

As shown in Figure 4, both the MLR and XGBoost models successfully captured the effects of drought on SR rates, indicating that SR rates decreased under drought treatments across all growth stages (JS, TS, FS, and GFS). However, the XGBoost model performed better than the MLR model, with its simulated values more closely aligning with the measured values, particularly under the control treatment across all four stages. In contrast, the MLR model exhibited significant discrepancies between its simulated and measured values, especially during drought treatments.

The performances of both models in simulating SR rates for summer maize varied across different treatments and growth stages. Under control treatment, the XGBoost model more accurately simulated SR rates, though it slight overestimated them by approximately 5.6% during the JS. In contrast, the MLR model consistently underestimated SR rates across all growth stages, with the most significant underestimation occurred during the JS (15.35%), and the least during the FS (7.32%). Under drought treatments, both models significantly overestimated SR rates across all stages. However, the MLR model’s overestimations were much larger than those of the XGBoost model. The MLR model overestimated SR rates by 87.25% during the JS, with the highest error occurring under drought treatments, while the smallest overestimation occurred during the GFS (4.54%). Although the XGBoost model also overestimated SR rates at all stages, its errors were much smaller, with the largest overestimation occurring during the JS stage (40.1%) and the smallest during the GFS stage (14.6%). These results indicate the superior performance of the XGBoost model in modeling SR under varying moisture conditions.

The sensitivity of SR rates to T s varied between the MLR and XGBoost models (Figure 5). Both models reasonably captured the relationship of T s on SR, as evidenced by their fitted curves aligning with the observed data points. However, the sensitivity of the simulated SR values to temperature (Q₁₀) decreased in both control and drought treatments. Despite this, the XGBoost model generally outperformed the MLR model. Under control treatments, the sensitivity coefficient of SR rates to T s simulated by the XGBoost model (Q₁₀ = 1.3418), was only 6.1% lower than the measured sensitivity coefficient (Q₁₀ = 1.4287). In contrast, the MLR model’s sensitivity coefficient (Q₁₀ = 1.1888) showed a more substantial decrease of 16.79%. Additionally, both models exhibited reduced explanatory power in their fitted functions, suggesting that discrepancies between simulated and measured values affected the Q₁₀ values. Nevertheless, the XGBoost model (R ² = 0.6584) provided better explanatory power than the MLR model (R ² = 0.6528). Under drought treatments, the XGBoost model’s sensitivity coefficient (Q₁₀ = 1.1208) was 4.49% lower than the measured coefficient (Q₁₀ = 1.1735), while the MLR model’s coefficient (Q₁₀ = 1.0544) decreased by 20.48%. Although both models showed reduced explanatory power for SR variability under drought conditions, the Q₁₀ values from the fitted functions in both models indicated higher explanatory power than the measured values.

In this study, we compared the performance of the MLR and XGBoost models in simulating SR across different growth stages under both drought and control treatments. The results consistently demonstrated that the XGBoost model outperformed the MLR model, as indicated by its higher R ² and lower RMSE values. The superior performance of the XGBoost model is primarily attributed to its ability to capture non-linear relationships between parameters (Chen and Guestrin, 2016; Ding, 2024).

A Pearson correlation analysis was conducted to examine the relationships between various parameters and SR (Figure 6). The analysis revealed that parameters, such as D b , D r , DVI, EVI, R g , R r , S D b , S D r , S D y and T s , exhibited clear nonlinear trends with SR, indicating that the response of SR to these parameters is not uniform but varies in intensity depending on other parameters. In contrast, parameters, such as λ b , λ g , and λ y , showed weak linear relationships with SR, with their correlations being statistically insignificant. This indicates that, while some parameters may exhibit linear relationships with SR, their overall contribution to SR variability is minimal.

The XGBoost, a decision tree-based gradient boosting framework, excels at handling non-linear relationships (Chen and Guestrin, 2016; Liang et al., 2020; Nabavi et al., 2023). The decision trees in the XGBoost model divide data into distinct regions, enabling the model to capture complex interactions. The XGBoost model builds these tree models incrementally, using a boosting method where each new tree corrects the errors of the previous one (Kiangala and Wang, 2021; Zhang et al., 2019). This recursive process allows the XGBoost model to capture intricate patterns and non-linear features in the data, whereas the traditional MLR model struggles due to its inherent linear assumptions. For instance, parameters like T s and D b , which showed high non-linearity with the SR rate (Figure 6), were better captured by the XGBoost model, while the MLR model failed to account for their non-linear impacts.

Additionally, the XGBoost model handles multicollinearity among parameters effectively (Chen et al., 2022). Its tree-based structure prioritizes important features during model construction without being limited by linear relationships (Kern et al., 2019; Tong et al., 2003). This ensures strong predictive performance even in the presence of highly correlated variables. For example, in this study, significant multicollinearity existed among parameters, such as NDVI, PRI, and T s , which posed challenges for the traditional MLR model (Garg and Tai, 2013). Since the MLR model assumes that predictor variables are independent, it struggles with stability and reliability when dealing with multicollinearity (Weaving et al., 2019; Chan et al., 2022). While the MLR model used AIC to select important predictors, including NDVI, RVI, PRI, T s , and S D b , it still struggled to manage the effects of multicollinearity, resulting in weaker performance. In contrast, XGBoost automatically accounts for variable interactions in each decision tree split, mitigating the negative effects of multicollinearity on model performance (Kavzoglu and Teke, 2022; Wu et al., 2024).

The XGBoost model stands out in identifying and leveraging feature interactions, making it suitable for complex, high-dimensional datasets (Hastie et al., 2009; Huang et al., 2022). Unlike MLR, which relies on predefined linear relationships and manually added interaction terms, XGBoost dynamically uncovers important feature interactions during training (Niazkar et al., 2024). This enables XGBoost to capture non-linear and higher-order interactions directly from the data, without the need for explicit feature engineering (Weaving et al., 2019). In contrast, MLR requires prior assumptions about feature interactions, which increases the risk of inaccuracies when dealing with complex variable interdependencies.

Furthermore, the XGBoost model also uses Lasso and Ridge regularization techniques to prevent overfitting, enhancing its modeling robustness (Friedman, 2001; Elavarasan and Vincent, 2020). Regularization penalizes overly complex models, allowing the XGBoost model to maintain strong performance even in noisy datasets or when faced with low-importance variables (Zhang and Jánošík, 2024). In contrast, the traditional MLR model, lacking these regularization treatments, is more vulnerable to overfitting, especially in the presence of multicollinearity (Dormann et al., 2013). Although AIC helps select optimal predictors in the MLR model, it does not fully mitigate the risk of overfitting, particularly when dealing with correlated variables or when the model becomes too complex. Hence, the XGBoost model’s ability to manage data complexity more effectively through regularization offers a clear advantage over the MLR model.

In summary, the XGBoost model’s ability to capture non-linear relationships, manage multicollinearity, and utilize regularization techniques significantly enhances its robustness and predictive accuracy. In contrast, the MLR model’s reliance on linear assumptions and vulnerability to overfitting limit its effectiveness when applied to complex datasets. Our study underscores the importance of selecting appropriate modeling techniques tailored to the complex and non-linear nature of ecological and agricultural data.

This study utilized hyperspectral remote sensing features to predict SR in summer maize, demonstrating the potential of hyperspectral data for non-destructive SR estimation. The correlation between SR and hyperspectral features arrised from the hyperspectral data’s ability to indirectly capture key vegetation and soil characteristics, which reflect key environmental and biological factors that influencing SR (Huang et al., 2014). Previous research has shown that hyperspectral data can indicate SR indirectly through vegetation indices, chlorophyll content, soil surface reflectance, and other spectral parameters (Cicuendez et al., 2015; Ding et al., 2021). These features are closely related to plant growth, soil moisture, and temperature conditions, all of which directly impact root respiration and microbial activity, thereby driving SR.

In prior studies, hyperspectral remote sensing has represented SR effectively by capturing vegetation spectral characteristics, such as chlorophyll concentration and biomass content, that are closely tied to plant productivity and photosynthetic activity (Ding et al., 2021). These processes influence root and microbial respiration, which in turn affect SR (Feilhauer et al., 2017). Additionally, hyperspectral data are sensitive to soil and plant water content, which can indicate SR fluctuations by revealing variation in soil moisture that influence SR rate. By analyzing specific spectral bands and indices, such as NDVI and chlorophyll-based indices, hyperspectral data can capture those plant and soil health indicators relevant to SR, thus enhancing the estimation accuracy of SR models (Ding et al., 2021; Yao et al., 2021).

However, several environmental and biological factors significantly influence the relationship between SR and hyperspectral data. For example, plant species and growth stage have key influence on spectral characteristics, as they show substantial variability in physiological responses, canopy structure, and leaf biochemistry, all of which alter spectral signatures (Feilhauer et al., 2017). Water condition directly impacts SR by affecting microbial activity and root respiration, which drive variation in SR rate (Philippot et al., 2024). Hyperspectral data, especially water absorption bands, can indirectly capture this influence on SR. Moreover, soil temperature is another significant factor. Higher temperatures tend to promote microbial and root respiration, and temperature changes influence vegetation spectral response, which in turn affects SR estimate derived from hyperspectral data (Yao et al., 2021).

Our findings align with some previously observed trends, though differences also exist. Similar to other studies, we found that specific vegetation indices (e.g., NDVI) effectively capture SR changes across different growth stages, indicating that hyperspectral data are robust in reflecting plant-soil interactions that drive SR (Cicuendez et al., 2015). However, the sensitivities of SR to drought treatments and growth stage variation are more pronounced in our study. These differences may arise from our experimental conditions, including maize growth stages under controlled drought treatments, as well as the local climate and soil properties differing from those in other studies.

Although we found that the performance of ML XGBoost model in simulating SR rates during the growth stages of maize cropland was better than the traditional MLR model, there are still some uncertainties in the study. One limitation is the absence of continuous drought treatments across all four growth stages (JS, TS, SS, and GFS). While the current experimental design provides insights into short-term SR responses, long-term drought exposure could induce more complex responses, potentially altering microbial activity, root respiration, and C cycling over time (Wang et al., 2014). Hence, future studies incorporating continuous drought treatments throughout all growth stages would be valuable for comprehensively assessing the long-term impacts of water stress on SR through ML models.

Further modelling research is needed to examine the effects of initiating drought during different growth stages. The timing of drought onset is crucial, as SR responses can vary depending on the developmental stage of the crop. For instance, early-stage drought may have a more pronounced effect on root development and microbial interactions, while drought at later stages may alter C allocation and respiration processes (Liu et al., 2022). Additional field and modeling experiments applying drought treatments at varying growth stages over extended periods would provide more robust estimates of SR dynamics, particularly when using hyperspectral remote sensing under varying environmental stress scenarios (Zhang et al., 2019).

Finally, this study was conducted with maize grown in potted plants, which may not fully represent the complexities of field conditions. Factors such as soil texture, microclimate, and micrograph, etc., could also influence SR (Conant et al., 2000). Therefore, future large-scale field experiments are necessary to strengthen the evaluation of the ML models using hyperspectral remote sensing in more complex, real-world conditions. These studies would provide a more realistic assessment of SR under various drought conditions and enhance the robustness of the conclusions drawn from this research.