Simulation of Winter Wheat Gross Primary Productivity Incorporating Solar-Induced Chlorophyll Fluorescence

Abstract

Gross primary productivity (GPP) is a key indicator for assessing carbon uptake capacity and photosynthetic productivity in agricultural ecosystems, playing a crucial role in regional carbon cycle evaluation and sustainable agriculture development. However, traditional mechanistic light use efficiency (LUE) models exhibit variable accuracy under different climatic conditions and crop types. Machine learning models, while demonstrating strong fitting capabilities, heavily depend on the selection of input features and data availability. This study focuses on winter wheat in the Guanzhong region, utilizing continuous field observation data from the 2020–2022 growing seasons to develop five machine learning models: Ridge Regression (Ridge), Random Forest (RF), Support Vector Regression (SVR), Gradient Boosting Regression (GB), and a stacking-based ensemble learning model (LSM). These models were compared with the LUE model under two scenarios, excluding and including solar-induced chlorophyll fluorescence (SIF), to evaluate the contribution of SIF to GPP estimation accuracy. The results indicate significant differences in GPP estimation performance among the machine learning models, with LSM outperforming others in both scenarios. Without SIF, LSM achieved an average R² of 0.87, surpassing individual models (0.72–0.83), demonstrating strong stability and generalization ability. With SIF inclusion, all machine learning models showed marked accuracy improvements, with LSM’s average R² rising to 0.91, highlighting SIF’s critical role in capturing photosynthetic dynamics. Although the LUE model approached machine learning model accuracy in some growth stages, its overall performance was limited by structural constraints. This study demonstrates that ensemble learning methods integrating multi-source observations offer significant advantages for high-precision winter wheat GPP estimation, and that incorporating SIF as a physiological indicator further enhances model robustness and predictive capacity. The findings validate the potential of combining ensemble learning and photosynthetic physiological parameters to improve GPP retrieval accuracy, providing a reliable technical pathway for agricultural ecosystem carbon flux estimation and informing strategies for climate change adaptation.

1. Introduction

Gross primary productivity (GPP) refers to the total amount of carbon fixed by vegetation through photosynthesis and serves as a fundamental indicator for assessing ecosystem productivity and carbon cycling processes [1]. In agricultural ecosystems, accurately estimating GPP is crucial for understanding crop growth dynamics, evaluating vegetation’s capacity to sequester atmospheric CO₂, and guiding precision agricultural management [2]. GPP reflects the efficiency with which vegetation converts solar radiation into biomass, providing an essential basis for assessing the impacts of environmental stressors—such as drought, heat, or nutrient limitations—on crop yield [3]. Therefore, under the context of climate change, achieving reliable and real-time monitoring of GPP is of great importance for optimizing irrigation strategies, improving yield forecasting accuracy, and formulating sustainable land management policies.

Currently, numerous model comparison studies based on flux observation data have been conducted, revealing the limitations of GPP retrieval algorithms and their main influencing factors. Wang et al. evaluated the latest MODIS GPP product (MOD17A2H) against EC flux-estimated GPP across different vegetation types and found poor performance at both the annual scale (R² = 0.62) and the 8-day scale (R² = 0.52) [4]. Chen et al. compared the spatiotemporal variations in GPP simulated by MODIS, the Breathing Earth System Simulator (BESS), and the Vegetation Photosynthesis Model (VPM) across China, showing that while all three models effectively captured the spatial patterns of GPP, their interannual variations differed considerably [5]. Lin et al. compared the simulation accuracy of solar energy utilization models across deciduous and coniferous forests, mixed forests, grasslands, croplands, shrubs, and evergreen broadleaf forests, reporting R² values ranging from 0.11 to 0.78 and RMSE values from 1.37 to 4.65 among the VPM, EC-LUE, and MODIS models [6].

At the field scale, GPP is often monitored using the eddy covariance (EC) technique [7]. This approach enables high-temporal-resolution measurements of net carbon fluxes between ecosystems and the atmosphere, and GPP can be derived by partitioning ecosystem respiration and net ecosystem exchange (NEE) [8]. It is one of the most widely adopted in situ monitoring methods to date. For instance, EC measurements in the Hegyhátsál region of Hungary from 1997 to 2018 were used to analyze the long-term characteristics of CO₂ fluxes and their relationships with climatic variables [9]. Despite its high accuracy and representativeness at the local scale, the EC technique faces several limitations, including high equipment and maintenance costs, sensitivity to terrain and atmospheric stability, and limited spatial representativeness, which hinder its applicability for large-scale, multi-regional GPP monitoring.

In contrast, the light use efficiency (LUE) model offers a mechanistic and parameterized approach for GPP estimation [10]. The model estimates GPP per unit area by multiplying the absorbed photosynthetically active radiation (APAR) by the photosynthetic efficiency. Owing to its concise structure and strong quantifiability, the LUE model has been widely applied in regional-scale GPP assessments [11]. Studies have shown that applying the LUE model, calibrating it with observed data, and validating its outputs can substantially improve predictive accuracy—explaining 49–65% of the daily GPP variation [12]. Xie et al. simulated daily GPP in mountainous areas using a two-leaf LUE model, achieving an RMSE of 1.84 gC·m⁻²·d⁻¹ [13]. Similarly, Nima Madani et al. reported a significant correlation between GPP estimated by the LUE model and EC flux-observed GPP, with R² = 0.77 and RMSE = 439 gC·m⁻²·yr⁻¹ [14]. However, the LUE model is highly sensitive to parameterization and oversimplifies plant physiological responses to varying environmental conditions, making it challenging to accurately capture the spatiotemporal dynamics of GPP, particularly in regions with highly variable meteorological conditions or frequent agricultural stress events.

Sun-induced chlorophyll fluorescence (SIF) is a faint radiative signal emitted by chlorophyll molecules during photosynthesis [15]. As a direct proxy for photosynthetic activity, SIF has attracted considerable attention in recent years, with studies consistently demonstrating its strong coupling with GPP [16]. Extensive empirical evidence has confirmed that SIF and GPP exhibit robust correlations across diverse vegetation types and temporal scales [17]. For example, ground-based tower measurements of SIF and an eddy covariance system at the Yangling winter wheat experimental station in China revealed a strong correlation between SIF and actual crop evapotranspiration (ETc act), with a correlation coefficient of p = 0.78, thereby providing solid scientific support for using SIF as an indicator of photosynthetic carbon uptake [18].

With the growing availability of SIF datasets from both ground-based and satellite platforms, machine learning (ML) models have emerged as an important approach for integrating SIF with meteorological and environmental variables to estimate GPP [19]. ML models bypass the need for explicit parameterization of complex physiological processes, enabling them to effectively capture nonlinear relationships among input variables [20]. For instance, Ma et al. developed a cross-domain transfer ML framework that combines SIF with flux tower GPP observations, employs representative sampling to address large-scale spatial and numerical heterogeneity, and successfully estimates GPP at the global scale [21]. Nevertheless, individual ML models are subject to inherent limitations, such as sensitivity to the distribution of training data, susceptibility to overfitting when samples are sparse, and insufficient generalization capacity [22]. These constraints highlight the urgent need for more robust and adaptable modeling frameworks to further enhance the accuracy and stability of GPP estimation.

In recent years, the rapid development of ensemble learning, transfer learning, and advanced machine learning methods in agricultural remote sensing has provided important theoretical and practical support for complex tasks such as SIF-GPP modeling. Ensemble learning improves accuracy and robustness in agricultural remote sensing tasks by combining predictions from multiple models. For example, Ang et al. (2022) used an XGBoost model based on Landsat time-series imagery to predict oil palm yield, reducing RMSE by approximately 12%, demonstrating the advantages of ensemble learning in handling multi-source data [23]. Transfer learning, by reusing features from pretrained models, effectively addresses the challenge of limited agricultural data labeling. For instance, Ashiqul Islam implemented rice leaf disease classification using a pretrained DenseNet-201 model, achieving over 95% accuracy across four models [24]. Advanced machine learning methods, such as Transformer-based vision–language models, further push the frontier of agricultural remote sensing. Gao et al. proposed the AgriCLIP model, which integrates high-resolution satellite imagery and climate data to predict potential distribution areas for double-cropped soybean [25].

In particular, stacking ensemble learning has gradually gained wide attention as an efficient prediction approach. [26]. This method combines multiple base learners to generate initial predictions, which are then integrated by a higher-level meta-learner to improve overall model performance. Stacking leverages the complementary strengths of different models, reducing the risk of overfitting while enhancing robustness and generalization capacity in complex data environments [27]. Compared with single models, stacking is better suited to addressing challenges frequently encountered in agricultural production, such as strong nonlinearity, high noise levels, and pronounced data heterogeneity [28]. It has been successfully applied to diverse agricultural tasks, including yield prediction, soil moisture estimation, evapotranspiration modeling, and crop classification. In recent years, studies have explored the application of stacking in agricultural remote sensing and ecological modeling, achieving significantly better results than conventional models. For instance, applying a stacking ensemble to meteorology-based evapotranspiration estimation produced substantially higher predictive accuracy compared with individual models [29]. These findings indicate that employing stacking to integrate SIF and meteorological data for GPP estimation holds considerable promise and practical value.

Although SIF-based GPP estimation has shown considerable potential for improving accuracy, most existing studies rely heavily on satellite-derived SIF and GPP products. These products are often constrained by low spatial resolution, cloud contamination, and limited temporal continuity, which restrict their applicability in small-scale areas such as croplands and, consequently, affect the accuracy and stability of model estimates [30]. To address the aforementioned issues, this study deployed an eddy covariance system and a ground-based tower SIF observation system in a winter wheat field to obtain continuous, high-frequency measurements of GPP and SIF, serving as standard values for model training and validation. Based on these data, the MIC was used to quantitatively assess the relationships between SIF and meteorological variables, providing insights into the relative contributions of different feature variables. Furthermore, this study systematically compared the performance of ground-based SIF integrated with various machine learning models and a stacking ensemble model, as well as a process-based LUE model, in estimating winter wheat GPP. This work aims to provide a feasible and reliable technical approach for efficient monitoring and modeling of carbon fluxes under actual agricultural conditions.

2. Materials and Methods

2.1. Study Area

The field experiment was conducted from October 2020 to June 2022 at a winter wheat field affiliated with the Key Laboratory of Agricultural Soil and Water Engineering, Northwest A&F University, China (34°17′45″ N, 108°04′07″ E), covering two consecutive growing seasons (Figure 1). The experimental site is located in a semi-humid arid zone and extends approximately 200 m from north to south and 250 m from east to west. The region experiences an annual mean sunshine duration exceeding 2000 h, an average air temperature of 12.9 °C, an average annual precipitation of about 560 mm, and an annual potential evaporation of roughly 1500 mm. The soil is classified as silty clay loam, with a field capacity of 0.235 cm³·cm⁻³ and a bulk density of 1.35 g·m⁻³.

Winter wheat is typically sown in mid-to-late October each year. Its growth cycle consists of the overwintering stage (from sowing to mid-January of the following year), greening stage (late January to mid-March), jointing stage (late March to mid-April), heading–grain-filling stage (late April to early May), and milk–maturity stage (mid-May to early June). Prior to sowing, a specialized calcium-amino acid compound fertilizer was applied at rates of 172.5 kg N ha⁻¹, 90 kg P₂O₅ ha⁻¹, and 37.5 kg K₂O ha⁻¹. Herbicides and insecticides were applied once during each growth stage to control weeds, pests, and diseases.

2.2. Data Measurement and Preprocessing

2.2.1. Gross Primary Productivity and Meteorological Data

An open-path eddy covariance (OPEC) system and a meteorological observation system were installed at the experimental site to collect meteorological variables and GPP data. All sensors were mounted at a height of 2 m above the ground. The OPEC system comprised a three-dimensional sonic anemometer (CSAT-3, Campbell Scientific, Logan, UT, USA) for measuring wind speed and direction; an open-path infrared gas analyzer (LI-7500A, LI-COR, Lincoln, NE, USA) for measuring CO₂ and H₂O concentrations; a data logger (LI-7550, 10 Hz, LI-COR, Lincoln, NE, USA); and an air temperature and humidity probe (HMP-60, Vaisala, Finland). The system simultaneously recorded latent heat and sensible heat fluxes between the ecosystem and the atmosphere.

Soil water content (SWC) at various depths was measured using TDR310s probes (Acclima, Meridian, MS, USA). Photosynthetically active radiation (PAR) was monitored by a radiation sensor installed at the same height. Air temperature (${\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}$) was obtained from the meteorological observation system.

All sensors were calibrated and tested prior to installation. Data were recorded at 10 Hz using a CR1000 datalogger (Campbell Scientific) and aggregated at 30 min intervals. Following the ChinaFLUX protocol, zero-offset and span calibrations were performed every six months.

The vapor pressure deficit (VPD) was calculated from 30 min air temperature and relative humidity data [31]. The specific calculation formula is as follows:

$$\mathrm{V}\mathrm{P}\mathrm{D}=0.61078\times {\mathrm{e}}^{{\displaystyle \frac{17.27\times {\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}}{{\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}+237.3}}}\times \left(1-\mathrm{R}\mathrm{H}\right)$$

(1)

where ${\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}$ is air temperature (°C) and $\mathrm{R}\mathrm{H}$ is relative humidity (%).

2.2.2. Solar-Induced Chlorophyll Fluorescence Data

During the 2020–2021 and 2021–2022 winter wheat-growing seasons, a six-channel automatic solar-induced chlorophyll fluorescence (SIF) observation system (AUTOSIF-2-8, Bergsun Inc., Beijing, China) was deployed around the eddy covariance system. The six channels were mounted on tripods at a height of 2 m. Compared with single-point SIF systems, this configuration provided better spatial coverage and matched the footprint of the eddy covariance measurements.

The system consisted of a customized spectroradiometer and an optical multiplexer. The spectroradiometer (QE Pro, Ocean Optics, Dunedin, FL, USA) had a signal-to-noise ratio of 1000, a spectral resolution of 0.34 nm, a sampling interval of 0.17 nm, and a spectral range of 645–805 nm. The optical multiplexer (MPM-2000, Ocean Optics, Dunedin, FL, USA), coupled with a cosine corrector (CC-3, Ocean Optics, Dunedin, FL, USA), enabled dark-current correction for blind channels and sequential switching among six bare optical fibers (field of view: 25°) to collect upward radiance. Each channel had a circular footprint with a diameter of approximately 0.9 m. Both the spectroradiometer and multiplexer were housed in a dry, temperature-controlled enclosure (25 ± 1 °C) to ensure measurement stability. All devices were radiometrically and spectrally calibrated prior to installation.

Before each observation, dark-current correction and integration time optimization were performed. The “sandwich” method was applied to reduce the influence of unstable weather conditions on the measurements [32].

SIF retrieval from continuous spectral measurements was performed using the singular value decomposition (SVD) method, which assumes that non-SIF spectra can be represented as a linear combination of singular vectors derived from a non-SIF training dataset [33]. The near-infrared canopy SIF signal was retrieved using a spectral fitting window of 740–780 nm, and the retrieved values were then aggregated to daily averages [34].

2.2.3. Data Normalization

All variables were aggregated to daily averages to match the temporal resolution of flux-derived GPP. After quality control, a total of 469 daily samples were obtained across the two winter wheat-growing seasons.

The measured $T_{air}$, PAR, SWC, VPD and SIF were used as input feature parameters for the machine learning model. Since these variables have different numerical ranges, which could affect model training performance, all four meteorological variables and SIF were normalized prior to feature importance assessment and model construction [35]. The normalization was performed using the following equation:

$${\mathrm{X}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m},\mathrm{i}}={\displaystyle \frac{{\mathrm{X}}_{\mathrm{i}}-{\mathrm{X}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{{\mathrm{X}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{X}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}}$$

(2)

where ${\mathrm{X}}_{\mathrm{i}}$ is the original value of the i-th sample, ${\mathrm{X}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ and ${\mathrm{X}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ represent the minimum and maximum values of the feature across all samples, and ${\mathrm{X}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m},\mathrm{i}}$ is the normalized value.

2.3. Research Methods

2.3.1. Correlation Analysis

To assess the relationship between SIF and GPP, Spearman’s rank correlation coefficient was calculated to quantify the association between the two nonlinear variables [36]. This method is based on the ranks of the variables and is computed as follows:

$$\mathrm{\rho }=1-{\displaystyle \frac{6\sum {\mathrm{d}}_{\mathrm{i}}^2}{\mathrm{n}\left({\mathrm{n}}^2-1\right)}}$$

(3)

where d_i represents the difference between the ranks of the two variables for the i-th sample, and n is the total number of samples.

2.3.2. Feature Importance Evaluation

Considering that high-dimensional feature inputs may degrade the simulation accuracy of machine learning (ML) models, this study employed the Maximal Information Coefficient (MIC) method to reduce feature dimensionality and determine the importance of each feature for predicting GPP. MIC is a non-parametric statistical measure of association capable of capturing both linear and nonlinear relationships while maintaining scale invariance across different types of relationships [37]. The MIC value ranges from 0 to 1, where higher values indicate stronger correlation; 0 denotes no association, and 1 represents a perfect correlation.

The computation was performed using the minepy library in the Python 3.10 environment. The resulting MIC values were used to rank feature importance and to compare differences in feature importance under scenarios with and without SIF inclusion. The calculation formula is as follows:

$$\mathrm{M}\mathrm{I}\mathrm{C}\left(\mathrm{X},\mathrm{Y}\right)=\underset{\mathrm{G}}{\mathrm{m}\mathrm{a}\mathrm{x}} \left[{\displaystyle \frac{\sum _{\mathrm{i},\mathrm{j}} \mathrm{P}\left(\mathrm{i},\mathrm{j}\right)\log \frac{\mathrm{P}\left(\mathrm{i},\mathrm{j}\right)}{\mathrm{P}\left(\mathrm{i}\right)\mathrm{P}\left(\mathrm{j}\right)}}{\log \min \left(\left|\mathrm{X}\right|,\left|\mathrm{Y}\right|\right)}}\right]$$

(4)

where X and Y represent the input feature and response variable, respectively; G denotes the grid partitioning scheme applied to X and Y; $\mathrm{P}(\mathrm{i},\mathrm{j})$ is the joint probability of X and Y falling into the i-th and j-th grid intervals; $\mathrm{P}\left(\mathrm{i}\right)$ and $\mathrm{P}\left(\mathrm{j}\right)$ are the marginal probabilities; and $\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{m}\mathrm{i}\mathrm{n}\left(\right|\mathrm{X}|,|\mathrm{Y}\left|\right)$ serves as the normalization factor, with $\left|\mathrm{X}\right|$ and $\left|\mathrm{Y}\right|$ representing the cardinalities of X and Y, ensuring the MIC value remains within the range [0, 1].

2.3.3. Machine Learning Models

In this study, five machine learning models were developed to simulate winter wheat GPP using Tair, PAR, SWC, VPD, and SIF as input features. These models included a linear ridge regression model (Ridge Regression, Ridge), three widely used nonlinear algorithms—Random Forest (RF), Support Vector Regression (SVR), and Gradient Boosting (GB)—and an ensemble learning model based on the stacking algorithm (Linear Stacking Model, LSM). The selection of these models was motivated by their complementary strengths in handling linear and nonlinear relationships, capturing variable interactions, and adapting to relatively small agricultural datasets. Ridge served as a robust linear benchmark; RF and SVR are well suited for small-sample and nonlinear regression tasks; and GB offers strong predictive capacity by iteratively optimizing weak learners. The LSM structure is illustrated in Figure 2, and its rationale can be summarized as follows: (1) parameter calibration and validation were performed for the three base machine learning models using observational data; (2) the calibrated models were used to simulate winter wheat GPP; and (3) the outputs of these models were then fed into the linear layer of the LSM, which was subsequently trained to produce the final GPP estimates.

Ridge model: Also known as Tikhonov regularization, this is a variant of linear regression. By introducing an L2 regularization term into the ordinary least squares (OLS) regression, Ridge regression addresses multicollinearity issues and enhances the model’s generalization capability and robustness [38].

RF model: It uses decision trees as base learners, combining the Bagging ensemble method with random feature selection to address both regression and classification problems [39]. The primary hyperparameters include n_estimators and max_depth. Model tuning was performed via randomized search with 10-fold cross-validation (10-fold CV), implemented using the RandomForestRegressor module in Python 3.10.

SVR model: It constructs an optimal hyperplane in a high-dimensional feature space to fit nonlinear relationships. The radial basis function (RBF) kernel was adopted to enhance the model’s ability to capture nonlinear separability [40]. The γ parameter was set to scale to adapt to the standard deviation of the features. The main tunable parameters were the penalty coefficient C and the kernel parameter γ, optimized through randomized search with 10-fold CV, using the SVR module in Python 3.10.

GB model: It iteratively optimizes model parameters along the gradient direction of the objective function, gradually improving predictive accuracy [41]. The key hyperparameters included n_estimators and learning_rate. Tuning was conducted via randomized search with 10-fold CV, using the GradientBoostingRegressor module in Python 3.10.

During model training and evaluation, 70% of the samples were used as the training set and 30% as the testing set to ensure data independence. In the training stage, 10-fold CV was employed for hyperparameter optimization, with the objective of maximizing R². Each model’s training–validation process was repeated 50 times to obtain performance distributions for assessing model stability and robustness. All model training and evaluation were conducted within the scikit-learn framework in Python 3.10.

Table 1. Detailed list of parameters used in the prediction model.

Machine Learning Models	Parameters
RF	N_estimators: [50, 100]
	max_depth: [10, 20]
SVR	C: [1, 10]
	Gamma: [‘scale’, ‘auto’]
GB	n_estimators: [50, 100]
	learning_rate: [0.05, 0.1]

summarizes the main parameter settings and ranges for the three nonlinear ML models.

To ensure fairness and reproducibility, Bayesian optimization combined with repeated 10-fold cross-validation (10-fold CV) was employed for hyperparameter tuning across all models, with the maximization of R² as the objective function. The specific search ranges of hyperparameters and the final selected values are summarized in Table 1. During model training and evaluation, 70% of the samples were used for training and 30% for independent testing to guarantee data independence. The training–validation process for each model was repeated 50 times to assess model stability and robustness. All models were implemented in Python 3.10 using the scikit-learn and xgboost libraries.

2.3.4. GPP Estimation Based on the Light Use Efficiency Mode

The LUE model is a semi-empirical approach based on photosynthesis theory, positing that vegetation GPP is jointly determined by the absorbed PAR and the light use efficiency (ε) [42]. Under sufficient light and favorable environmental conditions, the light use efficiency reaches its maximum value (${\mathrm{\epsilon }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$). However, under suboptimal conditions such as temperature and water stress, photosynthesis is inhibited, resulting in reduced light use efficiency. Based on this principle, the LUE model typically incorporates temperature and water stress modifiers, in addition to ${\mathrm{\epsilon }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$, to reflect the impact of environmental stresses on photosynthetic efficiency. The GPP estimated by the LUE model is expressed as follows:

$$\mathrm{G}\mathrm{P}\mathrm{P}=\mathrm{P}\mathrm{A}\mathrm{R}\times {\mathrm{\epsilon }}_{\mathrm{m}\mathrm{a}\mathrm{x}}\times {\mathrm{f}}_{\mathrm{r}}\left({\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}\right)\times {\mathrm{f}}_{\mathrm{w}}\left(\mathrm{S}\mathrm{W}\mathrm{C},\mathrm{V}\mathrm{P}\mathrm{D}\right)$$

(5)

where PAR is the measured photosynthetically active radiation; ${\mathrm{\epsilon }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum light use efficiency under optimal conditions, obtained by fitting the relationship between GPP and PAR derived from eddy covariance observations; ${\mathrm{f}}_{\mathrm{r}}\left({\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}\right)$ is the temperature response factor; and ${\mathrm{f}}_{\mathrm{w}}(\mathrm{S}\mathrm{W}\mathrm{C},\mathrm{V}\mathrm{P}\mathrm{D})$ is the water stress factor jointly determined by SWC and VPD. The calculation formula and parameter settings of temperature and moisture regulation factors are shown in

Table 2. Calculation formulas and parameter settings for the temperature and water stress modifiers.

Factor	Calculation Formula	Parameter Description	Value
${\mathrm{f}}_{\mathrm{r}}\left({\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}\right)$	$\left\{\begin{array}{c}{\displaystyle \frac{{\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}-{\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{{\mathrm{T}}_{\mathrm{o}\mathrm{p}\mathrm{t}}-{\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}},{\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}<{\mathrm{T}}_{\mathrm{o}\mathrm{p}\mathrm{t}}\\ {\displaystyle \frac{{\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}}{{\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{T}}_{\mathrm{o}\mathrm{p}\mathrm{t}}}},{\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}>{\mathrm{T}}_{\mathrm{o}\mathrm{p}\mathrm{t}}\end{array}\right.$	${\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$: minimum photosynthetic temperature; ${\mathrm{T}}_{\mathrm{o}\mathrm{p}\mathrm{t}}$: optimum temperature; ${\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$: maximum photosynthetic temperature	${\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ = 0, ${\mathrm{T}}_{\mathrm{o}\mathrm{p}\mathrm{t}}$ = 20, ${\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ = 40
${\mathrm{f}}_{\mathrm{s}\mathrm{w}}\left(\mathrm{S}\mathrm{W}\mathrm{C}\right)$	$\left\{\begin{array}{c}1, \mathrm{S}\mathrm{W}\mathrm{C}\ge \mathrm{S}\mathrm{W}{\mathrm{C}}_{\mathrm{t}\mathrm{h}\mathrm{r}}\\ {\displaystyle \frac{\mathrm{S}\mathrm{W}\mathrm{C}}{\mathrm{S}\mathrm{W}{\mathrm{C}}_{\mathrm{t}\mathrm{h}\mathrm{r}}}},\mathrm{S}\mathrm{W}\mathrm{C}<\mathrm{S}\mathrm{W}{\mathrm{C}}_{\mathrm{t}\mathrm{h}\mathrm{r}}\end{array}\right.$	$\mathrm{S}\mathrm{W}{\mathrm{C}}_{\mathrm{t}\mathrm{h}\mathrm{r}}$: Critical water content for no water stress	$\mathrm{S}\mathrm{W}{\mathrm{C}}_{\mathrm{t}\mathrm{h}\mathrm{r}}$ = 0.18 cm3·cm−3
${\mathrm{f}}_{\mathrm{v}\mathrm{p}\mathrm{d}}\left(\mathrm{V}\mathrm{P}\mathrm{D}\right)$	${\displaystyle \frac{\mathrm{V}\mathrm{P}{\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-\mathrm{V}\mathrm{P}{\mathrm{D}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{\mathrm{V}\mathrm{P}{\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-\mathrm{V}\mathrm{P}{\mathrm{D}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}}$	$\mathrm{V}\mathrm{P}{\mathrm{D}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$: Threshold for no stomatal restriction; $\mathrm{V}\mathrm{P}{\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$: Threshold for complete stomatal closure	$\mathrm{V}\mathrm{P}{\mathrm{D}}_{\mathrm{m}\mathrm{i}\mathrm{n}}=0.5 \mathrm{k}\mathrm{P}\mathrm{a}$$\mathrm{V}\mathrm{P}{\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}=3.0 \mathrm{k}\mathrm{P}\mathrm{a}$
${\mathrm{f}}_{\mathrm{w}}(\mathrm{S}\mathrm{W}\mathrm{C},\mathrm{V}\mathrm{P}\mathrm{D})$	${\mathrm{f}}_{\mathrm{w}}={\mathrm{f}}_{\mathrm{s}\mathrm{w}}\times {\mathrm{f}}_{\mathrm{v}\mathrm{p}\mathrm{d}}$	The product of these two represents the combined effect of soil and meteorological water stress.	/

.

2.4. Statistical Testing

The model performance was evaluated using the coefficient of determination ($R^2$) and the root mean square error (RMSE), calculated as follows:

$${\mathrm{R}}^2={\displaystyle \frac{{\left[\sum _{\mathrm{i}=1}^{\mathrm{n}} \left({\mathrm{X}}_{\mathrm{o}\mathrm{b}\mathrm{s},\mathrm{i}}-\overline{\mathrm{X}}\right)\left({\mathrm{Y}}_{\mathrm{p}\mathrm{r}\mathrm{e},\mathrm{i}}-\overline{\mathrm{Y}}\right)\right]}^2}{\sum _{\mathrm{i}=1}^{\mathrm{n}} {\left({\mathrm{X}}_{\mathrm{o}\mathrm{b}\mathrm{s},\mathrm{i}}-\overline{\mathrm{X}}\right)}^2\sum _{\mathrm{i}=1}^{\mathrm{n}} {\left({\mathrm{Y}}_{\mathrm{p}\mathrm{r}\mathrm{e},\mathrm{i}}-\overline{\mathrm{Y}}\right)}^2}}$$

(6)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n {\left(Y_{\mathrm{p}\mathrm{r}\mathrm{e},i}-Y_{\mathrm{o}\mathrm{b}\mathrm{s},i}\right)}^2}$$

(7)

where ${\mathrm{X}}_{\mathrm{o}\mathrm{b}\mathrm{s},\mathrm{i}}$ and ${\mathrm{Y}}_{\mathrm{o}\mathrm{b}\mathrm{s},\mathrm{i}}$ denote the observed values of the i-th sample; and ${\mathrm{X}}_{\mathrm{o}\mathrm{b}\mathrm{s},\mathrm{i}}$ can be the observed input feature, while ${\mathrm{Y}}_{\mathrm{o}\mathrm{b}\mathrm{s},\mathrm{i}}$ is the corresponding observed target value. ${\mathrm{Y}}_{\mathrm{p}\mathrm{r}\mathrm{e},\mathrm{i}}$ represents the predicted value from the model for the i-th sample, based on the input ${\mathrm{X}}_{\mathrm{o}\mathrm{b}\mathrm{s},\mathrm{i}}$. $\overline{\mathrm{X}}$ and $\overline{\mathrm{Y}}$ are the mean values of all observed inputs and outputs, respectively, reflecting the central tendency of the data. n is the total number of samples used in the evaluation. Each model training–validation process was repeated 50 times, and the reported ${\mathrm{R}}^2$ and RMSE values represent the mean performance on the independent test sets across these 50 runs.

To further assess the statistical significance of performance differences among models, statistical tests were conducted at the 5% significance level (p < 0.05). Boxplots were used to visualize the distributions of ${\mathrm{R}}^2$ and RMSE under two conditions: “Remove SIF” and “Contain SIF.” Post hoc pairwise comparisons were applied to determine significant differences, and distinct letters (e.g., a, b, c, d) were assigned to the models accordingly, where identical letters indicate no significant difference, and different letters indicate significant differences at the 5% level.

3. Results

3.1. Correlation and Simulation Between SIF and GPP

The temporal variations in SIF and GPP during the winter wheat-growing seasons from 2020 to 2022 are shown in Figure 3. It can be observed that the overall trends of SIF and GPP are generally consistent. However, the peak values of SIF typically occur around mid-April and gradually decline after May, whereas the peak values of GPP usually appear in early to mid-May. Consequently, from May until the maturity of winter wheat each year, the daily average normalized GPP values exceed those of SIF by more than 0.2.

Correlation analysis reveals a strong association between SIF and GPP, with a Spearman’s rank correlation coefficient of 0.89. Given this strong correlation, SIF was individually used as a feature parameter to establish machine learning models for GPP prediction. The simulation accuracies of these models are summarized in

Table 3. Simulation accuracy of each model based on SIF single factor.

Model	R2	RMSE (μmol·m−2·s−1)
Ridge	0.57	1.37
SVR	0.59	1.32
GB	0.63	1.28
RF	0.65	1.26
LSM	0.72	1.22

.

Comparing the evaluation metrics across the five models indicates that machine learning models using only SIF as input perform suboptimally in simulating GPP, with an average R² of only 0.68. Among the models, Ridge exhibited the lowest simulation accuracy with an R² of only 0.57, while LSM achieved the highest accuracy, with an R² of 0.72. In summary, using SIF alone as the input feature in machine learning models is insufficient for accurate GPP estimation. Integrating SIF with meteorological, crop physiological, and soil hydrothermal variables is necessary to enhance the fitting accuracy of these models.

3.2. Simulation Scenario Setup

Based on the MIC method, the importance rankings of features used to predict GPP in the machine learning models are presented in Figure 4. In Figure 4a, the feature ranking excludes SIF, whereas Figure 4b includes SIF.

Figure 4a shows that both PAR and ${\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}$ exhibit high importance scores (>0.6), with PAR having the highest score (0.79). The importance scores of SWC and VPD are relatively low (both <0.2), indicating that PAR and ${\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}$ are key predictors of GPP.

In Figure 4b, where SIF is included in the feature set, ${\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}$ and PAR still maintain high importance scores (>0.35), while VPD’s importance remains low (<0.2). However, SIF emerges as the most important feature with an importance score of 0.59. In this feature set, SIF, ${\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}$, and PAR are identified as critical predictors for GPP.

Overall, the presence of SIF substantially alters the distribution of feature importance. When SIF is included, it serves as a major predictive factor, underscoring its pivotal role in GPP estimation. Conversely, when SIF is excluded, the relative importance of other features increases, likely reflecting the model’s compensation for the absence of SIF by leveraging the remaining predictors. This shift indirectly highlights the unique contribution and significance of SIF in the modeling framework.

3.3. Machine Learning Model Simulation Accuracy

Figure 5 illustrates the simulation accuracy of different models for winter wheat GPP under two scenarios: excluding SIF and including SIF. Overall, both R² and RMSE metrics demonstrate significant performance improvements across all models after incorporating SIF.

From the R² results (Figure 5a,b), when SIF is excluded, the Ridge regression model has the poorest performance (R² = 0.72), while the LSM has the best performance (R² = 0.87). The RF, SVR, and GB models achieve intermediate R² values ranging from 0.80 to 0.83. Upon including SIF, all models exhibit increased R² values, with the LSM showing the most substantial improvement, reaching an R² of 0.91. The RF and GB models achieve R² values of 0.89 and 0.90, respectively, while the SVR model improves to 0.86. These results indicate that incorporating SIF effectively enhances the models’ ability to explain variations in GPP, particularly pronounced in the ensemble learning model.

The RMSE results (Figure 5c,d) mirror the trend observed in R². Without SIF, the Ridge model exhibits the highest RMSE (1.15 μmol·m⁻²·s⁻¹), indicating larger prediction errors, whereas the LSM achieves the lowest RMSE (0.92 μmol·m⁻²·s⁻¹), outperforming the other individual models. After incorporating SIF, the RMSE values decrease markedly for all models; the LSM’s RMSE further drops to 0.85 μmol·m⁻²·s⁻¹, that of the GB model decreases to 0.87 μmol·m⁻²·s⁻¹, and that of the RF model falls below 0.89 μmol·m⁻²·s⁻¹. These findings underscore the significant role of SIF in reducing prediction errors and enhancing accuracy, with more pronounced effects observed in the ensemble and gradient boosting models.

Considering both R² and RMSE metrics, the LSM consistently outperforms other models in both scenarios and exhibits the highest sensitivity to SIF inclusion. The GB model ranks second, while the Ridge model shows relatively weaker suitability for GPP estimation. This demonstrates that the ensemble learning framework, by integrating the strengths of multiple machine learning algorithms, more effectively captures the complex nonlinear relationships among GPP, meteorological, and biophysical factors. The predictive performance notably improves with the integration of photosynthetic physiological information such as SIF.

To preliminarily examine the robustness of the proposed framework, we conducted a simple sensitivity test by randomly reducing the training dataset by 30%. The LSM incorporating SIF exhibited only a marginal decrease in accuracy (average R² decline < 0.02 and RMSE increase < 0.05 μmol·m⁻²·s⁻¹), while other ML models showed similar stability. This result suggests that the modeling framework is relatively resilient under data-limited conditions, further supporting its applicability in diverse field scenarios.

3.4. Comparison of Machine Learning Models and LUE Model Simulation Accuracy of GPP at Different Growth Stages

Table 4. Winter wheat GPP estimation results (R²) using various machine learning models and LUE models under the SIF removal scenario.

Growing Period	Ridge	RF	SVR	GB	LSM	LUE
Seedling stage	0.81	0.88	0.88	0.87	0.91	0.88
Overwintering stage	0.78	0.86	0.85	0.85	0.90	0.86
Jointing stage	0.76	0.84	0.83	0.83	0.87	0.84
Grain-filling stage	0.68	0.81	0.78	0.79	0.84	0.79
Maturity stage	0.71	0.83	0.81	0.81	0.86	0.82

and

Table 5. Estimation results of winter wheat GPP by various machine learning models and the LUE model under SIF scenario (R²).

Growing Period	Ridge	RF	SVR	GB	LSM	LUE
Seedling stage	0.86	0.92	0.88	0.90	0.95	0.88
Overwintering stage	0.85	0.90	0.88	0.88	0.93	0.86
Jointing stage	0.81	0.89	0.85	0.86	0.90	0.84
Grain-filling stage	0.79	0.83	0.82	0.82	0.87	0.79
Maturity stage	0.76	0.87	0.84	0.85	0.89	0.82

present the GPP estimation accuracies (R²) of various machine learning models across different growth stages of winter wheat under scenarios excluding and including SIF, respectively. Additionally, the independently estimated results from the LUE model are included for comparison to evaluate performance differences between the LUE model and machine learning models at different phenological stages. It should be noted that the LUE model’s calculation method differs from that of the machine learning models, and its results are independent of the SIF inclusion scenario; therefore, only one fixed set of values is reported as a reference in the tables.

Under the scenario excluding SIF (Table 4), the LSM consistently performs best across all growth stages, with R² values ranging from 0.84 to 0.91. The RF model ranks second with values between 0.81 and 0.88. The SVR and GB models exhibit slightly lower overall accuracy, while the Ridge model shows the lowest accuracy during the grain-filling stage (R² = 0.68). The LUE model’s accuracy in this scenario is comparable to that of the RF model, performing well during the seedling and overwintering stages (0.88 and 0.86, respectively), but declining during the grain-filling and maturity stages (0.79 and 0.82). Overall, all models demonstrate a decreasing trend in accuracy from the seedling stage to maturity when SIF is excluded.

After incorporating SIF (Table 5), the simulation accuracy of all machine learning models generally improved, with the LSM exhibiting the most substantial enhancement. Specifically, the R² during the seedling stage increased to 0.95, while the maturity stage still maintained a relatively high level of 0.89. The RF model improved from 0.88 to 0.92 at the seedling stage, and the GB model increased from 0.83 to 0.86 during the jointing stage, both demonstrating marked improvements. The SVR model showed relatively smaller gains in some stages but, overall, still outperformed the Ridge regression model. Compared to the machine learning models, the LUE model’s accuracy across growth stages remained unaffected by SIF inclusion, with consistent results between both scenarios (ranging from 0.79 to 0.88), indicating its stability. However, in most stages, the LUE model’s accuracy was lower than that of the LSM, RF, and GB models under the SIF-included scenario.

Overall, the comparison indicates that the LSM outperforms other models under both scenarios, with its advantage becoming more pronounced after including SIF. The RF and GB models significantly surpass the LUE model after SIF introduction. Although the LUE model approaches the RF model’s accuracy in certain stages, its overall performance is constrained by its structural limitations, resulting in limited room for accuracy improvement. These results demonstrate that incorporating SIF can effectively enhance the accuracy and stability of machine learning models in simulating GPP across different growth stages, whereas the LUE model excels in stability but generally underperforms relative to the best-performing machine learning models in terms of accuracy.

4. Discussion

4.1. Performance Differences Among Machine Learning Models and the Advantages of LSM

Significant differences exist in the performance of various machine learning models for simulating winter wheat GPP, reflecting the distinct algorithmic characteristics and suitability of each model when handling complex ecosystem data. Ridge regression mitigates multicollinearity issues through L2 regularization and is suitable for scenarios with highly correlated features [43]. However, its linear assumption limits its ability to capture the nonlinear relationships between GPP and environmental factors such as PAR, ${\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}$, SWC, and VPD during the wheat growth stages [44]. This limitation is particularly evident during critical phenological phases such as jointing and grain-filling, where GPP is influenced by complex interactions among multiple environmental variables exhibiting dynamic variability.

The RF constructs multiple decision trees combined with random feature selection, enabling an effective capture of nonlinear relationships and high-dimensional feature interactions, which is well suited for the complexity of agricultural ecosystems [45]. Nonetheless, the inherent randomness in RF may lead to insufficient capture of certain key feature interactions, especially under noisy data conditions, resulting in slightly reduced model stability [46]. The SVR employs a radial basis function kernel to map data into a high-dimensional space for nonlinear regression, making it appropriate for moderate-sized datasets [47]. However, as feature dimensionality increases or data distribution becomes more complex, tuning hyperparameters such as the penalty coefficient C and kernel parameter γ becomes challenging, potentially limiting performance. The GB iteratively optimizes the model by following the gradient of the loss function, progressively improving predictive accuracy and effectively adapting to the dynamic changes in winter wheat growth [48]. Nevertheless, its sensitivity to noisy data can cause overfitting, thereby impacting the model’s generalization capability.

In contrast, the LSM based on the stacking ensemble strategy demonstrates significant advantages [49]. LSM first uses the predictions from RF, SVR, and GB as base learners’ outputs, and then applies a linear layer to optimally weight and combine these outputs. This approach integrates the strengths of individual models while overcoming their respective limitations. Such an ensemble methodology not only captures the complex nonlinear interactions among PAR, ${\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}$, SWC, and VPD but also dynamically adapts to data characteristics through weight optimization in the linear layer, significantly enhancing model robustness and stability. During the winter wheat growth period, GPP is affected by multifaceted environmental interactions, such as the synergistic effects of light and water stress [50]. LSM effectively addresses the data’s dynamic and high-dimensional nature by fusing multiple model predictions, yielding superior simulation accuracy. Furthermore, LSM’s ensemble framework reduces the overfitting risk inherent in single models, maintaining stable predictions especially when feature sets are complex or sample distributions uneven.

Compared with Ridge’s linear limitations, RF’s stochastic fluctuations, SVR’s tuning complexity, and GB’s sensitivity to noise, LSM significantly improves the capability to capture the dynamic variability in winter wheat GPP through multi-level learning and optimization [51]. This advantage makes LSM particularly effective for handling complex agricultural ecosystem data and provides a reliable tool for high-precision GPP estimation, laying a solid foundation for future model enhancement by integrating novel remote sensing data such as SIF.

4.2. Improvement in Machine Learning Model Accuracy by Incorporating SIF

The incorporation of SIF significantly enhances the ability of machine learning models to simulate winter wheat GPP, owing to SIF’s direct reflection of photosynthetic physiological processes and its sensitivity to dynamic environmental changes [52]. As an indicator of Photosystem II photochemical efficiency, SIF captures the fluorescence signals emitted by chlorophyll molecules following light absorption and is closely related to the activity of the photosynthetic electron transport chain [53]. Compared to traditional remote sensing indices such as NDVI and EVI, which primarily reflect vegetation structure and greenness, SIF more directly characterizes photosynthetic activity, enabling precise tracking of photosynthetic dynamics throughout winter wheat growth stages such as the seedling and jointing periods [54]. This physiological mechanism renders SIF a powerful predictor for GPP, especially under conditions of ample light or environmental stress (e.g., water deficit), where it sensitively captures fluctuations in photosynthetic efficiency. The MIC analysis further reveals the importance of SIF within the feature set, demonstrating its explanatory power for GPP surpasses that of PAR and ${\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}$, indicating that SIF not only supplements traditional environmental factors but also provides unique physiological signals [55].

From the perspective of model performance, the introduction of SIF strengthens the machine learning models’ ability to capture the complex nonlinear relationships underlying winter wheat GPP. Throughout the growing season, GPP is influenced by multifactor interactions among PAR, ${\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}$, SWC, and VPD, exhibiting high nonlinearity and dynamic variability. Single environmental factors alone cannot fully represent the intricate changes in photosynthesis, whereas SIF directly reflects the photochemical efficiency of the photosynthetic system, compensating for biophysical information that environmental variables fail to capture [56]. Particularly during the seedling and jointing stages, when photosynthetic activity peaks, SIF signals accurately reflect the peak variations in leaf photosynthetic capacity, thereby improving model fitting in high-GPP regions [57]. During maturity, although leaf senescence and photosynthetic activity decline, reducing SIF intensity, it still provides critical physiological information that helps models capture the downward trend of GPP.

The LSM further amplifies the contribution of SIF by integrating the predictions from RF, SVR, and GB, dynamically adjusting the weights of SIF and other features through its linear layer, thereby optimizing the model’s adaptability to complex ecosystem data. Compared with scenarios excluding SIF, models incorporating SIF show increased sensitivity to the dynamic changes in GPP during growth stages, and notably enhanced predictive stability under environmental stresses such as drought or high temperature. This improvement indicates that SIF not only enhances the explanatory power of models but also provides a novel physiological dimension to data-driven GPP estimations, laying a foundation for precise photosynthetic monitoring and yield prediction in precision agriculture [58].

4.3. Comparison of GPP Estimation Accuracy Between LUE Model and Machine Learning Models

The differences in the performance of the LUE model and ML models in simulating winter wheat GPP stem fundamentally from their distinct theoretical bases, data-processing approaches, and adaptability to complex ecosystems. The LUE model is grounded in photosynthetic theory and estimates GPP based on PAR and light use efficiency (ε), supplemented by temperature and water stress modifiers to reflect environmental constraints [59]. As a semi-empirical method with clear physiological foundations, the LUE model offers high computational efficiency and low data input requirements, making it suitable for rapid large-scale GPP estimation [60]. It employs predefined stress functions—such as optimal temperature, minimum photosynthetic temperature, and critical soil water content—to simulate environmental limitations on photosynthesis, showing good stability, especially during growth stages with relatively stable photosynthetic activity, such as the seedling and overwintering periods. However, its linear assumptions and simplified stress factors limit its ability to fully capture the complex nonlinear interactions among multiple environmental variables (PAR, ${\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}}$, SWC, VPD) affecting GPP throughout the winter wheat growth period. This limitation is particularly evident during jointing and grain-filling stages, where photosynthesis is influenced by synergistic effects of light, water, and temperature, and the LUE model’s response to these dynamic changes is insufficient, leading to constrained simulation accuracy. Additionally, the LUE model depends on regional calibration of parameters like ${\mathrm{\epsilon }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$, and inaccuracies in parameterization may further reduce its applicability [61].

In contrast, ML models—especially the LSM—adopt a data-driven approach that automatically learns nonlinear relationships and interactions among features, significantly enhancing the adaptability of GPP estimations. The LSM integrates predictions from RF, SVR, and GB models and optimizes their combined output via a linear layer, overcoming limitations inherent in individual models and effectively capturing the dynamic variation in GPP during the winter wheat growth cycle [62]. The inclusion of SIF, which directly reflects Photosystem II photochemical efficiency, further augments ML models by providing physiological information not captured by environmental factors, improving responsiveness to photosynthetic peaks and environmental stresses [63]. Compared to the fixed-parameter framework of the LUE model, ML models adapt to the complex and dynamic environmental conditions of the winter wheat ecosystem through data-driven feature learning, showing superior performance, particularly in stages of high photosynthetic activity or intense environmental stress [64]. However, ML models require high-quality training data and involve greater computational costs and hyperparameter tuning complexity, which may limit their efficiency in rapid-application scenarios [65].

Overall, the LUE model is well suited for scenarios with limited data resources or when rapid estimation is needed, whereas ML models—especially the SIF-integrated LSM—offer significant advantages in high-accuracy and complex ecosystem simulations. This provides a more flexible toolset for precise monitoring of winter wheat GPP and precision agriculture management, laying a theoretical and practical foundation for the future integration of remote sensing and data-driven modeling approaches.

4.4. Research Limitations and Future Perspectives

Although this study significantly improved the simulation accuracy of winter wheat GPP by integrating SIF and machine learning models, several limitations remain that warrant further optimization to enhance the generalizability and practical applicability of the findings. Firstly, the experiment was conducted at a single site in the Guanzhong region of Northwest China (34°17′45″ N, 108°04′07″ E), characterized by specific climatic conditions (annual precipitation of ~560 mm, mean temperature of 12.9 °C) and silty loam soil (field water-holding capacity of 0.235 cm³·cm⁻³). These site-specific characteristics may constrain the applicability of the models to other ecological regions, such as humid subtropical zones or extremely arid deserts. For instance, multi-site studies have indicated that regional climatic differences can lead to variations of approximately 15–20% in the SIF–GPP correlation, associated with differences in water availability and temperature fluctuations [66]. In addition, the use of daily averaged SIF and GPP data neglects diurnal photosynthetic dynamics, particularly during critical growth stages such as jointing and grain-filling. Short-term variations in light intensity or water stress during these stages can markedly affect GPP, which daily averages fail to capture [67]. A preliminary check using the original half-hourly dataset indicated that model residuals tended to increase during midday periods with high VPD, suggesting that high-frequency applications may reveal additional physiological mechanisms and further improve model robustness. Furthermore, SIF observations are influenced by weather conditions (e.g., cloud cover) and the complexities of instrument calibration, potentially causing data gaps or noise that affect the stability of model inputs [68]. While machine learning models—especially the LSM—exhibited strong performance, their reliance on high-quality training data and the computational cost associated with hyperparameter tuning may constrain their application in data-limited contexts. Although the LUE model is computationally efficient, its dependence on regionally calibrated parameters (e.g., maximum light use efficiency ${\mathrm{\epsilon }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$) might reduce its robustness when applied to different crops or ecosystems [69]. A simple sensitivity test in this study showed that reducing the training dataset by 30% only caused a minor accuracy decline (average R² drop < 0.02), suggesting that the framework is relatively robust even under data-limited conditions. However, further validation across multiple crops and regions is required to assess the scalability of this approach.

In terms of future perspectives, several directions merit exploration. First, validating the generalizability of SIF–ML frameworks across different climatic zones (e.g., humid and arid regions) and crop types (e.g., maize and rice) is essential. Previous studies have reported comparable SIF–GPP relationships for maize and rice [70,71,72], supporting the potential cross-crop applicability of the proposed framework. Second, the integration of high-frequency SIF and flux data will enable analysis of diurnal dynamics and stress responses, offering a more refined physiological interpretation. Third, incorporating additional remote sensing indices such as EVI or PRI, as well as high-resolution UAV data, may enrich feature sets and enhance adaptability in complex ecosystems. Fourth, the development of low-cost SIF sensors or the use of satellite-based SIF products (e.g., GOME-2, TROPOMI) would facilitate regional-to-global GPP monitoring. Meanwhile, optimizing hyperparameter tuning algorithms for machine learning models and exploring automated tuning approaches, such as Bayesian optimization, could lower computational costs and improve model portability. Furthermore, investigating transfer learning (e.g., pre-trained models), advanced machine learning techniques (e.g., Transformer architectures), and updated regression models (e.g., Prophet) could enhance model generalization, particularly in data-scarce scenarios [73]. For the LUE model, integrating dynamic parameter calibration or coupling with SIF data may enhance its ability to capture nonlinear responses.

Overall, while this study demonstrates the feasibility of integrating tower-based SIF with ensemble ML models for accurate GPP estimation in winter wheat, the preliminary sensitivity and sub-daily analyses presented here highlight the potential for broader applications. With further efforts in multi-scale, multi-crop validation and data fusion, SIF-ML approaches are poised to advance carbon flux estimation in agroecosystems and provide valuable support for agricultural management under carbon neutrality goals.

5. Conclusions

This study was conducted in a winter wheat field in the Guanzhong region, where continuous, high-frequency measurements of GPP and SIF were obtained using an EC system and a ground-based tower SIF observation system. MIC was applied to quantitatively assess the relative contributions of SIF and meteorological variables to GPP, providing insights into the importance of different features. Based on these observations, multiple approaches—including machine learning models (Ridge, RF, SVR, GB, and LSM) and the LUE model—were employed to estimate and compare winter wheat GPP throughout the growing season. The results indicate significant differences in simulation accuracy among machine learning models when SIF was excluded, with the ensemble learning model LSM achieving the best performance (R² = 0.87), significantly outperforming individual models and demonstrating the advantage of model fusion in enhancing prediction stability and robustness. Upon incorporating SIF, the accuracy of all machine learning models improved, especially that of LSM, whose R² increased to 0.91, highlighting SIF’s effectiveness in reflecting the physiological state of photosynthesis and providing critical auxiliary information to improve GPP model accuracy. Compared to this, the LUE model exhibited an overall performance comparable to that of some machine learning models but showed relatively lower adaptability across different growth stages compared to LSM. This suggests that although the LUE model offers physical and physiological interpretability, machine learning models integrating multi-source features may achieve superior accuracy under complex environmental conditions. Overall, the findings provide a viable technical approach for high-precision GPP estimation of winter wheat and hold significant implications for crop photosynthesis monitoring and carbon cycle studies at regional scales. Future research should validate these methods across broader regions, diverse crop types, and varying climate conditions while optimizing temperature and moisture correction parameters in the LUE model and exploring the fusion of multi-source remote sensing data (e.g., SIF, NIRv, and satellite GPP products) to further enhance the universality and spatiotemporal scalability of GPP estimation.