A Multimodal Data-Driven Framework for Enhanced Wheat Carbon Flux Monitoring

Abstract

Wheat is a critical economic and food crop in global agricultural production, with changes in wheat cultivation directly impacting the stability of the global food market. Therefore, developing a method capable of accurately estimating carbon flux in wheat is of significant importance for early warning agricultural production risks and guiding farming practices. This study constructs a multimodal model framework to estimate wheat carbon flux using MODIS data products, including the Leaf Area Index (LAI), the Normalized Difference Vegetation Index (NDVI), the Enhanced Vegetation Index (EVI), and meteorological data products. The results demonstrate that the constructed carbon flux detection model effectively estimates carbon flux across different growth stages of wheat. Evaluation of the model, using comprehensive accuracy metrics, shows an average adjusted R² of 0.88, an RMSE of 5.31 gC·m⁻²·8d⁻¹, and nRMSE of 0.05 across four growth stages, indicating high accuracy with minimal error. Notably, the model performs more accurately at the green-up stage compared to other stages. Interpretability analysis further reveals key features influencing model estimations, with the top five ranked features being (1) LAI, (2) NDVI, (3) EVI, (4) vapor pressure (Vap), and (5) the Palmer Drought Severity Index (PDSI). Remote sensing indices exhibit a greater influence on carbon flux estimation throughout the whole growth stages compared to meteorological indices. Under water-limiting conditions, the importance of evapotranspiration, precipitation, and drought-related factors fluctuates significantly. This study not only provides an important reference for monitoring wheat carbon flux, but also offers novel insights into the crop carbon cycling mechanisms within agroecosystems under the current environmental context.

1. Introduction

Wheat is one of the world’s major food crops, and timely and accurate acquisition of wheat carbon flux information is crucial for the rational planning of cultivation practices and the early warning of yield fluctuations. Remote sensing data have been increasingly applied to large-scale wheat growth monitoring [1,2,3]. Time-series crop growth parameters derived from remote sensing data reflect the growth status of wheat across different phenological stages and can be utilized for regional crop carbon flux estimation.

Gross Primary Productivity (GPP), net primary productivity (NPP), and Net Ecosystem Exchange (NEE) are all essential metrics for estimating vegetation carbon fluxes and assessing ecosystem carbon dynamics. Each of these indicators provides valuable insights into different components of the carbon cycle within ecosystems, and thus, they are frequently applied in ecological and environmental monitoring studies. Specifically, GPP quantifies the total carbon fixation by plants through photosynthesis, NPP represents the carbon remaining in plant biomass after autotrophic respiration, and NEE characterizes the net carbon exchange between the ecosystem and atmosphere, including both plant and soil microbial respiration. Prentice et al. [4] assessed the relationship between ecosystem net primary productivity (NPP) and climatic factors in Togo through regression analyses based on the MODIS NPP product (500 m resolution) combined with CHIRPS (Climate Hazards Group InfraRed Precipitation with Station) precipitation data and ECMWF (European Centre for Medium-Range Weather Forecasts) ERA5 (fifth-generation ECMWF atmospheric reanalysis of the global climate) temperature data, and found that precipitation has a dominant effect on carbon sink capacity, whereas a warmer climate may shorten the growing season and reduce carbon fixation capacity. Compared to NPP and NEE, GPP has a distinct advantage in remote sensing applications as it aligns closely with vegetation indices derived directly from satellite observations, accurately reflecting photosynthetic activity without requiring complex additional measurements (such as respiration rates). High GPP values indicate greater carbon absorption and fixation, stronger photosynthetic capacity, and enhanced carbon storage potential within ecosystems. Therefore, measuring and modeling GPP is a vital approach to evaluating crop carbon flux dynamics [5]. For instance, Biudes et al. [6] offer significant empirical support for the application of remotely sensed vegetation indices in assessing regional vegetation productivity. The findings indicate that satellite-derived vegetation indices, such as NDVI (Normalized Difference Vegetation Index), EVI (Enhanced Vegetation Index), and LSWI (Land Surface Water Index), are strongly correlated with GPP. These indices reflect seasonal variations in vegetation growth and provide valuable insights into how climate factors, including soil moisture and precipitation, influence GPP. Since then, multi-source remote sensing datasets have been incorporated into carbon flux monitoring to improve the accuracy of carbon flux estimation. Blaise et al. [7] combined MODIS GPP products (8-day interval) with Sentinel-2 SIF (Solar-Induced Chlorophyll Fluorescence) data to optimize carbon flux estimation using an optical–thermal infrared fusion model and Support Vector Regression (SVR), and found that rain-fed cotton was more carbon-efficient than irrigated cotton (15% increase in photosynthetic efficiency), with the correlation coefficient between SIF and GPP reaching 0.89.

In the early stages of research, scholars employed basic linear statistical models to predict agricultural crop carbon flux. Qiu et al. [8] developed the SIF-CO₂-GPP model, which integrates SIF and atmospheric CO₂ to estimate GPP, outperforming the nonlinear SIF-GPP model, especially by reducing seasonal over- and underestimation. Dechant et al. [9] employed hyperspectral data and PLSR (Partial Least Squares Regression) to estimate GPP, showing that multivariate methods like PLSR offer more accurate predictions than traditional reflectance-based and vegetation index approaches. This highlights the progression from basic linear models to more sophisticated statistical methods in GPP estimation. However, early simple linear models for carbon flux estimation had performance limitations. In contrast, research increasingly focuses on crop growth models, which simulate soil, climate, and biological interactions based on ecological mechanisms. By integrating remote sensing data, these models enable large-scale carbon flux estimation and capture the ecological processes affecting crop growth and carbon dynamics [10]. Pique et al. [11] developed the SAFY-CO₂ model, using high-resolution optical data to simulate winter wheat biomass, yield, and carbon budget, with excellent performance across sites in southwestern France. Zhuo et al. [12] introduced the crop data-model assimilation (CDMA) framework, improving regional-scale GPP and yield estimates for winter wheat by assimilating satellite-derived GPP into the WOFOST (World Food Studies) model (post-assimilation R² = 0.87). Although ecological process models, such as crop growth models, provide more accurate results than linear models, challenges like parameter acquisition, model calibration, input uncertainties, climate sensitivity, and heterogeneous validation data still lead to inaccuracies. Recently, the Eddy Covariance (EC) technique has become standard for measuring carbon fluxes, particularly for optimizing terrestrial vegetation GPP models. Wagle et al. [13] employed the EC technique to monitor farmland carbon balance, comparing the magnitude and temporal dynamics of winter wheat carbon flux using EVI and NDVI. Huang et al. [14] investigated the integration of NDVI data into the Eddy Covariance–Light Use Efficiency (EC-LUE) model to enhance carbon flux estimates. Their study demonstrated that incorporating high-resolution NDVI significantly improved model performance, particularly in heterogeneous landscapes such as savannas and croplands. In contrast to crop growth models, the EC technique relies on small-scale, site-specific observations, which makes it difficult to extrapolate results to larger regions. Therefore, a novel model is needed to overcome the limitations of both approaches and provide more scalable, accurate carbon flux predictions.

With advancements in computational power, the emergence of big data analytics has facilitated the development of increasingly complex algorithms. In particular, research on farmland carbon flux estimation based on machine learning or deep learning methods has progressively become a major research focus [15,16,17]. Wang et al. [18] estimated the carbon fluxes of moso bamboo forests based on the Bayesian improved BP neural network method (B-BPNN) using measured data from the flux tower and data on latent heat fluxes, incident radiation, soil temperatures, wind speed, and other climatic factors. The results showed that the correlation between the carbon flux estimation results and the measured values reached 0.93 (higher than that of the traditional BPNN), and the RMSE (root mean-square error) was lower, which proved that the B-BPNN could effectively reduce the estimation uncertainty and significantly improve the carbon flux prediction accuracy. Convolutional neural networks have been widely applied in carbon flux estimation due to their unique advantages in image feature extraction. Yuan et al. [19] applied machine learning algorithms, including convolutional neural networks (CNNs), Artificial Neural Networks (ANNs), Random Forests (RFs), and eXtreme Gradient Boosting (XGBoost), to estimate GPP. The CNN model outperformed the others, achieving an average R² of 0.93, significantly improving GPP estimation. However, when applying long-term sequence remote sensing images for monitoring crop growth, CNN-based models have certain limitations in learning image features. Recurrent neural networks (RNNs), on the other hand, have a greater advantage in learning the nonlinear features of sequential data [20]. Therefore, the combination of CNN and RNN in a network architecture can better extract features from long-term sequence remote sensing images, thereby improving crop growth estimation accuracy. Ahmad et al. [21] applied a convolutional long short-term memory (ConvLSTM) model, combining convolutional neural networks and recurrent neural networks, to forecast crop growth through NDVI estimation. Wang et al. [22] developed a novel CNN and gated recurrent unit combined (CNN-GRU) model to estimate crop growth using remotely sensed data, including Vegetation Temperature Condition Index (VTCI), Leaf Area Index (LAI), and Fraction of Photosynthetically Active Radiation (FPAR). The model effectively captured the time-series cumulative effects of crop growth, demonstrating its potential for accurate crop growth estimation.

Despite this, the explanatory potential of such models is limited due to their “black-box” nature [23]. This leads to the presence of uncertainties in the application of deep learning models, which may stem from factors such as the internal structure of the model, data selection during the training process, and parameter initialization [24]. As a result, the interpretability analysis of deep learning models has become an important research direction for improving model reliability and promoting their application. Shapley additive explanation (SHAP) values are a popular method for explaining machine learning model predictions [25]. Yang et al. [26] explored how SHAP values were used to quantify feature importance across various deep learning-based model modules, improving both the accuracy and transparency of the predictions. By applying SHAP at both the model and cell levels, they provided clear insights into the contribution of each feature, leading to better feature selection and a more interpretable model. Mariadass et al. [27] conducted an annual crop yield forecasting based on the XGBoost model and SHAP methodology, and evaluated the model to identify key features. The results showed that the model has an R² value of 0.98, which is better than the existing models. Li [28] employed the SHAP value to interpret XGBoost models, effectively extracting spatial effects and enhancing the understanding of complex geographical phenomena. Isik et al. [29] constructed a cotton yield prediction model based on the LSTM network using soil characteristic data, climate variable data, and EVI time-series data, and interpreted the model a posteriori using the SHAP interpretability analysis method. The results show that the method can effectively resolve the influence mechanism of each earth observation feature on cotton yield and reveal the quantitative relationship between different environmental factors and yield fluctuations.

Agricultural production is influenced by a complex interplay of climatic, soil, and anthropogenic factors. Within large agricultural areas, the physicochemical properties of the soil and meteorological conditions exhibit significant spatial variability. This heterogeneity leads to considerable variations in soil nutrients and crop growth, even within the same field [30], thereby reducing the accuracy of carbon flux estimations when extrapolated to larger scales. Previous research on carbon flux monitoring in agricultural settings has faced challenges related to scale, often failing to address the unique characteristics of agricultural ecosystems with complex terrain. Furthermore, many existing studies that estimate carbon flux using satellite remote sensing technologies tend to rely on single data products or overlook other critical factors affecting crop growth. In the domain of remote sensing, spatial heterogeneity and nonlinear relationships between variables present additional difficulties, as scaling issues often necessitate adjustments despite apparent similarities across scales. To overcome these limitations, this study integrates MODIS data with TerraClimate meteorological data to extract key multimodal features—encompassing both remote sensing and meteorological variables—that influence wheat crop growth. Building on the cumulative GPP data from MODIS, this study focuses on wheat carbon flux estimation, with an emphasis on the carbon cycling mechanisms within farmland ecosystems. A multimodal carbon flux estimation model for wheat is developed by combining CNN with GRU. Additionally, feature importance analysis is conducted, providing valuable insights into the contributions of various factors. This research offers a novel approach to applying deep learning algorithms in crop carbon flux estimation, thereby advancing the accuracy and applicability of carbon flux monitoring in agricultural systems.

2. Materials and Methods

2.1. Study Area

The study area is located in the Guanzhong Plain in northwestern China, covering a total area of approximately 36,000 km². It is one of China’s major grain-producing regions (Figure 1). The region is characterized by typical loess soils with moderate fertility, providing favorable conditions for agricultural production. It experiences a temperate continental monsoon climate, with an average annual precipitation ranging from approximately 500 to 700 mm, primarily concentrated between July and September, and an average annual temperature between 12 °C and 14 °C. The dominant cropping system includes winter wheat followed by summer maize, making it one of China’s major grain-producing regions. The region plays a significant role in regional carbon cycling and is suitable for evaluating and validating carbon flux estimation models. Winter wheat is sown in early October each year and harvested in early June of the following year. During its growth cycle, winter wheat undergoes several key stages, including tillering, overwintering, green-up (early to mid-March), jointing (late March to mid-April), heading–filling (late April to early May), and milk maturity (mid- to late May).

2.2. Remote Sensing Data

This study utilizes remote sensing data from the Guanzhong Plain’s wheat-growing regions during four growth stages in 2023. The data include the MODIS GPP product MOD17A2H, LAI product MCD15A3H, reflectance product MCD43A4, and the land cover product MCD12Q1, both of which are directly accessible via the Google Earth Engine (GEE) platform. The MODIS MOD17A2H product provides GPP data at an 8-day temporal resolution and a spatial resolution of 500 m. It estimates the amount of carbon fixed through photosynthesis by vegetation, based on remotely sensed vegetation indices combined with meteorological data. The MODIS MCD15A3H product provides LAI and FPAR at a spatial resolution of 500 m and a temporal resolution of 4 days. Derived from reflectance data using radiative transfer modeling, it delivers essential biophysical parameters that quantify vegetation canopy structure and function. The MODIS MCD43A4 product provides daily surface reflectance data at a spatial resolution of 500 m. It utilizes Bidirectional Reflectance Distribution Function (BRDF) modeling to correct reflectance data for viewing and solar angle effects, significantly enhancing the consistency and reliability of surface reflectance measurements over time. In this study, four remote sensing indices were acquired across the four main growth stages (green-up, jointing, heading–filling, and milk maturity stages) (

Table 1. Remote sensing indices.

Parameter	Abbreviation	Source	Unit
Remote Sensing Index	NDVI, EVI	MCD43A4
	LAI	MCD15A3H	m2·m−2
	GPP	MOD17A2H	gC·m−2·8d−1

). It is important to note that 8-day synthetic NDVI and EVI were calculated from MODIS MCD43A4 data products. LAI, NDVI, and EVI were selected for wheat carbon flux estimation because they comprehensively reflect the physiological characteristics of the crop in terms of key aspects such as canopy structure, growth status, etc. LAI quantifies the canopy structure of the vegetation and photosynthesis capacity, and is closely related to biomass accumulation; NDVI provides comprehensive information on the health of the vegetation and the growth status. By incorporating the blue band to correct for atmospheric scattering, and including coefficients that minimize soil background noise, EVI maintains sensitivity in high-biomass regions where NDVI typically saturates, thus providing more reliable estimates of canopy structure and function in dense vegetation areas. EVI serves as a valuable supplement to NDVI, offering improved accuracy in vegetation monitoring, especially under conditions of high canopy density or variable atmospheric influences.

In this study, the MCD12Q1 product was used to extract the land cover type layer for the study area. By applying a cropland mask from the relevant band, remote sensing and climate data were extracted. The product contains 13 bands, and the LC_Type1 band, which corresponds to the International Geosphere-Biosphere Programme (IGBP) classification, was used. Specifically, land cover type 12 (croplands) was selected to mask agricultural areas, enabling the acquisition of remote sensing and climate data specific to farmland in the Guanzhong Plain.

2.3. Meteorological and Soil Data

This study employs common model inputs from the TerraClimate dataset as a source of meteorological and soil information for regional wheat carbon flux estimation. The TerraClimate dataset provides monthly terrestrial meteorological and climatic water balance data globally, including key climate variables such as maximum temperature (Tmax), minimum temperature (Tmin), precipitation (Pr), vapor pressure (Vap), and vapor pressure deficit (Vpd). Additionally, it includes derived variables such as potential evapotranspiration (Pet), soil moisture (SM), and Palmer Drought Severity Index (PDSI). For key climatic variables like temperature, vapor pressure, and precipitation, the TerraClimate dataset offers supplemental information, including monthly surface soil moisture data. These data are calculated using a water balance model that integrates precipitation, evapotranspiration, and interpolated soil water holding capacity.

Meteorological data from TerraClimate were spatially interpolated to match the finer resolution of the MODIS remote sensing indices (500 m) using the Kriging interpolation method. Kriging is a geostatistical interpolation technique that leverages the spatial correlation among data points, estimating values at unsampled locations based on surrounding measurements and their spatial covariance structure. Specifically, we first computed empirical semivariograms for each meteorological variable (e.g., temperature, precipitation, vapor pressure) to characterize spatial dependencies and determine optimal variogram parameters. Subsequently, these parameters guided the ordinary Kriging interpolation, producing continuous meteorological surfaces at 500 m resolution. This method effectively captures local variations while ensuring consistency with observed regional climate patterns, thereby minimizing interpolation errors and enhancing compatibility between meteorological and remote sensing datasets.

2.4. Multimodal Carbon Flux Estimation Model

This study proposes a multimodal carbon flux estimation model for wheat, the MCFEW model, which integrates data from various sources, such as remote sensing and meteorological measurements, to provide a more accurate assessment of carbon flux in agricultural ecosystems. By combining different data types with advanced deep learning algorithms, the model improves both estimation accuracy and interpretability. The proposed architecture combines CNNs and GRUs, as shown in Figure 2. The CNNs are used to extract spatial features, capturing patterns and structures from remote sensing data. The GRU component models temporal dependencies, effectively capturing both short- and long-term trends (Equation (1)). This combined design allows the MCFEW model to integrate spatial and temporal information, leading to more accurate carbon flux predictions and a better understanding of how fluxes evolve over time.

$$GPP\left(t\right)=f(W_{\mathrm{C}\mathrm{N}\mathrm{N}}\cdot X_{\mathrm{M}\mathrm{O}\mathrm{D}\mathrm{I}\mathrm{S}}+W_{\mathrm{G}\mathrm{R}\mathrm{U}} \cdot X_{\mathrm{M}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{o}}+b)$$

(1)

where $W_{\mathrm{C}\mathrm{N}\mathrm{N}}$ and $W_{\mathrm{G}\mathrm{R}\mathrm{U}}$ are the network weights, and $X_{\mathrm{M}\mathrm{O}\mathrm{D}\mathrm{I}\mathrm{S}}$ and $X_{\mathrm{M}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{o}}$ are the input data.

For the CNN component, different types of convolutions are used to meet the specific needs of shallow and deep layers. At the shallow layer, a standard convolution (Conv2D) is applied to retain fine details in high-resolution images and fully integrate multi-spectral data. This ensures the network captures essential spatial patterns. At deeper layers, a separable convolution (SeparableConv2D) is used to reduce computational complexity by decomposing the convolution into depthwise and pointwise parts [31]. Compared to standard Conv2D, SeparableConv2D offers significant advantages in computational efficiency and parameter reduction. Specifically, SeparableConv2D decomposes the convolution process into two distinct operations: a depthwise convolution, which applies a single spatial filter independently for each input channel, followed by a pointwise convolution (a 1×1 convolution) that linearly combines these channels. This separation substantially reduces the number of parameters and the computational complexity. Consequently, SeparableConv2D significantly lowers memory usage and enhances computational speed, making it particularly suitable for deeper network architectures and scenarios involving large-scale remote sensing datasets, without compromising model accuracy.

While separable convolutions may not fully capture multispectral channel relationships, a channel attention module is introduced after the separable convolution to improve feature selection. The Convolutional Block Attention Module (CBAM) proposed by Woo et al. [32] consists of two sequential submodules: channel attention and spatial attention. The channel attention module first aggregates spatial information through average and max pooling, then weighs the pooled features using a shared multilayer perceptron (MLP). To establish channel-wise significance, these weighted features are concatenated along the channel axis and activated via a sigmoid function. In the spatial attention module, average pooling and max pooling are applied to the input features, and the resulting outputs are concatenated and processed through a 3 × 3 convolutional layer, followed by sigmoid activation to generate spatial attention maps. This spatial attention mechanism complements the information from the channel attention module. The sequential arrangement of both modules enables mutual reinforcement of feature refinement at both the channel and spatial levels.

Following feature refinement, the maps are then passed to a GRU layer. GRUs are well-suited for sequential data due to their simple structure, rapid convergence, and effectiveness in modeling short- and long-term dependencies, making them ideal for smaller datasets or real-time applications [22]. Through its gating mechanism, the GRU captures both short-term and long-term dependencies in carbon flux dynamics, enabling accurate simulations of crop carbon flux parameters (GPP estimates) across different growth stages. The single-timestep features extracted by the CNN-attention framework are processed through the GRU to estimate stage-specific carbon flux values. Given the input data with varying temporal resolutions, the GRU extracts temporal features separately for meteorological data and remote sensing indices based on distinct growth stages of winter wheat. Specifically, for each defined growth stage, the GRU independently models meteorological data and remote sensing indices (such as NDVI, EVI, and LAI, typically with 4-day to 8-day intervals). This strategy allows the GRU to effectively capture short-term variability in meteorological conditions and more gradual, stage-specific vegetation dynamics reflected by remote sensing indices, resulting in robust and meaningful feature representations aligned closely with the physiological patterns of wheat growth. As a result, the MCFEW model leverages both spatial features (extracted by CNNs) and temporal dependencies (captured by the GRU), utilizing complementary information from multimodal data sources to significantly improve the accuracy and interpretability of carbon flux estimations.

To clearly assess the model’s generalization capability and avoid overfitting, the dataset was split into independent training and testing subsets according to an 8:2 ratio, ensuring no overlap between the subsets. Specifically, 80% of the samples were randomly selected for training the model, and the remaining 20% were reserved exclusively for independent validation. This split accounted explicitly for both spatial and temporal variability, meaning that the validation set contains distinct spatial locations and time periods not used during training. The Mean Squared Error (MSE) loss function was chosen for training the model because it strongly penalizes larger prediction errors, making it highly sensitive to significant deviations between predicted and observed values. This property is particularly beneficial for carbon flux modeling, where large errors could severely impact the reliability of ecological assessments and management decisions. Additionally, MSE is smooth and differentiable, which makes it suitable for efficient optimization via gradient-based methods commonly used in deep learning models. Mathematically, the MSE is defined as

$$\mathrm{M}\mathrm{S}\mathrm{E}={\displaystyle \frac{1}{m}}{\sum }_{i=1}^m{(y_i-\widehat{y_i})}^2$$

(2)

where $y_i$ represents the observed value, $\widehat{y_i}$ is the predicted value by the model, and m denotes the total number of observations.

2.5. Model Interpretability

To quantify the contribution of individual input features to model predictions, we implemented SHAP [26], a game-theoretic framework widely adopted for interpreting machine learning model behavior. SHAP assigns feature importance scores by calculating each feature’s marginal contribution to output predictions through exhaustive coalitional analysis across all possible feature combinations. Our analysis systematically evaluated each data modality (remote sensing indices, meteorological parameters) to establish their relative importance in wheat carbon flux prediction. The SHAP framework was specifically adapted to the MCFEW model to disentangle the respective impacts of spatial versus temporal features on GPP estimation. For individual input features, SHAP values were calculated using KernelExplainer (adapted for deep neural architectures) [33], representing the differential between model predictions with and without each feature’s inclusion. Through sample-wise aggregation of SHAP values, we identified dominant predictive features across the dataset.

3. Results

3.1. Estimation of Winter Wheat Carbon Flux at Different Growth Stages

Multimodal predictions of wheat carbon flux for the Guanzhong Plain in 2023 were conducted for each of the four growth stages: green-up, jointing, heading–filling, and milk maturity. A comparison between the predicted and observed carbon flux values for these stages is presented in Figure 3. To assess the model’s performance in each growth stage, we examined the slope and intercept of the fitted curve. The fitted line visually represents the relationship between predicted and actual carbon flux values.

For the green-up stage, the slope of the fitted line is 0.93, close to 1, indicating a strong linear relationship between the model’s predictions and the observed values. The intercept is 1.79 gC·m⁻²·8d⁻¹, which—given the scale of the GPP cumulative values—can be regarded as nearly zero. This suggests minimal deviation between predicted and observed data. Most points cluster around the fitted line, demonstrating high accuracy, and the scatter plot shows a balanced distribution of points above and below the line, indicating stable predictions with no obvious bias. Cumulative carbon flux values range from 0 to 70 gC·m⁻²·8d⁻¹, reflecting the early growth phase of wheat when overall flux levels remain low.

For the jointing stage, the slope of the fitted line increases to 0.97, indicating a closer match between predictions and observations than in the green-up stage. The intercept is 2.89 gC·m⁻²·8d⁻¹, still near zero, signifying minimal deviation. Again, most data points lie close to the fitted line, indicating high prediction accuracy. The scatter plot reveals a slightly wider spread of points compared with the green-up stage, yet no significant outliers are apparent. Cumulative carbon flux values lie between 30 and 170 gC·m⁻²·8d⁻¹, corresponding to the vigorous growth phase of wheat. The model performs better here than in the green-up stage, suggesting its capability to provide accurate and stable predictions during active growth.

For the Heading–filling stage, the slope of the fitted line is 0.92, signifying a strong linear relationship between the model’s predictions and actual values. The intercept is 8.77 gC·m⁻²·8d⁻¹, with the majority of points tightly grouped around the fitted line, reflecting high prediction accuracy. The scatter plot likewise shows points that are evenly distributed, indicating reliable predictive performance. During the heading–filling stage, cumulative wheat carbon flux increases markedly, ranging from 50 to 170 gC·m⁻²·8d⁻¹. In most areas, GPP cumulative values exceed 100 gC·m⁻²·8d⁻¹, indicating active carbon assimilation and storage in this critical phase of wheat development.

For the milk maturity stage, the slope of the fitted line is 0.81, suggesting a weaker linear relationship than in earlier stages. The intercept is 17.76 gC·m⁻²·8d⁻¹, and most data points remain relatively close to the fitted line, implying that the model’s accuracy remains reasonably high. However, the data points are more scattered compared with previous stages, reflecting slightly reduced predictive stability. At this stage, cumulative carbon flux begins to slow, with values ranging from 30 to 150 gC·m⁻²·8d⁻¹. This decline arises from reduced biomass accumulation and a lower rate of carbon assimilation as wheat nears maturity, contributing to a decrease in overall carbon flux.

To further assess the model’s performance across the four growth stages, additional evaluation metrics were computed, as presented in

Table 2. Model accuracy evaluation for each phenological period in 2023.

Period	Adjusted R2	MAE (gC·m−2·8d−1)	RMSE (gC·m−2·8d−1)	nRMSE
Green-up stage	0.89	2.15	2.87	0.05
Jointing stage	0.94	4.57	5.90	0.04
Heading–filing stage	0.90	4.21	5.55	0.05
Milk maturity stage	0.79	5.33	6.90	0.06
Average value	0.88	4.07	5.31	0.05

. The adjusted R² values for the model’s predictions across all growth stages in 2023 ranged from 0.79 to 0.94, with an average of 0.88, indicating strong overall predictive performance. Notably, the R² values for the first three growth stages exceeded 0.89. The Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) values provide insight into the model’s prediction errors during different growth stages. The MAE values ranged from 2.15 to 5.33 gC·m⁻²·8d⁻¹, with an average of 4.07 gC·m⁻²·8d⁻¹, while the corresponding RMSE values ranged from 2.87 to 6.9 gC·m⁻²·8d⁻¹, with an average of 5.31 gC·m⁻²·8d⁻¹, reflecting the squared errors between predicted and actual values. The Normalized Root Mean Square Error (nRMSE), which expresses the error as a proportion of the actual values, offers a useful measure of the RMSE’s relative size. For all growth stages, the nRMSE values were approximately 0.05, indicating consistent predictive performance throughout 2023, with values close to zero suggesting minimal RMSE errors and robust accuracy. Specifically, the jointing stage exhibited the highest adjusted R² value and the lowest nRMSE value, signifying the best fit and smallest prediction errors. Based on the overall performance across these metrics, it can be concluded that the model demonstrates strong predictive capability, with high interpretability of the results and minimal errors. It shows a solid ability to accurately predict the carbon flux of winter wheat in the Guanzhong Plain.

3.2. Spatial Distribution of Winter Wheat Carbon Flux

A predictive model for wheat carbon flux in the Guanzhong Plain was developed and monitored based on multimodal data. Remote sensing data from 2023, including NDVI, EVI, and LAI, alongside meteorological and soil data provided by TerraClimate, were utilized. Data extraction, integration, and model training were performed using the GEE platform. Figure 4 presents the carbon flux estimation distribution across the four growth stages of 2023, offering an overview of the carbon flux dynamics in the region and revealing significant spatial heterogeneity.

In the green-up stage, carbon flux values ranged from below 50 gC·m⁻²·8d⁻¹ to 50 gC·m⁻²·8d⁻¹, with substantial variations in the carbon fixation capacity among crops within the region. The relatively flat topography of the Guanzhong Plain makes climatic factors—such as precipitation, temperature, and solar radiation—the primary determinants of the spatial distribution of carbon flux. In particular, areas with better drainage conditions promote crop growth, enhancing carbon fixation. During the green-up stage, wheat vegetation is in the early stages of development, resulting in relatively low carbon flux values. However, the rapid growth of vegetation during this period leads to significant carbon assimilation activity, although the overall flux remains low. The spatial distribution of carbon flux within the region is uneven, reflecting variations in planting density, crop health, and local environmental conditions.

From the jointing stage onward, a marked shift occurs in the spatial distribution of carbon flux. Areas with higher flux values—represented by yellow and red zones—expand significantly, while the extent of lower flux areas (blue zones) decreases. By the heading–filling stage, nearly all agricultural regions in the central-southern and western parts of the Guanzhong Plain are predominantly red, indicating high carbon flux. More than half of these areas exceed 150 gC·m⁻²·8d⁻¹, corresponding to the period when wheat reaches its peak biomass. This growth phase is characterized by high carbon assimilation, as the crops actively fix carbon to support rapid growth.

As wheat transitions into the milk maturity stage, a noticeable decline in overall carbon flux levels occurs. This decline is likely due to the gradual reduction in photosynthetic efficiency as the crops mature and growth slows. However, certain regions continue to exhibit relatively high carbon flux values, ranging from 100 gC·m⁻²·8d⁻¹ to 150 gC·m⁻²·8d⁻¹, reflecting the continued carbon fixation potential in areas with high crop biomass. This sustained carbon flux can be attributed to the high biomass of mature wheat, which helps to maintain significant carbon assimilation during the later growth stages, despite the decline in photosynthetic efficiency. The reduction in carbon flux at the milk maturity stage reflects the slowing down of biomass accumulation, a key feature of wheat as it nears harvest and its growth rate diminishes.

3.3. Importance of Winter Wheat Carbon Flux Estimation Feature

The estimation of wheat carbon flux across different growth stages using the MCFEW model was coupled with an analysis of the model’s post hoc interpretability. The feature importance was determined by calculating the SHAP values for each feature channel, as shown in Figure 5. The interpretability analysis revealed vegetation indices—particularly LAI, NDVI, and EVI—as primary contributors to model predictions, with climatic variables demonstrating a secondary influence on carbon flux estimation accuracy. The feature importance ranking for each stage is shown in

Table 3. Predictive model feature importance ranking in 2023.

Period	Top 5 Features
Green-up stage	(1) LAI (2) EVI (3) NDVI (4) Vap (5) Pr
Jointing stage	(1) LAI (2) EVI (3) NDVI (4) Vap (5) PDSI
Heading–filling stage	(1) LAI (2) NDVI (2) EVI (4) Pet (5) PDSI
Milk maturity stage	(1) LAI (2) NDVI (3) EVI (4) PDSI (5) SM

. For four growth stages, the top five ranked features are (1) LAI, (2) NDVI, (3) EVI, (4) vapor pressure (Vap), and (5) the Palmer Drought Severity Index (PDSI). This highlights that satellite remote sensing variables, such as LAI, NDVI, and EVI, alongside meteorological variables, including PDSI and Vap, are the most influential in predicting wheat carbon flux across all growth stages.

LAI represents the ratio of plant leaf area to ground area, which is crucial in assessing the density of vegetation. A higher LAI typically reflects greater photosynthetic capacity, directly influencing carbon flux. In Figure 5, LAI consistently shows the highest SHAP values across all growth stages, underscoring its critical role in determining wheat’s carbon assimilation. EVI, by reducing the impact of soil background and atmospheric conditions, provides a clearer and more accurate reflection of vegetation growth. This is particularly relevant for crops like wheat, which are sensitive to soil moisture and environmental conditions. The SHAP values for EVI are substantial, particularly in the heading–filling and jointing stages, indicating its importance in reflecting seasonal changes in vegetation health and biomass. NDVI, a widely used vegetation index, is a measure of vegetation coverage and health. As seen in Figure 5, NDVI shows substantial importance during the early to mid-growth stages, with the highest SHAP values observed during the green-up-to-jointing stage, when wheat biomass and chlorophyll content are at their peak. However, NDVI values tend to decrease in the later stages, particularly during the milk maturity stage, reflecting reduced photosynthetic activity and leaf senescence.

Among the meteorological parameters, PDSI integrates soil moisture and climate conditions, and it significantly influences wheat growth. PDSI is particularly important during periods of water stress, and its SHAP values are consistent across all growth stages, indicating its persistent role in predicting carbon flux. Similarly, Vap is a key indicator of atmospheric humidity, directly influencing plant transpiration and photosynthesis. Vap is especially important during the jointing and heading–filling stages, as indicated by its elevated SHAP values, suggesting that atmospheric humidity plays a critical role in determining the carbon flux during periods of rapid growth.

In addition to these key features, the comparison of feature importance across different growth stages reveals that the importance of the Pr feature varies significantly. At the green-up stage, Pr’s importance exceeds that of Pet and PDSI, highlighting the crop’s higher dependence on precipitation early in the growth cycle. However, at the milk maturity stage, the importance of Pr almost drops to zero, indicating that wheat’s reliance on precipitation decreases as it matures. This variation in Pr’s importance is likely related to the changing dependence of wheat on precipitation at different growth phases, as well as its interaction with other environmental factors such as soil moisture and temperature.

4. Discussion

This study successfully estimated wheat carbon flux across four key growth stages—green-up, jointing, heading–filling, and milk maturity stages in the Guanzhong Plain using the MCFEW model. The model demonstrated strong overall performance across all growth stages, with particularly high accuracy observed during the jointing stage. This aligns with the results from Franquesa et al. [34], who found that the prediction accuracy of crop carbon flux models is typically highest during periods of active growth. In contrast, the milk maturity stage exhibited slightly reduced accuracy, likely due to the physiological changes in the wheat crop as it nears harvest, resulting in a reduced rate of carbon assimilation and biomass accumulation, which is consistent with the findings of Guo et al. [35], who observed decreased flux stability in late-stage crops. The spatial distribution maps further reinforced this, showing that while carbon flux values remain high in some areas during the milk maturity stage, they generally decrease in regions where biomass accumulation has slowed.

The feature importance analysis revealed that LAI, NDVI, and EVI were the most influential features across all growth stages, with LAI consistently showing the highest SHAP values, highlighting its critical role in photosynthetic capacity and carbon assimilation, as emphasized by Yue et al. [36], due to its correlation with canopy structure and light interception. EVI, less influenced by SM and atmospheric interference than NDVI, was particularly important during the jointing and heading–filling stages, reflecting its ability to capture seasonal biomass changes and variations in GPP, in line with Moreira et al. [37], who found EVI to be a more reliable measure of vegetation productivity in areas with high soil variability. NDVI showed significant fluctuations, peaking during the green-up and jointing stages when crop biomass and chlorophyll content were maximal, and declining in the milk maturity stage, reflecting leaf aging and reduced photosynthetic activity, thus leading to lower carbon flux. Among meteorological variables, PDSI was consistently significant across all stages, particularly during water stress periods, as it integrates soil moisture and climate conditions. Vap, representing atmospheric humidity, was also highly relevant during the jointing and heading–filling stages, underscoring the importance of atmospheric conditions in regulating transpiration and photosynthesis. Notably, Pr was more significant than Pet and PDSI during the green-up stage, reflecting wheat’s greater dependence on precipitation early in growth, while in the milk maturity stage, Pr became less influential, indicating that wheat’s reliance on precipitation decreases with maturation, consistent with findings by Menefee et al. [5].

Although this study successfully predicted wheat carbon flux in the Guanzhong Plain, several issues still need to be addressed. First, there may be inconsistencies in the quality of the data used. The resolution of the multimodal data employed for GPP prediction varies across datasets. Even with the application of aggregation and averaging methods to standardize the data, inconsistencies remain, meaning not all features are equally prominent across all agricultural areas. This inconsistency can reduce the accuracy of the machine learning model and introduce potential errors in the prediction results [38]. Furthermore, while multimodal data provide valuable insights, they still lack comprehensiveness. Human activities, such as irrigation and fertilization, are critical for wheat growth, but due to data limitations, these factors could not be fully incorporated into the model [39]. Future research could explore the inclusion of alternative data sources or develop relationships between available datasets to better represent these human-driven factors. By integrating these variables into the multimodal framework, more accurate and reliable prediction models could be developed.

Deep learning is often regarded as a complex “black box,” where the training methods and adjustments to internal parameters introduce uncertainties in the model’s outcomes [40]. While the use of explainability analysis tools, such as SHAP, has provided insight into the contribution of individual features, this study mainly focused on their global importance without examining their temporal dynamics in greater detail. In this study, predictive models integrate both spatial and temporal scales, increasing the complexity of the dataset and the diversity of the features involved [41]. While this integration enhances the potential for achieving high prediction accuracy, it also makes the model more challenging to interpret. Therefore, future studies should explore the temporal aspects of feature importance, focusing on how time-dependent factors influence crop carbon flux across different years and growth cycles. This would help improve model performance over varying time scales and lead to a better understanding of the temporal mechanisms driving carbon flux.

5. Conclusions

This study utilized remote sensing data from various growth stages of wheat in the Guanzhong Plain, alongside meteorological and soil data from TerraClimate, to predict wheat carbon flux at different growth stages using the multimodal deep learning framework, the MCFEW model. The results of the wheat carbon flux estimates demonstrate that the model effectively simulates and forecasts wheat carbon flux in the region, achieving an average adjusted R² value of 0.88, which indicates strong explanatory power and predictive accuracy. The RMSE of 5.31 gC·m⁻²·8d⁻¹ and nRMSE of 0.05 further suggest that the model performs with low error, showing minimal fluctuations across the growth stages. Among the features, LAI, NDVI, and EVI were identified as the most influential for carbon flux estimation, underscoring the significant role of remote sensing indices. Among meteorological variables, Vap emerged as the most important feature, followed by Pet, PDSI, and Pr. These climatic factors are closely associated with drought conditions and crop water content, while temperature and soil conditions had a lesser impact on the carbon flux estimates. The spatial distribution maps of the estimation results revealed areas with generally good wheat growth, highlighting regions where local land quality and climate conditions are conducive to wheat cultivation. This study offers an effective methodology for monitoring and estimating wheat carbon flux, contributing valuable data and insights for future research and applications, while demonstrating the potential of the model for carbon flux prediction.