# A Multimodal Data-Driven Framework for Enhanced Wheat Carbon Flux Monitoring
## 3 Results  
### 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\(\cdot\)m\({}^{-2}\cdot\)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  
Figure 3: Accuracy of winter wheat carbon flux estimated by the MCFEW model ((**a**) green-up stage, (**b**) jointing stage, (**c**) Heading–filling stage, and (**d**) milk maturity stage). from 0 to 70 gC\(\cdot\)m\({}^{-2}\cdot\)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\(\cdot\)m\({}^{-2}\cdot\)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\(\cdot\)m\({}^{-2}\cdot\)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\(\cdot\)m\({}^{-2}\cdot\)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\(\cdot\)m\({}^{-2}\cdot\)8d\({}^{-1}\). In most areas, GPP cumulative values exceed 100 gC\(\cdot\)m\({}^{-2}\cdot\)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\(\cdot\)m\({}^{-2}\cdot\)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\(\cdot\)m\({}^{-2}\cdot\)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.