# A Multimodal Data-Driven Framework for Enhanced Wheat Carbon Flux Monitoring
## 2 Materials and Methods
### 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 \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Abbreviation** & **Source** & **Unit** \\ \hline \multirow{2}{*}{Remote Sensing Index} & NDVI, EVI & MCD43A4 & \\  & LAI & MCD15A3H & m\({}^{2}\)-m\({}^{-2}\) \\  & GPP & MOD17A2H & gC\(\cdot\)m\({}^{-2}\)-sd\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Remote sensing indices. 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. \[GPP(t)=f(W_{\text{CNN}}\cdot\ X_{\text{MODIS}}+W_{\text{GRU}}\ \cdot\ X_{\text{Meteo}}+b) \tag{1}\]  
where \(W_{\text{CNN}}\) and \(W_{\text{GRU}}\) are the network weights, and \(X_{\text{MODIS}}\) and \(X_{\text{Meteo}}\) 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\(\times\)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 [PERSON] 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  
Figure 2: MCFEW model framework (wheat carbon flux estimation model for multimodal and multi-temporal data). (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 \(\times\) 3 convolutional layer, followed by sigmoid activation to generate spatial attention maps. This spatial attention mechanism complements the information from the channel attention module.