## 2 Materials and Methods
### The Structures of Deep Learning Models  
In this research, two deep learning architectures, VGG11 and AlexNet, were chosen for the analysis. The VGG11 model is distinguished by its configuration of 5 convolutional layers and 3 fully connected layers. This network is a uniform structure, employing convolutional kernels with a size of 3 \(\times\) 3 and pooling layers with a size of 2 \(\times\) 2, following each group of convolutions. The design principle of utilizing small convolutional kernels in conjunction with multiple convolutional layers is intended to increase the depth of the neural network. Conversely, the foundational architecture of the AlexNet model consists of 3 convolutional groups and 3 fully connected layers, each accompanied by a pooling layer with a size of 3 \(\times\) 3 with a stride of 2. The structural designs of both models are depicted in Figure 3. In addition to the core components, which encompass convolutional layers, pooling layers, fully connected layers, and activation functions, this study integrated several supplementary elements aimed at enhancing model performance. Specifically, in order to reduce the possibility of overfitting, facilitate the parameter tuning process, and expedite training and convergence, a dropout layer was incorporated following the fully connected layer. Moreover, to mitigate challenges associated with gradient explosion or vanishing gradients, a batch normalization layer was added after each convolutional layer and fully connected layer.  
Figure 2: Schematic of a 2D matrix of 4 channels, including SST, longitude, latitude, and time.  
These two models are both convolutional neural network models, and the specific formulas for the convolution operation are delineated as follows:  
\[Y_{conv}=f\Big{(}\sum_{j=0}^{J-1}\sum_{i=0}^{J-1}X_{m+i,n+j}\;W_{ij}+b\Big{)} \tag{4}\]  
where \(X\) denotes a matrix with dimensions \(M\times\) N, where the variable \(m\) is restricted to the interval (\(0,M-1\)), and the variable \(n\) is confined to the interval (\(0,N-1\)). The constants \(I\) and \(J\) represent the dimensions of the convolution kernel \(W\). Furthermore, \(f(\cdot)\) indicates the activation function, and b denotes the additional bias or offset. The precise formula of the Maxpooling function employed by the model is shown as follows when the size of the pooling window is \(2\times 2\):  
\[f_{pool}=Max\Big{(}x_{m,n},x_{m+1,n},x_{m,n+1},x_{m+1,n+1}\Big{)} \tag{5}\]  
where the variable \(f_{pool}\) represents the outcome obtained following the application of maximum pooling.  
Additionally, the Rectified Linear Unit (ReLU) is employed as the activation function, which serves to decrease the computational load and reduce the phenomenon of gradient vanishing and overfitting. The ReLU function can also speed up the operation of convolutional neural networks. Its expression is presented as follows:  
\[f(x)=max(0,x) \tag{6}\]  
where \(x\) is the input of a neuron.  
The Softmax function is mainly used to convert the output of neurons (usually a vector of real numbers) into a probability distribution for multi-class classification problems, facilitating the understanding and comparison of classification results. In this study, the output of the fully connected layer is a two-dimensional vector of predicted results for high- and low-catch fishing areas. It is computed as 2 probability values by the function Softmax.  
\[\mathrm{P}(y_{j}|x)=\frac{e^{f(y_{j})}}{\sum_{k=1}^{n}e^{f(y_{k})}} \tag{7}\]  
where \(n\) is set to 2 as the number of classes. \(P\big{(}y_{j}|x\big{)}\) is the normalized probability of correctly classifying the label \(y_{j}\) given the 4-channel input factor \(x\).  
Figure 3: The network architecture diagram of the AlexNet model (**a**) and VGG\(11\) model (**b**).