## 3 Combined Numerical Forecast Model and Machine Learning
### Machine Learning Models
#### 3.4.1 ML Models  
In this study, we explore the CNN and MLP models for individually forecasting the meridional and zonal components of wind speed (U and V, respectively). Each ML model utilizes both U and V components of the atmospheric model as input and is evaluated on both high- and low-resolution WRF data. WRF data were extracted for the grid point closest to the labeling point at each resolution. For WRF1, at 35.583\({}^{\circ}\) E, 32.883\({}^{\circ}\) N, located 351 m east of Kfar Nahum, and for WRF9, at 35.610\({}^{\circ}\) E, 32.901\({}^{\circ}\) N, located 3570 m northeast of Kfar Nahum.  
The use of CNN for weather prediction and parameterization is similar to the method implied by [PERSON], [PERSON], and [PERSON] [71], which was used to predict rainfall in different locations. Our CNN model architecture, illustrated in Figure 4a, consists of multiple convolution layers originally designed to process image data effectively. The first CNN model layer consists of a 2D convolutional layer structure with 64 output channels, each employing a 3 \(\times\) 3 convolutional kernel, followed by a rectified linear unit (ReLU) activation function. A max pooling with a 2 \(\times\) 2 pool size and stride of 2 \(\times\) 2 was also applied. The second layer consists of a 2D convolutional layer structure with 128 channels, employing a  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **WRF9** & **WRF1** \\ \hline Model shape (x, y, z) & 89 \(\times\) 89 \(\times\) 45 & 78 \(\times\) 51 \(\times\) 45 \\ Area (km\({}^{2}\)) & 69,696 & 3850 \\ Output intervals & 3 h & 30 min \\ Number of samples & 1340 & 7600 \\ \hline \hline \end{tabular}
\end{table}
Table 1: WRF domains used by the ML models.  
\(3\times 3\) convolutional kernel, a ReLU activation function. A max pooling with a \(2\times 2\) pool size and stride of \(2\times 2\) was subsequently applied. Finally, the output feature maps are flattened to a 1D vector, producing 61,952 output shapes for WRF9 and 29,184 for WRF1 input data. The last layer is a fully connected layer that employs a SoftMax activation function that sorts the categorial classification into five classes. Figure 4b illustrates the MLP architecture employed in this study, comprising several dense, fully connected layers for effective feature extraction and classification. Each layer consists of multiple perceptrons, which are the fundamental building blocks of the network. A perceptron operates on multiple input features, each appropriately weighted; it aggregates these inputs and applies an activation function to generate an output. During the learning process, the perceptron undergoes weight adjustments to minimize the disparity between its output and the desired target output, facilitating the acquisition of patterns and the ability to make predictions. The first layer in the MLP model is a fully connected dense layer, with the number of perceptrons set to the size of the input shape's dimension (Table 1) and a sigmoid activation function. The second and third dense layers comprise 32 and 10 perceptrons, respectively, and use sigmoid activation. Similar to the CNN, the last layer consists of five fully connected SoftMax activation functions used to classify the model output into five categories. To regularize the model and avoid overfitting, L2 regularization with a penalty of 0.00001 is applied in every dense layer [72].