# Machine Learning Methods in Weather and Climate Applications: A Survey
## 5 Short-Term Weather Forecast
### Model Design
In a multi-mesh graph representation, nodes may represent specific regions of the Earth's surface, while edges may represent spatial relationships between these regions. In this way, models can capture spatial dependencies on a global scale and are able to utilize the power of GNNs to analyze and predict weather changes. * Decoder: It then maps the multi-mesh representation back to the latitude-longitude grid as a prediction for the next time step. The workflow of GraphCast begins with the input of weather state(s) defined on a high-resolution latitude-longitude-pressure-levels grid. The encoder processes these inputs into a multi-scale internal mesh representation, which then undergoes many rounds of message-passing in the processor to capture spatio-temporal relationships in the weather  
Figure 3: (**a**) The multi-layer transformer architecture; (**b**) two-step fine-tuning; (**c**) backbone model; (**d**) forecast model in free-running autoregressive inference mode. data. Finally, the decoder translates the multi-mesh representation back to the latitude-longitude grid to generate predictions for subsequent time steps. It is worth noting that, as shown in the next part, due to the multi-scale mesh mapping property, the model is able to capture both localized weather features on a high-resolution mesh and large-scale weather features on a low-resolution mesh at the same time. In essence, GraphCast encapsulates a pioneering stride in enhancing weather forecasting accuracy and efficiency through the amalgamation of machine learning and complex dynamical system modeling. It uniquely employs an autoregressive model structure underpinned by graph neural networks and a multi-scale mesh representation. The model's \"encode-process-decode\" configuration, executed through a novel multi-mesh graphical representation, adeptly captures spatial dependencies and facilitates global-scale weather prediction. By processing high-resolution weather data inputs through a systematic workflow of encoding, message-passing, and decoding, GraphCast not only generates precise weather predictions for subsequent time intervals but also exemplifies the profound potential of machine learning in advancing meteorological forecasting methodologies. **PanGu. ** In the rapidly evolving field of meteorological forecasting, PanGu emerges as a pioneering model shown in Figure 5, predicated on a three-dimensional neural network that transcends traditional boundaries of latitude and longitude. Recognizing the intrinsic relationship between meteorological data and atmospheric pressure, PanGu incorporates a neural network structure that accounts for altitude in addition to latitude and longitude. The initiation of the PanGu model's process involves Block Embedding, where the dataset is parsed into smaller subsets, or blocks. This operation not only mitigates spatial resolution and complexity but also facilitates subsequent data management within the network. Following block embedding, the PanGu model integrates the data blocks into a 3D cube through a process known as 3D Cube Fusion, thereby enabling data processing within a tri-dimensional space. Swin Encoding [86], a specialized transformer encoder utilized in the deep learning spectrum, applies a self-attention mechanism for data comprehension and processing. This encoder, akin to the Autoencoder, excels at extracting and encoding essential information from the dataset. The ensuing phases include Decoding, which strives to unearth salient information, and Output Splitting, which partitions data into atmospheric and surface variables. Finally, Resolution Restoration reinstates the data to its original spatial resolution, making it amenable for further scrutiny and interpretation. Figure 4: **(a)** The encoder component of the GraphCast architecture maps the input local regions (green boxes) to the nodes of the multigrid graph. **(b)** The processor component uses learned message passing to update each multigrid node.