# Machine Learning Methods in Weather and Climate Applications: A Survey
## 5 Short-Term Weather Forecast
### Model Design
This dataset is the outcome of a Bayesian estimation process known as data assimilation, fusing observational results with numerical models' output [83]. FourCastNet leverages the Adaptive Fourier Neural Operator (AFNO), uniquely crafted for high-resolution inputs, incorporating several significant strides within the domain of deep learning. The essence of AFNO resides in its symbiotic fusion of the Fourier Neural Operator (FNO) learning strategy with the self-attention mechanism intrinsic to Vision Transformers (ViT) [84]. While FNO, through Fourier transforms, adeply processes periodic data and has proven efficacy in modeling complex systems of partial differential equations, the computational complexity for high-resolution inputs is prohibitive. Consequently, AFNO deploys the Fast Fourier Transform (FFT) in the Fourier domain, facilitating continuous global convolution. This innovation reduces the complexity of spatial mixing to \(O(N\log N)\), thus rendering it suitable for high-resolution data [85]. The workflow of AFNO shown in Figure 3 encompasses data preprocessing, feature extraction with FNO, feature processing with ViT, spatial mixing for feature fusion, culminating in prediction output, representing future meteorological conditions such as temperature, pressure, and humidity. Tailoring AFNO for weather prediction, FourCastNet introduces specific adaptations. Given its distinct application scenario--predicting atmospheric variables utilizing the ERA5 dataset--a dedicated precipitation model is integrated into FourCastNet, predicting six-hour accumulated total precipitation [83]. Moreover, the training paradigm of FourCastNet includes both pre-training and fine-tuning stages. The former learns the mapping from the weather state at one time point to the next, while the latter forecasts two consecutive time steps. The advantages of FourCastNet are manifested in its unparalleled speed--approximately 45,000 times swifter than conventional NWP models--and remarkable energy efficiency--consuming about 12,000 times less energy compared with  
Figure 2: MetNet Structure. the IFS model [84]. The model's architectural innovations and its efficient utilization of computational resources position it at the forefront of high-resolution weather modeling. **GraphCast. ** GraphCast represents a notable advance in weather forecasting, melding machine learning with complex dynamical system modeling to pave the way for more accurate and efficient predictions. It leverages machine learning to model complex dynamical systems and showcases the potential of machine learning in this domain. It's an autoregressive model, built upon graph neural networks (GNNs) and a novel multi-scale mesh representation, trained on historical weather data from the European Centre for Medium-Range Weather Forecasts (ECMWF)'s ERA5 reanalysis archive. The structure of GraphCast shown in Figure 4 employs an \"encode-process-decode\" configuration utilizing GNNs to autoregressively generate forecast trajectories. In detail:  
* Encoder: The encoder component maps the local region of the input data (on the original latitude-longitude grid) onto the nodes of the multigrid graphical representation. It maps two consecutive input frames of the latitude-longitude input grid, with numerous variables per grid point, into a multi-scale internal mesh representation. This mapping process helps the model better capture and understand spatial dependencies in the data, allowing for more accurate predictions of future weather conditions. * Processor: This part performs several rounds of message-passing on the multi-mesh, where the edges can span short or long ranges, facilitating efficient communication without necessitating an explicit hierarchy. More specifically, the section uses a multi-mesh graph representation. It refers to a special graph structure that is able to represent the spatial structure of the Earth's surface in an efficient way.