# Machine Learning Methods in Weather and Climate Applications: A Survey
## 6 Medium-to-Long-Term Climate Prediction
### Model Design
A key component of this approach is the cycle consistency loss, which ensures a reliable translation between domains coupled with a constraint to maintain global precipitation values for physical consistency. By framing bias correction as an image-to-image translation task, CycleGANs have significantly improved spatial patterns and distributions in climate projections. The model's utilization of spatial spectral densities and fractal dimension measurements further emphasizes its spatial context awareness, making it a groundbreaking technique in the field of climate science. The CycleGAN model consists of two generators and two discriminators, along with a cycle consistency loss:  
* _Two Generators_: The CycleGAN model includes two generators. Generator \(G\) learns the mapping from the simulated domain to the real domain, and generator \(F\) learns the mapping from the real domain to the simulated domain [100]. * _Two Discriminators_: There are two discriminators, one for the real domain and one for the simulated domain. Discriminator \(D_{x}\) encourages generator \(G\) to generate samples that look similar to samples in the real domain, and discriminator \(D_{y}\) encourages generator \(F\) to generate samples that look similar to samples in the simulated domain. * _Cycle Consistency Loss_: To ensure that the mappings are consistent, the model enforces the following condition through a cycle consistency loss: if a sample is mapped from the simulated domain to the real domain and then mapped back to the simulated domain, it should get a sample similar to the original simulated sample. Similarly, if a sample is mapped from the real domain to the simulated domain and then mapped back to the real domain, it should get a sample similar to the original real sample. \[\mathcal{L}_{\text{cyc}}(G,F)=\mathbb{E}_{x\sim p_{\text{data}}(x)}[||F(G(x))- x||_{1}]+\mathbb{E}_{y\sim p_{\text{data}}(y)}[||G(F(y))-y||_{1}]\] (10)* _Training Process:_ The model is trained to learn the mapping between these two domains by minimizing the adversarial loss and cycle consistency loss between the generators and discriminators. \[\mathcal{L}_{\text{Gen}}(G,F)=\mathcal{L}_{\text{GAN}}(G,D_{y},X,Y)+\mathcal{L}_ {\text{GAN}}(F,D_{x},Y,X)+\lambda\mathcal{L}_{\text{cyc}}(G,F)\] (11)
* _Application to Prediction_: Once trained, these mappings can be used for various tasks, such as transforming simulated precipitation data into forecasts that resemble observed data. The bidirectional mapping strategy of Cycle-Consistent Generative Adversarial Networks (CycleGANs) permits the exploration and learning of complex transformation relationships between two domains without reliance on paired training samples. This attribute holds profound significance, especially in scenarios where only unlabeled data are available for training. In its specific application within climate science, this characteristic of CycleGAN enables precise capturing and modeling of the subtle relationships between real and simulated precipitation data. Through this unique bidirectional mapping shown in Figure 7, the model not only enhances the understanding of climatic phenomena but also improves the predictive accuracy of future precipitation trends. This provides a novel, data-driven methodology for climate prediction and analysis, contributing to the ever-expanding field of computational climate science. **DeepESD. ** Traditional GCMs, while proficient in simulating large-scale global climatic dynamics [101; 102], exhibit intrinsic limitations in representing finer spatial scales and specific regional characteristics. This inadequacy manifests as a pronounced resolution gap at localized scales, restricting the applicability of GCMs in detailed regional climate studies [103; 104]. In stark contrast, the utilization of CNNs symbolizes a significant breakthrough [105].