# Machine Learning Methods in Weather and Climate Applications: A Survey
## 6 Medium-to-Long-Term Climate Prediction
### Result Analysis  
**CGF:** In the utilization of deep probabilistic machine learning techniques, the figure compares the performance of the CGF model using both simulated samples and actual data against the traditional climate model, Cancm4. The findings illustrate that our model outperforms the conventional climate modeling approach in terms of accuracy, irrespective of the employment of simulated or real data sets. This distinction emphasizes the enhanced predictive capability of our method and underlines its potential superiority in handling complex meteorological phenomena. **CycleGANs:** In the context of long-term climate estimation, the application of deep learning for model correction has yielded promising results. As illustrated in the accompanying figure, the diagram delineates the mean absolute errors of different models relative to the W5E5v2 baseline facts. Among these, the error correction technique utilizing Generative Adversarial Networks (GANs) in conjunction with the ISIMIP3 BASD physical model has demonstrated the lowest discrepancy. This evidence underscores the efficacy of sophisticated deep-learning methodologies in enhancing the precision of long-termclimate estimations, thereby reinforcing their potential utility in climatological research and forecasting applications. **DeepESD:** In the conducted study, deep learning has been employed to enhance resolution, resulting in a model referred to as DeepESD. The following figure portrays the Probability Density Functions (PDFs) of precipitation and temperature for the historical period from 1979 to 2005, as expressed by the General Circulation Model (GCM) in red, the Regional Climate Model (RCM) in blue, and DeepESD in green. These are contextualized across regions such as the Alps, the Iberian Peninsula, and Eastern Europe as defined by the PRUDENCE area. In the diagram, solid lines represent the overall mean, while the shaded region includes two standard deviations. Dashed lines depict the distribution mean of each PDF. A clear observation from the graph illustrates that DeepESD maintains higher consistency with observed data in comparison to the other models. **NNCAM:**NNCAM has demonstrated proficient simulation of strong precipitation centers across maritime continental tropical regions, Asian monsoon areas, South America, and the Caribbean. The model maintains the spatial pattern and global average of precipitation over the subsequent 5 years in its simulation, showcasing its long-term stability. Overall, in terms of the spatial distribution of multi-annual summer precipitation, NNCAM results are closer to the standard values compared with those from CAM5, with smaller root mean square errors and global average deviations. Additionally, NNCAM operates at a speed that is 30 times faster than traditional models, marking a significant stride in enhancing computational efficiency. In Table 4, MAE is a metric commonly used to measure the magnitude of forecast errors. It calculates the average of the absolute errors between the actual and predicted values. This metric was selected because it provides a clear, intuitive way to understand the accuracy of model predictions. A low MAE value indicates better prediction accuracy, while a high MAE value indicates a larger prediction error. The Euclidean Distance to Observations in the Probability Density Function (PDF) is utilized to evaluate the performance of the model by comparing the distance difference in the PDFs between the predicted and actual observed data. This metric was selected because it provides a means of quantifying how well a model's predicted distribution aligns with the actual observed distribution, enabling the evaluation of model performance in complex systems, particularly when dealing with systems that possess inherent uncertainty and variability. While these four methods address different problems and, thus, a direct comparison is not feasible in this study, it is evident that they all exhibit significant improvements compared with traditional earth system models.