# Machine Learning Methods in Weather and Climate Applications: A Survey
## 2 Background
In contrast, climate models are scrutinized using different methodologies. Given their long-term nature, climate models are often validated using historical and paleoclimatic data. Statistical techniques like Empirical Orthogonal Functions (EOF) and Principal Component Analysis (PCA) are employed to identify and validate overarching climatic patterns. These models often have to account for high levels of uncertainty and are cross-validated against geological or even astronomical records, making immediate validation impractical. For weather forecasts, predictive accuracy within the scope of hours to days is paramount. Climate models, conversely, are evaluated based on their ability to accurately reproduce decadal and centennial patterns. **Bias correction. ** In the context of meteorology, climate science, machine learning, and statistical modeling, bias correction (or bias adjustment) refers to a set of techniques used to correct systematic errors (biases) in model simulations or predictions. These biases may arise due to various factors such as model limitations, uncertainties in parameterization, or discrepancies between model assumptions and real-world data. Bias Correction (Bias Adjustment) can be formally defined as the process of modifying the output of predictive models to align more closely with observed data. The primary objective is to minimize the difference between the model's estimates and the observed values, thereby improving the model's accuracy and reliability. In more formal terms, let \(M\) represent the model output and \(O\) represent the observed data. Bias \(B\) is defined as:  
\[B=M-O \tag{1}\]  
The aim of bias-correction is to find a function \(f\) such that:  
\[f(M)\approx O \tag{2}\]  
Various methods can be employed for bias-correction, including simple linear adjustments, quantile mapping, and more complex machine-learning techniques. The choice of method often depends on the specific characteristics of the data and the overarching objectives of the study. **Embulation. ** The term emulation is utilized here to denote the approach where machine learning models are employed to simulate or approximate components and processes of the original physical model. In meteorology, physical models are devised based on a comprehensive understanding of atmospheric dynamics, often entailing intricate hydrodynamic equations to elucidate atmospheric motions and interactions. However, to attain high computational efficiency in practical operations, direct resolution of these equations is frequently computationally demanding, particularly when high spatial and temporal resolution simulations are requisite. To alleviate these issues, modelers are already using fast and accurate ML simulations to simulate existing time-consuming parameterizations [26; 27; 28]. Machine learning methods are capable of delivering fast and precise approximations of complex physical processes by learning patterns and relationships from historical data or high-precision model runs. For instance, neural networks or other machine learning algorithms can be deployed to deal with Longwave and shortwave radiation parameterization [29; 30] and emulate nonlinear wave interactions in wind wave models [31]. Consequently, machine learning models can substitute traditional physical parameterization schemes in prediction models, significantly alleviating the computational burden while preserving or even augmenting the accuracy of predictions. **Down-scaling. ** Down-scaling in meteorology and climate science is a computational technique employed to bridge the gap between the spatial and temporal resolutions offered by General Circulation Models (GCMs) or Regional Climate Models (RCMs) and the scale at which specific applications, such as local weather predictions or hydrological assessments, operate. Given that GCMs and RCMs typically operate at a coarse resolution--spanning tens or hundreds of kilometers--Down-scaling aims to refine these projections to a more localized level, potentially down to single kilometers or less. **Extreme events.