# Machine Learning Methods in Weather and Climate Applications: A Survey
## 5 Short-Term Weather Forecast
### Model Design  
**Numerical Weather Model** Numerical Weather Prediction (NWP) stands as a cornerstone methodology in the realm of meteorological forecasting, fundamentally rooted in the simulation of atmospheric dynamics through intricate physical models. At the core of NWP lies a set of governing physical equations that encapsulate the holistic behavior of the atmosphere:  
* The Navier-Stokes Equations [73]: Serving as the quintessential descriptors of fluid motion, these equations delineate the fundamental mechanics underlying atmospheric flow. \[\
abla\cdot\mathbf{v}=0\] (3) \[\rho\left(\frac{\partial\mathbf{v}}{\partial t}+\mathbf{v}\cdot\
abla \mathbf{v}\right)=-\
abla p+\mu\
abla^{2}\mathbf{v}+\rho\mathbf{g}\] (4)
* The Thermodynamic Equations [74]: These equations intricately interrelate the temperature, pressure, and humidity within the atmospheric matrix, offering insights into the state and transitions of atmospheric energy. \[\frac{\partial\rho}{\partial t}+\
abla\cdot\left(\rho\mathbf{v}\right)=0 \text{ (Continuity equation)}\] (5) \[\frac{\partial T}{\partial t}+\mathbf{v}\cdot\
abla T=\frac{q}{c_{p}}\text{ (Energy equation)}\] (6) \[\frac{Dp}{Dt}=-\rho c_{p}\
abla\cdot\mathbf{v}\text{ (Pressure equation)}\] (7)  
The model is fundamentally based on a set of time-dependent partial differential equations, which require sophisticated numerical techniques for solving. The resolution of these equations enables the simulation of the inherently dynamic atmosphere, serving as the cornerstone for accurate and predictive meteorological insights. Within this overarching framework, a suite of integral components is embedded to address specific physical interactions that occur at different resolutions, such as cloud formation, radiation, convection, boundary layers, and surface interactions. Each of these components serves a pivotal role:* The Cloud Microphysics Parameterization Scheme is instrumental for simulating the life cycles of cloud droplets and ice crystals, thereby affecting [75; 76] and atmospheric energy balance. * Shortwave and Longwave Radiation Transfer Equations elucidate the absorption, scattering, and emission of both solar and terrestrial radiation, which in turn influence atmospheric temperature and dynamics. * Empirical or Semi-Empirical Convection Parameterization Schemes simulate vertical atmospheric motions initiated by local instabilities, facilitating the capture of weather phenomena like thunderstorms. * Boundary-Layer Dynamics concentrates on the exchanges of momentum, energy, and matter between the Earth's surface and the atmosphere which are crucial for the accurate representation of surface conditions in the model. * Land Surface and Soil/Ocean Interaction Modules simulate the exchange of energy, moisture, and momentum between the surface and the atmosphere, while also accounting for terrestrial and aquatic influences on atmospheric conditions. These components are tightly coupled with the core atmospheric dynamics equations, collectively constituting a comprehensive, multi-scale framework. This intricate integration allows for the simulation of the complex dynamical evolution inherent in the atmosphere, contributing to more reliable and precise weather forecasting. In Numerical Weather Prediction (NWP), a critical tool for atmospheric dynamics forecasting, the process begins with data assimilation, where observational data is integrated into the model to reflect current conditions. This is followed by numerical integration, where governing equations are meticulously solved to simulate atmospheric changes over time. However, certain phenomena, like the microphysics of clouds, cannot be directly resolved and are accounted for through parameterization to approximate their aggregate effects. Finally, post-processing methods are used to reconcile potential discrepancies between model predictions and real-world observations, ensuring accurate and reliable forecasts.