Stochastic methods for climate and weather forecasting

气候和天气预报模型是以大气和海洋流动方程的离散化为基础的：一个质量、动量和能量守恒的偏微分方程系统，加上一定数量的活跃和不活跃示踪剂，如二氧化碳、盐度和水混合比（蒸汽、云滴、冰晶、雨、雪、冰雹）。由于计算机的限制，通常使用10至100公里的空间网格尺寸和数分钟至数小时的时间步长。在这种粗糙的网格上，许多重要的物理过程，大大影响气候和天气变率，没有考虑。取而代之的是，子网格模型，或参数化，用于表示未解决的规模上的大尺度的影响。

Climate and weather forecasting models (GCMs) are based on a discretization of the equations of atmospheric and oceanic flows: a system of partial differential equations for the conservation of mass, momentum, and energy plus a certain number of active and inactive tracers such as carbon dioxide, salinity, and water mixing ratios (vapour, cloud droplets, ice crystals, rain, snow, hail). Due to computer limitations, spatial mesh sizes ranging from 10 to 100 km and time steps of minutes to hours are typically used. On such coarse grids, many important physical processes, which greatly affect climate and weather variability, are not accounted for. Instead, subgrid models, or parameterizations, are used to represent the effects of the unresolved scales on the large scales.