Stochastic methods for climate and weather forecasting

气候和天气预报模式（GCMs）基于大气和海洋流动方程的离散化：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性和非活性示踪剂，如二氧化碳、盐度和水混合比（蒸气、云滴、冰晶、雨、雪、冰雹）。由于计算机的限制，通常使用10到100公里的空间网格尺寸和分钟到小时的时间步长。在这种粗糙的网格中，许多重要的物理过程，极大地影响气候和天气变化，没有被考虑在内。相反，使用子网格模型或参数化来表示未解决的尺度对大尺度的影响。

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.