Stochastic methods for climate and weather forecasting

气候和天气预报模型(GCM)是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组加上一定数量的活跃和不活跃的示踪物，如二氧化碳、盐度和水的混合比率(水蒸气、云滴、冰晶、雨、雪、冰雹)。由于计算机的限制，通常使用从10到100公里的空间网格大小和几分钟到几小时的时间步长。在这种粗糙的网格上，许多对气候和天气变异性有很大影响的重要物理过程没有被考虑在内。取而代之的是，次网格模型或参数化被用来表示大尺度上未分辨尺度的影响。与云和降水相关的*过程是其中之一；它们对气候系统和社会也是至关重要的。政府间气候变化专门委员会的最新(第4次)报告再次指出，云和降水是全球气候变化机制中的两个主要不确定因素。云和水蒸气至少以两种不同的方式影响气候系统。它们直接影响辐射收支，并通过与水的相变相关的潜热迫使局地和全球大气环流。大气中的对流，即由潜热直接或间接引起的流动，在从中尺度(50-500公里)系统到行星尺度的季节内振荡的广泛尺度上发生，对全球天气和气候系统产生巨大影响。在世界上许多人口稠密的地方，相关的降水事件及其时间是至关重要的。虽然辐射强迫是众所周知的，但在GCM中，云的数量及其光学厚度以及大气中水蒸气和雨水的浓度是非常不确定的，因为与对流的表示有关的不准确。当它上升时，它通过膨胀冷却，变得过饱和，开始凝结并形成云。冷凝释放的热量通过膨胀克服了大部分冷却，并保持了气团的正浮力。然后，云滴和冰晶成长为雨滴、雪或冰雹颗粒，这些颗粒足够大，足以克服云层上升气流，以降水的形式落下。这种现象的复杂性，被广泛称为对流，是由于许多高度可变和不确定的因素造成的。特别是，当它们上升时，浮力气团携带了不可忽略的环境空气，并通过非常复杂和鲜为人知的湍流混合过程将它们的一些质量通量排出到环境中。这项建议的目的是开发和使用随机模型的层次结构来表示GCM中的这些复杂过程。

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. ***Processes associated with clouds and precipitation are among those; they are also of paramount importance for the climate system and for the society. The latest (4th) report of the Intergovernmental Panel on Climate Change, once more, identified clouds and precipitation as two of the major uncertainties in GCMs. Clouds and water vapor affect the climate system in at least two different ways. They directly impact the radiation budget and force local and global atmospheric circulation by the latent heat associated with phase changes of water. Convective flows in the atmosphere, i.e, flows that are directly or indirectly induced by latent heat, occur on a wide spectrum of scales, ranging from mesoscale (50- to 500 km) systems to planetary scale intra-seasonal oscillations, which have a huge impact on the global weather and climate system. The associated precipitation events and their timing are of vital importance in many largely populated places of the world. While radiative forcing is well understood, the amount of clouds and their optical depths as well as the concentrations of water vapor and rain in the atmosphere are very uncertain in GCMs because of inaccuracies associated with the representation of convection. ***Warm and moist air tends to rise. As it rises, it cools down by expansion, becomes over- saturated and starts to condensate and form clouds. The heat release from condensation overcomes most of the cooling by expansion and maintains the air parcels positively buoyant. The cloud droplets and ice crystals then grow into rain droplets, snow or hail particles that are big enough to overcome the cloud updrafts and fall as precipitation. The complexity of this phenomenon, known broadly as convection, is due to many factors that are highly variable and uncertain. In particular, as they rise, buoyant air parcels entrain non- negligible amounts of environmental air and detrain some of their mass flux into the environment through very complex and poorly understood turbulent mixing processes. The aim of this proposal is to develop and use a hierarchy of stochastic models to represent these complex processes in GCMs. **