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。***与云和降水有关的过程就是其中之一；它们对气候系统和社会也至关重要。政府间气候变化专门委员会的最新（第四次）报告再次将云和降水确定为gcm的两个主要不确定性。云和水蒸气至少以两种不同的方式影响着气候系统。它们直接影响辐射收支，并通过与水的相变相关的潜热强迫局部和全球大气环流。大气中的对流流动，即由潜热直接或间接引起的流动，发生在广泛的尺度上，从中尺度（50- 500公里）系统到行星尺度的季节内振荡，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区，相关的降水事件及其时间至关重要。虽然辐射强迫已被很好地理解，但由于对流表示的不准确性，在gcm中云的数量及其光学深度以及大气中水蒸气和雨的浓度是非常不确定的。温暖潮湿的空气趋于上升。当它上升时，它因膨胀而冷却，变得过饱和，开始凝结并形成云。冷凝释放的热量克服了大部分由膨胀引起的冷却，并保持空气包的正浮力。然后，云滴和冰晶成长为雨滴、雪或冰雹颗粒，它们足够大，可以克服云的上升气流，以降水的形式降落。这种被广泛称为对流的现象的复杂性是由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，浮力空气包裹携带了不可忽略的环境空气，并通过非常复杂和知之甚少的湍流混合过程将它们的一些质量通量释放到环境中。本提案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. **