Stochastic methods for climate and weather forecasting

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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 intra­seasonal 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.