Mathematical Sciences: Statistics in Atmospheric Sciences

大气环流模式的亚网格尺度变率问题，以及这种模式的降水部分质量普遍较差，表明需要基于大尺度大气过程的降水模式。一个现实的降水随机模型可以基于气象上均匀的天气状态，每个天气状态驱动一个简单的降水随机模型。为了确定适当的天气状态，开发了一种适用于相关数据的典型相关分析的变体。统计理论允许大气场的时空分解和随之而来的标准误差评估。当应用于主要规范变量时，这种方法可以隔离感兴趣的空间和时间尺度。另一种略有不同的方法是使用隐马尔可夫模型，该模型由大气数据驱动，其形式不像上面所表达的那样明确。这个模型在相对较小的空间尺度上，以及一年中时间上均匀的部分是相当准确的。将该隐马尔可夫模型方法扩展到季节模型，并将其性能与天气状态方法以及与一般气象预报模型进行了比较。用于评估气候变化的一般环流模式在降水方面表现相对较差。此外，为了评估气候变化对区域水文的影响，需要比环流模式具有更精细分辨率的模式，因为水文过程通常在比主导全球气候模式的大尺度大气过程小得多的尺度上运行。这组科学家没有开发精确的确定性降雨模型，而是建立了一类部分基于概率的模型，并将其与气象预报模型进行比较，并将其应用于天气数据和环流模型的输出。＊＊＊

9524770 Guttorp The problem of subgrid scale variability in general circulation models, and the generally poor quality of the precipitation part of such models, indicate the need for precipitation models based on large-scale atmospheric processes. A realistic stochastic model of precipitation can be based on meteorologically homogeneous weather states, each driving a simple stochastic model of precipitation. In order to determine appropriate weather states, a variant of canonical correlation analysis, appropriate for dependent data, is developed. Statistical theory allowing a space-time decomposition of atmospheric fields with attendant standard error assessment is developed. When applied to the leading canonical variates, such a method can isolate spatial and temporal scales of interest. A slightly different approach uses a hidden Markov model, driven by atmospheric data in a less explicit form than expressed above. This model is fairly accurate on relatively small spatial scales, and for temporally homogeneous parts of the year. This hidden Markov model approach is extended to a seasonal model, and its performance compared with the weather state approach, as well as with general meteorological forecast models. %%% The general circulation models used to assess climate change have relatively poor performance when it comes to precipitation. Furthermore, in order to assess the effect on regional hydrology of climate changes, models with a finer resolution than the circulation models are needed, since the hydrologic processes usually operate on a much smaller scale than the large-scale atmospheric processes that dominate the global climate models. Rather than developing precise deterministic models of rainfall, the researchers build a partly probability-based class of models, and compare it with meteorological forecast models and applied to both weather data and circulation model outputs. ***