Centrum Wiskunde and Informatica, Science Park 123, 1098 XG Amsterdam, The Netherlands.
Philos Trans A Math Phys Eng Sci. 2013 Apr 15;371(1991):20120374. doi: 10.1098/rsta.2012.0374. Print 2013 May 28.
Stochastic subgrid models have been proposed to capture the missing variability and correct systematic medium-term errors in general circulation models. In particular, the poor representation of subgrid-scale deep convection is a persistent problem that stochastic parametrizations are attempting to correct. In this paper, we construct such a subgrid model using data derived from large-eddy simulations (LESs) of deep convection. We use a data-driven stochastic parametrization methodology to construct a stochastic model describing a finite number of cloud states. Our model emulates, in a computationally inexpensive manner, the deep convection-resolving LES. Transitions between the cloud states are modelled with Markov chains. By conditioning the Markov chains on large-scale variables, we obtain a conditional Markov chain, which reproduces the time evolution of the cloud fractions. Furthermore, we show that the variability and spatial distribution of cloud types produced by the Markov chains become more faithful to the LES data when local spatial coupling is introduced in the subgrid Markov chains. Such spatially coupled Markov chains are equivalent to stochastic cellular automata.
随机子网格模型被提出以捕捉在一般环流模型中缺失的可变性和纠正系统性的中期误差。特别是，次网格尺度深对流的不良表示是随机参数化试图纠正的一个持续存在的问题。在本文中，我们使用来自深对流的大涡模拟（LES）得出的数据构建了这样一个子网格模型。我们使用数据驱动的随机参数化方法来构建描述有限数量的云状态的随机模型。我们的模型以计算成本低的方式模拟深对流分辨 LES。通过将马尔可夫链条件化到大尺度变量上，我们得到了一个条件马尔可夫链，它再现了云分数的时间演化。此外，我们表明，当在子网格马尔可夫链中引入局部空间耦合时，马尔可夫链产生的云类型的可变性和空间分布会更加忠实于 LES 数据。这种空间耦合的马尔可夫链相当于随机元胞自动机。
