大气边界层模式中随机参数的反演与不确定性分析

在大气边界层气象中湍流黏性系数是一个很重要的参数，通过直接观测往往无法得到其准确值，仅能通过间接观测获得大致范围.本文选用随机广义Ekman动力近似模式中的湍流黏性系数进行反演研究与不确定性分析.首先利用风速观测数据，并采用基于混沌多项式的集合Kalman滤波方法对系数进行反演，降低其不确定性，缩小可能取值的范围，该方法的核心思想是将集合Kalman滤波方法中求解模式不确定性传播的方法由蒙特卡罗法改为混沌多项式展开，从而避免大规模采样带来的计算资源耗费.然后进行数值实验，结果表明该方法能够有效且快速地求解出湍流黏性的后验概率分布，从而达到降低系数不确定性的目的.根据系数的先验分布计算出风速的先验分布，从而找到风速不确定性大的区域，且揭示了在不确定性大的区域内的观测数据进行系数反演可得到十分明显的效果，这对于观测点位置的选择提供了重要的指导.

Retrieval and uncertainty analysis of stochastic parameter in atmospheric boundary layer model

The eddy viscosity is an important parameter in the atmospheric boundary layer meteorology, and we usually cannot determine their exact values by direct measurements, but we can only obtain an approximate range by indirect approximate method. In this paper, the eddy viscosity in the stochastic general Ekman momentum approximation model is used for the retrieval research and uncertainty analysis. The main purpose of retrieval is to reduce the uncertainty and narrow the approximate range of eddy viscosity. First, the polynomial chaos-ensemble Kalman filter and the wind observations are used for eddy viscosity retrieval and uncertainty reduction. The main idea of this method is to replace the Monte-Carlo method with polynomial chaos in the uncertainty quantification of ensemble Kalman filter, and thusavoiding the consumption of computing resources brought by massive samples. The goal of uncertainty quantification is to investigate the effect of uncertainty in the eddy viscosity on the model and to subsequently provide a reliable distribution of simulation results. Then two numerical experiments are implemented, i.e. experiment I in which the eddy viscosity is assumed to be constant, and experiment Ⅱ in which the eddy viscosity is assumed to be a vertically varying random parameter. The uncertainty of eddy viscosity in experiment I is reduced quickly, at the same time the mean of eddy viscosity can converge to a reference value. The effect in experiment Ⅱ is also remarkable after 16 data assimilation steps. These results show that the polynomial chaos-ensemble Kalman filter is an effective and fast method of solving the posterior distribution of eddy viscosity and reducing the uncertainty of eddy viscosity. Finally, we calculate the prior distribution of wind speed according to the prior distribution of eddy viscosity and identify the heavy uncertainty area in wind speed. The results indicate that the posterior distribution of eddy viscosity solved with wind observations in the big uncertainty area is more accurate, which provides an important guidance for selecting the location of observation points.