The Stability of Incremental Analysis Update.
The Stability of Incremental Analysis Update.
复制标题
增量分析更新的稳定性。
作者：
L. Takacs;M. Suárez;R. Todling
最近试图将50公里的MERRA-2分析缩小到7公里，发现与增量分析更新程序有关的不稳定性，迄今为止尚未注意到。基于复频率简阻尼谐振子的理论研究提供了诊断该问题的框架，并提出了避免该问题的方法。避免不稳定性的三种可能途径是：（i）根据理论稳定性图选择IAU预测步和校正步长度的“理想”比例;（ii）对用于构建具有给定频率的IAU趋势的背景场进行时间平均;或（iii）对IAU趋势应用数字滤波器调制。所有这些都显示出控制不稳定性的一个广泛的分辨率时，做了放大或缩小，实验与NASA/GMAO大气环流模式。此外，它被发现，结合IAU的合奏重新定心步骤典型的混合合奏变分方法，也会导致不稳定性的基础上相同的机制在合奏的成员。在使用GMAO 12.8 km混合4D-EnVar系统进行的实验中出现了这种情况的一个例子。用数字滤波器调制系综IAU趋势可以避免不稳定性。此外，对某些4DIAU实现的稳定性进行了分析，并提出了改进的建议，但对这一问题的全面研究将推迟到后续工作。
A recent attempt to downscale the 50 km MERRA-2 analyses to 7 km revealed an instability associated with the Incremental Analysis Update (IAU) procedure that has thus far gone unnoticed. A theoretical study based on a simple damped harmonic oscillator with complex frequency provides the framework to diagnose the problem and suggests means to avoid it. Three possible approaches to avoid the instability are to: (i) choose an "ideal" ratio of the lengths of the Predictor and Corrector steps of IAU based on a theoretical stability diagram; (ii) time average the background fields used to construct the IAU tendencies with given frequency; or (iii) apply a digital filter modulation to the IAU tendencies. All these are shown to control the instability for a wide range of resolutions when doing up- or down-scaling, experiments with the NASA/GMAO atmospheric general circulation model. Furthermore, it is found that combining IAU with the ensemble re-centering step typical of hybrid ensemble-variational approaches, also results in an instability based on the same mechanisms in the members of the ensemble. An example of such occurrence arises in an experiment performed with the GMAO 12.8 km hybrid 4D-EnVar system. Modulation of the ensemble IAU tendencies with a digital filter is shown to avoid the instability. In addition, the stability of certain 4DIAU implementations is analyzed and a suggestion is made to improve its results, though a complete study of this subject is postponed to a follow up work.