Variational quality control of non-Gaussian innovations and its parametric optimizations for the GRAPES m3DVAR system

Abstract

The magnitude and distribution of observation innovations, which have an important impact on the analyzed accuracy, are critical variables in data assimilation. Variational quality control (VarQC) based on the contaminated Gaussian distribution (CGD) of observation innovations is now widely used in data assimilation, owing to the more reasonable representation of the probability density function of innovations that can sufficiently absorb observations by assigning different weights iteratively. However, the inaccurate parameters prevent VarQC from showing the advantages it should have in the GRAPES (Global/Regional Assimilation and PrEdiction System) m3DVAR system. Consequently, the parameter optimization methods are considerable critical studies to improve VarQC. In this paper, we describe two probable CGDs to include the non-Gaussian distribution of actual observation errors, Gaussian plus flat distribution and Huber norm distribution. The potential optimization methods of the parameters are introduced in detail for different VarQCs. With different parameter configurations, the optimization analysis shows that the Gaussian plus flat distribution and the Huber norm distribution are more consistent with the long-tail distribution of actual innovations compared to the Gaussian distribution. The VarQC’s cost and gradient functions with Huber norm distribution are more reasonable, while the VarQC’s cost function with Gaussian plus flat distribution may converge on different minimums due to its non-concave properties. The weight functions of two VarQCs gradually decrease with the increase of innovation but show different shapes, and the VarQC with Huber norm distribution shows more elasticity to assimilate the observations with a high contamination rate. Moreover, we reveal a general derivation relationship between the CGDs and VarQCs. A novel schematic interpretation that classifies the assimilated data into three categories in VarQC is presented. They are conducive to the development of a new VarQC method in the future.

Graphical abstract

Keywords

data assimilation / variational quality control / contaminated Gaussian distribution / non-Gaussian distribution / innovation

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