A Coordinate Change for Data Assimilation in Spherical Geometry of Frontal Structures

In this note, it is discussed how a coordinate transformation based on semigeostrophic theory can be introduced in a global data assimilation scheme in order to improve the analysis of frontal structures. An expression of the coordinate change on the sphere is proposed and an iterative procedure is defined to perform this transformation. This algorithm also includes an iterative filtering of the wind field used for the coordinate change. This filtering is equivalent to a filtering of the wind in the transformed space that nearly keeps unchanged the corresponding high cyclonic vorticity values in physical space associated with cold fronts. It is shown that the transformation can be built for a real meteorological case. The main impact of this transformation in the framework of data assimilation is that it enables the use of anisotropic forecast correlations that are flow dependent. As expected, the correlations in the vicinity of a front are found to be contracted in the horizontal but also vertically tilted.