Developments in the application of recursive filters to anisotropic covariances in NCEP’s Gridpoint Statistical Interpolation (GSI)

Yoshiaki Sato
JMA Visiting Scientist


Two topics will be presented in this seminar. The first involves ensemble based background error covariance estimation in the regional GSI; the second describes an alternative covariance construction space for the global GSI.

The NCEP GSI uses recursive filters to generate covariances. A horizontally isotropic covariance can be generated by applying the filter along each grid coordinate direction, but the filter also has the ability to generate three-dimensional anisotropic covariances with the “hexad algorithm”. This capability enables the synthesis of situation-dependent background covariances with shapes appropriately stretched or compressed to reflect ambient conditions.

As the first topic, the situation dependent background covariance is formulated by using the NCEP global ensemble forecast data, and the estimated covariance is applied in the regional GSI. It shows plausible shape and good consistency to the true ensemble perturbation correlations even when it uses only 20 ensemble members. However, the forecast skill is so far only comparable to that associated with the isotropic covariances. The possible cause for the small impact will be discussed.

Situation dependent background covariances can also be estimated in the global GSI, but the true ensemble perturbation correlation field often exhibit planetary scales in the stratosphere/mesosphere that warrant special consideration: The global GSI presently uses a three-patch system of overlapping grids to avoid the polar singularities. When correlation scales are of modest extent, an adequate degree of continuity of the synthesized covariances is obtained by combining a smooth blending operation with the filters applied within the overlapping portions. But this expedient fails for covariances of such very large scales. Thus it is desirable to augment the present three-patch GSI gridding with a special treatment designed to accommodate the whole globe in a horizontally uninterrupted grid system for planetary scale background error covariances for planetary scale background error covariances.

For this purpose, we developed a three-dimensional “cubic-patch”, gridded in Cartesian fashion, which contains the three-dimensional spherical shell occupied by the atmosphere’s upper layers in a configuration that avoids any coordinate singularity. Since the horizontally isotropic covariance projected into the cubic-patch is no longer isotropic, the anisotropic recursive filter is utilized for the covariance construction.

The formulation and preliminary test results will be presented as the second topic.