# Lili Lei, NOAA Earth System Research Lab

## Vertical localization for EnKF radiance assimilation

##### Coauthors

Jeffrey Whitaker, Lili Lei, Craig Bishop#### Abstract:

EnKF systems typically use 'observation-space' localization for
computational reasons. Observation space localization tapers the sample
covariance estimate to zero based on the distance between an observation
and model state variables. Ensemble-based variational update algorithms
use 'model-space' localization, which only depends on the distance
between model state variables. Observation (model) space localization
applies localization to the sample covariance estimate after (before)
the forward operator is applied in the computation of the Kalman gain.
Evidence suggests that ensemble-variational systems make better use of
radiance observations than EnKF systems. One reason for this could be
that observation-space localization can be problematic for radiances,
since the vertical distance between a radiance observation and a model
state variable is not well defined. To test this hypothesis, we develop
a method for applying model-space localization in the vertical in EnKF
systems, based upon the 'modulated-ensemble' approach described in a
series of papers by Bishop and Hodyss. In this approach, an augmented
ensemble is created which includes the effect of vertical localization
in model space, and then the EnKF algorithm is applied as usual, but
without vertical localization. Results from an experiment that
assimilates only radiance observations with the operational NCEP global
EnKF system show that using model space localization significantly
improves forecast skill. Strategies for optimizing the model-space
vertical localization algorithm are discussed, and it is suggested that
the computational cost of the model-space approach should not be
significantly larger than the observation space approach.