Variational Data Assimilation for the Global Ocean - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 317

development assimilates altimeter SSH by conversion of the along-track SSH slopes
to geostrophic velocity profiles. This method is described briefly in Sect. 13.7 .
While having the potential of adding important information in data-sparse areas,
the number of altimeter-derived synthetic observations computed can greatly exceed
and overwhelm the in situ observations in the analysis. Accordingly, the synthetic
observations are thinned prior to the analysis in four ways. First, it is assumed
that directly observed temperature and salinity profiles are a more reliable source
of subsurface information wherever such observations exist. Altimeter-derived
synthetic profiles, therefore, are not generated in the area surrounding an in situ
profile observation. Second, the observed SSH from the along-track data or the
analyzed incremental change in sea level must exceed a threshold value, defined
as the noise level of the satellite altimeters, to trigger the generation of a synthetic
observation. This value is typically set to 4 cm. Third, projection of the SSH signal
onto the model subsurface density field can produce unrealistic results when the
vertical stratification is weak. In the absence of specific knowledge about how to
partition SSH anomaly into baroclinic and barotropic structures in these weakly
stratified regions, synthetic profiles are rejected for assimilation when either of
the following occurs: (1) the top-to-bottom temperature difference of the MODAS
synthetic profile is less than 5 ı C; or (2) the maximum value of the Brunt-Vaisala

frequency calculated from the model density profile in the direct method is less
than 1.4. Fourth, there are problems with the SSH data in shallow water due
to contamination of the altimeter signal by tides. Accordingly, SSH data are not
assimilated in water depths less than 400 m.

13.5 NCODA System

NCODA is a comprehensive ocean data assimilation system. In addition to the
3DVAR it contains other components that perform functions useful for many
applications. These component capabilities are briefly summarized in this section.

13.5.1 Analysis Error Covariance

The analysis error covariance P a is estimated from the equation,

P a D P b P b H T . HP b H T C R/ 1 HP b

(13.9)

where P b and R are the background and observation error covariances previously
defined for ( 13.1 ). Unlike ( 13.1 ), which involves matrix-vector operations, ( 13.9 )
requires the use of matrix-matrix operations and is computationally expensive to
perform. The NCODA 3DVAR provides an estimate of the analysis error variance
(the diagonal of the second right-hand term) in the form of a normalized reduction