Variational Data Assimilation for the Global Ocean - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 303

the vertical correlation length scales at the two locations. The horizontal correlation
length scales vary with location and the vertical correlation length scales vary with
depth and location in the analysis. As described in the subsequent sections, both
correlation components evolve with time in accordance with information obtained
from the model forecast background valid at the update cycle interval.

13.3.1 Horizontal Correlations

The horizontal correlation length scales are set proportional to the first baroclinic
Rossby radius of deformation using estimates computed from the historical profile
archive by Chelton et al. ( 1998 ). Rossby length scales qualitatively characterize
scales of ocean variability and vary from 10 km at the poles to greater than 200 km in
the tropics. The Rossby length scales increase rapidly near the equator which allows
for stretching of the zonal scales in the equatorial wave guide. Flow-dependence is
introduced in the analysis by modifying the horizontal correlations with a tensor
computed from forecast model sea surface height (SSH) gradients. The flow-
dependent tensor spreads innovations along rather than across the SSH contours,
which are used as a proxy for the circulation field. Flow dependence is a desirable
outcome in the analysis, since error correlations across an ocean front are expected
to be characteristically shorter than error correlations along the front. Note that
other gradient fields can be used as a flow-dependent tensor in the analysis, such
as SST or potential vorticity ( Martin et al. 2007 ). The flow dependent correlation
tensor (C f /

is computed using either a SOAR or Gaussian model defined in ( 13.4 )
and ( 13.5 ), where the SSH difference between two locations is normalized by a
scalar that defines the strength of the flow dependence. Because the flow dependent
correlations are computed directly from the forecast SSH fields they depend strongly
on the accuracy of the model forecast. This dependence may prove not to be
very useful in practice if the forecast model fields are inaccurate. Accordingly, the
normalization scalar can be set to a relatively large value in order to reduce the
strength of the flow dependence in the analysis and prevent a model with systematic
errors from adversely affecting the analysis. Alternatively, the flow dependence can
be switched completely off. Figure 13.2 shows a zoom of the analysis increments
off South Africa from a global high resolution SST analysis executed using a 6-h
update cycle. The analysis has 12-km resolution at the equator, 9-km mid-latitude,
and is a FNMOC contribution to the Group for High Resolution SST (GHRSST).
Background SST gradients are used as the flow dependent tensor, with the result that
the SST analysis increments are constrained by the meanders and eddies associated
with the Agulhas retroflection current. The increments are both positive and negative
along the front and eddy locations, indicating that application of the flow dependent
tensor is a relatively weak constraint and the strength and position of features can
change from one update cycle to the next in the analysis.
To account for the discontinuous and non-homogeneous influence of coastlines
in the analysis a second tensor is introduced . C l / that rotates and stretches horizontal