22 
Longitude 
Fig.12: Observed (blue) and averaged (red) T,S-profiles 
used as input for the optimal interpolation. 
In most applications of optimal interpolation the negative squared exponential (called often 
’’Gaussian function”) has been favoured as the shape of the correlation function, although 
many other functions have been considered. A ’’gaussian” model of the autocorrelation 
function was used for this study, which employs a decorrelation length scale R: 
P (r) = exp (-r 2 /R 2 ) (3) 
We note, that our assumption of this covarience is highly arbitrary, and we choose the 
’’Gaussian” form because of the relatively simple structure as well as the lack of a more 
appropriate choice. The parameter R (decorrelation scale or e-folding length scale) is a 
measure of the spatial scale of correlation. The shortcomings of the ’’Gaussian” function 
when applied to a typical geophysical data can be summarised as a propensity to 
overestimate the weights at short lags and underestimate them at large lags (McIntosh, 
1990). This amounts to oversmoothing at small scales and may be countered by artificially 
lowering the value of A, causing the interpolation to follow the data more faithfully. 
It is well known, that many important features of the oceanic circulation and water mass 
distribution are closely connected to the bottom topography. Thus, most of the World Ocean 
boundary currents are situated above the continental slope, having a cross-current scale of 
o(50km), e.g. small compared with the typical size of the ocean basin. Similar, fresh water 
river plumes significantly alter property distributions in the coastal areas, but are effectively 
separated from the open ocean areas by sharp fronts. It is therefore desirable to preserve 
the ’’narrowness” of boundary currents in the analysed fields. Using large decorrelation 
scales would result in unrealistically wide boundary currents. We included the topographic 
information into the calculation of the characteristic length scale R. For each grid node the 
distance D between the node and the coast was determined, with the respective R 
determined from: 
R — Rmax for D >— D mgXt 
R = Rmin + (Rmax~Rmin) D/D max for 0 < D <D n 
(4)