Seasurface topography harmonic analysis.
## Harmonic analysis of Sea-surface topography.

Project participants: C.C.Tscherning, NBI, Per Knudsen and
Ole Andersen, DNSC. Start 2007-12-01.
The project is a follow on to the ESA GUTS project.

### Harmonic analysis.

2-degree mean SST
was received from Per Knudsen, and the
continents were filled with zero-values. The data-were modified so that
the global mean value became equal to zero also.

A set of spherical harmonic coefficients
were calculated to degree 90 using
Fast Spherical Collocation
in an iterative manner, because a covariance
function need to be known a-priori.

In the final step the covariance function (Fig.1)
was computed from (Fig. 2)
the degree-variances. Remarkable is the large value of the degree 2
degree-variance, showing that the difference between Equator and the
polar areas dominates the picture.

### Tampering at the coast.

A problem is the discontinuity at the coast, because the data are set to
zero on land, see Fig. 3 .
and Fig. 4 .
If general Fourier-analysis, tampering is used, normally
with a cosine function multiplied on the data at the edges.

It is a more complex issue here, since the coast-line
is very complex. A solution is to predict from the sst-values
at sea, values at land using a smooth predictor like least-squares
collocation.This has been investigated using the
GRAVSOFT program geogrid.f.

In a first try the correlation distance was set to 220 km (2 degrees),
see Fig. 5

Fig. 6
shows the standard deviation of the differences of the
coefficients per degree, and Fig.7
shows the differences.

Litterature

Project finished 2010.

Last update: 2012-11-15 by cct@gfy.ku.dk