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