Directional Spread Estimate

We were recently asked how directiona spead was calculated. 

As you may know the directional distribution of wave energy is commonly approximated with a Fourier expansion, whereby we have the first two pairs in the expasion at our disposal.  The directional spread is calculated from this first pair of Fourier coefficients (A1 and B1) at each of the discrete frequencies.  Typically we report the spreading at the Peak Period.

Spread = sqrt(2(1-r))

where r = sqrt(A1(f)^2 + B1(f)^2)

A1(f) and B1(f) are the Fourier coefficients for the discrete frequency f.

-Torstein