Since they are not orthogonal either to each other or to the cosines, they project on them, resulting in the blend shown in Fig. The singular spectra of the 2 synthetic cases discussed in the text. The empty blue diamonds are for the cosines-only case, while the solid red circles are for the case with all 4 generating patterns. It is always extremely important to examine the fraction of the total variance the various modes account for. For the 2 synthetic cases above, this is shown in Fig.
Higher modes differ.
In the cosine only, where the only reminder is noise, it is roughly equally distributed over the entire spectrum. There is a substantial body of literature about the issue of the appropriate cutoff of the singular spectrum, beyond which, it is assumed, there is little or no useful information. Finally, Fig. 4 shows an example of a real-life use of EOFs. And yet, when piped through the EOF algorithm, a very clear and coherent large scale structure emerges.