Hayashi, Y., 1977: On the coherence between progressive and retrogressive waves and a partition of space-time power spectra into standing and traveling parts. Journal of Applied Meteorology, 16 (4), 368-373.

Abstract: A formula is derived to express the PR coherence between the progressive and retrogressive components in terms of the CS coherence between the cosine and sine space-Fourier coefficients. By the use of the PR coherence the space-time power spectra are partitioned into standing and traveling wave parts..
If the PR coherence is zero, the progressive and retrogressive components do not interfere with each other to form standing wave oscillations with nodes. In this case the CS coherence also becomes zero, if and only if these components have equal amplitudes.