Three signatures are a displaced exoplanet thermal phase curve maximum, the day-night temperature contrast, and wind-induced Doppler shifts.
The maximum of an exoplanet thermal phase curve need not coincide with secondary eclipse. An eastward hot spot and a maximum before eclipse indicate eastward advection/atmospheric superrotation, provided reflected light and exoplanet clouds are accounted for.
The amplitude and shape of an exoplanet thermal phase curve measure day-night heat redistribution: a warm nightside and reduced day-night contrast imply effective transport relative to radiative relaxation time in a planetary atmosphere. Wavelength-dependent contrasts can reveal different circulation efficiencies at different contribution pressures.
High-resolution transmission or emission spectra can show line-centroid shifts/broadening relative to the orbital velocity. A limb blueshift is consistent with a dayside-to-nightside flow toward the observer; rotation and limb asymmetry affect the pattern. Such Doppler spectroscopy probes velocity directly, while phase curves probe the transported temperature pattern.
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