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tokens: rates and substellar velocities. Figure 13. Mid-tropospheric atmospheric temperature ( p = 658 hPa). The temperature reference in the lower right corner of each pane indicates the value of the highest temperature contour, with successive cooler contours at 2 K intervals. The central column (tidally locked) phase-curve examples are shown in Figure 12 . At this height in the atmosphere, , there is no frictional damping. In the stratified model, we find a more complicated relationship than in the shallow-water study. At the surface, the thermal response is tightly coupled to the forcing, and at all rotation rates, the peak integrated temperature is lagging the motion of the substellar point. However, at altitude, from where observed infrared emission will originate, the temperature distribution is sensitive to the speed of the diurnal cycle. Above the boundary layer, momentum and temperature are less strongly damped, thermal advection is efficient compared to friction, and the hot spot is advected by the wind field. Figure 13 shows the horizontal temperature structure in the mid-troposphere; for both eastward- and westward-propagating substellar points, eastward and westward hot spots are observed, depending on the rotation rate of the planet. As previously demonstrated in the hot Jupiter studies of Showman et al. ( 2015 ), a quickly moving substellar point, or rapidly rotating system results in a reduction in zonal variability. At the mid-troposphere example plots shown in Figure 13, there is an ∼65 K gradient between substellar and antistellar points in the equilibrium temperature T eq ; in contrast, the atmospheric temperature varies little, with an efficient thermal transport from dayside to nightside. The efficient heat transport and zonal redistribution with a rapidly moving substellar velocity predicts relatively warm nightside temperatures and a largely isothermal distribution of temperature in the upper atmosphere; this is perhaps expected from our intuition of Earth, which has a very rapid diurnal cycle relative to atmospheric radiative timescales, . The reduction in the meridional temperature gradient is also a result of the short diurnal timescale, providing an effective relaxation profile, as shown in Figure 7 and discussed above. The phase-curve offset is found by calculating the normalized phase curve relative to the substellar point using Equation ( 22 ) and then solving for the longitude of maximum integrated thermal emission. The panels of Figure 14 show the phase-curve offset as a function of substellar velocity near the surface and at several levels in the troposphere. Phase curves near the surface are a strong function of substellar velocity, with little influence from rotation rate; in general, the faster the substellar point moves, the further the thermal hot spot has lagged behind the point of maximal heating. This is due to the short timescales of both radiative and frictional damping in the bottom boundary of the