Evolution of upper atmospheric specific humidity and surface temperation with varying insolation. Panel (a) shows the time series of the global mean specific humidity at 10 mb isobar in the solid curves (corresponding to the left axis), and shows that of the global annual mean surface temperature in the dashed curves (corresponding to the right axis), as insolation gradually increases. The high-obliquity scenario is in red and the low obliquity is in black. The 1000 ppmv threshold for significant escape is marked by a thin black line. To demonstrate that the insolation change in the transient simulations is slow enough to allow climate to almost reach equilibrium, we repeat the simulation with insolation increased twice as fast. The progression of surface temperature (dots) and upper atmospheric specific humidity (circles) matches the slow-evolving transient experiment reasonably well. Panel (b) is the same as panel (a), except the insolation varies in the opposite direction, decreasing from 1760 to 1360 W m−2. As such, the climate remains on the warmer branch rather than the colder branch. Panel (c) scatters the global mean 10 mb specific humidity against the maximum monthly surface temperature achieved in that year (search among different latitudes and different months). High obliquity is in red, and low obliquity is in black. Extra feedback suppression experiments are also marked in the plot. The red circle denotes a high-obliquity experiment forced by fixed annual mean sea surface temperature (SST), the red “+” sign denotes a similar experiment except that the SST meridional distribution is reversed between the equator and the poles, and the red triangle denotes a high-obliquity simulation forced by fixed annual mean insolation. Please refer to the text for more detailed model setups. For reference, the estimated water abundance in the upper atmosphere by 1D model is plot in thin black lines. We, following Kasting & Pollack (1983), assume moist adiabat from the surface until the temperature falls below the specified stratospheric temperature (marked to the right of each curve).