  Terrestrial-type exoplanets orbiting nearby red dwarf stars (M dwarfs) are
the first potentially habitable exoplanets suitable for atmospheric
characterization in the near future. Understanding the stability of water in
cold-trap regions on such planets is critical because it directly impacts
transmission spectroscopy observations, the global energy budget, and long-term
surface water evolution. Here we diagnose the humidity distribution in
idealized general circulation model (GCM) simulations of terrestrial-type
exoplanets. We use the `tracer of last saturation' technique to study the
saturation statistics of air parcels. We find that on synchronously rotating
planets, the water vapor abundance in the nightside upper troposphere depends
weakly on planetary rotation, while more water vapor builds up in the nightside
lower troposphere on fast-rotating planets. We then discuss how last-saturation
statistics can elucidate the multiple moist climate equilibrium states on
synchronously and asynchronously rotating arid planets. We show that the
multiple moist climate states arise from the cold-trapping competition between
the substellar upper atmosphere and cold surface regions. We find that fast
synchronously rotating planets tend to trap surface water on the nightside as a
result of their weak atmospheric and strong surface cold traps compared to the
slow rotating case. These results elucidate the nature of the water cycle on
arid rocky exoplanets and will aid interpretation of atmospheric observations
in the future.
