  Terrestrial-type exoplanets orbiting nearby red dwarf stars (M-dwarfs) are
among the best targets for atmospheric characterization and biosignature
searches in the near future. Recent evolutionary studies have suggested that
terrestrial planets in the habitable zone of M-dwarfs are probably tidally
locked and have limited surface water inventories as a result of their host
stars' high early luminosities. Several previous climate simulations of such
planets have indicated that their remaining water would be transported to the
planet's permanent nightside and become trapped as surface ice, leaving the
dayside devoid of water. Here we use a three-dimensional general circulation
model with a water cycle and accurate radiative transfer scheme to investigate
the surface water evolution on slowly rotating tidally locked terrestrial
planets with limited surface water inventories. We show that there is a
competition for water trapping between the nightside surface and the substellar
tropopause in this type of climate system. Although under some conditions the
surface water remains trapped on the nightside as an ice sheet, in other cases
liquid water stabilizes in a circular area in the substellar region as a
wetland. Planets with 1 bar N$_2$ and atmospheric CO$_2$ levels greater than
0.1 bar retain stable dayside liquid water, even with very small surface water
inventories. Our results reveal the diversity of possible climate states on
terrestrial-type exoplanets and highlight the importance of surface liquid
water detection techniques for future characterization efforts.
