  CO2+H2 greenhouse warming has recently emerged as a promising scenario to
sufficiently warm the early martian surface to allow the formation of valley
networks and lakes. Here we present numerical 3-D global climate simulations of
the early martian climate that we have performed assuming dense CO2+H2
atmospheres. Our climate model, derived from earlier works by Forget et al.
(2013) and Wordsworth et al. (2013), is coupled to an asynchronous model of the
long-term evolution of martian glaciers and lakes. Simulations were carried out
at 40{\deg} obliquity to investigate how (i) water content and (ii) H2 content
(added to 1 or 2 bars of CO2) can shape the climate and hydrologic cycle of
early Mars. We show that the adiabatic cooling mechanism (Wordsworth et al.
2013) that leads to the accumulation of ice deposits in the southern highlands
in cold climate (the so called 'icy highland scenario') also works in warm
climates, with impact crater lakes acting as the main water reservoirs. This
produces rainfall mainly localized in the southern highlands of Mars. If one
adjust (i) the amount of CO2 and H2, (ii) the size and location of the water
reservoirs, and (iii) the ancient topography (i.e. by removing Tharsis), the
spatial patterns of surface runoff (from rainfall or snowmelt) in the
simulations can match -- with a few exceptions -- the observed distribution of
valley networks and impact crater lakes. Although our results are obtained for
CO2-dominated atmospheres enriched with H2, they should also apply to assess
the impact of any combination of powerful long-lived greenhouse gases on early
Mars.
