  We compare estimates of atmospheric precipitation during the Martian
Noachian-Hesperian boundary 3.8 Gyr ago as calculated in a radiative-convective
column model of the atmosphere with runoff values estimated from a
geomorphological analysis of dendritic valley network discharge rates. In the
atmospheric model, we assume CO2-H2O-N2 atmospheres with surface pressures
varying from 20 mb to 3 bar with input solar luminosity reduced to 75% the
modern value.
  Results from the valley network analysis are of the order of a few mm d-1
liquid water precipitation (1.5-10.6 mm d-1, with a median of 3.1 mm d-1).
Atmospheric model results are much lower, from about 0.001-1 mm d-1 of snowfall
(depending on CO2 partial pressure). Hence, the atmospheric model predicts a
significantly lower amount of precipitated water than estimated from the
geomorphological analysis. Furthermore, global mean surface temperatures are
below freezing, i.e. runoff is most likely not directly linked to
precipitation. Therefore, our results strongly favor a cold early Mars with
episodic snowmelt as a source for runoff.
  Our approach is challenged by mostly unconstrained parameters, e.g.
greenhouse gas abundance, global meteorology (for example, clouds) and
planetary parameters such as obliquity- which affect the atmospheric result -
as as well as by inherent problems in estimating discharge and runoff on
ancient Mars, such as a lack of knowledge on infiltration and evaporation rates
and on flooding timescales, which affect the geomorphological data.
Nevertheless, our work represents a first step in combining and interpreting
quantitative tools applied in early Mars atmospheric and geomorphological
studies.
