International audienceWe 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). Henc...