  We use a hierarchy of numerical models (a 3-D Global Climate Model, a 1-D
radiative-convective model and a 2-D Mantle Dynamics model) to explore the
environmental effects of very large impacts on the atmosphere, surface and
interior of early Mars.
  Using a combination of 1-D and 3-D climate simulations, we show that the
environmental effects of the largest impact events recorded on Mars are
characterized by: (i) a short impact-induced warm period; (ii) a low amount of
hydrological cycling of water; (iii) deluge-style precipitation; and (iv)
precipitation patterns that are uncorrelated with the observed regions of
valley networks. We show that the impact-induced stable runaway greenhouse
state predicted by Segura et al. 2012 is physically inconsistent. We confirm
the results of Segura et al. 2008 and Urata & Toon 2013 that water ice clouds
can significantly extend the duration of the post-impact warm period, and even
for cloud coverage lower than predicted in Ramirez & Kasting 2017. However, the
range of cloud microphysical properties for which this scenario works is very
narrow.
  Using 2-D Mantle Dynamics simulations we find that large impacts can raise
the near-surface internal heat flux up to several hundreds of mW/m$^2$ (i.e. up
to $\sim$ 10 times the ambient flux) for several millions years at the edges of
the impact crater. However, such internal heat flux is insufficient to keep the
martian surface above the melting point of water.
  Our numerical results support the prediction of Palumbo & Head 2018 that very
large impact-induced rainfall could have caused degradation of craters and
formed smooth plains, potentially erasing much of the previously visible
morphological surface history. Such hot rainfalls may have also led to the
formation of aqueous alteration products on Noachian-aged terrains.
