  Mars shares many similarities and characteristics to Earth including various
geological features and planetary structure. The remarkable bimodal
distribution of elevations in both planets is one of the most striking global
features suggesting similar geodynamic processes of crustal differentiation on
Earth and Mars. There also exist several evidences, based on geographic
features resembling ancient shorelines, for existence of an ancient martian
ocean in the northern hemisphere which covers nearly one third of the planet's
surface. However, the interpretation of some features as ancient shorelines has
been thoroughly challenged that left the existence of a primordial martian
ocean controversial. Moreover, if oceans were formerly present on Mars, there
is still a big ambiguity about the volume of water with the estimations ranging
over $4$ orders of magnitude. Here we map the martian sea level problem onto a
percolation model that provides strong evidence that the longest iso-height
line on Mars that separates the northern and southern hemispheres, acts as a
critical level height with divergent correlation length and plays the same role
as the present mean sea level does on Earth. Our results unravel remarkable
similarities between Mars and Earth, posing a testable hypothesis about the
level of the ancient ocean on Mars that can be answered experimentally by the
future investigations and spacecraft exploration.
