  The development of habitable conditions on Earth is tightly connected to the
evolution of its atmosphere which is strongly influenced by atmospheric escape.
We investigate the evolution of the polar ion outflow from the open field line
bundle which is the dominant escape mechanism for the modern Earth. We perform
Direct Simulation Monte Carlo (DSMC) simulations and estimate the upper limits
on escape rates from the Earth's open field line bundle starting from three
gigayears ago (Ga) to present assuming the present-day composition of the
atmosphere. We perform two additional simulations with lower mixing ratios of
oxygen of 1% and 15% to account for the conditions shortly after the Great
Oxydation Event (GOE). We estimate the maximum loss rates due to polar outflow
three gigayears ago of $3.3 \times10^{27}$ s$^{-1}$ and $2.4 \times 10^{27}$
s$^{-1}$ for oxygen and nitrogen, respectively. The total integrated mass loss
equals to 39% and 10% of the modern atmosphere's mass, for oxygen and nitrogen,
respectively. According to our results, the main factors that governed the
polar outflow in the considered time period are the evolution of the XUV
radiation of the Sun and the atmosphere's composition. The evolution of the
Earth's magnetic field plays a less important role. We conclude that although
the atmosphere with the present-day composition can survive the escape due to
polar outflow, a higher level of CO$_2$ between 3.0 and 2.0~Ga is likely
necessary to reduce the escape.
