confirmed the hypothesis for times as old as $\sim$2.5 billion years (Smirnov and Tarduno, 2004), notwithstanding considerable gaps in the paleomagnetic database of directions. For even deeper time, the global distribution of data does not yet permit a test, but we can proceed because the geocentric dipole assumption provides the maximum magnetic shielding [@Siscoe1980].

The key magnetic parameter to determine in learning about solar-terrestrial interactions in the deep past (eqn 1) then is magnetic field strength ($M_{E}$), but this is far more difficult to determine than paleodirections. Determining the ancient solar wind pressure is also challenging, especially for the first $\sim$700 million years of Earth’s history.

In this review, we will first tackle the observational challenge of determining ancient field strength by means of examples through Paleoarchean times. We will show how these data, when combined with constraints based on solar analogs, allow us to constrain the magnetopause some 3.45 billion years ago. We provide a review of atmospheric escape mechanisms, including contrarian views that question the importance of a shield created by the geomagnetic field. Within this context, we discuss the implications of the Paleoarchean magnetopause conditions for the evolution of Earth’s water inventory. As one peers back further 