Is there an atmospheric hydrogen cycle? There are various physical, chemical and biological processes that free up hydrogen from molecules (often hydrocarbons or water).

Once in the atmosphere, the hydrogen is lost to space (the Earth's gravity is too weak to hold onto it). So the Earth is losing hydrogen to space (perhaps at a very slow rate).

Is there any interaction between the Earth's atmosphere and high velocity protons in the solar wind (e.g. protons combining with atmospheric oxygen to form hydroxide) which is capable of balancing the hydrogen loss? How big is the hydrogen loss? Is the amount of hydrogen on Earth in equilibrium?
"Is there any interaction between the Earth's atmosphere and high velocity protons in the solar wind (e.g. protons combining with atmospheric oxygen to form hydroxide) which is capable of balancing the hydrogen loss?" I found Hydrogen ions in the solar wind react with oxygen in interplanetary dust grains to form little packets of water, potentially supplying Earth with its water, but they don't know how much.

"How big is the hydrogen loss?" 3 kilograms per second.

"Is the amount of hydrogen on Earth in equilibrium?" We are also gaining 50,000 tons of matter per year from space dust, but only a small part of that is hydrogen.