The most common, reactive stuff in the atmosphere are $\ce{-OH}$ radicals [(Wikipedia)][1]. So I guess they're the natural antagonist for $\ce{H2}$ molecules. 

Btw., as soon as it's diluted in the surrounding air, it will no longer rise. Only bulk masses have buoyancy. The g gradient in the atmosphere is much too small to separate gases.

  [1]: https://en.wikipedia.org/wiki/Hydroxyl_radical#Importance_in_Earth.27s_atmosphere