Tropospheric OH budget ($[\mathrm{OH}]=P/K$)

A local or box-model balance between hydroxyl-radical production and effective losses. For fixed production $P$ and pseudo-first-order total loss frequency $K$, $[\mathrm{OH}]=P/K$. Additional hydrogen, carbon monoxide or methane consumption can lower hydroxyl radical if production and other terms stay fixed; radical recycling and spatial transport can alter that simple result.

In a fixed-production hydroxyl radical box, adding hydrogen by $\Delta [{\mathrm{H}}_2]$ changes $K$ to $K+k_{{\mathrm{H}}_2+OH}\Delta [{\mathrm{H}}_2]$. Methane lifetime scales as $K/P$ when its hydroxyl radical reaction coefficient is held fixed. The pre-existing hydrogen contribution is already in $K$ and must not be counted again.