• *The box model*

It is instructive to consider a simple (but unrealistic) "box" model where, as atmospheric pressure changes, gas pressure changes instantly and uniformly within the entire box. If the subsurface where hydrogen is venting is permeable enough to some depth *bbox,* the atmospheric pressure change can be transmitted immediately, and the venting flux will be coincident with the rate of atmospheric pressure change:

$$V\_{\rm box}(\overline{z} = 0) = -\phi b\_{\rm box} \frac{\partial p}{\partial t} \beta\_{\mathcal{P}'} \tag{13}$$

For ϕ = 0.2, *bbox* = 1000 m, β*p* = 10−<sup>5</sup> Pa−1, and −∂*<sup>p</sup>*∂*t* = 25 mb d−<sup>1</sup> = 2500 Pa d−1, the gas flux from the box *Vbox* = 5md−1. For later discussion it is important to emphasize that the assumption of very rapid pressure transmission means that there is no phase shift between surface pressure change and surface gas flux.
