**3. Discussion**

From the above analysis, it is clear that the atmospheric pressure tide could cause the pulsation in hydrogen concentration measured at 1 m depth. The main evidence supporting the hypothesis that atmospheric pressure changes are modulating the measured hydrogen concentration is the hysteresis

in the observed Δp' vs. *[H2]1m* curve shown in Figure 2C. Figure 4C shows that the slow calculated di ffusion of pressure into the subsurface produces a hysteresis between the rate of venting at 1.2 m depth, *V1.2m*, and the measured *[H2]1m* that is very similar in form to that observed between Δp' and *[H2]1m*. (Note, the circulation is the same if <sup>Δ</sup>*p'* is replaced by −Δ*p'*.) If *[H2]1m* is proportional to *V1.2m*, this hysteresis similarity strongly suggests the di ffusion of pressure into the subsurface is the cause of the measured pulsing of the hydrogen venting.

A substantial reservoir of gas (compared to the volume of gas in the vents) must be compressed or expanded by the atmospheric pressure changes for hydrogen-free atmospheric air to be drawn to sensor depth. For the simple "box" model calculated above, the box must be ~1000 m thick to change *[H2]1m* in a fashion similar to that observed (Figure 7). Instantaneous pressure transmission to 1000 m depth would require an unrealistically high subsurface permeability, so the box depth of 1000 m simply indicates that the reservoir gas volume a ffected by atmospheric pressure changes must be at least ~1000 times larger than the gas volume between the surface and the *H*2 sensor at 1 m depth. Pressure wave calculations show that, in addition, the volume of gas accessible to the pressure wave must be about 25% of the full volume with which it could interact. This is required for the maximum venting rate, *V*, to coincide with the maximum *[H2]1m* (Figure 5A). If the vent has a very low gas volume compared to the reservoir with which it interacts, there will be very little transit delay for incoming air to reach the *H*2 gas sensors at 1 m depth. It is important to emphasize that the box modeling is 1D. Flow arises from vertical compression and decompression only. In reality gas would be supplied to vents laterally as well as vertically. Thus, the 25% of the potential draw should be interpreted as 25% of the 3D volume that feeds a particular vent.

It is reasonable that *[H2]1m* should be maximum at the maximum venting rate at 1 m depth. The advection–di ffusion solution shown in Figure 8 seems to sugges<sup>t</sup> di fferently. It shows the maximum *[H2]1m* occurs at the end of venting just before inflow begins. However, it is a 1D calculation that considers only vertical di ffusion. In actuality, *H*2 di ffuses laterally from the vent, and, as gas rich in *H*2 approaches the surface *H*2 will di ffuse laterally and be diluted. This dilution will be minimum when the gas e fflux is maximum, and thus the maximum *[H2]1m* should coincide with the maximum venting rate.

Observations as well as these modeling results sugges<sup>t</sup> that hydrogen is venting from a shallow reservoir lying between the surface and the water table under the barren zone, and that the venting occurs mainly on the periphery, as shown in Figure 9. The barren zone is a small topographic depression that fills periodically with water. It is plausible that the top of the barren zone could be less permeable than its periphery because, due to periodic flooding, it receives more fine sediment deposition, has more evaporative salt deposition, and is more altered. Because slumping permeability might also be concentrated at the barren zone margins. If the upper layer of the central portion of the barren zone is relatively impermeable, but underlain by permeable sediments, a sealed *H*2 reservoir could exist in the permeable sediments between the surface and the water table. The hypothetical reservoir could extend outside the barren zone if the sediments above the water table were as permeable outside as inside the barren zone. The reservoir in Figure 9 is shown being filled from depth by relatively pure (50 to 100%) hydrogen gas. Gas pushed into and out of the reservoir by atmospheric pressure tides through the periphery vents dilutes the reservoir near these vents as illustrated by the green hydrogen concentration contours surrounding the leftmost vent in Figure 9. Di fferent perimeter vents will interact with the reservoir in slightly (and perhaps substantially) di fferent ways if the permeability and porosity vary around the periphery of the reservoir. The time and concentration of the peak hydrogen concentration at di fferent sensors could therefore di ffer as observed. The vents will operate as observed provided the three-to-five-meter-thick reservoir constitutes ~25% of the potential pressure wave penetration depth and the gas volume in the vents is a very small fraction of the volume compressed and decompressed by the atmospheric pressure tides impacting each vent.

**Figure 9.** Schematic of H2 vent system suggested by the modeling results.

The possibility that the vent system is operating as illustrated in Figure 9 can be tested in several ways: A gas probe in the center of the barren zone would test if there is a gas reservoir between a sealed surface and the water table. The hydrogen concentration in the center of the barren zone should be >50% (or at least much greater than near the vents). Gas probes into the reservoir near sites of venting on the periphery could show how [*H*2] varies away from the vents. The gradient in [*H*2] and pressure variations at these probes could confirm the hypothesis that atmospheric-pressure variations cause the observed changes in measured *H*2. Measurements of permeability and porosity would also test this hypothesis and would provide data for the kind of 3D finite element analysis that will be needed to accurately model the *H*2 venting. Drill holes outside the barren zone would test the extent of the *H*2 reservoir.

There is much that is not covered in our analysis. For example, as the water table at the base of our hypothetical *H*2 reservoir rises and falls, accumulated *H*2 will be expelled and diluted. Tracking these changes could be important to the *H*2 content of the reservoir. The magnitude of *H*2 venting is best provided, at least in the short term, by integrating the *H*2 efflux from the periphery of the barren zone as has been done by Prinzhofer et al. (2019). We add nothing to Prinzhofer's estimates of the total *H*2 venting rate in this paper. Rather, the analysis presented in this paper suggests the kind of system that could operate as observed. Ultimately 3D finite element modeling will be needed to define the hydrogen resource. For 3D modeling to contribute beyond the analysis offered here, however, more needs to be known about the shallow *H*2 reservoir and its relation to the vents on the periphery of the barren zone. The needed information can be obtained by gas probe or shallow drilling.
