Comment by dredmorbius | Hacker News Reader

Comment by dredmorbius | Hacker News Reader

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If GNU units isn't lying to me:

The blast yield has been given as equivalent to 6 MT TNT,[1] equivalent to a large nuclear weapon. This estimate itself is probably based on shockwave, ejecta volume and velocity, or similar effects,[2] so I'm somewhat working backwards to the estimation basis, but let's roll with that.

6 megaton TNT is about 11,100 billion * 2260 J

2260 J is the latent heat of vaporisation of water (the energy required to turn 1g of 100C water to steam).

If the ocean water were at 100C before vapourisation, that works out to about 11 million m^3 (or 11 million tonnes) of seawater vapourised, about 0.011 km^3.

The actual amount would be less than this, as the seawater would have been heated from below 100C (at 4.18 joules/(g*degreeC)), and some of the heat would likely have been dissipated in other modes (e.g., kinetic energy).

But that's an upper bound.

Since steam occupies about 1,000 the volume of liquid water, that 11 million tonnes would have displaced 11 km^3 of atmosphere, or a cube 2.2 km on a side, or a sphere with a radius of about 1.37 km.

Which makes me wonder what the specific blast geometry would have been, and how that might have affected blast and gravity wave generation. A narrow column jetting straight up might have a much more pronounced gravity-wave effect than a generalised, say, hemispheric, blast.

As before: not a geologist.

Edit: It's also helpful to remember that that volume of steam has mass and momentum. Once it starts moving, it's going to take some resistive force to stop it, and atmospheric resistance and gravity are pretty much all we've got to work with. But 11 million tonnes moving at a good clip (up to around 600--1,100 kph, based on other estimates of the shockwave) has a significant stopping distance.

________________________________

Notes:

1. Initial estimates were 10 MT, but revised downward. https://www.npr.org/2022/01/18/1073800454/nasa-scientists-es...

2. Acoustic / shockwave methods are described here by Arrowsmith & Bowman, further methods are listed among references: https://asa.scitation.org/doi/10.1121/1.4984121#

The estimate is of the kinetic energy and doesn't include thermal energy so I think your derived estimate ends up being circular:

https://www.axios.com/nasa-tonga-volcano-blast-5-6-megatons-...

Another difficulty is that you're essentially estimating boiling a blob of water away but that's not what takes place - the process is explosive, quickly dumping lots of 'excess' energy elsewhere. It also doesn't stop heating the water once it hits 100c vapour.

The nature of rough physics back-of-the-envelope (or quick on-the-shell) estimation is to get a rough idea of values and quantities involved. My expectation is that my estimate is somewhere within an order of magnitude of actual values, and suspect it's well on the high side.

Modelling the specific events and characteristics of seawater infiltration to magma vents and chambers is well beyond my pay grade. I'm not representing to any extent that I've done this realistically. I'm simply showing what the maximimum potential vaporisation magnitude might be given a 6 MT energy input using a very naive heat of vaporisation conversion.

I'd noted the circularity in my note --- I'm estimating vapourisation effects and consequent blast yield using estimations of energy release which are based on the observed blast characteristics. Circular circularity is circularly circular.

The Axios article ... provides minimal insight on NASA's estimation methods. Though the comment on kinetic (blast) energies does suggest modeling based on the size, and probably rate of expansion, of the steam and ash plume. A forensic analysis of the 2020 Beiruit explosion discusses how total explosive force is estimated by blast diameter (see: https://forensic-architecture.org/investigation/beirut-port-...).

On thermal vs. blast effects: my estimate is based on the conversion of applied thermal energy into blast energy through vapourisation of water into steam. The 1,000-fold volumetric expansion provides that blast capability. It would then be much of the observed blast that the original 5--6 MT erruption energy is based on. My understanding is that "thermal effects" would refer to additional heat radiated from the erruption, exclusive of that heat which triggered the steam explosion itself.

FWIW, claims are now that the blast may have been 50 MT equivalent or larger. That's at least as large as the Tsar Bomba (50 MT) yield, the largest nuclear weapon ever detonated.

https://text.npr.org/1074438703

Nicely done! Agree the blast dynamics would likely have a substantial effect on the effect. If you watch the satellite view you can see oscillations at the ceiling of the cloud, almost like ripples in water. I wonder if that is what triggered the ripples being reported.

That seems like a plausible mechanism.

My non-expert confidence doesn't count for much here, of course.

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