# Volcanic Eruption Calculation?

I was trying to find the amount of energy created during a volcanic explosion, I have been looking around, There was one formula I found where I could use the Kinetic Energy, which is $$KE=\frac{1}{2}mv^2$$, but I feel that there is something more.

I am looking at Volcanic Explosivity Index for Krakatoa, which says that it is class 6, and it has a TNT equivalence to 200 megatons.

I was hoping if someone can give me the correct calculation to find the means of measuring a volcanic explosion in joules, tonnes or higher.

Or if there are other means or formula like finding the result in newtons, go ahead with that as well

Here is information about the Volcanic Explosivity Index

https://geology.com/stories/13/volcanic-explosivity-index/

It says you can measure it by volume of volcanic material, height of eruption column and duration of explosion.

• One ton of TNT is 4.184 gigajoules. (en.m.wikipedia.org/wiki/TNT_equivalent) Multiply this by 200 million.
– G. Smith
Jan 6, 2019 at 3:07
• Could the calculation be based on the work that goes into lifting the eruptive material a certain distance ($mgh$) rather than the kinetic energy afterward? Jan 6, 2019 at 9:03
• @Anders Sandberg if you are referring to Newton’s then that would work too, if you know of a formula, go ahead and type it Jan 6, 2019 at 14:06

## 1 Answer

There are apparently several ways of estimating total energy release in volcanic eruptions, all of them approximate. Energy is released as heat, vibrations, deformation of rock, kinetic energy of ejected material etc. Calculating an exact energy budget is hard.

The Volcanic Explosivity Index (VEI) indicates how much volume the ejecta of the eruption takes up. One can estimate the energy release as a function of VEI class $$M$$ as $$E=10^{aM+c}$$ Joule where $$a\approx 0.79$$ and $$c = 14$$ (based on de La Cruz-Reyna 1991). That was in turn based on estimates from Yokoyama (1957).

Another way of estimating is to look at seismic signals and calculate how much energy the eruption must have had to produce the measured waveforms. Seismologists have fairly decent models of the scaling of energy with shaking intensity, and one can estimate how much it attenuates with distance.

A third way is to consider how much the pressure in the magma chamber is reduced times the reduction in volume, $$E=\Delta P\cdot V$$. A pressure drop of 5 MPa is apparently typical, and the volume reduction is proportional to the ejected volume (with some scaling factor from packed rock to ejecta).

• Thanks, this will help me out a lot, have been looking for this for a long time now Jan 7, 2019 at 5:00
• I guess which ever calc get a result such as the 200 megatons from Krakatoa eruption Jan 7, 2019 at 5:06
• I suppose that an "obvious" approach would be to simply multiply the total volume of ejected magma by the typical mass density, heat capacity and temperature (minus the melting heat, I suppose). Nov 23, 2022 at 17:26