Eyjafjallajokull volcano plume 2010
By Boaworm (Own work) [CC BY 3.0], via Wikimedia Commons

I was stuck in traffic on the M8 travelling between Edinburgh and Glasgow when a news item really pricked my ears up. Scientists from Edinburgh University’s school of GeoSciences have been investigating better ways of measuring the extent of ash clouds following volcanic eruptions, looking at particle size.Following the Eyjafjallajokull Icelandic volcano eruption in 2010, the ash cloud drifted across the major flight paths in the North Atlantic and over Northern Europe and as a result, planes were grounded and people stranded. At first the airlines said they wouldn’t fly with any ash in the air, but as the days went on and it became apparent that the ash could hang around at reasonable concentrations for months, flights resumed. Contrary to media reports at the time, no aircraft fell from the skies.

The Edinburgh researchers compared the particle size (or as they call it, grain size) of the Eyjafjallajokull ash cloud, measured by satellites, with the particle size of samples obtained from peat bogs, and held in museums. They found that the satellite computations significantly under-estimated the particle sizes when they performed their analysis on the MET Office supercomputers.

The satellite measurements are made using a technique called Brightness Temperature Difference (or BTD) which is based on the comparison of infra-red light emitted by the ash cloud with that emitted from the Earth below. The intensity of the BTD signal depends on the concentration of the ash, the particle size and the height of the ash cloud.

There are some parallels here with laser diffraction. The extraction of the particle size is based on the use of optical models, similar to the ones that underpin laser diffraction results. As you may know, there are two models used in laser diffraction: Mie Theory and the Fraunhofer approximation.

Mie theory is the most general optical scattering theory we know. It requires optical properties of the sample and the dispersing medium – the ash and the air – and while the air might be well-characterized, the freshly erupted ash from a volcano probably is not.

The Fraunhofer approximation makes some additional assumptions to Mie theory, including that the particles are discs and are opaque, but it doesn’t need the optical properties and is relatively easy to calculate. On the downside, the Fraunhofer approximation increasingly over-estimates the proportion of fines as particle size decreases below 50um.

In this chart you can see data analyzed with both Mie theory and the Fraunhofer approximation:

Mie vs Fraunhofer

The ISO 13320:2009 standard for laser diffraction states:

For particles smaller than about 50μm Mie theory offers the best general solution…

If the Fraunhofer approximation is applied for samples containing an appreciable amount of small, transparent particles, a significantly larger amount of small particles may be calculated.

I don’t know the details of the calculations, but I have a strong suspicion that the satellites used a Fraunhofer-type approximation when analysing the ash cloud, due to limited computing resources and knowledge of the optical properties of the ash, and hence underestimate the particle size. This would explain the findings of the Edinburgh researchers. Either way, it’s been an interesting reminder of the relative merits of the two models.

Related Resources:

Application Note: Assessing the abrasivity of volcanic ash from the Eyjafjallajökulll volcano eruption using the Morphologi G3

Recorded Webinar: The life of Gustav Mie and the development of the Lorenz-Mie solution to Maxwell’s equations

Whitepaper: Mie theory: the first 100 years

Application Note: Basic principles of particle size analysis