Remote sensing of volcanic ash and sulfur dioxide - Volcanism and Global Environmental Change - page 103

where r is the particle radius and λ is wavelength. These optical regimes are:

-

the particle is small compared to the wavelength ( X Rayleigh 1)

Mie - the particle is of comparable size to the wavelength ( X 1)

Geometric - the particle is large compared to the wavelength ( X 1)

As the size distribution of particles in uences the way in which a cloud of particles

interacts with radiation, it is necessary to characterise the shape of different size
distributions and investigate how this affects optical parameters such as single scatter-
ing albedo, mass absorption coef cient and phase function. The size parameter is

useful for determining which optical regime describes how electromagnetic radiation
will interact with the particles, and guides the choice of wavelength to use for retrievals
of ash properties. Distal particle size distributions rarely fit a log-normal distribution

and are often polymodal. They typically show a coarser sub-population which
shifts to finer sizes and decreases in proportion with increasing distance from the

vent as the cloud is transported downwind due to coarser particles settling out. As
distance from the volcano increases, settling transitions from inertia-dominated single-
particle settling to aggregation-dominated settling of very mdiameter)

ash particles (Rose and Durant, 2009 ). Nevertheless, it is these particles that remain
in the atmosphere for longer and present a hazard to air traf

ne ( < 30 μ

c and human health

(Horwell and Baxter, 2006 ). The mass proportion of very mdiameter)

in explosive eruptions can vary from a few per cent (typical for basaltic eruptions)
to greater than 50% (in some silicic eruptions). In distal regions, this

ne ash ( < 30 μ

ner sub-
population typically retains consistent size characteristics but becomes proportionally
dominant. The effect of size parameter (and therefore particle size) on various optical
parameters can be modelled using Mie theory by varying the mean size parameter
and standard deviation from the fitted distribution. This is analogous to shifting
the size range of the distribution but maintaining its shape.

7.3.3 Optical properties

To retrieve fine-ash properties from remote sensing it is necessary to have know-

ledge of the spectral refractive index of ash. The amount of absorption of light
by the particle is controlled by the imaginary part of the refractive index ( R i ),
which is strongly dependent upon wavelength and composition. The absorption
coef cient k (m 1 ) can be expressed as

π R i ðλÞ

4

k ¼ : ð 7 : 2 Þ

λ

The compositional effects are manifest through the spectrally dependent refractive
index. Several efforts are underway to improve the measurement database of