Page 109 - Fundamentals of Physical Volcanology

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86 CHAPTER 6

10 10 2 10 3 10 4 10 5 10 6
50 50

40 Bezymianny, 1956 40
Fig. 6.7 The relationship between the
heights of some observed eruption
Plume height (km) 30 Santa Maria, 1902 0.3 30 eruption rates in the eruptions
1.0
plumes and the estimated mass
0.7
producing them. The curves are the
results of theoretical calculations and
Hekla, 1947
are labeled by the fraction of the heat
20
20
to drive the plume upward. Not all of
Hekla, 1970 Soufriere, 1902 contained in pyroclasts that is available
the pyroclast heat is available because
10 Fuego, 1971 10 some is removed by large clasts falling
Ngauruhoe, out of the plume. (Adapted from fig. 2
1974 in Wilson, L., Sparks, R.S.J., Huang,
Heimaey, 1973 T.-C. & Watkins, N.D. (1978) The
0 0
control of volcanic column heights
10 10 2 10 3 10 4 10 5 10 6 by eruption energetics and dynamics.
–1
3
Volume eruption rate (m s ) J. Geophys. Res. 83, 1829–1836.)
where H is the plume height in kilometers and M the match between theory and observation is sur-
f
−1
is the mass flux in kg s . prisingly good.
A “standard atmosphere” is one that is typical
of the whole of the Earth. In practice the thermal
structure of the atmosphere varies as a function of 6.6 Fallout of clasts from eruption plumes
latitude, longitude, elevation above sea level and
season of the year, as well as with the local, short- Thus far we have largely ignored the fact that the
term weather conditions, especially the humidity, rising eruption plume carries with it magma clasts
i.e., the water vapor content. One systematic con- or clots. This section looks at the fate of the clasts in

sequence of this is that, for the same eruption an eruption plume.
conditions, one expects to generate higher plumes
at lower latitudes.
6.6.1 Rise of clasts in an eruption plume
Figure 6.7 shows a plot of some observed erup-
tion plume heights as a function of the corres- If you drop an object, it falls through the air under
ponding estimated volume eruption rates, with gravity and accelerates until the gravity force acting
three theoretical curves superimposed. One of downward is balanced by the resisting frictional
these assumes that all of the available heat from drag force of the surrounding air. The clasts in the
the magma is used to drive the plume, as in eqn 6.7, eruption plume are no different from any other
and the others assume that either 70% or 30% of the object: they are also trying to fall under gravity. The
heat is lost due to the early fallout of large clasts. difference in the case of magma clasts is that they
There are inevitable uncertainties in the obser- are also being dragged upwards within a rising gas
vations of plume heights and mass fluxes: both stream. This is true of the clasts both when they are
change with time during an eruption, and the erup- still within the dike system above the fragmentation
tion rate estimate involves measuring the amount of level and when they are being carried upwards in
pyroclasts deposited around the vent over a finite the rising eruption plume above the vent. Thus a
time interval, and so it is only ever an average dur- clast is subject to two competing forces – the force
ing part of the eruption. Given all these problems, of gravity trying to making the clast fall and the drag