Estimation and propagation of volcanic source parameter uncertainty in an ash transport and dispersal model: application to the Eyjafjallajokull plume of 14--16 April 2010
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Abstract
Data on source conditions for the 14 April 2010 paroxysmal phase of
the eyja~ eruption, Iceland, have been used as inputs to a
trajectory-based eruption column model, . This model has in
turn been adapted to generate output suitable as input to the volcanic
ash transport and dispersal model, , which was used to
propagate the paroxysmal ash cloud toward and over Europe over the
following days. Some of the source parameters, specifically vent
radius, vent source velocity, mean grain size of ejecta and standard
deviation of ejecta grain size have been assigned probability
distributions based on our lack of knowledge of exact conditions at
the source. These probability distributions for the input variables
have been sampled in a Monte Carlo fashion using a technique that
yields what we herein call the Polynomial Chaos Quadrature Weighted
Estimate (PCQWE) of output parameters from the ash transport and
dispersal model. The advantage of PCQWE over Monte Carlo is that
since it intelligently samples the input parameter space, fewer model
runs are needed to yield estimates of moments and probabilities for
the output variables. At each of these sample points for the input
variables, a model run is performed. Output moments and probabilities
are then computed by properly summing the weighted values of the
output parameters of interest. Use of a computational eruption column
model coupled with known weather conditions as given by radiosonde
data gathered near the vent allows us to estimate that initial mass
eruption rate (MER) on 14 April 2010 may have been as high as $10^8$
kg/s and was almost certainly above $10^7$ kg/s. This estimate is
consistent with the probabilistic envelope computed by PCQWE for the
downwind plume. The results furthermore show that statistical moments
and probabilities can be computed in a reasonable time by using
$9^4=6561$ PCQWE model runs as opposed to millions of model runs that
might be required by standard Monte Carlo techniques. The output mean
ash cloud height plus three standard deviations -- encompassing
c. 99.7% of the probability mass -- compares well with
four-dimensional ash cloud position as retrieved from Meteosat-9
SEVIRI data for 16 April 2010 as the ash cloud drifted over
north-central Europe. Finally, the ability to compute statistical
moments and probabilities may allow for the better separation of
science and decision-making, by making it possible for scientists to
better focus on error reduction and decision makers to focus on
``drawing the line'' for risk assessment.
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