Currently, the
National Oceanic and Atmospheric Administration (NOAA) National Weather Service (NWS) runs the HYSPLIT dispersion model with
a unit mass release rate to predict the transport and dispersion of volcanic
ash. The model predictions provide information for the Volcanic Ash Advisory
Centers (VAAC) to issue advisories to meteorological watch offices, area
control centers, flight information centers, and others. This research aims
to provide quantitative forecasts of ash distributions generated by objectively
and optimally estimating the volcanic ash source strengths, vertical
distribution, and temporal variations using an observation-modeling inversion
technique. In this top-down approach, a cost functional is defined to
quantify the differences between the model predictions and the satellite
measurements of column-integrated ash concentrations weighted by the model
and observation uncertainties. Minimizing this cost functional by adjusting
the sources provides the volcanic ash emission estimates. As an example,
MODIS (Moderate Resolution Imaging Spectroradiometer) satellite retrievals of
the 2008 Kasatochi volcanic ash clouds are used to test the HYSPLIT volcanic
ash inverse system. Because the satellite retrievals include the ash cloud
top height but not the bottom height, there are different model diagnostic
choices for comparing the model results with the observed mass loadings.
Three options are presented and tested. Although the emission estimates vary
significantly with different options, the subsequent model predictions with
the different release estimates all show decent skill when evaluated against
the unassimilated satellite observations at later times. Among the three
options, integrating over three model layers yields slightly better results
than integrating from the surface up to the observed volcanic ash cloud top
or using a single model layer. Inverse tests also show that including the
ash-free region to constrain the model is not beneficial for the current
case. In addition, extra constraints on the source terms can be given by
explicitly enforcing no-ash for the atmosphere columns above or below the
observed ash cloud top height. However, in this case such extra constraints
are not helpful for the inverse modeling. It is also found that
simultaneously assimilating observations at different times produces better
hindcasts than only assimilating the most recent observations
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