  We present a coupled fluid-dynamic and electromagnetic model for volcanic ash
plumes. In a forward approach, the model is able to simulate the plume dynamics
from prescribed input flow conditions and generate the corresponding synthetic
thermal infrared (TIR) image, allowing a comparison with field-based
observations. An inversion procedure is then developed to retrieve ash plume
properties from TIR images.
  The adopted fluid-dynamic model is based on a one-dimensional, stationary
description of a self-similar (top-hat) turbulent plume, for which an
asymptotic analytical solution is obtained. The electromagnetic
emission/absorption model is based on the Schwarzschild's equation and on Mie's
theory for disperse particles, assuming that particles are coarser than the
radiation wavelength and neglecting scattering. [...]
  Application of the inversion procedure to an ash plume at Santiaguito volcano
(Guatemala) has allowed us to retrieve the main plume input parameters, namely
the initial radius $b_0$, velocity $U_0$, temperature $T_0$, gas mass ratio
$n_0$, entrainment coefficient $k$ and their related uncertainty. Moreover,
coupling with the electromagnetic model, we have been able to obtain a reliable
estimate of the equivalent Sauter diameter $d_s$ of the total particle size
distribution.
  The presented method is general and, in principle, can be applied to the
spatial distribution of particle concentration and temperature obtained by any
fluid-dynamic model, either integral or multidimensional, stationary or
time-dependent, single or multiphase. The method discussed here is fast and
robust, thus indicating potential for applications to real-time estimation of
ash mass flux and particle size distribution, which is crucial for model-based
forecasts of the volcanic ash dispersal process.
