Ash plume properties retrieved from infrared images: a forward and inverse modeling approach

Abstract

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.

In the inversion procedure, model parameters space is sampled to find the optimal set of input conditions which minimizes the difference between the experimental and the synthetic image. Two complementary methods are discussed: the first is based on a fully two-dimensional fit of the TIR image, while the second only inverts axial data. Due to the top-hat assumption (which overestimates density and temperature at the plume margins), the one-dimensional fit results to be more accurate. However, it cannot be used to estimate the average plume opening angle. Therefore, the entrainment coefficient can only be derived from the two-dimensional fit.

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.