# Computation of probabilistic hazard maps and source parameter estimation for volcanic ash transport and dispersion

## Abstract

Volcanic ash advisory centers are charged with forecasting the movement of volcanic ash plumes, for aviation, health and safety preparation. Deterministic mathematical equations model the advection and dispersion of these plumes. However initial plume conditions – height, profile of particle location, volcanic vent parameters – are known only approximately at best, and other features of the governing system such as the windfield are stochastic. These uncertainties make forecasting plume motion difficult. As a result of these uncertainties, ash advisories based on a deterministic approach tend to be conservative, and many times over/under estimate the extent of a plume. This paper presents an end-to-end framework for generating a probabilistic approach to ash plume forecasting. This framework uses an ensemble of solutions, guided by Conjugate Unscented Transform (CUT) method for evaluating expectation integrals. This ensemble is used to construct a polynomial chaos expansion that can be sampled cheaply, to provide a probabilistic model forecast. The CUT method is then combined with a minimum variance condition, to provide a full posterior pdf of the uncertain source parameters, based on observed satellite imagery. The April 2010 eruption of the Eyjafjallajökull volcano in Iceland is employed as a test example. The puff advection/dispersion model ismore »

- Authors:

- Department of Mechanical and Aerospace Engineering, University at Buffalo (United States)
- Department of Geology, University at Buffalo (United States)
- Geophysical Institute, University of Alaska, Fairbanks (United States)
- Center for Computational Research, University at Buffalo (United States)
- NOAA-NESDIS, Center for Satellite Applications and Research (United States)
- Department of Mathematics, University at Buffalo (United States)

- Publication Date:

- OSTI Identifier:
- 22314890

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 271; Conference: 1. international conference on frontiers in computational physics, Boulder, CO (United States), 16-20 Dec 2012; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ADVECTION; APPROXIMATIONS; ASHES; CHAOS THEORY; ERUPTION; HAZARDS; ICELAND; INTEGRALS; LOADING; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; PARTICLES; PLUMES; POLYNOMIALS; PROBABILISTIC ESTIMATION; PROBABILITY; STOCHASTIC PROCESSES; VOLCANOES

### Citation Formats

```
Madankan, R., Pouget, S., Singla, P., E-mail: psingla@buffalo.edu, Bursik, M., Dehn, J., Jones, M., Patra, A., Pavolonis, M., Pitman, E.B., Singh, T., and Webley, P..
```*Computation of probabilistic hazard maps and source parameter estimation for volcanic ash transport and dispersion*. United States: N. p., 2014.
Web. doi:10.1016/J.JCP.2013.11.032.

```
Madankan, R., Pouget, S., Singla, P., E-mail: psingla@buffalo.edu, Bursik, M., Dehn, J., Jones, M., Patra, A., Pavolonis, M., Pitman, E.B., Singh, T., & Webley, P..
```*Computation of probabilistic hazard maps and source parameter estimation for volcanic ash transport and dispersion*. United States. doi:10.1016/J.JCP.2013.11.032.

```
Madankan, R., Pouget, S., Singla, P., E-mail: psingla@buffalo.edu, Bursik, M., Dehn, J., Jones, M., Patra, A., Pavolonis, M., Pitman, E.B., Singh, T., and Webley, P.. Fri .
"Computation of probabilistic hazard maps and source parameter estimation for volcanic ash transport and dispersion". United States.
doi:10.1016/J.JCP.2013.11.032.
```

```
@article{osti_22314890,
```

title = {Computation of probabilistic hazard maps and source parameter estimation for volcanic ash transport and dispersion},

author = {Madankan, R. and Pouget, S. and Singla, P., E-mail: psingla@buffalo.edu and Bursik, M. and Dehn, J. and Jones, M. and Patra, A. and Pavolonis, M. and Pitman, E.B. and Singh, T. and Webley, P.},

abstractNote = {Volcanic ash advisory centers are charged with forecasting the movement of volcanic ash plumes, for aviation, health and safety preparation. Deterministic mathematical equations model the advection and dispersion of these plumes. However initial plume conditions – height, profile of particle location, volcanic vent parameters – are known only approximately at best, and other features of the governing system such as the windfield are stochastic. These uncertainties make forecasting plume motion difficult. As a result of these uncertainties, ash advisories based on a deterministic approach tend to be conservative, and many times over/under estimate the extent of a plume. This paper presents an end-to-end framework for generating a probabilistic approach to ash plume forecasting. This framework uses an ensemble of solutions, guided by Conjugate Unscented Transform (CUT) method for evaluating expectation integrals. This ensemble is used to construct a polynomial chaos expansion that can be sampled cheaply, to provide a probabilistic model forecast. The CUT method is then combined with a minimum variance condition, to provide a full posterior pdf of the uncertain source parameters, based on observed satellite imagery. The April 2010 eruption of the Eyjafjallajökull volcano in Iceland is employed as a test example. The puff advection/dispersion model is used to hindcast the motion of the ash plume through time, concentrating on the period 14–16 April 2010. Variability in the height and particle loading of that eruption is introduced through a volcano column model called bent. Output uncertainty due to the assumed uncertain input parameter probability distributions, and a probabilistic spatial-temporal estimate of ash presence are computed.},

doi = {10.1016/J.JCP.2013.11.032},

journal = {Journal of Computational Physics},

number = ,

volume = 271,

place = {United States},

year = {Fri Aug 15 00:00:00 EDT 2014},

month = {Fri Aug 15 00:00:00 EDT 2014}

}