## Inversion of Airborne Contaminants in a Regional Model

### Volkan Akcelik^{1}, George Biros^{2}, Andrei
Draganescu^{4}, Omar Ghattas^{3}, Judith Hill^{4}, and
Bart van Bloemen Waanders^{4}

^{1}
Stanford Linear Accelerator Center

volkan@slac.stanford.edu

^{2}
Department of Mechanical Engineering and Applied Mechanics, University of
Pennsylvania

biros@seas.upenn.edu">biros@seas.upenn.edu">biros@seas.upenn.edu

^{3}
Institute for Computational Engineering and Sciences, The University of Texas
at Austin

omar@ices.utexas.edu

^{4}
Optimization and Uncertainty Estimation Department, Sandia National
Laboratories

aidraga@sandia.gov

jhill@sandia.gov

bartv@sandia.gov

__Abstract__.
We are interested in a DDDAS problem of localization of airborne contaminant
releases in regional atmospheric transport models from sparse observations.
Given measurements of the contaminant over an observation window at a small
number of points in space, and a velocity field as predicted for example by a
mesoscopic weather model, we seek an estimate of the state of the contaminant
at the begining of the observation interval that minimizes the least squares
misfit between measured and predicted contaminant field, subject to the
convection-diffusion equation for the contaminant. Once the
“initial” conditions are estimated by solution of the inverse
problem, we issue predictions of the evolution of the contaminant, the
observation window is advanced in time, and the process repeated to issue a
new prediction, in the style of 4D-Var. We design an appropriate numerical
strategy that exploits the spectral structure of the inverse operator, and
leads to efficient and accurate resolution of the inverse problem. Numerical
experiments verify that high resolution inversion can be carried out rapidly
for a well-resolved terrain model of the greater Los Angeles area.

LNCS 3993, pp. 481-488.