Inversion of Airborne Contaminants in a Regional Model
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.
KeywordsInverse Problem Inverse Operator Observation Window Airborne Contaminant Forward Transport
- 2.Biros, G., Ghattas, O.: Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. Part II: The Lagrange Newton solver, and its application to optimal control of steady viscous flows. SIAM Journal on Scientific Computing 27(2), 714–739 (2005)Google Scholar
- 4.Drăgănescu, A.: Two investigations in numerical analysis: Monotonicity preserving finite element methods, and multigrid methods for inverse parabolic problems. PhD thesis, University of Chicago (2004)Google Scholar
- 5.Drăgănescu, A., Dupont, T.F.: Optimal order multi-level preconditioners for regularized ill-posed problems (2005) (to appear)Google Scholar
- 6.Balay, S., Buschelman, K., Gropp, W.D., Kaushik, D., McInnes, L.C., Smith, B.F.: PETSc home page (2001), http://www.mcs.anl.gov/petsc
- 8.Brooks, A.N., Hughes, T.J.R.: Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Computer Methods in Applied Mechanics and Engineering 32, 199–259 (1982)Google Scholar