Atmospheric Chemistry and Physics Discussions www.atmos-chem-phys-discuss.net 1680-7367 1680-7375 8 3 2008 10.5194/acpd-8-10791-2008 http://www.atmos-chem-phys-discuss.net/8/10791/2008/ http://www.atmos-chem-phys-discuss.net/8/10791/2008/acpd-8-10791-2008.html http://www.atmos-chem-phys-discuss.net/8/10791/2008/acpd-8-10791-2008.pdf 10791 10816 2008-06-05 Aerosol model selection and uncertainty modelling by adaptive MCMC technique M. Laine marko.laine@fmi.fi J. Tamminen Finnish Meteorological Institute, Helsinki, Finland We apply Bayesian model selection techniques on the statistical inversion problem of the GOMOS instrument. The motif is to study which type of aerosol model best fits the data and to show how the uncertainty of the aerosol model can be included in the error estimates. The competing models consist of various formulations, each having different unknown parameter vectors. We have developed an Adaptive Automatic Reversible Jump Markov chain Monte Carlo method (AARJ) for sampling values from the posterior distributions of the unknowns of the models. The algorithm is easy to implement and can readily be employed for model selection as well as for model averaging, to properly take into account the uncertainty of the modelling. Bertaux, J L., Kyrölä, E., and Wehr, T.: Stellar Occultation Technique for Atmospheric Ozone Monitoring: GOMOS on Envisat, Earth Observation Quarterly, 67, 17–20, 2000. ESA 2007: GOMOS Product Handbook Issue 3.0, European Space Agency, prefixhttp://envisat.esa.int/dataproducts/, 2007. Gamerman, D.: Markov Chain Monte Carlo – Stochastic simulation for Bayesian inference, Chapman & Hall, 1997. Green, P J.: Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, 82, 711–732, 1995. Green, P J.: Trans-dimensional Markov chain Monte Carlo, in: Highly Structured Stochastic Systems, edited by: Green, P J., Hjort, N L., and Richardson, S., 27, in Oxford Statistical Science Series, Oxford University Press, 179–198, 2003. Haario, H., Saksman, E., and Tamminen, J.: An adaptive Metropolis algorithm, Bernoulli, 7, 223–242, 2001. Haario, H., Laine, M., Lehtinen, M., Saksman, E., and Tamminen, J.: MCMC methods for high dimensional inversion in remote sensing, J. R. Stat. Soc. Ser., Series B, 66, 591–607, \doi10.1111/j.1467-9868.2004.02053.x, 2004. Haario, H., Laine, M., Mira, A., and Saksman, E.: DRAM: Efficient adaptive MCMC, Statistics and Computing, 16, 339–354, \doi10.1007/s11222-006-9438-0, 2006. Hastie, D.: Towards Automatic Reversible Jump Markov Chain Monte Carlo, Ph.D. thesis, University of Bristol Department of Mathematics, 2005. Kaipio, J P. and Somersalo, E.: Computational and Statistical Methods for Inverse Problems, Springer, 339 pp., 2004. Laine, M.: MCMC toolbox for Matlab website, prefixhttp://www.helsinki.fi/~mjlaine/mcmc/, 2008. Mira, A.: On Metropolis-Hastings algorithms with delayed rejection, Metron, LIX, 231–241, 2001. Tamminen, J.: Adaptive Markov chain Monte Carlo algorithms with geophysical applications, Finnish Meteorological Institute Contributions, 47, Finnish Meteorological Institute, Helsinki, 2004. Tamminen, J. and Kyrölä, E.: Bayesian solution for nonlinear and non-Gaussian inverse problem by Markov chain Monte Carlo method, J. Geophys. Res., 106, 14 377–14 390, 2001. Vanhellemont, F., Fussen, D., Dodion, J., Bingen, C., and Mateshvili, N.: Choosing a suitable analytical model for aerosol extinction spectra in the retrieval of UV/visible satellite occultation measurements, J. Geophys. Res., 111, 2006. Veihelmann, B., Levelt, P F., Stammes, P., and Veefkind, J P.: Simulation study of aerosol information content in OMI spectral reflectance measurements, Atmos. Chem. Phys., 7, 3115–3127, 2007.