Geoscientific Model Development Discussions www.geosci-model-dev-discuss.net 1991-9611 1991-962X 3 4 2010 10.5194/gmdd-3-1783-2010 http://www.geosci-model-dev-discuss.net/3/1783/2010/ http://www.geosci-model-dev-discuss.net/3/1783/2010/gmdd-3-1783-2010.html http://www.geosci-model-dev-discuss.net/3/1783/2010/gmdd-3-1783-2010.pdf 1783 1827 2010-10-22 Construction of non-diagonal background error covariance matrices for global chemical data assimilation K. Singh M. Jardak A. Sandu sandu@cs.vt.edu K. Bowman M. Lee D. Jones Department of Computer Science, Virginia Polytechnic Institute and State University, 2202 Kraft Drive, Blacksburg, VA 24060, USA Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 91109, USA Department of Physics, University of Toronto, ON M5S 1A7, Canada Center for Ocean-Atmospheric Prediction Studies (COAPS), Florida State University, Tallahassee, FL 32306, USA Chemical data assimilation attempts to optimally use noisy observations along with imperfect model predictions to produce a better estimate of the chemical state of the atmosphere. It is widely accepted that a key ingredient for successful data assimilation is a realistic estimation of the background error distribution. Particularly important is the specification of the background error covariance matrix, which contains information about the magnitude of the background errors and about their correlations. Most models currently use diagonal background covariance matrices. As models evolve toward finer resolutions, the diagonal background covariance matrices become increasingly inaccurate, since they captures less of the spatial error correlations. This paper discusses an efficient computational procedure for constructing non-diagonal background error covariance matrices which account for the spatial correlations of errors. The benefits of using the non-diagonal covariance matrices for variational data assimilation with chemical transport models are illustrated. Beer, R., Glavich, T. A., and Rider, D. M.: Tropospheric emission spectrometer for the Earth Observing System's Aura satellite, Appl. Optics, 40(15), 2356–2367, 2001. Bey, I., Jacob, D. J., Yantosca, R. M., Logan, J. A., Field, B., Fiore, A. M., Li, Q., Liu, H., Mickley, L. J., and Schultz, M.: Global modeling of tropospheric chemistry with assimilated meteorology: Model description and evaluation, J. Geophys. Res., 106, 23073–23096, 2001. Bowman, K. W., Worden, J., Steck, T., Worden, H. 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