References

ACP

Atmospheric Chemistry and Physics

ACP

1680-7324

Copernicus GmbH

Göttingen, Germany

10.5194/acp-7-6085-2007

Seeking for the rational basis of the Median Model: the optimal combination of multi-model ensemble results

Riccio

¹ Giunta

¹ Galmarini

Dept. of Applied Science, University of Naples "Parthenope", Napoli, Italy

European Commission – DG Joint Research Centre, Institute for Environment and Sustainability, Ispra, Italy

11 12 2007

7 24 6085 6098

This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

This article is available from http://www.atmos-chem-phys.net/7/6085/2007/acp-7-6085-2007.html

The full text article is available as a PDF file from http://www.atmos-chem-phys.net/7/6085/2007/acp-7-6085-2007.pdf

In this paper we present an approach for the statistical analysis of multi-model ensemble results. The models considered here are operational long-range transport and dispersion models, also used for the real-time simulation of pollutant dispersion or the accidental release of radioactive nuclides. <br><br> We first introduce the theoretical basis (with its roots sinking into the Bayes theorem) and then apply this approach to the analysis of model results obtained during the ETEX-1 exercise. We recover some interesting results, supporting the heuristic approach called "median model", originally introduced in Galmarini et al. (2004a, b). <br><br> This approach also provides a way to systematically reduce (and quantify) model uncertainties, thus supporting the decision-making process and/or regulatory-purpose activities in a very effective manner.

References 1

Berliner, L. M.: Physical-statistical modeling in geophysics, J Geophys Res., 108, 8776, doi:10.1029/2002JD002865, 2003.

Clyde, M. A.: Bayesian model averaging and model search strategies (with Discussion), in: Bayesian Statistics 6, edited by: Bernardo, J. M. et al., 157–185, Oxford University Press, Oxford, 1999.

Clyde, M. A. and George, E. I.: Flexible empirical Bayes estimation for wavelets, J. R. Stat. Soc. Ser. A–G, 62, 681–698, 2000.

Coelho, C. A. S., Pezzulli, S., Balmaseda, M., Doblas-Reyes, F. J., and Stephenson, D. B.: Forecast Calibration and Combination: A Simple Bayesian Approach for ENSO, J. Climate, 17, 1504–1516, 2004.

Cover, T. M. and Thomas, J. A.: Elements of Information Theory, Wiley, 1991.

Delle Monache, L. and Stull, R. B.: An ensemble air-quality forecast over western Europe during an ozone episode, Atmos. Environ., 37, 3469–3474, 2003.

Delle Monache, L., Deng, X., Zhou, Y., and Stull, R.: Ozone ensemble forecasts: 1. A new ensemble design, J Geophys Res., 111, D05307, doi:10.1029/2005JD006310, 2006a.

Delle Monache, L., Nipen, T., Deng, X., Zhou, Y., and Stull, R. B.: Ozone ensemble forecasts: 2. A Kalman filter predictor bias correction, J Geophys Res., 111, D05308, doi:10.1029/2005JD006311, 2006b

Delle Monache, L., Hacker, J. P., Zhou, Y., Deng, X., and Stull, R. B.: Probabilistic aspects of meteorological and ozone regional ensemble forecasts, J Geophys Res., 111, D24307, doi:10.1029/2005JD006917, 2006c.

Dijkstra, T. K.: On Model Uncertainty and its Statistical Implications, Springer Verlag, Berlin, 1988.

Fritch, J. M., Hilliker, J., Ross, J., and Vislocky, R. L.: Model consensus, Weather Forecast, 15, 571–582, 2000.

Galmarini, S., Bianconi, R., Bellasio, R., and Graziani, G.: Forecasting consequences of accidental releases from ensemble dispersion modelling, J. Environ. Radioactiv., 57, 203–219, 2001.

Galmarini, S., Bianconi, R., Klug, W., Mikkelsen, T., Addis, R., Andronopoulos, S., Astrup, P., Baklanov, A., Bartniki, J., Bartzis, J. C., Bellasio, R., Bompay, F., Buckley, R., Bouzom, M., Champion, H., D'Amours, R., Davakis, E., Eleveld, H., Geertsema, G. T., Glaab, H., Kollax, M., Ilvonen, M., Manning, A., Pechinger, U., Persson, C., Polreich, E., Potemski, S., Prodanova, M., Saltbones, J., Slaper, H.,Sofief, M. A., Syrakov, D., Sorensen, J. H., Van der Auwera, L., Valkama, I., and Zelazny, R.: Ensemble dispersion forecasting–Part I: concept, approach and indicators, Atmos. Environ., 38, 4607–4617, 2004a.

Galmarini, S., Bianconi, R., Addis, R., Andronopoulos, S., Astrup, P., Bartzis, J. C., Bellasio, R., Buckley, R.,Champion, H., Chino, M., D'Amours, R., Davakis, E., Eleveld, H., Glaab, H., Manning, A., Mikkelsen, T., Pechinger, U., Polreich, E., Prodanova, M., Slaper, H., Syrakov, D., Terada, H., and Van der Auwera, L.: Ensemble dispersion forecasting–Part II: application and evaluation, Atmos. Environ., 38, 4619–4632, 2004b.

Gelman, A. and Rubin, D. B.: Inference from iterative simulation using multiple sequences, Stat. Sci., 7, 457–472, 1992.

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B.: Bayesian Data Analysis, Chapman and Hall/CRC, Boca Raton, Florida, 2003.

Geman, S. and Geman, D.: Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721–741, 1984.

Gilks, W. R., Richardson, S., and Spiegelhalter, D. J.: Markov Chain Monte Carlo in Practice, Chapman and Hall/CRC, Boca Raton, Florida, 1996.

Girardi, F., Graziani, G., van Veltzen, D., Galmarini, S., Mosca, S., Bianconi, R., Bellasio, R., and Klug, W.: The ETEX project. EUR Report 181-43 EN. Office for official publications of the European Communities, Luxembourg, 108pp., 1998.

Grimit, E. P. and Mass, C. F.: Initial results of a mesoscale short-range ensemble forecasting system over the Pacific Northwest, Weather Forecast, 17, 192–205, http://isis.apl.washington.edu/bma/index.jsp, 2002.

Hyvärinen, A. and Oja, E.: Independent Component Analysis: Algorithms and Applications, Neural Networks, 13, 411–430, 2000.

Hou, D., Kalnay, E., and Droegemeier, K. K.: Objective verification of the SAMEX`98 ensemble forecast, Mon. Weather Rev., 129, 73–91, 2001.

Jeffreys, H.: Theory of Probability, 3rd Edition, Oxford University Press, 1961.

Krishnamurti, T. N., Kishtawal, C. M., Zhang, Z., LaRow, T., Bachiochi, D., Williford, E., Gadgil, S., and Surendran, S.: Multimodel ensemble forecasts for weather and seasonal climate. Mon. Weather Rev., 116, 907–920, 2000.

Mallet, V. and Sportisse, B: Ensemble-based air quality forecasts: A multimodel approach applied to ozone, J Geophys Res., 111, D18302, doi:10.1029/2005JD006675, 2006.

Molteni, F., Buizza, R., Palmer, T. N., and Petroliagis, T.: The ECMWF ensemble system: Methodology and validation, Q. J. Roy. Meteor. Soc., 122, 73–119, 1996.

Pagowski, M., Grell, G. A., McLeen, S. A., et al., 2005: A simple method to improve ensemble-based ozone forecasts, Geophys. Res. Lett., 32, L07814, doi:10.1029/2004GL022305

Pagowski, M., Grell, G. A., Devenyi, D., Peckham, S. E., McKeen, S. A., Gong, W., Delle Monache, L., McHenry, J. N., McQueen, J., and Lee, P.: Application of dynamic linear regression to improve the skill of ensemble-based deterministic ozone forecasts, Atmos. Environ., 40, 3240–3250, 2006a

Pagowski, M. and Grell, G. A.: Ensemble-based ozone forecasts: Skill and economic value, J Geophys Res., 111, D23S30, doi:10.1029/2006JD007124, 2006b.

Papoulis, A.: Probability, Random Variables, and Stochastic Processes, Mc-Graw-Hill, 1991.

Raftery, A. E., Madigan, D. and Hoeting, J. A.: Model selection and accounting for model uncertainty in linear regression models, J. Am. Stat. Assoc., 92, 179–191, 1997.

Raftery, A. E.and Zheng, Y.: Long-run performance of Bayesian model averaging, J. Am. Stat. Assoc., 98, 931–938, 2003.

Raftery, A. E., Gneiting, T., Balabdaoui, F., and Polakowski, M.: Using Bayesian Model Averaging to Calibrate Forecast Ensembles, Mon. Weather Rev., 133, 1155–1174, 2005.

Roberts, W. R.: Markov chain concepts related to sampling algorithms, in: Markov Chain Monte Carlo in Practice, edited by: Gilks, W. R., Richardson, S., and Spiegelhalter, D. J., Chapman and Hall, 45–57, 1996.

Toth, Z. and Kalnay, E.: Ensemble forecasting at the NMC: The generation of perturbations, B Am. Meteorol. Soc., 74, 2317–2330, 1993.

Viallefont, V., Raftery, A. E., and Richardson, S.: Variable selection and Bayesian model averaging in case-control studies, Statistics in Medicine, 20, 3215–3230, 2001.

Whitaker, J. S. and Loughe, A. F.: The relationship between Ensemble Spread and Ensemble Mean Skill, Mon. Weather Rev., 126, 3292–3302, 1998.

Zhang, F., Bei, N., Nielsen-Gammon, J. W., Li, G., Zhang, R., Stuart, A., and Aksoy, A.: Impacts of meteorological uncertainties on ozone pollution predictability estimated through meteorological and photochemical ensemble forecasts, J Geophys Res., 112, D04304, doi:10.1029/2006JD007429, 2007.