ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-9-8857-2009 Estimating trajectory uncertainties due to flow dependent errors in the atmospheric analysis Engström A. 1 Magnusson L. 1 Department of Meteorology, Stockholm University, Stockholm, Sweden 23 11 2009 9 22 8857 8867 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/9/8857/2009/acp-9-8857-2009.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/9/8857/2009/acp-9-8857-2009.pdf

The uncertainty of a calculated trajectory is dependent on the uncertainty in the atmospheric analysis. Using the Ensemble Transform method (originally adapted for ensemble forecasting) we sample the analysis uncertainty in order to create an ensemble of analyses where a trajectory is started from each perturbed analysis. This method, called the Ensemble analysis method (EA), is compared to the Initial spread method (IS), where the trajectory receptor point is perturbed in the horizontal and vertical direction to create a set of trajectories used to estimate the trajectory uncertainty. The deviation growth is examined for one summer and one winter month and for 15 different geographical locations. We find up to a 40% increase in trajectory deviation in the mid-latitudes using the EA method. A simple model for trajectory deviation growth speed is set up and validated. It is shown that the EA method result in a faster error growth compared to the IS method. In addition, two case studies are examined to qualitatively illustrate how the flow dependent analysis uncertainty can impact the trajectory calculations. We find a more irregular behavior for the EA trajectories compared to the IS trajectories and a significantly increased uncertainty in the trajectory origin. We conclude that by perturbing the analysis in agreement with the analysis uncertainties the error in backward trajectory calculations can be more consistently estimated.

 References Bannister, R N.: A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances, Q. J. Roy. Meteor. Soc., 134, 1951–1970, 2008. Bishop, C H. and Toth, Z.: Ensemble Transformation and Adaptive Observations, J. Atmos. Sci, 56, 1748–1765, 1999. Bofetta, G., Celani, A., Cencini, M., Lacorata, G., and Vulpiani, A.: Nonasymptotic properties of transport and mixing, Chaos, 10, 50–60, 2000. Buizza, R., Leutbecher, M., and Isaksen, L.: Potential use of an ensemble of analyses in the ECMWF Ensemble Prediction System, Q. J. Roy. Meteor. Soc., 134, 2051–2066, 2008. Corazza, M., ad~D J Patil, E K., Szunyogh, I., Hunt, B R., Ott, E., and Yorke, J A.: Use of the breeding technique to estimate the structure of the analysis "errors of the day", Nonlinear Proc. Geophys., 10, 233–243, 2003. Draxler, R R.: Evaluation of an Ensemble Dispersion Calculation, J. App. Meteorol., 42, 308–317, 2002. Harris, J M., Drexler, R R., and Oltmans, S J.: Trajectory model sensitivity to differences in input data and vertical transport method, J. Geophys. Res., 110, D14109, doi:10.1029/2004JD005750, 2005. Houtekamer, P L. and Mitchell, H L.: Data Assimilation Using an Ensemble Kalman Filter Technique, Mon. Weather Rev., 126, 796–811, 1998. Kalnay, E., Kanamitsu, M., Kistler, R., Collins, W., Deaven, D., Gandin, L., Iredell, M., Saha, S., White, G., Woollen, J., Zhu, Y., Leetmaa, A., Reynolds, R., Chelliah, M., Ebisuzaki, W., Higgins, W., Janowiak, J., Mo, K., Ropelewski, C., Wang, J., Jenne, R., , and Joseph, D.: The NCEP/NCAR 40-Year Reanalysis Project, Am. Meteor. Soc., 77, 437–471, 1996. Magnusson, L., Nycander, J., and Källen, E.: Flow-dependent versus flow-independent initial perturbations for ensemble forecasting, Tellus, 61A, 194–209, 2009. McLay, J G., Bishop, C H., and Reynolds, C A.: Evaluation of the Ensemble Transform Analysis Perturbation Scheme at NRL, Mon. Weather Rev., 136, 1093–1108, 2008. Merrill, J T., Bleck, R., and Avila, L.: Modeling Atmospheric Transport to the Marshall Island, J. Geophys. Res., 90, 12927–12936, 1985. Palmer, T N.: Extended-Range Atmospheric Prediction and the Lorenz Model, B. Am. Meteor. Soc., 74, 49–66, 1993. Palmer, T N., Buizza, R., Hagedorn, R., Lawrence, A., Leutbecher, M., and Smith, L.: Ensemble prediction: a pedagogical perspective, Newsletter 106, ECMWF, 2006. Scheele, M P. and Siegmund, P C.: Estimating errors in trajectory forecasts using ensemble predictions, Am. Meteor. Soc., 1223–1232, 2001. Stohl, A.: Computation, accuracy and applications of trajectories – A review and bibliography, Atmos. Environ., 32, 947–966, 1998. Straume, A G.: A More Extensive Investigation of the Use of Ensemble Forecasts for Dispersion Model Evaluation, J. Appl. Meteorol., 40, 425–445, 2001. Toth, Z. and Kalnay, E.: Ensemble Forecasting at NCEP and the Breeding Method, Mon. Weather Rev., 125, 3297–3319, 1997. Uppala, S M., Kållberg, P W., Simmons, A J., Andrae, U., Bechtold, V. D C., Fiorino, M., Gibson, J K., Haseler, J., Hernandez, A., Kelly, G A., Li, X., Onogi, K., Saarinen, S., Sokka, N., Allan, R P., Andersson, E., Arpe, K., Balmaseda, M A., Beljaars, A. C M., Berg, L. V D., Bidlot, J., Bormann, N., Caires, S., Chevallier, F., Dethof, A., Dragosavac, M., Fisher, M., Fuentes, M., Hagemann, S., Hólm, E., Hoskins, B J., Isaksen, L., Janssen, P. A. E M., Jenne, R., McNally, A P., Mahfouf, J.-F., Morcrette, J.-J., Rayner, N A., Saunders, R W., Simon, P., Sterl, A., Trenberth, K E., Untch, A., Vasiljevic, D., Viterbo, P., and Woollen, J.: The ERA-40 Re-Analysis, Q. J. Roy. Meteor. Soc., 131, 2961–3012, 2005. Verver, G H L., Sikka, D R., Lobert, J M., Stossmeister, G., and Zachariasse, M.: Overview of the meteorological conditions and atmospheric transport porcesses during INDOEX 1999, J. Geophys. Res., 106, 28399–28413, 2001. Wang, X. and Bishop, C.: A Comparison of Breeding and Ensemble Transform Kalman Filter Ensemble Forecast Schemes, J. Atmos. Sci., 60, 1140–1158, 2003. Wei, M., Toth, Z., Wobus, R., and Zhu, Y.: Initial Perturbations Based on the Ensemble Transform (ET) Technique in the NCEP Global Ensemble Forecast Systems, Tellus, 60A, 62–79, 2008.