PC proxy: a method for dynamical tracer reconstruction
A detailed development of the principal component proxy method of dynamical tracer reconstruction is presented, including error analysis. The method works by correlating the largest principal components of a matrix representation of the transport dynamics with a set of sparse measurements. The Lyapunov spectrum was measured and used to quantify the lifetime of each principal component. The method was tested on the 500 K isentropic surface with stratospheric ozone concentration measurements from the Polar Aerosol and Ozone Measurement III satellite instrument during October and November 1998 and compared with the older proxy tracer method which works by correlating measurements with a single other tracer or proxy. Using a 60 day integration time and five (5) principal components, cross validation of globally reconstructed ozone and comparison with ozone sondes returned root-mean-square errors of 0.16 and 0.36 ppmv, respectively. This compares favourably with the classic proxy tracer method in which a passive tracer equivalent latitude field was used for the proxy and which returned RMS errors of 0.22 and 0.59 ppmv for cross-validation and sonde validation respectively. The method seems especially effective for shorter lived tracers and was far more accurate than the classic method at predicting ozone concentration in the Southern hemisphere over the same time period. It is also more effective when reconstruction is performed over the entire Earth rather than a single hemisphere allowing for seamless reconstruction of global fields.
KeywordsTransport dynamics Interpolation methods Satellite remote sensing Assimilation models Flow tracers Numerical analysis Ozone Applied linear algrebra
Thanks to the National Center for Environmental Prediction and the National Center for Atmospheric Research for the reanalysis data used in the simulations. Thanks also to World Ozone and Ultraviolet Data Center and Environment Canada for ozone sonde data. And thanks especially to my former colleagues at the Naval Research Laboratory for POAM III ozone data. Contour maps were created with Generic Mapping Tools (GMT) while scatter plots and historgrams were done in Open Office.
- 3.Golub GH, van Loan CF (1996) Matrix computations. Johns Hopkins University Press, BaltimoreGoogle Scholar
- 4.Hare EW, Carty EJ, Wardle DI (2000) Guide to the WMO/GAW world ozone data centre. Technical Report, Meteorological Service of Canada, Environment CanadaGoogle Scholar
- 6.Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, Iredell M, Saha S, White G, Woollen J, Zhu Y, Chelliah M, Ebisuzaki W, Higgins W, Janowiak J, Mo K, Ropelewski C, Wang J, Leetmaa A, Reynolds R, Jenne R, Joseph D (1996) The NCEP/NCAR 40-year reanalysis project. Bull Am Meteorol Soc 77:437–470CrossRefGoogle Scholar
- 7.Lehoucq RB, Scott JA (1996) An evaluation of software for computing eigenvalues of sparse nonsymmetric matrices. Technical Report MCS-P547-1195, Argonne National LaboratoryGoogle Scholar
- 8.Lucke RL, Korwan DR, Bevilacqua RM, Hornstein JS, Shettle EP, Chen DT, Daehler M, Lumpe JD, Fromm MD, Debrestian D, Neff B, Squire M, Knig-Langlo GJ, Davies J (1999) The Polar Ozone and Aerosol Measurement (POAM) III instrument and early validation results. J Geophys Res 104(D15):18785–18799CrossRefGoogle Scholar
- 10.Mills P (2004) Following the Vapour trail: a study of chaotic mixing of water vapour in the upper troposphere. Master’s thesis, University of BremenGoogle Scholar
- 12.Ott E (1993) Chaos in dynamical systems. Cambridge University Press, CambridgeGoogle Scholar
- 13.Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
- 14.Randall CE, Lumpe JD, Bevilacqua RM, Hoppel KW, Fromm MD, Salawitch RJ, Swartz WH, Lloyd SA, Kyro E, von der Gathen P, Claude H, Davies J, DeBacker H, Dier H, Molyneux MJ, Sanchoi J (2002) Reconstruction of three-dimensional ozone fields using POAM III during SOLVE. J Geophys Res 107(D20):8299–8312CrossRefGoogle Scholar