Editorial Type:
Article
Article Type:
Research Article

Confidence Intervals and Significance Tests for Spherical Data Derived from Feature Tracking

K. I. Hodges Environmental Systems Science Center, University of Reading, Reading, United Kingdom

Search for other papers by K. I. Hodges in
Current site
Google Scholar
PubMed Close
Print Publication:
01 May 2008
DOI:
https://doi.org/10.1175/2007MWR2299.1
Page(s):
1758–1777
Restricted access

Abstract

A methodology is described that improves the efficiency with which statistical estimates of the distribution and mean attributes of dynamical weather systems, such as extratropical cyclones and tropical easterly waves, are derived from ensembles of the system trajectories using spherical kernel estimators. The improvement in the application of the spherical kernel estimators facilitates the use of the resampling methodology to estimate confidence intervals for weather system climatologies and to perform significance tests for the comparison between estimates derived from separate samples, for example, when the track data are partitioned with respect to teleconnection indices. The improvement in the statistical estimation makes use of spherical quad tree data structures based on a hierarchical decomposition of the sphere into spherical triangles into which the data and estimation points are partitioned. Examples are shown of the application of the new methodology to extratropical cyclones identified in reanalysis data of confidence intervals for the climatology and significance tests for differences between the positive and negative phases of the North Atlantic Oscillation teleconnection.

Corresponding author address: Kevin Hodges, ESSC, University of Reading, Harry Pitt Building, 3 Earley Gate, Whiteknights, Reading RG6 6AL, United Kingdom. Email: kih@mail.nerc-essc.ac.uk

Abstract

A methodology is described that improves the efficiency with which statistical estimates of the distribution and mean attributes of dynamical weather systems, such as extratropical cyclones and tropical easterly waves, are derived from ensembles of the system trajectories using spherical kernel estimators. The improvement in the application of the spherical kernel estimators facilitates the use of the resampling methodology to estimate confidence intervals for weather system climatologies and to perform significance tests for the comparison between estimates derived from separate samples, for example, when the track data are partitioned with respect to teleconnection indices. The improvement in the statistical estimation makes use of spherical quad tree data structures based on a hierarchical decomposition of the sphere into spherical triangles into which the data and estimation points are partitioned. Examples are shown of the application of the new methodology to extratropical cyclones identified in reanalysis data of confidence intervals for the climatology and significance tests for differences between the positive and negative phases of the North Atlantic Oscillation teleconnection.

Corresponding author address: Kevin Hodges, ESSC, University of Reading, Harry Pitt Building, 3 Earley Gate, Whiteknights, Reading RG6 6AL, United Kingdom. Email: kih@mail.nerc-essc.ac.uk

Save
Cover Monthly Weather Review
Monthly Weather Review

  • Annamalai, H., J. M. Slingo, K. R. Sperber, and K. Hodges, 1999: The mean evolution and variability of the Asian summer monsoon: Comparison of ECMWF and NCEP–NCAR reanalyses. Mon. Wea. Rev., 127 , 1157–1186.

    • Search Google Scholar
    • Export Citation

  • Atmospheric Model Intercomparison Project, 1996: AMIP II guidelines. Atmospheric Model Intercomparison Project Newsletter, No. 8, AMIP Project Office, Livermore, CA, 24 pp. [Available online at http://www-pcmdi.llnl.gov/projects/amip/NEWS/amipnl8.php.].

    • Search Google Scholar
    • Export Citation

  • Basney, J., and M. Livny, 1999: Deploying a high throughput computing cluster. Architectures and Systems, R. Buyya, Ed., Vol. 1, High Performance Cluster Computing, Prentice Hall PTR, 116–134.

    • Search Google Scholar
    • Export Citation

  • Baumgardner, J. R., and P. O. Frederickson, 1985: Icosahedral discretization of the two-sphere. SIAM J. Numer. Anal., 22 , 1107–1115.

    • Search Google Scholar
    • Export Citation

  • Bengtsson, L., K. I. Hodges, and E. Roeckner, 2006: Storm tracks and climate change. J. Climate, 19 , 3518–3543.

  • Bengtsson, L., K. I. Hodges, and M. Esch, 2007a: Tropical cyclones in a T159 resolution global climate model: Comparison with observations and reanalyses. Tellus, 59A , 396–416.

    • Search Google Scholar
    • Export Citation

  • Bengtsson, L., K. I. Hodges, M. Esch, N. Keenlyside, L. Kornblueh, J-J. Luo, and T. Yamagata, 2007b: How may tropical cyclones change in a warmer climate? Tellus, 59A , 539–561.

    • Search Google Scholar
    • Export Citation

  • Blackmon, M. L., 1976: A climatological spectral study of the 500 mb geopotential height of the Northern Hemisphere. J. Atmos. Sci., 33 , 1607–1623.

    • Search Google Scholar
    • Export Citation

  • Blender, R., K. Fraedrich, and F. Lunkeit, 1997: Identification of cyclone-track regimes in the North Atlantic. Quart. J. Roy. Meteor. Soc., 123 , 727–741.

    • Search Google Scholar
    • Export Citation

  • Bromwich, D. H., R. L. Fogt, K. I. Hodges, and J. E. Walsh, 2007: A tropospheric assessment of the ERA-40, NCEP and JRA-25 global reanalyses in the polar regions. J. Geophys. Res., 112 .D10111, doi:10.1029/2006JD007859.

    • Search Google Scholar
    • Export Citation

  • Davidson, R., and J. G. MacKinnon, 2003: Econometric Theory and Methods. Oxford University Press, 768 pp.

  • DiCiccio, T. J., and B. Efron, 1996: Bootstrap confidence intervals. Stat. Sci., 11 , 189–228.

  • Dutton, G., 1990: Locational properties of quaternary triangular meshes. Proc. Fourth Int. Symp. on Spatial Data Handling, Zurich, Switzerland, International Geographical Union, 901–910.

  • Efron, B., and R. J. Tibshirani, 1993: An Introduction to the Bootstrap. Chapman and Hall/CRC, 436 pp.

  • Fekete, G., 1990: Rendering and managing spherical data with sphere quadtrees. Proc. First IEEE Conf. on Visualization, San Francisco, CA, IEEE, 176–186.

    • Search Google Scholar
    • Export Citation

  • Fekete, G., A. Szalay, and J. Gray, 2003: Htm2: Spatial toolkit for the virtual observatory. Astronomical Data Analysis Software and Systems XIII, F. Ochsenbein, M. Allen, and D. Egret, Eds., Astronomical Society of the Pacific Conference Series, Vol. 314, Astronomical Society of the Pacific, 289–292.

    • Search Google Scholar
    • Export Citation

  • Froude, L. S. R., L. Bengtsson, and K. I. Hodges, 2007a: The predictability of extratropical storm tracks and the sensitivity of their prediction to the observing system. Mon. Wea. Rev., 135 , 315–333.

    • Search Google Scholar
    • Export Citation

  • Froude, L. S. R., L. Bengtsson, and K. I. Hodges, 2007b: The prediction of extratropical storm tracks by the ECMWF and NCEP ensemble prediction system. Mon. Wea. Rev., 135 , 2545–2567.

    • Search Google Scholar
    • Export Citation

  • Gargantini, I., 1982: An effective way to represent quadtrees. Commun. Assoc. Comput. Mach., 25 , 905–910.

  • Goodchild, M. F., and Y. Shiren, 1992: A hierarchical spatial data structure for global geographic information systems. CVGIP: Graphical Models Image Process., 54 , 31–44.

    • Search Google Scholar
    • Export Citation

  • Greeves, C. Z., V. D. Pope, R. A. Stratton, and G. M. Martin, 2007: Representation of Northern Hemisphere winter storm tracks in climate models. Climate Dyn., 28 , 683–702.

    • Search Google Scholar
    • Export Citation

  • Hayden, B. P., 1981: Cyclone occurrence mapping: Equal area or raw frequencies? Mon. Wea. Rev., 109 , 168–172.

  • Hodges, K. I., 1994: A general method for tracking analysis and its application to meteorological data. Mon. Wea. Rev., 122 , 2573–2586.

    • Search Google Scholar
    • Export Citation

  • Hodges, K. I., 1995: Feature tracking on the unit sphere. Mon. Wea. Rev., 123 , 3458–3465.

  • Hodges, K. I., 1996: Spherical nonparametric estimators applied to the UGAMP model integration for AMIP. Mon. Wea. Rev., 124 , 2914–2932.

    • Search Google Scholar
    • Export Citation

  • Hodges, K. I., 1999a: Adaptive constraints for feature tracking. Mon. Wea. Rev., 127 , 1362–1373.

  • Hodges, K. I., 1999b: Extension of spherical nonparametric estimators to nonisotropic kernels: An oceanographic application. Mon. Wea. Rev., 127 , 214–227.

    • Search Google Scholar
    • Export Citation

  • Hodges, K. I., and C. Thorncroft, 1997: Distributions and statistics of African mesoscale convective weather systems based on the ISCCP Meteosat imagery. Mon. Wea. Rev., 125 , 2821–2837.

    • Search Google Scholar
    • Export Citation

  • Hodges, K. I., B. J. Hoskins, J. Boyle, and C. Thorncroft, 2003: A comparison of recent reanalysis datasets using objective feature tracking: Storm tracks and tropical easterly waves. Mon. Wea. Rev., 131 , 2012–2037. Corrigendum, 132, 1325–1327.

    • Search Google Scholar
    • Export Citation

  • Hogg, A. M., P. D. Killworth, J. R. Blundell, and W. K. Dewar, 2005: Mechanisms of decadal variability of the wind-driven ocean circulation. J. Phys. Oceanogr., 35 , 512–531.

    • Search Google Scholar
    • Export Citation

  • Hopsch, S. B., C. Thorncroft, K. I. Hodges, and A. Aiyyer, 2007: West African storm tracks and their relationship to Atlantic tropical cyclones. J. Climate, 20 , 2468–2483.

    • Search Google Scholar
    • Export Citation

  • Hoskins, J. B., and K. I. Hodges, 2002: New perspectives on the Northern Hemisphere winter storm tracks. J. Atmos. Sci., 59 , 1041–1061.

    • Search Google Scholar
    • Export Citation

  • Hoskins, J. B., and K. I. Hodges, 2005: A new perspective on Southern Hemisphere storm tracks. J. Climate, 18 , 4108–4129.

  • Hurrell, J., Y. Kushnir, and M. Visbeck, 2001: The North Atlantic Oscillation. Science, 291 , 603–605.

  • Leckebusch, G. C., and U. Ulbrich, 2004: On the relationship between cyclones and extreme windstorm events over Europe under climate change. Global Planet. Change, 44 , 181–193.

    • Search Google Scholar
    • Export Citation

  • Lee, M., and H. Samet, 2000: Navigating through triangle meshes implemented as linear quadtrees. ACM Trans. Graphics, 19 , 79–121.

    • Search Google Scholar
    • Export Citation

  • Lim, E-P., and I. Simmonds, 2007: Southern Hemisphere winter extratropical cyclone characteristics and vertical organization observed with the ERA-40 data in 1979–2001. J. Climate, 20 , 2675–2690.

    • Search Google Scholar
    • Export Citation

  • Livezey, R. E., 1985: Statistical analysis of general circulation model climate simulation: Sensitivity and prediction experiments. J. Atmos. Sci., 42 , 1139–1150.

    • Search Google Scholar
    • Export Citation

  • Livezey, R. E., and W. Y. Chen, 1983: Statistical field significance and its determination by Monte Carlo techniques. Mon. Wea. Rev., 111 , 46–59.

    • Search Google Scholar
    • Export Citation

  • Murray, R. J., and I. Simmonds, 1991: A numerical scheme for tracking cyclone centres from digital data. Part I: Development and operation of the scheme. Aust. Meteor. Mag., 39 , 155–166.

    • Search Google Scholar
    • Export Citation

  • Neale, R. B., and B. J. Hoskins, 2000: A standard test for AGCMs including their physical parameterizations. I: The proposal. Atmos. Sci. Lett., 1 , 101–107.

    • Search Google Scholar
    • Export Citation

  • Nicholls, N., 2001: The insignificance of significance testing. Bull. Amer. Meteor. Soc., 82 , 981–986.

  • Raible, C. C., and R. Blender, 2004: Northern Hemisphere midlatitude cyclone variability in GCM simulations in different ocean representations. Climate Dyn., 22 , 239–248.

    • Search Google Scholar
    • Export Citation

  • Raible, C. C., M. Yoshimori, T. F. Stocker, and C. Casty, 2007: Extreme midlatitude cyclones and their implications for precipitation and wind speed extremes in simulations of the Maunder Minimum versus present day conditions. Climate Dyn., 28 , 409–423.

    • Search Google Scholar
    • Export Citation

  • Raible, C. C., P. Della-Marta, C. Schwierz, H. Wernli, and R. Blender, 2008: Northern Hemisphere extratropical cyclones: A comparison of detection and tracking methods and different reanalyses. Mon. Wea. Rev., 136 , 880–897.

    • Search Google Scholar
    • Export Citation

  • Sadourny, R., A. Arakawa, and Y. Mintz, 1968: Integration of the nondivergent barotropic vorticity equation with an icosahedral-hexagonal grid for the sphere. Mon. Wea. Rev., 96 , 351–356.

    • Search Google Scholar
    • Export Citation

  • Sahr, K., D. White, and A. J. Kimerling, 2003: Geodesic discrete global grid systems. Cartogr. Geogr. Info. Sci., 30 , 121–134.

  • Samet, H., 1990a: Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS. Addison-Wesley, 507 pp.

  • Samet, H., 1990b: The Design and Analysis of Spatial Data Structures. Addison-Wesley, 510 pp.

  • Schröder, P., and W. Sweldens, 1995: Spherical wavelets: Efficiently representing functions on the sphere. Proc. 22nd SIGGRAPH Conf. on Computer Graphics and Interactive Techniques, Los Angeles, CA, Association for Computing Machinery, 161–172.

    • Search Google Scholar
    • Export Citation

  • Silverman, B. W., 1986: Density Estimation for Statistics and Data Analysis. Chapman and Hall, 175 pp.

  • Stuhne, G. R., and W. R. Peltier, 1996: Vortex erosion and amalgamation in a new model of large scale flow on the sphere. J. Comput. Phys., 128 , 58–81.

    • Search Google Scholar
    • Export Citation

  • Taylor, K. E., 1986: An analysis of the biases in traditional cyclone frequency maps. Mon. Wea. Rev., 114 , 1481–1490.

  • Tegmark, M., 1996: An icosahedron based method for pixelizing the celestial sphere. Astrophys. J. Lett., 470 , 81–84.

  • Thorncroft, C., and K. I. Hodges, 2001: African easterly wave variability and its relationship to Atlantic tropical cyclone activity. J. Climate, 14 , 1166–1179.

    • Search Google Scholar
    • Export Citation

  • Thuburn, J., 1997: A PV-based shallow-water model on a hexagonal–icosahedral grid. Mon. Wea. Rev., 125 , 2328–2347.

  • Wang, J., J. S. Rao, and J. Shao, 1997: Weighted jackknife-after-bootstrap: A heuristic approach. Proc. 1997 Winter Simulation Conf., Atlanta, GA, IEEE, 240–245.

  • Wang, X. L., V. R. Swail, and F. W. Zwiers, 2006: Climatology and changes of extratropical cyclone activity: Comparison of ERA-40 with NCEP–NCAR reanalysis for 1958–2001. J. Climate, 19 , 3145–3166.

    • Search Google Scholar
    • Export Citation

  • White, R. A., and S. W. Stemwedel, 1992: The quadrilateralized spherical cube and quad-tree for all sky data. Astronomical Data Analysis Software and Systems I, D. M. Worrall, C. Biemesderfer, and J. Barnes, Eds., ASP Conference Series, Vol. 25, Astronomical Society of the Pacific, 379–381.

    • Search Google Scholar
    • Export Citation

  • Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences: An Introduction. Academic Press, 467 pp.

  • Wilks, D. S., 1997: Resampling hypothesis tests for autocorrelated fields. J. Climate, 10 , 65–82.

  • Xu, K-M., 2006: Using the bootstrap method for a statistical significance test of differences between summary histograms. Mon. Wea. Rev., 134 , 1442–1453.

    • Search Google Scholar
    • Export Citation

  • Zwiers, F. W., 1990: The effect of serial correlation on statistical inferences made with resampling procedures. J. Climate, 3 , 1452–1461.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1410 885 299
PDF Downloads 394 57 6