The Effects of Sampling Errors on the EnKF Assimilation of Inner-Core Hurricane Observations

Jonathan Poterjoy Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

Search for other papers by Jonathan Poterjoy in
Current site
Google Scholar
PubMed
Close
,
Fuqing Zhang Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

Search for other papers by Fuqing Zhang in
Current site
Google Scholar
PubMed
Close
, and
Yonghui Weng Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

Search for other papers by Yonghui Weng in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Atmospheric data assimilation methods that estimate flow-dependent forecast statistics from ensembles are sensitive to sampling errors. This sensitivity is investigated in the context of vortex-scale hurricane data assimilation by cycling an ensemble Kalman filter to assimilate observations with a convection-permitting mesoscale model. In a set of numerical experiments, airborne Doppler radar observations are assimilated for Hurricane Katrina (2005) using an ensemble size that ranges from 30 to 300 members, and a varying degree of covariance inflation through relaxation to the prior. The range of ensemble sizes is shown to produce variations in posterior storm structure that persist for days in deterministic forecasts, with the most substantial differences appearing in the vortex outer-core wind and pressure fields. Ensembles with 60 or more members converge toward similar axisymmetric and asymmetric inner-core solutions by the end of the cycling, while producing qualitatively similar sample correlations between the state variables. Though covariance relaxation has little impact on model variables far from the observations, the structure of the inner-core vortex can benefit from a more optimal tuning of the relaxation coefficient. Results from this study provide insight into how sampling errors may affect the performance of an ensemble hurricane data assimilation system during cycling.

Corresponding author address: Dr. Fuqing Zhang, Department of Meteorology, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. E-mail: fzhang@psu.edu

Abstract

Atmospheric data assimilation methods that estimate flow-dependent forecast statistics from ensembles are sensitive to sampling errors. This sensitivity is investigated in the context of vortex-scale hurricane data assimilation by cycling an ensemble Kalman filter to assimilate observations with a convection-permitting mesoscale model. In a set of numerical experiments, airborne Doppler radar observations are assimilated for Hurricane Katrina (2005) using an ensemble size that ranges from 30 to 300 members, and a varying degree of covariance inflation through relaxation to the prior. The range of ensemble sizes is shown to produce variations in posterior storm structure that persist for days in deterministic forecasts, with the most substantial differences appearing in the vortex outer-core wind and pressure fields. Ensembles with 60 or more members converge toward similar axisymmetric and asymmetric inner-core solutions by the end of the cycling, while producing qualitatively similar sample correlations between the state variables. Though covariance relaxation has little impact on model variables far from the observations, the structure of the inner-core vortex can benefit from a more optimal tuning of the relaxation coefficient. Results from this study provide insight into how sampling errors may affect the performance of an ensemble hurricane data assimilation system during cycling.

Corresponding author address: Dr. Fuqing Zhang, Department of Meteorology, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. E-mail: fzhang@psu.edu
Save
  • Aberson, S. D., B. L. Black, R. W. Burpee, J. J. Cione, C. W. Landsea, and F. D. Marks, 2006: Thirty years of tropical cyclone research with the NOAA P-3 aircraft. Bull. Amer. Meteor. Soc., 87, 10391055, doi:10.1175/BAMS-87-8-1039.

    • Search Google Scholar
    • Export Citation
  • Aksoy, A., 2013: Storm-relative observations in tropical cyclone data assimilation with an ensemble Kalman filter. Mon. Wea. Rev., 141, 506522, doi:10.1175/MWR-D-12-00094.1.

    • Search Google Scholar
    • Export Citation
  • Aksoy, A., D. C. Dowell, and C. Snyder, 2009: A multicase comparative assessment of the ensemble Kalman filter for assimilation of radar observations. Part I: Storm-scale analyses. Mon. Wea. Rev., 137, 18051824, doi:10.1175/2008MWR2691.1.

    • Search Google Scholar
    • Export Citation
  • Aksoy, A., S. Lorsolo, T. Vukicevic, K. J. Sellwood, S. D. Aberson, and F. Zhang, 2012: The HWRF Hurricane Ensemble Data Assimilation System (HEDAS) for high-resolution data: The impact of airport Doppler radar observations in an OSSE. Mon. Wea. Rev., 140, 18431862, doi:10.1175/MWR-D-11-00212.1.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2009: Spatially and temporally varying adaptive covariance inflation for ensemble filters. Tellus, 61A, 7283, doi:10.1111/j.1600-0870.2008.00361.x.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., and S. L. Anderson, 1999: A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Mon. Wea. Rev., 127, 27412758, doi:10.1175/1520-0493(1999)127<2741:AMCIOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Barker, D. M., W. Huang, Y.-R. Guo, A. J. Bourgeois, and Q. N. Xiao, 2004: A three-dimensional variational data assimilation system for MM5: Implementation and initial results. Mon. Wea. Rev., 132, 897914, doi:10.1175/1520-0493(2004)132<0897:ATVDAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chen, Y., and C. Snyder, 2007: Assimilating vortex position with an ensemble Kalman filter. Mon. Wea. Rev., 135, 18281845, doi:10.1175/MWR3351.1.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., 1995: On-line estimation of error covariance parameters for atmospheric data assimilation. Mon. Wea. Rev., 123, 11281145, doi:10.1175/1520-0493(1995)123<1128:OLEOEC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dowell, D. C., F. Zhang, L. J. Wicker, C. Snyder, and N. A. Crook, 2004: Wind and thermodynamic retrievals in the 17 May 1981 Arcadia, Oklahoma, supercell: Ensemble Kalman filter experiments. Mon. Wea. Rev., 132, 19822005, doi:10.1175/1520-0493(2004)132<1982:WATRIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99, 10 14310 162, doi:10.1029/94JC00572.

    • Search Google Scholar
    • Export Citation
  • Fujita, T., D. J. Stensrud, and D. C. Dowell, 2007: Surface data assimilation using an ensemble Kalman filter approach with initial condition and model physics uncertainties. Mon. Wea. Rev., 135, 18461868, doi:10.1175/MWR3391.1.

    • Search Google Scholar
    • Export Citation
  • Gall, R., J. Franklin, F. Marks, E. N. Rappaport, and F. Toepfer, 2013: The Hurricane Forecast Improvement Project. Bull. Amer. Meteor. Soc., 94, 329343, doi:10.1175/BAMS-D-12-00071.1.

    • Search Google Scholar
    • Export Citation
  • Gaspari, G., and S. E. Cohn, 1999: Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc., 125, 723757, doi:10.1002/qj.49712555417.

    • Search Google Scholar
    • Export Citation
  • Green, B. W., and F. Zhang, 2013: Impacts of air–sea flux parameterizations on the intensity and structure of tropical cyclones. Mon. Wea. Rev., 141, 23082324, doi:10.1175/MWR-D-12-00274.1.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. H., and J. S. Whitaker, 2001: Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter. Mon. Wea. Rev., 129, 27762790, doi:10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Houze, R. A., S. S. Chen, B. F. Smull, W.-C. Lee, and M. M. Bell, 2007: Hurricane intensity and eyewall replacement. Science, 315, 12351239, doi:10.1126/science.1135650.

    • Search Google Scholar
    • Export Citation
  • Huang, X.-Y., and Coauthors, 2009: Four-dimensional variational data assimilation for WRF: Formulation and preliminary results. Mon. Wea. Rev., 137, 299314, doi:10.1175/2008MWR2577.1.

    • Search Google Scholar
    • Export Citation
  • Kalman, R. E., and R. S. Bucy, 1960: New results in linear filtering and prediction theory. J. Basic Eng., 83, 95108, doi:10.1115/1.3658902.

    • Search Google Scholar
    • Export Citation
  • Knabb, R. D., J. R. Rhome, and D. P. Brown, 2005: Tropical cyclone report: Hurricane Katrina, 23–30 August 2005. NOAA/NHC, 43 pp. [Available online at www.nhc.noaa.gov/pdf/TCR-AL122005_Katrina.pdf.]

  • Marchok, T., 2010: Use of the GFDL vortex tracker. WRF tutorial for hurricanes, NOAA/GFDL, 40 pp. [Available online at http://www.dtcenter.org/HurrWRF/users/docs/presentations/tutorial02222010/tracker_slides.pdf.]

  • Meng, Z., and F. Zhang, 2007: Tests of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part II: Imperfect-model experiments. Mon. Wea. Rev., 135, 14031423, doi:10.1175/MWR3352.1.

    • Search Google Scholar
    • Export Citation
  • Meng, Z., and F. Zhang, 2008a: Tests of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part III: Comparison with 3DVar in a real-data case study. Mon. Wea. Rev., 136, 522540, doi:10.1175/2007MWR2106.1.

    • Search Google Scholar
    • Export Citation
  • Meng, Z., and F. Zhang, 2008b: Tests of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part IV: Comparison with 3DVAR in a month-long experiment. Mon. Wea. Rev., 136, 36713682, doi:10.1175/2008MWR2270.1.

    • Search Google Scholar
    • Export Citation
  • Mitchell, H. L., and P. L. Houtekamer, 2000: An adaptive ensemble Kalman filter. Mon. Wea. Rev., 128, 416433, doi:10.1175/1520-0493(2000)128<0416:AAEKF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., 2011: The Gaussian approach to adaptive covariance inflation and its implementation with the local ensemble transform Kalman filter. Mon. Wea. Rev., 139, 15191535, doi:10.1175/2010MWR3570.1.

    • Search Google Scholar
    • Export Citation
  • Parrish, D. F., and J. C. Derber, 1992: The National Meteorological Center’s spectral statistical-interpolation analysis system. Mon. Wea. Rev., 120, 17471763, doi:10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Poterjoy, J., and F. Zhang, 2011: Dynamics and structure of forecast error covariance in the core of a developing hurricane. J. Atmos. Sci., 68, 15861606, doi:10.1175/2011JAS3681.1.

    • Search Google Scholar
    • Export Citation
  • Sippel, J. A., S. A. Braun, F. Zhang, and Y. Weng, 2013: Ensemble Kalman filter assimilation of simulated HIWRAP Doppler velocity data in a hurricane. Mon. Wea. Rev., 141, 26832704, doi:10.1175/MWR-D-12-00157.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 125 pp. [Available online at http://www.mmm.ucar.edu/wrf/users/docs/arw_v3.pdf.]

  • Snyder, C., and F. Zhang, 2003: Assimilation of simulated Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 131, 16631677, doi:10.1175//2555.1.

    • Search Google Scholar
    • Export Citation
  • Talagrand, O., 1997: Assimilation of observations, an introduction. J. Meteor. Soc. Japan, 75, 191209.

  • Tong, M., and M. Xue, 2005: Ensemble Kalman filter assimilation of Doppler radar data with a compressible nonhydrostatic model: OSS experiments. Mon. Wea. Rev., 133, 17891807, doi:10.1175/MWR2898.1.

    • Search Google Scholar
    • Export Citation
  • Torn, R. D., and G. J. Hakim, 2008: Performance characteristics of a pseudo-operational ensemble Kalman filter. Mon. Wea. Rev., 136, 39473963, doi:10.1175/2008MWR2443.1.

    • Search Google Scholar
    • Export Citation
  • Torn, R. D., G. J. Hakim, and C. Snyder, 2006: Boundary conditions for a limited-area ensemble Kalman filter. Mon. Wea. Rev., 134, 24902502, doi:10.1175/MWR3187.1.

    • Search Google Scholar
    • Export Citation
  • Weatherford, C. L., and W. M. Gray, 1988: Typhoon structure as revealed by aircraft reconnaissance. Part I: Data analysis and climatology. Mon. Wea. Rev., 116, 10321043, doi:10.1175/1520-0493(1988)116<1032:TSARBA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Weng, Y., and F. Zhang, 2012: Assimilating airborne Doppler radar observations with an ensemble Kalman filter for convection-permitting hurricane initialization and prediction: Katrina (2005). Mon. Wea. Rev., 140, 841859, doi:10.1175/2011MWR3602.1.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., and T. M. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 19131924, doi:10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., and T. M. Hamill, 2012: Evaluating methods to account for system errors in ensemble data assimilation. Mon. Wea. Rev., 140, 30783089, doi:10.1175/MWR-D-11-00276.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., C. Snyder, and J. Sun, 2004: Impacts of initial estimate and observation availability on convective-scale data assimilation with an ensemble Kalman filter. Mon. Wea. Rev., 132, 12381253, doi:10.1175/1520-0493(2004)132<1238:IOIEAO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., Z. Meng, and A. Aksoy, 2006: Tests of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part I: Perfect-model experiments. Mon. Wea. Rev., 134, 722736, doi:10.1175/MWR3101.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., Y. Weng, J. A. Sippel, Z. Meng, and C. H. Bishop, 2009: Cloud-resolving hurricane initialization and prediction through assimilation of Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 137, 21052125, doi:10.1175/2009MWR2645.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., Y. Weng, J. F. Gamache, and F. D. Marks, 2011: Performance of convection-permitting hurricane initialization and prediction during 2008–2010 with ensemble data assimilation of inner-core airborne Doppler radar observations. Geophys. Res. Lett., 38, L15810, doi:10.1029/2011GL048469.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 344 49 3
PDF Downloads 185 43 6