Fitting Parametric Vortices to Aliased Doppler Velocities Scanned from Hurricanes

Qin Xu NOAA/National Severe Storms Laboratory, Norman, Oklahoma

Search for other papers by Qin Xu in
Current site
Google Scholar
PubMed
Close
,
Yuan Jiang Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma, and State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, and National Meteorological Center, China Meteorological Administration, Beijing, China

Search for other papers by Yuan Jiang in
Current site
Google Scholar
PubMed
Close
, and
Liping Liu State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China

Search for other papers by Liping Liu in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

An alias-robust least squares method that produces less errors than established methods is developed to produce reference radial velocities for automatically correcting raw aliased Doppler velocities scanned from hurricanes. This method estimates the maximum tangential velocity VM and its radial distance RM from the hurricane vortex center by fitting a parametric vortex model directly to raw aliased velocities at and around each selected vertical level. In this method, aliasing-caused zigzag discontinuities in the relationship between the observed and true radial velocities are formulated into the cost function by applying an alias operator to the entire analysis-minus-observation term to ensure the cost function to be smooth and concave around the global minimum. Simulated radar velocity observations are used to examine the cost function geometry around the global minimum in the space of control parameters (VM, RM). The results show that the global minimum point can estimate the true (VM, RM) approximately if the hurricane vortex center location is approximately known and the hurricane core and vicinity areas are adequately covered by the radar scans, and the global minimum can be found accurately by an efficient descent algorithm as long as the initial guess is in the concave vicinity of the global minimum. The method is used with elaborated refinements for automated dealiasing, and this utility is highlighted by an example applied to severely aliased radial velocities scanned from a hurricane.

Corresponding author address: Qin Xu, National Severe Storms Laboratory, 120 David L. Boren Blvd., Norman, OK 73072-7326. E-mail: qin.xu@noaa.gov

Abstract

An alias-robust least squares method that produces less errors than established methods is developed to produce reference radial velocities for automatically correcting raw aliased Doppler velocities scanned from hurricanes. This method estimates the maximum tangential velocity VM and its radial distance RM from the hurricane vortex center by fitting a parametric vortex model directly to raw aliased velocities at and around each selected vertical level. In this method, aliasing-caused zigzag discontinuities in the relationship between the observed and true radial velocities are formulated into the cost function by applying an alias operator to the entire analysis-minus-observation term to ensure the cost function to be smooth and concave around the global minimum. Simulated radar velocity observations are used to examine the cost function geometry around the global minimum in the space of control parameters (VM, RM). The results show that the global minimum point can estimate the true (VM, RM) approximately if the hurricane vortex center location is approximately known and the hurricane core and vicinity areas are adequately covered by the radar scans, and the global minimum can be found accurately by an efficient descent algorithm as long as the initial guess is in the concave vicinity of the global minimum. The method is used with elaborated refinements for automated dealiasing, and this utility is highlighted by an example applied to severely aliased radial velocities scanned from a hurricane.

Corresponding author address: Qin Xu, National Severe Storms Laboratory, 120 David L. Boren Blvd., Norman, OK 73072-7326. E-mail: qin.xu@noaa.gov
Save
  • Baynton, H. W., 1979: The case for Doppler radars along our hurricane affected coasts. Bull. Amer. Meteor. Soc., 60, 10141023.

  • Bluestein, H. B., C. W. Christopher, and A. L. Pazmany, 2004: doppler radar observations of dust devils in Texas. Mon. Wea. Rev., 132, 209224.

    • Search Google Scholar
    • Export Citation
  • Brown, R. A., 1998: Nomogram for aiding the interpretation of tornadic vortex signatures measured by Doppler radar. Wea. Forecasting, 13, 505512.

    • Search Google Scholar
    • Export Citation
  • Brown, R. A., and V. T. Wood, 1991: On the interpretation of single-Doppler velocity patterns within severe thunderstorms. Wea. Forecasting, 6, 3248.

    • Search Google Scholar
    • Export Citation
  • Browning, K. A., and R. Wexler, 1968: The determination of kinematic properties of a wind field using Doppler radar. J. Appl. Meteor., 7, 105113.

    • Search Google Scholar
    • Export Citation
  • Doviak, R. J., and D. S. Zrnic, 2006: Doppler Radar and Weather Observations. 2nd ed. Dover Publications, 562 pp.

  • Eilts, M. D., and S. D. Smith, 1990: Efficient dealiasing of Doppler velocities using local environment constraints. J. Atmos. Oceanic Technol., 7, 118128.

    • Search Google Scholar
    • Export Citation
  • Gao, J., and K. K. Droegemeier, 2004: A variational technique for dealiasing doppler radial velocity data. J. Appl. Meteor., 43, 934940.

    • Search Google Scholar
    • Export Citation
  • Gao, J., K. K. Droegemeier, J. Gong, and Q. Xu, 2004: A method for retrieving mean horizontal wind profiles from single-Doppler radar observations contaminated by aliasing. Mon. Wea. Rev., 132, 13991409.

    • Search Google Scholar
    • Export Citation
  • Golub, G. H., and C. F. Van Loan, 1983: Matrix Computations. Johns Hopkins University Press, 476 pp.

  • Gong, J., L. Wang, and Q. Xu, 2003: A three-step dealiasing method for Doppler velocity data quality control. J. Atmos. Oceanic Technol., 20, 17381748.

    • Search Google Scholar
    • Export Citation
  • Haase, G., and T. Landelius, 2004: Dealiasing of Doppler radar velocities using a torus mapping. J. Atmos. Oceanic Technol., 21, 15661573.

    • Search Google Scholar
    • Export Citation
  • Hodur, R. M., 1997: The Naval Research Laboratory’s Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS). Mon. Wea. Rev., 125, 14141430.

    • Search Google Scholar
    • Export Citation
  • Jou, B. J.-D., W.-C. Lee, S.-P. Liu, and Y.-C. Kao, 2008: Generalized VTD retrieval of atmospheric vortex kinematic structure. Part I: Formulation and error analysis. Mon. Wea. Rev., 136, 9951012.

    • Search Google Scholar
    • Export Citation
  • Lee, W.-C., B. J.-D. Jou, P.-L. Chang, and S.-M. Deng, 1999: Tropical cyclone kinematic structure retrieved from single-Doppler radar observations. Part I: Interpretation of Doppler velocity patterns and the GBVTD technique. Mon. Wea. Rev., 127, 24192439.

    • Search Google Scholar
    • Export Citation
  • Liou, Y. C., T.-C. C. Wang, W. C. Lee, and Y.-J. Chang, 2006: The retrieval of asymmetric tropical cyclone structures using Doppler radar observations and the method of extended GBVTD. Mon. Wea. Rev., 134, 11401160.

    • Search Google Scholar
    • Export Citation
  • Tabary, P., G. Scialom, and U. Germann, 2001: Real-time retrieval of the wind from aliased velocities measured by Doppler radars. J. Atmos. Oceanic Technol., 18, 875882.

    • Search Google Scholar
    • Export Citation
  • Vatistas, G. H., V. Kozel, and W. C. Mih, 1991: A simpler model for concentrated vortices. Exp. Fluids, 11, 7376.

  • Wang, M., K. Zhao, W.-C. Lee, B. Jong-Dao Jou, and M. Xue, 2012: The gradient velocity track display (GRVTD) technique for retrieving tropical cyclone primary circulation from aliased velocities measured by single-Doppler radar. J. Atmos. Oceanic Technol., 29, 10261041.

    • Search Google Scholar
    • Export Citation
  • Willoughby, H. E., R. W. R. Darling, and M. E. Rahn, 2006: Parametric representation of the primary hurricane vortex. Part II: A new family of sectionally continuous profiles. Mon. Wea. Rev., 134, 11021120.

    • Search Google Scholar
    • Export Citation
  • Wood, V. T., 1994: A technique for detecting a tropical cyclone center using a Doppler radar. J. Atmos. Oceanic Technol., 11, 12071216.

    • Search Google Scholar
    • Export Citation
  • Wood, V. T., and R. A. Brown, 1992: Effects of radar proximity on single-Doppler velocity of axisymmetric rotation and divergence. Mon. Wea. Rev., 120, 27982807.

    • Search Google Scholar
    • Export Citation
  • Wood, V. T., and L. W. White, 2011: A new parametric model of vortex tangential-wind profiles: Development, testing, and verification. J. Atmos. Sci., 68, 9901006.

    • Search Google Scholar
    • Export Citation
  • Wood, V. T., L. W. White, H. E. Willoughby, and D. P. Jorgensen, 2013: A new parametric tropical cyclone tangential wind profile model. Mon. Wea. Rev., 141, 18841909.

    • Search Google Scholar
    • Export Citation
  • Wurman, J., and C. R. Alexander, 2005: The 30 May 1998 Spencer, South Dakota, storm. Part II: Comparison of observed damage and radar-derived winds in the tornadoes. Mon. Wea. Rev., 133, 97119.

    • Search Google Scholar
    • Export Citation
  • Xu, Q., 2009: Bayesian perspective of the unconventional approach for assimilating aliased radar radial velocities. Tellus, 61A, 631634.

    • Search Google Scholar
    • Export Citation
  • Xu, Q., K. Nai, and L. Wei, 2007: An innovation method for estimating radar radial-velocity observation error and background wind error covariances. Quart. J. Roy. Meteor. Soc., 133, 407415.

    • Search Google Scholar
    • Export Citation
  • Xu, Q., K. Nai, L. Wei, and Q. Zhao, 2009: An unconventional approach for assimilating aliased radar radial velocities. Tellus, 61A, 621630.

    • Search Google Scholar
    • Export Citation
  • Xu, Q., K. Nai, and L. Wei, 2010: Fitting VAD wind to aliased radial-velocity observations—A minimization problem with multiple minima. Quart. J. Roy. Meteor. Soc., 136, 451461.

    • Search Google Scholar
    • Export Citation
  • Xu, Q., K. Nai, L. Wei, P. Zhang, S. Liu, and D. Parrish, 2011: A VAD-based dealiasing method for radar velocity data quality control. J. Atmos. Oceanic Technol., 28, 5062.

    • Search Google Scholar
    • Export Citation
  • Yamada, Y., and M. Chong, 1999: VAD-based determination of the Nyquist interval number of Doppler velocity aliasing without wind information. J. Meteor. Soc. Japan, 77, 447457.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 204 135 2
PDF Downloads 53 20 4