Advances in Atmospheric Sciences

, Volume 20, Issue 2, pp 195–204 | Cite as

Retrieval of single-Doppler radar wind field by nonlinear approximation

  • Zhao Kun
  • Liu Guoqing
  • Ge Wenzhong
  • Dang Renqing
  • Takao Takeda
Article
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Abstract

The methods employed in recent years to retrieve vector wind information from single-Doppler radar observation are reviewed briefly. These methods are based on a linearity hypothesis for the wind field, so the retrieved wind field is sometimes negatively affected by the non-linearity of wind. This paper proposes a new method based on a non-linear approximation technique. This method, which relies on the piecewise smooth property of the wind field and makes full use of the radar velocity data, is applied to two cases of the Huaihe River Basin Energy and Water Cycle Experiment (HUBEX) in 1998. Checked against the wind field observed by dual-Doppler radar, the retrieved wind field by the method presented in this paper yields a relatively accurate horizontal vector wind field with high resolution, as well as a reasonable estimate of the magnitude of vertical velocity.

Key words

nonlinear approximation piecewise smooth wind field basis function 
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References

  1. Bai J., Zhou X. B., Wang L. K., and Tao Z. Y., 2001: Error analysis of Doppler radar expanded VAD technique. Acta Scientiarum Naturalium Universitatis Pekinensis, 37(1), 48–54.Google Scholar
  2. Bai J., and Tao Z. Y., 2000: The pre-processing of Doppler radar wind retrieval VAP technique. Quarterly Journal of Applied Meteorology, 11(1), 21–26. (in Chinese)Google Scholar
  3. Bluestin, H., and D. Hazen, 1989: Doppler radar analysis of a tropical cyclone over land: Hurricane Alicia 1983 in Oklahoma. Mon. Wea. Rev., 117, 2594–2611.CrossRefGoogle Scholar
  4. Boccippio, D. J. 1995: A diagnostic analysis of the VVP single-Doppler retrieval technique. Journal of Atmospheric and Oceanic Technology, 12, 230–248.CrossRefGoogle Scholar
  5. Browning, K. A., and R. Welxler, 1968: The determination of kinematic properties of a wind field using Doppler radar. J. Appl. Meteor., 7, 105–113.CrossRefGoogle Scholar
  6. Chapelle, O., P. Haffner, and V. N. Vapnik, 1999: Support vector machines for histogram-based image classification. IEEE Trans. Neural Networks, 10, 1055–1064.CrossRefGoogle Scholar
  7. Cohen, A., and J. d’Ales, 1997: Nonlinear approximation of random functions. SIAM J. Appl. Math, 57, 518–540.CrossRefGoogle Scholar
  8. Coifman, R. B., Y. Meyer, and V. M. Wickerhauser, 1992: Entropy-based algorithms for best basis selection. IEEE Transactions on Information Theory, 38(2), 713–718.CrossRefGoogle Scholar
  9. Evgeniou T., 2000: Statistical learning theory: A primer. International Journal of Computer Vision, 38(1), 9–13.CrossRefGoogle Scholar
  10. Girosi, F., 1998: An equivalence between sparse approximation and support vector machines, 1998: Neural Computation, 10(6): 1455–1480.CrossRefGoogle Scholar
  11. Gorodnitsky, I. F., and B. D. Rao, 1997: Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm. IEEE Trans. Signal Processing, 45, 600–616.CrossRefGoogle Scholar
  12. Johnston, B. W., J. D. Marwitz, and R. Carbone, 1990: Single Doppler radar analysis of banded precipitation structures. J. Atmos. Oceanic Technol. 7(6), 866–875.CrossRefGoogle Scholar
  13. Tsuboki, K., B. Geng, and T. Takeda, 2000: Dual Doppler radar analysis of a squall line observed over the China continent during the HUBEX intensive field observation, International GAME/HUBEX Workshop, 12–14 September, Sapporo JAPAN, 69–75.Google Scholar
  14. Klimowski, B. A., and J. D. Marwitz, 1990: Single Doppler analysis of a severe squall line. Preprints, 16th Conf. on Severe Local Storms, Kananaskis, Alberta. Amer. Meteor. Soc., 252–255.Google Scholar
  15. Lhermitte, R. M., and D. Atlas, 1961: Precipitation motion by pulse Doppler. Proa, Ninth Weather Radar Conf., Boston. Amer. Meteor. Soc., 218–223.Google Scholar
  16. Liou, Y. C., Gal-Chen, and D. K. Lilly, 1991: Retrieval of wind temperature and pressure from single-Doppler radar and a numerical model, 25th International Conf. on Radar Meteorology, Paris. Amer. Meteor. Soc., 151–154.Google Scholar
  17. Liu S. Y., and Z. Y. Tao, 1999: The Retrieval of the horizontal divergence field from a single-Doppler radar velocity field. Quarterly Journal of Applied Meteorology, 10(1), 41–48. (in Chinese)Google Scholar
  18. Marwitz, J. D., and R. Carbone, 1990: Single Doppler analysis of banded precipitation structures. J. Atoms. Oceanic Technol., 7, 866–875.CrossRefGoogle Scholar
  19. Marwitz, J. D., 1990: A case study of heavy snowfall in Oklahoma. Preprints, Fourth Conf. on Mesoscale Processes, Boulder. Amer. Meteor. Soc., 61–62.Google Scholar
  20. Matejka, T., and R. C. Srivastava, 1991: An improved version of the extended velocity-azimuth display technique for analyzing single-Doppler radar data. J. Atmos. Oceanic. Technol., 8, 453–466.CrossRefGoogle Scholar
  21. Ogura, Y., and M. T. Liou, 1980: The structure of a midlatitude squall line: A case study. J. Atmos. Sci., 37, 553–567.CrossRefGoogle Scholar
  22. Peace, R. L., R. A. Brown, and H. G. Camnitz, 1969: Horizontal motion field observations with a single pulse Doppler radar. J. Atmos. Sci., 26, 1096–1103.CrossRefGoogle Scholar
  23. Qiu, C. J., and Q. Xu, 1992: A simple adjoint method of wind analysis for single-Doppler data. J. Atmos. Oceanic Technol., 9, 588–598.CrossRefGoogle Scholar
  24. Scialom, G., and J. Testud, 1986: Retrieval of horizontal wind field and mesoscale vertical vorticity in strati-form precipitation by conical scanning with Doppler radars. J. Atmos. Oceanic Technol., 3, 696–703.CrossRefGoogle Scholar
  25. Shusse, Y., H. Minda, B. Geng, K. Tsuboki, and T. Takeda, 2000: Three-dimensional airflow structure of deeply developed long-lived cumulonimbus cloud in the atmospheric situation of weak vertical wind shear, International GAME/HUBEX Workshop, 12–14 September, Sapporo JAPAN, 76–77.Google Scholar
  26. Smythe, G. R., and D. S. Zrnic, 1983: Correlation analysis of Doppler radar data and retrieval of the horizontal wind. J. Climate Appl. Meteor., 22, 297–311.CrossRefGoogle Scholar
  27. Srivastava, R. C, T. J. Matejka, and T. J. Lorello, 1986: Doppler radar study of the trailing anvil region associated with a squall line. J. Atmos. Sci., 43, 356–377.CrossRefGoogle Scholar
  28. Sun, J., D. W. Flicker, and D. K. Lilly, 1991: Recovery of three-dimensional wind and temperature fields from single-Doppler radar data. J. Atmos. Sci., 48, 876–890.CrossRefGoogle Scholar
  29. Suykens, J. A. K., L. Lukas, and J. Vandewalle, 1999: Sparse approximation using least squares Support vector machine. Internal Report 99–84, ESAT-SISTA, K. U. Leuven (Leuven, Belgium) Accepted for publication in Proc. of the IEEE International Symposium on Circuits and Systems (ISCAS 2000), Geneva, Switzerland, May 2000, 757–760.Google Scholar
  30. Takeda, T., Y. Shusse, H. Minda, Y. Wakatsuki, B. Geng, and K. Tsuboki, 1999: Three-dimensional structure of deeply developed long-lived cumulonimbus cloud in the HUBEX-IFO, Workshop on Meso-scale Systems in Meiyu/Baiu Front and Hydrological Cycle, 3–9 November, Xi’an, China, 79–80.Google Scholar
  31. Tao Z. T., 1992: The VAP method to retrieve the wind vectors field based on single-Doppler velocity field. Acta Meteor. Sinica, 50, 81 90. (in Chinese)Google Scholar
  32. Tikhonov, A. N., and V. Y. Arsenin, 1977: Solutions of Ill-posed Problems. W. H. Winston. Washington, D. C: 224pp.Google Scholar
  33. Tuttle, J. D., and G. B. Foote, 1990: Determination of the boundary layer airflow from a single-Doppler radar. J. Atmos. Oceanic Technol., 7, 218–232.CrossRefGoogle Scholar
  34. Vapnik, V. N., 1995: The Nature of Statistical Learning Theory. Springer-Verlag, New York., 188pp.Google Scholar
  35. Vapnik, V. N., 1998a: Statistical Learning Theory. Wiley, New York, 732pp.Google Scholar
  36. Vapnik, V. N., 1998b: The support vector method of function estimation. Nonlinear Modeling: Advanced Blackbox Techniques, J. A. K. Suykens, and J. Vandewalle, Eds., Kluwer Academic Publishers, Boston, 55–85.Google Scholar
  37. Vapnik, V. N., and A.Y. Chervonenkis, 1971: On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and Its Applications, 17(2), 264–280.CrossRefGoogle Scholar
  38. Vapnik, V. N., and S. Mukherjee, 2000: Support vector method for multivariate density estimation. Advances in Neural Information Processing Systems 12, S. A. Solla, T. K. Leen, and K. -R. Muller, Eds., MIT Press Cambridge, Massachusetts, 659–665.Google Scholar
  39. Waldteufel, P., and H. Corbin, 1979: On the analysis of single-Doppler radar data. J. Appl. Meteor., 18, 532–542.CrossRefGoogle Scholar
  40. Wei M., Dang R. Q., Ge W. Z., and T. Takeda, 1998: Retrieval of single-Doppler radar wind with variational assimilation method, Part I: Objective selection of functional weightings factors. Advances in Atmospheric Sciences, 15, 533–568.Google Scholar
  41. Xin, L., and G. W. Reuter, 1998: VVP technique applied to an Alberta storm. J. Atmos. Oceanic Technol., 15, 587–592.CrossRefGoogle Scholar
  42. Xu Q., and C. J. Qiu, 1994: Simple adjoint methods for single-Doppler wind analysis with strong constraint of mass conservation. J. Atmos. Oceanic Technol., 11, 289–298.CrossRefGoogle Scholar
  43. Xu, Q., C. J. Qiu, H. D. Gu, and J. X. Yu, 1995: Simple adjoint retrieval of microburst winds from single-Doppler radar data. Mon. Wea. Rev., 123, 1822–1833.CrossRefGoogle Scholar

Copyright information

© Advances in Atmospheric Sciences 2003

Authors and Affiliations

  • Zhao Kun
    • 1
  • Liu Guoqing
    • 2
  • Ge Wenzhong
    • 1
  • Dang Renqing
    • 1
  • Takao Takeda
    • 3
  1. 1.Department of Atmospheric SciencesNanjing UniversityNanjing
  2. 2.Department of MathematicsNanjing University of TechnologyNanjing
  3. 3.Institutes for Hydrospheric Atmospheric SciencesNagoya UniversityJapan

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