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Advances in Atmospheric Sciences

, Volume 36, Issue 3, pp 303–312 | Cite as

Determining Atmospheric Boundary Layer Height with the Numerical Differentiation Method Using Bending Angle Data from COSMIC

  • Shen Yan
  • Jie XiangEmail author
  • Huadong Du
Original Paper
  • 13 Downloads

Abstract

This paper presents a new method to estimate the height of the atmospheric boundary layer (ABL) by using COSMIC radio occultation bending angle (BA) data. Using the numerical differentiation method combined with the regularization technique, the first derivative of BA profiles is retrieved, and the height at which the first derivative of BA has the global minimum is defined to be the ABL height. To reflect the reliability of estimated ABL heights, the sharpness parameter is introduced, according to the relative minimum of the BA derivative. Then, it is applied to four months of COSMIC BA data (January, April, July, and October in 2008), and the ABL heights estimated are compared with two kinds of ABL heights from COSMIC products and with the heights determined by the finite difference method upon the refractivity data. For sharp ABL tops (large sharpness parameters), there is little difference between the ABL heights determined by different methods, i.e., the uncertainties are small; whereas, for non-sharp ABL tops (small sharpness parameters), big differences exist in the ABL heights obtained by different methods, which means large uncertainties for different methods. In addition, the new method can detect thin ABLs and provide a reference ABL height in the cases eliminated by other methods. Thus, the application of the numerical differentiation method combined with the regularization technique to COSMIC BA data is an appropriate choice and has further application value.

Key words

atmospheric boundary layer height numerical differentiation method COSMIC bending angle regularization 

摘要

本文提出一个基于COSMIC弯角数据来确定大气边界层高度的新方法.首先,使用数值微分方法结合正则化技术计算弯角廓线的一阶导数值, 然后把弯角导数廓线的最小值所在的高度定义为边界层高度.为了给出求得的边界层高度的可靠性, 本文根据求得的弯角导数廓线最小值的相对值定义了显著参数. 然后, 本文将该方法应用于2008年1,4,7,10月份的COSMIC弯角数据,求得边界层高度后,本文将其与COSMIC数据本身提供的两种边界层高度,基于COSMIC折射率数据使用有限差分法求得的边界层高度进行了对比.结果表明,对于显著的边界层顶情形(大的显著参数),不同方法求得的结果的偏差较小,即不确定性较小.相反,对于非显著边界层顶的情形(小的显著参数),不同方法之间的偏差较大,即不确定性较大.另外,本文提出的新方法可以识别薄层边界层顶的情形,为容易被其他方法使用质量控制而剔除的个例提供了参考的边界层顶高度.因此,使用数值微分方法结合正则化技术确定边界层高度是一个更优的选择,具有进一步的应用价值.

关键词

大气边界层高度 数值微分方法 COSMIC 弯角 正则化 

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Notes

Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grant No. 41475021). Thanks to the UCAR COSMIC project for providing occultation data, and thanks to Dr. HE for his help in downloading data. Finally, thanks to the anonymous reviewers for their valuable comments.

References

  1. Ao, C. O., D. E. Waliser, S. K. Chan, J. L. Li, B. J. Tian, F. Q. Xie, and A. J. Mannucci, 2012: Planetary boundary layer heights from GPS radio occultation refractivity and humidity profiles. J. Geophys. Res. Atmos., 117, 16117, https://doi.org/10.1029/2012JD017598.CrossRefGoogle Scholar
  2. Basha, G., and M. V. Ratnam, 2009: Identification of atmospheric boundary layer height over a tropical station using highresolution radiosonde refractivity profiles: Comparison with GPS radio occultation measurements. J. Geophys.cal Res. Atmos., 114, D16101, https://doi.org/10.1029/2008JD011692.CrossRefGoogle Scholar
  3. Chan, K. M., and R. Wood, 2013: The seasonal cycle of planetary boundary layer depth determined using COSMIC radio occultation data. J. Geophys. Res. Atmos., 118, 12 422–12 434, https://doi.org/10.1002/2013JD020147.CrossRefGoogle Scholar
  4. Cheng, J., X. Z. Jia, and Y. B. Wang, 2003: Numerical differentiation on the nonuniform grid and its error estimate. Recent Development In Theories and Numerics, Y. C. Hon, Ed., World Scientific Publishing Co. Pte. Ltd, https://doi.org/10.1142/97898127049240020.Google Scholar
  5. Dai, C., Q. Wang, J. A. Kalogiros, D. H. Lenschow, Z. Gao, and M. Zhou, 2014: Determining boundary-layer height from aircraft measurements. Bound.-Layer Meteor., 152, 277–302, https://doi.org/10.1007/s10546-014-9929-z.CrossRefGoogle Scholar
  6. Garratt, J. R., 1994: Review: The atmospheric boundary layer. Earth-Science Reviews, 37, 89–134, https://doi.org/10.1016/0012-8252(94)90026-4.CrossRefGoogle Scholar
  7. Guo, P., Y. H. Kuo, S. V. Sokolovskiy, and D. H. Lenschow, 2011: Estimating atmospheric boundary layer depth using COSMIC radio occultation data. J. Atmos. Sci., 68, 1703–1713, https://doi.org/10.1175/2011JAS3612.1.CrossRefGoogle Scholar
  8. Hanke, M., and O. Scherzer, 2001: Inverse problems light: Numerical differentiation. The American Mathematical Monthly, 108, 512–521, https://doi.org/10.1080/00029890.2001.11919778.CrossRefGoogle Scholar
  9. Hansen, P. C, 1992: Analysis of discrete ill-posed problems by means of the L-curve. SIAM Review, 34, 561–580, https://doi.org/10.1137/1034115.CrossRefGoogle Scholar
  10. Hong, Z. X., M. W. Qian, and F. Hu, 1998: Determination of atmospheric boundary layer structure by using ground-based remote sensing data. Scientia Atmospherica Sinica, 22, 613–624, https://doi.org/10.3878/j.issn.1006-9895.1998.04.21. (in Chinese with English abstract)Google Scholar
  11. Li, M. S., Y. X. Dai, Y. M. Ma, L. Zhong, and S. H. Lv, 2006: Analysis on structure of atmospheric boundary layer and energy exchange of surface layer over Mount Qomolangma region. Plateau Meteorology, 25, 807–813, https://doi.org/10.3321/j.issn:1000-0534.2006.05.006. (in Chinese with English abstract)Google Scholar
  12. Liao, Q. X., X. F. Zhao, H. Q. Shi, S. X. Huang, and J. Xiang, 2015: Spatial and temporal characteristics of the boundary layer height based on COSMIC radio occultation data. Journal of the Meteorological Sciences, 35, 737–743, https://doi.org/10.3969/2015jms.0066. (in Chinese with English abstract)Google Scholar
  13. Liou, Y. A., A. G. Pavelyev, S. F. Liu, A. A. Pavelyev, N. Yen, C. Y. Huang, and C. J. Fong, 2007: FORMOSAT-3/COSMIC GPS radio occultation mission: Preliminary results. IEEE Trans. Geosci. Remote Sens., 45, 3813–3826, https://doi.org/10.1109/TGRS.2007.903365.CrossRefGoogle Scholar
  14. Liu, Y., N. J. Tang, and X. S. Yang, 2016: Height of atmospheric boundary layer as detected by cosmic GPS radio occultation data. Journal of Tropical Meteorology, 22, 74–82, https://doi.org/10.16555/j.1006-8775.2016.01.009.Google Scholar
  15. Mao, M. J., W. M. Jiang, X. Q. Wu, F. D. Qi, R. M. Yuan, H. T. Fang, D. Liu, and J. Zhou, 2006: LIDAR exploring of the UBL in downtown of the Nanjing City. Acta Scientiae Circumstantiae, 26, 1723–1728, https://doi.org/10.3321/j.issn:0253-2468.2006.10.023. (in Chinese with English abstract)Google Scholar
  16. Medeiros, B., A. Hall, and B. Stevens, 2005: What controls the mean depth of the PBL? J. Climate, 18, 3157–3172, https://doi.org/10.1175/JCLI3417.1.CrossRefGoogle Scholar
  17. Ramm, A. G., and A. B. Smirnova, 2001: On stable numerical differentiation. Mathematics of Computation, 70, 1131–1154, https://doi.org/10.1090/S0025-5718-01-01307-2.CrossRefGoogle Scholar
  18. Rieder, M. J., and G. Kirchengast, 2001: Error analysis and characterization of atmospheric profiles retrieved from GNSS occultation data. J. Geophys. Res. Atmos., 106, 31 755–31 770, https://doi.org/10.1029/2000JD000052.CrossRefGoogle Scholar
  19. Seidel, D. J., C. O. Ao, and K. Li, 2010: Estimating climatological planetary boundary layer heights from radiosonde observations: Comparison of methods and uncertainty analysis. J. Geophys. Res. Atmos., 115, D16113, https://doi.org/10.1029/2009JD013680.CrossRefGoogle Scholar
  20. Smith, E. K., and S. Weintraub, 1953: The constants in the equation for atmospheric refractive index at radio frequencies. Proceedings of the IRE 41.8, 1035–1037.Google Scholar
  21. Sokolovskiy, S., Y. H. Kuo, C. Rocken, W. S. Schreiner, D. Hunt, and R. A. Anthes, 2006: Monitoring the atmospheric boundary layer by GPS radio occultation signals recorded in the open-loop mode. Geophys. Res. Lett., 33, L12813, https://doi.org/10.1029/2006GL025955.CrossRefGoogle Scholar
  22. Sokolovskiy, S. V., C. Rocken, D. H. Lenschow, Y. H. Kuo, R. A. Anthes, W. S. Schreiner, and D. C. Hunt, 2007: Observing the moist troposphere with radio occultation signals from COSMIC. Geophys. Res. Lett., 34, L18802, https://doi.org/10.1029/2007GL030458.CrossRefGoogle Scholar
  23. Tikhonov, A., and V. Y. Arsenin, 1977: Methods for Solving Ill-Posed Problems.Google Scholar
  24. von Engeln, A., J. Teixeira, J. Wickert, and S. A. Buehler, 2005: Using CHAMP radio occultation data to determine the top altitude of the Planetary Boundary Layer. Geophys. Res. Lett., 32, L06815, https://doi.org/10.1029/2004GL022168.Google Scholar
  25. Xu, X. D., and Coauthors, 2002: A comprehensive physical pattern of land-air dynamic and thermal structure on the Qinghai-Xizang Plateau. Science in China Series D: Earth Sciences, 45, 577–594, https://doi.org/10.1360/02yd9060.CrossRefGoogle Scholar

Copyright information

© Chinese National Committee for International Association of Meteorology and Atmospheric Sciences, Institute of Atmospheric Physics, Science Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Meteorology and OceanographyNational University of Defense TechnologyNanjingChina
  2. 2.Key Laboratory of Mesoscale Severe Weather of Ministry of EducationNanjingChina

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