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确定大气边界层顶高度的新方法及数值实验

周建印 项杰 黄思训

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确定大气边界层顶高度的新方法及数值实验

周建印, 项杰, 黄思训

New method of determining height of atmospheric boundary layer and numerical experiment

Zhou Jian-Yin, Xiang Jie, Huang Si-Xun
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  • 提出了一种确定大气边界层顶高度的数值微分新方法, 该方法使用了正则化技术, 把对弯角廓线求导数的数值微分问题转化为求目标泛函极小值的问题, 采用双参数模型函数方法来选择正则化参数, 最后利用最大梯度法确定边界层顶高度. 首先通过两个数值实验验证了新方法的有效性, 实验结果显示, 随着掩星资料噪音的增多, 由差分法和结合L曲线方案的数值微分方法得到的边界层顶高度波动增大, 而通过双参数模型函数方法得到的高度很稳定, 这说明新方法能够很好地过滤噪音, 从而保留廓线的主要信息. 随后基于2007—2011年1, 4, 7, 10月的COSMIC弯角数据, 利用新方法分析了全球海洋大气边界层顶高度的季节特征, 并与用掩星资料自带的大气边界层顶高度数据zbalmax得到的季节分布进行对比. 结果表明, 两者的季节分布特征十分一致: 海温相对周围海域高的区域, 边界层顶高度较高, 反之, 边界层顶高度较低; 在暖流经过的海域, 边界层顶高度较高, 在寒流经过的海域, 边界层顶的高度相对较低.
    In this paper, we propose a new method of numerical differentiation to determine the height of the top layer of the atmospheric boundary layer. In this method, a regularization technique is used to convert the problem of calculating the differential of the curve of the corners into the problem of finding the minimum value of the objective function. The two-parameter model function method is used to select the regularization parameters. Finally, the maximum gradient method is used to determine the top height of the boundary layer. Firstly, the effectiveness of the new method is validated through two numerical experiments. The experimental results show that as the noise of the occultation data increases, the fluctuation of the height of the boundary layer top obtained by the difference method and the numerical differentiation method combined with the L curve scheme increases. And the height obtained by the two-parameter model function method is very stable, which shows that the new method can filter the noise well, thereby retaining the main information about the profile. Then, based on the COSMIC angle data in January, April, July and October 2007-2011, the new method is used to analyze the seasonal characteristics of the height of the global oceanic and atmospheric boundary layer, compared with the seasonal distribution obtained by “zbalmax” with the occultation data. The results show that the seasonal distribution characteristics of the two data are very consistent: the height of the boundary layer is higher in the area where the sea surface temperature is higher than that in the surrounding sea area; on the contrary, the height of the boundary layer top is lower. In the sea area where the warm current passes, the height of the boundary layer is higher; in the sea area where the cold current passes, the height of the boundary layer is lower.
      通信作者: 黄思训, huangsxp@163.com
    • 基金项目: 国家级-国家自然科学基金(91730304)
      Corresponding author: Huang Si-Xun, huangsxp@163.com
    [1]

    Stull R B 1999 An Introduction to Boundary Layer Meteorology (Vol. 13) (Dordrecht: Kluwer Academic Publishers) pp3, 4

    [2]

    Seibert P, Beyrich F, Gryning S E, Joffre S, Rasmussen A, Tercier P 2000 Atmos. Environ. 34 1001Google Scholar

    [3]

    Zeng X, Brunke M A, Zhou M, Fairall C, Bond N A, Lenschow D H 2004 J. Clim. 17 4159Google Scholar

    [4]

    Chan K M, Wood R 2013 J. Geophys. Res. Atmos. 118 12Google Scholar

    [5]

    Ho S P, Peng L, Anthes R A, Kuo Y H, Lin H C 2015 J. Clim. 28 2856Google Scholar

    [6]

    Holzworth G C 1964 Mon. Weather Rev. 92 235Google Scholar

    [7]

    Coulter R L 1979 J. Appl. Meteorol. Climatol. 18 1495Google Scholar

    [8]

    Van Pul W A J, Holtslag A A M, Swart D P J 1994 Bound.-Layer Meteorol. 68 173Google Scholar

    [9]

    Bianco L, Wilczak J M 2002 J. Atmos. Oceanic Technol. 19 1745Google Scholar

    [10]

    Lokoshchenko M A 2002 J. Atmos. Oceanic Technol. 19 1151Google Scholar

    [11]

    Balsley B B, Frehlich R G, Jensen M L, Meillier Y 2006 J. Atmos. Sci. 63 1291Google Scholar

    [12]

    Sokolovskiy S, Kuo Y H, Rocken C, Schreiner W S, Hunt D, Anthes R A 2006 Geophys. Res. Lett. 33 12Google Scholar

    [13]

    Sokolovskiy S V, Rocken C, Lenschow D H, Kuo Y H, Anthes R A, Schreiner W S, Hunt D C 2007 Geophys. Res. Lett. 34 18Google Scholar

    [14]

    Baars H, Ansmann A, Engelmann R, Althausen D 2008 Atmos. Chem. Phys. 8 7281Google Scholar

    [15]

    Seidel D J, Ao C O, Li K 2010 J. Geophys. Res. Atmos. 115 16Google Scholar

    [16]

    Dai C, Wang Q, Kalogiros J A, Lenschow D H, Gao Z, Zhou M 2014 Bound.-Layer Meteorol. 152 277Google Scholar

    [17]

    Yan S, Xiang J, Du H 2019 Adv. Atmos. Sci. 36 303Google Scholar

    [18]

    Tikhonov A N 1963 Dokl. Akad. Nauk SSSR 151

    [19]

    Willoughby R A 1979 SIAM Rev. Soc. Ind. Appl. Math. 21 266Google Scholar

    [20]

    Tautenhahn U 2002 Inverse Prob. 18 191Google Scholar

    [21]

    张路寅 2011 硕士学位论文 (济南: 山东大学)

    Zhang L Y 2011 M.S. Thesis (Jinan: Shandong University) (in Chinese)

    [22]

    Hanke M, Neubauer A, Scherzer O 1995 Numer. Math. 72 21Google Scholar

    [23]

    Shirangi M G, Emerick A A 2016 J. Pet. Sci. Eng. 143 258Google Scholar

    [24]

    姜祝辉, 黄思训, 何然, 周晨腾 2011 物理学报 60 068401Google Scholar

    Jiang Z H, Huang S X, He R, Zhou C T 2011 Acta Phys. Sin. 60 068401Google Scholar

    [25]

    赵延来, 黄思训, 杜华栋, 仲跻芹 2011 物理学报 60 079202Google Scholar

    Zhao Y L, Huang S X, Du H D, Zhong Q Q 2011 Acta Phys. Sin. 60 079202Google Scholar

    [26]

    Zhang L, Huang S X, Shen C, Shi W L 2011 Chin. Phys. B 20 514Google Scholar

    [27]

    Zhong J, Huang S X, Fei J F, Du H D, Zhang L 2011 Chin. Phys. B 20 064301Google Scholar

    [28]

    谢正超, 王飞, 严建华, 岑可法 2015 物理学报 64 240201Google Scholar

    Xie Z C, Wang F, Yan J H, Ling K F 2015 Acta Phys. Sin. 64 240201Google Scholar

    [29]

    Hansen P C 1992 SIAM Rev. Soc. Ind. Appl. Math. 34 561Google Scholar

    [30]

    Hansen P C 1994 Numer. Algorithms 6 1Google Scholar

    [31]

    黄威, 刘磊, 高太长, 李书磊, 胡帅 2016 光谱学与光谱分析 36 3620Google Scholar

    Huang w, Liu L, Gao T C, Li S L, Hu S 2016 Spectrosc. Spect. Anal. 36 3620Google Scholar

    [32]

    Golub G H, Heath M, Wahba G 1979 Technometrics 21 215Google Scholar

    [33]

    Wen Y-W, Chan R H 2018 Inverse Prob. Imag. 12 1103Google Scholar

    [34]

    Scherzer O 1993 Computing 51 45Google Scholar

    [35]

    Morozov V A 1984 Methods for Solving Incorrectly Posed Problems (New York: Springer-Verlag) pp65−70

    [36]

    Kunisch K, Zou J 1998 Inverse Prob. 14 1247Google Scholar

    [37]

    Lu S, Pereverzev S V 2011 Numer. Math. 118 1Google Scholar

    [38]

    王泽文 2010 博士学位论文 (南京: 东南大学)

    Wang Z W 2010 Ph. D. Dissertation (Nanjing: Southeast University) (in Chinese)

    [39]

    刘继军 2005 不适定问题的正则化方法及应用 (北京: 科学出版社) 第83−89页

    Liu J J 2005 Regularization Method and Application of Ill-posed Problems (Beijing: Science Press) pp83−89 (in Chinese)

    [40]

    汪代维, 杨修群 2002 气象学报 02 129Google Scholar

    Wang D W, Yang X Q 2002 Acta Meteorol. Sin. 02 129Google Scholar

  • 图 1  2007−2011年1, 4, 7, 10月份掩星廓线数量的时间分布

    Fig. 1.  Temporal distribution of the number of occultation profiles in January, April, July and October, 2007−2011.

    图 2  双参数模型函数法流程图

    Fig. 2.  Flow chart of two-parameter model function method.

    图 3  由差分法和模型函数法得到的弯角梯度廓线(BA表示弯角) (a)弯角廓线添加随机误差$\delta = 0.0025$, 边界层顶高度${H_{\rm{M}}} = 1.2\;{\rm{km}}, {H_{\rm{d}}} = 1.4\;{\rm{km}}$; (b)弯角廓线添加随机误差$\delta = 0.005$, 边界层顶高度${H_{\rm{M}}} = 1.1\;{\rm{km}}, {H_{\rm{d}}} = 1.4\;{\rm{km}}$; (c)弯角廓线添加随机误差$\delta = 0.0075$, 边界层顶高度${H_{\rm{M}}} = 1.2\;{\rm{km}}, {H_{\rm{d}}} = 1.8\;{\rm{km}}$; (d)弯角廓线添加随机误差$\delta = 0.01$, 边界层顶高度HM = 1.2 km, Hd = 3.7 km

    Fig. 3.  Angle gradient profile obtained by the difference method and the model function method using the bending angle gradient profile (BA represents the bending angle): (a) Bending angle profile with uniform random error $\delta = 0.0025$, boundary layer top height ${H_{\rm{M}}} = 1.2\;{\rm{km}}, {H_{\rm{d}}} = 1.4\;{\rm{km}}$; (b) bending angle profile with uniform random error $\delta = 0.005$, boundary layer top height ${H_{\rm{M}}} = 1.1\;{\rm{km}}, {H_{\rm{d}}} = 1.4\;{\rm{km}}$; (c) bending angle profile with uniform random error $\delta = 0.0075$, boundary layer top height ${H_{\rm{M}}} = 1.2\;{\rm{km}}, {H_{\rm{d}}} = 1.8\;{\rm{km}}$; (d) bending angle profile with uniform random error $\delta = 0.01$, boundary layer top height ${H_{\rm{M}}} = 1.2\;{\rm{km}}, {H_{\rm{d}}} = 3.7\;{\rm{km}}$.

    图 4  由差分法、L曲线法和模型函数法得到的边界层顶高度 (a) 三种方法基于廓线1得到的边界层顶高度, Htrue = 3.15 km, std(HM) = 0.013, std(HL) = 0.44, std(HM) = 0.61; (b) 三种方法基于廓线2得到的边界层顶高度, Htrue = 4.55 km, std(HM) = 0.020, std(HL) = 0.89, std(HM) = 1.19

    Fig. 4.  Height of the boundary layer obtained by the three methods: (a) Three methods to get the height of the boundary layer top based on profile 1, Htrue = 3.15 km, std(HM) = 0.013, std(HL) = 0.44, std(HM) = 0.61; (b) three methods to get the height of the boundary layer top based on profile 2, Htrue = 4.55 km, std(HM) = 0.020, std(HL) = 0.89, std(HM) = 1.19

    图 5  用模型函数法得到的海洋5年平均的边界层顶高度(所用资料为2007—2011年1, 4, 7, 10四个月份的掩星弯角的资料) (a) 1月份平均边界层顶高度; (b) 4月份平均边界层顶高度; (c) 7月份平均边界层顶高度; (d) 10月份平均边界层顶高度

    Fig. 5.  The 5-year average boundary layer height of the ocean obtained by the model function method, the data used is the bending angle profile of the four months of 2007−2011 in January, April, July, and October: (a) The average height of the boundary layer in January; (b) the average height of the boundary layer in April; (c) the average height of the boundary layer in July; (d) the average height of the boundary layer in October.

    图 6  海洋5年平均的边界层顶高度(所用资料为2007—2011年1, 4, 7, 10四个月份的掩星自带zbalmax的资料) (a) 1月份平均边界层顶高度; (b) 4月份平均边界层顶高度; (c) 7月份平均边界层顶高度; (d) 10月份平均边界层顶高度

    Fig. 6.  The 5-year average boundary layer height of the ocean obtained by the model function method, the data used is the zbalmax provided by CDAAC of the four months of 2007−2011 in January, April, July, and October: (a) The average height of the boundary layer in January; (b) the average height of the boundary layer in April; (c) the average height of the boundary layer in July; (d) the average height of the boundary layer in October.

  • [1]

    Stull R B 1999 An Introduction to Boundary Layer Meteorology (Vol. 13) (Dordrecht: Kluwer Academic Publishers) pp3, 4

    [2]

    Seibert P, Beyrich F, Gryning S E, Joffre S, Rasmussen A, Tercier P 2000 Atmos. Environ. 34 1001Google Scholar

    [3]

    Zeng X, Brunke M A, Zhou M, Fairall C, Bond N A, Lenschow D H 2004 J. Clim. 17 4159Google Scholar

    [4]

    Chan K M, Wood R 2013 J. Geophys. Res. Atmos. 118 12Google Scholar

    [5]

    Ho S P, Peng L, Anthes R A, Kuo Y H, Lin H C 2015 J. Clim. 28 2856Google Scholar

    [6]

    Holzworth G C 1964 Mon. Weather Rev. 92 235Google Scholar

    [7]

    Coulter R L 1979 J. Appl. Meteorol. Climatol. 18 1495Google Scholar

    [8]

    Van Pul W A J, Holtslag A A M, Swart D P J 1994 Bound.-Layer Meteorol. 68 173Google Scholar

    [9]

    Bianco L, Wilczak J M 2002 J. Atmos. Oceanic Technol. 19 1745Google Scholar

    [10]

    Lokoshchenko M A 2002 J. Atmos. Oceanic Technol. 19 1151Google Scholar

    [11]

    Balsley B B, Frehlich R G, Jensen M L, Meillier Y 2006 J. Atmos. Sci. 63 1291Google Scholar

    [12]

    Sokolovskiy S, Kuo Y H, Rocken C, Schreiner W S, Hunt D, Anthes R A 2006 Geophys. Res. Lett. 33 12Google Scholar

    [13]

    Sokolovskiy S V, Rocken C, Lenschow D H, Kuo Y H, Anthes R A, Schreiner W S, Hunt D C 2007 Geophys. Res. Lett. 34 18Google Scholar

    [14]

    Baars H, Ansmann A, Engelmann R, Althausen D 2008 Atmos. Chem. Phys. 8 7281Google Scholar

    [15]

    Seidel D J, Ao C O, Li K 2010 J. Geophys. Res. Atmos. 115 16Google Scholar

    [16]

    Dai C, Wang Q, Kalogiros J A, Lenschow D H, Gao Z, Zhou M 2014 Bound.-Layer Meteorol. 152 277Google Scholar

    [17]

    Yan S, Xiang J, Du H 2019 Adv. Atmos. Sci. 36 303Google Scholar

    [18]

    Tikhonov A N 1963 Dokl. Akad. Nauk SSSR 151

    [19]

    Willoughby R A 1979 SIAM Rev. Soc. Ind. Appl. Math. 21 266Google Scholar

    [20]

    Tautenhahn U 2002 Inverse Prob. 18 191Google Scholar

    [21]

    张路寅 2011 硕士学位论文 (济南: 山东大学)

    Zhang L Y 2011 M.S. Thesis (Jinan: Shandong University) (in Chinese)

    [22]

    Hanke M, Neubauer A, Scherzer O 1995 Numer. Math. 72 21Google Scholar

    [23]

    Shirangi M G, Emerick A A 2016 J. Pet. Sci. Eng. 143 258Google Scholar

    [24]

    姜祝辉, 黄思训, 何然, 周晨腾 2011 物理学报 60 068401Google Scholar

    Jiang Z H, Huang S X, He R, Zhou C T 2011 Acta Phys. Sin. 60 068401Google Scholar

    [25]

    赵延来, 黄思训, 杜华栋, 仲跻芹 2011 物理学报 60 079202Google Scholar

    Zhao Y L, Huang S X, Du H D, Zhong Q Q 2011 Acta Phys. Sin. 60 079202Google Scholar

    [26]

    Zhang L, Huang S X, Shen C, Shi W L 2011 Chin. Phys. B 20 514Google Scholar

    [27]

    Zhong J, Huang S X, Fei J F, Du H D, Zhang L 2011 Chin. Phys. B 20 064301Google Scholar

    [28]

    谢正超, 王飞, 严建华, 岑可法 2015 物理学报 64 240201Google Scholar

    Xie Z C, Wang F, Yan J H, Ling K F 2015 Acta Phys. Sin. 64 240201Google Scholar

    [29]

    Hansen P C 1992 SIAM Rev. Soc. Ind. Appl. Math. 34 561Google Scholar

    [30]

    Hansen P C 1994 Numer. Algorithms 6 1Google Scholar

    [31]

    黄威, 刘磊, 高太长, 李书磊, 胡帅 2016 光谱学与光谱分析 36 3620Google Scholar

    Huang w, Liu L, Gao T C, Li S L, Hu S 2016 Spectrosc. Spect. Anal. 36 3620Google Scholar

    [32]

    Golub G H, Heath M, Wahba G 1979 Technometrics 21 215Google Scholar

    [33]

    Wen Y-W, Chan R H 2018 Inverse Prob. Imag. 12 1103Google Scholar

    [34]

    Scherzer O 1993 Computing 51 45Google Scholar

    [35]

    Morozov V A 1984 Methods for Solving Incorrectly Posed Problems (New York: Springer-Verlag) pp65−70

    [36]

    Kunisch K, Zou J 1998 Inverse Prob. 14 1247Google Scholar

    [37]

    Lu S, Pereverzev S V 2011 Numer. Math. 118 1Google Scholar

    [38]

    王泽文 2010 博士学位论文 (南京: 东南大学)

    Wang Z W 2010 Ph. D. Dissertation (Nanjing: Southeast University) (in Chinese)

    [39]

    刘继军 2005 不适定问题的正则化方法及应用 (北京: 科学出版社) 第83−89页

    Liu J J 2005 Regularization Method and Application of Ill-posed Problems (Beijing: Science Press) pp83−89 (in Chinese)

    [40]

    汪代维, 杨修群 2002 气象学报 02 129Google Scholar

    Wang D W, Yang X Q 2002 Acta Meteorol. Sin. 02 129Google Scholar

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    [20] 林鸿荪. 片流边界层中气流及热转移. 物理学报, 1954, 10(1): 71-88. doi: 10.7498/aps.10.71
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出版历程
  • 收稿日期:  2019-12-29
  • 修回日期:  2020-02-07
  • 刊出日期:  2020-05-05

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