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近70年有限区域流函数速度势算法研究的回顾和新进展

曹洁 陈海山 XU Qin

曹洁, 陈海山, XU Qin. 2023. 近70年有限区域流函数速度势算法研究的回顾和新进展[J]. 大气科学, 47(2): 502−516 doi: 10.3878/j.issn.1006-9895.2210.22143
引用本文: 曹洁, 陈海山, XU Qin. 2023. 近70年有限区域流函数速度势算法研究的回顾和新进展[J]. 大气科学, 47(2): 502−516 doi: 10.3878/j.issn.1006-9895.2210.22143
CAO Jie, CHEN Haishan, XU Qin. 2023. Studies of the Approaches for Computing Stream Function and Velocity Potential in a Limited Domain in the Past 70 Years and Their Recent Developments [J]. Chinese Journal of Atmospheric Sciences (in Chinese), 47(2): 502−516 doi: 10.3878/j.issn.1006-9895.2210.22143
Citation: CAO Jie, CHEN Haishan, XU Qin. 2023. Studies of the Approaches for Computing Stream Function and Velocity Potential in a Limited Domain in the Past 70 Years and Their Recent Developments [J]. Chinese Journal of Atmospheric Sciences (in Chinese), 47(2): 502−516 doi: 10.3878/j.issn.1006-9895.2210.22143

近70年有限区域流函数速度势算法研究的回顾和新进展

doi: 10.3878/j.issn.1006-9895.2210.22143
基金项目: 国家自然科学基金项目41875074
详细信息
    作者简介:

    曹洁,女,1983年出生,副研究员,主要从事中尺度动力学、灾害性天气诊断分析和数值预报方法研发。E-mail: 003542@nuist.edu.cn

    通讯作者:

    陈海山,E-mail: haishan@nuist.edu.cn

  • 中图分类号: P433

Studies of the Approaches for Computing Stream Function and Velocity Potential in a Limited Domain in the Past 70 Years and Their Recent Developments

Funds: National Natural Science Foundation of China (Grant 41875074)
  • 摘要: 流函数和速度势能很好反映流体的涡度和散度特征,一直广泛应用于全球和区域大气和海洋环流分析、污染物扩散和资料同化等研究领域。近年发现,有限区域流函数速度势常用算法计算中小尺度系统复杂流场和复杂下垫面驱动的边界层流场时,精度显著下降。本文全面回顾上世纪五十年代以来的五类常用算法,从数学原理和物理意义两方面简述优缺点,总结其适用范围;指出常用的调和—余弦法在可解性条件方面的科学问题,并设计订正方案,以提高其在求解复杂流场问题中的适用性和计算精度;通过理想函数和实际天气过程复杂流场的多组数值试验,直观定量显示并归纳总结适于不同分辨率资料的算法。本文旨在为流函数速度势及其相关变量在极端天气气候事件机理分析和数值预报等领域的有效应用,提供科学依据。
  • 图  1  $\bigtriangledown $χvχχ气象学梯度方向示意图

    Figure  1.  Schematic diagram of the directions of $\bigtriangledown $χ, vχ and the meteorological gradient of χ

    图  2  (a)2018年11月30日22:00(北京时,下同)新疆伊犁河谷地区距地面约0.5 km高度处的风场分布(灰框显示D1、D2、D3区域范围,阴影代表风速值,单位:m s−1)以及(b)地形高度(单位:m);(c)2020年6月25日20:00至26日02:00京津冀地区极大风分布(阴影代表蒲福风级)以及(d)地形高度(单位:m)

    Figure  2.  Distributions of (a) wind fields at approximately 0.5 km over the surface and (b) terrain height (units: m) in Ili Valley in Xinjiang at 2200 BJT (Beijing time) on November 30, 2018; the gray lines denote the boundaries of D1, D2, and D3, and the shaded areas denote velocity (units: m s−1). Distributions of (a) maximum winds and (d) terrain height (units: m) over the Beijing–Tianjin–Hebei Region from 2000 BJT June 25 to 0200 BJT June 26, 2020

    图  3  调和—余弦试验(a、b)RealD1、(c、d)RealD2和(e、f)RealD3中的原始风场(黑线)和三种方法重建的vs(左列)和vn(右列)沿边界的分布(单位:m s−1)。绿、蓝和红线分别代表调和—余弦法、调和—正弦余弦混合法和调和-余弦扰动法

    Figure  3.  Distributions of the original (black lines) and reconstructed vs (left column) and vn (right column) along the boundary of harmonic cosine expansion method experiments (a, b) RealD1, (c, d) RealD2, and (e, f) RealD3. The green, blue, and red lines denote the constructed wind components by the harmonic cosine expansion method, combined sine and cosine corrected method, and perturbation corrected method, respectively

    图  4  2020年6月24日20:00至25日19:00的原始风场与SOR法(左列)、混合法(右列)重建风场的SCC在整层的分布:(a,b)Res001;(c,d)Res0125;(e,f)Res05;(g,h)Res25。横坐标代表时刻,粗线代表SCC≥0.98,(c)中阴影填充色代表SCC≤0.8

    Figure  4.  Distributions of SCC (spatial correlation coefficient) at all vertical levels between the original winds and those reconstructed by the SOR method (left column) and the hybrid method (right column) in (a, b) Res001, (c, d) Res0125, (e, f) Res05, and (g, h) Res25. The x-axis denotes the temporal evolution from 2000 BJT 24 to 1900 BJT 25 June 2020. The thick lines denote the regions with SCC≥0.98, and the gray-shaded circles in (c) denote the regions with SCC≤0.8

    表  1  近70年有限区域(ψ, χ)算法分类及基本信息

    Table  1.   Basic information of the five categories of algorithms for computing (ψ, χ) in limited domains

    代表算法优点不足后续应用
    直接法Phillip(1958)计算快物理假设不合理、精度低迭代法
    迭代法Sangster(1960)计算快精度低、不收敛诊断分析数值模式
    Endlich(1967)精度较低、不收敛
    SOR法复杂流场精度低、难以客观选择收敛系数
    谱展开法双傅氏变换法计算快只能求解规则区域有限区域谱模式
    调和—正(余)弦法迭代不收敛、只能求解规则区域
    变分法正则化方法物理意义清楚、计算精度较高难以客观选择正则化参数沿岸流等不规则区域求解
    格林函数法Xu et al.(2011)物理意义清楚、精度高、迭代收敛复杂流场精度较低不规则区域、复杂流场求解
    混合法精度高、适合复杂流场、迭代收敛无上述缺点
    下载: 导出CSV

    表  2  调和—余弦试验中不同方法计算结果在可解性条件公式(6-1)和(6-2)左端项的归一化值和精度指标(加粗表示达到精度指标)

    Table  2.   Normalized values at both sides of the solvability conditions (Eqs. 6-1 and 6-2) and accuracy indices in the four experiments. Bold fonts denote those values where both SCC (spatial correlation coefficient) and RRD (relative root-mean-square difference) satisfy the accuracy adequacy criterion given at the end of section 2.2

    调和—余弦试验组方法SvsdsSvndsSCCRRD
    Ana调和—余弦法0.8681.0430.99050.1044
    调和—正弦余弦混合法0.8850.8830.99980.1045
    调和—余弦扰动法0.8680.8430.99980.1396
    RealD1调和—余弦法1.5271.1200.78750.4806
    调和—正弦余弦混合法1.5370.9550.78360.4800
    调和—余弦扰动法0.9220.9120.98820.1389
    RealD2调和—余弦法0.5761.1490.87130.2976
    调和—正弦余弦混合法0.4711.2600.86610.2986
    调和—余弦扰动法0.7750.9180.98730.1357
    RealD3调和—余弦法0.7250.9830.87150.5215
    调和—正弦余弦混合法0.6830.7770.87530.5483
    调和—余弦扰动法1.0291.0050.98630.1660
    下载: 导出CSV

    表  3  分辨率试验组基本信息

    Table  3.   Details of resolution experiments

    分辨率试验水平分辨率纬度范围经度范围垂直分辨率垂直范围
    Res0011 km40.2°~41°N116.2°~117°E0.5 km0.5~10 km
    Res01250.125°35°~45°N110°~120°E50 hPa1000~50 hPa
    Res0250.25°25°~45°N100°~120°E
    Res050.5°15°~55°N90°~130°E
    Res101.0°5°S~75°N70°~150°E
    Res252.5°75°S~75°N40°~160°E
    下载: 导出CSV

    表  4  六组分辨率试验在2020年6月25日18:00 900 hPa(或1 km)高度上的SCC、RRD(加粗表示达到精度指标)和CPU时间

    Table  4.   Accuracy indices and CPU times in the six resolution experiments at 900 hPa (or 1 km above the surface) at 1800 BJT on June 25, 2020

    分辨率试验方法SCCRRDCPU时间/s
    Res001SOR法0.69950.51400.135
    混合法0.99950.01900.533
    Res0125SOR法0.74640.97940.135
    混合法0.99920.03790.533
    Res025SOR法0.92380.27570.135
    混合法0.99910.02670.533
    Res05SOR法0.95300.16550.135
    混合法0.99720.04320.533
    Res10SOR法0.90960.28470.135
    混合法0.99390.06390.533
    Res25SOR法0.99040.13510.113
    混合法0.99300.12060.395
    下载: 导出CSV
  • [1] Abdeldym A, Basset H A, Sayad T, et al. 2019. Kinetic energy budget and moisture flux convergence analysis during interaction between two cyclonic systems: Case study [J]. Dyn. Atmos. Oceans, 86: 73−89. doi: 10.1016/j.dynatmoce.2019.03.007
    [2] Aimi A, Buffoni G, Groppi M. 2014. Decomposition of a planar vector field into irrotational and rotational components [J]. Appl. Math. Comput., 244: 63−90. doi: 10.1016/j.amc.2014.06.080
    [3] Bao X H, Yao X P. 2022. Intensity evolution of zonal shear line over the Tibetan Plateau in summer: A perspective of divergent and rotational kinetic energies [J]. Adv. Atmos. Sci., 39: 1021−1033. doi: 10.1007/s00376-021-1302-9
    [4] Batchelor G K. 1967. An Introduction to Fluid Dynamics [M]. Cambridge: Cambridge University Press, 615pp.
    [5] Bierdel L, Snyder C, Park S H, et al. 2016. Accuracy of rotational and divergent kinetic energy spectra diagnosed from flight–track winds [J]. J. Atmos. Sci., 73: 3273−3286. doi: 10.1175/JAS-D-16-0040.1
    [6] Bijlsma S J, Hafkenscheid L M, Lynch P. 1986. Computation of the streamfunction and velocity potential and reconstruction of the wind field [J]. Mon. Wea. Rev., 114: 1547−1551. doi: 10.1175/1520-0493(1986)114<1547:COTSAV>2.0.CO;2
    [7] Bishop C H. 1996a. Domain-independent attribution. Part I: Reconstructing the wind from estimates of vorticity and divergence using free space Green’s functions [J]. J. Atmos. Sci., 53: 241−252. doi: 10.1175/1520-0469(1996)053<0241:DIAPIR>2.0.CO;2
    [8] Bishop C H. 1996b. Domain-independent attribution. Part II: Its value in the verification of dynamical theories of frontal waves and frontogenesis [J]. J. Atmos. Sci., 53: 253−262. doi: 10.1175/1520-0469(1996)053<0253:DIAPII>2.0.CO;2
    [9] Boyd J P, Deng D F, Chen Q S, et al. 2013. Applications of Bivariate Fourier series for solving the Poisson equation in limited-area modeling of the atmosphere: Higher accuracy with a boundary buffer strip discarded and an improved order-raising procedure [J]. Mon. Wea. Rev., 141: 4154−4164. doi: 10.1175/MWR-D-13-00074.1
    [10] Brown J A, Neilon J R. 1961. Case studies of numerical wind analyses [J]. Mon. Wea. Rev., 89: 83−90. doi: 10.1175/1520-0493(1961)089<0083:CSONWA>2.0.CO;2
    [11] Buechler D E, Fuelberg H E. 1986. Budgets of divergent and rotational kinetic energy during two periods of intense convection [J]. Mon. Wea. Rev., 114: 95−114. doi: 10.1175/1520-0493(1986)114<0095:BODARK>2.0.CO;2
    [12] 蔡其发, 黄思训, 高守亭, 等. 2008. 计算涡度的新方法 [J]. 物理学报, 57: 3912−3919. doi: 10.7498/aps.57.3912

    Cai Qifa, Huang Sixun, Gao Shouting, et al. 2008. A new method for calculating vorticity [J]. Acta Phys. Sinica (in Chinese), 57: 3912−3919. doi: 10.7498/aps.57.3912
    [13] Cao J, Xu Q. 2011. Computing streamfunction and velocity potential in a limited domain of arbitrary shape. Part II: Numerical methods and test experiments [J]. Adv. Atmos. Sci., 28: 1445−1458. doi: 10.1007/s00376-011-0186-5
    [14] 曹洁, 高守亭, 周玉淑. 2008. 从流场分解角度改进Q矢量分析方法及其在暴雨动力识别中的应用 [J]. 物理学报, 57: 2600−2606. doi: 10.7498/aps.57.2600

    Cao Jie, Gao Shouting, Zhou Yushu. 2008. Improved Q vector analyses from the perspective of field separation and its application in a torrential rain event [J]. Acta Phys. Sinica (in Chinese), 57: 2600−2606. doi: 10.7498/aps.57.2600
    [15] Cao J, Ran L K, Li N. 2014. An application of the Helmholtz theorem in extracting the externally induced deformation field from the total wind field in a limited domain [J]. Mon. Wea. Rev., 142: 2060−2066. doi: 10.1175/MWR-D-13-00311.1
    [16] Cao J, Xu Q, Chen H S, et al. 2022. Hybrid methods for computing the streamfunction and velocity potential for complex flow fields over mesoscale domains [J]. Adv. Atmos. Sci., 39: 1417−1431. doi: 10.1007/s00376-021-1280-y
    [17] Chen T C. 1980. On the energy exchange between the divergent and rotational components of atmospheric flow over the tropics and subtropics at 200 mb during two northern summers [J]. Mon. Wea. Rev., 108: 896−912. doi: 10.1175/1520-0493(1980)108<0896:OTEEBT>2.0.CO;2
    [18] Chen T C, Wiin-Nielsen A C. 1976. On the kinetic energy of the divergent and nondivergent flow in the atmosphere [J]. Tellus, 28: 486−498. doi: 10.3402/tellusa.v28i6.11317
    [19] Chen Q S, Kuo Y H. 1992a. A harmonic-sine series expansion and its application to partitioning and reconstruction problems in a limited area [J]. Mon. Wea. Rev., 120: 91−112. doi: 10.1175/1520-0493(1992)120<0091:AHSSEA>2.0.CO;2
    [20] Chen Q S, Kuo Y H. 1992b. A consistency condition for wind–field reconstruction in a limited area and a harmonic-cosine series expansion [J]. Mon. Wea. Rev., 120: 2653−2670. doi: 10.1175/1520-0493(1992)120<2653:ACCFWF>2.0.CO;2
    [21] Chen Q S, Kuo Y H, Bromwich D H. 1996. A balanced ageostrophic initialization with a fixed external wind boundary value for limited-area models [J]. J. Meteor. Soc. Japan, 74: 325−342. doi: 10.2151/jmsj1965.74.3_325
    [22] Chen Q S, Bai L S, Bromwich D H. 1997. A harmonic-Fourier spectral limited-area model with an external wind lateral boundary condition [J]. Mon. Wea. Rev., 125: 143−167. doi: 10.1175/1520-0493(1997)125<0143:AHFSLA>2.0.CO;2
    [23] 陈海山, 陆昌根, 邵海燕, 等. 2013. 流体力学[M]. 北京: 气象出版社, 63–82

    Chen Haishan, Lu Changgen, Shao Haiyan, et al. 2013. Fluid Mechanics (in Chinese) [M]. Beijing: China Meteorological Press, 63–82.
    [24] Daley R. 1991. Atmospheric Data Analysis [M]. Cambridge: Cambridge University Press, 457pp.
    [25] Daley R, Barker E. 2001. NAVDAS: Formulation and diagnostics [J]. Mon. Wea. Rev., 129: 869−883. doi: 10.1175/1520-0493(2001)129<0869:NFAD>2.0.CO;2
    [26] Denis B, Côté J, Laprise R. 2002. Spectral decomposition of two-dimensional atmospheric fields on limited-area domains using the discrete cosine transform (DCT) [J]. Mon. Wea. Rev., 130: 1812−1829. doi: 10.1175/1520-0493(2002)130<1812:SDOTDA>2.0.CO;2
    [27] Dimego G J, Bosart L F. 1982. The transformation of tropical storm Agnes into an extratropical cyclone. Part II: Moisture, vorticity and kinetic energy budgets [J]. Mon. Wea. Rev., 110: 412−433. doi: 10.1175/1520-0493(1982)110<0412:TTOTSA>2.0.CO;2
    [28] 丁一汇. 1989. 天气动力学中的诊断分析方法[M]. 北京: 科学出版社, 204–214

    Ding Yihui. 1989. Diagnostic Analysis in Synoptic Dynamics (in Chinese) [M]. Beijing: Science Press, 204–214.
    [29] 丁一汇, 刘月贞. 1985. 台风中动能收支的研究——II. 辐散风动能和无辐散风动能的转换 [J]. 中国科学B辑, 15: 1045−1054.

    Ding Yihui, Liu Yuezhen. 1985. Studies on kinetic energy budget analysis in typhoons. II: Transmission of divergent kinetic energy and nondivergent one [J]. Science in China Series B (in Chinese), 15: 1045−1054.
    [30] 丁一汇, 胡国权. 2003. 1998年中国大洪水时期的水汽收支研究 [J]. 气象学报, 61: 129−145. doi: 10.3321/j.issn:0577-6619.2003.02.001

    Ding Yihui, Hu Guoquan. 2003. A study on water vapor budget over China during the 1998 severe flood periods [J]. Acta Meteor. Sinica (in Chinese), 61: 129−145. doi: 10.3321/j.issn:0577-6619.2003.02.001
    [31] 丁一汇, 赵深铭, 何诗秀. 1984. 全球夏季热带200mb平均环流研究的某些新结果 [J]. 科学通报, 29: 414−416. doi: 10.1360/csb1984-29-7-414

    Ding Yihui, Zhao Shenming, He Shixiu. 1984. Some next results of the global averaged circulation at 200mb over the tropics during the summer season [J]. Chinese Science Bulletin (in Chinese), 29: 414−416. doi: 10.1360/csb1984-29-7-414
    [32] Endlich R M. 1967. An iterative method for altering the kinematic properties of wind fields [J]. J. Appl. Meteor., 6: 837−844. doi: 10.1175/1520-0450(1967)006<0837:AIMFAT>2.0.CO;2
    [33] Forget G, Ferreira D. 2019. Global ocean heat transport dominated by heat export from the tropical Pacific [J]. Nature Geoscience, 12: 351−354. doi: 10.1038/s41561-019-0333-7
    [34] Fuelberg H E, Browning P A. 1983. Roles of divergent and rotational winds in the kinetic energy balance during intense convective activity [J]. Mon. Wea. Rev., 111: 2176−2193. doi: 10.1175/1520-0493(1983)111<2176:RODARW>2.0.CO;2
    [35] Fulton S R, Schubert W H. 1987. Chebyshev spectral methods for limited area models. Part I: Model problem analysis [J]. Mon. Wea. Rev., 115: 1940−1953. doi: 10.1175/1520-0493(1987)115<1940:CSMFLA>2.0.CO;2
    [36] 关吉平, 黄思训, 张立凤. 2014. 全球风场构建涡度、散度的新方法 [J]. 物理学报, 63: 179201. doi: 10.7498/aps.63.179201

    Guan Jiping, Huang Sixun, Zhang Lifeng. 2014. A new method for calculating vorticity and Divergence using global wind field [J]. Acta Phys. Sinica (in Chinese), 63: 179201. doi: 10.7498/aps.63.179201
    [37] Haltiner G J, Williams R T. 1980. Numerical Prediction and Dynamic Meteorology [M]. 2nd ed. New York: John Wiley & Sons, 477pp.
    [38] Hollingsworth A, Lönnberg P. 1986. The statistical structure of short-range forecast errors as determined from radiosonde data. Part I: The wind field [J]. Tellus, 38: 111−136. doi: 10.3402/tellusa.v38i2.11707
    [39] 黄思训, 伍荣生. 2001. 大气科学中的数学物理问题[M]. 北京: 气象出版社, 411–475

    Huang Sixun, Wu Rongsheng. 2001. Mathematic and Physical Problems in Atmospheric Sciences (in Chinese) [M]. Beijing: China Meteorological Press, 411–475.
    [40] 黄思训, 蔡其发, 项杰, 等. 2007. 台风风场分解 [J]. 物理学报, 56: 3022−3027. doi: 10.7498/aps.56.3022

    Huang Sixun, Cai Qifa, Xiang Jie, et al. 2007. On decomposition of typhoon flow field [J]. Acta Phys. Sinica (in Chinese), 56: 3022−3027. doi: 10.7498/aps.56.3022
    [41] Hurrell J W, Vincent D G. 1991. On the maintenance of short-term subtropical wind maxima in the Southern Hemisphere during SOP-1, FGGE [J]. J. Climate, 4: 1009−1022. doi: 10.1175/1520-0442(1991)004<1009:OTMOST>2.0.CO;2
    [42] 姜祝辉, 黄思训, 杜华栋, 等. 2010. 利用变分结合正则化方法对高度计风速资料调整海面风场的研究 [J]. 物理学报, 59: 8968−8977. doi: 10.7498/aps.59.8968

    Jiang Zhuhui, Huang Sixun, Du Huadong, et al. 2010. A new approach to adjusting sea surface wind using altimeter wind data by variational regularization method [J]. Acta Phys. Sinica (in Chinese), 59: 8968−8977. doi: 10.7498/aps.59.8968
    [43] Klasa C, Arpagaus M, Walser A, et al. 2019. On the time evolution of limited-area ensemble variance: Case studies with the convection-permitting ensemble COSMO-E [J]. J. Atmos. Sci., 76: 11−26. doi: 10.1175/JAS-D-18-0013.1
    [44] Knutson T R, Weickmann K M. 1987. 30–60 day atmospheric oscillations: Composite life cycles of convection and circulation anomalies [J]. Mon. Wea. Rev., 115: 1407−1436. doi: 10.1175/1520-0493(1987)115<1407:DAOCLC>2.0.CO;2
    [45] 孔凡铀. 1988. 用FFT法与SOR法求解二维泊松方程的比较 [J]. 气象科学, 8(1): 19−28.

    Kong Fanyou. 1988. Comparisons between FFT and SOR on solving the 2-D Poisson equations [J]. Scientia Meteorologica Sinica (in Chinese), 8(1): 19−28.
    [46] Krishnamurti T N. 1968. A study of a developing wave cyclone [J]. Mon. Wea. Rev., 96: 208−217. doi: 10.1175/1520-0493(1968)096<0208:ASOADW>2.0.CO;2
    [47] Li Z J, Chao Y, McWilliams J C. 2006. Computation of the streamfunction and velocity potential for limited and irregular domains [J]. Mon. Wea. Rev., 134: 3384−3394. doi: 10.1175/MWR3249.1
    [48] 黎爱兵, 张立凤, 臧增亮, 等. 2012. 有限区域求解流函数和速度势的迭代调整方法及其收敛性分析 [J]. 应用数学和力学, 33: 651−662. doi: 10.3879/j.issn.1000-0887.2012.06.002

    Li Aibing, Zhang Lifeng, Zang Zengliang, et al. 2012. Iterative and adjusting method for computing stream function and velocity potential in limited domains and its convergence analysis [J]. Applied Mathematics and Mechanics (in Chinese), 33: 651−662. doi: 10.3879/j.issn.1000-0887.2012.06.002
    [49] Li Z L, Qiao Z H, Tang T. 2017. Numerical Solution of Differential Equations: Introduction to Finite Difference and Finite Element Methods [M]. Cambridge: Cambridge University Press, 293pp. doi:10.1017/9781316678725
    [50] Li W L, Xia R D, Sun J H, et al. 2019. Layer-wise formation mechanisms of an Entire-Troposphere-Thick extratropical cyclone that induces a record–breaking catastrophic rainstorm in Beijing [J]. J. Geophys. Res., 124: 10567−10591. doi: 10.1029/2019JD030868
    [51] 李宏江, 曹洁, 李勋, 等. 2021. 基于有限区域风场分解的海南岛一次飑线过程演变特征分析 [J]. 自然灾害学报, 30(2): 24−35. doi: 10.13577/j.jnd.2021.0203

    Li Hongjiang, Cao Jie, Li Xun, et al. 2021. Application of wind partitioning technique in a limited domain to the characteristics of the evolution of a squall line over Hainan Island [J]. Journal of Natural Disasters (in Chinese), 30(2): 24−35. doi: 10.13577/j.jnd.2021.0203
    [52] 李永华, 周杰, 何卷雄, 等. 2022. 2020年6~7月西南地区东部降水异常偏多的水汽输送特征 [J]. 大气科学, 46: 309−326. doi: 10.3878/j.issn.1006-9895.2105.21002

    Li Yonghua, Zhou Jie, He Juanxiong, et al. 2022. Characteristics of water vapor transport associated with abnormal precipitation over the East of Southwestern China in June and July 2020 [J]. Chinese Journal of Atmospheric Sciences (in Chinese), 46: 309−326. doi: 10.3878/j.issn.1006-9895.2105.21002
    [53] 卢楚翰, 管兆勇, 李永华, 等. 2013. 太平洋年代际振荡与南北半球际大气质量振荡及东亚季风的联系 [J]. 地球物理学报, 56: 1084−1094. doi: 10.6038/cjg20130404

    Lu Chuhan, Guan Zhaoyong, Li Yonghua, et al. 2013. Interdecadal linkages between Pacific decadal oscillation and interhemispheric air mass oscillation and their possible connections with East Asian monsoon [J]. Chinese J. Geophys. (in Chinese), 56: 1084−1094. doi: 10.6038/cjg20130404
    [54] 卢长浩, 陈耀登, 孟德明. 2019. 两种动力控制变量对比分析及其对台风同化和预报的影响 [J]. 大气科学学报, 42: 916−925. doi: 10.13878/j.cnki.dqkxxb.20171018001

    Lu Changhao, Chen Yaodeng, Meng Deming. 2019. Comparative analysis of two dynamical control variables and their impacts on typhoon assimilation and prediction [J]. Transactions of Atmospheric Sciences (in Chinese), 42: 916−925. doi: 10.13878/j.cnki.dqkxxb.20171018001
    [55] Lynch P. 1988. Deducing the wind from vorticity and divergence [J]. Mon. Wea. Rev., 116: 86−93. doi: 10.1175/1520-0493(1988)116<0086:DTWFVA>2.0.CO;2
    [56] Lynch P. 1989. Partitioning the wind in a limited domain [J]. Mon. Wea. Rev., 117: 1492−1500. doi: 10.1175/1520-0493(1989)117<1492:PTWIAL>2.0.CO;2
    [57] Ma S P, Cao J, Zhao H J, et al. 2022. Decomposition of water vapor flux divergence and its application to a blizzard event over Ili Valley in Central Asia during 30 Nov to 1 Dec 2018 [J]. Atmos. Res., 270: 106079. doi: 10.1016/j.atmosres.2022.106079
    [58] Machenhauer B. 1979. The spectral method [M]//Numerical Methods Used in Atmospheric Models. Vol. II: Global Atmospheric Research Programme. GARP Publisher, 124–275.
    [59] Morse P M, Feshbach H. 1953. Methods of Theoretical Physics, Part I [M]. New York: McGraw-Hill, 657pp.
    [60] Oertel A, Schemm S. 2021. Quantifying the circulation induced by convective clouds in kilometer–scale simulations [J]. Quart. J. Roy. Meteor. Soc., 147: 1752−1766. doi: 10.1002/qj.3992
    [61] Parrish D F, Derber J C. 1992. The National Meteorological Center’s spectral statistical-interpolation analysis system [J]. Mon. Wea. Rev., 120: 1747−1763. doi: 10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2
    [62] Phillips N A. 1958. Geostrophic errors in predicting the Appalachian storm of November 1950 [J]. Geophysica, 6: 389−405.
    [63] Renfrew I A, Thorpe A J, Bishop C H. 1997. The role of the environmental flow in the development of secondary frontal cyclones [J]. Quart. J. Roy. Meteor. Soc., 123: 1653−1675. doi: 10.1002/qj.49712354210
    [64] Rosenthal S. 1963. A barotropic model for prediction in the Tropics [C]//Philippine Islands: The United States–Asian Military Weather Symposium.
    [65] Sangster W E. 1960. A method of representing the horizontal pressure force without reduction of station pressures to sea level [J]. J. Meteor., 17: 166−176. doi: 10.1175/1520-0469(1960)017<0166:AMORTH>2.0.CO;2
    [66] 沈桐立, 田永祥, 葛孝贞, 等. 2003. 数值天气预报 [M]. 北京: 气象出版社.

    Shen Tongli, Tian Yongxiang, Ge Xiaozhen, et al. 2003. Numerical Weather Prediction (in Chinese) [M]. Beijing: China Meteorological Press.
    [67] Shi N, Nakamura H. 2021. A new detection scheme of wave–breaking events with blocking flow configurations [J]. J. Climate, 34: 1467−1483. doi: 10.1175/JCLI-D-20-0037.1
    [68] Shukla J, Saha K R. 1974. Computation of non-divergent streamfunction and irrotational velocity potential from the observed winds [J]. Mon. Wea. Rev., 102: 419−425. doi: 10.1175/1520-0493(1974)102<0419:CONDSA>2.0.CO;2
    [69] Stephens J J, Johnson K W. 1978. Rotational and divergent wind potentials [J]. Mon. Wea. Rev., 106: 1452−1457. doi: 10.1175/1520-0493(1978)106<1452:RADWP>2.0.CO;2
    [70] Sun J Z, Wang H L, Tong W X, et al. 2016. Comparison of the impacts of momentum control variables on high-resolution variational data assimilation and precipitation forecasting [J]. Mon. Wea. Rev., 144: 149−169. doi: 10.1175/MWR-D-14-00205.1
    [71] Takaya K, Nakamura H. 2001. A formulation of a phase-independent wave–activity flux for stationary and migratory quasigeostrophic eddies on a zonally varying basic flow [J]. J. Atmos. Sci., 58: 608−627. doi: 10.1175/1520-0469(2001)058<0608:AFOAPI>2.0.CO;2
    [72] Tangri A C. 1966. Computation of streamlines associated with a low latitude cyclone [J]. Indian J. Meteor. Geophys., 17: 401−406.
    [73] Tatsumi Y. 1986. A spectral limited-area model with time-dependent lateral boundary conditions and its application to a multi-level primitive equation model [J]. J. Meteor. Soc. Japan, 64: 637−664. doi: 10.2151/jmsj1965.64.5_637
    [74] 王瑞春, 龚建东, 张林, 等. 2015. 热带风压场平衡特征及其对GRAPES系统中同化预报的影响研究II: 动力与统计混合平衡约束方案的应用 [J]. 大气科学, 39: 1225−1236. doi: 10.3878/j.issn.1006-9895.1412.14234

    Wang Ruichun, Gong Jiandong, Zhang Lin, et al. 2015. Tropical balance characteristics between mass and wind fields and their impact on analyses and forecasts in GRAPES system. Part Ⅱ: Application of linear balance equation–regression hybrid constraint scheme [J]. Chinese Journal of Atmospheric Sciences (in Chinese), 39: 1225−1236. doi: 10.3878/j.issn.1006-9895.1412.14234
    [75] Xie Y F, MacDonald A E. 2012. Selection of momentum variables for a three-dimensional variational analysis [J]. Pure and Applied Geophysics, 169: 335−351. doi: 10.1007/s00024-011-0374-3
    [76] Xu Q. 2019. On the choice of momentum control variables and covariance modeling for mesoscale data assimilation [J]. J. Atmos. Sci., 76: 89−111. doi: 10.1175/JAS-D-18-0093.1
    [77] Xu Q. 2021. A variational method for analyzing vortex flows in radar-scanned tornadic mesocyclones. Part I: Formulations and theoretical considerations [J]. J. Atmos. Sci., 78: 825−841. doi: 10.1175/JAS-D-20-0158.1
    [78] Xu Q, Cao J. 2021. Iterative methods for solving the nonlinear balance equation with optimal truncation [J]. Adv. Atmos. Sci., 38: 755−770. doi: 10.1007/s00376-020-0291-4
    [79] Xu Q, Liu S, Xue M. 2006. Background error covariance functions for vector wind analyses using Doppler-radar radial-velocity observations [J]. Quart. J. Roy. Meteor. Soc., 132: 2887−2904. doi: 10.1256/qj.05.202
    [80] Xu Q, Nai K, Wei L. 2007. An innovation method for estimating radar radial-velocity observation error and background wind error covariances [J]. Quart. J. Roy. Meteor. Soc., 133: 407−415. doi: 10.1002/qj.21
    [81] Xu Q, Cao J, Gao S T. 2011. Computing streamfunction and velocity potential in a limited domain of arbitrary shape. Part I: Theory and integral formulae [J]. Adv. Atmos. Sci., 28: 1433−1444. doi: 10.1007/s00376-011-0185-6
    [82] Yanai M, Nitta T. 1967. Computation of vertical motion and vorticity budget in a Caribbean easterly wave [J]. J. Meteor. Soc. Japan, 45: 444−466. doi: 10.2151/jmsj1965.45.6_444
    [83] Yang T, Li H Y, Cao J, et al. 2022. Investigating the climatology of North China’s urban inland lake based on six years of observations [J]. Sci. Total Environ., 826: 154120. doi: 10.1016/j.scitotenv.2022.154120
    [84] You C, Fung J C H. 2019. Characteristics of the sea–breeze circulation in the Pearl River Delta region and its dynamical diagnosis [J]. J. Appl. Meteor. Climatol., 58: 741−755. doi: 10.1175/JAMC-D-18-0153.1
    [85] Zhao S Y, Cook K H. 2021. Influence of Walker circulations on East African rainfall [J]. Climate Dyn., 56: 2127−2147. doi: 10.1007/s00382-020-05579-7
    [86] 赵平, 胡昌琼, 孙淑清. 1992. 一次西南低涡形成过程的数值试验和诊断II: 涡度方程和能量转换函数的诊断分析 [J]. 大气科学, 16: 177−184. doi: 10.3878/j.issn.1006-9895.1992.02.06

    Zhao Ping, Hu Changqiong, Sun Shuqing. 1992. Numerical simulation and diagnosis of the formation process of SW vortex. II: The diagnosis of vorticity equation and energy conversion function [J]. Chinese Journal of Atmospheric Sciences (Scientia Atmospherica Sinica) (in Chinese), 16: 177−184. doi: 10.3878/j.issn.1006-9895.1992.02.06
    [87] Zhao Q Y, Cook J, Xu Q, et al. 2006. Using radar wind observations to improve mesoscale numerical weather prediction [J]. Wea. Forecasting, 21: 502−522. doi: 10.1175/WAF936.1
    [88] 赵延来, 黄思训, 杜华栋. 2013. 基于变分方法的有限区域风场分解与重构I: 理论框架和仿真实验 [J]. 物理学报, 62: 039204. doi: 10.7498/aps.62.039204

    Zhao Yanlai, Huang Sixun, Du Huadong. 2013. Wind partitioning and reconstruction with variational method in a limited domain. I: Theoretical frame and simulation experiments [J]. Acta Phys. Sinica (in Chinese), 62: 039204. doi: 10.7498/aps.62.039204
    [89] 周军. 1986. 天气学诊断分析[M]. 南京: 南京气象学院, 63–77.

    Zhou Jun. 1986. Diagnostic Analyses on Synoptic Studies (in Chinese) [M]. Nanjing: Nanjing Institute of Meteorology, 63–77.
    [90] 周玉淑, 曹洁, 高守亭. 2008. 有限区域风场分解方法及其在台风SAOMEI研究中的应用 [J]. 物理学报, 57: 6654−6665. doi: 10.7498/aps.57.6654

    Zhou Yushu, Cao Jie, Gao Shouting. 2008. The method of decomposing wind field in a limited area and its application to typhoon SAOMEI [J]. Acta Phys. Sinica (in Chinese), 57: 6654−6665. doi: 10.7498/aps.57.6654
    [91] 周玉淑, 邓涤菲, 李建通. 2014. 登陆热带气旋Bilis(0604)暴雨增幅与风场结构变化 [J]. 大气科学, 38: 563−576. doi: 10.3878/j.issn.1006-9895.2013.12220

    Zhou Yushu, Deng Difei, Li Jiantong. 2014. Rainstorm amplification of typhoon Bilis (0604) and its wind structural change [J]. Chinese Journal of Atmospheric Sciences (in Chinese), 38: 563−576. doi: 10.3878/j.issn.1006-9895.2013.12220
    [92] 朱宗申, 朱国富, 张林. 2009. 用有限区域风速场准确求解流函数和速度势场的方法 [J]. 大气科学, 33: 811−824. doi: 10.3878/j.issn.1006-9895.2009.04.14

    Zhu Zongshen, Zhu Guofu, Zhang Lin. 2009. An accurate solution method of stream function and velocity potential from the wind field in a limited area [J]. Chinese Journal of Atmospheric Sciences (in Chinese), 33: 811−824. doi: 10.3878/j.issn.1006-9895.2009.04.14
    [93] 庄照荣, 李兴良, 陈春刚. 2021. 水平相关模型的性质及其在GRAPES三维变分系统中的应用 [J]. 大气科学, 45: 229−244. doi: 10.3878/j.issn.1006-9895.2010.20107

    Zhuang Zhaorong, Li Xingliang, Chen Chungang. 2021. Properties of horizontal correlation models and its application in GRAPES 3DVar system [J]. Chinese Journal of Atmospheric Sciences (in Chinese), 45: 229−244. doi: 10.3878/j.issn.1006-9895.2010.20107
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  • 收稿日期:  2022-08-11
  • 录用日期:  2022-10-26
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