Abstract
Research on vertical motion in mesoscale systems is an extraordinarily challenging effort. Allowing for fewer assumptions, a new form of generalized vertical motion equation and a generalized Omega equation are derived in the Cartesian coordinate system (nonhydrostatic equilibrium) and the isobaric coordinate system (hydrostatic equilibrium), respectively. The terms on the right-hand side of the equations, which comprise the Q vector, are composed of three factors: dynamic, thermodynamic, and mass. A heavy rain event that occurred from 18 to 19 July 2021 in southern Xinjiang was selected to analyze the characteristics of the diagnostic variable in the generalized vertical motion equation (Qz) and the diagnostic variable in the generalized Omega equation (Qp) using high-resolution model data. The results show that the horizontal distribution of the Qz-vector divergence at 5.5 km is roughly similar to the distribution of the Qp-vector divergence at 500 hPa, and that both relate well to the composite radar reflectivity, vertical motion, and hourly accumulated precipitation. The Qz-vector divergence is more effective in indicating weak precipitation. In vertical cross sections, regions with alternating positive and negative large values that match the precipitation are mainly concentrated in the middle levels for both forms of Q vectors. The temporal evolutions of vertically integrated Qz-vector divergence and Qp-vector divergence are generally similar. Both perform better than the classical quasigeostrophic Q vector and nongeostrophic Q vector in indicating the development of the precipitation system.
摘要
中尺度系统垂直运动研究是一项极具挑战的工作. 本文采用较少的假设, 分别从笛卡尔坐标系 (非静力平衡) 和等压坐标系 (静力平衡) 原始方程组推导新的广义垂直运动方程和广义 Omega 方程. 方程右侧 （Q 矢量) 由三项组成:动力强迫、 热力强迫和质量强迫. 选取新疆南部 2021 年 7 月 18 日至 19 日的一场暴雨过程, 利用高分辨率模拟数据分析广义垂直运动方程和广义 Omega 方程中 Q 矢量散度的特征. 结果表明, 5.5 km 高度 Qz 矢量散度水平分布与 500 hPa 的 Qp 矢量散度相似, 且两者均与组合雷达反射率、 垂直运动和小时累积降水量对应较好, Qz矢量散度在指示弱降水方面更有效. 在垂直剖面中, 与降水量相对应的正负大值交替变化的 Q 矢量散度主要集中在对流层中层. 垂直积分的 Qz 矢量散度和 Qp矢量散度的时间演变特征相似, 在指示降水系统的发展方面, 两者均比准地转 Q 矢量和非地转 Q 矢量表现更优.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cao, J., S. T. Gao, and Y. S. Zhou, 2008: Improved Q vector analyses from the perspective of field separation and its application in a torrential rain event. Acta Physica Sinica, 57(4), 2600–2606, https://doi.org/10.7498/aps.57.2600. (in Chinese with English abstract)
Davies-Jones, R., 1991: The frontogenetical forcing of secondary circulations. Part I: The duality and generalization of the Q vector. J. Atmos. Sci., 48(4), 497–509, https://doi.org/10.1175/1520-0469(1991)048<0497:TFFOSC>2.0.CO;2.
Dixon, M. A. G., A. J. Thorpe, and K. A. Browning, 2003: Layer-wise attribution of vertical motion and the influence of potential-vorticity anomalies on synoptic development. Quart. J. Roy. Meteor. Soc., 129, 1761–1778, https://doi.org/10.1256/qj.02.83.
Gao, S. T., and Y. S. Zhou, 2019: Progress in dynamics of mesoscale vortex in recent years. Torrential Rain and Disasters, 38(5), 431–439, https://doi.org/10.3969/j.issn.1004-9045.2019.05.005. (in Chinese with English abstract)
Gao, S. T., X. R. Wang, and Y. S. Zhou, 2004: Generation of generalized moist potential vorticity in a frictionless and moist adiabatic flow. Geophys. Res. Lett., 31(12), L12113, https://doi.org/10.1029/2003GL019152.
Gao, S. T., L. K. Ran, N. Li, and X. Zhang, 2013: The “Ensemble Dynamic Factors” approach to predict rainstorm. Torrential Rain and Disasters, 32(4), 289–302, https://doi.org/10.3969/j.issn.1004-9045.2013.04.001. (in Chinese with English abstract)
Hoskins, B. J., I. Draghici. 1977. The forcing of ageostrophic motion according to the semi-geostrophci equations and in an isentropic coordinate model. J Atmos Sci, 34(12): 1859–1867, https://doi.org/10.1175/1520-0469(1977)034<1859:TFOAMA>2.0.CO;2.
Hoskins, B. J., I. Draghici, and H. C. Davies, 1978: A new look at the ω-equation. Quart. J. Roy. Meteor. Soc., 104(439), 31–38, https://doi.org/10.1002/qj.49710443903.
Li, C. Q., 2018: Research on the application of potential vorticity inversion and generalized vertical. Ph. D. dissertation, Institute of Atmospheric Physics, Chinese Academy of Sciences. (in Chinese)
Räisänen, J., 1995: Factors affecting synoptic-scale vertical motions: A statistical study using a generalized omega equation. Mon. Wea. Rev., 123(8), 2447–2460, https://doi.org/10.1175/1520-0493(1995)123<2447:FASSVM>2.0.CO;2.
Ran, L. K., Z. Li, Y. B. Zhang, and Y. B. Qi, 2019: The diagnostic analysis of Q vector during a heavy rain event in North China. Torrential Rain and Disasters, 38(1), 17–30, https://doi.org/10.3969/j.issn.1004-9045.2019.01.003. (in Chinese with English abstract)
Rantanen, M., J. Raïsänen, J. Lento, O. Stepanyuk, O. Räty, V. A. Sinclair, and H. Järvinen, 2017: OZO v.1.0: Software for solving a generalised omega equation and the Zwack-Okossi height tendency equation using WRF model output. Geoscientific Model Development, 10(2), 827–841, https://doi.org/10.5194/gmd-10-827-2017.
Shen, Y., Y. Pan, J. J. Yu, P. Zhao, and Z. J. Zhou, 2013: Quality assessment of hourly merged precipitation product over China. Transactions of Atmospheric Sciences, 36(1), 37–46, https://doi.org/10.13878/j.cnki.dqkxxb.2013.01.005. (in Chinese with English abstract)
Strahl, J. L. S., and P. J. Smith, 2001: A diagnostic study of an explosively developing extratropical cyclone and an associated 500-hPa trough merger. Mon. Wea. Rev., 129(9), 2310–2328, https://doi.org/10.1175/1520-0493(2001)129<2310:ADSOAE>2.0.CO;2.
Vasilj, J. M., and P. J. Smith, 1997: A comparison of extended and quasigeostrophic dynamics for a case of small-rossby number extratropical cyclone development. Mon. Wea. Rev., 125(12), 3347–3356, https://doi.org/10.1175/1520-0493(1997)125<3347:ACOEAQ>2.0.CO;2.
Xu, Q., 1992: Ageostrophic pseudovorticity and geostrophic C-vector forcing—A new look at the Q vector in three dimensions. J. Atmos. Sci., 49(12), 981–990, https://doi.org/10.1175/1520-0469(1992)049<0981:APAGCV>2.0.CO;2.
Yang, S., S. T. Gao, and D. H. Wang, 2007: Diagnostic analyses of the ageostrophic \(\overrightarrow{Q}\) vector in the non-uniformly saturated, frictionless, and moist adiabatic flow. J. Geophys. Res.: Atmos., 112(D9), D09114, https://doi.org/10.1029/2006JD008142.
Yao, X. P., Y. B. Yu, and S. W. Shou, 2004: Diagnostic analyses and application of the moist ageostrophic vector Q. Adv. Atmos. Sci., 21(1), 96–102, https://doi.org/10.1007/BF02915683.
Yue, C. J., 2014: Progress in application study of Q vector, helicity, potential vorticity and its inversion to torrential rainfall associated with typhoon. Torrential Rain and Disasters, 33(3), 193–201, https://doi.org/10.3969/j.issn.1004-9045.2014.03.001. (in Chinese with English abstract)
Yue, C. J., J. Li, P. Y. Chen, T. Xu, and X. F. Wang, 2013: Study on improvement of moist Q vector interpretation technique. Plateau Meteorology, 32(6), 1617–1625, https://doi.org/10.7522/j.issn.1000-0534.2012.00155. (in Chinese with English abstract)
Zhu, Q. G., J. R. Lin, S. W. Shou, 2007: Principles and Methods of Meteorology. 619–636. (in Chinese)
Acknowledgements
This study was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA17010105), National Key Research and Development Program (Grant No. 2018YFC1507104), Science and Technology Development Plan Project of Jilin Province (20180201035SF), Flexible Talents Introducing Project of Xinjiang (2019), and the National Key Scientific and Technological Infrastructure project “Earth System Numerical Simulation Facility” (EarthLab).
Author information
Authors and Affiliations
Corresponding author
Additional information
Article Highlights
• Qz contains more thermodynamic and mass information than Qp.
• Both Qz and Qp relate well to the vertical velocity and rainband, and Qz is more effective at indicating weak precipitation.
This paper is a contribution to the special issue on the 14th International Conference on Mesoscale Convective Systems and High-Impact Weather.
Rights and permissions
About this article
Cite this article
Jiao, B., Ran, L., Li, N. et al. Comparative Analysis of the Generalized Omega Equation and Generalized Vertical Motion Equation. Adv. Atmos. Sci. 40, 856–873 (2023). https://doi.org/10.1007/s00376-022-1435-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00376-022-1435-5