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Efficient Anomalous Forcings for Linear Problems


doi: 10.1007/BF02658164

  • For linear forcing problems, a method is developed to provide a set of forcing modes which form a complete orthonormal basis for the finite-time response to steady forcing in the energy inner product space. The forcing modes are found by calculating eigenvectors of a positive definite and symmetric matrix determined from given equations of motion. The amplitude of responses to forcing modes is given in terms of the associated eigenvalues. This method is used in a nondivergent barotropic model linearized about the 300 hPa zonally-varying climatological flow both for northern summertime and wintertime. The results show that the amplitude of response varies considerably with dif-ferent forcing modes. Only a few of forcing modes associated with the leading eigenvalues, called efficient forcing mode, can excite significant response. The efficient forcing modes possess highly localized spatial structure with wavetrain appearance. Most of the efficient forcings are located to the south of regions of the jet cores. The forcings located over polar regions are also efficient. In addition, the response is larger in wintertime than in summertime for a given forcing.
  • [1] LI Shuanglin, CHEN Xiaoting, 2014: Quantifying the Response Strength of the Southern Stratospheric Polar Vortex to Indian Ocean Warming in Austral Summer, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 492-503.  doi: 10.1007/s00376-013-2322-x
    [2] FuZuntao, Zhao Qiang, QiaoFangli, Liu Shikuo, 2000: Response of Atmospheric Low-frequency Wave to Oceanic Forcing in the Tropics, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 569-575.  doi: 10.1007/s00376-000-0020-y
    [3] Bing XIE, Hua ZHANG, Zhili WANG, Shuyun ZHAO, Qiang FU, 2016: A Modeling Study of Effective Radiative Forcing and Climate Response Due to Tropospheric Ozone, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 819-828.  doi: 10.1007/s00376-016-5193-0
    [4] WANG Zhili, ZHANG Hua, SHEN Xueshun, 2011: Radiative Forcing and Climate Response Due to Black Carbon in Snow and Ice, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 1336-1344.  doi: 10.1007/s00376-011-0117-5
    [5] Ni Yunqi, Zou Li, Wu Aiming, 1996: Response Process of Ocean to Atmospheric Forcing and Optimal Response Frequency in the CZ Ocean Model, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 43-58.  doi: 10.1007/BF02657027
    [6] Xiang LI, Yiyong LUO, 2016: Response of North Pacific Eastern Subtropical Mode Water to Greenhouse Gas Versus Aerosol Forcing, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 522-532.  doi: 10.1007/s00376-015-5092-9
    [7] D. R. Chakraborty, P.S. Salvekar, 1989: An Efficient Accurate Direct Solution of Poisson’s Equation for Computation of Meteorological Parameters, ADVANCES IN ATMOSPHERIC SCIENCES, 6, 501-508.  doi: 10.1007/BF02659084
    [8] Yong. L. McHall, 1990: Generalized Available Potential Energy, ADVANCES IN ATMOSPHERIC SCIENCES, 7, 395-408.  doi: 10.1007/BF03008870
    [9] Wang Mingxing, 1985: SOURCE IDENTIFICATION AND APPORTIONMENT FOR ATMOSPHERIC AEROSOL BY FACTOR ANALYSIS, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 469-477.  doi: 10.1007/BF02678745
    [10] Sayed M. Elshazly, 1996: A Study of Linke Turbidity Factor over Qena / Egypt, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 519-532.  doi: 10.1007/BF03342042
    [11] Baofeng JIAO, Lingkun RAN, Na LI, Ren CAI, Tao QU, Yushu ZHOU, 2023: Comparative Analysis of the Generalized Omega Equation and Generalized Vertical Motion Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 40, 856-873.  doi: 10.1007/s00376-022-1435-5
    [12] Wu Guoxiong, 1988: MOUNTAIN TORQUE AND EXTERNAL FORCING, ADVANCES IN ATMOSPHERIC SCIENCES, 5, 141-148.  doi: 10.1007/BF02656776
    [13] GAO Shouting, XU Pengcheng, LI Na, 2012: On the Generalized Ertel--Rossby Invariant, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 690-694.  doi: 10.1007/s00376-012-1145-5
    [14] YANG Shuai, GAO Shouting, LU Chungu, 2014: A Generalized Frontogenesis Function and Its Application, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 1065-1078.  doi: 10.1007/s00376-014-3228-y
    [15] LU Weisong, SHAO Haiyan, 2003: Generalized Nonlinear Subcritical Symmetric Instability, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 623-630.  doi: 10.1007/BF02915505
    [16] Liu Yangang, 1995: On the Generalized Theory of Atmospheric Particle Systems, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 419-438.  doi: 10.1007/BF02657003
    [17] Samuel S. P. SHEN, Benedikt KRAMPS, Shirley X. SUN, Barbara BAILEY, 2012: An Approach to Quantify the Heat Wave Strength and Price a Heat Derivative for Risk Hedging, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 1-9.  doi: 10.1007/s00376-011-1020-9
    [18] Chunsheng ZHAO, Yingli YU, Ye KUANG, Jiangchuan TAO, Gang ZHAO, 2019: Recent Progress of Aerosol Light-scattering Enhancement Factor Studies in China, ADVANCES IN ATMOSPHERIC SCIENCES, 36, 1015-1026.  doi: 10.1007/s00376-019-8248-1
    [19] DAI Qiudan, SUN Shufen, 2006: A Generalized Layered Radiative Transfer Model in the Vegetation Canopy, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 243-257.  doi: 10.1007/s00376-006-0243-7
    [20] DAI Qiudan, SUN Shufen, 2007: A Simplified Scheme of the Generalized Layered Radiative Transfer Model, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 213-226.  doi: 10.1007/s00376-007-0213-8

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Manuscript History

Manuscript received: 10 October 1994
Manuscript revised: 10 October 1994
通讯作者: 陈斌, bchen63@163.com
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Efficient Anomalous Forcings for Linear Problems

  • 1. Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100080,Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100080

Abstract: For linear forcing problems, a method is developed to provide a set of forcing modes which form a complete orthonormal basis for the finite-time response to steady forcing in the energy inner product space. The forcing modes are found by calculating eigenvectors of a positive definite and symmetric matrix determined from given equations of motion. The amplitude of responses to forcing modes is given in terms of the associated eigenvalues. This method is used in a nondivergent barotropic model linearized about the 300 hPa zonally-varying climatological flow both for northern summertime and wintertime. The results show that the amplitude of response varies considerably with dif-ferent forcing modes. Only a few of forcing modes associated with the leading eigenvalues, called efficient forcing mode, can excite significant response. The efficient forcing modes possess highly localized spatial structure with wavetrain appearance. Most of the efficient forcings are located to the south of regions of the jet cores. The forcings located over polar regions are also efficient. In addition, the response is larger in wintertime than in summertime for a given forcing.

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