Editorial Type:
Article
Article Type:
Research Article

Parameterization of the Meridional Eddy Heat and Momentum Fluxes

Cheng-Zhi Zou School of Meteorology, University of Oklahoma, Norman, Oklahoma

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Tzvi Gal-Chen School of Meteorology, University of Oklahoma, Norman, Oklahoma

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Print Publication:
01 Jun 1999
DOI:
https://doi.org/10.1175/1520-0469(1999)056<1830:POTMEH>2.0.CO;2
Page(s):
1830–1842
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Abstract

Green’s eddy diffusive transfer representation is used to parameterize the meridional eddy heat flux. The structural function obtained by Branscome for the diagonal component Kyy in the tensor of the transfer coefficients is adopted. A least squares method that uses the observed data of eddy heat flux is proposed to evaluate the magnitude of Kyy and the structure of the nondiagonal component Kyz in the transfer coefficient tensor. The optimum motion characteristic at the steering level is used as a constraint for the relationship between Kyy and Kyz. The obtained magnitude of Kyy is two to three times larger than that of the Branscome’s, which is obtained in a linear analysis with the assumption of Kyz = 0.

Green’s vertically integrated expression for the meridional eddy momentum flux is used to test the coefficients obtained in the eddy heat flux. In this parameterization, the eddy momentum flux is related to the eddy fluxes of two conserved quantities: potential vorticity and potential temperature. The transfer coefficient is taken to be the sum of that obtained in the parameterization of eddy heat flux, plus a correction term suggested by Stone and Yao, which ensures the global net eddy momentum transport to be zero. What makes the present method attractive is that, even though only the data of eddy heat flux are used to evaluate the magnitude of the transfer coefficients, the obtained magnitude of the eddy momentum flux is in good agreement with observations. For the annual mean calculation, the obtained peak values of eddy momentum flux are 94% of the observation for the Northern Hemisphere and 101% for the Southern Hemisphere. This result significantly improves the result of Stone and Yao, who obtained 34% for the Northern Hemisphere and 16% for the Southern Hemisphere in a similar calculation, but in which Kyz = 0 was assumed.

* Deceased.

Corresponding author address: Dr. Cheng-Zhi Zou, QSS Group Inc., 4500 Forbes Blvd., #200, Lanham, MD 20706.

Abstract

Green’s eddy diffusive transfer representation is used to parameterize the meridional eddy heat flux. The structural function obtained by Branscome for the diagonal component Kyy in the tensor of the transfer coefficients is adopted. A least squares method that uses the observed data of eddy heat flux is proposed to evaluate the magnitude of Kyy and the structure of the nondiagonal component Kyz in the transfer coefficient tensor. The optimum motion characteristic at the steering level is used as a constraint for the relationship between Kyy and Kyz. The obtained magnitude of Kyy is two to three times larger than that of the Branscome’s, which is obtained in a linear analysis with the assumption of Kyz = 0.

Green’s vertically integrated expression for the meridional eddy momentum flux is used to test the coefficients obtained in the eddy heat flux. In this parameterization, the eddy momentum flux is related to the eddy fluxes of two conserved quantities: potential vorticity and potential temperature. The transfer coefficient is taken to be the sum of that obtained in the parameterization of eddy heat flux, plus a correction term suggested by Stone and Yao, which ensures the global net eddy momentum transport to be zero. What makes the present method attractive is that, even though only the data of eddy heat flux are used to evaluate the magnitude of the transfer coefficients, the obtained magnitude of the eddy momentum flux is in good agreement with observations. For the annual mean calculation, the obtained peak values of eddy momentum flux are 94% of the observation for the Northern Hemisphere and 101% for the Southern Hemisphere. This result significantly improves the result of Stone and Yao, who obtained 34% for the Northern Hemisphere and 16% for the Southern Hemisphere in a similar calculation, but in which Kyz = 0 was assumed.

* Deceased.

Corresponding author address: Dr. Cheng-Zhi Zou, QSS Group Inc., 4500 Forbes Blvd., #200, Lanham, MD 20706.

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  • Boville, B. A., 1987: The validity of the geostrophic approximation in the winter stratosphere and troposphere. J. Atmos. Sci.,44, 443–457.

  • Branscome, L. E., 1980: Scales and structures of baroclinic waves and their influence on climatic states. Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA, 201 pp. [Available from Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139-4307.].

  • ——, 1983: A parameterization of transient eddy heat flux on a beta-plane. J. Atmos. Sci.,40, 2508–2521.

  • ——, W. J. Gutowski Jr., and D. A. Stewart, 1989: Effect of surface fluxes on the nonlinear development of baroclinic waves. J. Atmos. Sci.,46, 460–475.

  • Eady, E. T., 1949: Long waves and cyclone waves. Tellus,1, 33–52.

  • Genthon, C., H. L. Treut, J. Jouzel, and R. Sadourny, 1990: Parameterization of eddy sensible heat transports in zonally averaged dynamic model of the atmosphere. J. Atmos. Sci.,47, 2475–2487.

  • Green, J. S. A., 1960: A problem in baroclinic instability. Quart. J. Roy. Meteor. Soc.,86, 237–251.

  • ——, 1970: Transfer properties of the large-scale eddies and the general circulation of the atmosphere. Quart. J. Roy. Meteor. Soc.,96, 157–185.

  • MacCracken, M. C., and S. J. Ghan, 1988: Design and use of zonally-averaged climate models. Physically Based Modeling and Simulation of Climate and Climate Change, M. E. Schlesinger, Ed., Kluwer Academic, 1084 pp.

  • Manabe, S., and T. B. Terpstra, 1974: The effects of mountains on the general circulation of the atmosphere as identified by numerical experiments. J. Atmos. Sci.,31, 3–42.

  • Oort, A. H., and J. P. Peixóto, 1983: Global angular momentum and energy balance requirements from observations. Adv. Geophys.,25, 355–490.

  • Plumb, R. A., 1979: Eddy fluxes of conserved quantities by small-amplitude waves. J. Atmos. Sci.,36, 1699–1704.

  • Salustri, G., and P. H. Stone, 1983: A diagnostic study of the forcing of the Ferrel cell by eddies, with latent heat effects included. J. Atmos. Sci.,40, 1101–1109.

  • Solomon, A. B., 1997: An observational study of the spatial and temporal scales of transient eddy sensible heat fluxes. J. Climate,10, 508–520.

  • Stone, P. H., 1984: Feedbacks between dynamical heat fluxes and temperature structure in the atmosphere. Climate Processes and Climate Sensitivity, Geophys. Monogr., No. 29, Amer. Geophys. Union, 6–17.

  • ——, and M.-S. Yao, 1987: Development of a two-dimensional zonally averaged statistical–dynamical model. Part II: The role of eddy momentum fluxes in the general circulation and their parameterization. J. Atmos. Sci.,44, 3769–3786.

  • ——, and ——, 1990: Development of a two-dimensional zonally averaged statistical–dynamical model. Part III: The parameterization of the eddy fluxes of heat and moisture. J. Climate,3, 726–740.

  • Wang, B., A. Barcilon, and L. N. Howard, 1985: Linear dynamics of transient planetary waves in the presence of damping. J. Atmos. Sci.,42, 1893–1910.

  • White, A. A., 1977: The surface flow in a statistical climate model—A test of a parameterization of large-scale momentum fluxes. Quart. J. Roy. Meteor. Soc.,103, 93–119.

  • ——, and J. S. A. Green, 1984: Transfer coefficient eddy flux parameterization in a simple model of the zonal average atmospheric circulation. Quart. J. Roy. Meteor. Soc.,110, 1035–1052.

  • Wiin-Nielsen, A., and J. Sela, 1971: On the transport of quasi-geostrophic potential vorticity. Mon. Wea. Rev.,99, 447–459.

  • Wu, G.-X., and A. A. White, 1986: A further study of the surface zonal flow predicted by an eddy flux parameterization scheme. Quart. J. Roy. Meteor. Soc.,112, 1041–1056.

  • Zou, C.-Z., 1995: Development of a 2-D zonally averaged climate model and study of the intertropical convergence zone dynamics. Ph.D. dissertation, University of Oklahoma, 217 pp. [Available from University of Oklahoma, 1000 Asp Avenue, Norman, OK 73019-4076.].

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