Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Transformations for Temperature Flux in Multiscale Models of the Tropics

  • 39 Accesses

  • 3 Citations


How much of the observed planetary-scale heating in the tropics is due to eddy flux convergence? A mathematical framework to address this important practical issue is developed here. We describe a pair of velocity transformations that remove components of the upscale temperature flux in the multiscale intraseasonal, planetary, equatorial synoptic-scale dynamics (IPESD) framework derived by Majda and Klein [J. Atmos. Sci. 60: 393–408, (2003)]. Using examples from the models of the Madden-Julian Oscillation of Biello and Majda [Proc. Natl. Acad. Sci. 101: 4736–4741, (2004); J. Atmos. Sci. 62: 1694–1721, (2005); Dyn. Oceans Atmos., in press] we demonstrate that the transformation for the meridional temperature flux convergence is possible with any restrictions on the heating profile, we show under which conditions the transformation for the vertical temperature flux convergence exists and, further, that the meridional transformation leads to a reinterpretation of lower troposphere Ekman dissipation as active heating plus zonal momentum drag. The meridional temperature flux transformation and induced meridional circulation is a new, tropical wave example of the transformed Eulerian mean theory in the case of strong vertical stratification of potential temperature. The asymptotic ordering of the flows means that the removal of the meridional temperature flux convergence has implications for how planetary-scale heating rates are inferred from velocity convergence measurements.

This is a preview of subscription content, log in to check access.


  1. 1.

    Andrews D.G., Holton J.R., Leovy C.B. (1987) Middle atmosphere dynamics. Academic, New York

  2. 2.

    Andrews D.G., McIntyre M.E. (1976) Planetary waves in horizontal and vertical shear: the generalized Eliassen–Palm relation and the mean zonal acceleration. J. Atmos. Sci. 33, 2031–2048

  3. 3.

    Andrews D.G., McIntyre M.E. (1978) Generalized Eliassen–Palm and Charney–Drazin theorems for waves on axisymmetric mean flows in compressible atmospheres. J. Atmos. Sci. 35, 175–185

  4. 4.

    Andrews D.G., McIntyre M.E. (1978) An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech. 89, 609–646

  5. 5.

    Biello J.A., Majda A.J. (2005) A new multi-scale model for the Madden–Julian Oscillation. J. Atmos. Sci. 62, 1694–1721

  6. 6.

    Biello J.A., Majda A.J. (2004) Boundary layer dissipation and the nonlinear interaction of equatorial baroclinic and barotropic Rossby waves. Geophys. Astro. Fluid Dyn. 98, 85–127

  7. 7.

    Biello, J.A., Majda, A.J.: Modulating synoptic scale convective activity and boundary layer dissipation in the IPESD models of the Madden–Julian Oscillation. Dyn. Oceans Atmos. (in press)

  8. 8.

    Grabowski W.W. (2001) Coupling cloud processes with large-scale dynamics using the Cloud-Resolving Convection Parametrization (CRCP). J. Atmos. Sci. 58, 978–997

  9. 9.

    Haynes P.H., Marks C.J., McIntyre M.E., Shepherd T.G., Shine K.P. (1991) On the “downward control” of extratropical diabatic circulations by eddy-induced mean zonal forces. J. Atmos. Sci. 48, 651–678

  10. 10.

    Majda A.J., Biello J.A. (2004) A multi-scale model for tropical intraseasonal oscillations. Proc. Natl. Acad. Sci. 101, 4736–4741

  11. 11.

    Majda A.J., Klein R. (2003) Systematic multi-scale models for the tropics. J. Atmos. Sci. 60, 393–408

  12. 12.

    Marshall J., Radko T. (2003) Residual-mean solutions for the Antarctic circumpolar current and its associated overturning circulation. J. Phys. Oceanogr. 33, 2341–2354

  13. 13.

    Moncrieff M. (2004) Analytic representation of the large-scale organization of tropical convection. J. Atmos. Sci. 61, 1521–1538

  14. 14.

    Moncrieff M., Klinker E. (1997) Organized convective systems in the tropical western Pacific as a process in general circulation models: A TOGA COARE case study. Quart. J. Roy. Met. Soc. 123, 805–827

  15. 15.

    Moskowitz B.M., Bretherton C.S. (2000) An analysis of frictional feedback on a moist equatorial Kelvin mode. J. Atmos. Sci. 57, 2188–2206

  16. 16.

    Nakazawa T. (1988) Tropical super clusters within intraseasonal variations over the western pacific. J. Meteor. Soc. Jpn. 66, 823–839

  17. 17.

    Neelin J.D. (1989) On the interpretation of the Gill model. J. Atmos. Sci. 46, 2466–2468

  18. 18.

    Plumb R.A., Ferrari R. (2005) Transformed Eulerian-mean theory. part I: nonquasigeostrophic theory for Eddies on a zonal-mean flow. J. Phys. Oceanogr. 35, 165–174

  19. 19.

    Straub K.H., Kiladis G.N. (2003) Interactions between the Boreal summer intraseasonal oscillation and higher-frequency tropical wave activity. Mon. Weather Rev. 131, 945–960

  20. 20.

    Yanai M., Esbensen S., Chu J.-H. (1973) Determination of bulk properties of tropical cloud clusters from large-scale heat and moisture budgets. J. Atmos. Sci. 30, 611–627

Download references

Author information

Correspondence to Joseph A. Biello.

Additional information

Communicated by R. Klein

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Biello, J.A., Majda, A.J. Transformations for Temperature Flux in Multiscale Models of the Tropics. Theor. Comput. Fluid Dyn. 20, 405–420 (2006). https://doi.org/10.1007/s00162-006-0021-2

Download citation


  • Multiscale models
  • Tropical meteorology
  • Transformed Eulerian mean