Editorial Type:
Article
Article Type:
Research Article

The Response of a Uniform Horizontal Temperature Gradient to Heating

Maarten H. P. Ambaum Department of Meteorology, University of Reading, Reading, United Kingdom

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Panos J. Athanasiadis Department of Meteorology, University of Reading, Reading, United Kingdom

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Print Publication:
01 Oct 2007
DOI:
https://doi.org/10.1175/JAS4038.1
Page(s):
3708–3716
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Abstract

The response of a uniform horizontal temperature gradient to prescribed fixed heating is calculated in the context of an extended version of surface quasigeostrophic dynamics. It is found that for zero mean surface flow and weak cross-gradient structure the prescribed heating induces a mean temperature anomaly proportional to the spatial Hilbert transform of the heating. The interior potential vorticity generated by the heating enhances this surface response. The time-varying part is independent of the heating and satisfies the usual linearized surface quasigeostrophic dynamics. It is shown that the surface temperature tendency is a spatial Hilbert transform of the temperature anomaly itself. It then follows that the temperature anomaly is periodically modulated with a frequency proportional to the vertical wind shear. A strong local bound on wave energy is also found. Reanalysis diagnostics are presented that indicate consistency with key findings from this theory.

Corresponding author address: Dr. Maarten Ambaum, Department of Meteorology, University of Reading, P.O. Box 243, Reading, RG6 6BB, United Kingdom. Email: m.h.p.ambaum@reading.ac.uk

Abstract

The response of a uniform horizontal temperature gradient to prescribed fixed heating is calculated in the context of an extended version of surface quasigeostrophic dynamics. It is found that for zero mean surface flow and weak cross-gradient structure the prescribed heating induces a mean temperature anomaly proportional to the spatial Hilbert transform of the heating. The interior potential vorticity generated by the heating enhances this surface response. The time-varying part is independent of the heating and satisfies the usual linearized surface quasigeostrophic dynamics. It is shown that the surface temperature tendency is a spatial Hilbert transform of the temperature anomaly itself. It then follows that the temperature anomaly is periodically modulated with a frequency proportional to the vertical wind shear. A strong local bound on wave energy is also found. Reanalysis diagnostics are presented that indicate consistency with key findings from this theory.

Corresponding author address: Dr. Maarten Ambaum, Department of Meteorology, University of Reading, P.O. Box 243, Reading, RG6 6BB, United Kingdom. Email: m.h.p.ambaum@reading.ac.uk

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  • Ambaum, M. H. P., 1997: Isentropic formation of the tropopause. J. Atmos. Sci., 54 , 555–568.

  • Bleeker, W., 1950: The structure of weather systems. Centenary Proceedings of the Royal Meteorological Society 1950, R. Watson-Watt, Ed., Royal Meteorological Society, 66–80.

  • Bolin, B., 1950: On the influence of the earth’s orography on the general character of the westerlies. Tellus, 2 , 184–195.

    • Search Google Scholar
    • Export Citation

  • Bretherton, F. P., 1966: Critical layer instability in baroclinic flows. Quart. J. Roy. Meteor. Soc., 92 , 325–334.

  • Charney, J. G., 1947: The dynamics of long waves in a baroclinic westerly current. J. Meteor., 4 , 135–162.

  • Charney, J. G., and A. Eliassen, 1949: A numerical method for predicting the perturbations of the middle latitude westerlies. Tellus, 1 , 38–54.

    • Search Google Scholar
    • Export Citation

  • Davies, H. C., and C. H. Bishop, 1994: Eady edge waves and rapid development. J. Atmos. Sci., 51 , 1930–1946.

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

  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Hayes, M., 1977: A note on group velocity. Proc. Roy. Soc. London, 354 , 533–535.

  • Haynes, P., J. Scinocca, and M. Greenslade, 2001: Formation and maintenance of the extratropical tropopause by baroclinic eddies. Geophys. Res. Lett., 28 , 4179–4182.

    • Search Google Scholar
    • Export Citation

  • Heifetz, E., C. H. Bishop, B. J. Hoskins, and J. Methven, 2004: The counter-propagating Rossby-wave perspective on baroclinic instability. I: Mathematical basis. Quart. J. Roy. Meteor. Soc., 130 , 211–231.

    • Search Google Scholar
    • Export Citation

  • Held, I. M., 1983: Stationary and quasi-stationary eddies in the extratropical troposphere: Theory. Large-Scale Dynamical Processes in the Atmosphere, B. J. Hoskins and R. Pearce, Eds., Academic Press, 127–168.

    • Search Google Scholar
    • Export Citation

  • Held, I. M., R. T. Pierrehumbert, S. T. Garner, and K. L. Swanson, 1995: Surface quasi-geostrophic dynamics. J. Fluid Mech., 282 , 1–20.

    • Search Google Scholar
    • Export Citation

  • Hoskins, B. J., and D. J. Karoly, 1981: The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci., 38 , 1179–1196.

    • Search Google Scholar
    • Export Citation

  • Hoskins, B. J., and K. I. Hodges, 2002: New perspectives on the Northern Hemisphere winter storm tracks. J. Atmos. Sci., 59 , 1041–1061.

    • Search Google Scholar
    • Export Citation

  • Joly, A., and A. J. Thorpe, 1990: Frontal instability generated by tropospheric potential vorticity anomalies. Quart. J. Roy. Meteor. Soc., 116 , 525–560.

    • Search Google Scholar
    • Export Citation

  • KÃ¥llberg, P., P. Berrisford, B. J. Hoskins, A. Simmons, S. Uppala, S. Lamy-Thépaut, and R. Hine, 2005: ERA-40 Atlas. ERA-40 Project Report Series 19, ECMWF, 191 pp.

  • Müller, J. C., H. C. Davies, and C. Schär, 1989: An unsung mechanism for frontogenesis and cyclogenesis. J. Atmos. Sci., 46 , 3664–3672.

    • Search Google Scholar
    • Export Citation

  • Rhines, P., 1970: Edge-, bottom-, and Rossby waves in a rotating stratified fluid. Geophys. Fluid. Dyn., 1 , 273–302.

  • Schär, C., and H. C. Davies, 1990: An instability of mature cold fronts. J. Atmos. Sci., 47 , 929–950.

  • Smagorinsky, J., 1953: The dynamical influence of large-scale heat sources and sinks on the quasi-stationary mean motions of the atmosphere. Quart. J. Roy. Meteor. Soc., 79 , 342–366.

    • Search Google Scholar
    • Export Citation

  • Straus, D. M., 1983: Conservation laws of wave action and potential enstrophy for Rossby waves in a stratified atmosphere. Pure Appl. Geophys., 121 , 917–946.

    • Search Google Scholar
    • Export Citation

  • Sutcliffe, R. C., 1951: Mean upper contour patterns of the Northern Hemisphere—The thermal-synoptic view-point. Quart. J. Roy. Meteor. Soc., 77 , 435–440.

    • Search Google Scholar
    • Export Citation

  • Swanson, K. L., 2001: Upper-tropospheric potential vorticity fluctuations and the dynamical relevance of the time mean. J. Atmos. Sci., 58 , 1815–1826.

    • Search Google Scholar
    • Export Citation

  • von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in Climate Research. Cambridge University Press, 484 pp.

  • Whitham, G. B., 1974: Linear and Nonlinear Waves. John Wiley and Sons, 636 pp.

  • Zimin, A. V., I. Szunyogh, D. J. Patil, B. R. Hunt, and E. Ott, 2003: Extracting envelopes of Rossby wave packets. Mon. Wea. Rev., 131 , 1011–1017.

    • Search Google Scholar
    • Export Citation
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