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CLIMATE/EARTH 401�Geophysical Fluid Dynamics�Dynamical Meteorology

Richard B. Rood

rbrood@umich.edu

https://clasp.engin.umich.edu/people/richard-b-rood/

https://openclimate.org/

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Thermal Wind: Thickness

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Geostrophic wind

Links horizontal temperature gradient

with vertical wind gradient.

Take p, height, derivative

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Relation between zonal mean temperature and wind is strong

  • This is a good diagnostic
    • And an excellent check of consistency of temperature and winds observations.
  • We see the presence of jet streams in the east-west direction, which are persistent on seasonal time scales.
    • Where do they come from?
    • Do you see jets in the tropics?

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Thermal wind

  • p is an independent variable, a coordinate.
  • Hence, x and y derivatives are taken with p constant.

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Thermal wind

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Thermal wind

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Thermal wind

Recognize from previous?

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From Previous Lecture on Thickness

Z2-Z1 = ZT ≡ Thickness - is proportional to temperature.

Note link of thermodynamic variables, and similarity to scale heights calculated in consideration of the hydrostatic equation.

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Similarity of the equations

There is clearly a relationship between thermal wind and thickness.

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Schematic of thermal wind.

  • Thickness of layers is related to temperature,
  • which causes a tilt of the pressure surfaces.

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Some previous work that has been invoked

  • Physical and intuitive meaning of mathematical manipulations
    • Exponential behavior of pressure with height
    • Logarithmic integrals and derivatives
  • Integral relationships represent that the average temperature has local impacts on winds above and below.

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End: Thermal Wind: Thickness

Richard B. Rood

rbrood@umich.edu

https://clasp.engin.umich.edu/people/richard-b-rood/

https://openclimate.org/