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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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QG3: Vorticity and Geopotential Equation

  • This material requires you to start with the material from the lecture on the scaled quasi-geostrophic momentum equation.

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Quasi-geostrophic horizontal momentum equation (p coordinates)

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Use definition of vorticity🡪 vorticity equation

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Compare to scaled vorticity equation for large-scale flow

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Compare to scaled vorticity equation for large-scale flow

We see that the QG vorticity equation is very similar to the scaled vorticity equation we developed before

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…with a few additional assumptions

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What are we going to do with this?

  • We want to describe the evolution of two key features of the atmosphere
    • Large-scale waves (how does the distribution of geopotential height change with time?)
    • Midlatitude cyclones (development of low- pressure systems in the lower troposphere)
      • Influence of vertical motion, temperature advection, and mass conservation.

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Develop an equation for geopotential tendency

Start with the QG �vorticity equation

Use the definition of geostrophic wind.

Plug this in, and we immediately have an equation for the time rate of change of the geopotential height.

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QG3: Vorticity and Geopotential Equation

Richard B. Rood

rbrood@umich.edu

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

https://openclimate.org/