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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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Material Derivative: Pressure Coordinate

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Material derivative in height (z) coordinates

By definition:

Example: Total derivative of the temperature (T) on constant z surfaces

(subscript omitted)

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Material derivative in pressure (p) coordinates

By definition:

Total derivative DT/Dt on constant pressure surfaces:

(subscript omitted)

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Characteristics of vertical motion in pressure coordinates

  • For upward motion, the sign of ‘w’,vertical velocity in height coordinates, is positive.
  • The sign of ω for upward vertical motion is negative.

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  • Pressure decreases with height.

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Vertical motion in pressure coordinates

  • ω is negative for upward motion
  • ω is positive for downward motion

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End: Material Derivative: Pressure Coordinate

Richard B. Rood

rbrood@umich.edu

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

https://openclimate.org/