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The Mathematics of Isentropic Analyses

The Mathematics of Isentropic Analyses. Getting a handle of slantwise ascent / descent. Slantwise Ascent / Descent. How do we get at slantwise ascent / descent using potential temperature?. Assume frozen wave…. Solving for : . Some issues….

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The Mathematics of Isentropic Analyses

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  1. The Mathematics of Isentropic Analyses Getting a handle of slantwise ascent / descent

  2. Slantwise Ascent / Descent

  3. How do we get at slantwise ascent / descent using potential temperature? Assume frozen wave… Solving for :

  4. Some issues… Very similar result we got earlier for using temperature, but still problems with denominator and we’re no further along toward assessing slantwise ascent / descent

  5. Before we move on…Is there anything to be learned from the diabatic term? Diabatic term Radiative cooling of 1-2 degrees Celsius per day above boundary layer Latent heating can be many degrees per day…let’s investigate

  6. Latent Heating… It follows that there are of latent heating per kilometer of ascent Synoptic-scale upward motion…

  7. Getting at Slantwise Ascent / Descent

  8. A Slightly Different Approach In x, y, z space… Measured on a constant height surface at altitude z at point x, y, z

  9. Switching from a constant height to a constant theta surface In x, y, space (isentropic surface), Tendency of p on the theta surface at our location flow of air on theta surface from one p value to another Note: Normally, so if there’s diabatic heating, then the diabatic term becomes more negative… enhanced upward motion Diabatic heating/cooling; makes parcel cross from one theta surface to another

  10. If adiabatic flow, … If weather system is moving without change in shape or intensity (frozen wave), then

  11. Application… In terms of natural coordinates, 800 upward motion (slantwise ascent) 900 Caveat: Isobars do NOT represent on isentropic surfaces…just a reference level or “altitude”

  12. Isentropic lift (overrunning)

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