1. Estimating Vertical Motions Using the 1st Law of Thermodynamics Lab 8 Atms 4310 / 7310 Tony Lupo

2. Estimating Vertical Motions Using the 1st Law of Thermodynamics Vertical motions:  are the result of “unbalanced” or ageostrophic motions.  result in the “so called” secondary / synoptic (or meridional / general circulation) circulations

3. Estimating Vertical Motions Using the 1st Law of Thermodynamics Vertical motions:  these are important to understanding atmospheric dynamics.  are important indicators of cloud formation and precipitation processes.

4. Estimating Vertical Motions Using the 1st Law of Thermodynamics Q: Can I measure vertical motions directly? A:HET! So we must calculate them, ….. but how? From hydrostatic balance we know:  = -  gw But several equations have an “omega” in them.

5. Estimating Vertical Motions Using the 1st Law of Thermodynamics There are several methods for calculation…… 1. Continuity (Kinematic method):

6. Estimating Vertical Motions Using the 1st Law of Thermodynamics 2. Primitive Equations (Omega Equation) dynamics+thermodynamics)

7. Estimating Vertical Motions Using the 1st Law of Thermodynamics 3. 1st Law of thermodynamics!  We can calculate quickly (typically in tropical meteorology)  Dynamics implicitly included (but less important)

8. Estimating Vertical Motions Using the 1st Law of Thermodynamics OK, derive! Solve for “dT”

9. Estimating Vertical Motions Using the 1st Law of Thermodynamics Sub in Equation of State and define omega: Term with Omega represents stability (dry adiabatic lapse rate)!

10. Estimating Vertical Motions Using the 1st Law of Thermodynamics Then, And redefine S = environmental lapse rate – dry adiabatic = Static Stability

11. Estimating Vertical Motions Using the 1st Law of Thermodynamics Finally, a bit o’ algebra and: In adiabatic form we can neglect Latent Heat Release!

12. Estimating Vertical Motions Using the 1st Law of Thermodynamics For most synoptic applications (in the troposphere of course): S > 0 or on order of 1 x 10 -3 K hPa -1

13. Estimating Vertical Motions Using the 1st Law of Thermodynamics Advantages of this method: 1. the lapse rate, R, T, g, , and thus S can be calculated from ONE SINGLE SOUNDING! (Qualitatively or Quantitatively) 2. temperature advections can be determined qualitatively from ONE SINGLE SOUNDING, or a fax chart if you must.

14. Estimating Vertical Motions Using the 1st Law of Thermodynamics Sounding (wind backing with height  cold advection). Here’s a view (Dr. Brad Muller) – Thermal Wind

15. Estimating Vertical Motions Using the 1st Law of Thermodynamics This is for the NH only, ….of course! 3. the local rate of change in temperature is easy to determine from ONE SINGLE SOUNDING. Only drawbacks: 1. the local change in temperature and the advection are typically of the same order of magnitude in the mid-latitudes and opposite in sign (in the absence of LHR), especially in the lower troposphere.

16. Estimating Vertical Motions Using the 1st Law of Thermodynamics 2. This method is sensitive to value of S, and only implicitly includes dynamics. Then, if we have a small change in local temperature, vertical motion can be determined via temperature advections!! WAA  upward motion (-  ) CAA  downward motion (  )

17. Estimating Vertical Motions Using the 1st Law of Thermodynamics The End!

18. Estimating Vertical Motions Using the 1st Law of Thermodynamics Questions? Comments? Criticisms?