Estimating Vertical Motions Using the 1st Law of Thermodynamics

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: w = -rgw • 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, r, 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 (-w) • CAA  downward motion (w)

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?