The Lapse Rate of Special Atmospheres and their application.

1. The Lapse Rate of Special Atmospheres and their application. Atms 4310 / 7310 Lab 5 Anthony R. Lupo

2. The Lapse Rate of Special Atmospheres and their application. • Take (Start with) the hypsometric equation for example: • H = RT/g (physical interpretation), there are two!!!

3. The Lapse Rate of Special Atmospheres and their application. • (The Big) “H”: This is scale height, the height of all the gas in the atmosphere if the gas had same pressure and temperature. • Another interpretation is that this is the height of the atmosphere at 1/e of the Surface pressure (e- folding depth) • Does it work?

4. The Lapse Rate of Special Atmospheres and their application. • Well, if 360 hPa = 7 km, H, assuming T = 250 K, is 7175 m. • Thus, it does work! • Ok, let’s take a look at a “special atmosphere” • -(zu – zl) / H = ln(pu/pl) • Take the antilog of both sides: • Exp (-(zu – zl) / H) = pu/pl

5. The Lapse Rate of Special Atmospheres and their application. • Or……. • pu = pl exp (-(zu – zl) / H) •  We get a relationship for pressure and height if we assume a constant temperature atmosphere (e.g., T = 250 K).

6. The Lapse Rate of Special Atmospheres and their application. •  This is what we call an isothermal atmosphere. Another name for it is “barotropic” (density is a function of pressure) but we’ll talk about this later (atms 4320). Thus, we can substitute r for p. • Uses of this “special atmosphere”: • Assume zl = 0 pl = sea level pressure. • P = Pslp exp(-z/H)

7. The Lapse Rate of Special Atmospheres and their application. •  We can then assume T = Tsurface. If we know the surface pressure, and our elevation, we can reduce our pressure to sea level!!! This is how it’s done to produce the sea level pressure map!!! • Give an example: • p = 1000 mb z station elevation= 200m • Tsurf = 68o F

8. The Lapse Rate of Special Atmospheres and their application. • But keep in mind: standard US practice is to average the previous 12 h with the current for Tsurf) • We get: Pslp = 1023.6 hPa

9. The Lapse Rate of Special Atmospheres and their application. • Now, let’s find a relationship that uses a constant lapse rate given a surface pressure (Po) and Temperature (To). • Start w/ hydro. Balance and Eqn of state (Like Hypsometric equation) • We can assume • T = (To – Ge z) • where Ge is the “environmental” lapse rate

10. The Lapse Rate of Special Atmospheres and their application. •  If surface is zo = 0 the integral is (we also need to “strategically” multiply by 1 to integrate as well, can you spot it?): • Then solve for z:

11. The Lapse Rate of Special Atmospheres and their application. •  Use of this relationship: • Typically use with “US standard atmosphere” where, • To = 288 K • Po = 1013.25 • lapse = 6.5 C/km • Then in potential vorticity (PV) thinking, this standard atmosphere can be used as the base, where PV anomalies are calculated relative to the base. (We will not touch this).

12. The Lapse Rate of Special Atmospheres and their application. • Calculation of Altimeter settings. • Convert to inches 1 mb = 0.02953 inches

13. The Lapse Rate of Special Atmospheres and their application. • The End!

14. The Lapse Rate of Special Atmospheres and their application. • Questions? • Comments? • Criticisms?