1. NATS 101 Lecture 12 Vertical Stability

2. Tennis Basics Piece of cake, right? Forehand: Drop Shot:
Racket velocity before hit
Ball speed approaching
Ball speed leaving
Forehand:
Racket velocity before hit
Ball speed approaching
Ball speed leaving
Drop Shot:
Piece of cake, right?

3. Air Molecules Act Similarly
Molecule speed approaching
Boundary velocity
Molecule speed leaving
Contracting Boundary:
Expanding Boundary:

4. Rising Air Cools-Sinking Air Warms
Rising air parcel expands
Expansion requires work against outside air
Air molecules rebound from “walls” at a slower speed, resulting in a cooler temperature
Assuming no transfer of heat across parcel walls (adiabatic expansion), cooling rate is 10oC/km
no heat transfer
494 m/s
10oC
502 m/s
502 m/s
494 m/s
8 m/s
1 km
Rising Expanding
Sinking Contracting
20oC
502 m/s
Ahrens, Fig 5.2

5. Adiabatic Cooling-Warming
Dew point decreases with height at a rate of 2oC/km b/c DP varies less with Pressure than Temp.
The rate is much less than cooling rate for air.
Thus, unsaturated air can become saturated IF it rises far enough.
10C 10C
20C 12C
30C 14C
Ahrens, Fig 5.2
Red=Temperature Blue=Dew Point

6. Rising, Saturated Air Cools Less
As a saturated parcel rises and expands, the release of latent heat mitigates the adiabatic cooling
Cooling for saturated air varies with mixing ratio.
We will use an average value of 6oC/km for moisture lapse rate
Note: sinking clear air always warms at dry lapse rate
no heat transfer
497 m/s
14oC
502 m/s
latent heating
502 m/s
497 m/s
5 m/s
1 km
Rising Expanding
Sinking Contracting
20oC
502 m/s
Ahrens, Fig 5.2

7. Moist Flow over a Mountain
-6C -6C
MAR
+10C +2C
DAR
-6C -6C
MAR
saturated
unsaturated
+10C +2C DAR
unsaturated
-10C -2C
DAR
+10C +2C
DAR
Ahrens, Fig 5.12
These concepts can be applied to understand Temp and DP changes for moist flow over a mountain

8. Brain Burners Rising and sinking unsaturated (clear) air
Temp changes at Dry Adiabatic Rate (DAR) of 10oC/km
Dew point changes at rate of 2oC/km
Rising and sinking saturated (cloudy) air
Temp cools at Moist Adiabatic Rate (MAR) of 6oC/km
Dew point decreases at rate of 6oC/km

9. Concept of Stability Stable Rock always returns to starting point
Unstable Rock never returns to starting point
Conditionally Unstable Rock never returns if rolled past top of initial hill
Ahrens, Fig 5.1

10. Archimedes’ Principle
Archimedes' principle is the law of buoyancy.
It states that "any body partially or completely submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body."
The weight of an object acts downward, and the buoyant force provided by the displaced fluid acts upward. If the density of an object is greater/less than the density of water, the object will sink/float.
Demo: Diet vs. Regular Soda.

11. Absolutely Stable: Top Rock
Stable air strongly resists upward motion
External force must be applied to an air parcel before it can rise
Clouds that form in stable air spread out horizontally in layers, with flat bases-tops
Ahrens, Fig 5.3

12. Absolutely Unstable: Middle Rock
Unstable air does not resist upward motion
Clouds in unstable air stretch out vertically
Absolute instability is limited to very thin layer next to ground on hot, sunny days
Superadiabatic lapse rate
Ahrens, Fig 5.5

13. Conditionally Unstable: Lower Rock
Ahrens, Fig 5.7

14. Environmental Lapse Rate (ELR)
ELR is the Temp change with height that is recorded by a weather balloon
6.5o C/km
6.0o C/km
ELR is 6.5o C/km, on average, and thus is conditionally unstable!
10.0o C/km
ELR is absolutely unstable in a thin layer just above the ground on hot, sunny days
Ahrens, Meteorology Today 5th Ed.

15. Lapse Rates and Cumulus Types
Ahrens, Meteorology Today 5th Ed.
The ELR and depth of unstable layer modulates the type of Cu.
As depth increases, the vertical extent of Cu generally increases.
As temp difference between the air parcel and the environment increases, the updraft speed and severity of Cb typically increase.

16. Summary: Key Concepts I
Rising unsaturated air, and all sinking air
Temp changes at DAR of 10oC/km
DP changes at rate of 2oC/km
Saturation occurs with sufficient lifting
Rising saturated air
Latent Heating Mitigates Adia. Cooling
Temp and DP cools at MAR of 6oC/km
Note that MAR is always less than DAR

17. Summary: Key Concepts II
Vertical Stability Determined by ELR
Absolutely Stable and Unstable
Conditionally Unstable
Temp Difference between ELR and Air Parcel, and Depth of Layer of Conditionally Instability Modulates
Vertical Extent and Severity of Cumulus

18. Assignment for Next Lecture
Topic - Precipitation Processes
Reading - Ahrens p
Problems , 5.16, 5.17