NATS 101

Lecture 12Vertical Stability

Tennis Basics

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?

Air Molecules Act Similarly

Contracting Boundary:

Expanding Boundary:

Molecule speed approaching

Boundary velocity

Molecule speed leaving

Molecule speed approaching

Boundary velocity

Molecule speed leaving

Rising Air Cools-Sinking Air Warms

8 m/s

494 m/s

502 m/s

502 m/s

494 m/s

Rising Expanding

Sinking Contracting

Rising air parcel expandsExpansion requires work

against outside airAir 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

10oC

20oC

no heat no heat transfertransfer

Ahrens, Fig 5.2

1 k

m

502 m/s

Adiabatic Cooling-Warming

30C 14C

20C 12C

10C 10C

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.

Red=Temperature Blue=Dew Point

Ahrens, Fig 5.2

Rising, Saturated Air Cools Less

5 m/s

497 m/s

502 m/s

502 m/s

497 m/s

Rising Expanding

Sinking Contracting

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 air always warms at dry lapse rate

14oC

20oC

no heat no heat transfertransfer

Ahrens, Fig 5.2

1 k

m

latent latent heatingheating

502 m/s

Moist Flow over a Mountain

Ahrens, Fig 5.12

These concepts can be applied to understand Temp and DP changes for moist flow over a mountain

-10C -2CDAR

-6C -6CMAR

-6C -6CMAR

+10C +2CDAR

+10C +2C DAR

+10C +2CDAR

satu

rate

d

unsaturatedun

satu

rate

d

Brain Burners

Rising unsaturated air, and all sinking air

Temp changes at Dry Adiabatic Rate (DAR) of 10oC/km

Dew point changes at rate of 2oC/km

Rising saturated air

Temp cools at Moist Adiabatic Rate (MAR) of 6oC/km

Dew point decreases at rate of 6oC/km

Concept of Stability

StableStable Rock Rock always returns always returns to starting pointto starting point

UnstableUnstable Rock Rock never returns never returns to starting pointto starting point

Conditionally UnstableConditionally Unstable Rock never returns if rolled Rock never returns if rolled

past top of initial hillpast top of initial hillAhrens, Fig 5.1

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. http://www.onr.navy.mil/focus/blowballast/sub/work2.htm

Ahrens, Fig 5.3

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 5.5

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

Conditionally Unstable: Lower Rock

Ahrens, Fig 5.7

Environmental Lapse Rate (ELR)ELR is the Temp change with height that is recorded by a weather balloon

ELR is absolutely unstable in a thin layer just above the ground on hot, sunny days

Ahrens, Meteorology Today 5th Ed.

ELR is 6.5o C/km, on average, and thus is conditionally unstable!

6.06.0oo C/km C/km

10.010.0oo C/km C/km

6.56.5oo C/km C/km

Summary: Key Concepts I

Rising unsaturated air, and all sinking airTemp changes at DAR of 10oC/kmDP changes at rate of 2oC/kmSaturation occurs with sufficient lifting

Rising saturated airLatent Heating Mitigates Adia. CoolingTemp and DP cools at MAR of 6oC/kmNote that MAR is always less than DAR

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

Assignment for Next Lecture

• Topic - Precipitation Processes

• Reading - Ahrens p121-134

• Problems - 5.14, 5.16, 5.17