NATS 101

Lecture 14Air PressureAir Pressure

Recoil Force

What is Air Pressure?

Pressure = Force/Area

What is a Force? It’s like a push/shove

In an air filled container, pressure is due to molecules pushing the sides outward by recoiling off them

Air Pressure

Concept applies to an “air parcel” surrounded by more air parcels, but molecules create pressure through rebounding off air molecules in other neighboring parcels

Recoil Force

Air Pressure

At any point, pressure is the same in all directions

But pressure can vary from one point to another point

Recoil Force

Higher density at the same temperature creates higher pressure by more collisions among molecules of average same speed

Higher temperatures at the same density creates higher pressure by collisions amongst faster moving molecules

Ideal Gas Law

• Relation between pressure, temperature and density is quantified by the Ideal Gas Law

P(mb) = constant x d(kg/m3) x T(K)

• Where P is pressure in millibars

• Where d is density in kilograms/(meter)3

• Where T is temperature in Kelvin

Ideal Gas Law

• Ideal Gas Law is complex

P(mb) = constant x d(kg/m3) x T(K)

P(mb) = 2.87 x d(kg/m3) x T(K)

• If you change one variable, the other two will change. It is easiest to understand the concept if one variable is held constant while varying the other two

Ideal Gas Law

P = constant x d x T (constant)With T constant, Ideal Gas Law reduces to

P varies with d Boyle's Law

Denser air has a higher pressure than less dense air at the same temperature

Why? You give the physical reason!

Ideal Gas Law

P = constant x d (constant) x TWith d constant, Ideal Gas Law reduces to

P varies with T Charles's Law

Warmer air has a higher pressure than colder air at the same density

Why? You answer the underlying physics!

Ideal Gas Law

P (constant) = constant x d x T

With P constant, Ideal Gas Law reduces to

T varies with 1/d Colder air is more dense (d big, 1/d small)

than warmer air at the same pressure

Why? Again, you reason the mechanism!

Summary

• Ideal Gas Law Relates

Temperature-Density-Pressure

Pressure-Temperature-Density

9.0

km

300 mb

1000 mb

400 mb

500 mb

600 mb

700 mb

800 mb

900 mb

Minneapolis Houston

9.0

km

Pressure

Decreases with height at same rate in air of same temperature

Constant Pressure (Isobaric) Surfaces

Slopes are horizontal

Pressure-Temperature-Density

Pressure (vertical scale highly distorted)

Decreases more rapidly with height in cold air than in warm air

Isobaric surfaces will slope downward toward cold air

Slope increases with height to tropopause, near 300 mb in winter

8.5

km 9.5

km

300 mb

1000 mb

400 mb

500 mb

600 mb

700 mb

800 mb

900 mb

Minneapolis Houston

COLD

WARM

Pressure-Temperature-Density8.

5 km 9.

5 km

300 mb

1000 mb

400 mb

500 mb

600 mb

700 mb

800 mb

900 mb

Minneapolis Houston

HHLL

LLHH

PressureHigher along horizontal

red line in warm air than in cold air

Pressure difference is a non-zero force

Pressure Gradient Force Pressure Gradient Force or PGF (red arrow)or PGF (red arrow)

Air will accelerate from column 2 towards 1

Pressure falls at bottom of column 2, rises at 1

AnimationSFC pressure rises SFC pressure falls

PGF

PGF

COLD

WARM

Summary

• Ideal Gas Law Implies

Pressure decreases more rapidly with height in cold air than in warm air.

• Consequently…..

Horizontal temperature differences lead to horizontal pressure differences!

And horizontal pressure differences lead to air motion…or the wind!

N. Pacific Pressure Analysis (isobars every 4 mb)

Pressure varies by 1 mb per 100 km horizontally or 0.0001 mb per 10 m

2000 km

Review: Pressure-HeightRememberPressure falls very rapidly with height near sea-level

3,000 m 701 mb2,500 m 747 mb2,000 m 795 mb1,500 m 846 mb1,000 m 899 mb500 m 955 mb0 m 1013 mb

1 mb per 10 m height

Consequently………. Vertical pressure changes from differences in station elevation dominate horizontal changes

Station Pressure

Pressure is recorded at stations with different altitudesStation pressure differences reflect altitude differences Wind is forced by horizontal pressure differences Since horizontal pressure variations are 1 mb per 100 km We must adjust station pressures to one standard level:

Mean Sea Level

Ahrens, Fig. 6.7

Reduction to Sea-Level-Pressure

Station pressures are adjusted to Sea Level PressureSea Level Pressure Make altitude correction of 1 mb per 10 m elevation

Ahrens, Fig. 6.7

Correction for TucsonElevation of Tucson AZ is ~800 m

Station pressure at Tucson runs ~930 mb

So SLP for Tucson would be

SLP = 930 mb + (1 mb / 10 m) x 800 m

SLP = 930 mb + 80 mb = 1010 mb

Correction for DenverElevation of Denver CO is ~1600 m

Station pressure at Denver runs ~850 mb

So SLP for Denver would be

SLP = 850 mb + (1 mb / 10 m) x 1600 m

SLP = 850 mb + 160 mb = 1010 mb

Actual pressure corrections take into account temperature and pressure-height variations, but 1 mb / 10 m is a good approximation

Sea Level Pressure Values

Ahrens, Fig. 6.3

(October, 2005)Wilma

882 mb (26.04 in.)

Summary

• Because horizontal pressure differences are the force that drives the wind

Station pressures are adjusted to one standard level…Mean Sea Level…to remove the dominating impact of different elevations on pressure change

Ahrens, Fig. 6.7

PGF

Key Points• Air Pressure

Force / Area (Recorded with Barometer)• Ideal Gas Law

Relates Temperature, Density and Pressure• Pressure Changes with Height

Decreases More Rapidly in Cold air than Warm • Station Pressure

Reduced to Mean-Sea-Level to Mitigate the Dominate Impact of Altitude on Pressure Change

Summary

• Because horizontal pressure differences are the force that drives the wind

Station pressures are adjusted to one standard level…Mean Sea Level…to mitigate the impact of different elevations on pressure

Ahrens, Fig. 6.7

PGF

Local ExampleThe station pressure at PHX is ~977 mb.

The station pressure at TUS is ~932 mb.

Which station has that higher SLP?

Correction for PhoenixElevation of PHX Airport is ~340 m

Station pressure at PHX was ~977 mb

So, SLP for PHX would be

SLP = 977 mb + (1 mb / 10 m) x 340 m

SLP = 977 mb + 34 mb = 1011 mb

Correction for TucsonElevation of TUS Airport is ~800 m

Station pressure at TUS was ~932 mb

So, SLP for TUS would be

SLP = 932 mb + (1 mb / 10 m) x 800 m

SLP = 932 mb + 80 mb = 1012 mb

The SLP was higher in TUS than PHX

Surface Maps

• Pressure reduced to Mean Sea Level is plotted and analyzed for surface maps.Estimated from station pressures

• Actual surface observations for other weather elements (e.g. temperatures, dew points, winds, etc.) are plotted on surface maps.

NCEP/HPC Daily Weather Map

Assignment

• Reading - Ahrens pg 148-157

include Focus on Special Topic: Isobaric Maps• Problems - 6.9, 6.10, 6.12, 6.13, 6.17, 6.19, 6.22