ATMO 336Weather, Climate and Society

Upper Air Maps

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

Law reduces to P varies with d

Boyle's LawDenser air has a higher pressure than less

dense air at the same temperature

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

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

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 increasing height

Animation

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

Summary

• Ideal Gas Law ImpliesPressure decreases more rapidly with height in cold air than in warm air.

• Consequently…..Horizontal temperature differences lead to sloping constant pressure surfaces, or horizontal pressure differences!(And horizontal pressure differences lead to air motion…or the wind!)

Isobaric Maps

• Weather maps at upper levels are analyzed on isobaric (constant pressure) surfaces.(Isobaric surfaces are used for mathematical reasons

that are too advanced to include in this course!)

• Isobaric maps provide the same information as constant height maps, such as:

Low heights on isobaric surfaces correspond to low pressures on constant height surfaces!

Cold temps on isobaric surfaces correspond to cold temperatures on constant height surfaces!

Isobaric Maps

Ahrens, Fig. 2, p141

504 mb504 mb

496 mb496 mb

PGF

Downhill(Constant height)

Some generalities:

1) High/Low heights on an isobar surface correspond to High/Low pressures on a constant height surface

2) Warm/Cold temps on an isobaric surface correspond to Warm/Cold temps on a constant height surface

3) The PGF on an isobaric surface corresponds to the downhill direction

Contour MapsHow we display

atmospheric fields

Portray undulations of 3D surface on 2D map

A familiar example is a USGS Topographic Map

It’s a useful way to display atmospheric quantities such as temperatures, dew points, pressures, wind speeds, etc.

Gedlezman, p15

Contour Maps “To successfully isopleth the 50-degree isotherm, imagine that you're a competitor in a roller-blading contest and that you're wearing number "50". You can win the contest only if you roller-blade through gates marked by a flag numbered slightly less than than 50 and a flag numbered slightly greater than 50.”

https://courseware.e-education.psu.edu/public/meteo/meteo101demo/Examples/Section2p02.htmlClick “interactive exercise”

https://courseware.e-education.psu.edu/public/meteo/meteo101demo/Examples/Section2p03.html

Click first “here”

https://courseware.e-education.psu.edu/public/meteo/meteo101demo/Examples/Section2p04.html

Click “interactive isotherm map”

From

Upper-Air Model

Conditions at specific pressure level

• Wind • Temperature (C)• Moisture (Later)• Height above MSL• UA 500mb AnalysisAhrens, p 427Ahrens, p 431

Responsible for boxed parameters

570 dam contour570 dam contour

576 dam contour576 dam contour

570 and 576 dam contours570 and 576 dam contours

All contours at All contours at 6 dam spacing6 dam spacing

All contours at All contours at 6 dam spacing6 dam spacing

-20 C and –15 C -20 C and –15 C Temp contoursTemp contours

-20 C, –15 C, -10 C -20 C, –15 C, -10 C Temp contoursTemp contours

All contours at All contours at 55oo C spacing C spacing

Height contours Height contours Temps shadedTemps shaded

Region of Region of HighHigh Heights Heights RIDGERIDGE

and and WarmthWarmth

Region of Region of LowLow Heights Heights TROUGHTROUGH

and and ColdCold

PGFWind

Do Rocks Always Roll Downhill?

Gedzelman, p 247

Upper-Level Winds

PGF

Today’s Question….

Take Home Points

• Station Pressure and Surface Analyses (later)

Reduced to Mean Sea Level Pressure (SLP) PGF Corresponds to Pressure Differences

• Upper-Air Maps

On Isobaric (Constant Pressure) Surfaces PGF Corresponds to Height Sloping Downhill

• Contour Analysis

Surface Maps-Analyze Isobars of SLP (later) Upper Air Maps-Analyze Height Contours

Take Home Points

• Wind Direction and PGF

Winds more than 1 to 2 km above the ground are perpendicular to PGF!

Analogous a marble rolling not downhill, but at a constant elevation with lower altitudes to the left of the marble’s direction. How can that be?

Weather, Climate and Society

Newton’s Laws of MotionUpper-Air Winds

Do Rocks Always Roll Downhill?

Gedzelman, p 247

Upper-Level Winds

PGF

Today’s Question….

Newton’s Laws of Motion

• Newton’s 1st LawAn object at rest will remain at rest and an object in motion will remain at a constant velocity (same speed and same direction) if the net force exerted on it is zeroAn external force is required to speed up, slow down, or change the direction of air

Newton’s Laws of Motion

• Newton’s 2nd Law

The net force exerted on an object equals its mass times its acceleration

Sum of All Forces = Mass x Acceleration

Acceleration = Velocity Change / Time

Acceleration = Change in Either Speed or Direction

Velocity, Acceleration and Force are Vectors

• Speed/Size Change

• Direction Change

Original Velocity

New Velocity Original

Velocity

New Velocity

Acceleration and Force

Original Velocity

New Velocity

Original Velocity

New Velocity

Acceleration and Force

Uniform, Circular Motion Requires Acceleration

Original Velocity

New Velocity

Acceleration directed toward center of circle Centripetal

Original Velocity

New Velocity

Circular Path

Accelerated Frame of Reference

You are glued to car’s floor and drop an egg.What happens if the car begins to accelerate?

Inside the car, it looks a mystery force is attracting the egg to the back of the car. Your frame of reference is accelerating.

Someone outside the car sees that the egg is just accelerating to the floor, you are accelerating with the box car. A force is accelerating the car. Their frame of reference is not accelerating.

Splat!

(rest)

tim

e

Life on a Rotating Platform

• From perspective of person not on merry-go-round, path of ball is straight.

• From perspective of person on merry-go-round, path of ball deflects to left. There is an apparent force.

(left click picture for animation) World Weather Project 2010 Courtesy of M. Ramamurthy U of Illinois, Urbana-Champaign Merry Go Round Link

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Earth’s Rotation

If viewed from space, earth is like a carousel!

Northern Hemisphere rotates counterclockwiseSouthern Hemisphere rotates clockwise

Gedzelman, p 240

Refinements

Simple, right?

But there are a couple of nuances

We will consider both…

Coriolis “force” varies with wind speed.

The earth is a sphere, not flat like a carousel.

Ball Appears to Deflect to the Right of the Observer

Gedzelman, p 242

Deflection increases if: Speed of ball increases

slow fast

Ball Appears to Go Straight

Gedzelman, p 242

If the ball is thrown parallel to the axis of rotation, there is no apparent deflection

Deflection Depends on Orientation of Axis of Rotation

and Velocity

Gedzelman, p 242

velocity

Apparent Deflection

No Deflection

Coriolis Force Varies with Latitude

Gedzelman, p 243

Airplane Link

Geostrophic Adjustment

A. Parcel at rest initially accelerates toward lower pressure.

B. Coriolis Force rotates parcel to right in NH.

C. As parcel speeds up, Coriolis Force increases.

D. Eventually (about a day), PGF equals CF and flow is parallel to isobars.(left click picture to animate)

World Weather Project 2010 Courtesy of M. Ramamurthy U of Illinois, Urbana-Champaign

Animate Picture

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Geostrophic Balance

Pressure Gradient Force

Coriolis Force

Geostrophic Wind

5640 m

5700 m

Geostrophic Wind Arises from a Balance Between the PGF and the Coriolis Force.

PGF + Coriolis Force = 0

(Technically, it can only exist for East-West flow and for straight contours, but we will ignore that technicality.)

Geostrophic Balance

Pressure Gradient Force

Coriolis Force

Geostrophic Wind

5640 m

5700 m

The Balance Leads to the Wind Blowing Parallel to the Height Contours, with Lower Heights to the Left of the Wind Direction in the NH.

Closer the Spacing Between the Height Contours- The Faster the Geostrophic Wind Speed.

PGFPGFCorCorGeoGeo

Take Home Points

• Rotation of Earth

Accelerated Frame of Reference• Introduce Coriolis “Force”

Apparent Force to Account for Deflection Depends on Rotation, Latitude, Wind Speed

• Geostrophic Balance and Wind

Balance Between PGF and Coriolis Force Geostrophic Wind Blows Parallel to Contours About One Day Required to Reach Balance

Do Rocks Always Roll Downhill?

Gedzelman, p 247

Upper-Level Winds

PGF

Not if the Hill is Big Enough!