Transcript Class Slides - Department of Atmospheric Sciences

ATMO 336
Weather, Climate and Society
Upper Air Maps
What is Air Pressure?
Recoil
Force
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
Recoil
Force
Concept applies to
an “air parcel”
surrounded by
more air parcels,
but molecules create
pressure through
rebounding off air
molecules in other
neighboring parcels
Air Pressure
Recoil
Force
At any point, pressure
is the same in all
directions
But pressure can vary
from one point to
another point
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 Law
Denser air has a higher pressure than less
dense air at the same temperature
Ideal Gas Law
P = constant x d (constant) x T
With 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
300 mb
500 mb
9.0 km
9.0 km
400 mb
600 mb
700 mb
800 mb
900 mb
Minneapolis
Houston
Pressure
Decreases with height
at same rate in air of
same temperature
Constant Pressure
(Isobaric) Surfaces
Slopes are horizontal
Pressure-Temperature-Density
WARM
8.5 km
9.5 km
COLD
Minneapolis
Houston
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
Summary
• Ideal Gas Law Implies
Pressure 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
(Constant height)
496 mb
504 mb
Some generalities:
1) The
2)
3)
Warm/Cold
High/Low
PGF on
heights
temps
an isobaric
on
onan
ansurface
isobar
isobaric
surface correspond
corresponds
to the downhill
to Warm/Cold
High/Low
direction
temps
pressures
on
a constant
on aheight
constant
surface
height surface
Ahrens, Fig. 2, p141
Contour Maps
How 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 50degree isotherm, imagine that
you're a competitor in a rollerblading 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.html
Click “interactive exercise”
From
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”
Upper-Air Model
Responsible for boxed parameters
Ahrens, p 431
Ahrens, p 427
Conditions at specific
pressure level
• Wind
• Temperature (C)
• Moisture (Later)
• Height above MSL
• UA 500mb Analysis
570 dam contour
576 dam contour
570 and 576 dam contours
All contours at
6 dam spacing
All contours at
6 dam spacing
-20 C and –15 C
Temp contours
-20 C, –15 C, -10 C
Temp contours
All contours at
5o C spacing
Region of
Low Heights
TROUGH
and Cold
Region of
High Heights
RIDGE
and Warmth
Height contours
Temps shaded
PGF
Wind
Do Rocks
Today’s
Always
Question….
Roll Downhill?
PGF
Gedzelman, p 247
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 Motion
Upper-Air Winds
Do Rocks
Today’s
Always
Question….
Roll Downhill?
PGF
Gedzelman, p 247
Newton’s Laws of Motion
• Newton’s 1st Law
An 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
zero
An 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
New
Velocity
Original New
Velocity Velocity
Original
Velocity
• Direction Change
New
Velocity
Original
Velocity
New
Velocity
Original
Velocity
Acceleration
and Force
Acceleration
and Force
Uniform, Circular Motion
Requires Acceleration
New
Velocity
Circular
Path
Original
Velocity
New
Velocity
Original
Velocity
Acceleration
directed toward
center of circle
Centripetal
Accelerated Frame of Reference
You are glued to car’s floor and drop an egg.
What happens if the car begins to accelerate?
time
(rest)
Inside the car, it looks a mystery force is
attracting the egg to the back of the car.
Your frame of reference is accelerating.
Splat!
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.
Life on a Rotating Platform
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
(left click picture for animation)
World Weather Project 2010
Courtesy of M. Ramamurthy
U of Illinois, Urbana-Champaign
• From perspective of
person not on merrygo-round, path of ball
is straight.
• From perspective of
person on merry-goround, path of ball
deflects to left. There
is an apparent force.
Merry Go Round Link
Earth’s Rotation
Gedzelman, p 240
If viewed from space, earth is like a carousel!
Northern Hemisphere rotates counterclockwise
Southern Hemisphere rotates clockwise
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
Deflection increases if:
Speed of ball increases
slow
fast
Gedzelman, p 242
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
Apparent
Deflection
No
Deflection
velocity
Gedzelman, p 242
Coriolis Force Varies with Latitude
Gedzelman, p 243
Airplane Link
Geostrophic Adjustment
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
(left click picture to animate)
World Weather Project 2010
Courtesy of M. Ramamurthy
U of Illinois, Urbana-Champaign
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.
Animate Picture
Geostrophic Balance
Pressure Gradient Force
5640 m
Geostrophic Wind
5700 m
Coriolis Force
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
5640 m
Geostrophic Wind
5700 m
Coriolis Force
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 ContoursThe Faster the Geostrophic Wind Speed.
PGF
Cor
Geo
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
DoNot
Rocks
if the
Always
Hill isRoll
Big Downhill?
Enough!
PGF
Gedzelman, p 247