Climatology Lecture 5

1
ClimatologyLecture 5

• Richard Washington
• Horizontal Motion in the Atmosphere

2
Course Outline

• Heat and the Earths Atmosphere
• Vertical Motion Stability
• Horizontal Motion Winds
• The General Circulation Midlatitudes
• The General Circulation Tropics
• Variability of the General Circulation

3
Wind

• Pressure gradient force
• Coriolis Force
• Geostrophic wind
• Gradient wind
• Friction and the Ekman spiral

4
Pressure Gradient Force
Wind is driven by differences in
pressure Differences in pressure arise both
vertically and horizontally Vertical differences
are balanced by gravity (hydrostatic
equilibrium) Horizontal differences in pressure
arise on a large scale Pressure gradient Force
(PGF) is directed from areas of high pressure to
low pressure perpendicular to isobars (closer
the isobar spacing, the greater the PGF)
p density dp/dn change of pressure over distance
5
Example of a sea level pressure distribution for
an arbitrary day. Note the scale of the gradient
i.e. how quickly (slowly) pressurechanges with
distance
6
Pressure Gradient Force
PGF is directed from areas of high pressure to
low pressure perpendicular to isobars (closer
the isobar spacing, the greater the
PGF) Pressure 1000 hPa, temperature 20 C,
density 1.2 kg/m-3 Pressure 500 hPa,
temperature 0 C, density 0.6 kg/ m-3 So at
500 hPa (5 km altitude), density is half that at
the surface PGF (for the same pressure
difference) is double Winds blow faster with
height!
p density, dp/dn change of pressure over
distance
7
Wind

• Pressure gradient force
• Coriolis Force
• Geostrophic wind
• Gradient wind
• Friction and the Ekman spiral

8
Coriolis Force

• deflection force
• depends on latitude (Ø), wind speed (v), earths
  rotation rate (w)
• 2wsinØV
• sine of latitude Ø equator zero, poles 1
• acts to the left in SH and to the right in NH
• acts at right angles to the wind
• deflection is proportion to wind speed

9
Deriving the CoriolisForce in 5 steps.
1) Air moves from a point O at latitude Ø, where
it was at rest, to point A with constant velocity
V. It will move through distance r in time t r
Vt (distance velocity x time) e.g. r 10
mph x 2 hrs 20 miles 2) In the meantime the
earth has rotated clockwise so that point A is
now point B. Rotation has happened through the
angle AOB or ? ? wsin Øt (faster rotation,
higher latitude, longer time all lead to larger
angle)
10
reminder of definitions so far r Vt
(distance velocity x time) ? wsin Øt 3) The
distance AB (i.e. amount of deflection) is given
by AB r ? Vt wsin Øt
11
B
A
B
A
r
?
r
O
?
Illustrating the influences on AB r Vt
(distance velocity x time) ? wsin Øt The
distance AB is given by AB r ? Vt
wsin Øt
O
12
B
A
r
?
O
r Vt (distance velocity x time) ? wsin
Øt The distance AB is given by AB r ?
Vt wsin Øt 5) The distance from A to B may
also be written AB(at2)/2 so
(at2)/2 Vt wsin Øt a 2 wsin ØV which is
Coriolis Force
13
(No Transcript)
14
Wind

• Pressure gradient force
• Coriolis Force
• Geostrophic wind
• Gradient wind
• Friction and the Ekman spiral

15
Geostrophic Wind

• Balance between PGF and Coriolis Force
• above the surface (above 1km) in extratropics
• wind blows parallel to isobars

16
Geostrophic Wind
17
(No Transcript)
18
Air initially at rest Moves north from High
to Low pressure under Pressure Gradient Force
Once air is moving, Coriolis Force has an effect
Wind is deflected to the right (in the Northern
Hemisphere) Wind picks up speed, Coriolis Force
strengthens proportionally Eventually vectors
balance to create Geostrophic Wind
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
Blue PGF Red CF
23
Wind

• Pressure gradient force
• Coriolis Force
• Geostrophic wind
• Gradient wind
• Friction and the Ekman spiral

24

• Geostrophic wind only applies to straight
  parallel isobars, but isobars are usually curved,
  and often arent parallel
• For air moving in a curve, we must consider an
  additional force

25
Centripetal force

• Tie a weight to some string and spin it around
  your head
• The tension you maintain on the rope pulls the
  weight around in a circle
• Inward force - centripetal

26
Centrifugal force

• e.g. Fairground ride
• Body thrown out against side
• Centrifugal force - outward

27
Which force do we work with?

• Both the same!
• Force apparent to rotating body
• outward - centrifugal
• Force apparent to external observer
• inward - centripetal

28
Pressure gradient force

• Identical pressure gradient in each case

LOW
LOW
LOW
HIGH
HIGH
HIGH
29
Centrifugal force

• Force needed for curved motion as viewed from
  above.

LOW
LOW
LOW
HIGH
HIGH
HIGH
30
Sub-geostrophic winds

• Wind speed less than geostrophic
• Cyclonic curvature - sub-geostrophic

LOW
HIGH
31
Super-geostrophic winds

• Wind speed more than geostrophic
• Anticyclonic curvature - super-geostrophic

32
Gradient wind

• Pressure gradient force dp/?dn
• Coriolis force 2wsin Ø V
• Centrifugal force V2/r
• V is the wind speed
• r is the radius of curvature
• Balance 2wsinØV V2/r dp/?dn 0

33
Questions

• When air blows around curved isobars will the
  wind speed be the same as of straight isobars?
• assuming the pressure gradient is the same
• Answer depends on curvature

34
Wind

• Pressure gradient force
• Coriolis Force
• Geostrophic wind
• Gradient wind
• Friction and the Ekman spiral

35
Friction

• Friction reduces wind speed
• Coriolis force is reduced
• Flow crosses isobars from high towards low
  pressure
• Applies near surface but not at upper levels
  where friction is insignificant

36
Friction

• Friction reduces wind speed
• Coriolis force is reduced
• Geostrophic balance is upset
• Flow crosses isobars from high towards low
  pressure
• Applies near surface but not at upper levels
  where friction is insignificant

37
(No Transcript)
38
(No Transcript)
39
(No Transcript)
40

• Friction reduces with altitude

Free atmosphere
LOW
Near surface
41
Surface pressure change

• Net inflow Net
  outflow
• P Increase P
  Decrease
• System Declines System Declines

LOW
42
Vertical motion

• Upward Downward

Free atmosphere
LOW
Near surface
43
Conclusions

• Curved flow is described by gradient wind
• Cyclonic curvature gives sub-geostrophic winds
• Anticyclonic curvature gives super-geostrophic
  winds
• PGF, CF, Friction and centrifugal forces describe
  wind systems adequately

44
HOT
COLD
45
(No Transcript)
46
Poles
Subtropics
47
Poles
Subtropics
Pressure Gradient Force
48
(No Transcript)
49
Air columns
700 hPa
3100m

• Each slab contains the same mass
• The depth of each mass is not the same
• As density decreases the depth increases

800 hPa
1900m
900 hPa
900m
1000 hPa
0 m
50
Warm or cold air
2900m
1750m
800m
0 m
0 m
COLD
WARM
51
700 hPa
HOT
52
dP g p Z cold air, p increases, Z must
decrease warm air, p decreases, Z must increase
700 hPa
HOT
53
Readings for todays lecture

• Barry and Chorley 1997 p76-86
• Briggs et al. 1997 Fundamentals of the Physical
  Environment p78-88
• Henderson-Sellers and Robinson 1999 p56-74
• Linacre and Geerts 1997 Climates and Weather
  Explained p127-145
• McIlveen 1992 p109-139