Download Topics covered in Course

Topics covered in Course:
Chapter 1: Earth with no Atmosphere (no rotation)
- Introduction
- Kepler Laws
- Milankovich Theory
- Seasons
- Energy Balance
Chapter 2: Earth with Atmosphere (no rotation)
- Atmospheric Composition
- Water Vapor
- Clouds and Climate
- Radiation (SW and LW)
- Scattering
Chapter 3: Vertical Motions in Atmosphere (no rotation)
- Thermodynamics
- Lapse Rates
- Atmospheric Layers
- Instability
- Clouds and Rain formation
Chapter 4: Horizontal Motions in Atmosphere (with rotation)
- General Circulation
- Coriolis Force
- Atmospheric Winds
- Jet stream
- Ocean currents
- Storms
Chapter 5: Global Issues (Science, Society and Politics)
- Ozone Hole
- Global Warming
General Circulation of the Atmosphere
‫צירקולציה כללית של האטמוספירה‬
How do we get from this…….
To this……?
Maximum Heating
at Equator
Earth’s Rotation = 24 hours
V= D/t = D/24
North Pole D ~ 0
Tel Aviv
D~34,000 km
Equator
D ~ 40,000 km
(D = 2R)
>
V (N. Pole) ~ 0 km/h
V (TA) ~ 1417 km/h
V (Equ) ~ 1667 km/h
But Earth does rotate!
Stationary
observer
Rotating
Observer
(i.e. stationary
Earth)
Velocity Zero at Center (south pole)
Velocity increases toward perimeter (equator)
Coriolis Effect
• If one moves northward in the Northern Hemisphere, one
is decreasing the distance to the pole
– Thus to conserve angular momentum, the angular
velocity must increase
M = r X mv
– Think of a figure skater who puts out or pulls in their
arms to change how fast they spin
French scientist
– To increase the angular velocity, an eastward
Gaspard-Gustave
acceleration must occur
Coriolis (1835)
– Thus the deflection to the east
r=5400km
r=6400km
• If air moves in zonal (east-west) direction
– If it moves eastward, it would take less time to complete one entire
rotation as it is travelling faster than the earth’s surface – OR
angular velocity increases
– If it moves westward, it is opposing the earth’s rotation and would
take longer to complete a rotation – OR angular velocity decreases
• Thus, for motion to the east in the Northern Hemisphere:
– An increase in angular velocity
– Thinking of a ‘ball’ orbiting on a string, an increase in angular
velocity means an increase in radius of the orbit
– The same thing applies here, with an increase in ‘radius’
meaning movement away from the axis of rotation, the pole
towards the Equator
Ω = Angular Velocity of Earth (radians/sec) [2/sec]
= 0.707 x 10-4 s-1
Ω
y = north
z = vertical
x = east
() ()
Ω=ω
φ
0
cosφ
sinφ
V=
ω
Corioli’s acceleration
ΩxV=
(
( )
ac = -2Ω x V = 2ω
i
j
Ωx Ωy
u v
k
Ωz
w
=
)
v sinφ – w cosφ
-u sinφ
u cosφ
Ωyw - Ωzv
Ωzu - Ωxw
Ωxv - Ωyu
u
v
w
When considering atmospheric or oceanic dynamics, w is generally small,
and the vertical component of Coriolis acceleration << gravity. Therefore,
we can consider only the horizontal components (w=0) and the horizontal
plane (ignore k vector):
()
V= u
v
In others words:
ac =
v
u
()f
ax = du = 2 ω v sinφ
dt
where f = 2ωsinφ
Corioli’s parameter
f= 0 at equator
f= 1.4 x 10-4 s-1 at pole
For northerly wind v>0  du/dt >0  eastward acceleration
For southerly wind v<0  du/dt <0  westward acceleration
ay = dv = -2 ω u sinφ
dt
For easterly wind u>0  dv/dt <0  southward acceleration
For westerly wind u<0  dv/dt >0  nothward acceleration
Fcor=2m x V
Corioli’s Acceleration
Wind
speed
M=mass
=earth’s rotation velocity
V=wind velocity
Latitude
(m/sec)
0o
20o
40o
60o
5
0
0.025
0.047
0.063
Units = [cm/sec2]
10
0
0.050
0.094
0.126
VERY SMALL!!
25
0
0.125
0.235
0.316
No effect in bathtub
Rossby Number:
How important is rotation of system on flow?
U = velocity of fluid
L = length scale of motion
f = Coriolis parameter
SMALL Ro implies Coriolis force is important
LARGE Ro implies inertial forces more important, rotation not important

Weather System: U=10m/s, L=1000km, f=7.6x10-5 s-1
Ro = 0.1
Baseball pitcher: U= 45m/s, L=18.3 m, f=7.6x10-5 s-1
Ro = 32000
Tornado ……..Ro Large
Unguided intercontinental missile ……Ro small
X
Pilots need to correct
for Coriolis Force when
flying in a N/S direction
ITCZ=Inter Tropical Convergence Zone
ITCZ
Monthly Rainfall Rates
Maximum along ITCZ
?
Polar Cell
Ferrel Cell
Hadley Cell
Horse Latitudes
Calm, light, variable surface winds
Hot, dry weather
Calm, light, variable surface winds
“dull” weather
Doldrums
19th Century
Slave Trade
30 N
Horse Latitudes
Atmospheric Water Vapor
13-15 Oct 2002
15-18 Dec 2002
Atmospheric winds
Equation of Motion:
F = d (MV) = M dV = Ma
dt
dt
(Newton’s second Law)
In general we can assume M=const. (not good for cumulus convection)
du = Fx
dt
M
(east-west winds)
dv = Fy
dt
M
(north-south winds)
dw = Fz
dt
M
(vertical winds)
Pressure Gradient Force:
F = PA

ΔP ~ ΔF
dz
Fx
Fx+dx
dy
x
dx
Fx = Px dy dz
Fx+dx = Px+dx dy dz
x+dx
If pressure Px and Px+dx are different from each other:
P
Px+dx = Px + ∂P dx
∂x
Px+dx
Px
Net force
F = Fx – Fx+dx
x
x+dx
= (Px – Px+dx) dy dz
= - ∂P dx dy dz
∂x
= -dm ∂P
ρ ∂x
Per unit mass:
(dVol = dx dy dz = dm )
ρ
Fx = - 1 ∂P
ρ ∂x
Fy = - 1 ∂P
ρ ∂y
Fz = - 1 ∂P
ρ ∂z
x
‫רוחות באטמוספירה‬
Atmospheric Motion and Winds
Pressure Gradient
Force (PGF)
‫כוח גרדיאנט הלחץ‬
Fy = - 1 ∂P
ρ ∂y
Large Scale Pressure Systems
‫רמה‬
‫שקע‬
Coriolis Effect causes deflection of winds when they are viewed
from a rotating reference frame.
In Northern
Hemisphere
Geostrophic Balance/Wind
‫רוח גיאוסטרופי‬
(PGF=Coriolis Force)
Vg = 1 ∂P
ρf ∂n
Fcor=2m x V
M=mass
=earth’s rotation velocity
V=wind velocity
Geostrophic balance does not occur instantaneously…
Wind Speed & Pressure Contours
Just as a river speeds and slows when its banks narrow and expand,
geostrophic winds blowing within pressure contours speed as
contour intervals narrow, and slow as contour intervals widen.
Smoothed Isobar Maps
Meridional & Zonal Flow
Wind direction and speed are indicated by lines, barbs, and flags,
and appear as an archer's arrow.
Upper level winds that travel a north-south path are meridional,
and those traveling a west-east path are zonal.
Sensing Highs & Lows
Constant Height Chart
Two ways of representing
pressure changes in Atmosphere
Maps of atmospheric
pressure, whether at
sea level or 3000 m
above sea level, show
variations in pressure
at that elevation.
Constant Pressure Chart
Maps of
constant
pressure
provide another
means for
viewing
atmospheric
dynamics.
In this example,
there is no
variation in
elevation for a
pressure of 500
mb.
Variation in Height
Isobaric (constant pressure) surfaces rise and fall in elevation with
changes in air temperature and density.
A low 500 mb height indicates denser air below, and less
atmosphere and lower pressure above.
Contour lines indicate rates of pressure change.
Ridges & Troughs
Figure 9.14
Upper level areas with high pressure are named ridges, and areas
with low pressure are named troughs.
These elongated changes in the pressure map appear as undulating
waves.
500mb Geopotential Height
https://www.windyty.com/
At the surface FRICTION is important
https://www.windyty.com/
Gradient Wind Balance
• Balance between PGF, Coriolis force, and centrifugal force
• Need sharp curvature in flow for this Centrifugal force to be
important
2
• Examples: hurricanes
V + f V = ∂P
R
∂n
Coriolis force linked to velocity of air
Hurricane Wilma
Cyclostrophic Balance
• Balance between PGF and centrifugal force
• Coriolis force not important
2
V = ∂P
• Example: tornadoes
R ∂n
PG
CTF
‫ לחץ אטמוספרי‬Atmospheric Pressure
Pressure=Force/Area
1000 mb
‫רוח תרמלי – זרם סילון‬
‫‪∂v = -R ∂T‬‬
‫‪∂p fp ∂x‬‬
‫‪∂u = R ∂T‬‬
‫‪∂p fp ∂y‬‬
‫זרם סילון‬
January Winds Aloft
July Winds Aloft
VE~1400 km/h
VE~1650 km/h
Vw=250km/h
Vw=0
Subtropical Jet Stream
https://www.windyty.com/
‫מונסון‬-Monsoon
(=season)
Winter
Monsoon regions
Summer
Sea Breeze
Figure 10.19A
Figure 10.19B
Changes in air temperature causing warm air to rise and cool air to
sink can also generate horizontal winds.
Rising warm air creates a surface low and upper level high.
Sinking cool air creates a surface high and upper level low.
Sea Breeze
‫בריזת הים‬
Daytime
Sea Breeze Convergence
Opposing
breezes may
converge on an
isthmus of land,
and this rising
moist unstable
air will trigger
thunderstorms.
Land Breeze
‫בריזת היבשה‬
Nighttime
Mountain Winds
‫רוחות הרים‬
Anabatic winds
‫רוחות אנבטיות‬
Katabatic winds
‫רוחות קטבטיות‬
Valley & Mountain Breezes
Chapter 4a
What have we learned?
 Due to the Coriolis Effect, winds in the northern/southern
hemisphere are deflected to the right/left of the direction of motion.
 In the tropics (+-30) this results in the easterly trade winds that
converge along the ITCZ, resulting in a band of rainfall close to the
equator.
 Due to the Coriolis Effect the rising air in the ITCZ moves
north/south and sinks around 30N and 30S (Hadley Cell)….desert
regions of the Earth.
 In total there are 3 meridional (north-south) cells in the atmosphere
in each hemisphere: Hadley, Ferrel and Polar cells.
 Between 30-60 latitude the surface winds are westerly, while from
60-90 latitude the surface winds change back to easterly.
 On small scales winds always blow from high pressure centers to
low pressure centers.
 On regional scales, due to Coriolis force, the winds blow around
low/high pressure centers (geostrophic winds). Balance between
the Pressure gradient force and the Coriolis force.
 In the northern/southern hemisphere the winds blow anticlockwise/clockwise around Low Pressure centers, and the opposite
direction around High Pressure centers.
 For fast large scale circulations (hurricanes), we need to take care of
the centripetal force (Gradient flow)
 For fast small scale cirulations (tornadoes), we can ignore the
Coriolis force (Cyclostrophic flow)
 The polar jet stream is caused (and positioned) by the north-south
surface temperature gradient on the Earth (thermal wind)
 The subtropical jet stream is caused by the conservation of angular
momentum as equatorial air flows north in the Hadley Cell.
 The Monsoon Rains are caused by the ITCZ moving over
continental regions in the tropics. Wet summers, dry winters.
 The sea/land breeze is caused by the differential heating (and hence
pressure gradient) produced along coastlines in summer months.
 Moutain/valley winds are similarly caused by daytime heating and
nighttime cooling of the air along the slopes of mountains.