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 (D = 2 R) North Pole D ~ 0 Tel Aviv D~34,000 km Equator D ~ 40,000 km > 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 To increase the angular velocity, an eastward acceleration must occur Thus the deflection to the east French scientist Gaspard-Gustave Coriolis (1835) 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] Ω = 0.707 x 10-4 s -1 y = north z = vertical x = east φ ω ( 0 ) Ω = ω cosφ V sinφ ( u ) = v w Corioli s acceleration a c = -2Ω x V = 2ω ( ) v sinφ w cosφ -u sinφ u cosφ Ω x V = i j k Ω x Ω y u v w Ω z = ( ) Ω y w - Ω z v Ω z u - Ω x w Ω x v - Ω y u
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 ( ) a c = ( v ) u f where f = 2ωsinφ Corioli s parameter In others words: a x = du = 2 ω v sinφ = fv dt 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 a y = dv = -2 ω u sinφ = -fu dt For easterly wind u>0 dv/dt <0 southward acceleration For westerly wind u<0 dv/dt >0 nothward acceleration
F cor =2m x V Corioli s Acceleration M=mass =earth s rotation velocity V=wind velocity Wind Latitude speed (m/sec) 0 o 20 o 40 o 60 o 5 0 0.025 0.047 0.063 Units = [cm/sec 2 ] 10 0 0.050 0.094 0.126 VERY SMALL!! 25 0 0.125 0.235 0.316 No effect in bathtub
Units = [cm/sec 2 ]
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 X Tornado..Ro Large Unguided intercontinental missile Ro small
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
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Polar Cell Ferrel Cell Hadley Cell
Horse Latitudes Calm, light, variable surface winds Hot, dry weather Calm, light, variable surface winds dull weather Doldrums
19 th 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 dt (MV) = M dv dt = Ma (Newton s second Law) In general we can assume M=const. (not good for cumulus convection) du dt = F x M (east-west winds) dv dt = F y M (north-south winds) dw dt = F z M (vertical winds)
Pressure Gradient Force: F = P A ΔP ~ ΔF dz F x F x+dx dy x dx x+dx F x = P x dy dz F x+dx = P x+dx dy dz
If pressure P x and P x+dx are different from each other: P P x+dx = P x + P dx x P x+dx P x Net force F = F x F x+dx = (P x P x+dx ) dy dz x x+dx x = - P dx dy dz x = -dm P ρ x dm ) (dvol = dx dy dz = ρ Per unit mass: F x F y F z = = = - 1 P ρ x - 1 P ρ y - 1 P ρ z
רוחות באטמוספירה Atmospheric Motion and Winds
Pressure Gradient Force (PGF) כוח גרדיאנט הלחץ F y = - 1 P ρ y
Large Scale Pressure Systems שקע רמה 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 F cor =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 Examples: hurricanes + f V = P 2 V R n
Coriolis force linked to velocity of air
Hurricane Wilma
Cyclostrophic Balance Balance between PGF and centrifugal force Coriolis force not important Example: tornadoes 2 V = P R n PG CTF
Atmospheric Pressure לחץ אטמוספרי 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
V E ~1400 km/h V w =250km/h V E ~1650 km/h V w =0
Subtropical Jet Stream
https://www.windyty.com/
-Monsoon מונסון (=season)
Winter Monsoon regions Summer
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. Mountain/valley winds are similarly caused by daytime heating and nighttime cooling of the air along the slopes of mountains.