Download Coriolis Force

Ques%ons you should be able to answer a2er this and next weeks lectures 1. 
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Why do we need temperature and momentum transport? What gives rise to the general circula%on? Why are there westerlies in the mid-­‐la%tudes and easterlies in the tropics? How does the general circula%on determine regional climate features and secondary circula%ons? Local Surface Energy Budget Latent Heat : Water
NET R = (SW -­‐ SW ) + (LW -­‐ LW ) + LH + SH + V NET R > 0 implies warming
NET R < 0 implies cooling
Sensible Heat :
Conduction +
Convection
Energy Imbalance of the Atmosphere Redistribu%ng Energy From Tropics to Poles Reason for Breezes –  Move heat energy around the globe –  Redistribute water around the globe –  Moderate Earth’s climate = Make a larger por%on of the planet suitable for life! Atmospheric General Circula%on COLD
UNEQUAL HEATING OF THE EARTH THERMAL IMBALANCE WARM
Conceptual Models 1-­‐D Atmosphere Convec%on 2-­‐D Atmosphere Advec%on COLD
3-­‐D Atmosphere Circula%on 3-­‐D Atmosphere Circula%on and Rota%on 3-­‐D Atmosphere Circula%on and Rota%on + Con%nents Physical Proper%es of Air •  Air Pressure: defined as force per unit area –  Ideal Gas Law: influenced by air density (ρ) and temperature –  Rewrite equa%on for density J
P = ρ RT; R = 287
kg ⋅ K
Warm Air Less dense Cold Air More dense Adiaba%c Lapse Rate (proof of deriva%on) Conserva9on of energy, if no net heat to system this requires a balance between temperature and volume Adiaba9c Law: a gas cools as it expands and warms as it is compressed Change in temperature: • caused only by a change in pressure • not caused by heat flowing in or out of the gas (diaba%c hea%ng) Influence of moisture implies a diaba%c process and limits cooling w/
height ∂T
g
−1 −1
= − ;c p = 1004Jkg K
∂Z
cp
Atmospheric Stability 1. Compare parcel temperature to environmental temperature 2. If air parcel is warmer than surrounding air it is less dense and will con%nue rising 3. “Warm Air Rises” Hydrosta%c Equa%on says… A B ΔP
ρg = −
Δz
Interpreta%on: The change in pressure with the change in height is directly related to the density of the air. Gravity varies slightly but can be treated as a constant. Hypsometric Equa%on RT
P2
ΔZ =
log( )
g
P1
The depth of a layer of air that spans a pressure interval is propor%onal to the temperature of the air mass Pressure Gradient Force dx
Pressure Gradient is the change of pressure over a distance: Pressure Gradient = pressure difference / distance F = − 1 ΔP
Tighter gradient = stronger force ρ Δx
Pucng Concepts Together Consider an idealized 2-­‐D “Earth” w/no spin or con%nents 1.  Dispropor%onal hea%ng/energy balance 2.  Air near surface warms near equator, cools near pole 3.  Atmospheric column more dense over pole, less over equator Smaller Scale Examples Land surface responds more acutely to insola%on Summer, day%me hea%ng disporpor%ately heats land vs. ocean •  warm air over land becomes buoyant and rises •  results in thermal “low” pressure at surface •  return flow from cooler air over ocean surface = “monsoon” Simplest Model: One-­‐Cell Thermally Driven Hadley Cell Assume 1) aqua planet 2) sun over equator 3) non-­‐rota%ng earth à Hadley cell energy deficit energy surplus © 2007, John Wiley and Sons, Inc.
Earth’s Rota%on Rotation Rate of Earth (angular velocity)
2π
−5
Ω=
24hr * 60 min* 60s
≈ 7.292 ⋅10 rad ⋅ s −1
Velocity of solid Earth (function of latitude [ϕ] )
uEARTH = Ω⋅ radiusEARTH ⋅ cos(φ )
Solid Earth’s Velocity •  Rota%on Velocity and deflec%on varies with la%tude Rota%on Velocity 0 kmph(0 mph) uEARTH = Ω⋅ radiusEARTH ⋅ cos(φ )
1,675 kmph(1041 mph) Greatest deflection Least deflection Coriolis Force • 
Coriolis Force: An apparent force that due to the rota%on of the Earth. –  Deflects moving objects from a straight path. –  In the Northern Hemisphere the Coriolis force deflects objects to the right of their intended path (reverse in Southern Hemisphere) Why??? Coriolis Force latitude
uEARTH = Ω⋅ radiusEARTH ⋅ cos(φ )
∂uEARTH
f=
= Ωsin(φ ) = 1⋅10 −4 @45°N = 0@0°
∂t
Coriolis Force (f) only acts on moving objects
Coriolis Force In Ac%on 1. Air accelerates in direc%on of pressure gradient force 2. Coriolis Force acts to the right of mo%on w/speed of air parcel 3. Eventually a balance is reached between -­‐ Pressure Gradient Force -­‐ Coriolis Force This is called geostrophic balance and the geostrophic wind 3 2 1 Es%ma%ng Geostrophic Winds Geostrophic winds assume balance between Coriolis and Pressure Gradient Force and no accelera%on g ΔZ
ug = −
f Δy
g ΔZ
vg =
f Δx
In midlatitudes f = 1x10 -4 1/s
Up in the Atmosphere “Thermal Wind” •  Air pressure drops fastest with height in cold air (ideal gas law) •  Strengthens pressure gradient with eleva%on (pressure gradient) •  Due to the Coriolis Force, this leads to westerly winds alo2 Wind: Driving Forces in the Atmosphere •  So far: –  Pressure gradient force –  Coriolis force –  Gravita%onal force –  FricAon force •  Drag on wind as it moves across surfaces •  Decreases with height (not important above mnts) •  Decreases effect from Coriolis force Review of General Circula%on (so far) Arises in response to thermal imbalance –  @ constant pressure, colder air is more dense –  Thermal instability drives buoyancy in areas of hea%ng –  Ver%cal mo%on drives horizontal mo%on (conserva%on) = SIMPLE 2-­‐D HADLEY CIRCULATION MODEL Coriolis Force –  Apparent accelera%on, forces curvature to right of mo%on in NH for large-­‐scale flow –  Geostrophic balance: PGF=CF, valid for flow away from the surface boundary layer –  Strong la%tudinal temperature gradient drives westerlies The Hadley cell that could •  Polly the parcel reaches the top of the ITCZ near the equator and follows the Hadley Cell poleward –  What will be her final zonal wind component if she moves to 60oN? Conserva%on of Angular Momentum Angular momentum: Mass * distance from axis of rota%on * angular velocity Think “the ice skater •  Earth rotates has fixed angular momentum, Me= Ωacosφ * acosφ •  where Ω=rota%on rate (radians/second), acosφ = distance from rota%on axis at la%tude φ •  At equator, Ue = 465 m/s Angular Momentum •  Parcel would be moving at 134 m/s at 30N! 435 m/s at the pole! •  Conserva%on of angular momentum w/ Coriolis Force lead to forma%on of the subtropical jet •  Observa%ons show subtropical jet ~35 m/s •  Yet, angular momentum must be conserved globally and this one-­‐cell model violates that idea What processes account for poleward momentum flux? …answer forthcoming… Three-­‐Cell Model of Atmospheric Circula%on Three Cell Model: La%tudinal Transect momentum
Atmosphere moving
faster than solid earth
Solid earth moving faster
than atmosphere
Three Cells Hadley Cell Tropics, thermally direct -­‐ warm air rising (heat source) -­‐cool air sinking (subtropics) Ferrel Cell (outdated term) Midla%tudes, thermally indirect, weak in zonal-­‐mean -­‐cools extratropics, heats subtropics -­‐accounted for by eddies and momentum fluxes (not really a cell) Polar Cell Tropics, thermally direct -­‐ warm air rising (polar front) -­‐cool air sinking (pole) General La%tudinal Pauerns •  Four dis%nct primary pressure systems: –  Equatorial low-­‐pressure –  Subtropical high-­‐pressure –  Midla%tude low-­‐pressure –  Polar high-­‐pressure Westerlies and Easterlies •  Diverging air from the subtropical high can go two direc%ons –  Flow toward the equator – tropical easterlies (trade winds) –  Flow toward the pole -­‐ Westerlies L Intertropical Convergence Zone (ITCZ) •  Narrow zone of low pressure formed due to great hea%ng following near maximum insola%on (thermal equator) •  Air from higher tropical la%tudes flows toward region •  Air converges to form the Intertropical Convergence Zone –  The ITCZ is not easy to see due to other tropical disturbances –  hup://weather.msfc.nasa.gov/GOES/goeseaswull.html Polar High Polar High: zone of high atmospheric pressure present at high la%tudes –  Mass of subsiding air –  Cold dry air mass sinks and forms a high pressure –  Rota%on directs cold, dry air toward the Equator Subtropical High: Band of high air pressure (sinking air), calm winds, and clear skies • 
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~15° -­‐ 30 ° la%tude Equatorward of stormtrack, poleward of ITCZ Home to the deserts “Horse” la%tudes in the subtropical oceanic highs Midla%tude Fronts •  Primary purpose of midlaAtude circulaAon is to mix cold polar air and warm tropical air –  Front: the contact in the midla%tudes between warm, tropical air and colder polar air Zonal Average Zonal Wind Important Features •  westerlies vs. easterlies •  Midlat Max m/s, Westerlies>0 •  Jet(s) •  Zero wind line u=0 •  Summer vs. Winter Why such differences? Westerlies Alo2 consequence of pole-equator temp. gradient modified by the Coriolis Force
COLD AIR WARM AIR Jet streams: high-­‐speed flow in narrow bands within the upper-­‐air westerlies and along certain other global la%tude zones at high levels (intensifica%on of westerlies due to strong temperature gradients) Meet “Eddy” Eddies are another term for large-­‐scale waves in the atmosphere scale of 1000-­‐km, think: weather systems Highs and Lows “StaAonary Eddies”: driven by “sta%onary” large-­‐scale geographic features (land/sea contrasts, hea%ng, topographic forcing) “Transients”: Weather systems (progressive) Transients • 
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Mid la%tude cyclone/an%cyclone couplets Grow via baroclinic instability (meridional temperature gradients) Stronger pole-­‐equator energy imbalance=stronger waves Demarked by well-­‐defined frontal boundaries separa%ng warm/
cold air masses •  A Constant baQle: Eddies use the jet stream (300hPa) as a guide. Eddies try to redistribute heat while radia%ve forces try to retain imbalance. Concepts of Baroclinicity (Temperature Gradients) Consider the Typical Developing Wave Cyclone Poleward heat flux in warm air sector of system Grow via baroclinic instability (meridional temperature Compensa%ng return flux of cold equatorward flowing air ogn radients) lee-­‐side Stronger pole-­‐equator energy imbalance=stronger waves Warm and cold conveyor belts Sta%onary Waves •  Fixed geographically* •  Slower response: driven by boundary condi%ons –  Topography –  Land/sea heat contrasts •  Large wavelengths ~10000s km •  Stronger in winter, especially for NH…why stronger in NH? •  Transport Heat/Momentum: set the climate Split flow
upper-level ridge
omega block
Poleward Heat Flux by Atmosphere “The Reason for Breezes” Hadley mean-­‐meridional-­‐circula%on [MMC] strong in tropics /poles Eddies and waves most important in midla%tudes •  Peak in Winter Hemisphere (max temperature gradients) •  Sta%onary accounts for ½ poleward flux in NH winter General Circula%on •  1-­‐Cell Model: Transports Energy, Fails in a rota%ng planet •  3-­‐Cell Model: Hadley and Polar Cells follow 1-­‐D model, Ferrel cell in midla%tudes with waves accoun%ng for bulk of poleward heat flux •  Stronger temperature/pressure imbalance during winter mandates stronger wave ac%on: stronger jet stream and synop%c storms in winter hemisphere Model vs. Reality •  Land-­‐water differences influence pressure pauerns. •  Rela%vely warmer areas generally have lower pressure •  Source regions for atmospheric moisture •  Large mountain barriers Seasonal Sea Level Pressure and Surface Winds Aleutian Low
1.  Seasonal Land-­‐
Ocean Temperature Gradients à Pressure Gradients 2.  Meridional Shi2s in pressure pauern by seasons 3.  Hemispheric Differences Subtropical High
Icelandic Low
Continental Low
Strong thermal imbalance and equator - pole temp gradient
Stronger jet, eddies needed for balance
ITCZ in SH, poleward over land masses
Sea level pressure and prevailing winds
“thermal equator” moves north, weak equator - pole temp gradient: winds
weaken
Prevailing wind direction along west and east coast of N. America.
Sea level pressure and prevailing winds
Monsoon: Reversal of Winds Winter “con%nental” high Summer “thermal” low •  Thermal heating à rising motion à surface pressure decrease
à low level surface convergence via horizontal winds
•  Moist air from high SST Indian and west Pacific converge to
create large precipitation rates
Subtropical Jet Stream •  Local influenced by sta%onary wave forcing (orography, land-­‐
sea contrasts, SST) •  Jet strongest downstream of prominent mountain forcing (temp gradient) •  Strongest in winter due to enhanced meridonal temperature gradients •  Weaker jet off the west coast Average 250mb zonal speed (m/s)
Precipita%on and Circula%on Ingredients for Precipita%on •  Moisture and Moisture Advec%on •  Rising mo%on (frontal/convec%ve/orographic) Upper-­‐level dynamics •  Temperature contrasts à dynamics of stormtrack + convec%on •  Provide steering or advec%on of moisture Lower-­‐level dynamics •  Surface hea%ng drives convec%on and inflow •  Moisture in lower-­‐atmosphere connected by lower-­‐level flow •  Topography can both enhance and reduce rainfall rates Eugene, OR
Pocatello, ID
Moscow, ID
Rapid City, SD