The general circulation: midlatitude storms
2
Motivation for this class
Provide understanding basic motions of the atmosphere:
• Ability to diagnose individual weather systems, and predict how they will change
• Understand the importance of atmospheric flow, and the role of weather systems in maintaining global circulation and planetary energy budget
3
Geostrophic adjustment (1)
4
Geostrophic adjustment (2)
5
Geostrophic adjustment (3)
6
Inertia-gravity waves “disturbance” is heating with condensation/latent heating
ETA model (test)
Geostrophic adjustment • Large scale state tends to wards balance geostrophic flow • Flow must satisfy conservation of PV the entire time (thus
defining a “path” to the steady state) • Specifically, PV conservation offers a constraint on the way
a steady state is reached. • Balance reached by emission of interia-gravity waves • It can be shown that a third of potential energy liberated
converted to potential energy (rest radiated away by waves)
• Flow adjusts to disturbance larger than Rossby radius (otherwise, disturbance adjusts to flow)
• Fluid away from the disturbance (x >> R) does not feel the disturbance
• Important problem/issue for numerical simulations (prediction, initialization, generation of waves)
Rossby radius of deformation • Length scale at which rotation effects are as important as
buoyancy/gravity effects
• Ratio of speed of gravity waves to rotational frequency
𝜆𝑅 =
𝑔𝐻
𝑓
Shallow fluid (i.e., barotropic)
𝜆𝑅 =𝑁𝐻
𝑓
Thermally stratified fluid (like real atmosphere)
e.g., sqrt (9.8 * 7.6km)/10-4 = 2700 km!
e.g., (1.3x10-2 x 7.6km)/10-4 ~ 1000 km!
Two results can be reconciled by using reduced gravity (g’) to account for buoyancy force. i.e., atmosphere is not a free surface. Recall g‘ ~ g(Dr/r)
The general circulation (The zonally symmetric version)
up
down
down
down
down
up
up
/surface low
/surface high
/surface high
/surface high
/ surface high
/ surface low
/surface low
11
Global energy budget
Houghton, IPCC 2001
12
Diabatic
heating
James, 1995
DJF
JJA
13
Zonal wind and potential temperature
James, 1995
DJF
JJA
14
Mass flux streamfunction
and
Zonal wind
DJF
JJA
James, 1995
15
Hadley 1735
16
Dove 1837
17
Ferrel 1856
The modern view
20
Eddy heat transport
(v’T’)
DJF
JJA
James, 1995
21
Eddy momentum
transport (u’v’)
DJF
JJA
James, 1995
Surface pressure and surface wind
Wind always spiraling out from high, spiraling in to lows
Direction different
In the tropics…
Warming near equator, cooling at higher latitudes (closer to poles)
Leads to …
• ascent along equator (“stretching” when atmosphere is warmed)
• Outflow at high altitudes, with pressure gradient
• Sinking (in the subtropis)
• Inflow at low altitudes, with pressure gradient
Circulation cells (the Hadley cell)
heating
cooling cooling
Convergence: Where the air comes together
Divergence: Where the air spreads apart
The geostrophic paradox!
• As fluid at the top moves inwards to is deflected to the right, and generates a “jet stream”
• If the flow is EXACTLY geostrophic, no energy is transported.
• This is very much like the Hadley cell that Hadley was thinking about.
• Explains the easterlies and westerlies, but not the energy balance
What if we have more rotation?
Stronger get via thermal wind balance
Ingreadients to make weather
1. Heating at poles, cooling at higher latitude 2. This causes pressure gradient to form 3. Pressure force balances Coriolis force (i.e., geostrophic) to make
winds westerly (so no energy is moved poleward past the edge of the Hadley cell!)
4. Temperature continues to build in the tropics, making the pressure force stronger
5. Finally, this can not be balanced by the Coriolis force, and the pile of air collapses (just like a growing pile of homework on piling up on my desk)
6. Since this occurs when the pressure force is stronger than the Coriolis force, we see the spinning in the direction of the pressure force.
7. This is a cyclone! Which must have low pressure.
Storm tracks? • Hadley cell moves heat (“temperature”) from equator to
subtropics • Then we know there is transport of energy as both sensible
(temperature) and latent (water) heat from the subtropics to midlatitudes.
• This is in the region of the Ferrell cell (recall the Ferrell cell is the one that looks like it goes “backwards”)
• This is done by storms a.k.a., mid-latitude weather systems a.k.a., cyclones a.k.a., low pressure systems a.k.a., baroclinic cyclones
Storm tracks winter
spring
summer
fall
http://www.cpc.noaa.gov/ products/precip/CWlink/stormtracks/strack.shtml
i.e., location of cyclones
Storm strength (pressure depth)
December-February
June-August June-August
December-February
Energy transport
• In the tropics, the overturning circulation moves heat from the equator to the subtropics
• Heat transport is by both temperature and water!
Baroclinic cyclogenesis
Summary • Movement of energy from low latitude to high latitude
includes both • sensible heat (temperature) and • latent heat (water)
• In the tropics, the Hadley cell moves temperature poleward
• In the midlatitudes, storms move both temperature and water poleward
• These storms occur because the temperature build up in the tropics eventually becomes unstable.
• When the instability occurs, storms are created • The storms occur near the polar front • As such, the mid-latitude storms are important for
weather (sure enough), but also very important for global energy balance and climate
Semester summaries
We now know: • Basis for quantifying atmospheric (and ocean, and stellar) motion • (Conservation of mass, energy and momentum) • Can explain vertical distribution of temperature, pressure, density, and
temperature • Latter requires account of moisture and convective instability • Explain relationship between surface pressure, winds for different latitude
bands • Explain existence of jets based on temperature gradients • Balanced (non changing) flow: geostrophic, cyclostrophic • Know why weather systems have characteristic scale ~ 1000 km • Have a basis for storm development from instability • (Also, established some foundational tools: linearization, perturbation
analysis, concepts of stability/instability, existence of waves….)