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….)