More on Ocean-Atmosphere (General Circulation) Models

Outline

• Overview of the “fluid dynamics” part of Climate models

• Two applications of climate models to non Global Warming problems…

!! Not examinable !!

Model (prognostic) variables

Newton’s law+mass conservation

• 3 components of velocity (u,v,w)

• Pressure (Oce.) & Geopotential (Atm.)

1st Law of Thermodynamics

• Temperature

“Tracer” conservation

• Moisture (Atm.) & Salinity (Oce.)

Eulerian approach: budgets applied to fixed volume elements

y

x

z

δx, δy and δz arethe model grid box dimensions

Newton’s Law in east-west (x) direction:Pressure force

P(x)δzδy

P(x+δx)δzδy

y

x

z

δx, δy and δz arethe model grid box dimensions

Newton’s Law in east-west (x) direction:fluid transport of momentum

ρ(x)u(x)δzδytimes u(x)

ρ(x+δx)u(x+δx)δzδytimes u(x+δx)

y

x

z

Newton’s law in east-west (x) direction:fluid transport of momentum

ρ(z)w(z)δxδytimes u(x,y,z)

ρ(z+δz)w(z+δz)δxδytimes u(x,y,z+δz)

y

x

z

NB: Non linear & couples the boxes

Horizontal resolution

• Atmospheric & Oceanic models (when used in climate mode) are run at ≈ δx=δy=2°(i.e., 200km X 200km) horizontal resolution.

… but, oceanic storms are smaller than 2° so must be parameterized. Atmospheric storms have a length scale of 10° and are represented.

NB: A “coupler” might be needed if O/A not run on same grid

Horizontal grid

• Problems with convergence of meridians at the poles…

cosRx

As Δx becomes small, the time stepmust become small in order to avoidnumerical instabilities… too expensive!

Ocean modeller solution…

Rotate grid andput poles over continents!

… but does not work for the atmosphere…

A possible solution: the “Cube-Sphere”

Sea level (m)

Snapshot of Atmospheric temperature (500mb) on a water world

“Corners”

Vertical coordinatesAtmosphere ~20 levels

Ocean~15 levels

Time discretization & computer performances

• Timestep δt is a few minutes for the Atmosphere and about 1h for the ocean.

• Atmosphere is the most expensive to run and typically is the bottle neck of climate models (Feynman’s “Dry & Wet fluid”).

• 1 week of computer time ≈ 50 yrs of simulated climate.

Total number of variables…

• About 6X15X180X90≈1-2 million for Oceans and Atmosphere.

• Coupled O-A General Circulation Models are thus very large systems of coupled, non linear, ordinary differential equations.

ΔTΨ

…

Lorenz (1963)

Which of the Oceans and the Atmosphere transport more

energy poleward?

Atmosphere

Ocean

+

Total poleward energy transport

=

Net energy loss at TOA in Extra-Tropics

Net energy gain at TOA in Tropics

NB: In lectures we considered the integratedvalue, which is … zero!

Poleward heat transport (by either Ocean or Atmosphere) is small…

oaoP HHPWRS ,120)1( 2

Energy exchanged at top-of-atmosphere :

Planetary albedo Solar constant

Warm waterparcels arecarried polewardby currents

High energy air parcels are carried polewardby winds

Trenberth & Caron, 2001

Simplify the problem…

-No continents-Flat ocean bottom

Simplify the problem… What is the relative contribution of ocean & atmosphere in a waterworld…?

-No continents-Flat ocean bottom

?

Coupled (O/A) GCM in water world geometry

Atmosphere

Ocean

NB: Quite different results with polar islands!

Insights from water world

• The energy carried by ocean and atmosphere is similar in middle latitudes

• … but the mass flowing across latitudes per second is greater in the atmospherere than in the ocean

Insights from water world

• The energy carried by ocean and atmosphere is similar in middle latitudes

• … but the mass flowing across latitudes per second is greater in the atmospherere than in the ocean!

1 kgsinHLvM

Comparison Water World / Real World

Continuous curves: Water world(coupled model)

Broken curves: Real World(Observations)

Is the Gulf Stream responsiblefor mild European Winters?

“Every West wind that blows crosses the Gulf Stream on its way to Europe,and carries with it a portion of this heat to temper there the Northern windsof winter. It is the influence of this stream upon climate that makes Erin the“Emerald Isle of the Sea”, and that clothes the shores of Albion in evergreenrobes; while in the same latitude, on this side, the coasts of Labrador are fastbound in fetters of ice.”

Maury, 1855.

Eddy surface airtemperature from NCAR reanalysis(January, CI=3K)

WARM!

COLD!

Lieutenant Maury “The Pathfinder of the Seas”

Model set-up (Seager et al., 2002)

• Full Atmospheric model

• Ocean only represented as a motionless “slab” of 50m thickness, with a specified “q-flux” to represent the transport of energy by ocean currents

FseaairS

OOO QQt

ThC

Atmosphere

seaairQ

FQ

Seager et al. (2002)

Seager et al. (2002)

Conclusions

• Climate models offer a large space to use one’s imagination.

• Basic climate questions are still debated and the field is open.

I leave it to Jenny…

• …but will be back for Lecture 22.

• Office hours: Tuesdays, 5-6pm in Huxley Room 726 until end of Term 2.