Dudley Chelton video
Satellite altimetry
2 satellites (upper)

1 satelliteKyoto FDEPS lectures 4-7 xi 2007
Dynamics of oceans and atmospheres
P.B. Rhines
University of Washington

DAY 3• 1. rotating, stratified fluids: oceans and atmospheres– vorticity: a vector-tracer in classical homogeneous fluids• geostrophic adjustment, thermal wind• 2. wave dynamics: fundamentals, group velocity, energetics, raytheory• potential vorticity (PV)– vortex stretching, Prandtl’ s ratio, geography of PV• 3. Rossby waves• 4. instability => geostrophic turbulence; subtropical gyres:dynamics, jets and gyres, topography effects• 5. Case study of topographic effect on atmospheric circulation:
Greenland and Atlantic storm track. 7. meridional overturning
circulations and the thermohaline circulation• 6. Teaching young undergraduates about the global environment?
• 7. Seminar: subpolar climate dynamics observed from above andbelow: altimetry and Seagliders

Hoskins+Ambrizzi
JAS 9300

Branstator JClimate 02

AGU, 2003

zonal wind (m/sec) at 45W with Greenland topography
JFM 1993“Svairdrups”

Topographic flows: we now introduce the effects ofmountainous topography, which owing to the ‘vertical stiffness’ imparted by rotation, isgreatly influential. On an f-plane, the Rossby number, U/fl, topographic height andFroude number Nh/U are key parameters.
(i) 2D stratified flow over bump of height h (buoyancy freq N upstream flow U)
Nh/U (ii) 3D stratified flow …over or around
Nh/U crit ~ 2(Schaer+Durran, JAS 1997)
dispersive lee waves softens the ‘sharp’ hydraulic effects(iii) f-plane rotation, unstratified: Taylor column dynamics
flows ‘around’ if h/H > Ro (Ro = U/fL).
(iv) f-plane rotation weakens blocking (Nh/U crit =>3)Taylor column => Taylor cone Nh/U > 1 again! (independent of Ro)(v) β-plane flows-large-scale potential vorticity (PV) gradient-contours of constant background PV (f/h = const)
bend Equatorward over a ridge, locatinga cyclone over its crest for very slow flow
-dispersive lee waves, semi-circular wavecrests-hydraulic structure in some limits (planetary geostrophic)
where the waves are non-dispersive-strong upstream blocking (‘Lighthill mode’) for
βL2/U>1

Nh/U = 1, 2, 2.5, 3, 4, 6

pressure drag occurs when the anticyclone shifts
upstream as wake vorticity is shed, placing theEquatorward flow over the lee downslope

Impulse (the time-integrated force on the solid Earth)is summed up by meridional PV flux:<q’v’> which expresses the x-averaged force on
the Eulerian fluid along a latitude circle ~ (f/H)<h’v’>Petersen, Olaffson,
Kristjannson
JAS2003

Lee Rossby-waves in the wake of a cylindrical mountain(McCartney JFM 1976)
Rossby waves are ‘one-way’: their phasepropagation has a westward component
relative to the fluid: thus they exist as lee
waves for an eastward flow but not a
westward flow. Wave drag peaks at:
8.2 δ/ε times the ‘naive estimate’,ρfUL2δH
where δ=h/H is the fractional mountain height, ε the
Rossby number, U the mean flow, L the radius and H
the total fluid depthnote strong correlation of meridional velocity
and topographic height…..wave drag. Also notethe beginnings of jet formation southeast of themountain, even in the linear theory

wavenumber diagram for Rossby waves in steady zonal
westerly flow (U>0)

A westerly (prograde, cyclonic) zonal flow
encounters a small mountain(at 2 o’clock). Rossby wave dynamics
produces standing waves downwind, aconvoluted lee cyclone, intense jet structurewrapping round the mountain, and a ‘Lighthill
block’ upstream. This stagnant blocking
region is (in linear, yet finite topography,
theory, a Rossby wave with vanishing intrinsic
frequency and upstream groupvelocity for merid. wavenumbers < (β/U)1/2 .
Note the ruddy pressure features which
are fine-scale evaporative convection cells,
pillar-like cyclones. The edge of the blockis outlined by convective rolls.
Here the controlling parameter βa2/U > 1
meaning that the wake is stable; smaller valuesof this parameter yield unstable wake and transien
Rossby waves which ironically fill the hemisphere(they are not simple lee waves). See Polvani,Esler, Plumb JAS 1999 for a numerical study
with some of these features.

Streak image of the same experiment (dots 2 sec apart) showing intensity of jets near mountain, lee Rossby waves and upstream
block

L

H

L
H

Greenland's effect on the Northern Hemisphere circulation:
downslope winds meet the Atlantic storm track.

P.B.Rhines
Oceanography & Atmospheric Sciences
UW

image: Petermann Glacier, NW Greenland
Konrad Steffen

Let’s remove the ice (only temporarily)
Konrad Steffen, Univ. of ColoR/V Knorr in Labrador Sea. At the time of this research cruise, the firstdeep ice cores were being drilled on the summit of Greenland.
The iceberg likely calved off the Jakobshavn glacier in west
Greenland. The strata, faintly visible, record climates back
120,000 years. Air bubbles in the ice accurately give us awhiff of ancient climates, showing the high correlation between
Earth’s temperature and the amount of carbon dioxide and methane in the air

etopo global topography

Red/blue =high/slow SLP
black contours:
Z250
yellow contours
Z50

Greenland is near the ‘center of action’ of the Icelandic low, with extreme activity of jet
stream, tropopause folds, storm track, meridional moisture- and heat-flux, stratospheric polar
vortex, oceanic global overturning circulation and implicitly the NAM/AO/NAO principal
EOF of hemispheric sea-level pressure• The next figures are animations of the northern hemispherecirculation for a high-NAO (1989) and low NAO (1996)
winter, respectively. They show many things, including
strong vertical interaction between clusters of cyclones andthe stratospheric polar vortex. Synoptic activity is felt in thestratosphere! A strong sudden warming is seen in 1989.
•
The two winters are very different. With low NAO (1996),
it seems the storm track is farther south, and does not excite
the stratospheric polar vortex overhead as strongly as withhigh NAO (1989)

1989 JFMA:NAO index positive

Synoptic storm
tracks arebeneath stratosphericpolar vortex

Greenlandcolors: 1000 HPa near-surface dynamic height(blue=low pressure, red=high)contours:
jet stream level 300 HPa, stratosphere 30 HPa

1996

JFMA
(NAO index
very negative)

Storm tracks areusually southof stratosphericpolar vortex
Greenlandcolors: 1000 HPa
red contours: 300 HPa
black contours: 30 HPa

In moderate-resolution simulations, Greenland’s topography (but not albedo) actually weakens the Icelandic low:interference pattern with hemispheric standing waves… sea-level pressure is lower to the west and higher to the east ofGreenland…model dependent?
SLP

500 hPa

DJF
no Greenland

500-1000 hPa
thickness
contour interval=5 hPa

control minus
no GreenlandPetersen, Kristjansson & Jonsson Tellus 04

• Numerical simulations (Petersen, Kristjansson & Olafsson Tellus 04 T106;
Kristjansson &McInness QJRMS 99) suggest that Greenland topography
reduces the strength of cyclonic systems in the Atlantic storm track,blocking cold-air outbreaks from Arctic Canada: Interference patternwith hemispheric standing waves•

Is this model dependent? Paradoxically, tip-jets and gap-jets(downslope winds) are frequently observed there and are very intense.
Winds in the Labrador and Greenland Seas can be very strong.
We are not contemplating removing Greenland until it melts

potential vorticity and Θ(Hoskins, McIntyre & Robertson QJRMS 1985)• despite this no-Greenland model study, winds are
extraordinarily there; pressure drag on Greenland’s slopes
can propagate upward, block westerly flow, and affect the
subpolar (and thus global-) ocean beneathfrom Dudley Chelton: Greenland tip jetpressure drag and the length of the day
Hide et al. JGR 1997

T159

Jan

July

resolved torgue ~ 5 x 1018 N m
Brown, QJRMS 2004

T511

6 month ECMWF model integrations at T95-T159
L60 and T255 L40, and case studies

Pressure drag on Greenland (using T511L60 ECMWF
model)‘normal’ dragevents (Greenland
pushes atmospherewestward , lowpressure to the east)1000 hPa fields correlated with high pressure drag eventsat lags -6 days to + 4days ERA-40 reanalysis data (T159L60)
1982-2001

0 lag

250 hPa

50 hPa hemispheric response with precursor: the SPV is pulled
toward Baffin Bay during high normal pressure drag events

1000 hPa fields correlated with high normal pressuredrag across Greenland: high-pass filtered eddies (2-10day)

Z1000 associated with ‘abnormal’ pressure drag (highpressure on eastern slopes of Greenland)effect of model resolution on resolved pressure drag,surface friction and parameterized gravity wave stressStorm tracks

splitting of storm track, some lows moving northward
on west side of Greenland (short lived), most moving north on easternside. Cyclones are also split vertically by the ‘knife-edge’occurrence of cyclones in ERA-40 data, and at various
model resolutions
200 km120 kmgrid

80 km

east-side storm tracks launched Irminger Sea (left) andGreenland Sea (right)

Two case studies, winter 2004/5 (strong, extraordinarily cold, elongatedstratospheric polar vortex arrived early in the season)
Limpusaven et al JGR 2007 event‘normal’ dragevents (Greenland
pushes atmospherewestward , lowpressure to the east)Θ on PV-2 surface (~tropopause) and SLP: Christmas 2004T511L60 ….3
storms in 10 days
Cold air sweeps through the summit gap of Greenland..even at thetropopause level

25 Dec 2004

gap jet2 x 10-6m2Ks-1kg-1

tip jet25-27 Dec 2004
surface winds
low-level vorticity

15-17 Jan 2005

0.31 f/N dU/dz

Lagrangian back-trajectoies (using softward of H. Wernli)vorticity colors
units of f

25-27 Dec 04

15-17 Jan 05

altitude colorshPaEffect on subpolar gyre of the Atlantic, and Greenland Sea:enhance air/sea heat flux: much intensified at higher model
resolution
T95
T255
T799

Principal eof of sea surface elevation, 1992-2006, which is mostly a simple
trend, showing deceleration of the subpolar Atlantic gyre over 15 years
Häkkinen & Rhines 2004 Science

Tip jets and reverse tip jets:
Doyle & Shapiro Tellus 1999, Moore & Renfrew J Clim 2005, Pickart et al. Nature
2004
Cape Farewell

Denmark Strait south

Denmark Strait northForecast effect of high-pressure drag events is short-lived,
particularly in Europe; skill of forecasting drag is highEP-flux: hemispheric impact; anomalous SPV acceleration(barotropization rather than simple mountain dragnote factor of 10 zoom for anomaly

80N

vectors

10N

Egger JAS 2006 finds that zonal momentum tendency can be
opposite to expected push by pressure drag…due to imported
meridional vorticity flux in transient eddies. Covariance fields
with pressure drag, barotropic model.
500 m
5500m

Gravity waves

Doyle & Shapiro Tellus 1999

ECMWF model runs: high-pressure drag events develop
downslope winds and upward propagating gravity waves
reaching the stratosphere at T511, T799….resolutions higher
than that T95
used in ‘no-Greenland/Greenland’T255
T799 model studies

Downslope winds increase wavedrag (by Bernoulli) here in a layer of CO2

Limpusaven et al. JGR 2007

gravity waves decelerating SPV: at rates 10-120 m sec-1day-1

300 hPa dyn height

Limpusavan et al JGR 2007

24 Jan 2005..an ‘abnormal’ pressure drag event (would lead to westerly accel ofatmos)

Limpusavan et al. JGR 2007

Mel Shapiro’s Greenland flights

Ro = ∞
Nh/U = 1.5

Ro = 0.42
Nh/U = 1.5

Petersen, Olaffson,
Kristjannson
JAS2003

Schär (JAS 93): PV is transported along the intersections of the Bernoulli-function and isentropic surfaces in a statisticallysteady flow….

Schär & Durran
JAS 97
also: tip horiz
vorticity to makevertical vorticity
Rottuno et al. JAS
99

Ertel potential voticity generation by breaking lee gravity wavesL the PV generation as well as the gravity-wave momentum flux alter the geostrophic
circulation

Chen, Hakim & Durran, JAS 2007 subm

t=20hPV and zonal flow
generation in flow
over a 1.5 km
high mountain(dipole of PV,
decelerated wake)Chen, Hakim & Durran,JAS 2007 in press

t=30h

t=40h

t=50h

Overturning circulations•

Some ‘burning’ questions for which we thought weknew the answers:(i) What drives the global meridional overturning circulation (MOC) of theoceans --- buoyancy or mechanical mixing induced by winds and tides?
(ii) Is high-latitude sinking and the deep, cold branch of the MOC adominant member of the meridional heat and fresh-water transport?
(iii) Does the ocean circulation substantially warm western Europe?
More generally, does heat transport by oceanic general circulation affectatmospheric climate?
(iv) What are the paths of upwelling of deep waters in the global oceanic
MOC?
(v) Where are the crucial sites for convection and water-masstransformation ?
(vi) What is the quantitative rate of water-mass production for the several
components of the North Atlantic DeepWater (for example, Labrador
Sea Water), and how are they altered before being ‘delivered’ to theglobal MOC?
(vii) How do convection and mixing drive diffusive overturning at many
scales, reaching to the distant circulation.

Oceanic overturning circulations: coexisting with ‘horizontal gyres of windforced circulation• MOCs have an easier time in the oceans than in theatmosphere:a ring of air moved 1000 km north gains westerly velocity
of 100 m sec-1 There is not enough energy available to utilize thismode: the Hadley cell is limited in north-south extent. Forces (eddymomentum flux from PV stirring) and non-symmetric circulation
are required to support extensive meridional excursion.

channels and conduits for heat- and fresh-watertransport

After Schmitz (1995)

(31%)

consider the differences between tropics and Arctic…(a)at 60N latitude
the sunshine incident per unit area is 50% of the full intensity withthe sun overhead; (b) the albedo (whiteness) is greater
source: IPCC-01

solar radiation (kilowatt-hours per square meter, per day)varies with latitude and season (here neglecting the great effect of cloudiness)

www.fao.org/DOCREP/003/X6541E/X6541E03.htm

Variation of Temperature With Latitude

Bare Earth• A simple radiative
calculation gives an Earthwith the correct average T,
but wrongly distributed
meridionally (north-south)

slide from K.Carslaw,
Univ. of Leeds

the zone
radiatingback
directly tospace hasaverage
temp of
290K = average surfac
about 250K,
255K (-180C)..the simple radiation

Global meridional heat transport divides roughly equally into 3 modes:(Bryden & Imawaki 2002)
1. atmosphere (dry static energy) cpT + Ф
2. ocean (sensible heat)
3. joint atmosphere/ocean mode: water vapor/latent heat transport Lq
The three modes of poleward transport are comparable in amplitude, and distinct incharacter (sensible heat flux divergence focused in tropics, latent heat flux divergence focus in thesubtropics) (based on Keith (Tellus 1995) climatology, similar to more modern: Trenberth et al. J.Clim 2003)(residual
method, TOA
radiation
1985-89 and
ECMWF/NMC
atmos obs:
90S
90N
redundantthenorthern subtropics show extremely active upward air/obsError est.: ± 9% at mid-latitude; Bryden est 2.0 ±0.42 pW at 24N(air sea flux)very similar numbers from Trenberth & Stepaniak,QJRMS 04

Flux of fresh water by the atmosphere is concentrated in the Pacific andAtlantic storm tracks
globally it carries ~ 2 petawatts of latent heat flux … whichis ~0.7 Sverdrup (0.7 megatonnes/sec) of freshwater flux
1993 JFM
1996 JFM

Trenberth & Caron JClim01

merid. heat transport at 35N: 78% A, 22% O; 18N: 50% A, 50% O

• So, ventilation of the tropics by atmosphere + ocean MOC’s
provides ~ 5 pW (5 x 1015 W); distributed over the area of the
Earth between 0N and 30N, averages 5 x 1015 W/πR2 =39 W m-2, delivering the same amount per m2 to the Earth northof 30N.
Fully as much heat is carried in the atmosphere by
0.8 Sverdrups (megatonnes s-1) moisture flux ~ 2 pW as by dry
static energy flux. (using the heat of vaporization, 2.25 MJ/kg)(It is useful to talk about both oceanic and atmosphericmass (water or air) transports in Sverdrups (Sv):
Gulf Stream 30-120 Sv
Antarctic Circumpolar Current~ 180 Sv
Atlantic MOC ~ 16-20 Sv
westerly winds/jet stream ~ 500 Sv
atmospheric MOC ~ 50 -100 Sv

Qnet, net atmosphere-ocean heat flux, watts/m2 (Keith Tellus 95)(annual average)

It should be noted that because the sun heats the ocean, O,
but does not cool the atmosphere, A, the most useful mapsof Qnet for A will differ those for O by the short-wave insolation.

Where is air-sea heat flux most intense? January (W m-2)
(SOC/NOC1.1a climatology based on COADS)The air/sea heat flux seen by the atmosphere(latent+sensible+long-wave rad)and by the ocean (latent+sensible+long-wave + shortwave solar rad)

Annual average ratio of convergence of heat flux by ocean
circulation divided by annual average heating of the atmosphereby ocean: (LH+SH+LW+SW)/(LH+SH+LW)

cold-air outbreaks: a source of deep convection(surface air temperature, 2 Jan 1993)

Held et al. (J.Clim.02) 100mb-1000mb diabatic heating for January

PV inversion: using a model of convective destruction of PV. The modelled
or diagnosed PV field is associated with a field of azimuthal circulation,
displaced mass, and interacts with the meridional overturning circulation
Marshall & Schott Revs Geophys 99

viscous overturning in a rotating cylider:
the radial/vertical plane transmits stress from the top plate (which is at restin the laboratory frame) and the bottom of the cylinder (which is rotating)

sugar
syrup

Overturning cells in an annulus of
fluid between concentric cylinders(the inner cyclinder is rotating, theouter cylinder is stationary(Taylor-Couette flow).
The cells transmit torque between
the solid cylinders more strongly
than would pure viscous diffusion.
(The same 2D equations govern
thermal convection, and theNusselt number expresses theanalogous increase in heat flux
above the diffusive rate).

Sink-driven flow in a rotating, stratified fluid: the cyclonic spin of the fluid
would be resisted by bottom Ekman friction (and all radial inflow
concentrated there in this tornado vortex); However, stable stratification
resists and forces continuing MOC within the fluid. The azimuthal velocity
and shear is so great that it tears up the stratification (originally 2 layers)

GFD lab, Univ of Washington

Dense plume flowing down a sloping valley in a rotating fluid(model of dense downslope flows in the Weddell Sea)
Elin Darelius, Univ of Washington GFD lab
particle paths are helical,
with Ekman driven meridional
overturning transmitting theboundary stress into thefluid. (Looking up the sloping
valley)The zonally averaged
overturning streamfunction,
North Atlantic/Arctic model of
Häkkinen driven by NCEP
winds and temperatures
This image of the ocean circulation is theusual output of climate models; many
essential processes are made invisible…theeast-west detail of the previous slides.
These ‘details’ are likely to be essential tounderstanding the global ocean transports.
The tendency for dominant sinking south ofGreenland in low-resolution climate models
is widespread: here in density- latitude
space the streamfunction reveals higher
latitude sinking and dense overflows.
The difference is expected from the eastwest tilt of potential density surfaces, sothat equal and opposite meridional velocities
at the same depth z may have very different
densities.

y-z spacey-potential density space

35S

90N

Bailey, Hakkinen, Rhines 2003103

Lumpkin & Speer’s JPO 03 discussion of the Atlantic MOC, here plotted against potential
density and latitude. Even though we know there is much east-west structure (boundary
currents, horizontal gyres as in Reid’s maps) the zonally averaged MOC ‘looks like’ thesimple 2-dimensional box models

Ssea
surface

O2

Lumpkin & Speer JPO 2003

The ACC is the only ocean current
with The Problem (how to flow meridionally, given
the absolute angular momentum constraint)..yet it has
ample topographic bottom slopes tolean on: these clearly balance thezonal wind stress that drives thisAAIWgreatest of all ocean currents
This may be a dominant site of
upwelling in the global MOC(with respect z and potential
NADW
density)
Salinity at 24W longitude

Oceanic
meridional
overturning
strength vs.
meridional
baroclinic
dynamic
heightgradient in
HADCM3(Thorpe et al 2001)

A change in the MOC transport may be associated with some measurable change in the meridional
density gradient. HadCM3 finds a very close correlation between Atlantic overturning rate and the S-N
gradient of steric height from 30S - 60N through the W Atlantic. But, there is a possible oversensitivity ofmodels to subpolar buoyancy/Labrador Sea.

THE END

An evacuated glass vessel with water in it illustrates the Clausius-Clapyron relation
between vapor pressure of water and temperature. The water is pushed from the vessel in
my hand to the ‘cold ball’, and the vapor pressure difference between the two ends is close
to the hydrostatic pressure measured by the column’s vertical displacement. One can fillout the curve and see the greater sensitivity (to temperature) of water vapor production at
high, ‘tropical’ temperature. This all works because we shake the vessel so that a thin filmof water lies under my warm hand. It illustrates a key variable in the climate system.
When shaken this water ‘clinks’ like metal,vapor cavities opening up and slamming shut.

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FDEPS Lectures, November 2007
P.B. Rhines, Oceanography and Atmospheric Sciences, University of Washington
Rhines@ocean.washington.edu
www.ocean.washington.edu/research/gfd
These lectures will address the dynamics of oceans and atmospheres, as seen through theory, laboratory
simulation and field observation. We will look particularly at high latitudes and climate dynamics of the ocean circulation
coupled to the atmospheric storm tracks. We will emphasize the dynamics that is difficult to represent in numericalcirculation models. We will discuss properties of oceans and atmospheres that are both fundamental, unsolved questionsof physics, and are also important, unsolved problems of global environmental change.
Lecture 1:
Is the ocean circulation important to global climate ? Does dense water drive the global conveyor circulation?
Fundamental questions about oceans and atmospheres that are currently under debate.
The field theory for buoyancy and potential vorticity.
Basic propagators: Rossby waves and geostrophic adjustment.
Potential vorticity: inversion and flux.
Lecture 2:
How do waves and eddies shape the general circulation, gyres and jet streams?
Almost invisible overturning circulations.
Lessons from Jupiter and Saturn.
The peculiar role of mountains, seamounts and continental-slope topography.
Lecture 3:
Dynamics of ocean gyres and their relation with the global conveyor circulation.
Water-mass transport, transformation and air-sea exchange of heat and fresh water.
Ocean overflows and their mixing.
Decadal trends in the global ocean circulation.
Lecture 4:
Heat, fresh-water, ice: convection in oceans and atmospheres and the texture of geophysical fluids.
Lecture 5:
Teaching young students about the global environment using the GFD laboratory: science meets energy andenvironment in the lives of Arctic natives
Seminar:
Exploring high-latitude ocean climate with Seagliders and satellites

Kelvin waves, inertial waves in shallow rotating fluid