Rossby and Kelvin Rossby and Kelvin Waves, Upwelling, Waves, Upwelling,

and Equatorial and Equatorial circulationcirculationOctober 15October 15

Rossby WavesRossby Waves

1

:Coriolis to

),(),(),(

Accel. Advective of Ratio

:#Rossby

0),,,(

:StateSteady

0

fL

UR

z

vuw

y

vuv

x

vuu

t

pwvu

L: measure of length over which U changes; also a measure of how far parcel travels before acted on by Coriolis

0t

in winds Changes

If R0<<1, ocean responds by wave propagation

Rossby waves exist because of:y

f

C

f3

f2

f1

,f

,f

constantH

f

ς=0 ς=0

ς<0 ς>0

0

vt

ς=0 ς=0

ς<0 ς>00t

0t

C<0

For west propagation:

balance ,0 ,0

vt

x

v

y

u

x

v

ς=0 ς=0

t0

t

For east propagation:

C>0

possible balance no ,0 ,0

vt

Assume: )(0

tkxievv

Then:

Ckk

k

vkvvvxt

2

00

At Mid latitudes: C ~ 1-10 cm/s

Equator: C ~ 1 m/s

Rossby waves and Kelvin eaves communicate information on changes in wind to different part of the basin – Responsible for quick reversal in Somali current – Play a large role in El Nino

Equator oceans respond much faster to changes in winds because of greater Rossby waves speed – Adjustment time scale ~ basin width

Rossby Wave Speed

Coastal UpwellingCoastal Upwelling Mid-ocean upwelling – driven by Mid-ocean upwelling – driven by

Ekman divergenceEkman divergence Get Ekman divergence at coastGet Ekman divergence at coast

Equatorial DynamicsEquatorial Dynamics

Recall… coastal upwelling is driven Recall… coastal upwelling is driven by Ekman divergence at the coastby Ekman divergence at the coast

Equatorial upwelling is driven by Equatorial upwelling is driven by Ekman divergence at the equatorEkman divergence at the equator

τ(x)

τ(x)

A’

A

B B’Equatorf=0

ME

ME

A’A

Equator

f<0 f=0 f>0

pgf pgf

Pycnocline is lifted at the Equator, pressure gradient force drives equatorial under current

fvx

p

1

x

pu

1

Surface current driven by wind is confined to the mixed layer

B’

B

pgf

Sea surface slopes up to the West

East – West slope of the pycnocline

)(x

x

p

Figure 14.5 in Stewart. Left: Cross-sectional sketch of the thermocline and sea-surface topography along the equator. Right: Eastward pressure gradient in the central Pacific caused by the density structure at left.

Figure 14.1 in Stewart. Average diabatic heating due to rain, absorbed solar and infrared radiation and between 700 and 50 mb in the atmosphere during December, January and February calculated from ECMWF data for 1983-1989. Most of the heating is due to the relaese of latent heat by rain. From Webster (1992).

Figure 14.2 in Stewart. The mean, upper-ocean, thermal structure along the equator in the Pacific from north of New Guinea to Ecuador calculated from data in Levitus (1982).

Figure 14.3 in Stewart. Average currents at 10m calculated from the Modular Ocean Model driven by observed winds and mean heat fluxes from 1981 to 1994. The model, operated by the NOAA National Centers for Environmental Prediction, assimilates observed surface and subsurface temperatures. From Behringer, Ji, and Leetmaa (1998).

Ocean’s response to changing windsOcean’s response to changing winds external (or surface)wavesexternal (or surface)waves

0t

Sea surface

pycnocline

Cp

Barotropic Wave

Cp

Sea Surface

pycnocline

3103

disp. interface Disp. Surface

Baroclinic Wave

Coastal Kelvin waves get trapped against Coastal Kelvin waves get trapped against horizontal boundaryhorizontal boundary

Side View

Lo

Hi

pgf Cf

pgf is balanced by Cf

Hi

Hi

Lo

divergence

convergence

p increasing

p increasing

p decreasing

C

v=0

Top View

Wave Phase Speed:Wave Phase Speed: eHgC

for baroclinic waves

~0.5 to 3 m/s for barotropc (external) waves

L: measure of how far a water parcel can travel L: measure of how far a water parcel can travel before it is affected by Coriolis:before it is affected by Coriolis:f is smallest near the equator and largest near the poles, L increases toward the equator, coastal waves are not trapped at the equator

2

equator) from(away

on Deformatiof iusRossby Rad

cL

f

cL

e

Equatorial Kelvin WavesEquatorial Kelvin Waves Equator acts like a coast, with water Equator acts like a coast, with water

on either sideon either side

Lo LoHi

pgf pgf pgf

pgfpgfpgf

C

Divergence Convergence

Equator

Equatorial Kelvin Waves move only to the East

Le ~250 km, C~3 m/s

Figure 14.10 in Stewart. Left: Horizontal currents associated with equatorially trapped waves generated by a bell-shaped displacement of the thermocline. Right: Displacement of the thermocline due to the waves. The figures show that after 20 days, the initial disturbance has separated into an westward propagating Rossby wave (left) and an eastward propagating Kelvin wave (right). From Philander et al. (1984).

Figure 14.4 in Stewart. Cross section of the Equatorial Undercurrent in the Pacific calculated from Modular Ocean Model with assimilated surface data (See §14.5). The section an average from 160°E to 170°E from January 1965 to December 1999. Stippled areas are westward flowing. From Nevin S. Fuckar.

El NiñoEl Niño

τ(x) τ(x)

80 m

300-400 m

Eq. under current

pycnocline

surfacez=0

180°

Winds relax – pycnocline flattens out

equator

Kelvin wave propagates eastward, depressing the pycnocline as it goes

pyc. depressed

upwelling shuts off

pyc. uplifted

2-3 months – hits the coast of South America, part of it reflects as a RossbyWave, part moves poleward as a coastal Kelvin wave

Rossby Wave

Rossby Wave

California CurrentCKW

Humbolt Current

Coastal Kelvin Waves (CKW) go all the way to Canada and Chile, altering Eastern Boundary Currents and shutting down upwelling

Figure 14.14 in Stewart. Tropical Atmosphere Ocean tao array of moored buoys operated by the NOAA Pacific Marine Environmental Laboratory with help from Japan, Korea, Taiwan, and France. Figure from NOAA Pacific Marine Environmental Laboratory.

Figure 14.6 in Stewart. Correlation coefficient of annual-mean sea-level pressure with pressure at Darwin. ---- Coefficient < - 0.4. From Trenberth and Shea (1987).

Figure 14.7 in Stewart. Normalized Southern Oscillation Index from 1951 to 1999. The normalized index is sea-level pressure anomaly at Tahiti divided by its standard deviation minus sea-level pressure anomaly at Darwin divided by its standard deviation then the difference is divided by the standard deviation of the difference. The means are calculated from 1951 to 1980. Monthly values of the index have been smoothed with a 5-month running mean. Strong El Niño events occurred in 1957–58, 1965–66, 1972–73, 1982–83, 1997–98. Data from NOAA.

Figure 14.8 in Stewart. Anomalies of sea-surface temperature (in °C) during a typical El Niño obtained by averaging data from El Niños between 1950 and 1973. Months are after the onset of the event. From Rasmusson and Carpenter (1982).

Figure 14.11 in Stewart. Sketch of regions receiving enhanced rain (dashed lines) or drought (solid lines) during an El Niño event. (0) indicates that rain changed during the year in which El Niño began, (+) indicates that rain changed during the year after El Niño began. From Ropelewski and Halpert (1987).

Figure 14.12 in Stewart. Changing patterns of convection in the equatorial Pacific during an El Niño, set up a pattern of pressure anomalies in the atmosphere (solid lines) which influence the extratropical atmosphere. From Rasmusson and Wallace (1983).

Figure 14.13 in Stewart. Correlation of yearly averaged rainfall averaged over all Texas each year plotted as a function of the Southern Oscillation Index averaged for the year. From Stewart (1994).