Measuring the Properties of Rossby Waves from Space

Peter Challenor, Paolo Cipollini

& the Laboratory for Satellite Oceanography

Southampton Oceanography Centre, U.K.

Outline

• Observations of planetary waves with satellite altimetry– Speed estimation techniques– Observed propagation speed vs theoretical speed

• Observations of planetary waves in other datasets– SST– Ocean Colour

• Possible mechanisms

• Looking for the single wave events

Some relevant properties of Planetary waves

• Amplitude of surface manifestation: 1-20cm• Propagation speeds: a few cm s-1

– They take months or years to cross the oceans– Speeds depends on latitude: faster for waves

closer to the equator – Speed is an important issue as it sets the

‘response time’ of the oceans to perturbations and climatic anomalies

Sea surface height anomaly from Topex/Poseidon altimeter; 10 day cycles

North Atlantic, 34°N

“Classic” techniques to study RWs

• Fourier Transform of longitude/time plots (Tokmakian and Challenor, 1993)– Peaks correspond to single sinusoidal

components of the propagating signal

• Radon Transform (2D-RT): projected sum of the diagram at an angle theta (Chelton and Schlax, 1996)– Then we look for the value of thetawhich

maximises the energy of the RT - good objective estimate of propagation speed.

Schematic of the 2-D Radon Transform

Global speed results by Fu and Chelton (2001)after Chelton & Schlax (1996)

Ratio to standard theory

Ratio to extended theory

Going 3-D…..

• We want to detect and study the possible deviations of RW propagation from pure Westward

• Need to add a N-S dimension (latitude)• The dataset is then a full 3-D cuboid (long x lat x

time)• We have developed a 3-D extension of the Radon

Transform (3D-RT) and implemented it with MATLAB and FORTRAN

The 3-D cuboid of data

The 3-D Radon TransformChallenor et al., JAOT, 2001

Example of 3D-RT analysis

Rossby waves in other datasets

• SST (both IR and microwave)– A signature could be expected as SST and SSH

have some degree of correlation

• Ocean colour ??

Rossby waves detected in the SST anomaly field

Ref: Hill et al, JGR, 2000

Speeds fromT/P SSH

Speeds fromATSR SST

Ref: Hill et al, JGR, 2000

Ratio to standard theory

Ratio to extended theory

Why do we see Rossby waves in Ocean colour?

Two main hypotheses:

1. Horizontal displacement

2. Vertical processes

Note: phase difference between SSH and OC will depend on the time the tracer (chl) anomaly takes to go back to equilibrium (relaxation time)

This can be modelled (Killworth & Blundell)….

Observed Chl v SSHphase

Pure H advection Chl v SSHphase

= 60 d

MODEL

DATA

1st conclusion: horizontal advection is important

• But does it explain all the signal we see in the colour field?– Need to focus on those regions where

observations and predictions do not match well..

– …and on those regions where the meridional gradient of chl is weak

Possible vertical mechanisms• Real pumping effect (vertical advection of nutrients into

the euphotic zone! ) - ‘rototiller effect’– This can be modelled and computed but it is

currently a puzzle - modelled signal is small but at the equator and phase does not seem to match the observations

– However modelling of this effect suffers from very poor nutrients climatology!

• Vertical advection of phytoplankton• Shoaling of DCM and its ‘erosion’ into the mixed layer

(suggested by Kawamiya and Oschlies, 2001)

Need further investigations…..• … vertical mechanisms could still be playing a

significant role in some places - and they would

phase-shift the SSH/SST/OC relationship

• They would also be very important for the biology

• Let’s see an example in the Indian Ocean…

A different methodological approach…..

• Techniques like FFTs, RTs and Crosscorrelations on

satellite data have yielded ‘mean’ properties.

• We want to look at the single wave events. Identify

them and study how their characteristics change as

they propagate across the ocean basins

• This can be done with a model-fitting approach -

Gaussian ‘crests’ and ‘troughs’

Four parameters each:• Amplitude• horizontal scale• Slope of track• intercept of track

Gaussian model fitting

• First of all, we split the longitude/time plots into ‘narrow’ partially overlapping sub-windows

Gaussian model fitting

• First of all, we split the longitude/time plots into ‘narrow’ partially overlapping sub-windows

Results: a table of wave parameters for each sub-windowResults: a table of wave parameters for each sub-window

In any sub-window, we fit and remove the In any sub-window, we fit and remove the strongest Gaussian, then we fit and remove the strongest Gaussian, then we fit and remove the next strongest, etc.next strongest, etc.

Finally, we “compact” the results, reconstructing Finally, we “compact” the results, reconstructing the trajectories of the single events.the trajectories of the single events.

Some pre-processing

• filter out annual cycle and any non-Westward signals

• taper both the longitude/time plot and the fitting function with a Hanning window in longitude– increases ‘localization’ of information– improves amplitude retrieval

QuickTime™ and aGIF decompressorare needed to see this picture.

+ 0.2 m

0

- 0.2m

Original sub-window

Fitted elementarywaves Residuals

34NOriginal data (filtered + tapered)

Fitted elementary waves

Joining waveslabel all waves in Emost

sub-window as ‘new’

Move 1 subw to the W

min(fc)< ?

couple (wave, wave to the E) compute COSTFUNCTION (fc)

(it’s a matrix whose elements depend on squared errors on amp., slope, intercept, width)

- Join the two waves- write off row and column in fc

yes

label all remaining waves as ‘new’ no

Move 1 subw to the Wetc…

34N

waveNA34_0097

MARThe story of a single wave…

Planetary wave forecast strategy

• Find ‘most similar wave’ (to the one to be propagated) in parameter space

• Propagate wave in accordance to behaviour of ‘most similar wave’

Example of hindcast

Std deviation of reference data

RMS error with simple ‘persistence’ of wave properties

RMSE - hindcast 2

RMSE - hindcast 1

Next….• increase number of parameters in the model• more comparisons with theory and other PW

estimating techniques• global ocean; look at interannual variability• extend to 3-D• Build forecast based on statistical distributions of

parameters in parameters’ space • Invert to get information on the ‘state’ of the

ocean