WISE 2008 Meeting – Helsinki, Finland 3 June 2008

Swell dissipation across ocean basinsFabrice Ardhuin, Bertrand Chapron and Fabrice Collard

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1. Motivations: old observation and « state of the art models »

2. ENVISAT ASAR wave mode data: the ultimate swell-measuring machine

3. Data mining and dissipation estimates

4. From observations to understanding5. … and on to wave modelling.

6. What next? a community effort to improve and validate

models

Outline

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1. Motivations: old observation and « state of the art models »

As early as the 1930sAs early as the 1930s, observations off Morocco suggested that swell , observations off Morocco suggested that swell dissipation is significant. Sverdrup and Munk (1947) proposed a Jeffreys-dissipation is significant. Sverdrup and Munk (1947) proposed a Jeffreys-type parameterization.type parameterization.

1963 “Swell across the Pacific” experiment -> waves with periods 1963 “Swell across the Pacific” experiment -> waves with periods 13 13 s are dissipated at a rate of 0.1 dB/degree (±0.05), i.e. s are dissipated at a rate of 0.1 dB/degree (±0.05), i.e. =dE/dT/E =dE/dT/E =2x10=2x10-7 -7 ss-1-1. . increases with swell amplitude increases with swell amplitude? ?

(Darbyshire 1958, Snodgrass et al. 1966).(Darbyshire 1958, Snodgrass et al. 1966).

Today, only NCEP and FNMOC produce global wave forecasts that Today, only NCEP and FNMOC produce global wave forecasts that include specific swell dissipation processes (Tolman and Chalikov 1996, include specific swell dissipation processes (Tolman and Chalikov 1996, Tolman 2002).Tolman 2002).Others implicitly expect Komen et al. (1984) to do the job … Others implicitly expect Komen et al. (1984) to do the job … NOBODY has a clear idea of how much swell dissipation there really is … NOBODY has a clear idea of how much swell dissipation there really is … -> -> models are hard to tune models are hard to tune !!-> in order to -> in order to dissipate swelldissipate swell properly… you also have to properly… you also have to generategenerate it it properly ...properly ...

-> WE NEED DATA-> WE NEED DATA

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2. The data: ENVISAT ASAR wave mode level 2

Level 2 processing uses no model first guess, is based on multi-look co-spectra (Engen & Johnsen 1995), and provides unambiguous and accurate estimations of swell fields height, period and direction, for 2 <U10< 15 m/s and Tp > 11 s.

Important: real-time level2 products were rather bad until November 2007. We thus use reprocessed data.

<- Validation: Collard et al. (OceanSAR 2006)

Further validation with > 1000 data points: Ardhuin, Chapron & Collard (submitted to Nature Geosci.)

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2. The data: ENVISAT ASAR wave mode level 2

Wave mode data are small 10 by 20 km imagettes acquired every 100 km along the orbit. This sparse sampling is ideally suited to measure large-scale swell fields

ENVISAT ASARENVISAT RA2

JASON

The « Snodgrass et al. » track …Poor sampling of SAR,

lots of islands !!

Good track: good sampling, no islands

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3. Swell dissipation: no dissipation ?

Without dissipation the far field energy decreases like like

1/ sin Where =X/R. This is generally well reproduced with accurate numerical schemes.

gains or losses of swell energy are thus given by the deviation from this asymptote. This analysis is thus limited to far-fields. In practice we worked with X > 4000 km.

Propagation test: Gaussian storm on the Equator (red)Propagation in WW3 for 11 days with PR1(-.-) or PR3 (--) And comparison to ray-tracing (-)

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3. Swell dissipation: the numbers

Tp (

s)

Distance along great circle (x1000 km)

Lp (

m)

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3. Swell dissipation: the numbers

Spatial decay: -4 < <37 x 10-8 m-1

(e-folding scale: 3,000 to >30,000 km)

Time decay: -0.4 < < 4 x 10-6 s-1

-> Increase with swell steepness-> Threshold not a function

of wave period ?

Increase with wind speed ?

Tp (

s)

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4. From observations to understandingSwell dissipation theories: - ocean turbulence : linear, too weak (Ardhuin and Jenkins 2006) - pressure-slope correlations: linear, crazy numbers (Kudryavtsev & Makin 2004), or too large (Janssen in WISE paper)-air-sea friction:

- viscous theory by Dore (1978):

- turbulent extension (Ardhuin and Collard, work in progress)

Smooth oscillatory boundary layer is turbulent for Re = aorb uorb/ > 2x105

(Jensen et al. JFM 1989)

Significant swell values of aorb and uorbgive a swell Reynolds number Res

from the SAR data

Res = 4 aorb,s uorb,s/ or a total windsea+swell number Re = 4 aorb uorb/

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4. From observations to understanding

- No small decay for Res > 2x105

Decay against swell Reynolds number Res

From Res to Re : using a wave model?(OK on average, but largest swells appear underestimated at the source)

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5. … and on to modelling

Smooth boundary layer data of Jensen et al. (1989)

Re for PM spectrum U10=6 m/s

fw=0.004

Smooth or rough …? If rough …how much roughness ?

Error due to understimation of uorb?

x105

X10-7

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WW3 wind input in ST3 – v 3.13-SHOM

if Re < 100000

Otherwise (in TEST350) in TEST332: max of the 2

In TEST350: In TEST332: 0.5 0.015 0.018

fe,GM is given by Grant and Madsen’s (1979) boundary layer theory …And we take a roughness of 0.04 z0

(because most of the surface roughness for the wind is due to pressure-slope correlations and not skin friction)

Warning: TEST350 is not fully tuned !

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6. What next? a community effort to improve and validate

a new source term balance

How? Multi-scale ,multi-code (WW3, SWAN, WAM ..), all weather validation, for wave forecasting and other purposes (remote sensing, microseisms …)Testing of all proposed and reasonable parameterizations

First step: with the DIA- Global/regional scale wave forecasting

-> better results than Bidlot et al. (2005), see next talk- Coastal scales -> work in progress (A. van der Westhuysen, A. Roland …)- Hurricanes - high frequency tail

-> validation with buoy and satellite mean square slopes (mss)-> work in progress (M. Hamon)

… Second step: with « exact »-NL: already feasible for global 1° grid. Filtering ?

Join in and let’s get organized!

+ …

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WW3 breaking dissipation in ST3 – v 3.13-SHOM

Definition of a non-isotropic dissipation function :

with Br=1.2x 10-3 , =70°, and δ=0.25.

-> better fit to fetch-limited mean directions and directional spreads

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Coastal validation (work in progress)

Hindcasts of SHOWEX, lake George, EPEL2003, NCEX2003, GM2007 …other data sets ?

Example: use of SHOWEX data to refine the

anisotropy of Sds

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WW3 wind input in ST3 – v 3.13-SHOM

In TEST350: max = 1.75 and z = 0.005In TEST332: max = 1.7 and z = 0.005In WAM: max = 1.2 and z = 0.011

And the wind stress is reduced at high frequency (possibly too much with su=1):

'

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High frequency tail (work by M. Hamon)

m. s. s. decrease with wave height!

Effect of u*’ ? Comparisons of pseudo-mss: ∫E(f) (2πf)4/g2 df , 0 to 0.5 Hz

buoy and altimeter data:m.s.s. = function of U10 and swell or wave development, represented by

the surrogate variable Hs(e.g. Vandemark et al. 2004).

This is well reproduced with saturation-based dissipation.

… However, in WAM4-type dissipations

<k> decreases with swell… partially

compensated by Etot in

-> (k/<k>)2 increases -> more h.f. dissipation

-> k/<k> decreases -> less peak dissipation

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Better offshore -> better coastal …?Evaluation of A. Roland’s N, PSI and FCT schemes in WW3 – 3.14a-SHOMModule by A. Roland integrated by F. Birrien)

12000 nodes (bad) grid of thearea around Brest (France) Coastal Hs sensitive to offshore directional

spectrum (same problem in NCEX dataset)

PSIscheme

Nscheme

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Conclusions

-> From « state of the knowledge » to « state of the art »

-> first truly spectral dissipation term (no predefined shape or tail)

-> adding physics improves model results (answer to last year’s question)-> swell dissipation is non-linear

our SAR and 4 year global hindcast available at ftp.ifremer.fr/

ifremer/cersat/products/gridded/wavewatch3/HINDCAST/-> swell dissipation is important

(> 40% Hs bias without it at Hawaii, California …)

- The Komen et al. (1984) dissipation has provided great service. It can now be retired from active duty.

- Lots of work to do: open wave database (like biologists do with DNA sequences), validation in wide variety of conditions (not just global scale) … who wants to do what?

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3. Data mining … can we get enough?

Top: Energy and mean directions at Xmas Island buoy (51028)

Bottom: Directions of swell peaks at a « virtual SAR buoy » centered on Xmas Island

If needed, SAR data can be propagated to increase coverage… this is Dr. Fab’s swell

http://cersat.ifremer.fr/data/view/movies/swell_animation_from_envisat_asar_instrument/pacific_ocean

http://cersat.ifremer.fr/data/view/movies/swell_animation_from_envisat_asar_instrument/atlantic_ocean

http://cersat.ifremer.fr/data/view/movies/swell_animation_from_envisat_asar_instrument/indian_ocean

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Comparison BAJ-TEST350: Hs bias BAJ

TEST350

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Description of the WW3 experiments

Code version: 3.13-SHOM as of May 15 2008 (changes, including A. Roland’s module, ported into 3.14a to make a

3.14a-SHOM)

Implementation: 0.5° global grid using NCEP’s bathy and island filterTime steps: DTG=3600 s, DTXY=480 s, DT=1200 s, DTMIN=120 sSpectral grid: fmin=0.0373 Hz, NK=32, NTH=24, XFR=1.1Advection: « PR3 » (UQ with GSE correction) except for BAJ-PR1Source term integration: fully implicit with Tolman’s WW2 limiter. 4 experiments (all using the ST3 switch): « BAJ » (ECMWF physics with BETAMAX=1.25)TEST332 (saturation + swell dissipation without Reynolds threshold)TEST350 (saturation + swell dissipation with Reynolds threshold)BAJ-PR1 (same as BAJ but with PR1 propagation)

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BAJ

TEST350

Comparison BAJ-TEST350: NRMSE