1. WISE 2008 Meeting – Helsinki, Finland3 June 2008 Swell dissipation across ocean basins Fabrice Ardhuin, Bertrand Chapron and Fabrice Collard

2. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.2 / 19 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 understanding 5. … and on to wave modelling. 6. What next? a community effort to improve and validate models Outline

3. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.3 / 19 1. Motivations: old observation and « state of the art models » As early as the 1930s, observations off Morocco suggested that swell dissipation is significant. Sverdrup and Munk (1947) proposed a Jeffreys-type parameterization. 1963 “Swell across the Pacific” experiment -> waves with periods  13 s are dissipated at a rate of 0.1 dB/degree (±0.05), i.e.  =dE/dT/E =2x10 -7 s -1.  increases with swell amplitude? (Darbyshire 1958, Snodgrass et al. 1966). Today, only NCEP and FNMOC produce global wave forecasts that include specific swell dissipation processes (Tolman and Chalikov 1996, Tolman 2002). Others implicitly expect Komen et al. (1984) to do the job … NOBODY has a clear idea of how much swell dissipation there really is … -> models are hard to tune ! -> in order to dissipate swell properly… you also have to generate it properly... -> WE NEED DATA

4. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.4 / 19 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 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.)

5. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.5 / 19 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 ASAR ENVISAT RA2 JASON The « Snodgrass et al. » track … Poor sampling of SAR, lots of islands !! Good track: good sampling, no islands

6. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.6 / 19 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 (-)

7. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.7 / 19 3. Swell dissipation: the numbers Tp (s) Distance along great circle (x1000 km) Lp (m)

8. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.8 / 19 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)

9. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.9 / 19 4. From observations to understanding Swell 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 = a orb u orb / > 2x10 5 (Jensen et al. JFM 1989) Significant swell values of a orb and u orb give a swell Reynolds number Re s from the SAR data Re s = 4 a orb,s u orb,s / or a total windsea+swell number Re = 4 a orb u orb /

10. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.10 / 19 4. From observations to understanding - No small decay for Re s > 2x10 5 Decay against swell Reynolds number Re s From Re s to Re : using a wave model? (OK on average, but largest swells appear underestimated at the source)

11. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.11 / 19 5. … and on to modelling Smooth boundary layer data of Jensen et al. (1989) Re for PM spectrum U 10 =6 m/s f w =0.004 Smooth or rough …? If rough …how much roughness ?  Error due to understimation of u orb ? x10 5 X10 -7

12. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.12 / 19 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 f e,GM is given by Grant and Madsen’s (1979) boundary layer theory … And we take a roughness of 0.04 z 0 (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 !

13. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.13 / 19 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! + …

14. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.14 / 19 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

15. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.15 / 19 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 

16. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.16 / 19 WW3 wind input in ST3 – v 3.13-SHOM In TEST350:  max = 1.75 and z  = 0.005 In TEST332:  max = 1.7 and z  = 0.005 In WAM:  max = 1.2 and z  = 0.011 And the wind stress is reduced at high frequency (possibly too much with s u =1): '

17. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.17 / 19 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 /g 2 df, 0 to 0.5 Hz buoy and altimeter data: m.s.s. = function of U 10 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 decreases with swell… partially compensated by E tot in -> (k/ ) 2 increases -> more h.f. dissipation -> k/ decreases -> less peak dissipation

18. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.18 / 19 Better offshore -> better coastal …? Evaluation of A. Roland’s N, PSI and FCT schemes in WW3 – 3.14a-SHOM Module by A. Roland integrated by F. Birrien) 12000 nodes (bad) grid of the area around Brest (France) Coastal Hs sensitive to offshore directional spectrum (same problem in NCEX dataset) PSI scheme N scheme

19. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.19 / 19 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?

20. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.20 / 19 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

21. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.21 / 19 Comparison BAJ-TEST350: Hs bias BAJ TEST350

22. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.22 / 19 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 filter Time steps: DTG=3600 s, DTXY=480 s, DT  =1200 s, DTMIN=120 s Spectral grid: fmin=0.0373 Hz, NK=32, NTH=24, XFR=1.1 Advection: « PR3 » (UQ with GSE correction) except for BAJ-PR1 Source 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)

23. WISE 2008 – Helsinki, FinlandF. Ardhuin et al.23 / 19 BAJ TEST350 Comparison BAJ-TEST350: NRMSE