Observation of swell dissipation across oceans

arXiv:0809.2497v4 [physics.ao-ph] 23 Feb 2009 GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1029/, Observation of swell dissipation across oceans Fabrice Ardhuin Service Hydrographique et Oc´eanographique de la Marine, Brest, France Bertrand Chapron Ifremer, Laboratoire d’Oc´eanographie Spatiale, Centre de Brest, Plouzan´e, France Fabrice Collard Collecte Localisation Satellites, division Radar, Plouzan´e, France Global observations of ocean swell, from satellite Syn- thetic Aperture Radar data, are used to estimate the dis- sipation of swell energy for a number of storms. Swells can be very persistent with energy e-folding scales exceed- ing 20,000 km. For increasing swell steepness this scale shrinks systematically, down to 2800 km for the steepest observed swells, revealing a significant loss of swell energy. This value corresponds to a normalized energy decay in time β = 4.2 × 10−6 s −1. Many processes may be responsible for this dissipation. The increase of dissipation rate in dis- sipation with swell steepness is interpreted as a laminar to turbulent transition of the boundary layer, with a thresh- old Reynolds number of the order of 100,000. These obser- vations of swell evolution open the way for more accurate wave forecasting models, and provides a constraint on swell- induced air-sea fluxes of momentum and energy. 1. Introduction Swells are surface waves that outrun their generating wind, and radiate across ocean basins. At distances of 2000 km and more from their source, these waves closely follow principles of geometrical optics, with a constant wave period along geodesics, when following a wave packet at the group speed [e.g. Snodgrass et al., 1966; Collard et al., 2009]. These geodesics are great circles along the Earth surface, with minor deviations due to ocean currents. Because swells are observed to propagate over long dis- tances, their energy should be conserved or weakly dissi- pated [Snodgrass et al., 1966], but little quantitative infor- mation is available on this topic. As a result, swell heights are relatively poorly predicted [e.g. Rogers, 2002; Rascle et al., 2008]. Numerical wave models that neither account specifically for swell dissipation, nor assimilate wave mea- surements, invariably overestimate significant wave heights (Hs) in the tropics. Typical biases in such models reach 45 cm or 25% of the mean observed wave height in the East Pacific [Rascle et al., 2008]. Further, modelled peak periods along the North American west coast exceed those measured by open ocean buoys, on average by 0.8 s [Rascle et al., 2008], indicating an excess of long period swell energy. Theories proposed so far for nonlinear wave evolution or air-sea in- teractions [e.g. Watson, 1986; Tolman and Chalikov, 1996], require order-of-magnitude empirical correction in order to produce realistic wave heights [e.g. Tolman, 2002]. Swell evolution over large scales is thus not understood. Copyright 2018 by the American Geophysical Union. 0094-8276/18/$5.00 Swells are also observed to modify air-sea interactions [Grachev and Fairall, 2001], and swell energy has been sug- gested as a possible source of ocean mixing [Babanin, 2006]. A quantitative knowledge of the swell energy budget is thus needed both for marine weather forecasting and Earth sys- tem modelling. The only experiment that followed swell evolution at oceanic scales was carried out in 1963. Using in situ mea- surements, a very uncertain but moderate dissipation of wave energy was found [Snodgrass et al., 1966]. The dif- ficulties of this type of analysis are twofold. First, very few storms produce swells that line up with any measurement array, and second, large errors are introduced by having to account for island sheltering. Qualitative investigations by Holt et al. [1998] and Heimbach and Hasselmann [2000] demonstrated that a space-borne synthetic aperture radar (SAR) could be used to track swells across the ocean, using the coherent persistence of swells along their propagation tracks. Building on these early studies, Collard et al. [2009] demonstrated that SAR-derived swell heights can provide estimates of the dissipation rate. Here we make a system- atic and quantitative analysis of four years of global SAR measurements, using level 2 wave spectra [Chapron et al., 2001] from the European Space Agency’s (ESA) ENVISAT satellite. The swell analysis method is briefly reviewed in section 2. The resulting estimates of swell dissipation rates are interpreted in section 3, and conclusions follow in section 4. 2. Swell tracking and dissipation estimates Our analysis uses a two step method. Firstly, using SAR- measured wave periods and directions at different times and locations, we follow great circle trajectories backwards at the theoretical group velocity. The location and date of a swell source is defined as the spatial and temporal center of the convergence area and time of the trajectories. We define the spherical distance α from this storm cent

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