Internal waves and tides in SWOT data: incoherence and disentanglement from mesoscale/submesoscale signatures

Aurélien PONTE, Michael Dunphy, Patrice Klein LOPS, Ifremer, Brest

MOTIVATION • Internal waves and tides appear to have a more significant signatures on sea level at the length

scales newly resolved by SWOT (15-100 km) than at larger ones (see SWOT SDT white papers, Richman et al. 2012)

• These contributions will affect estimates of the ocean circulation from the data. The figure below illustrates what may happen when an internal tide “contaminates a observations of sea level” when surface currents are estimates from sea level according to geostrophy:

• We thus need to develop methods to mitigate these issues !!!!

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SCIENTIFIC OBJECTIVES !This project goes in two directions of research simultaneously which can be summarized by the following questions: 1. How do internal waves propagate in turbulent eddy fields? 2. How do internal tides become incoherent and how does the incoherence level depends on the

mesoscale/submesoscale flow characteristics? 3. What dynamical model and how much information about mesoscale/submesoscale flows are

required in order to predict the evolution of internal tides? 1. Can we devise methods that disentangles the signatures of internal waves from that of

mesoscale/submesoscale flows? !This work focus more particularly on internal waves with a slowly varying vertical structure (low-modes) whose signature on altimetric data is visible and most significant (Ray and Zaron 2011)

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METHOD !We set up idealized numerical simulations where a plane-wave semi-diurnal low-mode internal tide impinges on a patch of mesoscale/submesoscale turbulence. The turbulence is generated from the destabilization of a baroclinically unstable jet. The numerical model is ROMS, the numerical domain is a zonally periodical channel of dimension 1000 km x 3000 km with a depth of 4 km. The horizontal resolution is 4 km or 2 km depending on each particular studies. There is only 1 active tracer. Time filtering separates fluctuations associated with the slower mesoscale/submesoscale turbulence (1d average) from that associated with the internal wave (harmonic fit on a 1 day window).

INCOHERENCE (COMPLETED) • This study investigated the sensitivity of internal wave/tide incoherence to the strength of the mesoscale/submesoscale

turbulence in a series of idealized numerical simulations. The strength of the turbulence is controlled by the North/South difference of initial density profiles. We found that:

• Incoherence emerges as the strength of the turbulence is strengthened. • In strongly turbulent situations, the internal tide signature on sea level forms complex interference patterns with large amplifications

of the initial internal wave. These patterns evolve more rapidly than the signature of the turbulent eddy field on sea level and with with decorrelation time scales down to several days in strongly turbulent situations.

LOW MODE INTERNAL WAVE DYNAMICS IN AN EDDYING FIELD (SUBMITTED) In order to understand what dynamics controls the propagation of a low-mode internal wave within a turbulent eddy field we project equations of motions onto vertical modes. Coupling terms between the slower mesoscale flow (denoted with overbars in the equations below) and the internal wave flow (denoted with hats) represent the effect of mesoscales on the internal wave propagation. These coupling terms involve potentially other vertical modes. We studied the nature of the coupling terms and their sensitivities to one’s knowledge of mesoscale fields (horizontal, vertical, temporal resolutions).

INTERNAL WAVE - MESOSCALE/SUBMESOSCALE SEPARATION VIA SSH - SST SYNERGY (ONGOING) In this work, we attempt to develop a method that blends simultaneous snapshots of sea surface height and sea surface density (maybe obtained from a satellite observation of temperature in practice) The internal wave has a weak signature on sea surface temperature and correlates with interior potential vorticity anomalies. Sea surface density may thus be used in order to estimate the balanced contribution to sea level following approaches described in Lapeyre and Klein 2016. Results show that we are able to identify the internal wave contributions to sea level away from the meandering jet but, nearby the jet, the method is not accurate enough.

FUTURE WORK • Regarding our efforts in order to better understand low-mode internal wave propagation within a turbulent mesoscale eddy field, we are planning on building upon present results in order to predict the

evolution of internal waves with a simplified model of propagation. • The inclusion of bathymetry will then be considered. • Regarding our efforts in order to develop method to, we need to find a way to better estimate/constrain interior potential vorticity anomalies from synthetic observations. Considering data at multiple

times or other type of satellite information (salinity, color) will be considered !REFERENCES

• M. Dunphy, A. L. Ponte, P. Klein, and S. Le Gentil. Low-mode internal propagation in a turbulent eddy field. J. Phys. Oceanogr., submitted. • G. Lapeyre and P. Klein. Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory. J. Phys. Oceanogr., 36:165–176, 2006. • A. L. Ponte and P. Klein. Incoherent signature of internal tides on sea level in idealized numerical simulations. Geophys. Res. Lett., 42, 2015. • A. L. Ponte, P. Klein, Michael Dunphy, and S. Le Gentil. Low-mode internal tides and balanced dynamics disentanglement in altimetric ob- servations. J. Phys. Oceanogr., to be submitted (soon). • R. D. Ray and E. D. Zaron. Non-stationary internal tides observed with satellite altimetry. Geophys. Res. Lett., 38:L17609, 2011. • J. G. Richman, B. K. Arbic, J. F. Shriver, and E. Joseph Metzger. Inferring dynamics from the wavenumber spectra of an eddying global ocean model with embedded tides. J. Geophys. Res., 117(C12012),

2012. doi: 10.1029/2012JC008364.

From left to right: instantaneous values of the zonal flow, geostrophic flow obtained from the instantaneous sea level, difference between the actual zonal flow and the geostrophic estimate.

Results from idealized numerical simulations described in the METHOD section.

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Overview of the idealized numerical simulations: on the left, 1d averaged surface relative vorticity illustrates the developed mesoscale/submesoscale turbulence; on the right, harmonic sea level illustrates the effect of the

eddy field on the internal wave propagation. Distortions of the incoming wave from zonal uniformity evolve in time which embodies the internal wave incoherence.

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Time mean (solid black line) and standard deviation (gray shading) of the harmonic value of sea level along a meridional section going through the center of the domain for simulations with four different levels of mesoscale/submesoscale intensity

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Left column: results with an intermediate strength of mesoscale/submesoscale turbulence. Right column: results with a very strongly turbulent mesoscale/submesoscale turbulence. Top: 1d averaged sea level. Bottom: internal wave sea level fluctuations. Variables are shown as a function of time (x axis) and meridional direction (y axis). You can notice both the initial northward propagation of the internal wave (20 days) and the destabilization of the initial jet with the emergence of incoherence (quantified by time variations of the harmonic sea level)

v momentum (left) and pressure (right) coupling terms in corresponding evolutions equations of motions. Values are nondimensionalized by the averaged amplitude of v momentum and pressure time rate of change respectively. The discontinuity for the pressure coupling is due to a decomposition of diagnostics in three domains (with different stratifications and hence modal structures) and illustrates the importance of horizontal changes of stratification for prediction the internal wave propagation and evolution.

Skill in estimating the coupling terms when the horizontal resolution (top) and the temporal resolution (bottom) of the

mesoscale background field are degraded. Different colors represent different parts of the coupling

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From left to right: 1/surface density anomalies induced by the low-mode internal wave (from an harmonic fit) 2/instantaneous surface density 3/quasi-geostrophic potential vorticity at 500m depth 4/quasi-geostrophic potential vorticity at 1000m depth 5/ instantaneous sea level 6/ 1d averaged sea level 7/ internal tide sea level (from harmonic fit) 8/ sea level estimated from instantaneous surface density 9/ difference between 1d

averaged sea level and sea level from surface density 10/ difference between instantaneous sea level and its estimates from surface density.

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