The internal gravity wave spectrum: A new frontier in global ocean modeling

Brian K. Arbic

Department of Earth and Environmental Sciences University of Michigan

Supported by funding from: Office of Naval Research (ONR) National Aeronautics and Space Administration (NASA) National Science Foundation (NSF)

Brian K. Arbic Internal wave spectrum in global ocean models Collaborators

• Naval Research Laboratory Stennis Space Center: Joe Metzger, Jim Richman, Jay Shriver, Alan Wallcraft, Luis Zamudio • University of Southern Mississippi: Maarten Buijsman • University of Michigan: Joseph Ansong, Steve Bassette, Conrad Luecke, Anna Savage • McGill University: David Trossman • Bangor University: Patrick Timko • Norwegian Meteorological Institute: Malte M¨uller • University of Brest and The University of Texas at Austin: Rob Scott • NASA Goddard: Richard Ray • Florida State University: Eric Chassignet • Others including many members of the NSF-funded Climate Process Team led by Jennifer MacKinnon of Scripps

Brian K. Arbic Internal wave spectrum in global ocean models Motivation

• Breaking internal gravity waves drive most of the mixing in the subsurface ocean. • The internal gravity wave spectrum is just starting to be resolved in global ocean models. • Somewhat analogous to resolution of mesoscale eddies in basin- and global-scale models in 1990s and early 2000s. • Builds on global internal tide modeling, which began with 2004 Arbic et al. and Simmons et al. papers utilizing Hallberg Isopycnal Model (HIM) run with tidal foricng only and employing a horizontally uniform stratification.

Brian K. Arbic Internal wave spectrum in global ocean models Motivation continued...

• Here we utilize simulations of the HYbrid Coordinate Ocean Model (HYCOM) with both atmospheric and tidal forcing. • Near-inertial waves and tides are put into a model with a realistically varying background stratification. • Nonlinear interactions fill out the frequency-wavenumber spectrum. • Note other groups are following suit with tide+circulation models (Harper Simmons, personal communication; Dimitris Menemenlis, personal communication; M¨ulleret al. 2012). • Talk focuses on the development of an internal gravity wave spectrum, after briefly discussing our other results.

Brian K. Arbic Internal wave spectrum in global ocean models Implementaon of des in HYCOM

--Add astronomical dal potenal of largest semidiurnal and diurnal constuents (8 in run analyzed here, 5 in newest runs) --Add self-aracon and loading term (scalar approximaon in run analyzed here, almeter model in newest runs) --Apply parameterized topographic wave drag to dal part of flow in boom 500 meters HYCOM vs TPXO M2 barotropic tides (Shriver et al. 2012)

C10024 SHRIVER ET AL.: BAROTROPIC AND INTERNAL TIDES IN HYCOM C10024

Figure 2. Amplitude (cm) of M2 surface tidal elevation in (a) TPXO7.2 (an update to that described by Egbert et al. [1994]), a barotropic tide model constrained by satellite altimetry, and (b) HYCOM simula- tions in which the tide is unconstrained by satellite altimetry. Lines of constant phase plotted every 45 in Figures 2a and 2b are overlaid in white.

altimetry-constrained barotropic tide model [Egbert et al., and observed internal tides have utilized regional models of 1994] and the internal tides in HYCOM to results from an strong internal tide generation sites forced by specified bar- analysis of along-track satellite altimetry data [Ray and otropic tides at their horizontal boundaries [e.g., Cummins Mitchum, 1996]. Several previous comparisons of modeled et al., 2001; Kang et al., 2000; Merrifield et al., 2001].

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Brian K. Arbic Internal wave spectrum in global ocean models HYCOM vs along-track altimetric estimates of surface signature of M2 internal tides (Shriver et al. 2012)

• Computed from high-passing total M2 signal

60°N A. 40°N

20°N

0°

20°S

40°S

60°S 60°N B.

40°N

20°N

0°

20°S

40°S

60°S 0° 40°E 80°E 120°E 160°E 160°W 120°W 80°W 40°W 0° cm

Figure 7. The M2 internal tide amplitude from the (a) altimetric-based and (b) HYCOM tidal analyses. The five subregions denoted by black boxes in (b) are used to compute the area- averaged amplitudes in Table 2.

Brian K. Arbic Internal wave spectrum in global ocean models Now on to today’s main topic...internal gravity wave spectrum

Brian K. Arbic Internal wave spectrum in global ocean models Internal gravity wave kinetic energy frequency spectra (M¨ulleret al. in press GRL)

• Note logarithmic smoothing employed.

Brian K. Arbic Internal wave spectrum in global ocean models Internal gravity wave kinetic energy frequency-horizontal wavenumber spectra (M¨ulleret al. in press GRL)

Brian K. Arbic Internal wave spectrum in global ocean models Nonlinear internal gravity wave kinetic energy frequency-horizontal wavenumber spectral transfers (M¨ulleret al. in press GRL) ∗ • T (k, ω) = Re[−~ub · [~u\· ∇~u]]

Brian K. Arbic Internal wave spectrum in global ocean models Application of frequency-horizontal wavenumber spectrum to altimetry

• We will compute the frequency-horizontal wavenumber spectrum of SSH to separate low-frequency, internal tide, and non-tidal internal wave contributions.

Brian K. Arbic Internal wave spectrum in global ocean models Frequency spectra of temperature (Bassette et al. and Luecke et al. in preparation)

Temperature Power Spectrum: HYCOM and CMA Temperature Power Spectrum: HYCOM and CMA −1 0 10 10

−2 −1 10 10 CPD) CPD) / / 2 2 −3 −2 10 10 C C ◦ ◦ oe ( Power oe ( Power

−4 −3 10 10 Location Location Latitude: 53.14 Latitude: 46.59 Longitude: 189.71 Longitude: 151.63 Depth: 500.00 Depth: 269.96 −5 −4 10 10 −3 −2 −1 0 1 2 −3 −2 −1 0 1 2 10 10 10 10 10 10 10 10 10 10 10 10 Frequencies (CPD) Frequencies (CPD) CMA HYCOM (Exp 6.1) Diurnal Frequency Semi−diurnal Frequency Coriolis Frequency Temperature Power Spectrum: HYCOM and CMA Temperature Power Spectrum: HYCOM and CMA −1 0 10 10

−2 −1 10 10 CPD) CPD) / / 2 2 −3 −2 10 10 C C ◦ ◦ oe ( Power oe ( Power

−4 −3 10 10 Location Location Latitude: 38.96 Latitude: 38.99 Longitude: 207.97 Longitude: 175.01 Depth: 669.00 Depth: 648.00 −5 −4 10 10 −3 −2 −1 0 1 2 −3 −2 −1 0 1 2 10 10 10 10 10 10 10 10 10 10 10 10 Frequencies (CPD) Frequencies (CPD)

Brian K. Arbic Internal wave spectrum in global ocean models Summary

• Models with concurrent atmospheric and tidal forcing are beginning to develop an internal gravity wave spectrum, especially as resolution increases. • Frequency-horizontal wavenumber spectrum of modeled internal gravity wave kinetic energy fills in along predicted linear dispersion curves, and fills out more completely with higher model resolution. • Kinetic energy frequency spectra lie closer to observations, and nonlinear interactions are more vigorous, when model resolution is increased. • We are now investigating internal gravity wave temperature variance.

Brian K. Arbic Internal wave spectrum in global ocean models