Enhanced generation of internal tides under global warming

The study examines how global warming–induced changes in ocean stratification affect the conversion of barotropic tidal energy into internal (baroclinic) tides, a key driver of deep-ocean turbulent diapycnal mixing that influences the meridional overturning circulation (MOC) and global climate. Internal tide generation and its modal partition (low vs high vertical modes) control where and how mixing occurs: low modes can radiate far and affect background mixing, whereas high modes dissipate locally over rough topography, creating mixing hotspots. Many coupled global climate models (CGCMs) assume constant tidal conversion and modal partition over time, despite observed and projected strengthening of ocean stratification, especially in the upper ocean. Prior regional studies have reported both increases and decreases in tidal conversion with enhanced stratification, leaving the global response and modal dependence unresolved. The research question is how total tidal energy conversion and its modal partition respond globally to warming-driven changes in stratification. The study applies a linear internal tide generation model, driven by CMIP6 projections, to quantify these responses and their implications for deep-ocean mixing and climate.

Background work establishes that deep-ocean mixing is spatially heterogeneous and enhanced over rough topography, largely due to internal tide breaking. Global barotropic-to-baroclinic tidal energy conversion is about 1 TW, a substantial fraction of the power needed to sustain the MOC. Modal structure determines propagation and dissipation scales: low modes (1–3) propagate long distances with weak shear, while high modes (≥4) dissipate locally due to strong shear and slow group velocity. Many CGCMs parameterize tidal mixing with time-invariant conversion and partition. Warming is known to enhance upper-ocean stratification, with a common view that stronger stratification suppresses turbulence, but this perspective often overlooks how stratification modifies the generation of internal tides and their modal wavenumbers. Regional studies have shown both enhanced and reduced tidal energy conversion under increased stratification, but a consistent global-scale assessment of conversion magnitude and modal partition under climate change has been lacking.

The authors use a linear internal tide generation framework (Bell theory; St. Laurent & Garrett formulation) to estimate spectral density of tidal energy conversion in horizontal wavenumber space from barotropic tidal velocities (TPXO8), local stratification, Coriolis and tidal frequencies, and topographic spectrum (SRTM15+, 15-arc sec). They compute azimuthally averaged spectral density and project it onto vertical modes obtained by solving the Sturm–Liouville eigenvalue problem with boundary conditions at surface and bottom to determine modal eigenspeeds and horizontal wavenumbers. Energy conversion into mode n is calculated by integrating spectral density over a wavenumber band centered on the modal wavenumber. Calculations are restricted to depths >500 m where linear theory (subcritical topography) is applicable; for supercritical topography a correction divides conversion by γ². They compute conversion for M2, S2, and K1 constituents and scale to the eight principal constituents using published factors. Historical stratification (1995–2004) is from WOA18 on 0.25° grid; near-bottom buoyancy frequency Nb is averaged over 0–300 m above bottom; depth-averaged buoyancy frequency N is also computed. Future stratification changes (ΔN, ΔNb) are derived from 25 CMIP6 CGCMs under SSP585 (2091–2100 minus 1995–2004), drift-corrected using corresponding PI-control trends; Δ fields are added to observed climatology to minimize historical bias. Energy conversion is computed for modes 1–50 (bathymetry resolution limits higher modes). Sea floor roughness is defined as RMS topography over 0.5° cells after removing large-scale background by polynomial fit. To assess mixing implications, they parameterize local high-mode (modes 4–50) dissipation-driven diapycnal diffusivity κρ = (Γ E4–50 /(ρ0 N²)) F(z), with Γ=0.2 and vertical decay scale η=500 m, and analyze the vertical-mean of the bottom 1000 m. They also separate contributions of changes in near-bottom vs depth-averaged stratification by recomputing conversion with one held fixed at historical values.

• Stratification changes: CMIP6 ensemble projects a nearly global increase in depth-averaged stratification N by 10.2 ± 1.4% (2091–2100 vs 1995–2004). Near-bottom stratification Nb increases by 2.7 ± 0.5% on average, with spatial heterogeneity.
• Historical energy conversion: Globally integrated E1–50 = 864 GW; low-mode E1–3 = 568 GW; high-mode E4–50 = 296 GW. Conversion concentrates over rough topography (ridges, seamounts).
• Warming impact on total and modal conversion: Global E1–50 increases by 28 ± 3.5 GW. This rise is dominated by high modes: E4–50 increases by 23 ± 2.2 GW, about +7.8 ± 0.7% (8%). Low modes change little: E1–3 increases by 5 ± 1.3 GW (+0.9 ± 0.2%), with regional positive and negative patterns.
• Mechanisms via stratification components: • Increased near-bottom stratification elevates E1–50 by 16 ± 5.1 GW and increases both E1–3 and E4–50 by similar fractions (about +2.1 ± 0.5% vs +1.4 ± 0.7%), consistent with near-linear dependence on Nb. • Increased depth-averaged stratification elevates E1–50 by 12 ± 3.8 GW but redistributes energy across modes by reducing modal horizontal wavenumbers: it decreases globally integrated E1–3 by 6 ± 0.6 GW and increases E4–50 by 18 ± 3.9 GW.
• Spectral interpretation: Regions with monotonic decreasing topographic spectral density see reduced modal wavenumber increase both low- and high-mode conversion; regions with flatter spectra and peaks near modal wavenumbers experience increased high-mode but decreased low-mode conversion when modal wavenumber is reduced.
• Robustness: The high-mode increase and dominance in total conversion change are robust across time windows and also under a medium-emission scenario (≈+5% in E4–50 by century end).
• Mixing implications: Parameterized deep-ocean (bottom 1000 m) diapycnal diffusivity increases over most regions; globally averaged κρ rises by ~6% by 2091–2100, with local increases >20%, implying hotter mixing hotspots over rough topography.
• Potential climate impacts: Preliminary analyses suggest ~10% acceleration of the lower limb of the Atlantic MOC and ~10% increase in the peak of globally integrated diautral upwelling linked to enhanced high-mode conversion (subject to parameterization uncertainties).

The study demonstrates that global warming strengthens ocean stratification, especially in a depth-averaged sense, and this modifies internal tide generation in a mode-dependent way. Enhanced near-bottom stratification increases conversion across modes, while enhanced depth-averaged stratification lowers modal horizontal wavenumbers, shifting conversion toward higher modes and slightly away from low modes. As a result, high-mode (locally dissipative) internal tide energy conversion increases by about 8% by late century, whereas low-mode conversion remains nearly unchanged globally. These findings address the research question by revealing that warming does not simply suppress mixing through stronger stratification; instead, it can increase the local energy supply to turbulent mixing over rough topography via enhanced high-mode generation. The increased high-mode conversion leads to stronger parameterized deep-ocean mixing, particularly near generation sites, with likely ramifications for abyssal tracer transport, diautral upwelling, and the MOC (e.g., potential partial offset of an AMOC slowdown). The results emphasize the need to represent evolving stratification and its effects on internal tide generation and dissipation in climate models to improve projections.

The work provides a global, mode-resolved assessment of how warming-driven stratification changes affect internal tide generation. By coupling a linear internal tide generation model with CMIP6 projections, the authors find a robust late-21st-century increase (~8%) in high-mode tidal energy conversion, negligible net change in low modes, and a corresponding rise (~6% globally) in parameterized deep-ocean diffusivity, with pronounced local enhancements over rough topography. The distinct roles of near-bottom versus depth-averaged stratification explain the modal redistribution. These insights call for incorporating time-evolving stratification and mode-dependent tidal mixing parameterizations into CGCMs. Future work should: (a) implement interactive, stratification-aware tidal mixing schemes; (b) quantify feedbacks on circulation and tracers in fully coupled simulations; (c) refine representation over supercritical topography and in shallow regions; and (d) reduce uncertainties in mixing efficiency and dissipation pathways through observations and high-resolution modeling.

• Linear theory assumption: Valid primarily for subcritical topography; supercritical regions require an empirical γ² correction, introducing uncertainty.
• Depth exclusion: Calculations exclude waters shallower than 500 m, neglecting any downward radiation from shelf and slope generation (assumed small for deep-ocean budgets).
• Modal truncation: Only modes 1–50 are resolved due to bathymetric resolution limits; higher modes are neglected though expected to contribute little to global totals.
• Parameterization uncertainty: Diapycnal diffusivity estimates rely on assumed mixing efficiency (Γ=0.2) and prescribed vertical decay scale (η=500 m); results such as AMOC and diautral upwelling responses are preliminary and sensitive to these choices.
• Forcing and model biases: Future stratification changes are derived from CMIP6 SSP scenarios and rely on bias-corrected ensemble means; structural model uncertainties and scenario dependence remain.
• Modal separation diagnostics (e.g., N component notation) and regional spectral characteristics may introduce interpretation uncertainties in partitioning mechanisms.