Sea State Dependence of the Wind Stress Over the Ocean Under Hurricane Winds

The impact of the surface wave field (sea state) on the wind stress over the ocean is investigated with fetch-dependent seas under uniform wind and with complex seas under idealized tropical cyclone winds. Two different approaches are employed to calculate the wind stress and the mean wind profile. The near-peak frequency range of the surface wave field is simulated using the WAVEWATCH III model. The high-frequency part of the surface wave field is empirically determined using a range of different tail levels. The results suggest that the drag coefficient magnitude is very sensitive to the spectral tail level but is not as sensitive to the drag coefficient calculation methods. The drag coefficients at 40 m/s vary from to depending on the saturation level. The misalignment angle between the wind stress vector and the wind vector is sensitive to the stress calculation method used. In particular, if the cross-wind swell is allowed to contribute to the wind stress, it tends to increase the misalignment angle. Our results predict enhanced sea state dependence of the drag coefficient for a fast moving tropical cyclone than for a slow moving storm or for simple fetch-dependent seas. This may be attributed to swell that is significantly misaligned with local wind

Parameterizing Vertical Mixing Coefficients in the Ocean Surface Boundary Layer using Neural Networks

Vertical mixing parameterizations in ocean models are formulated on the basis of the physical principles that govern turbulent mixing. However, many parameterizations include ad hoc components that are not well constrained by theory or data. One such component is the eddy diffusivity model, where vertical turbulent fluxes of a quantity are parameterized from a variable eddy diffusion coefficient and the mean vertical gradient of the quantity. In this work, we improve a parameterization of vertical mixing in the ocean surface boundary layer by enhancing its eddy diffusivity model using data-driven methods, specifically neural networks. The neural networks are designed to take extrinsic and intrinsic forcing parameters as input to predict the eddy diffusivity profile and are trained using output data from a second moment closure turbulent mixing scheme. The modified vertical mixing scheme predicts the eddy diffusivity profile through online inference of neural networks and maintains the conservation principles of the standard ocean model equations, which is particularly important for its targeted use in climate simulations. We describe the development and stable implementation of neural networks in an ocean general circulation model and demonstrate that the enhanced scheme outperforms its predecessor by reducing biases in the mixed-layer depth and upper ocean stratification. Our results demonstrate the potential for data-driven physics-aware parameterizations to improve global climate models

Langmuir Turbulence Parameterization in Tropical Cyclone Conditions

The Stokes drift of surface waves significantly modifies the upper-ocean turbulence because of the Craik–Leibovich vortex force (Langmuir turbulence). Under tropical cyclones the contribution of the surface waves varies significantly depending on complex wind and wave conditions. Therefore, turbulence closure models used in ocean models need to explicitly include the sea state–dependent impacts of the Langmuir turbulence. In this study, the K-profile parameterization (KPP) first-moment turbulence closure model is modified to include the explicit Langmuir turbulence effect, and its performance is tested against equivalent large-eddy simulation (LES) experiments under tropical cyclone conditions. First, the KPP model is retuned to reproduce LES results without Langmuir turbulence to eliminate implicit Langmuir turbulence effects included in the standard KPP model. Next, the Lagrangian currents are used in place of the Eulerian currents in the KPP equations that calculate the bulk Richardson number and the vertical turbulent momentum flux. Finally, an enhancement to the turbulent mixing is introduced as a function of the nondimensional turbulent Langmuir number. The retuned KPP, with the Lagrangian currents replacing the Eulerian currents and the turbulent mixing enhanced, significantly improves prediction of upper-ocean temperature and currents compared to the standard (unmodified) KPP model under tropical cyclones and shows improvements over the standard KPP at constant moderate winds (10 m s−1)

Impact of Sea-State-Dependent Langmuir Turbulence on the Ocean Response to a Tropical Cyclone

Tropical cyclones are fueled by the air–sea heat flux, which is reduced when the ocean surface cools due to mixed layer deepening and upwelling. Wave-driven Langmuir turbulence can significantly modify these processes. This study investigates the impact of sea-state-dependent Langmuir turbulence on the three-dimensional ocean response to a tropical cyclone in coupled wave–ocean simulations. The Stokes drift is computed from the simulated wave spectrum using the WAVEWATCH III wave model and passed to the three-dimensional Princeton Ocean Model. The Langmuir turbulence impact is included in the vertical mixing of the ocean model by adding the Stokes drift to the shear of the vertical mean current and by including Langmuir turbulence enhancements to the K-profile parameterization (KPP) scheme. Results are assessed by comparing simulations with explicit (sea-state dependent) and implicit (independent of sea state) Langmuir turbulence parameterizations, as well as with turbulence driven by shear alone. The results demonstrate that the sea-state-dependent Langmuir turbulence parameterization significantly modifies the three-dimensional ocean response to a tropical cyclone. This is due to the reduction of upwelling and horizontal advection where the near-surface currents are reduced by Langmuir turbulence. The implicit scheme not only misses the impact of sea-state dependence on the surface cooling, but it also misrepresents the impact of the Langmuir turbulence on the Eulerian advection. This suggests that explicitly resolving the sea-state-dependent Langmuir turbulence will lead to increased accuracy in predicting the ocean response in coupled tropical cyclone–ocean models

Langmuir Turbulence under Hurricane Gustav (2008)

Extreme winds and complex wave fields drive upper-ocean turbulence in tropical cyclone conditions. Motivated by Lagrangian float observations of bulk vertical velocity variance (VVV) under Hurricane Gustav (2008), upper-ocean turbulence is investigated based on large-eddy simulation (LES) of the wave-averaged Navier–Stokes equations. To realistically capture wind- and wave-driven Langmuir turbulence (LT), the LES model imposes the Stokes drift vector from spectral wave simulations; both the LES and wave model are forced by the NOAA Hurricane Research Division (HRD) surface wind analysis product. Results strongly suggest that without LT effects simulated VVV underestimates the observed VVV. LT increases the VVV, indicating that it plays a significant role in upper-ocean turbulence dynamics. Consistent with observations, the LES predicts a suppression of VVV near the hurricane eye due to wind-wave misalignment. However, this decrease is weaker and of shorter duration than that observed, potentially due to large-scale horizontal advection not present in the LES. Both observations and simulations are consistent with a highly variable upper ocean turbulence field beneath tropical cyclone cores. Bulk VVV, a TKE budget analysis, and anisotropy coefficient (ratio of horizontal to vertical velocity variances) profiles all indicate that LT is suppressed to levels closer to that of shear turbulence (ST) due to misaligned wind and wave fields. VVV approximately scales with the directional surface layer Langmuir number. Such a scaling provides guidance for the development of an upper-ocean boundary layer parameterization that explicitly depends on sea state

Comparing ocean surface boundary vertical mixing schemes including langmuir turbulence

Six recent Langmuir turbulence parameterization schemes and five traditional schemes are implemented in a common single‐column modeling framework and consistently compared. These schemes are tested in scenarios versus matched large eddy simulations, across the globe with realistic forcing (JRA55‐do, WAVEWATCH‐III simulated waves) and initial conditions (Argo), and under realistic conditions as observed at ocean moorings. Traditional non‐Langmuir schemes systematically underpredict large eddy simulation vertical mixing under weak convective forcing, while Langmuir schemes vary in accuracy. Under global, realistic forcing Langmuir schemes produce 6% (−1% to 14% for 90% confidence) or 5.2 m (−0.2 m to 17.4 m for 90% confidence) deeper monthly mean mixed layer depths than their non‐Langmuir counterparts, with the greatest differences in extratropical regions, especially the Southern Ocean in austral summer. Discrepancies among Langmuir schemes are large (15% in mixed layer depth standard deviation over the mean): largest under wave‐driven turbulence with stabilizing buoyancy forcing, next largest under strongly wave‐driven conditions with weak buoyancy forcing, and agreeing during strong convective forcing. Non‐Langmuir schemes disagree with each other to a lesser extent, with a similar ordering. Langmuir discrepancies obscure a cross‐scheme estimate of the Langmuir effect magnitude under realistic forcing, highlighting limited understanding and numerical deficiencies. Maps of the regions and seasons where the greatest discrepancies occur are provided to guide further studies and observations

Parameterizing Vertical Mixing Coefficients in the Ocean Surface Boundary Layer Using Neural Networks

Abstract Vertical mixing parameterizations in ocean models are formulated on the basis of the physical principles that govern turbulent mixing. However, many parameterizations include ad hoc components that are not well constrained by theory or data. One such component is the eddy diffusivity model, where vertical turbulent fluxes of a quantity are parameterized from a variable eddy diffusion coefficient and the mean vertical gradient of the quantity. In this work, we improve a parameterization of vertical mixing in the ocean surface boundary layer by enhancing its eddy diffusivity model using data‐driven methods, specifically neural networks. The neural networks are designed to take extrinsic and intrinsic forcing parameters as input to predict the eddy diffusivity profile and are trained using output data from a second moment closure turbulent mixing scheme. The modified vertical mixing scheme predicts the eddy diffusivity profile through online inference of neural networks and maintains the conservation principles of the standard ocean model equations, which is particularly important for its targeted use in climate simulations. We describe the development and stable implementation of neural networks in an ocean general circulation model and demonstrate that the enhanced scheme outperforms its predecessor by reducing biases in the mixed‐layer depth and upper ocean stratification. Our results demonstrate the potential for data‐driven physics‐aware parameterizations to improve global climate models

Wind-wave misalignment effects on Langmuir turbulence in tropical cyclones conditions

This study utilizes a large eddy simulation (LES) approach to systematically assess the directional variability of wave‹driven Langmuir turbulence (LT) in the ocean surface boundary layer (OSBL) under tropical cyclones (TCs). The Stokes drift vector, which drives LT through the Craik‹Leibovich vortex force, is obtained through spectral wave simulations. LT\u27s direction is identified by horizontally elongated turbulent structures and objectively determined from horizontal autocorrelations of vertical velocities. In spite of TC\u27s complex forcing with great wind and wave misalignments, this study finds that LT is approximately aligned with the wind. This is because the Reynolds stress and the depth‹averaged Lagrangian shear (Eulerian plus Stokes drift shear) that are key in determining the LT intensity (determined by normalized depth-averaged vertical velocity variances) and direction, are also approximately aligned with the wind relatively close to the surface. A scaling analysis of the momentum budget suggests that the Reynolds stress is approximately constant over a near surface layer with predominant production of LT, which is confirmed from the LES results. In this layer, Stokes drift shear, which dominates the Lagrangian shear, is aligned with the wind because of relatively short, wind‹driven waves. On the contrary, Stokes drift exhibits considerable amount of misalignments with the wind. This wind‹wave misalignment reduces LT intensity, consistent with a simple turbulent kinetic energy model. Our analysis shows that both the Reynolds stress and LT are aligned with the wind for different reasons: the former is dictated by the momentum budget, while the latter is controlled by wind‹forced waves