Ayet and Redelsperger (2019) derived a closed-form expression for the vertically integrated wind divergence of the marine atmospheric boundary layer (MABL) over a sea-surface-temperature (SST) front, coupling the divergence to multiple-order derivatives of the SST field (in particular its Laplacian and downwind gradient) with coefficients that depend on the inverse Ekman number and undergo regime transitions. This predicts that the MABL divergence response depends on the spatial scale of the front, a prediction the authors explicitly left untested against observations over sharp fronts; the underlying analytical model is further restricted to low Rossby numbers (no nonlinear advection), a prescribed wind boundary condition, and a turbulent structure calibrated linearly in potential temperature. The open problem, in the authors' own future-work call, is to investigate whether the MABL wind-divergence response changes with the spatial scale of the front, based on observations over sharp SST fronts; the stated model restrictions frame where the closed-form prediction is expected to hold or fail.

Background

The marine atmospheric boundary layer (MABL) is the turbulent lowest few hundred meters to ~1 km of the atmosphere over the ocean, in near-equilibrium with the sea surface. Satellite observations show that sea-surface-temperature (SST) fronts - sharp horizontal transitions in ocean surface temperature, from mesoscale (tens to hundreds of km) down to submesoscale (1-10 km) - imprint on surface winds and wind stress, with stronger stress and wind speed over warm water. Two mechanisms explain this coupling. In the pressure-adjustment mechanism, the cross-front temperature contrast creates a hydrostatic pressure-gradient force that accelerates the boundary-layer flow, so wind convergence and divergence follow the SST Laplacian. In the downward momentum mixing (DMM) mechanism, warm water destabilizes the MABL and enhances turbulent mixing, which mixes higher wind from aloft down to the surface, tying wind and stress divergence to the downwind SST gradient. Both act within an Ekman-like regime, where the horizontal momentum balance in the boundary layer is between the Coriolis force, the pressure-gradient force, and the vertical divergence of the turbulent Reynolds stress; the relative weight of the mechanisms is measured by an Ekman number, here comparing the height-averaged turbulent diffusivity KeK_e with rotation and MABL height hh (roughly Ke/(fh2)K_e/(fh^2), with ff the Coriolis parameter), so that its inverse measures the ratio of MABL height to turbulence strength. The Rossby number Ro=∣U+Ug∣/(fL)Ro = |U+U_g|/(fL) (ageostrophic plus geostrophic wind, i.e. the total wind measured relative to the wind in Coriolis-pressure-gradient balance, over the product of ff and the front width LL) measures the importance of nonlinear momentum advection. Idealized and realistic simulations (Spall, 2007; Kilpatrick et al., 2014; Schneider and Qiu, 2015) and large-eddy simulations of submesoscale fronts (Wenegrat and Arthur, 2018) had established the resulting vertical wind structure and its scale and wind-speed dependence, but with vertically constant or strongly constrained diffusivity and generally numerical solutions. Because MABL divergence forces vertical motion at the boundary-layer top, its scaling controls how strongly SST fronts couple the ocean to the free troposphere. Ayet and Redelsperger (2019) closed part of this gap analytically: for a cross-front geostrophic wind (wind in Coriolis-pressure-gradient balance) blowing from cold to warm water at low RoRo (advection neglected, so the momentum balance solves in independent vertical columns), a well-mixed MABL, a turbulent diffusivity that is parabolic in the vertical and decoupled from the MABL height, and MABL height and turbulence prescribed as linear functions of potential temperature calibrated on simulations, they obtained the ageostrophic wind in terms of Legendre functions (the classical solutions of Legendre's differential equation) and a closed-form vertically integrated wind divergence. This divergence is a linear combination of the SST Laplacian and the downwind SST gradient - more generally, of multiple-order SST derivatives - with coupling coefficients that vary with the inverse Ekman number and display distinct dynamical regimes. Since different-order SST derivatives dominate at different horizontal scales, the response of the MABL to an SST front should change with the front's spatial scale, and with the environmental parameters that set the turbulent structure. The model was validated against an idealized numerical simulation, but only away from the front where advection is negligible; above the front the assumed linear relation between MABL height and potential temperature breaks down, the framework cannot address the observed SST-surface wind-stress correlation coefficient because it imposes a condition on the wind rather than on the momentum flux at the surface, and the predicted scale dependence has not been confronted with observations over sharp fronts (for which high-resolution satellite SST datasets such as that of Chevallier et al., 2014 were suggested as a basis).

Problem Statement

Determine, as three explicitly linked sub-goals, (i) how the wind-divergence response of the marine atmospheric boundary layer to a sea-surface-temperature front depends on the front's spatial scale, (ii) how it depends on the environmental parameters that set the coupling coefficients - namely the inverse Ekman number and the MABL height and turbulent-diffusivity structure it reflects - and (iii) whether that dependence is borne out against observations over sharp SST fronts. The observational confrontation targets the closed-form prediction that the vertically integrated MABL wind divergence is a linear combination of multiple-order SST derivatives - in particular the SST Laplacian (pressure-adjustment mechanism) and the downwind SST gradient (downward momentum mixing) - with coupling coefficients that vary with the inverse Ekman number, display distinct dynamical regimes, and are sensitive to environmental parameters; the investigation should establish how the response changes with the front's spatial scale and where the prediction holds or fails, confronting the modelled vertically integrated divergence with observed surface wind divergence alongside the high-resolution SST fields.

Three source-stated restrictions frame the validity of the closed-form prediction: (i) the model assumes a low Rossby number - as the front scale decreases, advection might start playing a role in the momentum balance and thus invalidate the model assumptions, and the model reproduces numerical simulations at higher Rossby numbers except on top of the SST gradient, where advection is important; relaxation of the low-Rossby condition would require solving the momentum balance with a numerical scheme including the first-order non-linear advection term (e.g. Schneider and Qiu 2015); (ii) the SST-surface wind-stress correlation coefficient is out of the scope of the model, which imposes a condition on the wind rather than on the momentum flux at the surface; (iii) the MABL height and diffusivity profile are prescribed as linear functions of potential temperature calibrated on simulations, a link that becomes non-linear above the front due to non-linear advection in the heat equation.

References

  1. Ayet, A., and Redelsperger, J.-L. (2019). An analytical study of the atmospheric boundary-layer flow and divergence over an SST front. Quarterly Journal of the Royal Meteorological Society 145(723), 2549-2567. DOI: 10.1002/qj.3578. https://doi.org/10.1002/qj.3578 (author accepted manuscript: https://hal.science/hal-04202310)
  2. Jacquet, H., Ayet, A., and Couvreux, F. (2025). Atmosphere Response to an Oceanic Submesoscale SST Front: A Coherent Structure Analysis. Journal of Geophysical Research: Atmospheres 130(4), e2024JD042312. DOI: 10.1029/2024JD042312. https://doi.org/10.1029/2024JD042312 (open-access manuscript: https://hal.science/hal-04729066)
  3. Schneider, N. (2020). Scale and Rossby Number Dependence of Observed Wind Responses to Ocean-Mesoscale Sea Surface Temperatures. Journal of the Atmospheric Sciences 77(9), 3171-3192. DOI: 10.1175/JAS-D-20-0154.1. https://doi.org/10.1175/JAS-D-20-0154.1
  4. Masunaga, R., and Schneider, N. (2022). Surface Wind Responses to Mesoscale Sea Surface Temperature over Western Boundary Current Regions Assessed by Spectral Transfer Functions. Journal of the Atmospheric Sciences 79(6), 1549-1573. DOI: 10.1175/JAS-D-21-0125.1. https://doi.org/10.1175/JAS-D-21-0125.1
  5. Yang, H., Chen, Z., Sun, S., Li, M., Cai, W., Wu, L., Cai, J., Sun, B., Ma, K., Ma, X., Jing, Z., and Gan, B. (2024). Observations Reveal Intense Air-Sea Exchanges Over Submesoscale Ocean Front. Geophysical Research Letters 51(2), e2023GL106840. DOI: 10.1029/2023GL106840. https://doi.org/10.1029/2023GL106840
  6. Redelsperger, J.-L., Bouin, M.-N., Pianezze, J., Garnier, V., and Marié, L. (2019). Impact of a sharp, small-scale SST front on the marine atmospheric boundary layer on the Iroise Sea: Analysis from a hectometric simulation. Quarterly Journal of the Royal Meteorological Society 145(725), 3692-3714. DOI: 10.1002/qj.3650. https://doi.org/10.1002/qj.3650
  7. Foussard, A., Lapeyre, G., and Plougonven, R. (2019). Response of Surface Wind Divergence to Mesoscale SST Anomalies under Different Wind Conditions. Journal of the Atmospheric Sciences 76(7), 2065-2082. DOI: 10.1175/JAS-D-18-0204.1. https://doi.org/10.1175/JAS-D-18-0204.1
  8. Lemarié, F., Samson, G., Redelsperger, J.-L., Giordani, H., Brivoal, T., and Madec, G. (2021). A simplified atmospheric boundary layer model for an improved representation of air-sea interactions in eddying oceanic models: implementation and first evaluation in NEMO (4.0). Geoscientific Model Development 14(1), 543-572. DOI: 10.5194/gmd-14-543-2021. https://doi.org/10.5194/gmd-14-543-2021
  9. Spall, M. A. (2007). Midlatitude Wind Stress-Sea Surface Temperature Coupling in the Vicinity of Oceanic Fronts. Journal of Climate 20(15), 3785-3801. DOI: 10.1175/JCLI4234.1. https://doi.org/10.1175/JCLI4234.1
  10. Kilpatrick, T., Schneider, N., and Qiu, B. (2014). Boundary Layer Convergence Induced by Strong Winds across a Midlatitude SST Front. Journal of Climate 27(4), 1698-1718. DOI: 10.1175/JCLI-D-13-00101.1. https://doi.org/10.1175/JCLI-D-13-00101.1
  11. Schneider, N., and Qiu, B. (2015). The Atmospheric Response to Weak Sea Surface Temperature Fronts. Journal of the Atmospheric Sciences 72(9), 3356-3377. DOI: 10.1175/JAS-D-14-0212.1. https://doi.org/10.1175/JAS-D-14-0212.1
  12. Wenegrat, J. O., and Arthur, R. S. (2018). Response of the Atmospheric Boundary Layer to Submesoscale Sea Surface Temperature Fronts. Geophysical Research Letters 45(24), e2018GL081034. DOI: 10.1029/2018GL081034. https://doi.org/10.1029/2018GL081034
  13. Chevallier, C., Herbette, S., Marié, L., Le Borgne, P., Marsouin, A., Péré, S., Levier, B., and Reason, C. (2014). Observations of the Ushant front displacements with MSG/SEVIRI derived sea surface temperature data. Remote Sensing of Environment 146, 3-10. DOI: 10.1016/j.rse.2013.07.038. https://doi.org/10.1016/j.rse.2013.07.038