Dampening of Submesoscale Currents by Air-Sea Stress Coupling in the Californian Upwelling System

Oceanic submesoscale currents (SMCs) occur on an scale of 0.1–10 km horizontally and have a large influence on the oceanic variability and on ecosystems. At the mesoscale (10–250 km), oceanic thermal and current feedbacks are known to have a significant influence on the atmosphere and on oceanic dynamics. However, air-sea interactions at the submesoscale are not well known because the small size of SMCs presents observational and simulation barriers. Using high-resolution coupled oceanic and atmospheric models for the Central California region during the upwelling season, we show that the current feedback acting through the surface stress dominates the thermal feedback effect on the ocean and dampens the SMC variability by ≈17% ± 4%. As for the mesoscale, the current feedback induces an ocean sink of energy at the SMCs and a source of atmospheric energy that is related to induced Ekman pumping velocities. However, those additional vertical velocities also cause an increase of the injection of energy by baroclinic conversion into the SMCs, partially counteracting the sink of energy by the stress coupling. These stress coupling effects have important implications in understanding SMC variability and its links with the atmosphere and should be tested in other regions.


Methods
The numerical models and configurations are similar to the ones employed in Renault et al. (2016b), and the following models descriptions are derived from there with minor modifications. a. Models description

1) CROCO
The oceanic simulations were performed with the Regional Oceanic Modeling System (ROMS) (Shchepetkin and McWilliams 2005;Shchepetkin 2015) in its CROCO (Coastal and Regional Ocean Community) version (Debreu et al. 2012). CROCO is a free-surface, terrain-following coordinate model with split-explicit time stepping and with Boussinesq and hydrostatic approximations. The model is implemented in a configuration with four offline nested grids. As in Renault et al. (2016b) x 762 points with a resolution of 1 km and 1000 x 1520 points with a resolution of 500 m, respectively. As in Capet et al. (2008a), the assumption underlying this approach is that SMCs developing at higher resolutions do not have significant upscaling effects on the mesoscale or mean circulation outside the Central California domain. The models have a similar configuration to Renault et al. (2016b), with 42 vertical levels for the 4 km and 1 km grids, and 60 for the 500 m grid; the vertical grid is stretched for increased boundary layer resolution using stretching surface and bottom parameters of h cline = 250 m, θ b = 1.5, and θ s = 6.5. gives the ocean model hourly averages of freshwater, heat, and momentum fluxes; whereas, the ocean model sends WRF the hourly SST. In the second set (CFB4, CFB1, CFB500), the ocean model sends WRF both SST and surface currents,, and the surface stress is estimated using the relative wind to the ocean motions: Note that the use of relative winds also involves a modification of both the surface-layer vertical mixing parameterization (MYNN2.5 in our case) and the tridiagonal matrix for vertical turbulent diffusion Lemarié (2015).

2) WRF
WRF (version 3.7.1, Skamarock et al. 2008) is implemented in a configuration with three grids. The domains is slightly larger than the ocean domains to avoid the effect of the WRF sponge (4 points). They have a horizontal resolution of 18 km, 6 km, and 2 km. The 18 km and 6 km domains are initialized with the Climate Forecast System Reanalysis (CFSR) (≈ 40 km spatial resolution; Saha et al. 2010) from 30th December 1994 and integrated for 5.5 years with time-dependent boundary conditions interpolated from the same six-hourly reanalysis. Forty vertical levels are used, with half of them in the lowest 1.5 km, as in Renault et al. (2016a). The parameterizations used are the same as Renault et al. (2016b). Note WRF has a slight coarser spatial resolution than the ocean model mainly because of the computational cost, which is much higher for an atmospheric model. Moreover, when coupling a 500-m oceanic model, having a 2-km atmospheric model is enough because (1) as shown by Renault et al. (2017), s τ depends on the large scale wind, and (2) in the atmospheric model, the Planet Boundary Layer (MYNN2.5) response to the current and thermal feedbacks is basically 1D and the CROCO effective resolution is about 4δx (i.e., ≈ 2.5km for a 500m solution), thus, a 2-km resolution in the atmospheric model is enough to reproduce the atmospheric response to the current and thermal feedbacks.

b. Current Feedback in a Coupled Model
In a coupled model the current feedback to the atmosphere is simply represented by using a bulk formulae for stress with the surface wind relative to the oceanic current: where U a and U o are the surface wind and the surface current at the closest model grid levels to the surface, respectively. When neglecting the current feedback, the wind U a is used instead of the relative wind U r .
As described by Lemarié (2015), because of the implicit treatment of the bottom boundary condition in most atmospheric models, the use of relative winds involves a modification of both the surface-layer vertical mixing parameterization (MYNN2.5 in our case) and the tridiagonal matrix for vertical turbulent diffusion.

c. Submesoscale characterization
As in Capet et al. (2008a), the submesoscale is isolated from the signal using a high-pass spatial filter that consists of a five-point operator with a 12-km smoothing length and 2-days smoothing. Note, the use or not of the 2-days smoothing does not change qualitatively the results.

d. Spectrum
To compute the spectrum the area mean is first removed and a symmetrization is performed using an Hanning window Jenkins and Watts (1968).

e. KE budget
Following Capet et al. (2008b) and Marchesiello et al. (2011), a spectral decomposition of the KE balance for the Primitive Equations has been computed. To that end, the co-spectrum between velocity and the term that enters the momentum equations is computed on each 6-hours snapshots and, then, averaged over the 3 months-period considered here and over 100m depth (note similar results are found when considering only e.g., 70m depth). It is expressed as: where b is buoyancy (b = −g ρ ρ0 ) and K v is the vertical viscosity. The caret stands for an horizontal Fourier transform after removing the area mean and applying a 2D Hanning window Jenkins and Watts (1968), which has the effect to symmetrize the signal and suppressing the advective horizontal fluxes through the boundary. * denotes the complex conjugate operator; R represents the real part operator; indicates an average over the 3-months considered here and over 100m depth, (at 100m depth the vertical flux is small, choosing 70m depth does not qualitatively change the results). C represents an injection of energy by baroclinic conversion; P is the 3D pressure work; V corresponds to the wind and vertical mixing work; A represents the horizontal and vertical advection contribution; and the horizontal mixing (H).

f. Coupling Coefficient s τ
In this study the submesoscale s τ is defined as the linear regression between submesoscale surface stress curl and oceanic current vorticity and is evaluated over the 500 m domain and over the summer 2000. The fields are first temporally averaged using a 1-day running mean.

g. Available Potential Energy
The mesoscale APE is estimated as Fox-Kemper et al. (2008); Srinivasan et al. (2017): where b M E represents the mesoscale component estimated using a spatial low-pass filter of 250 km, and the depth average is computed over the mixed layer depth H b . H b is estimated using the classic approach of the depth at which the density is 0.03 • C below that at 10 m depth (de Boyer Montégut et al. (2004)).

h. Surface Stress Induced Ekman Pumping
The Ekman pumping induced by the surface stress is computed as: where f is the Coriolis frequency.