# The combined effects of SST and oceanic currents on eddy-scale air-sea interactions: a modeling study

Florian Lemarié, François Colas, James C. McWilliams

► To cite this version:

Florian Lemarié, François Colas, James C. McWilliams. The combined effects of SST and oceanic currents on eddy-scale air-sea interactions: a modeling study. Drakkar Ocean Modelling Workshop, Jan 2013, Grenoble, France. [hal-04468963](https://hal-inriaHal) [https://inria.hal.science/hal-04468963v1](https://inria.hal.science/hal-04468963v1)

Submitted on 20 Feb 2024

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<figure><img src="image_1.png" /></figure>

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# The combined effects of SST and oceanic currents on eddy-scale air-sea interactions : a modeling study

F. Lemarié<fnref n="1" />,<fnref n="2" />, F. Colas<fnref n="3" />,<fnref n="1" />, J.C. McWilliams<fnref n="1" />

<footnote n="1">¹ UCLA Department of atmospheric and oceanic sciences</footnote>

<footnote n="2">² INRIA Grenoble (MOISE) / Laboratoire Jean Kuntzmann</footnote>

<footnote n="3">³ IRD, LOCEAN, Paris</footnote>
▷ Investigate air-sea interactions in mesoscale eddies from two fully-coupled simulations for summertime off US west coast ($\Delta x_{oce} = \Delta x_{atm} = 5\text{km}$).

* Quantify the influence of oceanic surface currents on air-sea momentum transfer.

* Determine the eddy-related SST and surface currents influence on air-sea interactions

* Evaluate results against existing observational studies (AMSR, QuikSCAT)
# Thermal Coupling (1/2)

Businger J. & Shaw W., 1984. The response of the marine boundary layer to mesoscale variations in sea-surface temperature. DAO

⇒ Surface layer / SST coupling through sea-state dependent drag coefficient

<figure><img src="image_2.png" /><figcaption>Fig. 10. Schematic diagram indicating some of the interactions that result when a stationary boundary layer flow moves over a warm ocean eddy. The dimensions of the eddy may be assumed to be 50–100 km.</figcaption></figure>

↓ ↓ ↓ $u_a = (0, -6.5)$

<figure><img src="image_3.png" /></figure>
# Thermal Coupling (2/2)

D. Chelton et al., 2007. Summertime coupling between sea surface temperature and wind stress in the california current system. JPO

↓ ↓ ↓ $u_a = (0, -6.5)$

<figure><img src="image_4.png" /><figcaption>Fig. 3. Schematic summary of the influence of SST on winds near a mesoscale SST front. The wind stress magnitudes (expressed by the lengths of the vectors) are relatively strong over warm water and weak over cold water, which generates local curl and divergence of the wind stress. The curl is stronger where the winds slow parallel to isobath (hatched regions) and the divergence is stronger where winds slow perpendicular to isobath (equipped regions). The wind stress curl and divergence are therefore related (obliquely related to the local observed and downwind components of the SST gradient, respectively see Fig. 3 below).</figcaption></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

⇒ expected to be a PBL mixing / SST coupling

$$ \left\{ \begin{aligned} \nabla \times \tau &= c_1 \nabla \text{SST} \times \hat{\tau} \\ \nabla \cdot \tau &= c_2 \nabla \text{SST} \cdot \hat{\tau} \end{aligned} \right. $$
# "Top" drag [a.k.a. understress (Bye, 1986)] (1/2)

Dewar & Flierl, 1987. *Some Effects of the Wind on Rings*. JPO

$$ 
\begin{aligned}
\tau_{\lambda} &= \rho_{3}C_{D}\|\mathbf{u}_{a} - \lambda\mathbf{u}_{o}\|(\mathbf{u}_{a} - \lambda\mathbf{u}_{o}) \\
&= \rho_{3}u_{s}^{2}(\mathbf{u}_{a}, \lambda\mathbf{u}_{o}) \left( \frac{\mathbf{u}_{a} - \lambda\mathbf{u}_{o}}{\|\mathbf{u}_{a} - \lambda\mathbf{u}_{o}\|} \right)
\end{aligned}
$$

<figure><img src="image_7.png" /></figure>

⇒ the air-sea interface exerts a drag on both the atmosphere (via wind stress) and the ocean (via understress).

$$ \downarrow \downarrow \downarrow \mathbf{u}_{a} = (0, -6.5) $$

<figure><img src="image_8.png" /></figure>
# "Top" drag [a.k.a. understress (Bye, 1986)] (2/2)

Duhaut & Straub, 2006. Wind stress dependence on ocean surface velocity : Implications for mechanical energy input to ocean circulation. JPO

$$ \tau_{\text{diff}} \equiv \tau_0 - \tau_1 \approx \rho_a C_D \|\mathbf{u}_a\| \|\mathbf{u}_o\| + \rho_a C_D (\mathbf{u}_o \cdot \hat{\mathbf{u}}_a) \mathbf{u}_a $$

$$ \mathbf{P}_{\text{diff}} \equiv \tau_{\text{diff}} \cdot \mathbf{u}_o \approx \rho_a C_D \|\mathbf{u}_a\| \left[ \|\mathbf{u}_o\|^2 + (\mathbf{u}_o \cdot \hat{\mathbf{u}}_a)^2 \right] $$

⇒ $\mathbf{u}_o$-dependence in $\tau_1$ acts to reduce the power source

<figure><img src="image_9.png" /><figcaption>FIG. 2. Time series of various terms in the energy equation (W m⁻²) for simulation S1: $P_o$ (top curve), $P_t$ (second from top), bottom dissipation (third from top), and lateral dissipation (bottom).</figcaption></figure>
<figure><img src="image_10.png" /></figure>
# Numerical simulations and coupling strategy

## Summertime off US West coast

* intense frontal activity (Castelao et al., 2006)

* high wind steadiness (about 0.96)

* low gustiness (0.3)

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

* previously used in (Boé et al., 2011)

* modified **bulk and tridiagonal solver** to include the effect of currents on wind stress

* simulations from Jun. to Sept. 2006
Mesoscale wind-SST coupling relation

$$ \begin{cases} \nabla \times \tau = c_1 \nabla \text{SST} \times \hat{\tau} \\ \nabla \cdot \tau = c_2 \nabla \text{SST} \cdot \hat{\tau} \end{cases} $$

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

⇒ wind-SST coupling spectrally broad band across scales
Mean kinetic energy $\frac{(\bar{\mathbf{u}}_o)^2}{2}$

<figure><img src="image_15.png" /></figure>

⇒ MKE reduction of approximately 15%
Eddy-kinetic energy

$$ \frac{\langle u_o^2 \rangle}{2} $$

<figure><img src="image_16.png" /></figure>

⇒ EKE reduction of approximately 20%
* Composite averaging in an eddy-centric coordinate

* Identify mesoscale eddies by closed SLA-contours [Kurian et al., 2011]

* Additional constraints on distance to the coast and wind direction

<table><thead><tr><th></th><th colspan="2">USW5[τ<sub>1</sub>]</th><th colspan="2">USW5[τ<sub>0</sub>]</th></tr><tr><th></th><th>cyc</th><th>anti</th><th>cyc</th><th>anti</th></tr></thead><tbody><tr><th>total</th><td>692</td><td>1058</td><td>794</td><td>1336</td></tr></tbody></table>

TABLE : Number of detected eddies in USW5[τ₁] and USW5[τ₀].
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>
PBL mixing (1/2)

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>
PBL mixing (2/2)

$$ \nabla \cdot \tau = c_2 \nabla \text{SST} \cdot \hat{\tau} $$

<figure><img src="image_25.png" /></figure>

Corr ≈ 0.9, Coeff = 0.0244 N m⁻² °C⁻¹
(c₂ = 0.0222 N m⁻² °C⁻¹, Chelton et al., 2007 from observations)
Composite wind stress curl

<figure><img src="image_26.png" /></figure>
Temperature anomalies

<figure><img src="image_27.png" /></figure>

$T'[\tau_1]$ (cyc)

<figure><img src="image_28.png" /></figure>

$T'[\tau_0]$ (cyc)

<figure><img src="image_29.png" /></figure>

$T'[\tau_1]$ (anti)

<figure><img src="image_30.png" /></figure>

$T'[\tau_0]$ (anti)

<figure><img src="image_31.png" /></figure>
SST fronts and currents

<figure><img src="image_32.png" /></figure>

→ fronts tend to be intensified where the currents are aligned with wind stress
<figure><img src="image_33.png" /></figure>

⇒ Eddy-induced Ekman pumping has same order of magnitude as the one associated with SCOW wind stress
* The coupled model reproduces the known air-sea interactions

* $u_o$-dependence induces a reduction of oceanic motions

* PBL anomalies over oceanic fronts

* Eddy-induced Ekman pumping

* Fronts distribution and intensity are altered by air-sea coupling

* Same resolution is required in the ocean and the atmosphere to represent most of those effects

## Perspectives :

* Test in a climate-type global eddying model to assess the large scale impact (ANR PULSATION, S. Masson)

* Open question on the best practice to force an eddying oceanic model (Bulk ? CheapAML ? [Deremble et al., 2011] .... ??? .... Coupled)
# Bulk formulation

Starting from the Reynolds averaged equations the following assumptions (supposed valid in the atmospheric surface layer) are done

* hydrostaticity + Boussinesq assumption

* horizontal homogeneity

* quasi-stationarity

* Coriolis force and HPG are negligible

* valid only at a certain distance from the air-sea interface, above the direct influence of the surface roughness elements.

## B. Large, Ocean Weather Forecasting: An Integrated View of Oceanography:

> "The sign of turbulent fluxes can be uncertain on time scales less than 10 minutes and hourly fluxes are more relevant"

> "When averaging, the uncertainty should diminish as wave effects start to average out"

> "The transfer coefficients $C_D$ and $C_H$ are determined empirically from measurements averaged over about an hour (e.g. Large and Pond 1981) and are not applicable for instantaneous output from an atmospheric model grid point."