Mixed Layer Lateral Eddy Fluxes Mediated By Air-sea Interactions

Mixed layer lateral eddy fluxes mediated by air-sea interaction Guillaume Maze John Marshall David Ferreira Emily Shuckburgh March 9, 2007

global high resolution model

ECCO project

Most of the eddy heat is transported poleward in the top 200m by diabatic eddies

How ?

Oceanic mesoscale

Qnet, daily mean May 5th 2003

Surface heat flux modulation by eddies

Rapid atmospheric synoptic scale

A snapshot reveals 2 different scales

Huge spatial variability at mesoscale

Qnet, monthly mean May 2003

Surface heat flux modulation by eddies

Atmospheric synoptic scale averaged out

Jan, 27th 2006 MicroWave SST NCEP v,T,q, bulk formulae

Qnet

CLIMODE Experiment Air-sea fluxes mesured by cruises (here from the Atlantis, WHOI)

Eddies advect anomalous warm/cold water

Schematic of the process studied

Cooling

which are strongly damped

Warming

T-

T+

How can the lateral eddy flux be estimated and what are its implications ?

leading to lateral eddy flux

Results from a global high resolution model MITgcm.org 1.

Model description and method used

2.

Eddy fluxes

3.

Eddy diffusivities

4.

Role of air-sea fluxes

5.

In the Southern Ocean

1/5 Model description

• Global, 1/8x1/8 degrees, lat/lon grid • 50 vertical levels with KPP mixed layer • Atmospheric boundary layer with NCEP v,T,q • bulk formulae allow the ocean-atmosphere interactions • 3 years of simulation from 2001 to 2003

ws to compute second terms on each RHS from the reconstructed ti h are then reinterpollated on the 1/8o grid of the outputs. The resul

1/5the time average one more time yields to: taking Method " !2 T 1 ! ! ! ! ! ! ! ! ! [v T · ∇T sc + ] + [[v]T · ∇T ] + [v T · ∇[T ]] = [Q 2 U! = U − Usc − [U] ρo Cpo H n

orizontal by air-sea heat associated w Extract the fluxes eddy part T eddy = Tdiffusivity − T − [T induced ] sc the SST: he Q!net = equation Qnet − Qof n: pronostic net − [Qnet ]

" ∂T! !2 " ! Qnet into the temperature !2 ∂ T T 1 + v · ∇T = ! ! ! ! equation ∂t C H T ] [Q + v · ρ∇ + [v T ] · ∇[T ] = o po net

∂t

2

2

ρo Cpo H

sitive downward. Splitting their time mean [·] and ed net intoequation: leads T to and the TQvariance " get (H is taken!fixe !2 in time):

D T 1 ! ! ! ! + [v T ] · ∇[T ] = [Q T ] net 1 ρo Cpo H 2 ! ! Dt ! ! + v · ∇T + [v] · ∇T + v · ∇[T ] = ([Qnet ] + Q!net ) ρo Cpo H rest here, balance occurs between: !

Eddy temperature [v! T ! ] · ∇[T flux 1] = !

1 Modulation [Q!net T !of] Q by T’ ρo Cpo H

Poleward Localized on the turbulent path of the GS

Surface intensified

2/5 Temperature eddy flux

[U! T ! ] and [T ]

[T’2]

Systematic damping on the turbulent path of the GS

[Q’T’]

also in the ACC

Q’ and T’ of opposite sign

2/5 Air-sea eddy heat flux

! ! [Qnet T ]

and [T ]

n: !2

T 2

"

! " !2 ! !2 "T ! ! ! !2 " 1 3/5 ∂+ vT· ∇ [Q!net T ! ] + [v T T] · ∇[T ] = ! ! 2+ v · ∇ + [vρTo C]po·H ∇[T ] =

Eddy2diffusivity ∂t !

1 [Q!net T ! ] ρo Cpo H

2

"

1 ! ! ! " + [v T ]!2· ∇[T ] = [Q!net T ! ] D T 1 ! ρo!Cpo H + [v T ] · ∇[T ] = [Q!net T ! ] Dt between: 2 ρo Cpo H balance occurs !2

D T Dt 2

est here,! balance occurs 1 between: ! ! !

[v T ] · ∇[T ] = [Qnet T ] ρo Cpo Hflux, Eddy temperature 1 ! ! direct computation [v T ] · ∇[Tof] K: = [v! T ! ] = −K · ∇[T ]

Q !modulation ! ] [QnetbyT T’ ρo Cpo H

sis: coefficient in a steady state: ivity

! ! ! ! ! ! [v T ]∇[T ] [Q T ] −1 [v T ] = −K · ∇[T ] net air eddy ! ! Ksea = K =− −1 [Qnet T ] ρCpo H ∇[T ] · ∇[T ] K= ∇[T ] · ∇[T ] dy diffusivity coefficient steady state: ρo Cpo H ∇[Tin ]·a ∇[T ]

K=

−1

[Q!net T ! ]

m2/s 105

air Ksea

and

[T ]

log10

103

0 3/5 Diffusivity from air-sea eddy flux

High values south of the Gulf Stream, low values in the core

m2/s 105

K

eddy

and

[T ]

High values south of the Gulf Stream, low values in the core

log10

103

0 3/5 Surface diffusivity from eddy temperature flux

But we didn’t removed the rotational part of [v’T’] ... A useful insight is obtained when averaging along isotherms

K eddy (z, T ) =

!!

T

[v! T ! ]∇[T ] − dS ∇[T ] · ∇[T ]

Mixed Layer Depth

Keddy increases

3/5 Diffusivity “section” from eddy temperature flux

Surface enhancement of Keddy

0

1000 m2/s

2000

MLD

-100

Keddy strongly increases at the surface

K

eddy

(z, Ti ) =

!!

T

[v! T ! ]∇[T ] − dS ∇[T ] · ∇[T ]

-200m

Keddy(z) for various T: 6, 10, 14, 18oC and all T class average

-300

3/5 Diffusivity profiles from eddy temperature flux

-400

2000 m2/s

~GS axis

Modulation of Q by T’: Kair-sea

Keddy in the mixed layer: eddy Kmld

1000

Keddy in the interior: !

eddy Kinterior

=

=

!

0

K eddy

H

eddy Kmld !

eddy air Kinterior + Ksea

H

K

eddy

−400

small scales processes: everywhere

South

0 22oC

14oC

4/5 Role of air-sea heat fluxes

6oC

North

Kair-sea is almost half the Keddy in the mixed layer

Passive advection of a tracer q: ∂q + v · ∇q ∂t

A=A(q,t)

is reduced to a purely diffusion problem when passing into area coordinates: (Nakamura,1996) ∂q ∂t

q contour

= k∇2 q

=

∂ ∂A

!

∂q κef f (A) ∂A

In physical space: Kef f

5/5 Diffusivity from tracer analysis

L2eq = k 2 Lmin

L: contours length

"

explicit process k!2q, which is central to the Nakamura algorithm [see Eq. (3)]. Figure 1 shows (a) the initial tracer distribution and (b) the tracer after 1 yr of integration from a simulation at a (1/20)° resolution with a diffusivity of k " 50 m2 s#1. A large number of such calculations were carried out, as set out in Table 1. Many are of subdomains—patches embedded in the larger-scale flow— and some are at a resolution as high as (1/100)°, which is much higher than was possible in the global domain. This enabled the explicit diffusivity to be reduced to low levels, allowing our calculations to span over a larger range of Pe. Figure 2 shows a number of patch calculations carried at different resolutions and with difference values of k, and hence Pe. Because the velocity field is very smooth at small scales, a good description of the evolution of the q field is qt $ Sxqx " qxx, where S " (V/L) is the strain rate, where V and L are typical scales for eddy speed and size. A balance between advection and diffusion occurs on the scale % " &(k/S), a “Batchelor scale.” The Pe number for these flows, comparing the advective time scale (L/V) with the diffusive time scale (L2/k), is then Pe " (VL/k) " (SL2/k) " (L/%)2. From Table 1, we see that in our numerical experiments the Batchelor scale exceeds the grid spacing for all but the very smallest values of k used at the various resolutions. The results from such experiments must therefore be considered suspect. The tracer field is extracted from the advection–diffusion simulation at regular time intervals and the effective diffusivity is calculated from it as described in the following section.

q: t=0

∂q + v · ∇q ∂t

Eddy diffusivity from tracer analysis

= k∇2 q

1814

JOURNAL OF PHYSIC

Keff after 1year

q: t=1y

trigger of the Keddy in the interior previously shown

3. Estimates of surface eddy diffusivity

FIG. 1. (a) Time-mean geostrophic streamfunction 'g (dotted contours are negative, contour interval 2 ( 106 m2 s#1) and initial tracer distribution (colors). (b) Instantaneous tracer distribution, ranging in value from 0 to 1, after 1 yr of integration at 1/20° with k " 50 m2 s#1.

Equation (9) is stepped forward numerically on the sphere using the infrastructure of the Massachusetts Institute of Technology (MIT) general circulation model (Marshall et al. 1997). We choose to use an Adams– Bashforth time-stepping scheme in conjunction with a simple centered second-order discretization in space that conserves q and q2 and introduces no spurious diffusion. We prefer not to use higher-order or “limited” schemes that, for example, conserve extrema, because they introduce diffusion that would compete with the

To compute Keff, the gradient of the tracer is calculated at each grid point, and its square is integrated over the area bounded by the desired tracer contour. This integrated |!q|2 is then differentiated with respect to area by taking finite differences. The resulting quantity is then divided by the square of the areal gradient of the tracer to obtain L2eq(q), as defined in Eq. (A5). To obtain L2min we take advantage of the fact that Leq tends to Lmin for Pe K 1. We therefore conduct an advection–diffusion integration with a large diffusivity k, which is chosen after sensitivity studies to be k " 104 m2 s#1, from which we estimate Lmin. The effective diffusivity Keff is then computed from Eq. (4). There is an initial period of adjustment, lasting a few eddy turnover times, during which the initial tracer field adjusts to align with the flow. Following this adjustment time, the effective diffusivity remains approxi-

5/5 In the Southern Ocean

No damping Marshall et al, JPO 2006

∂q + v · ∇q ∂t

= k∇2 q − λ(q − q ∗ ) new, damping of the tracer...

representing the air-sea heat flux interactions:

Qnet ! −λ(T − T ) ∗

5/5 In the Southern Ocean

With damping

2000 m2/s

Keff 1000

Once again: the eddy diffusivity is enhanced by eddy air-sea interactions

Damping time scale (months)

0

∂q + v · ∇q ∂t

= k∇2 q − λ(q − q ∗ )

5/5 In the Southern Ocean

With damping

Conclusion • All over the ocean, most of the meridional eddy heat transport is achieved in the top 200m by mesoscale eddies

• The net air-sea heat flux is strongly modulated at the eddy scale, as seen in a high resolution model and in observations (CLIMODE)

• Induced damping of eddies triggers an additional poleward heat transfert which has been analyzed through coefficients of diffusion

• Eddy diffusivity is shown to be strongly intensified at the surface • Half of the surface diffusivity is attributed to eddy air-sea damping • This is also found in the Southern Ocean from tracer analysis • This process is believed to occur all over places of strong eddy activity and then may have implications for example in: ‣ eddy parametrisation in coarse resolution models ‣ mechanisms with key role of air-sea fluxes, especially water mass formation (CLIMODE)

Thank you

Global: Air-sea eddy heat flux

[Q’netT’]

Meridional heat transport

Eddy vs Total

Qnet ρCpo H

= −λ(T − T ∗ )

[Q!net T ! ] = −λ[T !2 ] ρCpo H

GS core: < 50 days Lower part: >100 days

Dissipation time scale

1 [T !2 ] = −ρCpo H ! λ [Qnet T ! ]