.

OCEANIC SUBMESOSCALE SAMPLING

WITH WIDE-SWATH ALTIMETRY

James C. McWilliams

Department of Atmospheric & Oceanic Sciences

Institute of Geophysics & Planetary Physics

U.C.L.A.

Recall the long-standing

mystery of “spirals on the

sea” (Munk et al., 2000)

seen in slick patterns and

SAR images on a scale of

kilometers — (top) near

Catalina Island; (bottom) in

the Mediterranean (Scully-

Power, 1986) — but never

measured in situ nor even

remotely in u, η, or T .

mesoscale currents:

∼ 40 km horizontally, 1 km verti-

cally, & 1 week temporally

arising from instabilities of the

general circulation

dominance of horizontal veloc-

ity spectrum and isopycnal eddy

fluxes

≈ energetically conservative and

adiabatic in interior

statistically well sampled by Ja-

son/TOPEX/Poseidon altimetry

relatively well understood

submesoscale currents:

∼ 4 km horizontally, 100 m verti-

cally, & 1 day temporally

arising by frontogenesis from the

messocale

dominance of near-surface

vertical velocity spectrum and

diapycnal eddy fluxes

energetically dissipative and

diabatic

an opportune target for wide-

swath altimetry

a scientific frontier

3d turbulence

OCEANIC GENERAL CIRCULATIONENERGY BUDGET FOR THE

KE & PE

wind work

"eddy−viscous"

general circulation energy:

& forward cascadebalance breakdown

boundary layers eddy instabilityinterior

buoyancy work

dissipation

tidal work

internal−wave induced

SST image in (250 km)2 off California with associated measurements in situ.

Notice fronts and frontal instabilities (Flament et al., 1985).

Criterion: large ∆T over ∆x = 5 km (Castelao et al., 2006).

−−−T(z)

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upwelling

eddies

undercurrent

surface current

EASTERN BOUNDARY CURRENT

current

N E

fronts

Computational Simulations:

(Capet et al., 2006)

• steady τττ, Q, F

• flat bottom & straight coast

• embedded in equilibrium EBC

domain with ∆x = 12 km

• interior domain: (750 km)2

with ∆x = 12 → 0.75 km

grid sizes [spanning the subme-

soscale transition]

• ROMS code (Shchepetkin &

McWilliams, 2005)

10−5

10−4

10−3

10−4

10−2

100

102

k [rad/m]

KE

(2m

) [m

3 /s2 ]

Horizontal velocity u⊥

spectrum at the surface

with ∆x = 12 → 0.75 km

grid sizes:

• convergent shape

∼ k−2 in submesoscale

range (dashed; cf.,

Stammer, 1997)

• currents are mostly

geostrophic

• not enstrophy cascade

of geostrophic turbu-

lence, k−3 (dot-dashed)

• not kinetic energy

inertial-range cascade,

k−5/3 (dotted)

x [km]

y [k

m]

−600 −400 −200 00

100

200

300

400

500

600

10

11

12

13

14

15

16

17

18

19

20

Simulated SST [C] with mesoscale eddies and submesoscale fronts and frontal

instabilities.

x [km]

y [k

m]

−600 −400 −200 00

100

200

300

400

500

600

−1

−0.5

0

0.5

1

1.5

2

Simulated vertical vorticity normalized by f : submesoscale is most active between

mesoscale eddies.

x [km]

y [k

m]

−600 −400 −200 00

100

200

300

400

500

600

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

Simulated sea-surface height [m]: submesoscale is subtle finestructure.

Submesoscale Restratification Flux

. ∆x = 0.75 km ∆x = 6 km

Equilibrium buoyancy balance, b = g(αT − βS):

∂tb = −∇∇∇⊥ · (u⊥b) − ∂z(wb) + ∂z(κ∂zb)

. ≈ 0 mesoscale boundary-layer

. submeoscale [τττ, Q, F ]

Submesoscale vertical restratification flux is O(100) W m−2, largely

balanced by boundary-layer turbulent flux.

x [km]

y [k

m]

−490 −485 −480 −475 −470 −465360

365

370

375

380

385

23.8

23.9

24

24.1

24.2

x [km]

y [k

m]

−490 −485 −480 −475 −470 −465360

365

370

375

380

385

−5

0

5

Horizontal pattern for two adjacent fronts: b (left) & w (right).

One is evidently stable and the other actively unstable.

BAROTROPIC

INSTABILITYSUBMESOSCALE

FRONTOGENESIS

(Kelvin−Helmholz)ISOTROPIZATION

DISSIPATION

INSTABILITY

BAROCLINIC &CLIMATE

FORCING

LARGE−SCALE MICROSCALESUBMESOSCALEMESOSCALE

PROCESS

SCALE

The submeoscale range connects the mesoscale to the microscale by

downscale energy transfers, both potential and kinetic.

It is an inherently different dynamical regime — neither mesoscale

(Ro = V/fL ≪ 1) nor microscale (Ro ≫ 1).

Its primary effects are restratification, interior – boundary-layer

material exchange (ecosystems), frontogenesis, frontal instabilty &

breakdown, partial geostrophic imbalance, and forward energy cas-

cade toward dissipation.

Submesoscale Altimetric Measurements

There are few measurements in situ because of difficult sampling

requirements.

Computational simulations are new but will proliferate.

[OSSEs are possible.]

Principle altimetric objective is documenting global variety, especially

in regions with small ∆SST where surface fronts are obscure and with

differing mesoscale activity levels.

Wide-swath sampling limit (Fu): δη = 1 cm over ∆x = 1 km (cf., 2

cm over 7 km now) ⇒ partial coverage of submesoscale range down

to 4 km radian scale based on k−2ug spectrum, with sparse temporal

sampling.

Issue of confusion with internal tide and other inertia-gravity waves.

[Pattern discrimination is likely to work well.]

Desirability of burst sampling at higher (x, t)-resolution, if feasible

(Alsdorf).

.

Summary

Wide-swath altimetry is a great

opportunity for exploratory measure-

ments of submesoscale (geostrophic)

currents that are probably important

for their roles in oceanic general cir-

culation and biological productivity...

...as well, of course, for its utility for

mesoscale currents.