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“Combining Ocean Velocity Observations and Altimeter Data for

OGCM Verification”

Peter Niiler

Scripps Institution of Oceanography

with original material from

N. Maximenko, M.-H.Rio, L. Centurioni, C. Ohlmann, B. Cornuelle, V. Zlotnicki,, D.-K. Lee

Method of Calculating Ocean Surface Circulation Combines Drifter and

Satellite Observations Between 1/1/88 and 12/1/06 1988 10,561 drifters drogued to 15m depth

were released in the global ocean, with array of 1250 since 9/18/05

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Satellite Observationssea level = altimeter height - geoid height

• Altimeters: GEOS, T/P, JASIN, ERS I&II• Data from 1992 - Present (rms noise: +/- 4cm

relative to geoid)• GRACE’04: Estimated accuracy of geoid: +/-3 cm

at 400 km horizontal scale• Sea level gradient, or geostrophic velocity,

depends upon method and scale of averaging, or mapping, of sea level data

Drifter velocity observations are accurate (+/- 0.015 m/sec daily averages), but spatial distribution of data

can result in biased averages in space and time

Altimeter data is used to calculate geostrophic velocity with “smoothing” scales (and amplitude

correction) consistent with drifter data: e.g. AVISO

0 10 20 30 40 50

40

60

80

100

120

140

160

Bin Center Latitude

Geostrophic Velocity Smoothing Scale vs. Latitude

N. Hemi

S. Hem i

N. Hemi dmn

S. Hemi dmn

N. Hemi nolev

S. Hemi nolev

• • •

••

••

••

• N/S ; *E/W AVISO Correlation Scales

*

*

B. Cornuelle

Drifter observed rms velocity variance [<u’2>+<v’2>]1/2



N.Maximenko

Log10 (Eddy Energy/ Mean Energy)1/2



N. Maximenko

The” simple method” of obtaining a velocity map

€

rV G =

r V o + A <

r V 'G−AVISO >

r V GD =

v V D −

r V EK (W , f ,...)

Minimize E relative to A,r V o :

E = <r V GD −

drifter obs<>

∑r V o − A

r V 'G−AVISO >2

Solution depends on vector correlation : C =<

r V 'DG ⋅

r V 'G−AVISO >

[<r V 'DG ⋅

r V 'DG ><

r V 'G−AVISO ⋅

r V 'G−AVISO >]1/ 2

MAP :r V MAP =

r V o + A

r V 'G−AVISO +

r V EK

Vector Correlation between drifter and altimeter

derived AVIO geostrophic velocity anomalies

N.Maximenko

“East Sea”: 3 day average velocity from “simple method” vs drifter obs. 8/01-11/03

D.-K. Lee

Comparison drifter and ECCO 15m zonal velocity components in tropical Pacific

18

Mean U (cm/s) at 15m depth from Drifters

B. Cornuelle

Vector correlation and scatter plots of “geostrophic” velocity residuals from drifters and AVISO in California Current

L.Centurioni

HYCOM NLOM POP ROMS

spatial domain global global global ~1000 x 2000 km (USWC)

vertical coordinates hybrid layers levels sigma (ETOPO5)

horizontal resolution 1/12° (~7 km) 1/32° (~3.5 km) 1/10° (~10 km) ~5 km

vertical layers/levels 26 6 + ML 40 20

time step 6 hour 6 hour 6 hour 15 minute

mixed layer KPP Kraus-Turner KPP KPP

wind forcing ECMWF NOGAPS/HR NOGAPS COADS (seasonal)

heat forcing ECMWF NOGAPS ECMWF COADS (seasonal)

buoyancy forcing COADS(restored to

Levitus)

Levitus(restoring)

Levitus (restoring)

COADS (seasonal); parameterization for

Columbia River outflow

integration time 1990-2001 1991-2000 1990-2000 9 years

assimilation none SST, SSH none none

other Low computational

cost

open boundaries

C. Ohlmann

L.Centurioni and C. Ohlmann

Unbiased drifter and satellite derived geostrophic 15m velocity (on left) and ROMS 5km resolution sea level (right)

Geostrophic zonal velocity from drifter and altimeter data

L. Centurioni

Decadal MEAN SEA LEVEL (cm) in models of the California Current

C. Ohlmann

OGCM (Eddy Energy)1/2: California Current

NLMHYCO

POP ROMS

Geostrophic EKE0.5 ROMS (left) corrected AVISO (right) (0-20 cm s-1)

L. Centurioni and C. Ohlmann

Ageostrohic 15m velocity and MSL in 5km resolution ROMS of California Current

C. Ohlmann

THE GLOBAL SOLUTIONS

1. Time mean surface momentum balance for surface sea level gradient:

• Observed drifter = “D”

• Computed Ekman = “E”

€

−< ∇η >= ˆ f x<r v D −

r v E > + < d

r v D / dt >≡ −

r F

€

uE + ivE = A(lat)(Wx + iWy )( NCCEP wind)

2. Compute sea level that minimized the global cost function in least square

The solution is also minimized relative to parameters of Ekman force and GRACE altimeter referenced sea level, Go, is averaged on 1000km scales.

Maximenko-Niiler

€

∂∂ηo

{4π 2

L2| Go

globe

∫∫ − ηo |2 dS + | ∇η o −r F |2

globe

∫∫ dS + 4δ 2 | ∇2η o |2

globe

∫∫ dS} = 0

with (ηoglobe

∫∫ )dS = 0; L = 1000km; δ =1

2

o

(km)€

ηo

€

ηo

3. Perform an objective mapping of sea level, with mesoscale based, geostrophic, correlation

functions, as a linear combination of:

• Levitus 1500m relative steric level, • GRACE referenced altimeter derived sea level

• Drifter geostrophic velocity.

RIO(05), Knudsen-Andersen

1992-2002 Mean Sea Level: Maximenko (05)

Zonal, unbiased geostrophic velocity (-10,+10 cm/sec)

1993-1999 Mean Sea Level: RIO (05)

M.-H. Rio

Difference between Maximenko(‘05)-Rio(‘05) MSL with both data adjusted to 1993-1999 period

M.-H. Rio : RMS difference of 5cm

Comparison of 15m velocity from SURCOLF and MERCATOR near real time maps of Gulf Stream

region with drifter data

M.-H. Rio

Mean Sea Level: Knudsen-Anderson

V. Zlotnicki

ECCO-2 CUBE49 (18km horizontal, global assimilation with flux and diff.par.optim.)

V. Zlotnicki

ECCO-2 cube 37 and 49 east velocity difference from Maximenko (05) and Knudsen-Anderson

V. Zlotnicki

CONCLUSIONS

• Combined drifter and altimeter derived velocity anomalies can be used to make regional, realistic, near real time maps of 15m ocean circulation.

• Global, absolute sea level on 50km scale from combined data displays new circulation features.

• OGCM solutions are most stringently tested with velocity fields derived from combined drifter and altimeter observations.

“Why does our view of ocean circulation always have such a

dreamlike quality…”...Henry Stommel

THE DREAM HAS COME TRUE…

we are observing the circulation

peter niiler

East-west average vorticity balance at 15m depth (black line is from Ekman’s 1906 model, shaded is drifter data; 100 km coastal and western

boundary currents excluded)

The eddy transport of vorticity

The eddy transport vector of vorticity is computed around the Gulf Stream eddy energy maximum.

€

< dr v /dt > −d <

r v > /dt =

1

2∇(<

r v '⋅

r v '>) + ˆ k × < ς '

r v '>

The eddy vorticity transport vector is < ς 'r v '>, where

relative vorticity is ς = ∂v /∂x − ∂u /∂y. In quasi − geostrophic

theory, ς '= (g∇ 2η ') / f0;η ' is obtained from altimeters.

North Atlantic:

0.25º resolution sea level (upper) and “simple” geostrophic velocity (lower).

The 1992-2000 time average quasi-geostrophic eddy vorticity flux vector in the

Gulf Stream region.

The mean kinetic energy at 15m depth from drifters. This quantity graphed is (<v’•v’>/2g) and represents the sea level change caused by Bernoulli effect

of ocean time variable eddies.

SST convergence (x10-7Cºsec-1) at 15m depth:

€

< r

v > ⋅∇(< SST >)

€

1978-2003 Average drifter velocity with QSCT/NCEP blended wind-stress divergence

Conservation of vorticity in the Agulhas Extension Current

Drifter geostrophic velocity compared with ocean circulation model sea-level in California Current in POP (left) and UCLA/ROMS (right)

POP SSH (1990-2000) and geostrophic drifter velocity

132oW 128oW 124oW 120oW 116oW

28oN

32oN

36oN

40oN

44oN

20 cm s 1

10

15

20

25

Global streamlines of 1992-2002 average 15m depth velocity

Zonal, unbiased geostrophic velocity (-40,+40cm/sec)