Ocean data assimilation David Anderson Thanks to Magdalena Balmaseda, Patrick Vidard, Alberto Troccoli,Tim Stockdale

Ocean data assimilation

David AndersonThanks to

Magdalena Balmaseda,Patrick Vidard,

Alberto Troccoli,Tim Stockdale

Outline of lecture

• The ocean observing system

• The assimilation scheme and applications

• Salinity and altimetry

• Bias correction

• Future developments 3dVar, 4dVar, EnKF

Why do we do ocean analyses

• To provide initial conditions for seasonal forecasts.• To provide initial conditions for monthly forecasts

• To provide initial conditions for multi-annual forecasts (experimental only at this stage)

• To monitor the state of the ocean

• We make regular ocean reanalyses covering more than 40 years, but data coverage is limited in early years.

The observing system

• Moorings (Tao, PIRATA AND TRITON) (T)• XBTs (dropped from ships of opportunity) (T)• CTDs (High quality but very few- obtained by research

ships) T and S• SST from satellite (IR,MW), ship and buoys.• SSS from a few ships, from a few moorings, from satellite in

future. (eg SMOS, Aquarius)• Sea level from altimetry (ERS,TOPEX, Jason1, 2)• Current meters (very few ~5 along equatorial pacific)• Subsurface temperature and salinity from ARGO• (T=Temperature, S=Salinity, SST=Sea Surface Temperature, SSS=Sea Surface Salinity, IR=infrared,

MW=micro-wave)

Atlas moorings are the backbone of the equatorial ocean

observing system. They measure T at 10

depths from the surface to 500m. The data are transmitted

via satellite and are on the GTS within a few

hours.

Operating method of ARGO floats.

Floats at 1000m for 10 days then rises to the surface measuring T and S as

they rise. Measurements are then

transmitted by satellite. Some floats descend to 2000m before rising to the

surface.

• Operating

Distribution of 3000 floats.

Upper on a regular grid

(unachievable) and on a random

distribution which might be more

akin to what could be achieved.

Data coverage for March 1993Red =TAO moorings, black = XBTs

Data coverage for March 2002Blue =ARGO

Ocean data assimilationCURRENT SYSTEM-2

• The data assimilation is OI.• The window length is 10 days, with a 6 day delay

for receipt of data.• No assimilation in the upper layer but there is a

strong relaxation (~2days) to observed SST and a weaker relaxation to observed climatological SSS (Sea surface salinity).

• Only T is analysed directly• Salinity and velocity are updated in physical space

(rather than through covariances) • Analysis is done on model levels, one at a time.

• Unlike the atmosphere, a great deal of information about the ocean state can be extracted from the forcing fields, in particular the tropical winds.

• Ocean data can compensate for inaccurate winds, and model errors.

• Any ocean analysis system therefore consists of forcing the ocean model as well as assimilating ocean data.

• The forcing is needed for the previous several years as this is a typical adjustment time for the upper ocean.

• In any event we want the ocean analyses to cover as many years as possible for (seasonal and monthly) forecast validation.

The background error covariance function is highly non isotropic to reflect the nature of equatorial waves- Equatorial Kelvin

waves which travel rapidly along the equator ~2m/s but have only a limited meridional scale as they are trapped to the equator.

Example of ocean analysis EW section along the equator. Atlantic in rightmost panel, Pacific in the middle, Indian in left panel. NS sections also available on web. Most of the action is near the thermocline ~100-50m (also see later).

50OE 100OE 150OE 160OW 110OW 60OW 10OW

Longitude

300

250

200

150

100

50

0

Dep

th (

met

res)

300

250

200

150

100

50

0Plot resolution is 1.4062 in x and 10 in yZonal section at .00 deg NPotential temperature contoured every 1 deg CASSIM: E0 Anomaly (1987-2001 clim)

Interpolated in y

20040328 ( 7 days mean)

-9.5-8.5-7.5-6.5-5.5-4.5-3.5-2.5-1.5-0.50.51.52.53.54.55.56.57.58.59.5

MAGICS 6.8 leda - emos Sun Apr 11 15:02:39 2004

Temperature difference between assimilation and simulation. The assimilation is too warm near the equator. One might

expect the OI to cool the model where it is too warm. Does it?

20O

S 16O

S 12O

S 8OS 4

OS 0O

4ON 8

ON 12

O

N 16O

N 20O

N

Latitude

500

400

300

200

100

0

Dep

th (

met

res)

500

400

300

200

100

0Plot resolution is 2 in x and 10 in yMeridional section at 164.5 deg EPotential temperature contoured every 0.5 deg C: EXPT odoi - odcn

Interpolated in x and y19790101 + 20 yrs 74 days ( 20 year mean)

difference from19790101 + 20 yrs 74 days ( 20 year mean)

-2

-1.5

-1

-1 -1

-1

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

0.5

0.5

0.5

0.5

0.5

0.5

1

1

1

1

1

1.5

1.5

2

2

2

-6

-5

-4

-3

-2

-1

0.5

1.5

2.5

3.5

4.5

5.5

MAGICS 6.6 leda - neh Mon Apr 28 17:07:47 2003

Mean temperature increment. This pattern does not look like the previous figure. Data assimilation is correcting for systematic error but not in an obvious way. Propagation, advection, data distribution all contribute,

including a possible spurious circulation set up by the assimilation itself (see later).

20O

S 16O

S 12O

S 8OS 4

OS 0O

4ON 8

ON 12

O

N 16O

N 20O

N

Latitude

500

400

300

200

100

0

Dep

th (

met

res)

500

400

300

200

100

0Plot resolution is 2 in x and 10 in yMeridional section at 164.5 deg Eassim_incr contoured every 3 decC/y: EXPT odoi

Interpolated in x and y

19790101 + 20 yrs 74 days ( 20 year mean)

-12-9

-6

-6

-3-3

-3

-3

3

3

6

6

912

-36

-30

-24

-18

-12

-6

3

9

15

21

27

33

MAGICS 6.6 leda - neh Mon Apr 28 16:55:43 2003

Univariate data assimilation can be a problem

• We have temperature data to assimilate but until recently, no salinity data. Velocity data remain scarce.

• Unfortunately leaving salinity untouched can lead to instabilities. The following slide shows the problems that can occur if salinity is not corrected. A partial solution is to preserve the water-mass (T-S) properties below the surface mixed layer. In system-1, salinity was not corrected. It is corrected but not analysed in system-2. It is corrected and analysed in system-3.

• The OI increments are spread uniformly throughout the assimilation window, to allow the model to spin-up its own velocity field.

3 months into assimilation

Stratified Temp at I.C

Meridional Sections (Y-Z) 30W

Temperature

Salinity

Constraint: To update salinity to preserve the water mass properties

(Troccoli et al 2001)

Temperature

SalinitySpurious

Convection Develops

• So, by modifying S to conserve the model T-S profile, gross errors in S and T can be avoided, even though there are few measurements of S. Comparison of model sea level to altimetry shows that the fit in the Pacific is good and that in the Atlantic is improved but still not ideal.

How many analyses?

• An ensemble of ocean analyses is created.• Five ocean analyses are created by perturbing the

wind stress with perceived uncertainty. (These analyses are used to create an ensemble of forecasts.) The purpose of creating an ensemble of ocean analyses is to represent some of the uncertainty in knowing the ocean state. These analyses are used in creating the ensemble of forecasts in System-2 (the current ECMWF seasonal forecast system and in the monthly forecast system).

This plot shows a north-south section along 140W in the Pacific (upper) and the standard deviation of the temperature induced by the wind perturbations but controlled by data assimilation.

Note the different scales.

The variability (uncertainty) is not particularly small compared with the size of the signal.

Delayed Ocean Analysis ~11 days

Real Time Ocean Analysis ~8 hours

New

ECMWF:

Weather and Climate Dynamical Forecasts

ECMWF:

Weather and Climate Dynamical Forecasts

10-Day Medium-Range

Forecasts

10-Day Medium-Range

Forecasts

Seasonal Forecasts

Seasonal Forecasts

Monthly Forecasts

Monthly Forecasts

Atmospheric model

Wave model

Ocean model

Atmospheric model

Wave model

Real Time Ocean Analysis•“Delayed” Ocean Analysis:

•Used as I.C. of Seasonal Forecasts

•Early delivery Ocean Analysis:

•Used as I.C. for Monthly Forecasts

Ocean Analysis (seas)

Real time ocean analysis

Heat,Wind stress, P-E

t-11 days

Heat,Wind stress, P-E

todayObs-OI

Obs-OI

The future• Later this year• We plan to implement an updated analysis system as part of System-3• S assimilation• Altimeter assimilation • Bias correction• Different wind and temperature perturbations

• Longer Term• Under development is a 3d and 4d var system.• These use the incremental approach as in meteorology.• In 4d var• a) Full nonlinear model is used for outer loops• b) An approximation to this is linearised• c) An exact adjoint to b) is generated• The cost function is quadratic and minimisation speeded up.• 5 inner loops to 1 outer loop

New Features

•ERA-40 fluxes to initialize ocean

•Retrospective Ocean Reanalysis back to 1959.

•Multivariate on-line Bias Correction .

•Assimilation of salinity data.

•Assimilation of altimeter-derived sea level anomalies.

•3D OI

System-3

•Ocean model: HOPE (~1degx1deg, increasing to 1/3deg near the equator to resolve equatorially trapped waves such as the Kelvin wave)

•Assimilation Method OI

•Assimilation of T + Balanced relationships (T-S, ρ-U)

•10 days assimilation windows, increment spread in time

System 3: Assimilation of Salinity Observations

Idea: perform a second OI using T+S data to correct the T/S relationship (Haines et al 2005 ECMWF TECH Memo)

T/S

Changedinsituinsitu ST ,

aa ST ,

T/S

conserved

', aa ST

2

2

2

2 )(

'K R

oa

T

TT

R

r

ee

Motivations: • Known drift in salinity• S of T scheme improves S and T but not enough• Number of salinity data recently increased (ARGO)

insituT

' ' '( ) ( ) K ( ( ) H ( ))a a a a o o a oS T S T S T S T

• By analysing S on T surfaces, rather than z, we can spread the influence of data over larger distances, and so extract more information from the S data.

Altimetery

• From satellites such as Topex, Jason and ERS, one can detect changes in the bending of the top surface of the ocean. This bending is small- in many places only a few cms, in some places up to ~30cms during El Nino for example. How to use this surface data to alter the density field beneath the surface?

• The way it is done here is to displace the T-S profile vertically to match the sea-level. This preserves the T-S relation, which is a reasonable approximation throughout much of the water column but less likely to hold in the surface layer. Measurements of surface salinity would help.

• Measurements of mean sea level would help to correct the mean state. Three satellites to help improve the mean sea level are in progress. (Two are already in orbit). GRACE, CHAMP, GOCE

• Using a mean sea level from geodetic missions has proved difficult. So we have reverted to using the model mean state.

System3: Assimilation of Altimeter Data

How to extract T/S information from Sea Level?How to combine Sea level and subsurface data?

altaltbckobs ST ,

insituinsitu ST ,

11 , bckbck ST

Cooper and Haines, 1999

bckTbckS

aTaS

Based on altimetry, we modify the model T and S. These are then used as

background fields in an OI assimilating T and correcting S to preserve TS.

Assimilation in the ECMWF operational system 3- Altimetry and salinity. Altimeter data are used first,

then in situ S

T/S

conserved

alt T/S

Changedinsituinsitu ST ,

aa ST ,

Assimilation of S(T) not S(z)

insituT

T/S

conserved

', aa STbckT

Assimilation of Salinity

1S 2S

1 2

0 ( ) ( )

( ) ( )

a b o bT

a b o o b oS S

T T T z T z

S S S T S T

K

K K

Contribution To ENACT: Assimilation of salinity along T surfaces

are orthogonaland

(TM #458, Haines et al MWR)

Nice property:

Data coverage for Nov 2005

60°S 60°S

30°S30°S

0° 0°

30°N30°N

60°N 60°N

60°E

60°E

120°E

120°E

180°

180°

120°W

120°W

60°W

60°W

0°

0°

X B T p r o b e s : 9 3 7 6 p r o f i l e sOBSERVATION MONITORING Changing observing

system is a challenge for consistent reanalysis

Today’s Observations will be used in years

to come

60°S 60°S

30°S30°S

0° 0°

30°N30°N

60°N 60°N

60°E

60°E

120°E

120°E

180°

180°

120°W

120°W

60°W

60°W

0°

0°

▲Moorings: SubsurfaceTemperature

◊ ARGO floats: Subsurface Temperature and Salinity

+ XBT : Subsurface Temperature

Data coverage for June 1982

North Atlantic:

T300 anomaly

North Atlantic:

S300 anomaly

Climate Signals….

…or spurious trends due to changing observing system?

Salinity Trend in North Atlantic

ALL NO_ALTI NO_ARGO NEITHER Without ARGO, the salinity trend is half the size

• ECMWF participated in the EU project ENACT

• This involved multi model, multi method, multi-annual ocean reanalysis.

• The data are freely available for anyone interested

anom GLOBAL Averaged temperature over the top 300m

1965 1970 1975 1980 1985 1990 1995 2000Time

-0.3

-0.2

-0.1

0.0

0.1

0.2

3DVAR(T)-CERFACS (0.077)

OI(T)-ECMWF (0.064)

OI(T)-INGV(0.073)

OI(T+S)-MetOffice (0.077)

OI(T+S)-ECMWF (0.067)

OI(T+S)-INGV(0.073)

Obj Analysis (0.069)

CTL-OPA (0.038)

CTL-HOPE (0.040)

CTL-UM (0.039)

anom GLOBAL Averaged salinity over the top 300m

1965 1970 1975 1980 1985 1990 1995 2000Time

-0.04

-0.02

0.00

0.02

0.04


OI(T)-ECMWF (0.011)

OI(T)-INGV(0.007)



OI(T+S)-INGV(0.007)


CTL-OPA (0.002)

CTL-HOPE (0.009)

CTL-UM (0.007)

ENACT

Multi-model, multi assimilation methods ocean reanalysis

anom GLOBAL Averaged temperature over the top 300m

1965 1970 1975 1980 1985 1990 1995 2000Time

-0.3

-0.2

-0.1

0.0

0.1

0.2


OI(T)-ECMWF (0.064)

OI(T)-INGV(0.073)



OI(T+S)-INGV(0.073)


CTL-OPA (0.038)

CTL-HOPE (0.040)

CTL-UM (0.039)

anom NINO3 Averaged temperature over the top 300m

1965 1970 1975 1980 1985 1990 1995 2000Time

-2

-1

0

1

2

3

4


OI(T)-ECMWF (0.749)

OI(T)-INGV(0.715)



OI(T+S)-INGV(0.715)


CTL-OPA (0.629)

CTL-HOPE (0.633)

CTL-UM (0.652)

anom NINO3 Averaged salinity over the top 300m

1965 1970 1975 1980 1985 1990 1995 2000Time

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20


OI(T)-ECMWF (0.038)

OI(T)-INGV(0.024)



OI(T+S)-INGV(0.024)


CTL-OPA (0.023)

CTL-HOPE (0.021)

CTL-UM (0.021)

For the Nino3 region in the equatorial east Pacific, most analyses agree on the T; the intermodel variation is small compared to the signal. For salinity this is not true.

The Ensemble Kalman Filter (EnKF)

• The advantage of the EnKF approach is that it is based on the full nonlinear equations. No linearizations or closure assumptions are needed as for the extended Kalman filter and no adjoint equations are needed as for 4d var.

• The EnKF will be tested at ECMWF in the coming year using a global ocean GCM. The size of the ensemble will be ~100. Is this big enough? This work is part of the ENSEMBLES project of the EU.

ENSEMBLE KALMAN FILTERING

The equation for EnKF looks just like OI except A, D are matrices. Typically A would be n x N where n is the dimension of model space and N is the size of the ensemble (~100). An SVD of the first bracketed term allows for practical solution of this equation.

)()( 1 HADRHHPHPAA eT

eT

ea

)()( 1 fjje

Tfe

Tfe

fj

aj HdRHHPHP

)()( 1 fTfTffa HdRHHPHP

TTe

Te UURHHP

Some references related to ocean data assimilation at ECMWF

• Ocean data assimilation for seasonal forecasting. D Anderson in ECMWF Seminar Proceedings Sept 2000.

• Three and four dimensional variational assimilation with a general circulation model of the tropical Pacific. Weaver, Vialard, Anderson and Delecluse. ECMWF Tech Memo 365 March 2002. See also Monthly Weather Review 2003, 131, 1360-1378 and MWR 2003, 131, 1378-1395.

• Balanced ocean data assimilation near the equator. Burgers et al J Phys Ocean, 32, 2509-2519.• Salinity adjustments in the presence of temperature adjustments. Troccoli et al Monthly weather rev

130, 89-102.• Comparison of the ECMWF seasonal forecast Systems1 and 2.. Anderson et al ECMWF Tech Memo

404.• Sensitivity of dynamical seasonal forecasts to ocean initial conditions. Alves, Balmaseda, Anderson

and Stockdale. Tech Memo 369. Quarterly Journal Roy Met Soc. 2004. February 2004• Recent developments in data assimilation for atmosphere and ocean. ECMWF Seminar Sept 2003.

See Balmaseda and Weaver articles.• An ensemble Kalman smoother for nonlinear dynamics. Evensen and van Leeuwen Mon Weather Rev

128, 1852-1867.• The ensemble Kalman filter: theoretical formulation and practical implemenation. Evensen. Ocean

Dynamics 2003. 53, 343-367. • Salinity assimilation usinf S(T) relationships. K Haines et al Tech Memo 458. Mon Wea Rev in press.

Documents

Ocean data assimilation David Anderson Thanks to Magdalena Balmaseda, Patrick Vidard, Alberto Troccoli,Tim Stockdale