Training Course 2009 – NWP-DA: Ocean Data Assimilation 1 Data assimilation in the ocean Magdalena A. Balmaseda

Training Course 2009 – NWP-DA: Ocean Data Assimilation 1

Data assimilation in the ocean

Magdalena A. Balmaseda


Outline of lecture

• Applications of ocean data assimilation: Importance of ocean data assimilation on the seasonal forecasts. Ocean data assimilation and historical ocean reanalyses.

• The ocean observing system

• Typical ocean data assimilation system Background co-variances: spatial scales Balance relationships for salinity and velocity Altimeter and Salinity data Bias correction

• Future directions Ocean in the Medium Range forecast Ocean initialization for climate projections. The “myth” of coupled data assimilation


Why do we do ocean analyses?

• Climate Resolution (global ~1x1 degrees)

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 reconstruct the history of the ocean (re-analysis)

• High resolution ocean analysis (regional, ~1/3-1/9-1/12

degrees)

To monitor and to forecast the state of the oceanDefense, commercial applications (oil rings…)


Ocean Data Assimilation Activities in the Community

• Operational real time high resolution, mostly regional, no reanalysis:

FOAM (MO), MERCATOR, NRL,CSIRO,…

• Operational real time, global, reanalysis (seasonal/decadal forecasts): ECMWF, MO, Meteo-France/MERCATOR, NCEP, MRI, JMA…

• Research, mainly climate reanalysis: ENACT consortium, ECCO consortium, GSOP.


Delayed Ocean Analysis ~12 days

Real Time Ocean Analysis ~Real time

ECMWF:

Weather and Climate Dynamical Forecasts

ECMWF:

Weather and Climate Dynamical Forecasts

18-Day Medium-Range

Forecasts

18-Day Medium-Range

Forecasts

Seasonal Forecasts

Seasonal Forecasts

Monthly Forecasts

Monthly Forecasts

Ocean model

Atmospheric model

Wave model

Atmospheric model

Ocean model

Wave model


Basis for extended range forecasts: monthly, seasonal, decadal

• The forecast horizon for weather forecasting is a few days. Sometimes it is longer e.g. in blocking situations 5-10 days.

• Sometimes there might be predictability even longer as in the intra-seasonal oscillation or Madden Julian Oscillation.

• But how can you predict seasons, years or decades ahead?

• The feature that gives longer potential predictability is forcing given by slow changes on boundary conditions, especially the to the Sea Surface Temperature (SST)

Atmospheric responds to SST anomalies, especially large scale tropical anomalies El Nino/Southern Oscillation is the main mode for controlling the predictability of the

interannual variability.


•In the equatorial Pacific, there is considerable interannual variability. • The EQSOI ( INDO-EPAC) is especially useful: it is a measure of pressure shifts in the tropical atmosphere but is more representative than the usual SOI (Darwin – Tahiti). •Note 1983, 87, 88, 97, 98 .

Sea Level Pressure (SOI) Sea Surface Temperature (Nino 3)

Nino 3Nino 3.4

•SST variability is linked to the

atmospheric variability seen on previous

slide suggesting a strongly coupled

process.


Need to Initialize the subsurface of the ocean


Equatorial Atlantic: Taux anomalies

Equatorial Atlantic upper heat content anomalies. No assimilation

Equatorial Atlantic upper heat content anomalies.

Assimilation

ERA15/OPS

ERA40

Uncertainty in Surface Fluxes:

Need for Data Assimilation

• Large uncertainty in wind

products lead to large

uncertainty in the ocean

subsurface

• The possibility is to use

additional information from

ocean data (temperature,

others…)

• Questions:

1. Does assimilation of ocean data constrain the ocean state?

2. Does the assimilation of ocean data improve the ocean estimate?

3. Does the assimilation of ocean data improve the seasonal forecasts


ORA-S3• Main Objective: Initialization of seasonal forecasts

Historical reanalysis brought up-to-date (12 days behind real time) Source of climate variability

Main Features

•ERA-40 daily fluxes (1959-2002) and NWP thereafter

•Retrospective Ocean Reanalysis back to 1959

•Multivariate on-line Bias Correction (pressure gradient)

•Assimilation of temperature, salinity, altimeter sea level anomalies an global sea level trends.

•3D OI, Salinity along isotherms

•Balance constrains (T/S and geostrophy)

•Sequential, 10 days analysis cycle, IAUBalmaseda etal 2007/2008


Correlation with OSCAR currents

Monthly means, period: 1993-2005

Seasonal cycle removed

No Data Assimilation Assimilation:T+S

Assimilation:T+S+Alt

Data Assimilation improves the interannual variability of the ocean analysis


Ocean data assimilation also improves the forecast skill

(Alves et al 2003)

Data Assimilation

Data Assimilation

No

Da

ta

As

sim

ila

tio

nN

o D

at a

A

ss

imi l

at i

on

Impact of Data Assimilation

Forecast Skill


OCEAN REANALYSIS

• As well as initializing the seasonal forecasts, the ocean reanalysis is an important source for climate variability studies: Meridional Overturning Circulation Trends in the upper ocean heat content Attribution of Sea level rise


This cartoon shows the 3 dimension circulation of the ocean. Note the differences between the North Atlantic which has deep water formation and the North Pacific which does not. Note also

the Indonesian throughflow.

Thermohaline Circulation


Estimation of the Atlantic MOC

Assimilation No-Data Bryden etal 2005 Cunningham etal 2007

From Balmaseda etal 2007


North Atlantic:

T300 anomaly

North Atlantic:

S300 anomaly

Climate Signals….


Ocean circulation: some facts

• The radius of deformation in the ocean is small (~30km). So one expects things to happen on much smaller scales than in the atmosphere where the radius of deformation is ~3000km.

[Radius of deformation =c/f where c= speed of gravity waves. In the ocean c~<3m/s for baroclinic processes.]

• The time scales for the ocean cover a much larger range than

for the atmosphere: slower time scales for adjustment.• The ocean is strongly stratified in the vertical.• The ocean is forced at the surface by the wind, by

heating/cooling and by fresh water fluxes (precip-evap).• The electromagnetic radiation does not penetrate into the

ocean, which makes the ocean difficult to observe from satellites.


The Ocean Observing system

ARGO floatsXBT (eXpandable BathiThermograph)Moorings

Satellite

SST

Sea Level


Time evolution of the Ocean Observing System

XBT’s 60’s Satellite SST Moorings/Altimeter ARGO

1982 1993 2001

1998-1999 PIRATA

TRITON

Gravity info:

GRACE

GOCE

2008

SSS info:

Aquarius

SMOS


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

Ocean Observing System


•The background error correlation scales are 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.

Length scales for a typical climate model:

~2 degree at mid latitudes

~15-20 degrees along the eq.

Typical cycling: 10 day window

Complex structures an smaller length scales near coastlines are usually ignored.

Background errors


Density dependent correlation scales

•The 3-D background length scales can also depend on both geographical distance and density differences.


• From , a salinity increment by preserving the water mass characteristics (Troccoli et al, MWR,2002)

S(T) scheme: Temperature/Salinity relationship is kept constant

• From ,velocity is also updated by introducing dynamical constraints (Burgers et al, JPO 2002)

It prevents the disruption of the geostrophic balance and the degradation of the circulation. Important close to the equator, where the time scales for inertial adjustment are long.

Updates to Salinity and Velocity

,T S

T BalS


Balance relationship for Salinity

• 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 the last decades there have been 3 generations of ocean data assimilation systems:

G1: salinity was not corrected. G2: “ is corrected but not analysed in system-2 (Troccoli etal 2002). G3: “ is corrected and analysed in system-3 (Haines etal 2006).


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 2002)

Temperature

SalinitySpurious

Convection Develops


Updating Salinity: S(T) SCHEME

S

A) Lifting of the profile

Tanal

Tmodel

B) Applying salinity Increments

Sanal

Smodel


Sea Level Anomaly from Altimetry

El Nino 197/98Sea Level anomaly

Equatorial Temperature anomaly


Balance relationship: vertical projection of sea level anomaly

•Vertically stratified fluid: Lets take a 2 layer model, where the density of the second layer is

only a little greater than that of the upper layer.

Typically

•A 10cm displacement of the top surface is associated with a 30m

displacement of the interface (the thermocline).

10cm

30 m

If we observe sea level, one can infer information on the vertical density structure

' / / 300og g g


A linearized balance operator for global ocean assimilation

• Define the balance operator symbolically by the sequence of equations

kU

kB

kU

kkvp

k

kU

kB

kU

kkup

k

kU

kB

kU

kkk

kU

kB

kU

kkST

k

kkk

vvvpv

uuupu

SSSTS

TTT

1

1

1

1

K

K

K

K

kp

kp

k

kkS

kkT

k

p

ST

KK

KK

11

Treat as approximately mutually independent

Temperature

Salinity

SSH

u-velocity

v-velocity

Density

Pressure(Weaver et al., 2005, QJRMS)


Components of the balance operator

kfk

B

kfk

B

zz

k

Hz

kB

k

TTSS

kkB

p

af

Wv

p

aa

W

f

Wu

dzzdzH

TTz

zSS

kk

~

cos

11

~111

/)(

0

0

0

0

0

111

Salinity balance(approx. T-S conservation)

SSH balance(baroclinic)

u-velocity balance(geostrophy with β-plane approx. near eq.)

v-velocity(geostrophy, zero at eq.)

Density(linearized eq. of state)

Pressure(hydrostatic approx.)

k

UkB

zz

kk

kU

kB

kkkk

gzdgzzp

SST

0

0

110

)()(~

correctionplane


• Example: 3D-Var assimilation of a single T obs. at 100m on the eq.

• The β-plane geostrophic approximation results in a continuous zonal velocity increment across the equator.

Multivariate structures implied by the balance opt.

Courtesy of A. Weaver


Projecting altimeter data into the subsurface via the balance

operator (and its adjoint)

• Example: 3D-Var assimilation of a single SSH obs. at the eq.

• The anisotropic response is a combination of a background state dependence in 1) the salinity balance; 2) the linearized equation of state; and 3) the temperature error variance parameterization. Courtesy of A. Weaver


Assimilation of altimeter data

Ingredients:

• The Mean Sea Level is a separate variable, and can be derived from Gravity information from GRACE (Rio4/5 from CLS, NASA, …) and future GOCE. But the choice of the reference global mean is not trivial and the system can be quite sensitive to this choice. Active area of research.

• The GLOBAL sea level changes can also assimilated:

Ocean models are volume preserving, and can not represent changes in GLOBAL sea level due to density changes (thermal expansion, ….).

The difference between Altimeter SL and Model Steric Height is added to the model as a fresh water flux.

alt'

obsalt '

Observed SLA from T/P+ERS+GFORespect to 7 year mean of measurements

A Mean Sea Level


Mean Dynamic Topography differences

•Systematic differences between MODEL-MDT and GRACE derived products:

Pacific-Atlantic SL gradient is steeper in MODEL-MDT

•We need appropriate methods to treat this systematic difference in the assimilation scheme.

•If correct, the information from GRACE-MDT could be used before the altimeter era.

For System 3 we have chosen the MODEL_MDT


Results are very sensitive to the MDT

TRATL Averaged temperature over the top 300m

1992 1994 1996 1998 2000 2002 2004Time

17.8

18.0

18.2

18.4

18.6 MODEL MDTNASA MDTRIO5 MDT

Not good for consistent historical reanalysis


Why a bias correction scheme?

• A substantial part of the analysis error is correlated in time.

• Changes in the observing system can be damaging for the representation of the inter-annual variability.

• Part of the error may be induced by the assimilation process.

What kind of bias correction scheme?

• Multivariate, so it allows to make adiabatic corrections (Bell et al 2004)

• It allows time dependent error (as opposed to constant bias).

• First guess of the bias non zero would be useful in early days (additive

correction rather than the relaxation to climatology in S2)

• Generalized Dee and Da Silva bias correction scheme

Balmaseda et al 2007

Bias Correction Scheme


Impact of data assimilation on the mean

Assim of mooring data

CTL=No data

Large impact of data in the mean state: Shallower thermocline

PIRATA

EQATL Depth of the 20 degrees isotherm

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002Time

-95

-90

-85

-80

-75

-70ega8 omona.assim_an0edp1 omona.assim_an0


The systematic error may be the result of the assimilation process

T-Assim incr (C.I=0.05 C/10 days)

Vertical velocity (C.I=0.5m/day)

No-data assim

-0.8 -0.4 0 0.4 0.8temperature

-200

-100

Dept

h (m

)

S2-a S2-cMean(198901-200101) of Model minus Observ ations

nino3-All in situ dataMean Analysis – ObsNINO 3: Eastern Pac

100m

200m


The Assimilation corrects the ocean mean state

Free model

Data Assimilation

z

(x)Equatorial Pacific

Data assimilation corrects 2 sorts of systematic errors:

• The depth of the equatorial thermocline:

•Probably diabatic. Possible to correct

• The slope of the equatorial thermocline

•Adiabatic: not easy to correct

by diabatic corrections.


Bias evolution vector-equation

Some notation (Temperature,Salinity,Velocity)

1( ) ;

, , ;

, , ; , ,

f f a fk k k k k k k k

T

T T T T TT S T SU U

x x b b d y H x

x T S U

b b b b L K L L

k

U

S

T

a

kU

S

T

kU

S

T

a

kU

S

T

d

L

L

K

b

b

b

b

b

b

b

b

b~

1

prescribed (constant/seasonal)k

fkk

fk

b

bbb ; 1

kb


Bias and circulation

T-Assim incr (C.I=0.05 C/10 days)

Vertical velocity (C.I=0.5m/day)

Standard

Balmaseda etal 2007

Bias corrected: pressure


Effect of bias correction on the time-evolution

Assim of mooring dataCTL=No dataBias corrected Assim

EQATL Depth of the 20 degrees isotherm

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002Time

-95

-90

-85

-80

-75

-70

-65 ega819930101 omona.assim_an0edp119930101 omona.assim_an0000119590101 omona.assim_an0


Future directions:

• Pros and Cons of uncoupled versus coupled data assimilation: A feasible solution is to have a 2-tier approach: atmosphere initialization

including and ocean model. It is desirable to use the same model in the assimilation and in the forecast

• Interactive ocean in the medium range weather forecasts?

Lead/lag relationship between SST and tropical convection

The initialization at high of the ocean subsurface may be important in the

prediction of tropical cyclones.

• Ocean initialization for decadal forecasts.

Is it relevant?

How to do it?


Initialization: uncoupled versus coupled

• Advantages: It is possible

The systematic error during the initialization

is small(-er)

• Disadvantages: Model is different during the initialization and

forecast

Possibility of initialization shock

No synergy between ocean and atmospheric observations

•Full Coupled Initialization:

No clear path for implementation in operational

systems due to the different time scales.

Difficult to initialize the atmosphere and the

ocean simultaneously

•Weakly-coupled initialization

IT IS FEASIBLE

Atmosphere initialization with a coupled model

Ocean initialization with a coupled model.

Need of a good algorithm to treat model error.

Uncoupled: Most common Other Strategies


Example: Phase between SST and tropical convection

Composites of SST anomalies (contours) and OLR (colours) of MJO events. SST and

convection are in quadrature.

The lead-lag relationship between SST and deep convection seems instrumental for setting the propagation speed of the MJO.

A two way coupling is required, but may not be enough. Thin ocean layers are needed to represent this phase relationship.


From Ginis 2008Ocean Initial Conditions may be important


Future developments at ECMWF

• NEMOVAR: Variational DA for the NEMO model Incremental approach 3d and later 4dvar Different resolutions in inner-outer loop

• Ongoing scientific developments: Ensemble methods for flow dependent covariances

(with 3d-var) Choice of control variables (density/spiciness) Treatment of Observation and Model bias


Summary

• Data assimilation in the ocean serves a variety of purposes, from climate monitoring to

initialization of coupled model forecasts.

• Compared to the atmosphere, ocean observations are scarce. The main source of

information are Temperature and salinity profiles (ARGO/moorings/XBTs), sea level from

altimeter, SST from satellite/ships and Geoid from gravity missions.

• Assimilation of ocean observations reduces the large uncertainty(error) due to the forcing

fluxes. It also improves the initialization of seasonal forecasts, and it can provide useful

reconstructions of the ocean climate.

• Data assimilation changes the ocean mean state. Therefore, consistent ocean reanalysis

requires an explicit treatment of the bias. More generally, we need a methodology that

allows the assimilation of different time scales.

• The DA activities in the ocean are reaching maturity, after a steep learning curve during the

90’s. However, the results provided by the different assimilation methods is “too” diverse.

Work is needed for the consolidation and development of methodologies.

• The separate initialization of the ocean and atmosphere systems can lead to initialization

shock during the forecasts. A more balance “coupled” initialization is desirable, but it

remains challenging.


Some references related to ocean data assimilation at ECMWF

• The ECMWF System 3 ocean analysis system, Balmaseda et al 2008. To appear in Mon. Wea. Rev. See also ECMWF Tech-Memo 508.

• 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., MWR..

• 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

• A Multivariate Treatment of Bias for Sequential Data Assimilation: Application to the Tropical Oceans. Q. J. R. Meteorol. Soc., 2007. Balmaseda et al.

• A multivariate balance operator for variational ocean data assimilation. Q.J.R.M.S, 2006, Weaver et al.

• Salinity assimilation usinfS(T) relationships. K Haines et al Tech Memo 458. MWR, 2006.

• Impact of Ocean Observing Systems on the ocean analysis and seasonal forecasts, MWR. 2007, Vidard et al.

• Impact of ARGO data in global analyses of the ocean, GRL,2007. Balmaseda et al.

• Historical reconstruction of the Atlantic Meridional Overturning Circulation from the ECMWF ocean reanalysis. GRL 2007. Balmaseda et al.

Documents

Training Course 2009 – NWP-DA: Ocean Data Assimilation 1 Data assimilation in the ocean Magdalena A. Balmaseda