Training Course 2009 – NWP-DA: Ocean Data Assimilation 1 Data assimilation in the ocean Magdalena A. Balmaseda
Mar 27, 2015
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 2
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 3
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…)
Training Course 2009 – NWP-DA: Ocean Data Assimilation 4
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.
Training Course 2009 – NWP-DA: Ocean Data Assimilation 5
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 6
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.
Training Course 2009 – NWP-DA: Ocean Data Assimilation 7
•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.
Training Course 2009 – NWP-DA: Ocean Data Assimilation 8
Need to Initialize the subsurface of the ocean
Training Course 2009 – NWP-DA: Ocean Data Assimilation 11
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 12
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 13
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 14
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 15
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 16
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 17
Estimation of the Atlantic MOC
Assimilation No-Data Bryden etal 2005 Cunningham etal 2007
From Balmaseda etal 2007
Training Course 2009 – NWP-DA: Ocean Data Assimilation 18
North Atlantic:
T300 anomaly
North Atlantic:
S300 anomaly
Climate Signals….
Training Course 2009 – NWP-DA: Ocean Data Assimilation 21
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.
Training Course 2009 – NWP-DA: Ocean Data Assimilation 23
The Ocean Observing system
ARGO floatsXBT (eXpandable BathiThermograph)Moorings
Satellite
SST
Sea Level
Training Course 2009 – NWP-DA: Ocean Data Assimilation 24
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 25
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 26
•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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 27
Density dependent correlation scales
•The 3-D background length scales can also depend on both geographical distance and density differences.
Training Course 2009 – NWP-DA: Ocean Data Assimilation 28
• 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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 29
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).
Training Course 2009 – NWP-DA: Ocean Data Assimilation 30
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 31
Updating Salinity: S(T) SCHEME
S
A) Lifting of the profile
Tanal
Tmodel
B) Applying salinity Increments
Sanal
Smodel
Training Course 2009 – NWP-DA: Ocean Data Assimilation 32
Sea Level Anomaly from Altimetry
El Nino 197/98Sea Level anomaly
Equatorial Temperature anomaly
Training Course 2009 – NWP-DA: Ocean Data Assimilation 33
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 34
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)
Training Course 2009 – NWP-DA: Ocean Data Assimilation 35
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 36
• 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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 37
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 38
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 39
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 40
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 41
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 42
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 43
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 44
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.
Training Course 2009 – NWP-DA: Ocean Data Assimilation 45
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 46
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 47
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 48
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?
Training Course 2009 – NWP-DA: Ocean Data Assimilation 49
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 50
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.
Training Course 2009 – NWP-DA: Ocean Data Assimilation 51
From Ginis 2008Ocean Initial Conditions may be important
Training Course 2009 – NWP-DA: Ocean Data Assimilation 52
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
Training Course 2009 – NWP-DA: Ocean Data Assimilation 53
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.
Training Course 2009 – NWP-DA: Ocean Data Assimilation 54
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.