1. Data assimilation in the ocean
Magdalena A. Balmaseda

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

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 ocean
Defense, commercial applications (oil rings…)

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.

5. Weather and Climate Dynamical Forecasts
ECMWF:
Weather and Climate Dynamical Forecasts
18-Day
Medium-Range
Forecasts
Monthly
Forecasts
Seasonal
Forecasts
Ocean model
Atmospheric model
Wave model
Atmospheric model
Ocean model
Wave model
This slide shows the operational activities at ECMWF that require ocean model initialization after the implementation of VarEPS:
The extended range forecast (up to 18 days) also uses the coupled model.
The coupled model needs ocean initial conditions.
Delayed Ocean Analysis ~12 days
Real Time Ocean Analysis ~Real time

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.

7. Sea Level Pressure (SOI)
Sea Surface Temperature (Nino 3)
Nino 3
Nino 3.4
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 .
SST variability is linked to the atmospheric variability seen on previous slide suggesting a strongly coupled process.

8. Need to Initialize the subsurface of the ocean

9. Main Objective: to provide ocean Initial conditions for coupled forecasts
Ocean reanalysis
Real time Probabilistic Coupled Forecast
time
Coupled Hindcasts, needed to estimate climatological PDF, require a historical ocean reanalysis
To provide initial conditions for the seasonal forecasts, we need a historical reanalysis as well as the real time initial conditions.
Why? Because of model error, the forecast need calibration (at least removing the error in the mean state).
This is done by performing a set of historical hindcasts. The historical hindcasts used for the calibration need initial conditions, which are provided by a long ocean-reanalysis.
It is important that the historical ocean re-analysis is consistent with the real time.
The degree of consistency and quality of the ocean re-analysis will influence the calibration, and therefore the quality of the real time forecast.
This is a challenge when the observing system is non-stationary, and models have errors (see later)
Consistency between historical and real-time initial initial conditions is required
Quality of reanalysis affects the climatological PDF

10. Operational Ocean Analysis Schedule
Time (days) 11 12 10 9 8 7 6 5 4 3 2 1
BRT ocean analysis: D1-12
NRT ocean analysis: D1
Assimilation at D1-12
Assimilation at D1-5
BRT ( Behind real time ocean analysis): ~12 days delay to allow data reception
For seasonal Forecasts.
Continuation of the historical ocean reanalysis
NRT (Near real time ocean analysis):~ For Var-EPS/Monthly forecasts
At ECMWF, the ocean reanalysis that provides initial conditions for the seasonal forecasts runs 12 days Behind Real Time (BRT).
The reason for this delay is to wait for data reception and ensure that we use all possible information.
However, to initialize the Monthly/Var-EPS a more timely ocean analysis is need.
To satisfy the requirements of both seasonal and monthly, the ocean analysis system has 2 streams:
-BRT: for seasonal, running 12 days behind real time. Updated daily. Continuation of the long historical reanalysis.
-NRT: for monthly/Var-EPS, (or Near Real time). The BRT analysis is accelerated on a daily basis and brought up to real time.

11. Uncertainty in Surface Fluxes: Need for Data Assimilation
Equatorial Atlantic: Taux anomalies
Equatorial Atlantic upper heat content anomalies. No assimilation
ERA15/OPS
ERA40
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:
Does assimilation of ocean data constrain the ocean state?
Does the assimilation of ocean data improve the ocean estimate?
Does the assimilation of ocean data improve the seasonal forecasts
Equatorial Atlantic upper heat content anomalies. Assimilation
A way of generating ocean initial conditions is to forced an ocean model with atmospheric fluxes:
Unlike the atmosphere, a great deal of information about the ocean state can be extracted from the forcing fields, in particular the tropical winds.
Typically, ocean analyses use daily fluxes of momentum, heat (short and long wave), fresh water flux.
From atmospheric reanalysis ( and from NWP for the real time).
However, uncertainty in the fluxes in large. It should be desirable to reduce the uncertainty by using information from the ocean observations. Hence the reason for 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 ( ) 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, IAU
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-3 (the current ECMWF seasonal forecast system and in the monthly forecast system).
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).
Sequential Assimilation of data streams (altimeter, T and S)
There is an on-line bias correction scheme
Salinity and velocity are updated in physical space (rather than through covariances)
Analysis is done on model levels.
Balmaseda etal 2007/2008

13. Assimilation:T+S+Alt
Data Assimilation improves the interannual variability of the ocean analysis
No Data Assimilation
Assimilation:T+S
Assimilation:T+S+Alt
Correlation with OSCAR currents
Monthly means, period:
Seasonal cycle removed
Time correlation of zonal velocity from OSCAR and different ocean analysis.
Assimilating Temperature and Salinity improves the interannual variability.
The improvement is larger when altimeter information is added.

14. Impact of Data Assimilation
Forecast Skill
Data Assimilation
No Data Assimilation
Ocean data assimilation also improves the forecast skill
(Alves et al 2003)
Scatter diagrams comparing the error in the forecasts of SST in regions Nino3 and Nino4 when using ocean initial conditions obtained with and without data assimilation. The figure shows that the assimilation significantly improve the forecast skill.
However, this is not always the case. Sometimes model error is a serious handicap to improve the forecast. Or in other words, the current state of the art coupled models are not a good tool to gauge the quality of the ocean analysis.

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

16. Thermohaline Circulation
This cartoon shows the 3 dimension circulation of the ocean, or the so called conveyor belt: Water sinks in the North Atlantic and in the Weddle Sea, and rises almost everywhere.
This ocean circulation is responsible for transporting heat at high latitudes and for maintaining the vertical stratification of the ocean.
It has been shown that the Atlantic branch is important for the European climate.
Nomenclature: Atlantic Meridional Overturning circulation (AMOC)
Atlantic Thermohaline Circulation (ATHC)
Note the differences between the North Atlantic which has deep water formation and the North Pacific which does not.
Note also the Indonesian throughflow.
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.

17. Estimation of the Atlantic MOC
Although the previous cartoon was catchy, little is know about the strength, variability of the Atlantic MOC.
Observational studies, based of 5 snap-shot, suggested a rapid deceleration in the strength of the MOC (Bryden et al 2005, red bullets).
Latter observational estimates (for 2004), using RAPID data (Cunningham et al 2007), show the large discrepancy with the corresponding value from Bryden et al,
Suggesting the large degree of uncertainty.
Ocean analysis where data has been assimilated (black line) are closer to the observational estimates than analysis where no data has been assimilated (blue line). However, the figure shows the large range of variability of the MOC at different time scales.
There is a slight downward trend.
Assimilation No-Data Bryden etal 2005 Cunningham etal 2007
From Balmaseda etal 2007

18. Climate Signals…. North Atlantic: T300 anomaly North Atlantic:
S300 anomaly
Time evolution of the upper ocean heat content (upper right) in the North Atlantic as measured by the average temperature in the upper 300m (T300). The figure shows the evolution of the 5 ensemble members that constitute the ocean reanalysis is system 3.
Note the rapid increased in heat content after the mid 1980’s and the stabilization after 2000.
The lower figure shows the time evolution of the salinity averaged in the upper 300m (S300) in the North Atlantic. It shows large decadal fluctuations. Notice the large increase after 2000 associated with the advent of Argo.
Question: which is the uncertainty in these estimations?

19. Uncertainty in Ocean Reanalysis: GSOP
EQPAC
EQATL
EQIND TRPAC
TRATL
NPAC
NATL
GLOBAL
Signal to noise ratio:
T300
S300
This slide shows results from the CLIVAR-GSOP Ocean Reanalysis Intercomparsion.
Left figures show the uncertainty in the variability of the upper ocean heat content from different ocean reanalysis in the Equatorial Pacific (upper) and North Atlantic (lower panel).
The uncertainty between reanalysis is large, comparable to the magnitude of the signal (right panels). Only in the Equatorial Pacific the signal to noise ratio is large enough (right panels).
The uncertainty in salinity is even larger!

20. Impact on ECMWF-S3 Seasonal Forecast Skill
S3 Nodata S3 Assim
The graphic shows that the errors in the forecasts of SST initialized with data assimilation (red solid curve) are smaller than those initialized only with atmospheric fluxes (blue solid curve). Note that the improvement is clear from the beginning, and the advantage is sustained during the 7 months of the forecast. The experiments have been conducted with the same initial conditions an model version as for the S3 seasonal forecasting system
For comparison, the forecasts using just persistence of the anomalies are also shown (black line).
The dashed lines show the ensemble spread of each forecast (5 ensemble members).
Balmaseda et al 2007

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.

22. Ocean Circulation Wind Driven:
Gyres
Western Boundary Currents
Density Driven: Thermohaline Circulation
Sinking of water in localized areas
Ubiquitous upwelling maintaining the stratification
Deep circulation concentrated in the western boundary (Stommel)
Adjusment processes
Equatorial Kelvin waves (c ~2-3m/s) (months)
Planetary Rossby waves (months to decades)

23. The Ocean Observing system
ARGO floats
XBT (eXpandable BathiThermograph)
Moorings
Satellite
SST
Sea Level
Ocean Observing System: the ocean has been poorly observed.
The electromagnetic radiation does not penetrate into the ocean (it is trapped in the upper meters), which is a major problem for full explotation of the satellite revolution
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)

24. Time evolution of the Ocean Observing System
XBT’s 60’s Satellite SST Moorings/Altimeter ARGO
1982
1993
2001
2008
PIRATA
TRITON
Gravity info:
GRACE
GOCE
The ocean observing system has been slowly evolving in time. Only with the advent of the Argo program (completed in 2007), has the subsurface of the ocean (temperature and salinity) been observed with truly global coverage.
SSS info:
Aquarius
SMOS

25. Ocean Observing System
Data coverage for June 1982
Changing observing system is a challenge for consistent reanalysis
Data coverage for Nov 2005
Today’s Observations will be used in years to come
The figures show the different observation coverage in 1982 and In 1982 there are far less observations in the Southern hemisphere, while there are many more XBTs (ship of opportunity) in the Northern Hemisphere. Note as well the presence of several scientific cruises.
In 2005 the XBTs (in black) have decreased, while Argo (blue) populates the global oceans. Note the mooring arrays (TAO/TRITON, and PIRATA) in the equatorial oceans (in red).
▲Moorings: SubsurfaceTemperature
◊ ARGO floats: Subsurface Temperature and Salinity
+ XBT : Subsurface Temperature

26. Background errors
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.

27. Density dependent correlation scales
The 3-D background length scales can also depend on both geographical distance and density differences.
In System 3 the background covariance is 3-D, and depends on both geographical distance and density differences. Therefore, some flow dependency is implicit in the formulation.
Some flow-dependency is also imposed in the diagonal elements, where the variance value depends on the stratification of the background field

28. Updates to Salinity and Velocity
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.
Corrections to temperature and salinity produce corrections in density and in the pressure gradient. It not properly balanced, the corrections can disapper quite quickly via gravity waves. A simple solution is to apply corrections to the velocity field to ensure geostrophic balance. This is specially important at the equator. However, at the equator, geostrophy is quite limited, and only corrections to the zonal velocity are applied that balance the second derivative (in the meridional direction) of the pressure. The equatorial zonal pressure gradient remains unbalanced (see later).

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).

30. Spurious Convection Develops
Stratified Temp at I.C
Meridional Sections (Y-Z) 30W
3 months into assimilation
Temperature
Salinity
Temperature
Salinity
Spurious Convection Develops
Constraint: To update salinity to preserve the water mass properties
(Troccoli et al 2002)
Balance Relationship
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 (Troccoli etal 2002). It is corrected and analysed in system-3 (Haines etal 2006).
The OI increments are spread uniformly throughout the assimilation window, to allow the model to spin-up its own velocity field (Incremental Analysis Update or IAU, Bloom etal 1996).
In addition, the velocity field is updated imposing geostrophy. (Burgers etal 2002) This is important mainly at the equator, where the adjustment times are slower. Here, the zonal velocity increments are proportional to the second y-derivative of the pressure

31. Updating Salinity: S(T) SCHEME
A) Lifting of the profile
Tanal
Tmodel
B) Applying salinity Increments
Sanal
Smodel S
The idea behind the S(T) scheme balance relationship is to preserve the water mass properties by assuming that most of the errors come from vertical displacements of the water column. This is not a bad assumption in most of the tropics. It does not work that well in areas where vertical mixing and convection act quickly (except for the mixed layer, high latitudes).
Imagine that we only have temperature observations, which via the data assimilation will correct the background profiles. One can assume that the ithe corrections in temperature have been produced by vertical displacements of the water column. It is possible to compute that displacement and then apply it to the vertical salinity profile, thus producing a correction to the background salinty.

32. Sea Level Anomaly from Altimetry
El Nino 197/98
Equatorial Temperature anomaly
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. (Cooper and Haines 1996 ,CH96 in what follows)

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).
If we observe sea level, one can infer information on the vertical density structure
10cm
30 m

34. A linearized balance operator for global ocean assimilation
Define the balance operator symbolically by the sequence of equations
Treat as approximately
mutually independent
Temperature
Salinity
SSH
u-velocity
v-velocity
Density
Pressure
The balance relationship described above between Temperature and Salinity and density and velocity can be expressed in a matrix form adequate for a multivariate 3D-var. Weaver et al Note the separation into balance and unbalance components.
(Weaver et al., 2005, QJRMS) 34

35. Components of the balance operator
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.) 35

36. Multivariate structures implied by the balance opt.
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.
Courtesy of A. Weaver 36

37. Example: 3D-Var assimilation of a single SSH obs. at the eq.
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 37

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.
A Mean Sea Level
Observed SLA from T/P+ERS+GFO
Respect to 7 year mean of measurements
However the altimeter only provides information about the time anomaly, respect a mean sea surface height (SSH) or mean sea level (usually as the time mean ). Also called Mean Dynamic Topography (MDT)
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 is an active area of reasearch.

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

40. Results are very sensitive to the MDT
Not good for consistent historical reanalysis

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

42. Impact of data assimilation on the mean
Assim of mooring data
CTL=No data
This figure shows the time evolution of the depth of the equatorial thermocline in the Atlantic for 2 experimens:
CTL, (ocean forced by wind, in black), and Assim (in red, where the subsurface data have been assimilated)
The advent of the temperature data for the PIRATA moorings in 1998/1999 can be appreciated in the ASSIM experiment by the sudden shallowing of the thermocline:
The PIRATA data corrects for a systematic error of the background (which has too depth thermocline). The net effect is an spurious jump that induces spurious interannual variability.
To prevent this sort of behaviour, an adequate and explicit treatment of background bias is required
PIRATA
Large impact of data in the mean state: Shallower thermocline

43. Vertical velocity (C.I=0.5m/day)
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
Mean Analysis – Obs
NINO 3: Eastern Pac
100m
200m
The figure on the left shows the difference Analysis-Obs for an ocean analysis produced with data assimilation (red, Assim) and another produced by forcing the ocean model with atmospheric forcing (black, No-Data). In the upper ocean, Assim has the opposite sign of No-Data, and it is biased positive (while No-data was biased negative).
The mean temperature assimilation increment (shown in the right upper panel) shows a large magnitude, with a dipolar structure, as if the assimilation is trying to correct the slope of the equatorial thermocline. The negative increment in the Eastern Equatorial Pacific generates some spurious downwelling circulation (lower-right figure) near the South American coast. This downwelling circulation is responsible for decreasing the cooling in this area, and generating an error: the assimilation process is correcting for errors induced by the assimilation itself.

44. The Assimilation corrects the ocean mean state
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. z
(x)
Equatorial Pacific
Because of errors in the winds and in the ocean model, the data assimilation is correcting the ocean mean state.
In the Pacific, it deepens and increase the slope of the equatorial thermocline. The corrections are not always maintained by the system. The corrections to the slope of the thermocline, associated with weak easterly winds, are not easily mantained.
Is there a way of making the system retain this information? Maybe by applying the correction to the pressure gradient rather than to the thermal structure?
Free model
Data Assimilation

45. prescribed (constant/seasonal)
Bias evolution vector-equation k f b ; 1 - + =
prescribed (constant/seasonal)
Some notation
(Temperature,Salinity,Velocity)
Main features of the bias 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

46. Vertical velocity (C.I=0.5m/day)
Bias and circulation
T-Assim incr (C.I=0.05 C/10 days)
Standard
Bias corrected: pressure
Vertical velocity (C.I=0.5m/day)
Impact of the bias correction in the mean temperature increment (upper panels) and vertical velocity (lower panels).
Note that the bias correction reduces the mean temperature increment and gets rid of the spurious vertical circulation in the eastern Pacific.
Balmaseda etal 2007

47. Effect of bias correction on the time-evolution
The a-priori (iterative) estimation of the bias corrects the solution before the PIRATA moorings appear, hence preventing the shock.
Assim of mooring data
CTL=No data
Bias corrected Assim

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?

49. Initialization: uncoupled versus coupled
Uncoupled: Most common
Other Strategies
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.

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.

51. Ocean Initial Conditions may be important
From Ginis 2008

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

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.

54. Some references related to ocean data assimilation at ECMWF
The ECMWF System 3 ocean analysis system, Balmaseda et al 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 See also Monthly Weather Review 2003, 131, and MWR 2003, 131,
Balanced ocean data assimilation near the equator. Burgers et al J Phys Ocean, 32,
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 February 2004
A Multivariate Treatment of Bias for Sequential Data Assimilation: Application to the Tropical Oceans. Q. J. R. Meteorol. Soc., 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 MWR, 2006.
Impact of Ocean Observing Systems on the ocean analysis and seasonal forecasts, MWR , 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 Balmaseda et al.