Mercator Ocean newsletter 25

Mercator Ocean International
Mercator Ocean InternationalMercator Ocean International

Greetings all, Nowadays, several datasets are -or will be- available in a near future to improve operational forecasting in most aspects, like the ocean dynamics modeling, and the assimilation efficiency, that aims now to optimize the combination of temperature/salinity in situ profiles, drifter's velocities, and sea surface height deduce from altimeter's data and GRACE or future Goce geoid. But also strengthen forecasting system's applications, like the climate monitoring. For all these issues, an optimal use of ocean data, always too sparse and not enough numerous, is mandatory. Such studies are at the heart of this Newsletter issue. It begins with a Rio M.H. and Hernandez F. review of the Goce Mission, dedicated to focus and document the shortest scales of the Earth's gravity field. Goce satellite is due to fly in December 2007. With the next article Guinéhut S. and Larnicol G. investigate the influence of the in situ temperature profiles sampling on the thermosteric sea level estimation. They show that the impact is not negligible, and can introduce large errors in the estimation. In the second article, Benkiran M. and Greiner E. are evaluating the benefits of the drifter's velocities assimilation in the Mercator Océan 1/3° Tropical and North Atlantic operational system. A description of the assimilation scheme upgrade to take into account velocity control is given. Castruccio F. & al. describe in the third article the performance of an improved MDT reference for altimetric data assimilation. They concentrate their study on the Tropical Pacific Ocean. Finally, the Newsletter comes to an end with the Benkiran M. article. In his study, based on the 1/3° Mercator system, the impact of several altimeters data on the assimilation performance is assessed Have a good read

Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 1
GIP Mercator Ocean
Quarterly Newsletter
Editorial – April 2007
Goce satellite
Credits : ESA - AOES Medialab
Greetings all,
Nowadays, several datasets are -or will be- available in a near future to improve operational forecasting in most aspects, like the
ocean dynamics modeling, and the assimilation efficiency, that aims now to optimize the combination of temperature/salinity in
situ profiles, drifter's velocities, and sea surface height deduce from altimeter's data and GRACE or future Goce geoid. But also
strengthen forecasting system's applications, like the climate monitoring. For all these issues, an optimal use of ocean data,
always too sparse and not enough numerous, is mandatory.
Such studies are at the heart of this Newsletter issue. It begins with a Rio M.H. and Hernandez F. review of the Goce Mission,
dedicated to focus and document the shortest scales of the Earth's gravity field. Goce satellite is due to fly in December 2007.
With the next article Guinéhut S. and Larnicol G. investigate the influence of the in situ temperature profiles sampling on the
thermosteric sea level estimation. They show that the impact is not negligible, and can introduce large errors in the estimation. In
the second article, Benkiran M. and Greiner E. are evaluating the benefits of the drifter's velocities assimilation in the Mercator
Océan 1/3° Tropical and North Atlantic operational system. A description of the assimilation scheme upgrade to take into account
velocity control is given. Castruccio F. & al. describe in the third article the performance of an improved MDT reference for
altimetric data assimilation. They concentrate their study on the Tropical Pacific Ocean. Finally, the Newsletter comes to an end
with the Benkiran M. article. In his study, based on the 1/3° Mercator system, the impact of several altimeters data on the
assimilation performance is assessed
Have a good read
Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 2
GIP Mercator Ocean
Contents
GOCE review.......................................................................................................................................................... 3
Data assimilation of drifter velocities in the Mercator Ocean system .............................................................. 6
Influence of the sampling of temperature data on the interannual variability of the global mean
thermosteric sea level index............................................................................................................................... 13
GRACE: an improved MDT reference for altimetric data assimilation............................................................ 20
Altimeter data assimilation in the Mercator Ocean system ............................................................................. 32
Notebook.............................................................................................................................................................. 40
Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 3
News: GOCE review
News: GOCE review
By Marie Hélène Rio1
and Fabrice Hernandez2
1
CLS, Space Oceanography Division, 8/10 rue Hermès. 31520 Ranonville st Agne
2
Mercator Ocean , 8/10 rue Hermès. 31520 Ranonville st Agne
Satellite Altimetry and the Mean Dynamic Topography issue
Altimetric data from satellites are a key component of the observational constraints on which any operational ocean forecasting
system can rely to ensure its ocean dynamics consistency. The satellite altimeters offer global and repetitive measurements of
the sea level, with a unique resolution and accuracy. Its success and accomplishment in ocean dynamics sciences is yet proven
[e.g., Fu and Cazenave, 2001].
However, since the beginning of satellite altimetry, more than 15 years ago, due to the lack of an accurate geoid, only the
variable part of the ocean dynamic topography can be extracted with sufficient accuracy (few centimetres) for oceanographic
applications. For the correct interpretation of these altimetric Sea Level Anomalies (SLA) in terms of sea level and geostrophic
circulation, the provision of an accurate Mean Dynamic Topography (MDT) is mandatory. This has proved to bring significant
improvement in ocean forecasting systems where assimilation of SLA provides better ocean circulation description, from large
to mesoscales [Knudsen et al., 2005, and EU GOCINA projects main outcomes; Le Provost et al., 1999; Le Traon et al., 2002].
In addition, the MDT is the missing key element for the correct interpretation of all past, present and future altimetric data and
their use for oceanographic long term analyses.
Strong improvements have been made recently using satellite gravimetry products, in particular the recent geoid models based
on GRACE data. Subtracting the last model EIGEN-GL4S computed by the GFZ/GRGS from an altimetric Mean Sea Surface
allows computing the ocean Mean Dynamic Topography at scales larger than 400 km with accuracy of the order of few
centimetres [Rio et al., 2005; Tapley et al., 2003].
But the MDT is expected to present scales as small as ten’s of km. To retrieve the missing shortest scales, different methods
have been developed where in-situ oceanographic data (hydrologic profiles, drifting buoy velocities) are combined with the large
scale derived MDT to estimate global, high resolution MDT [Niiler et al., 2003; Rio and Hernandez, 2004; Rio et al., 2005; Rio et
al, 2007; Maximenko et al, 2005].
However the definitive jump toward absolute altimetry is still to come and the springboard is called GOCE.
GOCE mission
GOCE (Gravity Field and Steady-State Ocean Circulation) is the first core Earth Explorer mission from ESA’s Living Planet
programme and is due to fly in December 2007. The nominal duration of the mission is 20 months, with a 3 month
commissioning and calibration phase followed by two science measurement phases of 6 months separated by a 5 month
eclipse hibernation period.
Mission objectives are to determine the gravity field’s anomalies with an accuracy of 1 mGal (=10-5 m/s2) and the Earth geoid
with an accuracy of 1-2 cm for a spatial resolution of 100 km. In order to meet these requirements, the principle of the GOCE
mission is based on the combination of two techniques, a satellite to satellite tracking technique relative to GPS for retrieving the
long wavelengths of the Earth Gravity field, associated to the use of a gradiometer (composed of three pairs of three-axis
accelerometers) for measuring the shortest scales.
The two Level-2 products of interest for oceanographers that will be delivered by ESA are the set of spherical harmonics
coefficients of the Earth gravity field up to degree and order 200 (100 km resolution) as well as the full error covariance matrix of
the coefficients.
GOCE/GRACE complementarity
The GOCE satellite has been designed to focus on the retrieval of the Earth’s gravity field short scales while the previous
GRACE US-German mission was designed to resolve with millimetre accuracy the spatial scales of the Earth’s gravity field
longer than 400 km. Both missions are then complementary so that the best static geoid model will certainly be obtained
through a combination of gravity data from the two missions.
The MDT solutions based on a combination of satellite and in-situ data mentioned above, will play an important role for the
validation of these future GOCE/GRACE derived MDTs.
Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 4
News: GOCE review
Toward the shortest scales
GOCE data will give access with reasonable accuracy to the spatial scales of the ocean Mean Dynamic Topography larger than
100 km. However, in some areas (semi-enclosed seas as the Mediterranean Sea, coastal areas, straits) the MDT is expected to
contain even shorter scales [Rio et al., 2007]. The combination methods to other, independent estimates of the MDT, based on
in-situ oceanographic measurements, will therefore still be essential to achieve higher resolution where needed. Also, in order to
improve the geoid resolution, local solutions can be computed combining GOCE data to in-situ (ship or airborne) gravimetric
measurements.
Opening new issues
Geoids, accurate enough to be used together with satellite altimetry to provide a full description of the ocean mesoscale (10-
1000km) have been expected for long time.. But the Russian dolls game is not over. The access to the geoid short scales with a
centimetric accuracy now pushes us toward the limits of altimetry: This covers two key issues. The first is the need to improve
the accuracy of altimetric measurement in coastal areas, through improved processing. The second is to correctly assess the
errors on the different models used for altimetric corrections in order to better understand at last what the true error levels on
altimetric data (MSS, SLA) are.
Getting ready
Oceanographers have been used for years to work on altimetric Sea Level Anomalies, focusing only to the ocean mesoscale
variability. The GOCE data will make us enter a new era where we will at last have access to the absolute dynamic topography
and to the absolute ocean geostrophic currents, not only for the forthcoming altimetric missions but also back in the past since
the first altimetric measurements. This will open a number of new scientific issues. This will also have a huge impact for ocean
and climate monitoring and forecasting and the operational forecasting centres must prepare from now to it, thinking about the
best way to assimilate this new information (the geoid and its error covariance matrix) into their systems.
References
Fu, L.-L., and A. Cazenave, Satellite Altimetry and Earth Sciences. A handbook of Techniques and Applications, 463 pp.,
Academic Press, San Diego, CA, USA, 2001.
Knudsen, P., O.B. Andersen, R. Forsberg, A.V. Olesen, A.L. Vest, H.P. Föh, D. Solheim, O.D. Omang, R. Hipkin, A. Hunegnaw,
K. Haines, R.J. Bingham, J.-P. Drecourt, J.A. Johannessen, H. Drange, F. Siegismund, F. Hernandez, G. Larnicol, M.-H. Rio,
and P. Schaeffer, GOCINA, Geoid and Ocean Circulation in the North Atlantic, pp. 70, Danish National Space Center,
Copenhagen, 2005.
Le Provost, C., P. Le Grand, E. Dombrowsky, P.-Y. Le Traon, M. Losch, F. Ponchaut, J. Schröter, B.M. Sloyan, and N. Sneeuw,
Impact of GOCE for ocean circulation studies, ESA, 1999.
Le Traon, P.-Y., F. Hernandez, M.-H. Rio, and F. Davidson, How operational oceanography can benefit from dynamic
topography estimates as derived from altimetry and improved geoid, in ISSI workshop. Earth gravity field from space - From
sensors to Earth sciences, Bern, Switzerland. Edited by G. Beutler, M.R. Drinkwater, R. Rummel, and R. von Steiger, in Space
and Science Reviews, (108), pp. 239-249, Kluwer Academic Publisher, 2002
Maximenko, N.A., and P.P. Niiler, 2005: Hybrid decade-mean global sea level with mesoscale resolution. In N. Saxena (Ed.)
Recent Advances in Marine Science and Technology, 2004, pp. 55-59. Honolulu: PACON International
Niiler, P.P., N.A. Maximenko, and J.C. McWilliams, Dynamically balanced absolute sea level of the global ocean derived from
near-surface velocity observations, Geophys. Res. Lett., 30 (22), 2164, doi:10.1029/2003GL018628, 2003.
Rio, M.-H., and F. Hernandez, A Mean Dynamic Topography computed over the world ocean from altimetry, in-situ
measurements and a geoid model, J. Geophys. Res., 109 (C12), C12032 1-19 - doi10.1029/2003JC002226, 2004.
Rio, M.-H., Schaeffer, P., Hernandez, F., Lemoine, J.-M., 2005. The estimation of the ocean Mean Dynamic Topography
through the combination of altimetric data, in-situ measurements and GRACE geoid: From global to regional studies.
Proceedings of the GOCINA Workshop in Luxembourg (April, 13-15 2005).
Rio, M.-H., P.-M. Poulain, A. Pascual, E. Mauri, G. Larnicol, and R. Santoleri, 2007: A Mean Dynamic Topography of the
Mediterranean Sea computed from altimetric data, in-situ measurements and a general circulation model., J. Mar. Sys., 65
(2007) 484-508.
Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 5
News: GOCE review
Tapley, B.D., D.P. Chambers, S. Bettadpur, and J.C. Ries, Large scale ocean circulation from the GRACE GGM01 Geoid,
Geophys. Res. Lett., 30 (22), 2163, doi:10.1029/2003GL018622, 2003.
Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 6
Data assimilation of drifter velocities in the Mercator Ocean system
Data assimilation of drifter velocities in the Mercator Ocean system
By: Mounir Benkiran and Eric Greiner1
1
CLS / Mercator Ocean – 8/10 rue Hermès. 31520 Ramonville st Agne
Introduction
The aim of this paper is to document the drifter’s velocities data assimilation, in addition to other data already assimilated, in the
Mercator-Ocean system using a multivariate data assimilation scheme. The latter has been upgraded and a new set of empirical
modes have been defined, which takes into account the drifter zonal and meridional velocities. We describe here the various
upgrades of the data assimilation system as well the first results from the drifter velocities data assimilation.
The drifter velocities
For this study, besides data used in the operational system (Sea Level Anomaly, Temperature and salinity profiles and Sea
Surface Temperature), we used the drifter velocity at 15 meters depth over the year 2004. Those are three days filtered, which
allows filtering the gravity waves.
The PSY1v3 experimental system
We describe here the various upgrades of the data assimilation system in order to assimilate the drifter velocities. The chosen
experimental system (called PSY1v3) is a derived version of the 1/3° Mercator-Ocean Tropical and North Atlantic operational
system (PSY1v2) with an upgrade of the data assimilation scheme (formerly SAM1v2 and now called SAM1v3) in order to take
into account the drifter velocity data in the state vector.
The multivariate SAM1v2 data assimilation scheme is used operationally at Mercator-Ocean since early 2004. The model minus
altimeter and insitu data differences of the multivariate analysis are performed using the SOFA (System for Ocean Forecasting
and Analysis) optimal interpolation scheme (De Mey and Benkiran, 2002; Etienne and Benkiran, 2007). The specificity of the
SOFA scheme is to split the horizontal and vertical correlations, where the covariance matrix of the forecast error Br in the
reduced space is described by:
Br = S B S
T
= D
1/2
C D
1/2
• D the forecast error variance.
• B the forecast error
• S the vertical modes (vertical correlation)
• C the correlation function (as a fonction of the time-space correlation radius):
C = (1 + dr + 1/3 dr
2
) exp (-dr ) exp (-dt
2
)
The operational SOFA sequential data assimilation scheme (SAM1v2) allows assimilating sea level observations (derived from
altimeter data sea level anomalies), sea surface temperature, temperature and salinity vertical profiles, and temperature and
salinity climatological values. The latter uses an optimal interpolation in a reduced space, for which a statistical method based
on empirical modes (EOFs) is used.
The state vector is split into 2 parts: a barotropic component (barotropic height) and a baroclinic component evaluated from
temperature and salinity vertical profiles. We first add the (U, V) baroclinic velocity components in the state vector. We then
compute a new EOFs set with the new state vector X=[ψ ,T1,…..,Tjpk,S1,..Sjpk,U1,…,Ujpk,V1,….Vjpk]
T
(where jpk is the total
number of vertical levels of the ocean model), including the new (U, V) baroclinic velocity. ψ is the barotropic stream function.
The Ti, Si, Ui, Vi variables are respectively the temperature, salinity, zonal and meridional velocity anomalies with respect to a
seasonal mean at the corresponding i vertical level.
Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 7
Data assimilation of drifter velocities in the Mercator Ocean system
In order to compute the new set of EOFs, we use every 3 days instantaneous outputs of a one year long simulation for the year
2004 from the PSY1v2 system with double IAU
1
(Incremental Update Analysis, Ourmières & al) . IAU has been used to avoid
every 7 days (length of the assimilation cycle) spikes in the analysis fields triggered by the sequential data assimilation scheme
(Figure 1). Moreover, in order to keep the seasonal cycle, we compute a different set of EOF per season.
We now have N vectors X, corresponding to the N vertical profiles. In order to compress the information containing the outputs
variability using M vectors X (with M << N), we express the vectors X in a new canonical orthonormal base S={en} of dimension
kz. This base represents the directions along which the N profiles variances have a local extremum. Hence, we make sure using
this method, that two eigen modes are statistically not coupled and that the dominant modes are not coupled with the others.
We then present which normalisation is applied to the state vector X, composed of several ocean variables (ψ , T, S, U, V).
Indeed, each of these variables has its own variability with different order of magnitude (typically of several degrees Celsius for
the temperature, or of the order of 0.25 psu for the salinity). Hence, a normalisation is needed in order to extract the relevant
dominating modes of the state vector. The chosen normalisation method is not very different from the one used in the
operational Mercator-Ocean system PSY1v2. It is based on a linearisation of the Bernoulli function. A scaling is used so that
each variable of the state vector becomes proportional to a sea level height. The state vector is then described by the following
equation:
]*.....*,*.....*,*.....,*......*,1[ 1111 jpkpkjpkjpk dzdzdzjdzdzdzdzdzScale γγγγββαα=








−
= .klevelatdepth:,gravitytodueonaccelarati:,energyKinetic:,
)0(
*2
.exp:
.exp:
.:
k
k
k
ztgEc
Hztg
Ec
tcoefficienansionSalinity
tcoefficienansionThermal
thicknessklayerdz
γ
β
α
Figure 2 shows the percentage of explained variance by the first twenty mode in winter 2005 using the new state vector from the
SAM1v3 scheme (left panel) and the old state vector from the SAM1v2 scheme (no IAU) (right panel). The new scheme allows
increasing the percentage of explained variance with the same amount of eigen modes used. The percentage of explained
variance is ~100% everywhere except in the equatorial band where it reaches 92%. This is due to the strong stratification
present in the equatorial area which would require more than 20 modes to be fully represented. Hence, a test has been set up
allowing using the right amount of mode at each grid point in order to explain 99% of the variance at each grid point.
1
IAU refers to a more complex assimilation method than the classical sequential assimilation. In the sequential method, a
forecast is followed by an analysis of the final conditions, which once corrected become initial conditions for the next forecast.
With the IAU method, instead of correcting the forecast initial condition, the correction is spread along the integration period of
the model. The system state is thus modified while controlling its error. IAU is a more complex and computer costly method as it
requires an additional model integration. Double IAU is a variant of the IAU which parameterises the model error using two
analysis corrections, weighted by sinusoidal complementary functions.
Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 8
Data assimilation of drifter velocities in the Mercator Ocean system
Figure 1
Time series of the horizontal velocities divergence (cm/s) over the whole North and tropical Atlantic for 2004. (Red) with
sequential data assimilation. (Purple) in a free run without data assimilation. (black) using Incremental Analysis Update
(IAU).
Figure 2
Explained variance for the first 20 modes during winter 2004 (Left panel) with SAM1v3 scheme, (Right panel) with SAM2v1
scheme.
Another originality of the SAM1v3 scheme lays in the correction applied to baroclinic velocities. With the SAM1v2 scheme,
baroclinic velocities corrections are deduced from the 1
st
order thermal wind equation (and 2
nd
order in the equatorial band):
Velocity corrections are deduced from the geostrophic increments derived from the temperature and salinity corrections. In the
SAM1v3 scheme, baroclinic velocity corrections are now deduced from the statistical EOF projection in the reduced space. This
allows correcting the geostrophic as well as the ageostrophic component of the velocity. Figure 3 displays the initialisation
procedure used after the model analysis.
Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 9
Data assimilation of drifter velocities in the Mercator Ocean system
Brest 12/05/2006 Benkiran et al
SAM1v3 : The Mercator Assimilation System version 3
Schematically :
ROOI
(SOFA)
Delta (ir)r
δT, δS
δUbac, δVbac
δΨ
δU, δV
δUbar, δVbar
baroclinic
barotropic
Full
space
1D EOFs
Static instability
of the water column
Sets to 0 the divergent
part of the current
baroclinic
Figure 3
Initialisation procedure after analysis in the SAM1v3 scheme.
Preliminary results: comparison of the SAM1v2 and SAM1v3 data assimilation
schemes and impact of drifter’s velocities data assimilation in the SAM1v3
system.
We present here preliminary results, first comparing the SAM1v2 and SAM1v3 data assimilation schemes and, second, showing
the impact of drifter velocities data assimilation in the SAM1v3 system.
First, the SAM1v2 and v3 schemes are compared with no drifter velocity data assimilation. Two simulations in the exact same
conditions have been performed in order to assess the differences between the SAM1v2 and SAM1v3 schemes. Simulations
are performed for the year 2004 when enough data are available, assimilating the same observations (Jason, Envisat and Gfo
for altimeter data, Coriolis temperature and salinity vertical profiles, Reynolds Sea Surface Temperature). Alimeter data from a
fourth satellite (Topex) are also available as independent observations. Figure 4 shows the biases between the Topex
observations and the model. The Root Mean Square (RMS) (Top panel) is lower for SAM1v3 than in SAM1v2 scheme. This is
mainly due to the ageostrophic velocity corrections. Moreover, the biases averages (lower panel) are close to zero in both
schemes.
Figure 5 compares the Sea Surface Temperature (SST) forecasted by the model and the Reynolds SST which is assimilated.
We notice that the biases are reduced in SAM1v3 compared to v2, especially close to the continental shelf, in the Gulf Stream
and the Caribbean areas. Figure 6 shows that this is mostly due to the ageostrophic velocity correction applied in SAM1v3.
Indeed, in the SAM1V2 scheme, only the barotropic and geostrophic baroclinic velocities are corrected. This does not allow the
current to develop on the continental plateau. Figure 6 shows the mean velocities in the North West Atlantic in the two schemes.
The Greenland Current feeding the Labrador Current is more developed on the continental shelf with SAM1v3 than v2 scheme.
Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 10
Data assimilation of drifter velocities in the Mercator Ocean system
Figure 4
(Top panel) RMS of the biases (cm) between Topex and model, in the 7 days forecast fields over the whole tropical and North
Atlantic domain. (Lower panel) Misfit average (cm). Blue line: With no altimeter data assimilation. Brown line: SAM1v3 with
altimeter data assimilation (Envisat, Jason and Gfo). Black line: SAM1v2 with altimeter data assimilation (Envisat, Jason and
Gfo)
Figure 5
SST biases (Unit: [-1.5-1.5] °C).between the model forecast and the assimilated Reynolds SST. (Left) with SAM1V2 ; (right) with
SAM1V3.
Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 11
Data assimilation of drifter velocities in the Mercator Ocean system
Figure 6
Mean current (m/s) for year 2004. (Left panel) with SAM1V2 ; (right panel) with SAM1V3.
Figure 7
Drifters buoys trajectories during year 2004 in the tropical and North Atlantic. (Right) zonal ; (left) meridional component.
Second, the SAM1v3 scheme is used to assimilate drifter’s velocities. A simulation is performed where only drifter’s velocities
data are assimilated every 7 days over the year 2004. Drifter’s data are available daily, but treated with a 3 days filter. We first
want to check whether our new set of EOFs is compatible with the drifter’s velocities data. Moreover, we want to check which
error is associated with these data and which impact it will have on the system once assimilated.
Figure 7 shows the drifter’s buoys trajectories during 2004 in the tropical and North Atlantic. Zonal equatorial currents, as well
as stronger currents in the Gulf Stream area can be noticed.
Figure 8 displays the sum of the forecast differences between the model and the drifter data for the zonal component of the
velocity (left panel), as well as the sum of the increments after analysis for the zonal component of the velocity (right panel). We
notice that the information contained in the drifter’s data is not use at 100%, but that only a small part of it is used in the whole
domain except in the tropical area where corrections are larger. We suggest some reasons for this:
• The observation error associated with the drifter data is constant over the whole basin (0.10 m/s). We made a test
with a weaker error (5 cm/s, not shown here), where more mesoscales structures are kept.
• The new set of EOFs released within the SAM1v3 scheme might not include the drifter data signal, although the zonal
and meridional components of the velocity have been included in the state vector.
• The optimal interpolation scheme used here with a vertical projection, as well as the resolution of the system, might
not be compatible with the mesoscale structures present in the drifter’s data.
• As these data are 3 days filtered, we should also filter the model equivalent in order to filter the model gravity wave.
This is not done in this study and will be done in future work.
Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 12
Data assimilation of drifter velocities in the Mercator Ocean system
Figure 8
(Left panel) Sum of the forecast differences (m/s) between the model and the drifter’s data for the zonal component of the
velocity. (Right panel) Sum of the increments (m/s) after analysis for the zonal component of the velocity.
Conclusion
This study allowed us to conclude on the following points:
• It is important to use the baroclinic component of the velocity in the state vector. It adds an ageostrophic correction to
the velocity after analysis, which is not taken into account when this correction is simply inferred from the thermal
wind equation.
• This first experiment of drifter velocity data assimilation in Mercator Ocean System gave us encouraging preliminary
results. Further work and improvements are needed and will be conducted, in order hopefully to reach better results.
References
De Mey, P. and M. Benkiran, 2002: A multivariate reduced-order optimal interpolation method and its application to the
Mediterranean basin-scale circulation, Ocean Forecasting: Conceptual basis and applications, N. Pinardi, Springer-Verlag,
Berlin, Heidelberg, New York, 281-306.
Etienne, H. and M. Benkiran, 2007: Multivariate assimilation in MERCATOR project: new statistical parameters from forecast
error estimation. Journal of Marine Systems 65, 430-449.
Ourmières, Y., J. M. Brankart, L. Berline, P. Brasseur & J. Verron, in press : Incremental analysis update implementation into a
sequential ocean data assimilation system, Journal of Atmospheric and Oceanic Technology.
Acknowledgment
Laurence Crosnier is greatly acknowledged for the translation of this paper.
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 13
Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index
Influence of the sampling of temperature data on the interannual
variability of the global mean thermosteric sea level index
By Stéphanie Guinehut and Gilles Larnicol1
1
CLS, Space Oceanography Division, 8/10 rue Hermès. 31520 Ranonville st Agne
Introduction
Global mean sea level change results from two main causes: (1) volume change due to seawater density change in response to
temperature and salinity variations, (2) mass change due to exchange of water with atmosphere and continents via the
hydrological cycle. Satellite altimeters measure global mean sea level including volume and mass changes almost globally
(60°S-60°N) and continuously since the launch of Topex/Poseidon in October 1992. In situ temperature and salinity data sets
are used to quantify volume change due to temperature change (thermosteric sea level – heat content) and temperature and
salinity change (steric sea level).
Different groups have recently estimated interannual variability of global ocean heat content and global ocean thermosteric sea
level change for the 1993-2006 periods (Willis et al., 2004; Ishii et al., 2006; Lyman et al., 2006). Unfortunately, in situ
measurements are discrete in time and space and are far from sampling the total surface of the ocean. The main objective of
this study is thus to quantify the sampling influence of the temperature data sets on the interannual variability of the global mean
thermosteric sea level. Sampling errors depend on three components: 1) the geographical and temporal repartition of the in situ
measurements, 2) the vertical resolution of the measurements and 3) the method used to calculate global mean from non-global
observations. The influence of these three terms has been quantified and their impacts in terms of global trend of interannual
variability of the global mean thermosteric sea level are thus presented.
The different data sets involved in this study are first presented in section 2. The method used to map the individual temperature
observations into grid fields is then described in section 3. The impact of the temporal, geographical and vertical repartition of
the in situ measurements is studied in section 4 and the impact of the method used to calculate the global mean from non-global
fields is presented in section 5. Finally, section 6 offers discussions.
Data sets
Data sets involved in this study include:
• Delayed mode maps of SLA from the SSALTO/DUACS center (Ssalto/Duacs User Handbook, 2006). These maps are
defined on a 1/3° horizontal grid at a weekly period;
• T and S in situ profiles from the ENACT/ENSEMBLE-EN2 data base for the years 1993-2004 (Ingleby and
Huddleston, 2006) – the third upgrade of the data set (EN3) was unfortunately not available at the time of the study;
• T and S in situ profiles from the CORIOLIS data base for the years 2005-2006 (http://www.coriolis.eu.org/).
The preprocessing of the in situ data sets consists only in removing redundant observations – only one observation is kept per
day for the same instrument in a region of 0.1° in latitude by 0.1° in longitude. No additional qualification is performed on the
observations; we absolutely rely on the data centers for this particular point.
Mapping method
In situ data sets being discrete measurements in time and in space, a mapping method is used prior to analysis. We construct
global thermosteric sea level maps at a monthly period, on a 1/3° resolution grid and for the 0-700 m layer from the individual
temperature profiles. The mapping method is very similar to the one developed by Larnicol et al. (2006) for the ARMOR-3D
Mercator observed products. It is based on an optimal interpolation method with the following parameters:
• Temporal correlation scale of 45 days;
• Spatial correlation scale – 5 times the one used to produce the SSALTO/DUACS SLA maps (from 1500 km at the
equator to 700 km at 50°N);
• Error associated to each in situ measurement as thermosteric sea level equal to 20 % of the variance of the
SSALTO/DUACS SLA maps, in order to take into account error associated to the aliasing of the mesoscale variability.
Besides, the time-mean and seasonal cycle were removed from the altimeter and in situ data prior to analysis.
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 14
Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index
Impact of the temporal, geographical and vertical repartition of the in situ
measurements
Each observation being characterised by a geographical position (latitude and longitude) and a date, the temporal and
geographical repartition of the in situ measurements could not be studied independently of one another. The vertical sampling of
the in situ observations is studied in a second step. Figure 1 shows three typical repartitions of in situ temperature profiles valid
up to 700 m (the thermosteric sea level is calculated down to 700 m). The year 1993 shows medium repartition of the in situ
measurements with large under-sampled areas in the Southern Ocean. As we will see later, we are able to reconstruct almost
85 % of the ocean thermosteric signal between 60°S and 60°N (the area of the study) for this year. For the year 2000, very large
areas in the Indian Ocean, the South Atlantic and Pacific Oceans are hardly sampled if at all. This year is the worst sampled
year with only 70 % of the ocean reconstructed. Thanks to the development of the Argo array, the ocean is almost totally
sampled during the year 2006 with more than 95 % of the 60°S-60°N area reconstructed.
Impact of the temporal and geographical sampling - Method
Errors on the global ocean thermosteric sea level have been estimated in a very similar way as in Lyman et al. (2006):
• Annual mean reference fields are computed from weekly SSALTO/DUACS SLA maps for the years 1993-2005;
• For each of these 13 annual mean SLA reference fields, 144 (12 months x 12 years from 1993 to 2004) monthly sets
of simulated observations are created by sub sampling the reference fields at the time and position of the in situ
temperature profiles.;
• Monthly SLA maps are next reconstructed for each of the 13x144 sets of simulated observations. The mapping
method used is the one described in section 0;
• Finally, differences between the reconstructed fields and the reference fields as global averages for the 60°S-60°N
area are calculated for the 1993-2004 periods and for each of the 13 realizations. Errors in the global thermosteric
sea level are calculated from the rms over the 13 realizations.
Figure 1
Number of in situ temperature profiles valid up to 700-meter depth in 1°x1° boxes for the year 1993, 2000 and 2006. Color
scale: from 2 to 18 every 4.
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 15
Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index
Two tests have been performed using this method. For the first test (test 1), the global mean (between 60°S and 60°N) is
calculated from the reconstructed areas – the mean is thus sometimes far from being global (Figure 2). For the second test (test
2), the reconstructed fields are first completed by zero values in order to create global fields before the calculation of the global
mean. As we will see, large differences between test 1 and test 2 can appear because of large-unreconstructed area in very
poor sampled years (Figure 2).
Figure 2
Annual mean reference SLA field for the year 1993 (left) and monthly reconstructed field for January 2000 obtained using the
mapping method of the sub sampled 1993 reference field at the January 2000 observations (right). Color scale: from -10 to 10
every 1 cm.
Impact of the temporal and geographical sampling – Results
Results indicate that errors associated to the global mean thermosteric sea level vary from one year to another as a function of
the temporal and geographical repartition of the in situ measurements and thus as a function of the percentage of reconstructed
ocean (Figure 3, Figure 4). The percentage of reconstructed ocean is calculated by comparing the area of the ocean
reconstructed by the mapping method using the in situ observation (area in colour on Figure 2-right) to the area sampled by the
reference field (Figure 2-left) between 60°S and 60°N.
Results also indicate that errors quite differ between test 1 (uncompleted field) and test 2 (field completed by zero values). For
test 1, errors vary from 0.09 cm rms for well sampled years (1995, 2004 for example) to 0.17 cm rms for less well sampled
years (2000, 2001). Errors are much larger for test 2 and vary from 0.10 cm rms for the year 2004 which is well sampled with
more than 95 % of the ocean reconstructed to 0.44 cm rms for the year 2000 which is really less well sampled with only 70 % of
the ocean reconstructed.
It is therefore really difficult to evaluate the true errors associated to the global mean thermosteric sea level. We think,
nevertheless, that test 1 minimizes the error since it assumes that the missing field is centred on zero and that test 2 maximizes
the errors since it assumes that the missing field is everywhere equal to zero. The truth errors might thus be situated between
the green and the bleu curves on Figure 3. They might vary from 0.1 cm rms for a well sampled ocean and between 0.17 and
0.44 cm rms when the ocean is less well reconstructed.
Additionally, a clear linear relationship is observed between the error on the global mean thermosteric sea level and the
percentage of the reconstructed ocean (Figure 4). This linear relationship is a very powerful tool to infer the error as a function
of the geographical repartition of the in situ measurements and to anticipate and emphasis the need of new in situ observations
in term of array design experiment. Results indicate also that the errors can be very high (from 0.5 cm rms to 1.5 cm rms) in
area with just a few in situ measurements and for which the percentage of reconstructed ocean is very low (<10 %).
Of course these results are also attached to the mapping method used. There is a compromise between the mapping method
which smoothes the individual observations onto a spatially consistent field and the temporal and spatial repartition of the in situ
observations.
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 16
Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index
Figure 3
Monthly rms error on global mean thermosteric sea level for the period 1993-2004 (cm). Green curve: test 1 (see text), Blue
curve: test 2, Turquoise curve: percentage of reconstructed ocean for the area 60°S-60°N. The dotted lines correspond to 12-
month averages.
Figure 4
Rms error on global mean thermosteric sea level as a function of percentage of reconstructed ocean (cm). Green curve: test 1
(see text), Bleu curve: test 2.
Impact of the vertical sampling
The impact of the vertical sampling of the in situ measurements is also studied as it varies as a function of probe type and thus
as a function of time.
High-resolution XBT and CTD measurements have usually 1-dbar vertical resolution from top to bottom as low-resolution CTD
have very dispersed vertical sampling characteristics and as profiling float measurements have roughly 10-dbar vertical
resolution near the surface and wider resolution at depth for a mean number of 80 observations between the surface and 2000-
meter depth. Simple statistics calculated for the top 700-meter depth and for the 1993-2006 period show that the mean vertical
interval between two measurements was between 10-dbar and 15-dbar at the beginning of the period, that it increased to 20-
dbar for the year 2000 and up to 30-dbar for the year 2003. After this year, it decreased to 15-dbar with the development of
profiling float measurements. The depth of the first measure at the surface has also deepened from 2-dbar from 1993 to 2002 to
4-dbar since the coming of profiling float measurements.
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 17
Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index
In order to quantify the impact of the vertical sampling of the in situ measurements on the interannual variability of the global
mean thermosteric sea level, global temperature and salinity fields from the global PSY3v1 Mercator system (Drévillon et al.,
2006) are used. The fields used are the one publicly available and re-interpolated every 5-meter in the top 30 meters then every
10 to 15-meters down to 75-meters and then every 25-meters down to 700-meters.
The method consists in interpolating the PSY3v1 fields at the position of the in-situ measurements using two vertical
interpolation procedures: 1) keeping the vertical resolution of the PSY3v1 system, 2) interpolating the PSY3v1 temperature and
salinity fields on the in-situ z-levels. The two sets of synthetic observations are then used to calculate global mean thermosteric
sea level. Results (not showed) indicate that the vertical sampling of the in situ measurements have no significant impact on the
results which means that the past and actual vertical sampling of the in situ measurements are suitable to study climate signals.
Impact of the method used to calculate global mean thermosteric sea level
Results presented in section 0 show that errors on the global mean thermosteric sea level due to sampling characteristics of the
in situ measurements present values which vary as a function of the temporal and geographical repartition of the in situ
measurements but also as a function of the method used to calculate the global mean thermosteric sea level (fields completed
or not before the calculation of the global mean).
Three tests have been performed in order to quantify the errors associated to the method used to calculate the global mean
thermosteric sea level calculated from the in situ observations. As the geographical repartitions of the in situ measurements are
not global, they don’t allow the calculation of a “true” global mean of the thermosteric fields. An important question is thus to
know if it is necessary or not to complete the thermosteric field before the calculation of the global mean and if the answer is
yes, with what values.
Three tests have thus been performed in order to calculate global mean thermosteric sea level:
• Test 1: from non global in situ mapped fields;
• Test 2: from global in situ mapped fields completed by the time-mean field (i.e. Levitus annual mean climatology)
which is a static field during the whole period;
• Test 3: from global in situ mapped fields completed by “steric” altimeter SLA fields which are time-variable fields. The
“steric” altimeter SLA fields are deduced from regression coefficients computed from a global altimeter (SLA) / in situ
(steric-height) comparison study (Guinehut et al., 2006).
Figure 5
Global mean thermosteric sea level for the three tests: black, green and blue curves (see text) (in cm). The turquoise curve
corresponds to the percentage of reconstructed ocean for the area 60°S-60°N. Thick lines correspond to 12-month running
mean.
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 18
Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index
The three tests show quite similar results (Figure 5). The global tendencies are very close but the associated trends can be
relatively different. Results are sensitive to the method used to complete or not the fields, particularly when the percentage of
reconstructed ocean are lower like during the years 2000 and 2001. Differences between the three tests can then be of the
order of 0.5 cm for percentage of reconstructed ocean of 70 %.
The values are completely coherent with the ones presented on Figure 4. They show additionally that upper bound values
presented on Figure 4 are totally realistic. It is obviously almost impossible to tell if one estimation of the global mean
thermosteric sea level is more realistic than the others but this study helps to understand the dispersions observed between the
different published estimates (see for example http://sealevel.colorado.edu/steric.php for a review).
Discussion
Additionally to other uncertainty related to measurements accuracy/bias for example, error bars on the global mean thermosteric
sea level due to sampling characteristics of the in situ measurements vary as a function of temporal and geographical repartition
of the in situ measurements but also and coherently as a function of the method used to calculate the global mean thermosteric
sea level (fields completed or not and with what values before the calculation of the global mean).
As it has been specified in section 0, no additional qualification has been performed on the in situ temperature measurements.
An important notice has been recently made to Argo data users rising pressure offset errors on SOLO floats equipped with FSI
CTD. The consequence was the introduction of a significant cold bias in the analyses by these instruments (Figure 6). At the
same time, there are lots of discussions concerning XBT measurements which are the primary source of the data used in the
different studies on thermosteric sea level interannual variability. Some published (Gouretski and Koltermann, 2007) or ongoing
studies (Wijffels et al., in prep.) have recently showed that XBT measurements exhibit warm bias of the order of 0.4 et 0.5 °C on
the water column around 100-meter depth by comparison to other data sets resulting in depth-averaged values from 0.1°C in
the 90s to 0.3°C in 2000-2001 (Gouretski and Koltermann, 2007). The warm bias suspected at the beginning of the period of the
study combined to the cold bias due to some Argo float measurements problem suggest that care much be taken when using
simultaneously all these data sets and when interpreting the results. Results by Lyman et al. (2006) have, for example, recently
been revisited by Willis et al. (2007) and they demonstrate that the recent cooling signal in the upper ocean (as the one
presented on Figure 6) is an artifact of the simultaneous use of Argo floats and XBT measurements and that the introduced
biases are larger than the sampling errors. Results showed on Figure 6 must then be taken cautiously.
Figure 6
Interannual variability of the global mean altimeter sea level (black curve) and thermosteric sea level calculated with all available
in situ temperature measurements valid up to 700-meter depth (blue curve) and calculated with all available temperature
measurements except the SOLO-FSI floats data (green curve) (in cm). Error bars are from Figure 4 and Figure 5. The turquoise
curve corresponds to the percentage of reconstructed ocean for the thermosteric estimation and for the area 60°S-60°N, the
dash line corresponding to the no SOLO-FSI case.
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 19
Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index
There are thus very strong needs for careful and precise validation/calibration of the different in situ data sets. Uncertainties still
persist on different points including: fall rate equation of the XBT measurements, coarse automated quality control procedure on
real-time profiling float data, salinity drifts on profiling float instruments.
In spite of these reserves, the Argo almost global profiling float array now offers the opportunity to study deeper thermal
contributions than 700-meters but also the impact of salinity field on sea level interannual variability. Additionally, studies using
independent data sets like GRACE measurements which provide estimates of mass change must be carried on (see for
example Lombard et al, 2006) in order to close the sea level budget.
References
Drévillon, M., Y. Drillet, G. Garric, J.-M. Lellouche, E. Rémy, C. Deval, R. Bourdallé-Badie, B. Tranchant, M. Laborie, N. Ferry,
E. Durand, O. Legalloudec, P. Bahurel, E. Greiner, S. Guinehut, M. Benkiran, N. Verbrugge, E. Dombrowsky, C.-E. Testut, L.
Nouel, F. Messal, 2006: The GODAE/Mercator global ocean forecasting system: results, applications and prospects, World
Maritime technology conference proceedings.
Gouretski, V. and K. P. Koltermann, 2007: How much is the ocean really warming?, Geophys. Res. Lett., 34, L01610,
doi:10.1029/2006GL027834.
Guinehut, S., P.-Y. Le Traon, and G. Larnicol, 2006: What can we learn from Global Altimetry/Hydrography comparisons?,
Geophys. Res. Lett., 33, L10604, doi:10.1029/2005GL025551.
Ingleby, B., and M. Huddleston, 2006: Quality control of ocean temperature and salinity profiles - historical and real-time data.
To appear in Journal of Marine Systems.
Ishii, M., M. Kimoto, K. Sakamoto, and S.I. Iwasaki, 2006: Steric sea level changes estimated from historical ocean subsurface
temperature and salinity analyses, Journal of Oceanography, 62 (2), 155-170.
Larnicol, G., S. Guinehut, M.-H. Rio, M. Drevillon, Y. Faugere and G. Nicolas, 2006: The Global Observed Ocean Products of
the French Mercator project, Proceedings of 15 Years of progress in Radar Altimetry Symposium, ESA Special Publication, SP-
614.
Lombard, A., D. Garcia, G. Ramillien, A. Cazenave, R. Biancale, J.M. Lemoine, F. Flechtner, R. Schmidt and M. Ishii, 2006:
Estimation of steric sea level variations from combined GRACE and Jason-1 data, submitted to EPSL.
Lyman, J.M., J.K. Willis, and G.C. Johnson, 2006: Recent Cooling of the Upper Ocean, Geophys. Res. Lett., 33 (18, L18604).
Ssalto/Duacs User Handbook, 2006: (M)SLA and (M)ADT Near-Real Time and Delayed Time Products, SALP-MU-P-EA-21065-
CLS, Edition 1.5.
Willis, J.K., D. Roemmich, and B. Cornuelle, 2004: Interannual variability in upper ocean heat content, temperature, and
thermosteric expansion on global scales, J. Geophys. Res., 109 (C12036, doi:10.1029/2003JC002260), 13.
Willis, J.K., J.M. Lyman, G.C. Johnson and J. Gilson, 2007: Correction to “Recent Cooling of the Upper Ocean, Geophys. Res.
Lett., submitted.
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 20
GRACE: an improved MDT reference for altimetric data assimilation
GRACE: an improved MDT reference for altimetric data assimilation
By Frédéric Castruccio1
, Jacques Verron 1
, Lionel Gourdeau2
, Jean Michel Brankart1
and Pierre
Brasseur1
1
Laboratoire des Ecoulements Géophysiques et Industriels, BP 53. 38041 Grenoble Cedex 9
2
IRD Institut de recherche pour le développement, BP A5. 98848 Nouméa cedex. Nouvelle-Calédonie
Introduction
Since 1992, the altimetric satellites provide a high precision, high resolution and quasi-synoptic observation of the Sea Surface
Height (SSH), the sea level above a reference ellipsoid. The SSH signal is the sum of (i) the geoid and (ii) the dynamic
topography. Only the later is relevant for oceanographic applications. However, the poor knowledge of the geoid has prevented
the oceanographers to fully exploit the altimetric measurement, and altimetric applications have concentrated on ocean
variability, through the analysis of the Sea Level Anomaly (SLA). The SLA has been widely and successfully used to improve
our knowledge of the ocean dynamics [Fu and Cazenave, 2001]. Nevertheless, it is still challenging to infer the ocean dynamic
topography (DT) from the altimetric signal because of geoid uncertainties. Absolute Dynamic Topography have only been
accessible by the addition of a Mean Dynamic Topography (MDT) estimate to the SLA.
In the context of altimetric data assimilation, the definition of a reliable MDT reference is a recurrent issue [Blayo et al., 1994 ;
Birol et al., 2004]. A variety of methods have been applied to generate MDT products, but none of them was found fully
satisfactory.
Several geodetic missions like CHAMP (2000), GRACE (2002) and GOCE scheduled for 2007, are dedicated to provide a
precise estimate of the ocean geoid (with a centimetric precision for short-wavelength features around 100 km). Several studies
have recently concluded that the actual resolution of the MDT reference computed using gravimetric data is now compatible
with the use in a context of data assimilation experiments [Gourdeau et al., 2003], in particular in the tropical Pacific Ocean,
which is our region of interest.
The objective of this study is to investigate the impact of a mean dynamic topography deduced from a GRACE geoid on the
assimilation of altimetric data along with in-situ temperature profiles. The emphasis is on the better compatibility between both
types of observation data sets. This better mean state compatibility contributes to provide a more efficient data assimilation,
making a better use of the data complementarity. The results are promising and represent a clear improvement regarding
previous studies [e.g. Parent et al., 2003]. Nevertheless, some limitations persist, most of them related to the resolution of the
geoid.
The investigation is performed with a primitive equation model of the tropical Pacific Ocean where an easily accessible and
rather synoptical set of in-situ data is available, thanks to the TAO/TRITON moorings, to complement the altimetric
observations. The Singular Evolutive Extended Kalman (SEEK) filter is used to jointly assimilate the TOPEX/POSEIDON and
ERS1&2 SSH referenced to the GRACE geoid, and the TAO/TRITON temperature profiles. Two 6-year hindcast experiments
over the 1993-1998 period, encompassing the strong 1997-1998 El Niño/La Niña event, have been performed. They only differ
by the use of data assimilation.
This note is divided in 5 sections. Following introduction, the model, the assimilation scheme and the assimilated data are
described in section 2. Section 3 is dedicated to the mean sea surface reference issue and the so-called GRACE MDT used to
reference altimetric residual component. Results of the 6-year hindcast experiment are analyzed in section 4. Section 5
discusses and summaries the results.
Assimilation Experiment: model, method and data sets
Model
The assimilation experiments were performed with the OPA
1
OGCM. The configuration is the so-called ORCA2 configuration: a
global low resolution 2°x2° ORCA type grid [Madec et Imbard, 1996] with a variable meridional resolution varying from 0.5° at
the equator to 2° poleward of 20° in latitude in order to improve the equatorial dynamics. The model solves the primitive
equations of ocean dynamics and use a free surface formulation [Roullet and Madec, 2000]. The temporal scheme is a leap-frog
scheme with a 5760 seconds time step. Along the vertical, there are 31 z-coordinate levels. This model has been used
1
http://www.lodyc.jussieu.fr/NEMO
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 21
GRACE: an improved MDT reference for altimetric data assimilation
extensively for tropical dynamics studies and validated accordingly [e.g. Grima et al., 1999 ; Lengaigne et al., 2003 ; Alory et al.,
2005].
The model is forced at the surface boundary with heat, freshwater and momentum fluxes. The ERS scatterometer wind stresses
complemented by TAO derived stresses [Menkes et al., 1998] which together tend to produce more realistic thermocline and
zonal currents, are used. The heat and fresh water fluxes are computed online through bulk formulae and depend on prognostic
sea surface temperature (SST) and NCEP
2
atmospheric interannual data provided by the NOAA-CIRES ESRL/PSD Climate
Diagnostics branch. The observed monthly mean precipitation field from Xie and Arkin [1997] is used instead of NCEP rainfall.
No relaxation on SST is used but a restoring term is applied on sea surface salinity (SSS) to avoid unrealistic drift due to our
poor knowledge of the fresh water fluxes.
Prior to the interannual simulations, the model starts from rest, with the Levitus temperature and salinity fields [Levitus, 1998]. It
is spun up during 2 years using a climatological forcing calculated from the 1993-1998 interannual forcing fields. In order to limit
the drift in the mean thermohaline structure, a Newtonian damping term is added in the temperature and salinity equations
during the spin up.
Method: The SEEK filter
The assimilation method used in this study is derived from the singular evolutive extended Kalman (SEEK) filter, which is a
reduced-order Kalman filter introduced by Pham et al. [1998]. This sequential method has already been described and used in
various types of studies [e.g. Verron et al., 1999 ; Gourdeau et al., 2000 ; Parent et al., 2003 ; Durand et al., 2003 ; Brankart et
al., 2003 ; Birol et al., 2004 ; Skachko et al., 2007]. A recent review of the developments of the SEEK filter method for data
assimilation in oceanography since the original paper by Pham et al. [1998] can be found in Brasseur and Verron [2006]. In the
present implementation, the error subspace basis is assumed to be temporally persistent as in the works by Verron et al. [1999],
Gourdeau et al. [2000] and Parent et al. [2003]. We also make use of the local variant of the SEEK filter described in Brankart et
al. [2003] and Testut et al. [2003]. The weak correlation associated with distant variables, which are considered as irrelevant in
the reduced space, are set to zero. Therefore the analysis for each water column will only depend on the observations within a
specific influence bubble. A box of 15 X 9 grid points is used to take into account the anisotropic nature of the tropical Pacific
dynamics.
Data assimilation is only applied in our region of interest, i.e. the tropical Pacific, even though the model is global. The tropical
Pacific domain is defined – following Durand et al. [2003] - between 20°N and 25°S in latitude and from 120°E to the American
coast in longitude. Buffer zones are used to smoothly connect the assimilated domain to the rest of the model domain.
Continuous data assimilation method: IAU
In addition to the regular SEEK filter procedure an Incremental Analysis Update (IAU) algorithm has been implemented
[Ourmières et al., 2006]. Indeed, a significant drawback of sequential methods is the time discontinuity of the solution resulting
from intermittent corrections of the model state. This discontinuity can lead to spurious high frequency oscillations and data
rejection. The IAU algorithm acts like a continuous data assimilation method. The principle is to incorporating the sequential
analysis increment δx directly in the prognostic equations of the model as a forcing term:
λ(t)δx+M=
t
V
∂
∂
where M are the right hand side members of the prognostic equation of the state variable V and λ a parameter such that:
Parametrization of the error covariances
The assimilation sequence must be initialized with some initial guess for the state X0 and the associated error covariance
matrix P0. Following Pham et al. [1998], a convenient method to initialize the error covariance matrix is to use a limited number
of three-dimensional, multivariate empirical orthogonal functions (EOFs) describing the dominant modes of free-model
variability. The underlying hypothesis is that the mean model state is representative of the mean true ocean. The assimilation of
an absolute altimetric signal implies a control of the mean model state. This change concerning the role of the assimilation leads
us to develop a specific protocol to parameterize the reduced order forecast error covariance matrix Pf
of the SEEK filter.
2
http://www.ncep.noaa.gov
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 22
GRACE: an improved MDT reference for altimetric data assimilation
An ensemble procedure is used to identify the appropriate reduced space for Pf
instead of EOFs of the model variability, as it is
usually done in the SEEK filter [Cane et al., 1996 ; Verron et al., 1999 ; Gourdeau et al., 2000]. It is first assumed that a model
simulation with a strong relaxation towards climatological fields provides a good approximation of the mean true ocean. Then by
using this reference run to reinitialize the free run every 5 days during one year, an ensemble of differences between this
reference simulation and the free model 5-day forecasts without nudging is generated. This ensemble of 73 members
represents the 5-day forecast error between the model and the reference trajectory. The covariance of this ensemble turns out
to be an appropriate estimate of the model error covariance, needed to parameterize the SEEK filter. The rank of this matrix is
reduced using a limited number (30) of three-dimensional, multivariate empirical orthogonal functions (EOFs) describing the
dominant modes of the ensemble covariance.
Regarding the parameterization of the observation errors covariance, a diagonal matrix is used with respectively 5 cm and 0.4°C
standard deviation for altimetry and temperature data.
Data sets
Altimetric Data
The altimeter products were produced by Ssalto/Duacs and distributed by Aviso
3,
with support from Cnes. The altimetric
observations consist of along-track sea surface topography, obtained as the sum of along-track TOPEX/Poseidon and/or ERS
altimeter SLA, and the mean dynamic topography (see next section). The assimilation window is five days. Each analysis is
computed using all available data gathered within a 5-day interval (2.5 days before and after the analysis time).
TAO Data
The TOGA-TAO observation system was designed to provide continuous, high-quality measurements in the equatorial Pacific
waveguide to improve the description, understanding, and prediction of El Nino [McPhaden et al., 1998]. The full array consists
of approximately 70 moorings in the tropical Pacific Ocean, located between 8°N–8°S, and 137°E–95°W, and at depths ranging
from 0 to 500 m. They provide among other things high-quality measurements of temperature profiles. The 1-day averaged data
available on the TAO Web site
4
are used for assimilation in the model. As for the altimetry, each analysis is computed using all
available data gathered within a 5-day interval.
The mean sea surface reference issue
Problem definition
The altimeters measure with a centimetric level accuracy the Sea Surface Height (SSH) above a reference ellipsoid (see Figure
1). The SSH value takes then account of effects such as: (i) the effect due to the ocean circulation called the dynamic
topography and (ii) the effect due to the earth gravity field variation called the geoid. The dynamic topography (DT = SSH –
geoid) is the signal of interest for the oceanographers. However the DT is contaminated by large geoid errors, especially with
high order harmonics (harmonics of order 20 and higher). Alternatively, the temporal mean of the SSH signal, the Mean Sea
Surface Height (MSSH) is known with a high accuracy (thanks to the repetitiveness of altimetric missions) and the variable part
of the dynamic topography (Sea Level Anomaly – SLA) can be deduced with high precision. The DT can then be deduced by
adding the SLA to an estimation of the Mean Dynamic Topography (MDT = MSSH – geoid).
The lack of an adequate knowledge of the MDT reference is a recurrent issue [Blayo et al., 1994 ; Birol et al., 2004] for altimetric
data assimilation. It is surmounted leaning either on a numerical model (the model MDT is assumed to be perfect and used as a
reference for altimetric residuals) or on synthetic solutions based on other data sources (in-situ in general) after a more or less
sophisticated treatment [e.g. Mercier et al., 1986 ; LeGrand, 1998, Niiler et al., 2003 ; Rio et al., 2004]. No solution was found
fully satisfactory. Synthetic solutions are not straightforward to build and often suffer from a lack of resolution. They are often
based on a set of assumptions (geostrophic balance, spatial and temporal colocalisation of altimetric and in situ data, …) that
are on several respects inadequately accurate for our purposes. Sometimes, when they are based on long range climatological
data, they suffer from an excessive smoothing for relatively short term applications. And most often, they include a significant
bias on the reference level that is a critical issue both from the theoretical point of view of data assimilation and from the point of
3
http://www.jason.oceanobs.com
4
http://www.pmel.noaa.gov/tao
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 23
GRACE: an improved MDT reference for altimetric data assimilation
view of the complementarity of multiple observation systems. Errors on the MDT are known to have a strong impact on the
realism of the ocean circulation simulated with data assimilation [Birol et al., 2004].
Figure 1
Schematic representation of the altimetric measurement principle.
A fully observed MDT
Tracking data from some satellite constellations has been used over the last three decades to study the Earth gravity field,
leading to substantial improvement in our knowledge of the geoid [Nerem et al., 1995]. While these conventional methods have
provides accurate information, especially at long wavelength [Lemoine et al., 1998 ; Biancale et al., 2000], they have insufficient
accuracy to provide the short wavelength of the geoid required to evaluate a relevant MDT. Recent satellite missions such as
CHAMP
5
(2000), GRACE
6
(2002) and GOCE
7
scheduled for 2007 are changing this perspective. They have been devised to
provide high resolution, highly accurate geoids. The MDT references computed using this gravimetric data are now compatible
with their use in a context of data assimilation experiments [Gourdeau et al., 2003 ; Birol et al., 2005].
GRACE gravimetric data
The geoid used in this study is the EIGEN-GRACE02S geoid from the GeoForschungsZentrum (GFZ) of Potsdam, Germany
[Reigber et al., 2005]. It is a medium-wavelength gravity field model based on 110 days of GRACE tracking data. The solution
has been derived solely from satellite orbit perturbations and is independent from oceanic and continental surface gravity data.
This model represented by a spherical harmonic expansion is complete to degree 150. It resolves the geoid with an accuracy of
better than 1 mm at a resolution of 1000 km [see Reigber et al., 2005].
GRACE MDT
The so called GRACE MDT used in this study was computed by the direct method, i.e. by subtracting the EIGEN-GRACE02S
geoid and an MSSH product. The MSSH used here corresponds to a 7-year mean (1993-1999) based on the most recently
processed TOPEX/POSEIDON, ERS1&2 and GEOSAT altimetric satellite data (SMO CLS01, Hernandez et al. [2001]). In order
to overcome the issue of the non-compatibility of the spectral content of both surfaces, the difference is developed into spherical
harmonics and then truncated to degree 60 (i.e. a resolution of 333km). The formal cumulated error of the mean dynamic
topography reaches 4 cm at degree 60.
This GRACE MDT solution reasonably fits the real tropical Pacific MDT. It has been assessed against in-situ observations of the
0/500 dbar dynamic height deduced from the TAO/TRITON moorings [Castruccio et al., 2006 ; Castruccio et al., 2007] and
represents a clear improvement regarding the climatology and moreover regarding prior results using CHAMP gravimetric data
[Gourdeau et al., 2003].
5
http://www.gfz-potsdam.de/pb1/op/champ/index_CHAMP.html
6
http://www.gfz-potsdam.de/pb1/op/grace/index_GRACE.html
7
http://www.esa.int/esaLP/LPgoce.html
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 24
GRACE: an improved MDT reference for altimetric data assimilation
Hindcast experiment (1993-1998)
Two simulations are performed for the 1993-1998 period, encompassing the strong 1997-1998 El Niño/La Niña event, probably
the strongest of the 20
th
century. The first is a free run without data assimilation. The second only differs with respect to the
assimilation of altimetric data referenced with the GRACE MDT along with in-situ TAO temperature profiles. The same initial
condition and the same forcing scheme are used.
Figure 2
Absolute dynamic topography (left panel, in m) and temperature (right panel, in °C) RMS Differences over the 1993-1998 period
with respect to assimilated observations over the tropical Pacific. The free run (green) and the assimilated run (black) are
plotted.
Validation with respect to assimilated data
Model-Observation misfit
The evolution of the RMS Differences (RMSD) between the assimilated observations and the model predictions are shown in
Figure 2 for the free run and the IAU run. During the free simulation, the DT RMSD has an average value of 8.1 cm. The data
assimilation enables the RMSD to be decreased by nearly 2 cm down to 6.3 cm. Regarding the TAO, the mean RMSD is
reduced from 1.54 °C for the simulation without data assimilation down to 0.9 °C for the experiment assimilating jointly altimetric
and TAO data. This simultaneous reduction of the RMSD regarding both types of assimilated data sets represents a clear
improvement compared to previous results, thanks to the better data mean state compatibility brought by the use of GRACE
data [Castruccio et al., 2006]. Performing a joint assimilation of SLA data with in-situ data may reach a deadlock due to the
different reference mean states of the two types of data [Parent et al., 2003]
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 25
GRACE: an improved MDT reference for altimetric data assimilation
Figure 3
Mean dynamic topography (in meter, left) and section of the standard deviation of the temperature along the equator (in °C,
right) related to the 1993-1998 period obtained from observation (top panels), the model without assimilation (middle panels)
and the model with joint assimilation (bottom panels).
Comparison with observations
One of the interests of an absolute dynamic topography assimilation is to constrain the mean model state in addition to its
variability. Figure 3 shows the MDT and the isotherms mean depths over the 1993-1998 period for the observations and the 2
simulations. Data assimilation has a strong and benefic impact on both fields. The MDT simulated with data assimilation is more
realistic, in particular in the south central tropical Pacific, where the free run MDT compares poorly with observations. The ridge
associated with the North Equatorial Counter Current (NECC) along 8/10°N is also in better agreement with the observations
with steeper meridional gradient. Nevertheless, the MDT simulated with joint data assimilation exhibits unusually small patterns
along 8/10°N. These patterns are not found in the observed MDT nor in the free run MDT.
The mean depth of the isotherms and the standard deviation of the temperature along the equator are also shown in Figure 3.
The structure and the variability of the temperature fields have been improved. In particular, the variability of subsurface
temperature along the thermocline, which is too weak in the free run simulation, has been intensified by data assimilation. The
variability is however still under-estimated compared to observations. Along with this strengthening of the variability, the data
assimilation shallowed the thermocline which is too deep (approximatively 20 m deeper than in the observations) in the free run
simulation.
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 26
GRACE: an improved MDT reference for altimetric data assimilation
Validation with independant data
Surface currents
Figure 4
Mean zonal velocity (in m.s
-1
) at 15 m depth. Respectively from top to bottom, the Niiler [2001] climatology (top panel), the mean
related to the 1993-1998 period obtained from the model without assimilation (middle panel) and the model with joint
assimilation (bottom panel).
Tropical oceans exhibit mainly zonal circulation. The analysis of the zonal surface current is a stringent test for validating our
simulations as currents are very sensitive to the meridional gradient of the dynamic topography, particularly towards the
equator, where the Coriolis force vanishes. The maps of the mean zonal current at 15 m depth for the Niiler [2001] climatology
and 2 runs are shown in Figure 4. Niiler [2001] climatology of near-surface currents has been estimated from satellite-tracked
SVP (Surface Velocity Program) drifting buoys and provides observations of near-surface circulation at unprecedented
resolution. The alternate bands of eastward- and westward- flowing currents characterizing the tropical Pacific Ocean circulation
are present in the free run model simulation as well as in the simulation with data assimilation. However, the free run currents
are too weak. The surface zonal currents simulated with joint data assimilation are in better agreement with the Niiler [2001]
climatology. The NECC has been strengthened accordingly with the steepening of the meridional gradient of the dynamic
topography and reaches 40 cm.s
-1
. The South Equatorial Current (SEC) has also been intensified. The North and South
branches of the SEC are clearly identified in the central Pacific but not in the far east of the basin. The wrong representation of
the SEC separation is a recurrent issue for ORCA simulation [Lengaigne et al., 2003] and the assimilation is not able to tackle
this problem. In the north, the North Equatorial Current (NEC) reaches 20 cm.s
-1
, still slightly under estimated compared to the
observations. In the south hemisphere, the surface zonal velocity patterns are closest to the drifter climatology with a South
Equatorial Counter Current (SECC) near 9°S confined in the West Pacific and the weak eastward flows (the return branch of the
subtropical gyre) flowing south of 20°S as in the climatology.
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 27
GRACE: an improved MDT reference for altimetric data assimilation
Figure 5
Horizontal distributions of XBT profiles available for the 6 years of the assimilation experiment. Superimposed in red the position
of the 3 selected rails corresponding to the Tokyo-Auckland, San Fransisco-Auckland and Panama-Auckland maritime lines.
XBT
To further assess the results, we evaluated the experiments using independent XBT data from the VOS
8
(Voluntary
Observation Ships) program. The data set used in this study has been downloaded from the CORIOLIS
9
Web site.
Approximatively 60000 profiles are available over the 6 years of the experiment. Figure 5 shows the irregular spatial distribution
of the XBT profiles. Three ship lines, routinely sampled by VOS vessels, typical of the Western, Central, and Eastern Pacific are
selected (see Figure 5).
Figure 6
Differences between the XBT mean temperature section over the 1993-1998 period along the West (left
panels), Central (middle panels) and East (right panels) Pacific rails and the mean temperature section
simulated without data assimilation (top) and with assimilation (bottom). The black lines correspond to
the mean depth of the 12-16-20-24 and 28 °C isotherms over the 1993-1998 period from the XBT data.
8
http://www.vos.noaa.gov
9
http:/www.coriolis.eu.org
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 28
GRACE: an improved MDT reference for altimetric data assimilation
Figure 6 exhibits the mean structure difference between the observations and the 2 simulations. Most of the errors are initially
concentrated in the thermocline and the equatorial wave guide with magnitude up to 5 °C. These errors are drastically reduced
in the run using joint data assimilation, even off the TAO array area. This confirms the better mean thermocline depth simulated
with data assimilation. Nevertheless, high errors exist below the thermocline at 10°N on the Central line, i.e. just under a TAO
mooring (9°N-140°W). These high errors are not present in the free run model. Joint data assimilation appears to be in question
in this specific region as it has already been sugested by Figure 3 showing unrealistic small patterns for 6-year mean dynamic
topography along the ridge associated with the NECC.
Discussion and conclusion
In this paper, we have presented a 6-year hindcast experiment over the 1993-1998 period jointly assimilating an observed
absolute dynamic topography deduced from GRACE data and the in-situ TAO temperature profiles in a primitive equation model
of the tropical Pacific Ocean.
The objective of this study was to assess how the use of a GRACE geoid could improve the modeling of tropical Pacific
dynamics through data assimilation of altimetric and in-situ data. The study was motivated by the fact that defining the MDT
reference is a recurrent problem in altimetric data assimilation studies and that ongoing and future satellite missions dedicated
to the improvement of the earth geoid are likely to change this situation. The benefits brought by the use of a GRACE MDT in
the assimilation system are clear. Although altimetric data and in-situ temperature profiles are utterly complementary, the joint
assimilation of these two types of data can be conflictual. Errors on the mean dynamic topography reference can lead to
discrepancies between the two types of observations as noted by Parent et al. [2003]. These discrepancies are greatly reduced
by the used of the GRACE MDT [Castruccio et al., 2006]. Nevertheless, the joint assimilation is still problematic in the region
along 8/10°N. The resolution of the GRACE geoid is too low for the dynamic topography to correctly represent the fine latitudinal
structure relative to the NECC ridge introducing some inadequacies between the altimetic and TAO data in this region. These
inadequacies are clearly illustrated by Figure 7 showing the differences between the observed MDT and the MDT simulated with
and without data assimilation. The global RMSD is reduced from 4.5 cm down to 3.1 cm with data assimilation. However Figure
7 exhibits high error patches arround most of the TAO moorings along 8°N. These patches explain the rather noisy structure of
the mean dynamic topography simulated with data assimilation in this region (cf Figure 3). They are due to a mean state
difference between the two observation data sets assimilated in the model.
Figure 7
Differences between GRACE MDT and MDT of the model without assimilation (left panel) and the MDT of the model with joint
assimilation (right panel) related to the 1993-1998 period.
The mean state difference is illustrated by Figure 8 showing two meridional sections of MDT. The observed GRACE MDT (also
used to reference the assimilated altimetric signal) and the MDT simulated with and without data assimilation are plotted. The
two selected sections are 140°W (i.e. a section sampled by the TAO moorings) and 145°W (i.e. a section between two TAO
longitudes). The mean TAO dynamic height is also plotted for the section at 140°W. In-situ and satellite observations are in
good agreement except for the mooring at 9°N. The steep meridional slope of the mean dynamic topography can not be
accurately represented due to the relatively coarse resolution (333 km) of the GRACE MDT. This results in the presence of
errors in the assimilated dynamic topography leading to incompatibilities between altimetry and in-situ data. These
incompatibilities prove to be problematic for the joint assimilation of both data sets. Locally, TAO informations are dominant
(TAO data are daily vertical profiles). The analyzed states estimated by the SEEK filter are then close to TAO observations at
TAO positions. Between TAO moorings, we do not have anymore in-situ information, but we still have satellite altimetric data.
The analyzed states tend to be closer to altimetry (see Figure 8). The mean state difference between the two observation data
sets along 8/10°N then explains the patches seen on Figure 7 [see Castruccio et al., 2007].
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 29
GRACE: an improved MDT reference for altimetric data assimilation
Figure 8
MDT related to the 1993-1998 period along 145°W (left) and 140°W (right) for the model without assimilation (green line), the
model with joint assimilation (black line) and the observed GRACE MDT (black dashed line). The pink triangles for the section
along 145°W stand for the mean TAO dynamic height related to the 1993-1998 period.
To summarize, a data assimilation system based on the SEEK filter has been developed in order to assimilate the absolute
dynamic topography deduced from the TOPEX/POSEIDON and ERS1&2 altimetric data and the GRACE gravimetric data. The
altimetric signal is assimilated along with the in-situ TAO temperature profiles into a tropical Pacific Ocean model. We have
demonstrated the efficiency of such a system using a 6-year hindcast experiment over the 1993-1998 period. The results are
promising and represent a clear improvement regarding previous studies [e.g. Parent et al., 2003], thanks to the better data
compatibility brought by the use of GRACE MDT. Nevertheless, some limitations always exist. Most of them are related to the
resolution of the geoid. The next estimations of the geoid are expected to go well beyond the present accuracy.
The use of an absolute dynamic topography opens the way for the development of efficient assimilation systems based on
multiple data sets (in nature, space and time distribution). The integration of multiple data sets through operational systems is
crucial for our better understanding of the ocean system and for our capability to forecast its evolution at diverse time scale.
Further improvements in the knowledge of the MDT itself might result from converging studies on assimilated data resolution
and accuracy, both from space and in situ, on modeling and on assimilation techniques, within the context of operational
oceanography systems [Dobricic, 2005].
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Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 32
Altimeter data assimilation in the Mercator Ocean system
Altimeter data assimilation in the Mercator Ocean system
By: Mounir Benkiran1
1
Mercator Ocean - 8-10 rue Hermes. 31520 Ramonville St Agne
Introduction
To show the complementarities of the various altimetric data (Jason, Envisat and Gfo) used in PSY1V2 (MNATL 1/3 ° -
SAM1v2) prototype, we analyse here their respective impact on the analysis. We compare several simulations combining these
data sets with a reference simulation Sref. In this simulation Sref, we assimilate the complete data set (Jason, Ers2/Envisat and
Gfo). For all the simulations which are presented here, the same restart has been used. We made these simulations over the
years 2004/2005. In this paper, we only present the results over the year 2004. First of all, we show that it is important to use
the altimetric data stemming from various satellites, in particular when their spatial resolutions are different (Jason, Envisat and
Gfo). In the same way we show the impact of the fourth satellite (Topex) in a model with a resolution of 1/3 °.
Descrpition of the assimilation system
Mercator-Ocean operates a multivariate multi data assimilation system in real time since January 2004. This system called
PSY1v2, gives an oceanic large scale description and a two-week forecast of the North and tropical Atlantic (70°N-20°S) on a
weekly basis. The model is eddy permitting (1/3°, 27km) for basin scale studies. Satellite altimetry and sea surface temperature
(SST) are assimilated, as well as in situ data. The assimilation is based on a reduced order optimal interpolation (ROOI).
Model
The PSY1v2 system uses the ocean model OPA8.0 (http://www.lodyc.jussieu.fr/opa) developed at LOCEAN (Madec and
Imbard, 1996), (see Newsletter #13). The model uses primitive equations with Boussinesq approximation. It covers the North
Atlantic basin from 20°S to 70°N and from 99°W to 20°E. The horizontal grid is a 1/3° Mercator grid, and the average resolution
is 27km. This is not fine enough to resolve the eddies, but it can permit to an eddy (set by assimilation) to have a reasonable
lifetime (not trajectory). The vertical grid is a "Z"-type grid. Vertical levels are distributed with 43 levels, 20 of which are in the
first 1000 meters of the ocean. The levels vary in depth from 12 meters at the surface to 200 meters below 1500 meters. The
depth of the bottom level is 5600 meters. Note that the first temperature model node is at 6m depth. The temperature and
salinity near the artificial boundaries are restored to the seasonal climatology (Reynaud & al., 1998). A monthly climatology of
attenuation depth for the solar penetrating flux is derived from SEAWIFS (1997-2003). Salt rejection during ice formation and
fresh water production during melting are parametrised (Greiner & al., 2004). The daily forcings come from the Europeen Center
for Medium-Range Weather Forecasts (ECMWF) operational outputs. 12h-24h echeances from the 0h forecast are cumulated
with the 12h-24h echeances from the 12h forecast in order to have the best balanced daily windstress, heat flux, precipitation
and evaporation.
Data
Sea Level Anomalies
Along tracks altimetric data from Jason-1, Ers/Envisat and Gfo are assimilated. Data processing is performed by
SSALTO/DUACS (http://www-aviso.cnes.fr) and is distributed through the AVISO user service. The along track resolution is
typically 20km. The Sea Level Anomaly (SLA) errors are 2 cm for the Jason altimeter and 3.5 cm for Ers, Gfo and Envisat.
Only the observed SLA is kept as final data for the assimilation. Note that the SLA is rejected under the model ice. To compare
the model to the observed SLA, we have to subtract an estimate of the mean Sea Surface Height (MSSH) to the model SSH:
SLA
d
= tracks anomalies
SLA
m
= SSH
m
– MSSH
d
More precisely the altimetric data are track anomalies relatively to the 1993-99 period. The unknown difference, namely the
MSSH (Version 5.1 from June 2005), is the height corresponding to the mean oceanic circulation, and to the geoid variations. It
is estimated with an objective analysis mapping including altimetry, hydrology, drifters and gravimetry from GRACE (Rio &
Hernandez, 2004). The MSSH is the most critical parameter of a multivariate system, but today, it is still not accurately known.
The MSSH error typically ranges from 3cm to 6cm, which is slightly higher than the SLA error, and sometimes even larger than
the sea level variability. The system would be greatly improved by having a better estimate of the MSSH, but we are still waiting
for the results of the accurate gravimetry from the GOCE mission. Meanwhile, sensitivity tests to various MSSH products, as
Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 33
Altimeter data assimilation in the Mercator Ocean system
well as data withholding (in situ and/or altimetry) suggest that the MSSH inaccuracy can typically lead to regional biases of 2°C
and 1psu at the pycnocline level.
Other data sets
Another important data is the satellite SST. The RTG_SST 0.5°x0.5° analysis (Thiébaux & al., 2003) is produced daily by the
NOAA/NCEP (http://polar.ncep.noaa.gov/sst/). Details of the procedure can be found in the above reference, but the main
points are listed here. It is a refined version of the 1°x1° weekly Reynolds analysis (Reynolds & Smith, 1994). This analysis uses
in situ SST and NOAA-16/NESDIS satellite SST. Daytime and night time data are treated separately, and known biases are
corrected, but cloud cover and aerosols are still a source of uncertainty. Ship and buoy data are used to remove the remaining
biases.
The daily analysis is used once at the end of the ocean analysis cycle (Wednesday), at a degraded resolution of 1/3°x1/3°. SST
error is set to 0.6°C.
In situ observations include low and high resolution profiles of temperature and salinity. Depths vary from a few tens of meters,
to 2000m for the ARGO profilers. The data acquisition and quality control (Coriolis, 2002) is performed by the Coriolis Data
Centre (http://www.coriolis.eu.org). The data is gathered for Mercator-Ocean by the ARMOR chain (Guinehut, 2004) where
other checks and a data thinning are performed.
Assimilation
PSY1v2 has been the first Mercator-Ocean system to perform multivariate assimilation of altimetry data and in situ data. This
system uses the analysis tool SOFA3.0 developed by Pierre De Mey (De Mey & al, 2002) at LEGOS, and PALM from
CERFACS (Lagarde & al., 2001), the generalised coupler used to resolve large-scale assimilation problems on distributed
memory computers.
The standard Optimal Linear Estimation theory is used (De Mey & al., 2002). We recall below the equations that will come into
play in the results. If the true state is xt, H the observation operator, and ε the errors, then the observation y° (measurement) at
this time can be written as:
y° = H(xt) + ε
We can write the misfit (innovation) as a function of the model forecast xf and of the observation:
d= y° - H(xf)
Assuming that the prediction and observation errors are unbiased and have a normal distribution as well as known covariances
(B
f
and R respectively), the best estimate of x is xa, such as, by using the Kalman gain, K:
xa
= x
f
+ K (y°-H(x
f
))
As in optimal interpolation methods used in meteorology, we assume that correlation of errors from the matrices B
f
and R that
form the gain matrix, are homogeneous, stationary and given by empirical formulae:
B
f
=(D
f
)
1/2
C (D
f
)
1/2
D
f
: guess variance error
C: correlation matrix, constant in time
We assume that the correlations decrease toward zero with distance. Data and model differences, which are represented by the
innovation vector, are therefore only taken into account within an area of influence around each analysis point. The size of this
influence bubble is taken as twice the spatial decorrelation scales. This makes the method less than optimal, but means that
calculations are easier through the parallelisation of codes.
The method for reducing the state tries to satisfy both the need for robustness (we do not want to project onto a broad and
unknown subset), and for reducing calculations. The problem is truncated by using only dominant modes. The relationship
between the gain in the complete space K
ROOI
(ROOI: Reduced-Order Optimal Interpolation) and the gain in the reduced space
Kr can be written using S, the matrix made of the empirical orthogonal functions (EOFs) of the error covariance:
KROOI
= ST
Kr
Kr = Br
f
Hr
T
(Hr Br
f
Hr
T
+ Rr )
-1
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Mercator Ocean newsletter 25

  • 1. Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 1 GIP Mercator Ocean Quarterly Newsletter Editorial – April 2007 Goce satellite Credits : ESA - AOES Medialab Greetings all, Nowadays, several datasets are -or will be- available in a near future to improve operational forecasting in most aspects, like the ocean dynamics modeling, and the assimilation efficiency, that aims now to optimize the combination of temperature/salinity in situ profiles, drifter's velocities, and sea surface height deduce from altimeter's data and GRACE or future Goce geoid. But also strengthen forecasting system's applications, like the climate monitoring. For all these issues, an optimal use of ocean data, always too sparse and not enough numerous, is mandatory. Such studies are at the heart of this Newsletter issue. It begins with a Rio M.H. and Hernandez F. review of the Goce Mission, dedicated to focus and document the shortest scales of the Earth's gravity field. Goce satellite is due to fly in December 2007. With the next article Guinéhut S. and Larnicol G. investigate the influence of the in situ temperature profiles sampling on the thermosteric sea level estimation. They show that the impact is not negligible, and can introduce large errors in the estimation. In the second article, Benkiran M. and Greiner E. are evaluating the benefits of the drifter's velocities assimilation in the Mercator Océan 1/3° Tropical and North Atlantic operational system. A description of the assimilation scheme upgrade to take into account velocity control is given. Castruccio F. & al. describe in the third article the performance of an improved MDT reference for altimetric data assimilation. They concentrate their study on the Tropical Pacific Ocean. Finally, the Newsletter comes to an end with the Benkiran M. article. In his study, based on the 1/3° Mercator system, the impact of several altimeters data on the assimilation performance is assessed Have a good read
  • 2. Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 2 GIP Mercator Ocean Contents GOCE review.......................................................................................................................................................... 3 Data assimilation of drifter velocities in the Mercator Ocean system .............................................................. 6 Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index............................................................................................................................... 13 GRACE: an improved MDT reference for altimetric data assimilation............................................................ 20 Altimeter data assimilation in the Mercator Ocean system ............................................................................. 32 Notebook.............................................................................................................................................................. 40
  • 3. Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 3 News: GOCE review News: GOCE review By Marie Hélène Rio1 and Fabrice Hernandez2 1 CLS, Space Oceanography Division, 8/10 rue Hermès. 31520 Ranonville st Agne 2 Mercator Ocean , 8/10 rue Hermès. 31520 Ranonville st Agne Satellite Altimetry and the Mean Dynamic Topography issue Altimetric data from satellites are a key component of the observational constraints on which any operational ocean forecasting system can rely to ensure its ocean dynamics consistency. The satellite altimeters offer global and repetitive measurements of the sea level, with a unique resolution and accuracy. Its success and accomplishment in ocean dynamics sciences is yet proven [e.g., Fu and Cazenave, 2001]. However, since the beginning of satellite altimetry, more than 15 years ago, due to the lack of an accurate geoid, only the variable part of the ocean dynamic topography can be extracted with sufficient accuracy (few centimetres) for oceanographic applications. For the correct interpretation of these altimetric Sea Level Anomalies (SLA) in terms of sea level and geostrophic circulation, the provision of an accurate Mean Dynamic Topography (MDT) is mandatory. This has proved to bring significant improvement in ocean forecasting systems where assimilation of SLA provides better ocean circulation description, from large to mesoscales [Knudsen et al., 2005, and EU GOCINA projects main outcomes; Le Provost et al., 1999; Le Traon et al., 2002]. In addition, the MDT is the missing key element for the correct interpretation of all past, present and future altimetric data and their use for oceanographic long term analyses. Strong improvements have been made recently using satellite gravimetry products, in particular the recent geoid models based on GRACE data. Subtracting the last model EIGEN-GL4S computed by the GFZ/GRGS from an altimetric Mean Sea Surface allows computing the ocean Mean Dynamic Topography at scales larger than 400 km with accuracy of the order of few centimetres [Rio et al., 2005; Tapley et al., 2003]. But the MDT is expected to present scales as small as ten’s of km. To retrieve the missing shortest scales, different methods have been developed where in-situ oceanographic data (hydrologic profiles, drifting buoy velocities) are combined with the large scale derived MDT to estimate global, high resolution MDT [Niiler et al., 2003; Rio and Hernandez, 2004; Rio et al., 2005; Rio et al, 2007; Maximenko et al, 2005]. However the definitive jump toward absolute altimetry is still to come and the springboard is called GOCE. GOCE mission GOCE (Gravity Field and Steady-State Ocean Circulation) is the first core Earth Explorer mission from ESA’s Living Planet programme and is due to fly in December 2007. The nominal duration of the mission is 20 months, with a 3 month commissioning and calibration phase followed by two science measurement phases of 6 months separated by a 5 month eclipse hibernation period. Mission objectives are to determine the gravity field’s anomalies with an accuracy of 1 mGal (=10-5 m/s2) and the Earth geoid with an accuracy of 1-2 cm for a spatial resolution of 100 km. In order to meet these requirements, the principle of the GOCE mission is based on the combination of two techniques, a satellite to satellite tracking technique relative to GPS for retrieving the long wavelengths of the Earth Gravity field, associated to the use of a gradiometer (composed of three pairs of three-axis accelerometers) for measuring the shortest scales. The two Level-2 products of interest for oceanographers that will be delivered by ESA are the set of spherical harmonics coefficients of the Earth gravity field up to degree and order 200 (100 km resolution) as well as the full error covariance matrix of the coefficients. GOCE/GRACE complementarity The GOCE satellite has been designed to focus on the retrieval of the Earth’s gravity field short scales while the previous GRACE US-German mission was designed to resolve with millimetre accuracy the spatial scales of the Earth’s gravity field longer than 400 km. Both missions are then complementary so that the best static geoid model will certainly be obtained through a combination of gravity data from the two missions. The MDT solutions based on a combination of satellite and in-situ data mentioned above, will play an important role for the validation of these future GOCE/GRACE derived MDTs.
  • 4. Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 4 News: GOCE review Toward the shortest scales GOCE data will give access with reasonable accuracy to the spatial scales of the ocean Mean Dynamic Topography larger than 100 km. However, in some areas (semi-enclosed seas as the Mediterranean Sea, coastal areas, straits) the MDT is expected to contain even shorter scales [Rio et al., 2007]. The combination methods to other, independent estimates of the MDT, based on in-situ oceanographic measurements, will therefore still be essential to achieve higher resolution where needed. Also, in order to improve the geoid resolution, local solutions can be computed combining GOCE data to in-situ (ship or airborne) gravimetric measurements. Opening new issues Geoids, accurate enough to be used together with satellite altimetry to provide a full description of the ocean mesoscale (10- 1000km) have been expected for long time.. But the Russian dolls game is not over. The access to the geoid short scales with a centimetric accuracy now pushes us toward the limits of altimetry: This covers two key issues. The first is the need to improve the accuracy of altimetric measurement in coastal areas, through improved processing. The second is to correctly assess the errors on the different models used for altimetric corrections in order to better understand at last what the true error levels on altimetric data (MSS, SLA) are. Getting ready Oceanographers have been used for years to work on altimetric Sea Level Anomalies, focusing only to the ocean mesoscale variability. The GOCE data will make us enter a new era where we will at last have access to the absolute dynamic topography and to the absolute ocean geostrophic currents, not only for the forthcoming altimetric missions but also back in the past since the first altimetric measurements. This will open a number of new scientific issues. This will also have a huge impact for ocean and climate monitoring and forecasting and the operational forecasting centres must prepare from now to it, thinking about the best way to assimilate this new information (the geoid and its error covariance matrix) into their systems. References Fu, L.-L., and A. Cazenave, Satellite Altimetry and Earth Sciences. A handbook of Techniques and Applications, 463 pp., Academic Press, San Diego, CA, USA, 2001. Knudsen, P., O.B. Andersen, R. Forsberg, A.V. Olesen, A.L. Vest, H.P. Föh, D. Solheim, O.D. Omang, R. Hipkin, A. Hunegnaw, K. Haines, R.J. Bingham, J.-P. Drecourt, J.A. Johannessen, H. Drange, F. Siegismund, F. Hernandez, G. Larnicol, M.-H. Rio, and P. Schaeffer, GOCINA, Geoid and Ocean Circulation in the North Atlantic, pp. 70, Danish National Space Center, Copenhagen, 2005. Le Provost, C., P. Le Grand, E. Dombrowsky, P.-Y. Le Traon, M. Losch, F. Ponchaut, J. Schröter, B.M. Sloyan, and N. Sneeuw, Impact of GOCE for ocean circulation studies, ESA, 1999. Le Traon, P.-Y., F. Hernandez, M.-H. Rio, and F. Davidson, How operational oceanography can benefit from dynamic topography estimates as derived from altimetry and improved geoid, in ISSI workshop. Earth gravity field from space - From sensors to Earth sciences, Bern, Switzerland. Edited by G. Beutler, M.R. Drinkwater, R. Rummel, and R. von Steiger, in Space and Science Reviews, (108), pp. 239-249, Kluwer Academic Publisher, 2002 Maximenko, N.A., and P.P. Niiler, 2005: Hybrid decade-mean global sea level with mesoscale resolution. In N. Saxena (Ed.) Recent Advances in Marine Science and Technology, 2004, pp. 55-59. Honolulu: PACON International Niiler, P.P., N.A. Maximenko, and J.C. McWilliams, Dynamically balanced absolute sea level of the global ocean derived from near-surface velocity observations, Geophys. Res. Lett., 30 (22), 2164, doi:10.1029/2003GL018628, 2003. Rio, M.-H., and F. Hernandez, A Mean Dynamic Topography computed over the world ocean from altimetry, in-situ measurements and a geoid model, J. Geophys. Res., 109 (C12), C12032 1-19 - doi10.1029/2003JC002226, 2004. Rio, M.-H., Schaeffer, P., Hernandez, F., Lemoine, J.-M., 2005. The estimation of the ocean Mean Dynamic Topography through the combination of altimetric data, in-situ measurements and GRACE geoid: From global to regional studies. Proceedings of the GOCINA Workshop in Luxembourg (April, 13-15 2005). Rio, M.-H., P.-M. Poulain, A. Pascual, E. Mauri, G. Larnicol, and R. Santoleri, 2007: A Mean Dynamic Topography of the Mediterranean Sea computed from altimetric data, in-situ measurements and a general circulation model., J. Mar. Sys., 65 (2007) 484-508.
  • 5. Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 5 News: GOCE review Tapley, B.D., D.P. Chambers, S. Bettadpur, and J.C. Ries, Large scale ocean circulation from the GRACE GGM01 Geoid, Geophys. Res. Lett., 30 (22), 2163, doi:10.1029/2003GL018622, 2003.
  • 6. Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 6 Data assimilation of drifter velocities in the Mercator Ocean system Data assimilation of drifter velocities in the Mercator Ocean system By: Mounir Benkiran and Eric Greiner1 1 CLS / Mercator Ocean – 8/10 rue Hermès. 31520 Ramonville st Agne Introduction The aim of this paper is to document the drifter’s velocities data assimilation, in addition to other data already assimilated, in the Mercator-Ocean system using a multivariate data assimilation scheme. The latter has been upgraded and a new set of empirical modes have been defined, which takes into account the drifter zonal and meridional velocities. We describe here the various upgrades of the data assimilation system as well the first results from the drifter velocities data assimilation. The drifter velocities For this study, besides data used in the operational system (Sea Level Anomaly, Temperature and salinity profiles and Sea Surface Temperature), we used the drifter velocity at 15 meters depth over the year 2004. Those are three days filtered, which allows filtering the gravity waves. The PSY1v3 experimental system We describe here the various upgrades of the data assimilation system in order to assimilate the drifter velocities. The chosen experimental system (called PSY1v3) is a derived version of the 1/3° Mercator-Ocean Tropical and North Atlantic operational system (PSY1v2) with an upgrade of the data assimilation scheme (formerly SAM1v2 and now called SAM1v3) in order to take into account the drifter velocity data in the state vector. The multivariate SAM1v2 data assimilation scheme is used operationally at Mercator-Ocean since early 2004. The model minus altimeter and insitu data differences of the multivariate analysis are performed using the SOFA (System for Ocean Forecasting and Analysis) optimal interpolation scheme (De Mey and Benkiran, 2002; Etienne and Benkiran, 2007). The specificity of the SOFA scheme is to split the horizontal and vertical correlations, where the covariance matrix of the forecast error Br in the reduced space is described by: Br = S B S T = D 1/2 C D 1/2 • D the forecast error variance. • B the forecast error • S the vertical modes (vertical correlation) • C the correlation function (as a fonction of the time-space correlation radius): C = (1 + dr + 1/3 dr 2 ) exp (-dr ) exp (-dt 2 ) The operational SOFA sequential data assimilation scheme (SAM1v2) allows assimilating sea level observations (derived from altimeter data sea level anomalies), sea surface temperature, temperature and salinity vertical profiles, and temperature and salinity climatological values. The latter uses an optimal interpolation in a reduced space, for which a statistical method based on empirical modes (EOFs) is used. The state vector is split into 2 parts: a barotropic component (barotropic height) and a baroclinic component evaluated from temperature and salinity vertical profiles. We first add the (U, V) baroclinic velocity components in the state vector. We then compute a new EOFs set with the new state vector X=[ψ ,T1,…..,Tjpk,S1,..Sjpk,U1,…,Ujpk,V1,….Vjpk] T (where jpk is the total number of vertical levels of the ocean model), including the new (U, V) baroclinic velocity. ψ is the barotropic stream function. The Ti, Si, Ui, Vi variables are respectively the temperature, salinity, zonal and meridional velocity anomalies with respect to a seasonal mean at the corresponding i vertical level.
  • 7. Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 7 Data assimilation of drifter velocities in the Mercator Ocean system In order to compute the new set of EOFs, we use every 3 days instantaneous outputs of a one year long simulation for the year 2004 from the PSY1v2 system with double IAU 1 (Incremental Update Analysis, Ourmières & al) . IAU has been used to avoid every 7 days (length of the assimilation cycle) spikes in the analysis fields triggered by the sequential data assimilation scheme (Figure 1). Moreover, in order to keep the seasonal cycle, we compute a different set of EOF per season. We now have N vectors X, corresponding to the N vertical profiles. In order to compress the information containing the outputs variability using M vectors X (with M << N), we express the vectors X in a new canonical orthonormal base S={en} of dimension kz. This base represents the directions along which the N profiles variances have a local extremum. Hence, we make sure using this method, that two eigen modes are statistically not coupled and that the dominant modes are not coupled with the others. We then present which normalisation is applied to the state vector X, composed of several ocean variables (ψ , T, S, U, V). Indeed, each of these variables has its own variability with different order of magnitude (typically of several degrees Celsius for the temperature, or of the order of 0.25 psu for the salinity). Hence, a normalisation is needed in order to extract the relevant dominating modes of the state vector. The chosen normalisation method is not very different from the one used in the operational Mercator-Ocean system PSY1v2. It is based on a linearisation of the Bernoulli function. A scaling is used so that each variable of the state vector becomes proportional to a sea level height. The state vector is then described by the following equation: ]*.....*,*.....*,*.....,*......*,1[ 1111 jpkpkjpkjpk dzdzdzjdzdzdzdzdzScale γγγγββαα=         − = .klevelatdepth:,gravitytodueonaccelarati:,energyKinetic:, )0( *2 .exp: .exp: .: k k k ztgEc Hztg Ec tcoefficienansionSalinity tcoefficienansionThermal thicknessklayerdz γ β α Figure 2 shows the percentage of explained variance by the first twenty mode in winter 2005 using the new state vector from the SAM1v3 scheme (left panel) and the old state vector from the SAM1v2 scheme (no IAU) (right panel). The new scheme allows increasing the percentage of explained variance with the same amount of eigen modes used. The percentage of explained variance is ~100% everywhere except in the equatorial band where it reaches 92%. This is due to the strong stratification present in the equatorial area which would require more than 20 modes to be fully represented. Hence, a test has been set up allowing using the right amount of mode at each grid point in order to explain 99% of the variance at each grid point. 1 IAU refers to a more complex assimilation method than the classical sequential assimilation. In the sequential method, a forecast is followed by an analysis of the final conditions, which once corrected become initial conditions for the next forecast. With the IAU method, instead of correcting the forecast initial condition, the correction is spread along the integration period of the model. The system state is thus modified while controlling its error. IAU is a more complex and computer costly method as it requires an additional model integration. Double IAU is a variant of the IAU which parameterises the model error using two analysis corrections, weighted by sinusoidal complementary functions.
  • 8. Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 8 Data assimilation of drifter velocities in the Mercator Ocean system Figure 1 Time series of the horizontal velocities divergence (cm/s) over the whole North and tropical Atlantic for 2004. (Red) with sequential data assimilation. (Purple) in a free run without data assimilation. (black) using Incremental Analysis Update (IAU). Figure 2 Explained variance for the first 20 modes during winter 2004 (Left panel) with SAM1v3 scheme, (Right panel) with SAM2v1 scheme. Another originality of the SAM1v3 scheme lays in the correction applied to baroclinic velocities. With the SAM1v2 scheme, baroclinic velocities corrections are deduced from the 1 st order thermal wind equation (and 2 nd order in the equatorial band): Velocity corrections are deduced from the geostrophic increments derived from the temperature and salinity corrections. In the SAM1v3 scheme, baroclinic velocity corrections are now deduced from the statistical EOF projection in the reduced space. This allows correcting the geostrophic as well as the ageostrophic component of the velocity. Figure 3 displays the initialisation procedure used after the model analysis.
  • 9. Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 9 Data assimilation of drifter velocities in the Mercator Ocean system Brest 12/05/2006 Benkiran et al SAM1v3 : The Mercator Assimilation System version 3 Schematically : ROOI (SOFA) Delta (ir)r δT, δS δUbac, δVbac δΨ δU, δV δUbar, δVbar baroclinic barotropic Full space 1D EOFs Static instability of the water column Sets to 0 the divergent part of the current baroclinic Figure 3 Initialisation procedure after analysis in the SAM1v3 scheme. Preliminary results: comparison of the SAM1v2 and SAM1v3 data assimilation schemes and impact of drifter’s velocities data assimilation in the SAM1v3 system. We present here preliminary results, first comparing the SAM1v2 and SAM1v3 data assimilation schemes and, second, showing the impact of drifter velocities data assimilation in the SAM1v3 system. First, the SAM1v2 and v3 schemes are compared with no drifter velocity data assimilation. Two simulations in the exact same conditions have been performed in order to assess the differences between the SAM1v2 and SAM1v3 schemes. Simulations are performed for the year 2004 when enough data are available, assimilating the same observations (Jason, Envisat and Gfo for altimeter data, Coriolis temperature and salinity vertical profiles, Reynolds Sea Surface Temperature). Alimeter data from a fourth satellite (Topex) are also available as independent observations. Figure 4 shows the biases between the Topex observations and the model. The Root Mean Square (RMS) (Top panel) is lower for SAM1v3 than in SAM1v2 scheme. This is mainly due to the ageostrophic velocity corrections. Moreover, the biases averages (lower panel) are close to zero in both schemes. Figure 5 compares the Sea Surface Temperature (SST) forecasted by the model and the Reynolds SST which is assimilated. We notice that the biases are reduced in SAM1v3 compared to v2, especially close to the continental shelf, in the Gulf Stream and the Caribbean areas. Figure 6 shows that this is mostly due to the ageostrophic velocity correction applied in SAM1v3. Indeed, in the SAM1V2 scheme, only the barotropic and geostrophic baroclinic velocities are corrected. This does not allow the current to develop on the continental plateau. Figure 6 shows the mean velocities in the North West Atlantic in the two schemes. The Greenland Current feeding the Labrador Current is more developed on the continental shelf with SAM1v3 than v2 scheme.
  • 10. Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 10 Data assimilation of drifter velocities in the Mercator Ocean system Figure 4 (Top panel) RMS of the biases (cm) between Topex and model, in the 7 days forecast fields over the whole tropical and North Atlantic domain. (Lower panel) Misfit average (cm). Blue line: With no altimeter data assimilation. Brown line: SAM1v3 with altimeter data assimilation (Envisat, Jason and Gfo). Black line: SAM1v2 with altimeter data assimilation (Envisat, Jason and Gfo) Figure 5 SST biases (Unit: [-1.5-1.5] °C).between the model forecast and the assimilated Reynolds SST. (Left) with SAM1V2 ; (right) with SAM1V3.
  • 11. Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 11 Data assimilation of drifter velocities in the Mercator Ocean system Figure 6 Mean current (m/s) for year 2004. (Left panel) with SAM1V2 ; (right panel) with SAM1V3. Figure 7 Drifters buoys trajectories during year 2004 in the tropical and North Atlantic. (Right) zonal ; (left) meridional component. Second, the SAM1v3 scheme is used to assimilate drifter’s velocities. A simulation is performed where only drifter’s velocities data are assimilated every 7 days over the year 2004. Drifter’s data are available daily, but treated with a 3 days filter. We first want to check whether our new set of EOFs is compatible with the drifter’s velocities data. Moreover, we want to check which error is associated with these data and which impact it will have on the system once assimilated. Figure 7 shows the drifter’s buoys trajectories during 2004 in the tropical and North Atlantic. Zonal equatorial currents, as well as stronger currents in the Gulf Stream area can be noticed. Figure 8 displays the sum of the forecast differences between the model and the drifter data for the zonal component of the velocity (left panel), as well as the sum of the increments after analysis for the zonal component of the velocity (right panel). We notice that the information contained in the drifter’s data is not use at 100%, but that only a small part of it is used in the whole domain except in the tropical area where corrections are larger. We suggest some reasons for this: • The observation error associated with the drifter data is constant over the whole basin (0.10 m/s). We made a test with a weaker error (5 cm/s, not shown here), where more mesoscales structures are kept. • The new set of EOFs released within the SAM1v3 scheme might not include the drifter data signal, although the zonal and meridional components of the velocity have been included in the state vector. • The optimal interpolation scheme used here with a vertical projection, as well as the resolution of the system, might not be compatible with the mesoscale structures present in the drifter’s data. • As these data are 3 days filtered, we should also filter the model equivalent in order to filter the model gravity wave. This is not done in this study and will be done in future work.
  • 12. Mercator Ocean Quarterly Newsletter #25 – April 2007 – Page 12 Data assimilation of drifter velocities in the Mercator Ocean system Figure 8 (Left panel) Sum of the forecast differences (m/s) between the model and the drifter’s data for the zonal component of the velocity. (Right panel) Sum of the increments (m/s) after analysis for the zonal component of the velocity. Conclusion This study allowed us to conclude on the following points: • It is important to use the baroclinic component of the velocity in the state vector. It adds an ageostrophic correction to the velocity after analysis, which is not taken into account when this correction is simply inferred from the thermal wind equation. • This first experiment of drifter velocity data assimilation in Mercator Ocean System gave us encouraging preliminary results. Further work and improvements are needed and will be conducted, in order hopefully to reach better results. References De Mey, P. and M. Benkiran, 2002: A multivariate reduced-order optimal interpolation method and its application to the Mediterranean basin-scale circulation, Ocean Forecasting: Conceptual basis and applications, N. Pinardi, Springer-Verlag, Berlin, Heidelberg, New York, 281-306. Etienne, H. and M. Benkiran, 2007: Multivariate assimilation in MERCATOR project: new statistical parameters from forecast error estimation. Journal of Marine Systems 65, 430-449. Ourmières, Y., J. M. Brankart, L. Berline, P. Brasseur & J. Verron, in press : Incremental analysis update implementation into a sequential ocean data assimilation system, Journal of Atmospheric and Oceanic Technology. Acknowledgment Laurence Crosnier is greatly acknowledged for the translation of this paper.
  • 13. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 13 Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index By Stéphanie Guinehut and Gilles Larnicol1 1 CLS, Space Oceanography Division, 8/10 rue Hermès. 31520 Ranonville st Agne Introduction Global mean sea level change results from two main causes: (1) volume change due to seawater density change in response to temperature and salinity variations, (2) mass change due to exchange of water with atmosphere and continents via the hydrological cycle. Satellite altimeters measure global mean sea level including volume and mass changes almost globally (60°S-60°N) and continuously since the launch of Topex/Poseidon in October 1992. In situ temperature and salinity data sets are used to quantify volume change due to temperature change (thermosteric sea level – heat content) and temperature and salinity change (steric sea level). Different groups have recently estimated interannual variability of global ocean heat content and global ocean thermosteric sea level change for the 1993-2006 periods (Willis et al., 2004; Ishii et al., 2006; Lyman et al., 2006). Unfortunately, in situ measurements are discrete in time and space and are far from sampling the total surface of the ocean. The main objective of this study is thus to quantify the sampling influence of the temperature data sets on the interannual variability of the global mean thermosteric sea level. Sampling errors depend on three components: 1) the geographical and temporal repartition of the in situ measurements, 2) the vertical resolution of the measurements and 3) the method used to calculate global mean from non-global observations. The influence of these three terms has been quantified and their impacts in terms of global trend of interannual variability of the global mean thermosteric sea level are thus presented. The different data sets involved in this study are first presented in section 2. The method used to map the individual temperature observations into grid fields is then described in section 3. The impact of the temporal, geographical and vertical repartition of the in situ measurements is studied in section 4 and the impact of the method used to calculate the global mean from non-global fields is presented in section 5. Finally, section 6 offers discussions. Data sets Data sets involved in this study include: • Delayed mode maps of SLA from the SSALTO/DUACS center (Ssalto/Duacs User Handbook, 2006). These maps are defined on a 1/3° horizontal grid at a weekly period; • T and S in situ profiles from the ENACT/ENSEMBLE-EN2 data base for the years 1993-2004 (Ingleby and Huddleston, 2006) – the third upgrade of the data set (EN3) was unfortunately not available at the time of the study; • T and S in situ profiles from the CORIOLIS data base for the years 2005-2006 (http://www.coriolis.eu.org/). The preprocessing of the in situ data sets consists only in removing redundant observations – only one observation is kept per day for the same instrument in a region of 0.1° in latitude by 0.1° in longitude. No additional qualification is performed on the observations; we absolutely rely on the data centers for this particular point. Mapping method In situ data sets being discrete measurements in time and in space, a mapping method is used prior to analysis. We construct global thermosteric sea level maps at a monthly period, on a 1/3° resolution grid and for the 0-700 m layer from the individual temperature profiles. The mapping method is very similar to the one developed by Larnicol et al. (2006) for the ARMOR-3D Mercator observed products. It is based on an optimal interpolation method with the following parameters: • Temporal correlation scale of 45 days; • Spatial correlation scale – 5 times the one used to produce the SSALTO/DUACS SLA maps (from 1500 km at the equator to 700 km at 50°N); • Error associated to each in situ measurement as thermosteric sea level equal to 20 % of the variance of the SSALTO/DUACS SLA maps, in order to take into account error associated to the aliasing of the mesoscale variability. Besides, the time-mean and seasonal cycle were removed from the altimeter and in situ data prior to analysis.
  • 14. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 14 Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index Impact of the temporal, geographical and vertical repartition of the in situ measurements Each observation being characterised by a geographical position (latitude and longitude) and a date, the temporal and geographical repartition of the in situ measurements could not be studied independently of one another. The vertical sampling of the in situ observations is studied in a second step. Figure 1 shows three typical repartitions of in situ temperature profiles valid up to 700 m (the thermosteric sea level is calculated down to 700 m). The year 1993 shows medium repartition of the in situ measurements with large under-sampled areas in the Southern Ocean. As we will see later, we are able to reconstruct almost 85 % of the ocean thermosteric signal between 60°S and 60°N (the area of the study) for this year. For the year 2000, very large areas in the Indian Ocean, the South Atlantic and Pacific Oceans are hardly sampled if at all. This year is the worst sampled year with only 70 % of the ocean reconstructed. Thanks to the development of the Argo array, the ocean is almost totally sampled during the year 2006 with more than 95 % of the 60°S-60°N area reconstructed. Impact of the temporal and geographical sampling - Method Errors on the global ocean thermosteric sea level have been estimated in a very similar way as in Lyman et al. (2006): • Annual mean reference fields are computed from weekly SSALTO/DUACS SLA maps for the years 1993-2005; • For each of these 13 annual mean SLA reference fields, 144 (12 months x 12 years from 1993 to 2004) monthly sets of simulated observations are created by sub sampling the reference fields at the time and position of the in situ temperature profiles.; • Monthly SLA maps are next reconstructed for each of the 13x144 sets of simulated observations. The mapping method used is the one described in section 0; • Finally, differences between the reconstructed fields and the reference fields as global averages for the 60°S-60°N area are calculated for the 1993-2004 periods and for each of the 13 realizations. Errors in the global thermosteric sea level are calculated from the rms over the 13 realizations. Figure 1 Number of in situ temperature profiles valid up to 700-meter depth in 1°x1° boxes for the year 1993, 2000 and 2006. Color scale: from 2 to 18 every 4.
  • 15. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 15 Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index Two tests have been performed using this method. For the first test (test 1), the global mean (between 60°S and 60°N) is calculated from the reconstructed areas – the mean is thus sometimes far from being global (Figure 2). For the second test (test 2), the reconstructed fields are first completed by zero values in order to create global fields before the calculation of the global mean. As we will see, large differences between test 1 and test 2 can appear because of large-unreconstructed area in very poor sampled years (Figure 2). Figure 2 Annual mean reference SLA field for the year 1993 (left) and monthly reconstructed field for January 2000 obtained using the mapping method of the sub sampled 1993 reference field at the January 2000 observations (right). Color scale: from -10 to 10 every 1 cm. Impact of the temporal and geographical sampling – Results Results indicate that errors associated to the global mean thermosteric sea level vary from one year to another as a function of the temporal and geographical repartition of the in situ measurements and thus as a function of the percentage of reconstructed ocean (Figure 3, Figure 4). The percentage of reconstructed ocean is calculated by comparing the area of the ocean reconstructed by the mapping method using the in situ observation (area in colour on Figure 2-right) to the area sampled by the reference field (Figure 2-left) between 60°S and 60°N. Results also indicate that errors quite differ between test 1 (uncompleted field) and test 2 (field completed by zero values). For test 1, errors vary from 0.09 cm rms for well sampled years (1995, 2004 for example) to 0.17 cm rms for less well sampled years (2000, 2001). Errors are much larger for test 2 and vary from 0.10 cm rms for the year 2004 which is well sampled with more than 95 % of the ocean reconstructed to 0.44 cm rms for the year 2000 which is really less well sampled with only 70 % of the ocean reconstructed. It is therefore really difficult to evaluate the true errors associated to the global mean thermosteric sea level. We think, nevertheless, that test 1 minimizes the error since it assumes that the missing field is centred on zero and that test 2 maximizes the errors since it assumes that the missing field is everywhere equal to zero. The truth errors might thus be situated between the green and the bleu curves on Figure 3. They might vary from 0.1 cm rms for a well sampled ocean and between 0.17 and 0.44 cm rms when the ocean is less well reconstructed. Additionally, a clear linear relationship is observed between the error on the global mean thermosteric sea level and the percentage of the reconstructed ocean (Figure 4). This linear relationship is a very powerful tool to infer the error as a function of the geographical repartition of the in situ measurements and to anticipate and emphasis the need of new in situ observations in term of array design experiment. Results indicate also that the errors can be very high (from 0.5 cm rms to 1.5 cm rms) in area with just a few in situ measurements and for which the percentage of reconstructed ocean is very low (<10 %). Of course these results are also attached to the mapping method used. There is a compromise between the mapping method which smoothes the individual observations onto a spatially consistent field and the temporal and spatial repartition of the in situ observations.
  • 16. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 16 Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index Figure 3 Monthly rms error on global mean thermosteric sea level for the period 1993-2004 (cm). Green curve: test 1 (see text), Blue curve: test 2, Turquoise curve: percentage of reconstructed ocean for the area 60°S-60°N. The dotted lines correspond to 12- month averages. Figure 4 Rms error on global mean thermosteric sea level as a function of percentage of reconstructed ocean (cm). Green curve: test 1 (see text), Bleu curve: test 2. Impact of the vertical sampling The impact of the vertical sampling of the in situ measurements is also studied as it varies as a function of probe type and thus as a function of time. High-resolution XBT and CTD measurements have usually 1-dbar vertical resolution from top to bottom as low-resolution CTD have very dispersed vertical sampling characteristics and as profiling float measurements have roughly 10-dbar vertical resolution near the surface and wider resolution at depth for a mean number of 80 observations between the surface and 2000- meter depth. Simple statistics calculated for the top 700-meter depth and for the 1993-2006 period show that the mean vertical interval between two measurements was between 10-dbar and 15-dbar at the beginning of the period, that it increased to 20- dbar for the year 2000 and up to 30-dbar for the year 2003. After this year, it decreased to 15-dbar with the development of profiling float measurements. The depth of the first measure at the surface has also deepened from 2-dbar from 1993 to 2002 to 4-dbar since the coming of profiling float measurements.
  • 17. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 17 Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index In order to quantify the impact of the vertical sampling of the in situ measurements on the interannual variability of the global mean thermosteric sea level, global temperature and salinity fields from the global PSY3v1 Mercator system (Drévillon et al., 2006) are used. The fields used are the one publicly available and re-interpolated every 5-meter in the top 30 meters then every 10 to 15-meters down to 75-meters and then every 25-meters down to 700-meters. The method consists in interpolating the PSY3v1 fields at the position of the in-situ measurements using two vertical interpolation procedures: 1) keeping the vertical resolution of the PSY3v1 system, 2) interpolating the PSY3v1 temperature and salinity fields on the in-situ z-levels. The two sets of synthetic observations are then used to calculate global mean thermosteric sea level. Results (not showed) indicate that the vertical sampling of the in situ measurements have no significant impact on the results which means that the past and actual vertical sampling of the in situ measurements are suitable to study climate signals. Impact of the method used to calculate global mean thermosteric sea level Results presented in section 0 show that errors on the global mean thermosteric sea level due to sampling characteristics of the in situ measurements present values which vary as a function of the temporal and geographical repartition of the in situ measurements but also as a function of the method used to calculate the global mean thermosteric sea level (fields completed or not before the calculation of the global mean). Three tests have been performed in order to quantify the errors associated to the method used to calculate the global mean thermosteric sea level calculated from the in situ observations. As the geographical repartitions of the in situ measurements are not global, they don’t allow the calculation of a “true” global mean of the thermosteric fields. An important question is thus to know if it is necessary or not to complete the thermosteric field before the calculation of the global mean and if the answer is yes, with what values. Three tests have thus been performed in order to calculate global mean thermosteric sea level: • Test 1: from non global in situ mapped fields; • Test 2: from global in situ mapped fields completed by the time-mean field (i.e. Levitus annual mean climatology) which is a static field during the whole period; • Test 3: from global in situ mapped fields completed by “steric” altimeter SLA fields which are time-variable fields. The “steric” altimeter SLA fields are deduced from regression coefficients computed from a global altimeter (SLA) / in situ (steric-height) comparison study (Guinehut et al., 2006). Figure 5 Global mean thermosteric sea level for the three tests: black, green and blue curves (see text) (in cm). The turquoise curve corresponds to the percentage of reconstructed ocean for the area 60°S-60°N. Thick lines correspond to 12-month running mean.
  • 18. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 18 Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index The three tests show quite similar results (Figure 5). The global tendencies are very close but the associated trends can be relatively different. Results are sensitive to the method used to complete or not the fields, particularly when the percentage of reconstructed ocean are lower like during the years 2000 and 2001. Differences between the three tests can then be of the order of 0.5 cm for percentage of reconstructed ocean of 70 %. The values are completely coherent with the ones presented on Figure 4. They show additionally that upper bound values presented on Figure 4 are totally realistic. It is obviously almost impossible to tell if one estimation of the global mean thermosteric sea level is more realistic than the others but this study helps to understand the dispersions observed between the different published estimates (see for example http://sealevel.colorado.edu/steric.php for a review). Discussion Additionally to other uncertainty related to measurements accuracy/bias for example, error bars on the global mean thermosteric sea level due to sampling characteristics of the in situ measurements vary as a function of temporal and geographical repartition of the in situ measurements but also and coherently as a function of the method used to calculate the global mean thermosteric sea level (fields completed or not and with what values before the calculation of the global mean). As it has been specified in section 0, no additional qualification has been performed on the in situ temperature measurements. An important notice has been recently made to Argo data users rising pressure offset errors on SOLO floats equipped with FSI CTD. The consequence was the introduction of a significant cold bias in the analyses by these instruments (Figure 6). At the same time, there are lots of discussions concerning XBT measurements which are the primary source of the data used in the different studies on thermosteric sea level interannual variability. Some published (Gouretski and Koltermann, 2007) or ongoing studies (Wijffels et al., in prep.) have recently showed that XBT measurements exhibit warm bias of the order of 0.4 et 0.5 °C on the water column around 100-meter depth by comparison to other data sets resulting in depth-averaged values from 0.1°C in the 90s to 0.3°C in 2000-2001 (Gouretski and Koltermann, 2007). The warm bias suspected at the beginning of the period of the study combined to the cold bias due to some Argo float measurements problem suggest that care much be taken when using simultaneously all these data sets and when interpreting the results. Results by Lyman et al. (2006) have, for example, recently been revisited by Willis et al. (2007) and they demonstrate that the recent cooling signal in the upper ocean (as the one presented on Figure 6) is an artifact of the simultaneous use of Argo floats and XBT measurements and that the introduced biases are larger than the sampling errors. Results showed on Figure 6 must then be taken cautiously. Figure 6 Interannual variability of the global mean altimeter sea level (black curve) and thermosteric sea level calculated with all available in situ temperature measurements valid up to 700-meter depth (blue curve) and calculated with all available temperature measurements except the SOLO-FSI floats data (green curve) (in cm). Error bars are from Figure 4 and Figure 5. The turquoise curve corresponds to the percentage of reconstructed ocean for the thermosteric estimation and for the area 60°S-60°N, the dash line corresponding to the no SOLO-FSI case.
  • 19. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 19 Influence of the sampling of temperature data on the interannual variability of the global mean thermosteric sea level index There are thus very strong needs for careful and precise validation/calibration of the different in situ data sets. Uncertainties still persist on different points including: fall rate equation of the XBT measurements, coarse automated quality control procedure on real-time profiling float data, salinity drifts on profiling float instruments. In spite of these reserves, the Argo almost global profiling float array now offers the opportunity to study deeper thermal contributions than 700-meters but also the impact of salinity field on sea level interannual variability. Additionally, studies using independent data sets like GRACE measurements which provide estimates of mass change must be carried on (see for example Lombard et al, 2006) in order to close the sea level budget. References Drévillon, M., Y. Drillet, G. Garric, J.-M. Lellouche, E. Rémy, C. Deval, R. Bourdallé-Badie, B. Tranchant, M. Laborie, N. Ferry, E. Durand, O. Legalloudec, P. Bahurel, E. Greiner, S. Guinehut, M. Benkiran, N. Verbrugge, E. Dombrowsky, C.-E. Testut, L. Nouel, F. Messal, 2006: The GODAE/Mercator global ocean forecasting system: results, applications and prospects, World Maritime technology conference proceedings. Gouretski, V. and K. P. Koltermann, 2007: How much is the ocean really warming?, Geophys. Res. Lett., 34, L01610, doi:10.1029/2006GL027834. Guinehut, S., P.-Y. Le Traon, and G. Larnicol, 2006: What can we learn from Global Altimetry/Hydrography comparisons?, Geophys. Res. Lett., 33, L10604, doi:10.1029/2005GL025551. Ingleby, B., and M. Huddleston, 2006: Quality control of ocean temperature and salinity profiles - historical and real-time data. To appear in Journal of Marine Systems. Ishii, M., M. Kimoto, K. Sakamoto, and S.I. Iwasaki, 2006: Steric sea level changes estimated from historical ocean subsurface temperature and salinity analyses, Journal of Oceanography, 62 (2), 155-170. Larnicol, G., S. Guinehut, M.-H. Rio, M. Drevillon, Y. Faugere and G. Nicolas, 2006: The Global Observed Ocean Products of the French Mercator project, Proceedings of 15 Years of progress in Radar Altimetry Symposium, ESA Special Publication, SP- 614. Lombard, A., D. Garcia, G. Ramillien, A. Cazenave, R. Biancale, J.M. Lemoine, F. Flechtner, R. Schmidt and M. Ishii, 2006: Estimation of steric sea level variations from combined GRACE and Jason-1 data, submitted to EPSL. Lyman, J.M., J.K. Willis, and G.C. Johnson, 2006: Recent Cooling of the Upper Ocean, Geophys. Res. Lett., 33 (18, L18604). Ssalto/Duacs User Handbook, 2006: (M)SLA and (M)ADT Near-Real Time and Delayed Time Products, SALP-MU-P-EA-21065- CLS, Edition 1.5. Willis, J.K., D. Roemmich, and B. Cornuelle, 2004: Interannual variability in upper ocean heat content, temperature, and thermosteric expansion on global scales, J. Geophys. Res., 109 (C12036, doi:10.1029/2003JC002260), 13. Willis, J.K., J.M. Lyman, G.C. Johnson and J. Gilson, 2007: Correction to “Recent Cooling of the Upper Ocean, Geophys. Res. Lett., submitted.
  • 20. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 20 GRACE: an improved MDT reference for altimetric data assimilation GRACE: an improved MDT reference for altimetric data assimilation By Frédéric Castruccio1 , Jacques Verron 1 , Lionel Gourdeau2 , Jean Michel Brankart1 and Pierre Brasseur1 1 Laboratoire des Ecoulements Géophysiques et Industriels, BP 53. 38041 Grenoble Cedex 9 2 IRD Institut de recherche pour le développement, BP A5. 98848 Nouméa cedex. Nouvelle-Calédonie Introduction Since 1992, the altimetric satellites provide a high precision, high resolution and quasi-synoptic observation of the Sea Surface Height (SSH), the sea level above a reference ellipsoid. The SSH signal is the sum of (i) the geoid and (ii) the dynamic topography. Only the later is relevant for oceanographic applications. However, the poor knowledge of the geoid has prevented the oceanographers to fully exploit the altimetric measurement, and altimetric applications have concentrated on ocean variability, through the analysis of the Sea Level Anomaly (SLA). The SLA has been widely and successfully used to improve our knowledge of the ocean dynamics [Fu and Cazenave, 2001]. Nevertheless, it is still challenging to infer the ocean dynamic topography (DT) from the altimetric signal because of geoid uncertainties. Absolute Dynamic Topography have only been accessible by the addition of a Mean Dynamic Topography (MDT) estimate to the SLA. In the context of altimetric data assimilation, the definition of a reliable MDT reference is a recurrent issue [Blayo et al., 1994 ; Birol et al., 2004]. A variety of methods have been applied to generate MDT products, but none of them was found fully satisfactory. Several geodetic missions like CHAMP (2000), GRACE (2002) and GOCE scheduled for 2007, are dedicated to provide a precise estimate of the ocean geoid (with a centimetric precision for short-wavelength features around 100 km). Several studies have recently concluded that the actual resolution of the MDT reference computed using gravimetric data is now compatible with the use in a context of data assimilation experiments [Gourdeau et al., 2003], in particular in the tropical Pacific Ocean, which is our region of interest. The objective of this study is to investigate the impact of a mean dynamic topography deduced from a GRACE geoid on the assimilation of altimetric data along with in-situ temperature profiles. The emphasis is on the better compatibility between both types of observation data sets. This better mean state compatibility contributes to provide a more efficient data assimilation, making a better use of the data complementarity. The results are promising and represent a clear improvement regarding previous studies [e.g. Parent et al., 2003]. Nevertheless, some limitations persist, most of them related to the resolution of the geoid. The investigation is performed with a primitive equation model of the tropical Pacific Ocean where an easily accessible and rather synoptical set of in-situ data is available, thanks to the TAO/TRITON moorings, to complement the altimetric observations. The Singular Evolutive Extended Kalman (SEEK) filter is used to jointly assimilate the TOPEX/POSEIDON and ERS1&2 SSH referenced to the GRACE geoid, and the TAO/TRITON temperature profiles. Two 6-year hindcast experiments over the 1993-1998 period, encompassing the strong 1997-1998 El Niño/La Niña event, have been performed. They only differ by the use of data assimilation. This note is divided in 5 sections. Following introduction, the model, the assimilation scheme and the assimilated data are described in section 2. Section 3 is dedicated to the mean sea surface reference issue and the so-called GRACE MDT used to reference altimetric residual component. Results of the 6-year hindcast experiment are analyzed in section 4. Section 5 discusses and summaries the results. Assimilation Experiment: model, method and data sets Model The assimilation experiments were performed with the OPA 1 OGCM. The configuration is the so-called ORCA2 configuration: a global low resolution 2°x2° ORCA type grid [Madec et Imbard, 1996] with a variable meridional resolution varying from 0.5° at the equator to 2° poleward of 20° in latitude in order to improve the equatorial dynamics. The model solves the primitive equations of ocean dynamics and use a free surface formulation [Roullet and Madec, 2000]. The temporal scheme is a leap-frog scheme with a 5760 seconds time step. Along the vertical, there are 31 z-coordinate levels. This model has been used 1 http://www.lodyc.jussieu.fr/NEMO
  • 21. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 21 GRACE: an improved MDT reference for altimetric data assimilation extensively for tropical dynamics studies and validated accordingly [e.g. Grima et al., 1999 ; Lengaigne et al., 2003 ; Alory et al., 2005]. The model is forced at the surface boundary with heat, freshwater and momentum fluxes. The ERS scatterometer wind stresses complemented by TAO derived stresses [Menkes et al., 1998] which together tend to produce more realistic thermocline and zonal currents, are used. The heat and fresh water fluxes are computed online through bulk formulae and depend on prognostic sea surface temperature (SST) and NCEP 2 atmospheric interannual data provided by the NOAA-CIRES ESRL/PSD Climate Diagnostics branch. The observed monthly mean precipitation field from Xie and Arkin [1997] is used instead of NCEP rainfall. No relaxation on SST is used but a restoring term is applied on sea surface salinity (SSS) to avoid unrealistic drift due to our poor knowledge of the fresh water fluxes. Prior to the interannual simulations, the model starts from rest, with the Levitus temperature and salinity fields [Levitus, 1998]. It is spun up during 2 years using a climatological forcing calculated from the 1993-1998 interannual forcing fields. In order to limit the drift in the mean thermohaline structure, a Newtonian damping term is added in the temperature and salinity equations during the spin up. Method: The SEEK filter The assimilation method used in this study is derived from the singular evolutive extended Kalman (SEEK) filter, which is a reduced-order Kalman filter introduced by Pham et al. [1998]. This sequential method has already been described and used in various types of studies [e.g. Verron et al., 1999 ; Gourdeau et al., 2000 ; Parent et al., 2003 ; Durand et al., 2003 ; Brankart et al., 2003 ; Birol et al., 2004 ; Skachko et al., 2007]. A recent review of the developments of the SEEK filter method for data assimilation in oceanography since the original paper by Pham et al. [1998] can be found in Brasseur and Verron [2006]. In the present implementation, the error subspace basis is assumed to be temporally persistent as in the works by Verron et al. [1999], Gourdeau et al. [2000] and Parent et al. [2003]. We also make use of the local variant of the SEEK filter described in Brankart et al. [2003] and Testut et al. [2003]. The weak correlation associated with distant variables, which are considered as irrelevant in the reduced space, are set to zero. Therefore the analysis for each water column will only depend on the observations within a specific influence bubble. A box of 15 X 9 grid points is used to take into account the anisotropic nature of the tropical Pacific dynamics. Data assimilation is only applied in our region of interest, i.e. the tropical Pacific, even though the model is global. The tropical Pacific domain is defined – following Durand et al. [2003] - between 20°N and 25°S in latitude and from 120°E to the American coast in longitude. Buffer zones are used to smoothly connect the assimilated domain to the rest of the model domain. Continuous data assimilation method: IAU In addition to the regular SEEK filter procedure an Incremental Analysis Update (IAU) algorithm has been implemented [Ourmières et al., 2006]. Indeed, a significant drawback of sequential methods is the time discontinuity of the solution resulting from intermittent corrections of the model state. This discontinuity can lead to spurious high frequency oscillations and data rejection. The IAU algorithm acts like a continuous data assimilation method. The principle is to incorporating the sequential analysis increment δx directly in the prognostic equations of the model as a forcing term: λ(t)δx+M= t V ∂ ∂ where M are the right hand side members of the prognostic equation of the state variable V and λ a parameter such that: Parametrization of the error covariances The assimilation sequence must be initialized with some initial guess for the state X0 and the associated error covariance matrix P0. Following Pham et al. [1998], a convenient method to initialize the error covariance matrix is to use a limited number of three-dimensional, multivariate empirical orthogonal functions (EOFs) describing the dominant modes of free-model variability. The underlying hypothesis is that the mean model state is representative of the mean true ocean. The assimilation of an absolute altimetric signal implies a control of the mean model state. This change concerning the role of the assimilation leads us to develop a specific protocol to parameterize the reduced order forecast error covariance matrix Pf of the SEEK filter. 2 http://www.ncep.noaa.gov
  • 22. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 22 GRACE: an improved MDT reference for altimetric data assimilation An ensemble procedure is used to identify the appropriate reduced space for Pf instead of EOFs of the model variability, as it is usually done in the SEEK filter [Cane et al., 1996 ; Verron et al., 1999 ; Gourdeau et al., 2000]. It is first assumed that a model simulation with a strong relaxation towards climatological fields provides a good approximation of the mean true ocean. Then by using this reference run to reinitialize the free run every 5 days during one year, an ensemble of differences between this reference simulation and the free model 5-day forecasts without nudging is generated. This ensemble of 73 members represents the 5-day forecast error between the model and the reference trajectory. The covariance of this ensemble turns out to be an appropriate estimate of the model error covariance, needed to parameterize the SEEK filter. The rank of this matrix is reduced using a limited number (30) of three-dimensional, multivariate empirical orthogonal functions (EOFs) describing the dominant modes of the ensemble covariance. Regarding the parameterization of the observation errors covariance, a diagonal matrix is used with respectively 5 cm and 0.4°C standard deviation for altimetry and temperature data. Data sets Altimetric Data The altimeter products were produced by Ssalto/Duacs and distributed by Aviso 3, with support from Cnes. The altimetric observations consist of along-track sea surface topography, obtained as the sum of along-track TOPEX/Poseidon and/or ERS altimeter SLA, and the mean dynamic topography (see next section). The assimilation window is five days. Each analysis is computed using all available data gathered within a 5-day interval (2.5 days before and after the analysis time). TAO Data The TOGA-TAO observation system was designed to provide continuous, high-quality measurements in the equatorial Pacific waveguide to improve the description, understanding, and prediction of El Nino [McPhaden et al., 1998]. The full array consists of approximately 70 moorings in the tropical Pacific Ocean, located between 8°N–8°S, and 137°E–95°W, and at depths ranging from 0 to 500 m. They provide among other things high-quality measurements of temperature profiles. The 1-day averaged data available on the TAO Web site 4 are used for assimilation in the model. As for the altimetry, each analysis is computed using all available data gathered within a 5-day interval. The mean sea surface reference issue Problem definition The altimeters measure with a centimetric level accuracy the Sea Surface Height (SSH) above a reference ellipsoid (see Figure 1). The SSH value takes then account of effects such as: (i) the effect due to the ocean circulation called the dynamic topography and (ii) the effect due to the earth gravity field variation called the geoid. The dynamic topography (DT = SSH – geoid) is the signal of interest for the oceanographers. However the DT is contaminated by large geoid errors, especially with high order harmonics (harmonics of order 20 and higher). Alternatively, the temporal mean of the SSH signal, the Mean Sea Surface Height (MSSH) is known with a high accuracy (thanks to the repetitiveness of altimetric missions) and the variable part of the dynamic topography (Sea Level Anomaly – SLA) can be deduced with high precision. The DT can then be deduced by adding the SLA to an estimation of the Mean Dynamic Topography (MDT = MSSH – geoid). The lack of an adequate knowledge of the MDT reference is a recurrent issue [Blayo et al., 1994 ; Birol et al., 2004] for altimetric data assimilation. It is surmounted leaning either on a numerical model (the model MDT is assumed to be perfect and used as a reference for altimetric residuals) or on synthetic solutions based on other data sources (in-situ in general) after a more or less sophisticated treatment [e.g. Mercier et al., 1986 ; LeGrand, 1998, Niiler et al., 2003 ; Rio et al., 2004]. No solution was found fully satisfactory. Synthetic solutions are not straightforward to build and often suffer from a lack of resolution. They are often based on a set of assumptions (geostrophic balance, spatial and temporal colocalisation of altimetric and in situ data, …) that are on several respects inadequately accurate for our purposes. Sometimes, when they are based on long range climatological data, they suffer from an excessive smoothing for relatively short term applications. And most often, they include a significant bias on the reference level that is a critical issue both from the theoretical point of view of data assimilation and from the point of 3 http://www.jason.oceanobs.com 4 http://www.pmel.noaa.gov/tao
  • 23. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 23 GRACE: an improved MDT reference for altimetric data assimilation view of the complementarity of multiple observation systems. Errors on the MDT are known to have a strong impact on the realism of the ocean circulation simulated with data assimilation [Birol et al., 2004]. Figure 1 Schematic representation of the altimetric measurement principle. A fully observed MDT Tracking data from some satellite constellations has been used over the last three decades to study the Earth gravity field, leading to substantial improvement in our knowledge of the geoid [Nerem et al., 1995]. While these conventional methods have provides accurate information, especially at long wavelength [Lemoine et al., 1998 ; Biancale et al., 2000], they have insufficient accuracy to provide the short wavelength of the geoid required to evaluate a relevant MDT. Recent satellite missions such as CHAMP 5 (2000), GRACE 6 (2002) and GOCE 7 scheduled for 2007 are changing this perspective. They have been devised to provide high resolution, highly accurate geoids. The MDT references computed using this gravimetric data are now compatible with their use in a context of data assimilation experiments [Gourdeau et al., 2003 ; Birol et al., 2005]. GRACE gravimetric data The geoid used in this study is the EIGEN-GRACE02S geoid from the GeoForschungsZentrum (GFZ) of Potsdam, Germany [Reigber et al., 2005]. It is a medium-wavelength gravity field model based on 110 days of GRACE tracking data. The solution has been derived solely from satellite orbit perturbations and is independent from oceanic and continental surface gravity data. This model represented by a spherical harmonic expansion is complete to degree 150. It resolves the geoid with an accuracy of better than 1 mm at a resolution of 1000 km [see Reigber et al., 2005]. GRACE MDT The so called GRACE MDT used in this study was computed by the direct method, i.e. by subtracting the EIGEN-GRACE02S geoid and an MSSH product. The MSSH used here corresponds to a 7-year mean (1993-1999) based on the most recently processed TOPEX/POSEIDON, ERS1&2 and GEOSAT altimetric satellite data (SMO CLS01, Hernandez et al. [2001]). In order to overcome the issue of the non-compatibility of the spectral content of both surfaces, the difference is developed into spherical harmonics and then truncated to degree 60 (i.e. a resolution of 333km). The formal cumulated error of the mean dynamic topography reaches 4 cm at degree 60. This GRACE MDT solution reasonably fits the real tropical Pacific MDT. It has been assessed against in-situ observations of the 0/500 dbar dynamic height deduced from the TAO/TRITON moorings [Castruccio et al., 2006 ; Castruccio et al., 2007] and represents a clear improvement regarding the climatology and moreover regarding prior results using CHAMP gravimetric data [Gourdeau et al., 2003]. 5 http://www.gfz-potsdam.de/pb1/op/champ/index_CHAMP.html 6 http://www.gfz-potsdam.de/pb1/op/grace/index_GRACE.html 7 http://www.esa.int/esaLP/LPgoce.html
  • 24. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 24 GRACE: an improved MDT reference for altimetric data assimilation Hindcast experiment (1993-1998) Two simulations are performed for the 1993-1998 period, encompassing the strong 1997-1998 El Niño/La Niña event, probably the strongest of the 20 th century. The first is a free run without data assimilation. The second only differs with respect to the assimilation of altimetric data referenced with the GRACE MDT along with in-situ TAO temperature profiles. The same initial condition and the same forcing scheme are used. Figure 2 Absolute dynamic topography (left panel, in m) and temperature (right panel, in °C) RMS Differences over the 1993-1998 period with respect to assimilated observations over the tropical Pacific. The free run (green) and the assimilated run (black) are plotted. Validation with respect to assimilated data Model-Observation misfit The evolution of the RMS Differences (RMSD) between the assimilated observations and the model predictions are shown in Figure 2 for the free run and the IAU run. During the free simulation, the DT RMSD has an average value of 8.1 cm. The data assimilation enables the RMSD to be decreased by nearly 2 cm down to 6.3 cm. Regarding the TAO, the mean RMSD is reduced from 1.54 °C for the simulation without data assimilation down to 0.9 °C for the experiment assimilating jointly altimetric and TAO data. This simultaneous reduction of the RMSD regarding both types of assimilated data sets represents a clear improvement compared to previous results, thanks to the better data mean state compatibility brought by the use of GRACE data [Castruccio et al., 2006]. Performing a joint assimilation of SLA data with in-situ data may reach a deadlock due to the different reference mean states of the two types of data [Parent et al., 2003]
  • 25. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 25 GRACE: an improved MDT reference for altimetric data assimilation Figure 3 Mean dynamic topography (in meter, left) and section of the standard deviation of the temperature along the equator (in °C, right) related to the 1993-1998 period obtained from observation (top panels), the model without assimilation (middle panels) and the model with joint assimilation (bottom panels). Comparison with observations One of the interests of an absolute dynamic topography assimilation is to constrain the mean model state in addition to its variability. Figure 3 shows the MDT and the isotherms mean depths over the 1993-1998 period for the observations and the 2 simulations. Data assimilation has a strong and benefic impact on both fields. The MDT simulated with data assimilation is more realistic, in particular in the south central tropical Pacific, where the free run MDT compares poorly with observations. The ridge associated with the North Equatorial Counter Current (NECC) along 8/10°N is also in better agreement with the observations with steeper meridional gradient. Nevertheless, the MDT simulated with joint data assimilation exhibits unusually small patterns along 8/10°N. These patterns are not found in the observed MDT nor in the free run MDT. The mean depth of the isotherms and the standard deviation of the temperature along the equator are also shown in Figure 3. The structure and the variability of the temperature fields have been improved. In particular, the variability of subsurface temperature along the thermocline, which is too weak in the free run simulation, has been intensified by data assimilation. The variability is however still under-estimated compared to observations. Along with this strengthening of the variability, the data assimilation shallowed the thermocline which is too deep (approximatively 20 m deeper than in the observations) in the free run simulation.
  • 26. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 26 GRACE: an improved MDT reference for altimetric data assimilation Validation with independant data Surface currents Figure 4 Mean zonal velocity (in m.s -1 ) at 15 m depth. Respectively from top to bottom, the Niiler [2001] climatology (top panel), the mean related to the 1993-1998 period obtained from the model without assimilation (middle panel) and the model with joint assimilation (bottom panel). Tropical oceans exhibit mainly zonal circulation. The analysis of the zonal surface current is a stringent test for validating our simulations as currents are very sensitive to the meridional gradient of the dynamic topography, particularly towards the equator, where the Coriolis force vanishes. The maps of the mean zonal current at 15 m depth for the Niiler [2001] climatology and 2 runs are shown in Figure 4. Niiler [2001] climatology of near-surface currents has been estimated from satellite-tracked SVP (Surface Velocity Program) drifting buoys and provides observations of near-surface circulation at unprecedented resolution. The alternate bands of eastward- and westward- flowing currents characterizing the tropical Pacific Ocean circulation are present in the free run model simulation as well as in the simulation with data assimilation. However, the free run currents are too weak. The surface zonal currents simulated with joint data assimilation are in better agreement with the Niiler [2001] climatology. The NECC has been strengthened accordingly with the steepening of the meridional gradient of the dynamic topography and reaches 40 cm.s -1 . The South Equatorial Current (SEC) has also been intensified. The North and South branches of the SEC are clearly identified in the central Pacific but not in the far east of the basin. The wrong representation of the SEC separation is a recurrent issue for ORCA simulation [Lengaigne et al., 2003] and the assimilation is not able to tackle this problem. In the north, the North Equatorial Current (NEC) reaches 20 cm.s -1 , still slightly under estimated compared to the observations. In the south hemisphere, the surface zonal velocity patterns are closest to the drifter climatology with a South Equatorial Counter Current (SECC) near 9°S confined in the West Pacific and the weak eastward flows (the return branch of the subtropical gyre) flowing south of 20°S as in the climatology.
  • 27. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 27 GRACE: an improved MDT reference for altimetric data assimilation Figure 5 Horizontal distributions of XBT profiles available for the 6 years of the assimilation experiment. Superimposed in red the position of the 3 selected rails corresponding to the Tokyo-Auckland, San Fransisco-Auckland and Panama-Auckland maritime lines. XBT To further assess the results, we evaluated the experiments using independent XBT data from the VOS 8 (Voluntary Observation Ships) program. The data set used in this study has been downloaded from the CORIOLIS 9 Web site. Approximatively 60000 profiles are available over the 6 years of the experiment. Figure 5 shows the irregular spatial distribution of the XBT profiles. Three ship lines, routinely sampled by VOS vessels, typical of the Western, Central, and Eastern Pacific are selected (see Figure 5). Figure 6 Differences between the XBT mean temperature section over the 1993-1998 period along the West (left panels), Central (middle panels) and East (right panels) Pacific rails and the mean temperature section simulated without data assimilation (top) and with assimilation (bottom). The black lines correspond to the mean depth of the 12-16-20-24 and 28 °C isotherms over the 1993-1998 period from the XBT data. 8 http://www.vos.noaa.gov 9 http:/www.coriolis.eu.org
  • 28. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 28 GRACE: an improved MDT reference for altimetric data assimilation Figure 6 exhibits the mean structure difference between the observations and the 2 simulations. Most of the errors are initially concentrated in the thermocline and the equatorial wave guide with magnitude up to 5 °C. These errors are drastically reduced in the run using joint data assimilation, even off the TAO array area. This confirms the better mean thermocline depth simulated with data assimilation. Nevertheless, high errors exist below the thermocline at 10°N on the Central line, i.e. just under a TAO mooring (9°N-140°W). These high errors are not present in the free run model. Joint data assimilation appears to be in question in this specific region as it has already been sugested by Figure 3 showing unrealistic small patterns for 6-year mean dynamic topography along the ridge associated with the NECC. Discussion and conclusion In this paper, we have presented a 6-year hindcast experiment over the 1993-1998 period jointly assimilating an observed absolute dynamic topography deduced from GRACE data and the in-situ TAO temperature profiles in a primitive equation model of the tropical Pacific Ocean. The objective of this study was to assess how the use of a GRACE geoid could improve the modeling of tropical Pacific dynamics through data assimilation of altimetric and in-situ data. The study was motivated by the fact that defining the MDT reference is a recurrent problem in altimetric data assimilation studies and that ongoing and future satellite missions dedicated to the improvement of the earth geoid are likely to change this situation. The benefits brought by the use of a GRACE MDT in the assimilation system are clear. Although altimetric data and in-situ temperature profiles are utterly complementary, the joint assimilation of these two types of data can be conflictual. Errors on the mean dynamic topography reference can lead to discrepancies between the two types of observations as noted by Parent et al. [2003]. These discrepancies are greatly reduced by the used of the GRACE MDT [Castruccio et al., 2006]. Nevertheless, the joint assimilation is still problematic in the region along 8/10°N. The resolution of the GRACE geoid is too low for the dynamic topography to correctly represent the fine latitudinal structure relative to the NECC ridge introducing some inadequacies between the altimetic and TAO data in this region. These inadequacies are clearly illustrated by Figure 7 showing the differences between the observed MDT and the MDT simulated with and without data assimilation. The global RMSD is reduced from 4.5 cm down to 3.1 cm with data assimilation. However Figure 7 exhibits high error patches arround most of the TAO moorings along 8°N. These patches explain the rather noisy structure of the mean dynamic topography simulated with data assimilation in this region (cf Figure 3). They are due to a mean state difference between the two observation data sets assimilated in the model. Figure 7 Differences between GRACE MDT and MDT of the model without assimilation (left panel) and the MDT of the model with joint assimilation (right panel) related to the 1993-1998 period. The mean state difference is illustrated by Figure 8 showing two meridional sections of MDT. The observed GRACE MDT (also used to reference the assimilated altimetric signal) and the MDT simulated with and without data assimilation are plotted. The two selected sections are 140°W (i.e. a section sampled by the TAO moorings) and 145°W (i.e. a section between two TAO longitudes). The mean TAO dynamic height is also plotted for the section at 140°W. In-situ and satellite observations are in good agreement except for the mooring at 9°N. The steep meridional slope of the mean dynamic topography can not be accurately represented due to the relatively coarse resolution (333 km) of the GRACE MDT. This results in the presence of errors in the assimilated dynamic topography leading to incompatibilities between altimetry and in-situ data. These incompatibilities prove to be problematic for the joint assimilation of both data sets. Locally, TAO informations are dominant (TAO data are daily vertical profiles). The analyzed states estimated by the SEEK filter are then close to TAO observations at TAO positions. Between TAO moorings, we do not have anymore in-situ information, but we still have satellite altimetric data. The analyzed states tend to be closer to altimetry (see Figure 8). The mean state difference between the two observation data sets along 8/10°N then explains the patches seen on Figure 7 [see Castruccio et al., 2007].
  • 29. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 29 GRACE: an improved MDT reference for altimetric data assimilation Figure 8 MDT related to the 1993-1998 period along 145°W (left) and 140°W (right) for the model without assimilation (green line), the model with joint assimilation (black line) and the observed GRACE MDT (black dashed line). The pink triangles for the section along 145°W stand for the mean TAO dynamic height related to the 1993-1998 period. To summarize, a data assimilation system based on the SEEK filter has been developed in order to assimilate the absolute dynamic topography deduced from the TOPEX/POSEIDON and ERS1&2 altimetric data and the GRACE gravimetric data. The altimetric signal is assimilated along with the in-situ TAO temperature profiles into a tropical Pacific Ocean model. We have demonstrated the efficiency of such a system using a 6-year hindcast experiment over the 1993-1998 period. The results are promising and represent a clear improvement regarding previous studies [e.g. Parent et al., 2003], thanks to the better data compatibility brought by the use of GRACE MDT. Nevertheless, some limitations always exist. Most of them are related to the resolution of the geoid. The next estimations of the geoid are expected to go well beyond the present accuracy. The use of an absolute dynamic topography opens the way for the development of efficient assimilation systems based on multiple data sets (in nature, space and time distribution). The integration of multiple data sets through operational systems is crucial for our better understanding of the ocean system and for our capability to forecast its evolution at diverse time scale. Further improvements in the knowledge of the MDT itself might result from converging studies on assimilated data resolution and accuracy, both from space and in situ, on modeling and on assimilation techniques, within the context of operational oceanography systems [Dobricic, 2005]. References Alory, G., C. Cravatte, T. Izumo, and K. B. Rodgers, Validation of a decadal OGCM simulation for the tropical Pacific, Ocean Modelling, 10, 272–282, 2005. Biancale, R., G. Balmino, J.-M. Lemoine, J.-C.Marty, B.Moynot, F. Barlier, P. Exertier, O. Laurain, P. Gegout, P. Schwintzer, C. Reigber, A. Bode, R. König, F.-H. Massmann, J.-C. Raimondo, R. Schmidt, and S. Zhu, A new global Earth’s gravity field model from satellite orbit perturbations : GRIM5-S1, Geophysical Research Letters, 27, 3611–3614, 2000. Birol, F., J.-M. Brankart, J.-M. Lemoine, P. Brasseur, and J. Verron, Assimilation of satellite altimetry referenced to the new GRACE geoid estimate, Geophysical Research Letters, 32, L06601, doi:10.1029/2004GL021329, 2005. Birol, F., J.-M. Brankart, F. Castruccio, P. Brasseur, and J. Verron, Impact of ocean mean dynamic topography on satellite data assimilation, Journal of Marine Geodesy, 27, 59–78, 2004. Brankart, J.-M., C.-E. Testut, P. Brasseur, and J. Verron, Implementation of a multivariate data assimilation scheme for isopycnic coordinate ocean models : Application to a 1993-96 hindcast of the North Atlantic Ocean circulation, Journal of Geophysical Research, 108 (C3), 1–20, 2003. Castruccio, F., J. Verron, L. Gourdeau, J.-M. Brankart, and P. Brasseur, On the role of the GRACE mission in the joint assimilation of altimetric and TAO data in a tropical Pacific Ocean model, Geophysical Research Letters, 33, L14616, doi:10.1029/2006GL025823, 2006. Castruccio, F., J. Verron, L. Gourdeau, J.-M. Brankart, and P. Brasseur, Contribution of the GRACE MDT to the joint assimilation of altimetric and in-situ data in the Tropical Pacific Ocean, in preparation, 2007. de Boyer Montégut, C., J. Vialard, S. S. C. Shenoi, D. Shankar, F. Durand, C. Ethé, and G. Madec, Simulated seasonal and interannual variability of mixed layer heat budget in the northern Indian Ocean, J. Climate, 2006.
  • 30. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 30 GRACE: an improved MDT reference for altimetric data assimilation Dobricic, S., New mean dynamic topography of the Mediterranean calculated from assimilation system diagnostics, Geophysical Research Letters, 32, L11606, doi:10.1029/2005GL022518, 2005. Durand, F., L. Gourdeau, T. Delcroix, and J. Verron, Can we improve the representation of modeled ocean mixed layer by assimilating surface-only satellite-derived data ? A case study for the Tropical Pacific during the 1997-1998 El Niño, Journal of Geophysical Research, 108 (C6), 3200, 2003. Fu, L.-L., and A. Cazenave, Satellite Altimetry and Earth Sciences : A Handbook of Techniques and Applications, International Geophisics Series, vol. 69, Academic Press, San Diego, CA, 2001. Gourdeau, L., J. Verron, T. Delcroix, A. J. Busalacchi, and R. Murtugudde, Assimilation of Topex/Poseidon altimeter data in a primitive equation model of the Tropical Pacific Ocean, during the 1992-1996 ENSO period, Journal of Geophysical Research, 105 (C5), 8473–8488, 2000. Gourdeau, L., J.-M. Lemoine, M. H. Rio, and F. Hernandez, Estimating mean dynamic topography in the tropical Pacific Ocean from gravity and altimetry satellites, Geophysical Research Letters, 30 (20), 2062, 2003. Grima, N., A. Bentamy, K. Katsaros, and Y. Quilfen, Sensitivity of an oceanic general circulation model forced by satellite wind stress fields, Journal of Geophysical Research, 104 (C4), 7967-7989, 1999. Hernandez, F., M. Schaeffer, M. H. Calvez, J. Dorandeu, Y. Faugre, and F. Mertz, Surface moyenne océanique : Support scientifique à la mission altimétrique JASON-1, et à une missions micro-satellite altimétrique, Tech. rep., Contract SSALTO 2945 - Lot 2 - A.1, Rapport n° CLS/DOS/NT/00.341, 2001. Le Grand, P., An inverse modelling estimate of the geoid height in the North Atlantic, Tech. Rep. 9 :1-2, CERSAT, 1998. Lemoine, F., S. Kenyon, J. Factor, R. Trimmer, N. Pavlis, D. Chinn, C. Cox, S. Klosko, S. Luthcke, M. Torrence, Y. Wang, R. Williamson, E. Pavlis, R. Rapp, and T. Olson, The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential model EGM96, Tech. Rep. NASA/TP-1998-206861, NASA Technical Paper, Goddard Space Flight Center, Greenbelt, 1998. Lengaigne, M., G. Madec, and Menkes C., Impact of isopycnal mixing on the tropical ocean circulation, Journal of Geophysical Research, 108 (C11), 3345, 2003. Levitus, S., World ocean atlas 1998 data, Tech. rep., NOAA-CIRES Clim. Diag. Cent., Boudler, Colorado, 1998. McPhaden, M., A. J. Busalacchi, R. Cheney, J. R. Donguy, K. S. Gage, D. Halpern, M. Ji, P. Julian, G. Meyers, G. T. Mitchum, P. P. Niiler, J. Picaut, R. W. Reynolds, N. Smith, and Takeuchi K., The Tropical Ocean-Global Atmosphere observing system : A decade of progress, Journal of Geophysical Research, 103, 14,169–14,240, 1998. Menkes, C., J. Boulanger, A. Busalacchi, J. Vialard, P. Delecluse, M. J. McPhaden, E. Hackert, and N. Grima, Impact of TAO vs. ERS wind stresses onto simulations of the tropical Pacific Ocean during the 1993-1998 period by the OPA OGCM, in Climate Impact of Scale Interaction for the Tropical Ocean-Atmosphere System, Euroclivar Workshop Report, vol. 13, 1998. Mercier, H., Determining the general circulation of the ocean : a non-linear inverse problem, Journal of Geophysical Research, 91, 5103–5109, 1986. Nerem, R. S., C. Jekeli, and W. M. Kaula, Gravity field determination and characteristics retrospective and prospective, Journal of Geophysical Research, 100 (B8), 1995. Niiler, P., The world ocean surface circulation, International Geophysics Series 77, vol. Ocean circulation and climate, Siedler, G. and Church, J. and Gould, J. ed., Academic Press, 2001. Niiler, P. P., N. A. Maximenko, and J. McWilliams, Dynamically balanced absolute sea level of the global ocean derived from near-surface velocity observations, Geophysical Research Letters, 30 (22), 2164, 2003. Ourmières, Y., J.-M. Brankart, L. Berline, P. Brasseur, and J. Verron, Incremental Analysis Update implementation into a sequential ocean data assimilation system, Journal of Atmospheric and Oceanic Technology, 2006. Parent, L., C.-E. Testut, J.-M. Brankart, J. Verron, P. Brasseur, and L. Gourdeau, Comparative assimilation of Topex/Poseidon and ERS altimeter data and of TAO temperature data in the Tropical Pacific Ocean during 1994-1998, and the mean sea- surface height issue, Journal of Marine Systems, 40, 2003. Pham, D. T., J. Verron, and M. C. Roubaud, Singular evolutive extended Kalman filter with EOF initialization for data assimilation in oceanography, Journal of Marine Systems, 16, 323–340, 1998. Reigber, C., R. Schmidt, F. Flechtner, R. König, U. Meyer, K.-H. Neumayer, P. Schwintzer, and S. Yuan Zhu, An Earth gravity field model complete to degree and order 150 from GRACE : EIGEN-GRACE02S, Journal of Geodynamics, 39 (1), 1–10, 2005.
  • 31. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 31 GRACE: an improved MDT reference for altimetric data assimilation Rio, M.-H., and F. Hernandez, A mean dynamic topography computed over the world ocean from altimetry, in situ measurements, and a geoid model, Journal of Geophysical Research, 109 (C12032), 2004. Roulet, G., and G. Madec, Salt conservation, free surface, and varying levels: a new formulation for ocean general circulation models, Journal of Geophysical Research, 105 (C10), 23,927–23,942, 2000. Skachko, S., J. M. Brankart, F. Castruccio, P. Brasseur, and J. Verron, Estimating the turbulent air-sea flux bulk parameters by sequential data assimilation, Remote Sensing of Environment, under review, 2007. Testut, C.-E., P. Brasseur, J.-M. Brankart, and J. Verron, Assimilation of sea-surface temperature and altimetric observations during 1992–1993 into an eddy permitting primitive equation model of the North Atlantic Ocean, Journal of Marine Systems, 40, 2003. Verron, J., L. Gourdeau, D. T. Pham, R. Murtugudde, and A. J. Busalacchi, An extended Kalman filter to assimilate satellite altimeter data into a nonlinear numerical model of the Tropical Pacific : method and validation, Journal of Geophysical Research, 104, 5441–5458, 1999. Xie, P., and P. Arkin, Analyses of global monthly precipitation using gauge observations, satellite estimates, and numerical model predictions, Journal of Climate, 2, 840–858, 1996.
  • 32. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 32 Altimeter data assimilation in the Mercator Ocean system Altimeter data assimilation in the Mercator Ocean system By: Mounir Benkiran1 1 Mercator Ocean - 8-10 rue Hermes. 31520 Ramonville St Agne Introduction To show the complementarities of the various altimetric data (Jason, Envisat and Gfo) used in PSY1V2 (MNATL 1/3 ° - SAM1v2) prototype, we analyse here their respective impact on the analysis. We compare several simulations combining these data sets with a reference simulation Sref. In this simulation Sref, we assimilate the complete data set (Jason, Ers2/Envisat and Gfo). For all the simulations which are presented here, the same restart has been used. We made these simulations over the years 2004/2005. In this paper, we only present the results over the year 2004. First of all, we show that it is important to use the altimetric data stemming from various satellites, in particular when their spatial resolutions are different (Jason, Envisat and Gfo). In the same way we show the impact of the fourth satellite (Topex) in a model with a resolution of 1/3 °. Descrpition of the assimilation system Mercator-Ocean operates a multivariate multi data assimilation system in real time since January 2004. This system called PSY1v2, gives an oceanic large scale description and a two-week forecast of the North and tropical Atlantic (70°N-20°S) on a weekly basis. The model is eddy permitting (1/3°, 27km) for basin scale studies. Satellite altimetry and sea surface temperature (SST) are assimilated, as well as in situ data. The assimilation is based on a reduced order optimal interpolation (ROOI). Model The PSY1v2 system uses the ocean model OPA8.0 (http://www.lodyc.jussieu.fr/opa) developed at LOCEAN (Madec and Imbard, 1996), (see Newsletter #13). The model uses primitive equations with Boussinesq approximation. It covers the North Atlantic basin from 20°S to 70°N and from 99°W to 20°E. The horizontal grid is a 1/3° Mercator grid, and the average resolution is 27km. This is not fine enough to resolve the eddies, but it can permit to an eddy (set by assimilation) to have a reasonable lifetime (not trajectory). The vertical grid is a "Z"-type grid. Vertical levels are distributed with 43 levels, 20 of which are in the first 1000 meters of the ocean. The levels vary in depth from 12 meters at the surface to 200 meters below 1500 meters. The depth of the bottom level is 5600 meters. Note that the first temperature model node is at 6m depth. The temperature and salinity near the artificial boundaries are restored to the seasonal climatology (Reynaud & al., 1998). A monthly climatology of attenuation depth for the solar penetrating flux is derived from SEAWIFS (1997-2003). Salt rejection during ice formation and fresh water production during melting are parametrised (Greiner & al., 2004). The daily forcings come from the Europeen Center for Medium-Range Weather Forecasts (ECMWF) operational outputs. 12h-24h echeances from the 0h forecast are cumulated with the 12h-24h echeances from the 12h forecast in order to have the best balanced daily windstress, heat flux, precipitation and evaporation. Data Sea Level Anomalies Along tracks altimetric data from Jason-1, Ers/Envisat and Gfo are assimilated. Data processing is performed by SSALTO/DUACS (http://www-aviso.cnes.fr) and is distributed through the AVISO user service. The along track resolution is typically 20km. The Sea Level Anomaly (SLA) errors are 2 cm for the Jason altimeter and 3.5 cm for Ers, Gfo and Envisat. Only the observed SLA is kept as final data for the assimilation. Note that the SLA is rejected under the model ice. To compare the model to the observed SLA, we have to subtract an estimate of the mean Sea Surface Height (MSSH) to the model SSH: SLA d = tracks anomalies SLA m = SSH m – MSSH d More precisely the altimetric data are track anomalies relatively to the 1993-99 period. The unknown difference, namely the MSSH (Version 5.1 from June 2005), is the height corresponding to the mean oceanic circulation, and to the geoid variations. It is estimated with an objective analysis mapping including altimetry, hydrology, drifters and gravimetry from GRACE (Rio & Hernandez, 2004). The MSSH is the most critical parameter of a multivariate system, but today, it is still not accurately known. The MSSH error typically ranges from 3cm to 6cm, which is slightly higher than the SLA error, and sometimes even larger than the sea level variability. The system would be greatly improved by having a better estimate of the MSSH, but we are still waiting for the results of the accurate gravimetry from the GOCE mission. Meanwhile, sensitivity tests to various MSSH products, as
  • 33. Mercator Ocean Quarterly Newsletter #25– April 2007 – Page 33 Altimeter data assimilation in the Mercator Ocean system well as data withholding (in situ and/or altimetry) suggest that the MSSH inaccuracy can typically lead to regional biases of 2°C and 1psu at the pycnocline level. Other data sets Another important data is the satellite SST. The RTG_SST 0.5°x0.5° analysis (Thiébaux & al., 2003) is produced daily by the NOAA/NCEP (http://polar.ncep.noaa.gov/sst/). Details of the procedure can be found in the above reference, but the main points are listed here. It is a refined version of the 1°x1° weekly Reynolds analysis (Reynolds & Smith, 1994). This analysis uses in situ SST and NOAA-16/NESDIS satellite SST. Daytime and night time data are treated separately, and known biases are corrected, but cloud cover and aerosols are still a source of uncertainty. Ship and buoy data are used to remove the remaining biases. The daily analysis is used once at the end of the ocean analysis cycle (Wednesday), at a degraded resolution of 1/3°x1/3°. SST error is set to 0.6°C. In situ observations include low and high resolution profiles of temperature and salinity. Depths vary from a few tens of meters, to 2000m for the ARGO profilers. The data acquisition and quality control (Coriolis, 2002) is performed by the Coriolis Data Centre (http://www.coriolis.eu.org). The data is gathered for Mercator-Ocean by the ARMOR chain (Guinehut, 2004) where other checks and a data thinning are performed. Assimilation PSY1v2 has been the first Mercator-Ocean system to perform multivariate assimilation of altimetry data and in situ data. This system uses the analysis tool SOFA3.0 developed by Pierre De Mey (De Mey & al, 2002) at LEGOS, and PALM from CERFACS (Lagarde & al., 2001), the generalised coupler used to resolve large-scale assimilation problems on distributed memory computers. The standard Optimal Linear Estimation theory is used (De Mey & al., 2002). We recall below the equations that will come into play in the results. If the true state is xt, H the observation operator, and ε the errors, then the observation y° (measurement) at this time can be written as: y° = H(xt) + ε We can write the misfit (innovation) as a function of the model forecast xf and of the observation: d= y° - H(xf) Assuming that the prediction and observation errors are unbiased and have a normal distribution as well as known covariances (B f and R respectively), the best estimate of x is xa, such as, by using the Kalman gain, K: xa = x f + K (y°-H(x f )) As in optimal interpolation methods used in meteorology, we assume that correlation of errors from the matrices B f and R that form the gain matrix, are homogeneous, stationary and given by empirical formulae: B f =(D f ) 1/2 C (D f ) 1/2 D f : guess variance error C: correlation matrix, constant in time We assume that the correlations decrease toward zero with distance. Data and model differences, which are represented by the innovation vector, are therefore only taken into account within an area of influence around each analysis point. The size of this influence bubble is taken as twice the spatial decorrelation scales. This makes the method less than optimal, but means that calculations are easier through the parallelisation of codes. The method for reducing the state tries to satisfy both the need for robustness (we do not want to project onto a broad and unknown subset), and for reducing calculations. The problem is truncated by using only dominant modes. The relationship between the gain in the complete space K ROOI (ROOI: Reduced-Order Optimal Interpolation) and the gain in the reduced space Kr can be written using S, the matrix made of the empirical orthogonal functions (EOFs) of the error covariance: KROOI = ST Kr Kr = Br f Hr T (Hr Br f Hr T + Rr ) -1