A MULTIVARIATE OPTIMAL INTERPOLATION SCHEME FOR DATA ASSIMILATION
IN A GLOBAL OCEAN GENERAL CIRCULATION MODEL.
A. Bellucci, S.Masina and P. Di Pietro (Istituto Nazionale di Geofisica e Vulcanologia, Italy)
We present the development and first applications of an ocean data assimilation (ODA) system based on a
reduced order multivariate optimal interpolator (OI) scheme combined with a global ocean general
circulation model (OGCM). The present ODA system – developed within the framework of the EU ENACT
(Enhanced Ocean Data Assimilation and Climate Prediction) Project and undergoing further extensions
within the EU ENSEMBLES Project - has been used to produce an extensive set of analyses, for different
data stream lengths and by assimilating vertical temperature and salinity profiles. The impact of
assimilating observed hydrographic data on the ocean mean state and temporal variability is assessed. A
special focus of the present work is on the ODA system skill in reproducing a realistic ocean salinity state.
In particular the salinity sensitivity analysis to the horizontal and temporal resolution of the EOF data set
will be investigated.
performed experiments are summarised in Table
1.
1. The ODA system.
The reduced order optimal interpolation SOFA 3.0
scheme (De Mey and Benkiran, 2002) is used to
2. The impact of assimilation on the model
assimilate observed vertical temperature and
mean state and time variability.
salinity profiles from the ENACT in situ data set
The impact of temperature assimilation on the
(Ingleby and Huddleston, 2006). Order reduction is
model mean state and temporal variability is
achieved by projecting the state vector onto modelsummarized in figures 1-2, where results from an
derived bivariate (temperature and salinity) vertical
analysis for the 1962-2001 stream obtained by
empirical orthogonal functions (EOFs) and then
assimilating only temperature, but correcting
truncating the EOF expansion to the dominant 10
salinity as well through EOF-derived correlations
modes. In the EOF computation a domain splitting
(hereafter OI(T)) are shown. Levitus climatology
approach has been adopted, consisting in the
will be adopted as an observational reference.
partition of the global ocean domain into 21 subregions characterised by homogenous dynamical
regimes. The guess error correlation is based on a
space-time analytical Gaussian model, with
isotropic and homogenous correlation radii of 300
Km and 7 days for all modes. The observational
error is assumed to be uncorrelated in space and
time. The SOFA is combined with a global OGCM
(OPA 8.2;Madec et al. 1998) having a 2° horizontal
resolution everywhere, except for the 20N-20S
latitude belt, where the meridional grid-spacing is
progressively decreased to 0.5°.
The present ODA system has been used to
produce an extensive set of global ocean analyses
covering two different periods: the 1962-2001
stream, and a shorter 1990-2001 stream. In order
to evaluate the impact of the assimilation on the
ocean state, a control run, where the model is
simply forced with atmospheric fluxes but without
assimilating any data, has also been performed.
For each numerical experiment (assimilation and
control), the surface temperatures are relaxed to
Reynolds daily temperatures (Reynolds, 1988) with
a 12 days restoring time scale (for a 50 m mixed
layer thickness), while for surface salinity no
Figure 1. OI(T)-Levitus (top panel) and CTRL-Levitus
relaxation has been used. On the other hand a full
(bottom panel)
differences for climatological
depth 3 years relaxation to Levitus climatology is
temperature at 100 m (oC).
applied both on temperature and salinity. The
Temperature residuals with respect to Levitus, at
100 m, appear to be considerably reduced after
assimilation has been applied (figure 1).
Experiment
Control
OI(T)
OI(T+S)
OI(T+S)-HR
Assimilated
data
No assim.
T
T,S
T,S
Integration/EOFs
period (regions)
1962-2001
1962-2001 (21)
1962-2001 (21)
1990-2001 (195)
Table 1. List of experiments. In the left column, the
experiment label is indicated. In the mid column, the type
of assimilated data is specified, with T and S denoting
temperature and salinity, respectively. In the right
column, the integration time interval (or, equivalently, the
period over which the EOFs have been computed) is
indicated, together with the number of regions used in
the EOFs computation (in brackets).
The impact of assimilation is particularly evident in
the Northern Hemisphere, due to the higher data
coverage. Temperature variability in the analysis is
assessed against observations in the Tropical
Pacific region. In figure 2 we show the analysis
(and control) minus observations (collected from
TAO moorings) root-mean-square (rms) as a
function of depth, in the Nino3 and Nino4 areas.
The largest deviations from observations are
detected in the thermocline region, at about 100
and 200 meters depth, for the Nino3 and Nino4
areas, respectively.
Figure 2: Vertical profiles of OI(T) (solid) and control
(dashed) minus TAO observations rms for temperature
in the Nino3 (red) and Nino4 (blue) areas. The rms
profiles have been obtained by collecting all TAO data
available in [160E,210E, 5S,5N] (Nino4) and
[210E,270E, 5S,5N] (Nino3).
The assimilation of vertical temperature profiles
reduces the rms deviation from observations below
1 oC, with a sensible improvement with respect to
the control experiment.
If the benefits on the model temperature deriving
from the assimilation of thermal profiles are
evident, the impact on salinity state appears to be
more problematic. The climatological surface
salinity patterns diagnosed from the analysis and
the control experiment, are compared to Levitus
climatology (not shown). The analysis residuals
computed with respect to Levitus exhibit a basin
scale fresh anomaly extending over the subtropical
and tropical North Atlantic areas of about 2 PSU,
while discrepancies in the control show an overall
smaller size anomaly in the same region. These
results indicate that the corrections on salinity
implied by the model T/S EOF statistics are not
concurring to generate an improved (compared to
the control experiment) surface salinity mean state.
Deviations from salinity observations progressively
decrease with depth, both in the control and the
assimilation experiment.
3. Improving salinity representation by
direct assimilation of vertical salinity
profiles.
A first step towards a better representation of
salinity can be performed by including the available
salinity
observations
in
the
assimilation
hydrographic data set.
However,
since
temperature
observations
numerically exceed the amount of salinity profiles,
the resulting salinity analysis will be still partly
depending upon the bivariate EOF statistics,
whereby only temperature data are available.
In order to test the impact of direct salinity
assimilation on salinity analysis, an additional
experiment assimilating both temperature and
salinity profiles for the 1962-2001 stream has been
performed, and it will be hereafter indicated as
OI(T+S).
In figure 3, the analysis-Levitus sea surface salinity
residuals are shown for the two analyses in the
North Atlantic. Climatological fields for the
assimilation experiments have been computed
over the entire stream length.
Here we focus on the North Atlantic area, where
the effects associated with the direct assimilation
of salinity are particularly evident. The model
surface salinity bias in the Gulf Stream region is
sensibly reduced when salinity observations are
assimilated.
The long term variability of the upper ocean salt
content is tested against salinity observations
collected at Bermuda Hydrostation (BH) in the
subtropical North Atlantic (64.5W, 32N). In figure 4
we show the salinity rms differences with respect
to BH observations for OI(T), OI(T+S) and the
control, at different levels in the top 500 meters.
The occurrence of a strong freshening signal
starting on 1995, deteriorates the representation
of salinity in OI(T+S) and, to a lesser extent, OI(T)
analyses. Hence we select two different periods for
the rms computation, with and without the 19952001 tail.
Figure 4: Vertical profiles of analysis (and control) minus
observations root-mean-square for salinity at Bermuda
Hydrostation (64.5W, 32N; in psu). The displayed
curves refer to OI(T) (green), OI(T+S) (black) and
control (red) experiments, for the 1962-1995 (solid) and
1962-2001 (dashed) periods.
4. Salinity analysis sensitivity to spatial
and time resolution of the EOF data set.
Figure 3: Analysis-Levitus
sea surface salinity
differences (PSU) in the North Atlantic region for the
assimilation
experiments (top) OI(T) and (bottom)
OI(T+S).
When only temperature is assimilated, salinity
increments produce a sensible reduction of the salt
content in the upper layers compared to
observations, resulting in larger than 0.3 psu rms
differences. After salinity assimilation is included,
the departure from the observations in the rms
sense reduces to less than 0.1 psu values before
1995, also improving the salinity representation
with respect to the control experiment. The midnineties freshening, however, increases the
OI(T+S) salinity deviation from the observations,
with rms differences for the full length 1962-2001
stream sensibly larger than in the control
experiment in the upper 150 meters.
Two distinct causes seem to concur to create the
mentioned late-90s freshening detected in OI(T+S)
experiment. First it must be mentioned that most of
the salinity data from Bermuda station did not pass
the quality check from approximately 1995 onward,
and therefore were not included in the assimilation
data set. This in turn implies that salinity
corrections in the last segment of the OI(T+S) time
series are entirely based on the T/S EOFs. The
inaccuracies associated with the salinity analysis
then suggest that the T/S relationships embodied
in the EOFs do not correctly parameterize the
background error statistics. A further step towards
a better salinity representation can be done by
enhancing both the spatial and time resolution of
the bivariate EOFs. For this purpose, a new
experiment, indicated as OI(T+S)-Hr, is designed
which makes use of a higher resolution domain
partition for the EOF computation. In the new
partition the domain is split into 195 regions, hence
increasing by one order of magnitude the number
of regions adopted in the first set of experiments.
Using the high resolution partition, a new set of
EOFs has been diagnosed from the control
experiment, but only for the 1990-1999 time
period. The new EOFs have been tested by
producing an analysis starting from January 1990
initial conditions from OI(T+S) experiment, and
covering the 1990-2001 period.
Prediction)
and ENSEMBLES (ENSEMBLE-based
Predictions of Climate Changes and their Impacts) EU
projects.
References.
De Mey, P. and M. Benkiran: A multivariate reducedorder optimal interpolation method and its application to
the Mediterranean basin-scale circulation, In Ocean
Forecasting: Conceptual basis and applications, Edited
by N. Pinardi and J. D. Woods, Springer Verlag, 2002.
Ingleby B. and M. Huddleston: Quality control of ocean
temperature and salinity profiles: historical and real-time
data, to appear on Journal of Marine Systems, 2006.
Figure 5. Left panel: Mean salinity profile at Bermuda
from OI(T+S) (black), OI(T+S)-Hr (magenta), control
(red) and BH observations (blue). Right panel: As in
figure 4, but for OI(T+S) (black), OI(T+S)-Hr (magenta)
and the control (red).
The statistics have been
computed for the January 1990-December 2001 period.
This particular decade was selected so as to
correct the 90s North Atlantic freshening detected
in the OI(T+S) experiment. The impact of the high
resolution EOFs is evaluated by looking at the
analyses and control statistics in Bermuda, for the
1990-2001 time interval. In figure 5 (left panel) we
show the mean salinity profile at the BH location.
A bias affecting salinity in both the control and
OI(T+S) over most part of the water column
appears to be reduced in the OI(T+S)-Hr analysis.
Also, the mid-nineties freshening, responsible for
the sub-surface salinity maximum breakdown in
OI(T+S), is absent in the high resolution analysis
(not shown). The improved EOF representation
does not only impact on the mean salinity state,
but it also concurs to sensibly reduce the distance
from the observations in the rms sense (figure 5,
right panel), with deviations of smaller amplitude
compared to the control run.
5. Final remarks.
The present results suggest that an improved
representation of the ocean salinity state can be
achieved by increasing the spatial and temporal
resolution of the EOFs used to parameterize the
background error covariance. A natural extension
of this approach – currently under way - will be to
increase the EOF spatial resolution up to the gridpoint scale and to use time dependent EOFs.
Acknowledgements.
The present work has been supported by
ENACT(Enhanced Ocean Data Assimilation and Climate
Madec, G., P. Delecleuse, M. Imbard, and C. Levy,
1998: OPA, release 8.1:Ocean general circulation model
reference manual.LODYC/IPSL Tech. Note 11, Paris,
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Reynolds, R.W., 1988: A real-time global sea surface
temperature analysis. J. Climate, 1, 75-86.