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BODAS – Bluelink Ocean
Data Assimilation System Dr
Peter R. Oke Summary ● Description ● _Characteristics
of BODAS link
to a complete list of publications Oke, P. R., G. B.
Brassington, D. A. Griffin and A. Schiller, 2007: The Bluelink Ocean Data
Assimilation System (BODAS), Ocean Modelling, doi:10.1016/j.ocemod.2007.11.002. Oke, P. R., A.
Schiller, G. A. Griffin, G. B. Brassington 2005: Ensemble data assimilation
for an eddy-resolving ocean model. Quarterly Journal of the Royal Meteorological
Society, 131,
3301-3311. The primary test-bed for BODAS in BRAN. BODAS
Users
BODAS is an ensemble optimal interpolation system that uses an
ensemble of intraseasonal anomalies from a free
running model to estimate the background error covariances
(BECs). The ensemble-based BECs
are multivariate and inhomogeneous and are shown to reflect the
length-scales, the anisotropy and the covariability
of mesoscale oceanic processes.
Analyses
of sea-level η,
T, S, and
horizontal currents (u,v),
are computed by solving the analysis equations,
where
is the state vector; superscripts a, b, o and * denote analysis,
background, observed and matrix transpose, respectively (here the background
field refers to a model-generated estimate of the ocean state at the analysis
time; sometimes called the first guess); K is the gain matrix; H is an operator that
interpolates from the model grid to observation locations; ρ is a
correlation function used to localise the
ensemble-based BECs in P; R is the observation error
covariance matrix; and the open circles denote a Schur,
or Hadamard, product (an element-by-element matrix
multiplication). This formulation of the analysis equations is the same as
that of Houtekamer and
Mitchell (2001). Estimates of the BECs in (2) are given by
where n is the ensemble size and A
is an ensemble of model anomalies. Each anomaly field consists of all model
variables included in (3). The
calculation of the anomalies for an EnOI system is critical to the
performance of the scheme. They should be computed in such a way that the
scales of variability and features represented by the anomalies resemble the
dominant errors of the model. For example, for application to OFAM, where we
seek to correctly reproduce the mesoscale variability around Australia, we
expect that the errors of an individual forecast will be dominated by the
errors associated with mis-placement of eddies.
Section 4 shows that
this turns out to be true, although it is also true that errors at other
scales exist. We hope to address this compromise in the future. Consequently,
for application to OFAM, the ensemble of anomalies are generated by
calculating intraseasonal anomalies derived from
the spin-up run:
where α is a scalar that can tune the magnitude of the covariances for a particular application (for BRAN1.5, α=1); The BECs in (4) are localised in the horizontal around each
observation in (2) using the localising correlation function ρ. Elements
of ρ are
defined by the quasi-Gaussian function of Gaspari
and Cohn (1992), after Houtekamer
and Mitchell (2001). Localisation
has been shown to reduce the effects of sampling error for applications of an
EnKF (e.g., Hamill et al., 2001) and EnOI (Oke et al., 2007). The localising correlation function in ρ forces
the BECs to reduce to exactly zero, over L_ from an
observation location. Note that in the application, we do not localise the covariances in the
vertical direction. The present implementation of BODAS uses a uniform
horizontal radial distance L = 8_, corresponding to an e-folding scale of about 3.5_. This
has several ramifications for the system’s performance. Firstly, the rank of
the estimated BECs in P is increased
significantly. Using an ensemble size of n, the rank of P without localisation is at most n-1. By contrast, using an ensemble of only 72 with localisation
with L = 8_
we estimate that the effective rank of ρ The primary
test-bed for BODAS is BRAN. BRAN is a multi-year integration of OFAM, where BODAS is
used to sequentially assimilate observations once every 7 days. Observations
assimilated in BRAN include SLA from satellite altimetry,
satellite-derived sea-surface temperature (SST) and in situ T and S profiles.
Conceptually, BRAN is a three-dimensional time-varying synthesis of
oceanic observations that uses OFAM as a dynamic interpolator. The sequential
nature of the assimilation used here means that BRAN can be regarded as a series of 7-day “forecasts”.
Of course, the skill of BRAN should exceed that of an equivalent real-time
forecast system with a 7-day update cycle, because of the use of real-time
surface fluxes and observations; and particularly because of the latency of
real-time altimetry in the operational system. Despite these differences, we
assess the short-range predictive skill of the system for SLA and SST in BRAN as a way of measuring the potential performance of
the operational system. As stated above, one
of the advantages of EnOI is that the BECs are
inhomogeneous and anisotropic, reflecting the variability and length-scales
of the ocean circulation. An example of the anisotropy and inhomogeneity of the ensemble-based BECs
used by BODAS is shown in Fig. 4. The chosen examples show the localised
ensemble-based cross-correlation between sea-level
at a reference location and sea-level in the surrounding region. These fields
demonstrate the region of influence of an observation at the reference
location. Where the correlation is positive, the increment that is given by
the term K(wo-Hwb)
in (1), due to each observation has the same sign as the background
innovation (wo-Hwb).
So if the observed sea-level is higher than the
background field at the reference location, in the absence of other
observations in the same region, the solution to (1) will produce an increment that is also positive. The magnitude of the
increment depends on the relative magnitudes of the estimated background
error and observation error covariances (i.e., the
relative magnitudes of H(ρ Fig.
4. Examples of the ensemble-based cross-correlations between sea-level at a reference location, denoted by the star,
and sea-level in the surrounding region for a reference location (a) on the
continental shelf, (b) over the continental slope and (c) over the deep ocean
off eastern Australia (panel (d)). Contour intervals are 0.2; zero is bold, dotted is negative, correlations
above 0.6 are shaded. The
reference locations for the examples presented in Fig.
4 are at 32.5_S, corresponding to the typical separation point of the EAC
(Godfrey
et al., 1980). These examples include correlations when the reference
location is on the continental shelf at 115 m depth, where the
correlation field has short decorrelation scales in
the across-shore direction and long decorrelation
scales in the alongshore direction (Fig.
4a). The long length-scales in the alongshore direction are probably a
reflection of the covariability associated with
northward propagation of slow-moving coastal trapped waves and the
along-shore advection of the EAC and wind-driven circulation. Also shown is a
correlation map when the reference location is over the continental slope at
1800 m depth (Fig.
4b), less than 50 km east of the shelf example (Fig.
4a). This field shows a more isotropic correlation, but with a tendency
to have higher correlations to the east and south-east,
in the typical direction of the EAC as it separates from the coast. The final
example considered here shows correlations when the reference location is
over the deep ocean at 4500 m depth (Fig.
4c). This field shows a somewhat isotropic correlation field, but also
shows areas of weak negative correlation to the north-east
and south-west. These negative correlations may be related to variations in sea-level associated with the typical eddy field in this
region. The correlation fields presented in Fig.
4 highlight the anisotropy and inhomogeneity of
the ensemble-based correlations, with relatively long quasi-isotropic
correlations in the deep ocean, transitioning to very anisotropic
correlations nearer the coast. An
example of the multivariate nature of BODAS is demonstrated in Fig.
5 and Fig.
6, showing the increments from a single observation analysis (i.e., where
an analysis is computed by combining a single observation with a background
field). In this example, an observation of sea-level
at the coast is presumed to be 20 cm lower than the background
sea-level. BODAS is used to calculate the increments to the full model state (η,T,S,u,v) in the
surrounding region. We choose to use sea-level from
a coastal location off South Australia at 140.35_E and 37.85_S. This location
is arguably the best region for observing wind-driven, coastal upwelling
along the Australian coastline (e.g., [Lewis,
1981] and [Kampf et al., 2004]). We therefore expect the
increments to be consistent with a conceptual model of upwelling (i.e.,
consistent with the oceanic response to south-easterly winds). Fig.
5. Increments to sea-level (grey scale) and surface currents (vectors)
based on a single observation of sea-level, denoted by the Fig.
6. Increments to (a) sea-level, (b) across-shore currents (dashed
contours are offshore; bold contour is zero) and (c) along-shore currents
(solid contours are into the page; bold contour is zero); and the background
field (solid contours) and analysis (dashed contours) for (d) T and (e) S, based on
a single observation of sea-level at the coast as in Fig.
5. Decreased
sea-level at the coast may be due to a number of
factors that include, but are not limited to, wind-driven upwelling. However,
the dominance of locally wind-driven circulation in this region leads us to
the expectation that it will also dominate the statistical properties of the
ensemble fields here. We find that the increments to sea-level and surface
currents in Fig.
5 are consistent with wind-driven upwelling, with reduced sea-level along
the coast, a relatively strong coastal jet and weak south-westerly flow in
the deep ocean. Fig.
6 shows the impact of the observation along a shore-normal section
offshore of the observation location. This figure shows that the negative
sea-level increment is strongest at the coast as we expect, and approaches
zero moving offshore in a quasi-exponential fashion. Increments to the
across-shore currents show an offshore flow of up to 5 cm s−1
over the top 30 m, that is consistent with an offshore wind-driven Ekman layer, and a weak, shoreward return flow at depth.
Increments to the along-shore currents are consistent with a baroclinic, wind-driven coastal jet, with the strongest
currents of 0.5 m s−1 at the surface near the coast. Fig.
6d and e shows the background and analysed T and S fields.
Both of these fields show an uplift of isotherms and isohalines, with an
implied vertical excursion of about 25 m near the shelf break and
40–50 m over the upper slope. From this analysis, we conclude that the
statistical properties of the ensemble are consistent with a conceptual model
of wind-driven upwelling in the region considered. The
analysis described above indicates that if the model does not produce an
upwelling event, due to incorrect surface forcing for example, and we
assimilate a single observation of sea-level at the coast that reflects the
upwelling through reduced sea-level, then BODAS will compute increments that
more closely match the observation at the coast, and in a manner that is
consistent with wind-driven upwelling. While this feature is presented here
as a benefit of EnOI, there is also a down-side.
Suppose the model-observation mismatch is due to a mis-represented
process other than wind-driven upwelling. Say, the encroachment of an eddy,
or the propagation of a coastal trapped wave. Then
the EnOI-derived increments will still be consistent with upwelling as in Fig.
5 and Fig.
6. This may not be desirable, and may result in a reanalysed
state that is somewhat inconsistent with reality. However, we note that the
example described here is very idealised. In
practice, we typically assimilate multiple observations of various types
(e.g., sea-level, T and S) and in the presence of additional observations that provide a
more complete picture of the ocean state, BODAS will
compute increments that more appropriately represent the true circulation. Another
limitation of EnOI that can be seen from the example described by Fig.
5 and Fig.
6 is that it implies a symmetry in the increments for an
observation-model mis-match of the opposite sign.
Suppose that the observation-model difference considered above is reversed.
That is, the observation is 20 cm higher than the background sea-level. In this case, the increments simply have the
opposite sign to those presented in Fig.
5 and Fig.
6. This might occur if a modelled upwelling is
too strong, or perhaps if the model fails to represent a downwelling
event. However, we note that studies into the dynamics of idealised
wind-driven upwelling (e.g., Allen
et al., 1995) and wind-driven downwelling
(e.g., Allen
and Newberger, 1996) on the continental shelf
have shown that they are very different, and do not simply result in
symmetric anomalies about some mean field as the EnOI-based increments would
imply. These problems are the result of assuming ergodicity
in the BECs. A better approach is to employ some flavour of the EnKF (e.g., [Evensen,
2003] and [Sakov
and Oke, in press]), where the anomalies in (5)
evolve in time and more accurately reflect the dominant dynamical processes
for a particular time. However, these types of filters require an ensemble of
states to be evolved, which is currently too computationally expensive for
applications as large as OFAM. |
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Last updated 22/09/06 | Legal Notice and
Disclaimer |
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