272
PIERRE BRASSEUR
models with reality, leading to potential improvements in modelling and
observing systems. It is therefore likely that applied ocean research will
benefit strongly from operational progress, and vice versa. The question
concerning the dominant energetic activity of the mesoscale ocean, its
non-deterministic nature and the interactions with the large-scale circulation make the challenge unique, requiring sophisticated numerical
models and assimilation methods that make the best use of sparse observations. To produce reliable forecasts, the models must be initialized
with conditions that represent as accurately as possible the actual state
of the ocean at eddy-resolving resolution. Due to the chaotic properties of ocean dynamics, the forecast range cannot be extended beyond
the limit of predictability of the system and the model has to be reinitialized intermittently by correcting the forecast with the most recent
observations. Fortunately, the arrival of satellite observations, in particular satellite altimetry, has provided the observational basis needed to
respond appropriately to the “high-resolution challenge”. In order to extract the best possible information from the new data, it is necessary to
assess how reliable the model forecast and the observations are. Therefore, error estimates on the measurements and the model prediction are
inherent in the assimilation process.
Data assimilation is traditionally formulated as a least-squares estimation problem. Among the various methodological approaches, the theory
of optimal statistical estimation, and more specifically the Kalman filtering approach, is well suited to provide a solution to the Best Linear
Unbiased Estimation. Since Kalman in 1960, sequential filtering methods have been thoroughly explored and applied to state estimation. An
extended version of the Kalman Filter (KF) has been derived for nonlinear models, known as the Extended Kalman Filter (EKF) [Jazwinski,
1970; Gelb, 1974]. In spite of a fairly simple theoretical framework,
the question of its applicability in assimilating observations into highresolution, non-linear numerical models of the ocean circulation is far
from trivial. As stated by Courtier [1997], the scientific di!culty associated with data assimilation is in finding algorithms which simplify the
search for an aordable solution in terms of computer resources, while
preserving some of the essential characteristics. A hierarchy of approximations to the Kalman filter has been defined to make the methodology
suitable for solving large-dimension problems. These developments represent a substantial part of the research eort devoted to oceanic and
atmospheric data assimilation over the past 10 years.
Compared with variational approaches such as the 4D-VAR, statistical algorithms require less initial investment in terms of coding and are
naturally designed to incorporate gradual developments. This is one of
PIERRE BRASSEUR
models with reality, leading to potential improvements in modelling and
observing systems. It is therefore likely that applied ocean research will
benefit strongly from operational progress, and vice versa. The question
concerning the dominant energetic activity of the mesoscale ocean, its
non-deterministic nature and the interactions with the large-scale circulation make the challenge unique, requiring sophisticated numerical
models and assimilation methods that make the best use of sparse observations. To produce reliable forecasts, the models must be initialized
with conditions that represent as accurately as possible the actual state
of the ocean at eddy-resolving resolution. Due to the chaotic properties of ocean dynamics, the forecast range cannot be extended beyond
the limit of predictability of the system and the model has to be reinitialized intermittently by correcting the forecast with the most recent
observations. Fortunately, the arrival of satellite observations, in particular satellite altimetry, has provided the observational basis needed to
respond appropriately to the “high-resolution challenge”. In order to extract the best possible information from the new data, it is necessary to
assess how reliable the model forecast and the observations are. Therefore, error estimates on the measurements and the model prediction are
inherent in the assimilation process.
Data assimilation is traditionally formulated as a least-squares estimation problem. Among the various methodological approaches, the theory
of optimal statistical estimation, and more specifically the Kalman filtering approach, is well suited to provide a solution to the Best Linear
Unbiased Estimation. Since Kalman in 1960, sequential filtering methods have been thoroughly explored and applied to state estimation. An
extended version of the Kalman Filter (KF) has been derived for nonlinear models, known as the Extended Kalman Filter (EKF) [Jazwinski,
1970; Gelb, 1974]. In spite of a fairly simple theoretical framework,
the question of its applicability in assimilating observations into highresolution, non-linear numerical models of the ocean circulation is far
from trivial. As stated by Courtier [1997], the scientific di!culty associated with data assimilation is in finding algorithms which simplify the
search for an aordable solution in terms of computer resources, while
preserving some of the essential characteristics. A hierarchy of approximations to the Kalman filter has been defined to make the methodology
suitable for solving large-dimension problems. These developments represent a substantial part of the research eort devoted to oceanic and
atmospheric data assimilation over the past 10 years.
Compared with variational approaches such as the 4D-VAR, statistical algorithms require less initial investment in terms of coding and are
naturally designed to incorporate gradual developments. This is one of