118 Keith Haines
ocean has a long memory when viewed from a Lagrangian perspective, and this
can, and should, be taken advantage of in constructing data assimilation systems.
Consider 2 states of the ocean separated in time by 1 year. Most of the differences in these ocean states are due to advection of water masses which have
occured in the intervening period. The total volume and properties of each water
mass has probably hardly changed. Because of this the second state can largely be
obtained by an adiabatic and tracer preserving re-arrangement of the waters in the
tirst state. Even during decadal timescale fluctuations, such as those seen in the
strength and depth of the N Atlantic subtropical gyre, Levitus (1989), the water
properties often remain fairly constant, as reflected by unchanging T -S relationships, although on this timescale the relative volumes ofthe water masses are likely
to have changed. When low frequency variations are examined in ocean models,
e.g. Cox (1987), the variations are often in the form of baroclinic Rossby waves
propagating slowly westward in the subtropical gyre. The water mass variability
associated with such wave propagation would also be well represented through displacements of in situ water masses. Such low frequency signals may also produce
SST anomalies and therefore identifying such events in ocean data sets and initialising ocean models to contain them is probably one ofthe most important problems
facing the ocean assimilation community if the ocean models are then to contribute
to improving climate prediction.
Retuming to the data assimilation problem, when we have observations of sea
level this can tell us about the location of ocean eddies and Rossby wave positions,
in other words the position of water mass fronts and distributions. It tells us very
little about the water masses themselves. For this reason it is conceptually realistic
to consider the altimeter assimilation problem as one of deriving a 'Lagrangian'
redistribution ofwater masses already present rather than an 'Eulerian' alteration of
existing water masses to make them consistent with the local sea level data. In
practice of course the same analysed hydrography can be obtained by either
method but it is not easy to ensure that integrated water masses are preserved using
the Eulerian method, especially when local hydrography changes are based on statistical correlations.
It is interesting to view the physics ofthe 4Dvar and 3D sequential data assimilation methods in the light ofthe above arguements. The 4Dvar assimilation scheme
is often set up to seek the best initial conditions which will allow a model trajectory
launched from these conditions to pass close to some set of observations distributed over some time interval. If we accept that the most important processes taking
place during this time interval are essentially advective then the 4Dvar scheme is
seeking the correct initial spatial water mass distribution which will thereafter
undergo dynamically detined displacements as the model integrates forward, in
order to match the observations at subsequent times. In a 3D sequential scheme we
initially have no accurate idea of the water spatial distribution although we might
assume we already have a good knowledge of the integrated water properties, e.g.
we might start from Levitus, or some better climatology if available. As each new
data set comes in we can seek a redistribution ofthe existing water properties to be
ocean has a long memory when viewed from a Lagrangian perspective, and this
can, and should, be taken advantage of in constructing data assimilation systems.
Consider 2 states of the ocean separated in time by 1 year. Most of the differences in these ocean states are due to advection of water masses which have
occured in the intervening period. The total volume and properties of each water
mass has probably hardly changed. Because of this the second state can largely be
obtained by an adiabatic and tracer preserving re-arrangement of the waters in the
tirst state. Even during decadal timescale fluctuations, such as those seen in the
strength and depth of the N Atlantic subtropical gyre, Levitus (1989), the water
properties often remain fairly constant, as reflected by unchanging T -S relationships, although on this timescale the relative volumes ofthe water masses are likely
to have changed. When low frequency variations are examined in ocean models,
e.g. Cox (1987), the variations are often in the form of baroclinic Rossby waves
propagating slowly westward in the subtropical gyre. The water mass variability
associated with such wave propagation would also be well represented through displacements of in situ water masses. Such low frequency signals may also produce
SST anomalies and therefore identifying such events in ocean data sets and initialising ocean models to contain them is probably one ofthe most important problems
facing the ocean assimilation community if the ocean models are then to contribute
to improving climate prediction.
Retuming to the data assimilation problem, when we have observations of sea
level this can tell us about the location of ocean eddies and Rossby wave positions,
in other words the position of water mass fronts and distributions. It tells us very
little about the water masses themselves. For this reason it is conceptually realistic
to consider the altimeter assimilation problem as one of deriving a 'Lagrangian'
redistribution ofwater masses already present rather than an 'Eulerian' alteration of
existing water masses to make them consistent with the local sea level data. In
practice of course the same analysed hydrography can be obtained by either
method but it is not easy to ensure that integrated water masses are preserved using
the Eulerian method, especially when local hydrography changes are based on statistical correlations.
It is interesting to view the physics ofthe 4Dvar and 3D sequential data assimilation methods in the light ofthe above arguements. The 4Dvar assimilation scheme
is often set up to seek the best initial conditions which will allow a model trajectory
launched from these conditions to pass close to some set of observations distributed over some time interval. If we accept that the most important processes taking
place during this time interval are essentially advective then the 4Dvar scheme is
seeking the correct initial spatial water mass distribution which will thereafter
undergo dynamically detined displacements as the model integrates forward, in
order to match the observations at subsequent times. In a 3D sequential scheme we
initially have no accurate idea of the water spatial distribution although we might
assume we already have a good knowledge of the integrated water properties, e.g.
we might start from Levitus, or some better climatology if available. As each new
data set comes in we can seek a redistribution ofthe existing water properties to be