so-called representation error (e.g. Lorenc, 1986),
which corresponds to real processes that are measured but are not represented or resolvable by the
models, should be considered part of the uncertainties of the data constraint (R) instead of those
of the model constraint (Q). Consequently, data
constraint error R, like model constraint error Q,
is model dependent.
Representation errors are processes beyond the
model phase space. Such errors are not resolvable
by models and thus inconsistent with them. Such
errors include, for instance, eddies for non-eddyresolving models, and tides and diabatic processes
for quasi-geostrophic models. Forcing models to
fit representation errors necessarily increases the
model constraint error, Q. Consequently, such
corrections can result in so-called ‘overfitting’ of
models to data that lead to model degradation
rather than improvement by the assimilation, in
particular, for aspects of the model that are not
directly measured. Therefore, representation errors
should generally be considered part of data constraint error, i.e. part of the model error that cannot be corrected by data assimilation. It should be
noted, however, that possible effects of representation error on processes within the modelled phase
space can be corrected, because such effects, as
opposed to their sources, are within the model
space. For example, eddy effects on large-scale circulation as simulated by a non-eddy-permitting
model can be corrected, even when the eddies
themselves cannot be resolved by assimilation.
A better understanding of what models and
observing systems do and do not represent is
arguably one of the most urgent and important
issues in estimation. While some components of
representation errors are distinguishable (e.g. eddies
for non-eddy-resolving models), many are not as
easily identifiable because it is not necessarily clear
what the model phase space really is. Even when
distinguishable, a quantitative description of representation errors is often lacking. Data representation is also an issue. Many in-situ measurements are
sparse and information on what the observations
accurately resolve is often unavailable. For instance,
some island tide gauge stations may not reflect conditions of the open ocean nearby. Variabilities associated with geographically or temporally offset
hydrographic stations or mooring measurements
are not accurately known but can provide information of the measurement’s representativeness.
Advancing model and data representations can
only be achieved by improving model physics, forcing, boundary conditions, etc., or making more
comprehensive observations that contribute more
information. Therein lie the relative merits of
modelling, observations and assimilation. Assimilation is not a panacea that can correct all model
errors and compensate all deficiencies of observations. Data assimilation does not add information
independent from observations or model physics,
but merely allows compensation of one by the
other within their common phase space essentially
through averaging the two. Although assimilation
provides a new dimension to ocean state estimation, results are ultimately limited to what models
and observations resolve and especially our understanding of their nature.
A major difficulty in assessing model and data
uncertainties has been a lack of global oceanic
data sets of sufficient quality and duration. The
advent of TOPEX/POSEIDON altimetry and the
other systematic large-scale ocean observing systems, including those of WOCE, have made significant contributions to this end. Fu et al. (1993)
devised a simple means of evaluating model and
data errors by comparing observations and model
simulations. Menemenlis and Chechelnitsky (2000)
and Tokmakian and Challenor (1999) extended
the approach by utilizing time-lagged model–data
differences and multiple data sets, respectively.
Adaptive Kalman filter methods have also been
explored to estimate simultaneously from observations prior errors in addition to the oceanic state
(Blanchet et al., 1997).
However, error estimates resulting from these
empirical methods are limited due to duration and
extent of the data sets, and the methods only provide partial guidance for error specification. The
validity of these and other error specifications
must be carefully assessed in terms of their consistencies (e.g. Fukumori et al., 1999). In the absence
of a wide user community, such as exists for meteorological analyses, accurate ocean state estimation will require a concerted effort within the
general oceanographic community, i.e. modellers,
observationalists and assimilators alike, to quantify and assess the various assumptions that form
the basis of data assimilation. Namely, what do
available observations and numerical models represent, how accurately do they do so, and how do
we improve upon them?
7.1 Towards a WOCE Synthesis
541
Talley, Stammer and Fukumori
which corresponds to real processes that are measured but are not represented or resolvable by the
models, should be considered part of the uncertainties of the data constraint (R) instead of those
of the model constraint (Q). Consequently, data
constraint error R, like model constraint error Q,
is model dependent.
Representation errors are processes beyond the
model phase space. Such errors are not resolvable
by models and thus inconsistent with them. Such
errors include, for instance, eddies for non-eddyresolving models, and tides and diabatic processes
for quasi-geostrophic models. Forcing models to
fit representation errors necessarily increases the
model constraint error, Q. Consequently, such
corrections can result in so-called ‘overfitting’ of
models to data that lead to model degradation
rather than improvement by the assimilation, in
particular, for aspects of the model that are not
directly measured. Therefore, representation errors
should generally be considered part of data constraint error, i.e. part of the model error that cannot be corrected by data assimilation. It should be
noted, however, that possible effects of representation error on processes within the modelled phase
space can be corrected, because such effects, as
opposed to their sources, are within the model
space. For example, eddy effects on large-scale circulation as simulated by a non-eddy-permitting
model can be corrected, even when the eddies
themselves cannot be resolved by assimilation.
A better understanding of what models and
observing systems do and do not represent is
arguably one of the most urgent and important
issues in estimation. While some components of
representation errors are distinguishable (e.g. eddies
for non-eddy-resolving models), many are not as
easily identifiable because it is not necessarily clear
what the model phase space really is. Even when
distinguishable, a quantitative description of representation errors is often lacking. Data representation is also an issue. Many in-situ measurements are
sparse and information on what the observations
accurately resolve is often unavailable. For instance,
some island tide gauge stations may not reflect conditions of the open ocean nearby. Variabilities associated with geographically or temporally offset
hydrographic stations or mooring measurements
are not accurately known but can provide information of the measurement’s representativeness.
Advancing model and data representations can
only be achieved by improving model physics, forcing, boundary conditions, etc., or making more
comprehensive observations that contribute more
information. Therein lie the relative merits of
modelling, observations and assimilation. Assimilation is not a panacea that can correct all model
errors and compensate all deficiencies of observations. Data assimilation does not add information
independent from observations or model physics,
but merely allows compensation of one by the
other within their common phase space essentially
through averaging the two. Although assimilation
provides a new dimension to ocean state estimation, results are ultimately limited to what models
and observations resolve and especially our understanding of their nature.
A major difficulty in assessing model and data
uncertainties has been a lack of global oceanic
data sets of sufficient quality and duration. The
advent of TOPEX/POSEIDON altimetry and the
other systematic large-scale ocean observing systems, including those of WOCE, have made significant contributions to this end. Fu et al. (1993)
devised a simple means of evaluating model and
data errors by comparing observations and model
simulations. Menemenlis and Chechelnitsky (2000)
and Tokmakian and Challenor (1999) extended
the approach by utilizing time-lagged model–data
differences and multiple data sets, respectively.
Adaptive Kalman filter methods have also been
explored to estimate simultaneously from observations prior errors in addition to the oceanic state
(Blanchet et al., 1997).
However, error estimates resulting from these
empirical methods are limited due to duration and
extent of the data sets, and the methods only provide partial guidance for error specification. The
validity of these and other error specifications
must be carefully assessed in terms of their consistencies (e.g. Fukumori et al., 1999). In the absence
of a wide user community, such as exists for meteorological analyses, accurate ocean state estimation will require a concerted effort within the
general oceanographic community, i.e. modellers,
observationalists and assimilators alike, to quantify and assess the various assumptions that form
the basis of data assimilation. Namely, what do
available observations and numerical models represent, how accurately do they do so, and how do
we improve upon them?
7.1 Towards a WOCE Synthesis
541
Talley, Stammer and Fukumori