ICHIRO FUKUMORI
340
Data assimilation concerns correcting models using observations.
straightforward, there are various subtleties involved
both what data assimilation solves and how the computation is carried out.
A
ught. However, given that all models are in one way or another
app
ions that consist of those relating the model state to the
obs
moothers
add
el error corrections,
and
udgets of heat
and
6. Summary
Although the concept is
in
careful understanding of these issues is helpful in assimilating
observations, in utilizing their results, and in further improving their
estimates.
Data assimilation can be considered a process of fitting models to
observations. A solution that is consistent with both observations and model
physics is so
roximations of the real world (ocean), there are some, sometimes many,
aspects of the observations that are real but inconsistent with the models.
These aspects that models cannot inherently simulate (representation errors)
therefore cannot be part of the assimilated solution and must be properly
accounted for. Forcing models to agree with such measurements can lead to
increased inaccuracies and inconsistencies. An assessment of what models
do and do not simulate is important in carrying out the assimilation, and an
understanding of what the assimilated estimates resolve is fundamental to
utilizing the results.
Mathematically, data assimilation is an inverse problem. The temporally
evolving state of the model and sources of model error are estimated by
inverting model equat
ervations and those describing the model’s temporal evolution.
The Kalman filter and other common filtering methods are inversions of
the model equivalent of the observations but not of the model evolution, and,
therefore, do not completely solve the assimilation problem. S
itionally invert the model evolution completing the estimation, providing
estimates of both model state and model error sources.
While state estimation is often used synonymously with data
assimilation, it is in fact the estimation of the model error sources (process
noise) that is most fundamental. Given smoothed mod
apart from corrections to the initial condition, the smoothed state can be
derived by integrating the model in time, but not vice versa.
Because of model errors, data assimilated state estimates by themselves
are not physically consistent, in the sense that the estimated states’ temporal
evolution cannot be physically accounted for. For instance, b
other properties cannot be closed in terms of explicit physical processes.
The smoother’s explicit estimation of model error sources resolves the
physical inconsistency, rendering the assimilated solution amenable to
various process studies and applications.
340
Data assimilation concerns correcting models using observations.
straightforward, there are various subtleties involved
both what data assimilation solves and how the computation is carried out.
A
ught. However, given that all models are in one way or another
app
ions that consist of those relating the model state to the
obs
moothers
add
el error corrections,
and
udgets of heat
and
6. Summary
Although the concept is
in
careful understanding of these issues is helpful in assimilating
observations, in utilizing their results, and in further improving their
estimates.
Data assimilation can be considered a process of fitting models to
observations. A solution that is consistent with both observations and model
physics is so
roximations of the real world (ocean), there are some, sometimes many,
aspects of the observations that are real but inconsistent with the models.
These aspects that models cannot inherently simulate (representation errors)
therefore cannot be part of the assimilated solution and must be properly
accounted for. Forcing models to agree with such measurements can lead to
increased inaccuracies and inconsistencies. An assessment of what models
do and do not simulate is important in carrying out the assimilation, and an
understanding of what the assimilated estimates resolve is fundamental to
utilizing the results.
Mathematically, data assimilation is an inverse problem. The temporally
evolving state of the model and sources of model error are estimated by
inverting model equat
ervations and those describing the model’s temporal evolution.
The Kalman filter and other common filtering methods are inversions of
the model equivalent of the observations but not of the model evolution, and,
therefore, do not completely solve the assimilation problem. S
itionally invert the model evolution completing the estimation, providing
estimates of both model state and model error sources.
While state estimation is often used synonymously with data
assimilation, it is in fact the estimation of the model error sources (process
noise) that is most fundamental. Given smoothed mod
apart from corrections to the initial condition, the smoothed state can be
derived by integrating the model in time, but not vice versa.
Because of model errors, data assimilated state estimates by themselves
are not physically consistent, in the sense that the estimated states’ temporal
evolution cannot be physically accounted for. For instance, b
other properties cannot be closed in terms of explicit physical processes.
The smoother’s explicit estimation of model error sources resolves the
physical inconsistency, rendering the assimilated solution amenable to
various process studies and applications.