542
ANDREAS OSCHLIES
is remembered by the algorithm. In many applications, the parameter
“gene” is defined as the sequence of the components of the parameter
vector written in binary notation, though a binary notation is not a necessary element of the method. As is the case with simulated annealing,
convergence cannot generally be proven and will in practice depend on
tunable parameters of the algorithm (mutation rate, population size).
6.
Achievements and perspectives
The above assimilation and minimisation methods have so far been
applied to ecosystem models that essentially all belong to the NPZDtype category. At present, there is no clear consensus on which method
might be most efficient for this type of models. Sequential assimilation
methods seem to have largest prospects in operational or near real-time
applications that require good state estimates and that do not care that
much about occasional jumps in the model trajectory. Variational methods, on the other hand, seem to be better suited for research issues that
can take advantage of the dynamically self-consistent model trajectory.
In principle, it is possible to obain a smooth model trajectory from
sequential methods as well by applying a so-called smoother, which
sentially consists of an integration backward in time. For linear systems
it can be shown that sequential and variational algorithms can indeed
produce identical results [Bennett, 1989].
A main advantage of stochastic optimisation techniques is the easy access to information about the posterior error of the parameter estimate.
The large number of cost-function evaluations gives a reasonable picture
of the cost function’s sensitivity to changes in the individual parameters
[e.g., Schartau and Oschlies, 2003a]. Particularly for strongly non-linear
systems this may be more informative than local evaluations of the cost
function’s curvature via the Hessian matrix [Fennel et al., 2001].
What is, to my knowledge, common to all of the assimilation studies
performed so far is that at most 10 to 15 ecological model parameters
could be constrained by the available observations. Although all these
studies have so far employed relatively simple NPZD-type models, there
were always a few parameters (or linear combinations of parameters)
that could not be constrained. This indicates that even NPZD-type
models have too many degrees of freedom and that models with fewer
parameters should be able to reproduce the observations similarly well.
Looking closer at how “well” the models can actually reproduce the
data, one finds that even the optimised models fit the data very poorly.
Usually, model-data misfits still amount to several standard deviations
of the estimated prior errors. Such poor fits indicate that models need
es
ANDREAS OSCHLIES
is remembered by the algorithm. In many applications, the parameter
“gene” is defined as the sequence of the components of the parameter
vector written in binary notation, though a binary notation is not a necessary element of the method. As is the case with simulated annealing,
convergence cannot generally be proven and will in practice depend on
tunable parameters of the algorithm (mutation rate, population size).
6.
Achievements and perspectives
The above assimilation and minimisation methods have so far been
applied to ecosystem models that essentially all belong to the NPZDtype category. At present, there is no clear consensus on which method
might be most efficient for this type of models. Sequential assimilation
methods seem to have largest prospects in operational or near real-time
applications that require good state estimates and that do not care that
much about occasional jumps in the model trajectory. Variational methods, on the other hand, seem to be better suited for research issues that
can take advantage of the dynamically self-consistent model trajectory.
In principle, it is possible to obain a smooth model trajectory from
sequential methods as well by applying a so-called smoother, which
sentially consists of an integration backward in time. For linear systems
it can be shown that sequential and variational algorithms can indeed
produce identical results [Bennett, 1989].
A main advantage of stochastic optimisation techniques is the easy access to information about the posterior error of the parameter estimate.
The large number of cost-function evaluations gives a reasonable picture
of the cost function’s sensitivity to changes in the individual parameters
[e.g., Schartau and Oschlies, 2003a]. Particularly for strongly non-linear
systems this may be more informative than local evaluations of the cost
function’s curvature via the Hessian matrix [Fennel et al., 2001].
What is, to my knowledge, common to all of the assimilation studies
performed so far is that at most 10 to 15 ecological model parameters
could be constrained by the available observations. Although all these
studies have so far employed relatively simple NPZD-type models, there
were always a few parameters (or linear combinations of parameters)
that could not be constrained. This indicates that even NPZD-type
models have too many degrees of freedom and that models with fewer
parameters should be able to reproduce the observations similarly well.
Looking closer at how “well” the models can actually reproduce the
data, one finds that even the optimised models fit the data very poorly.
Usually, model-data misfits still amount to several standard deviations
of the estimated prior errors. Such poor fits indicate that models need
es