  Data assimilation refers to the problem of finding trajectories of a
prescribed dynamical model in such a way that the output of the model (usually
some function of the model states) follows a given time series of observations.
Typically though, these two requirements cannot both be met at the same
time--tracking the observations is not possible without the trajectory
deviating from the proposed model equations, while adherence to the model
requires deviations from the observations. Thus, data assimilation faces a
trade-off. In this contribution, the sensitivity of the data assimilation with
respect to perturbations in the observations is identified as the parameter
which controls the trade-off. A relation between the sensitivity and the
out-of-sample error is established which allows to calculate the latter under
operational conditions. A minimum out-of-sample error is proposed as a
criterion to set an appropriate sensitivity and to settle the discussed
trade-off. Two approaches to data assimilation are considered, namely
variational data assimilation and Newtonian nudging, aka synchronisation.
Numerical examples demonstrate the feasibility of the approach.
