Over the years data assimilation methods have been developed to obtain
estimations of uncertain model parameters by taking into account a few
observations of a model state. The most reliable methods of MCMC are
computationally expensive. Sequential ensemble methods such as ensemble Kalman
filers and particle filters provide a favourable alternative. However, Ensemble
Kalman Filter has an assumption of Gaussianity. Ensemble Transform Particle
Filter does not have this assumption and has proven to be highly beneficial for
an initial condition estimation and a small number of parameter estimation in
chaotic dynamical systems with non-Gaussian distributions. In this paper we
employ Ensemble Transform Particle Filter (ETPF) and Ensemble Transform Kalman
Filter (ETKF) for parameter estimation in nonlinear problems with 1, 5, and
2500 uncertain parameters and compare them to importance sampling (IS). We
prove that the updated parameters obtained by ETPF lie within the range of an
initial ensemble, which is not the case for ETKF. We examine the performance of
ETPF and ETKF in a twin experiment setup and observe that for a small number of
uncertain parameters (1 and 5) ETPF performs comparably to ETKF in terms of the
mean estimation. For a large number of uncertain parameters (2500) ETKF is
robust with respect to the initial ensemble while ETPF is sensitive due to
sampling error. Moreover, for the high-dimensional test problem ETPF gives an
increase in the root mean square error after data assimilation is performed.
This is resolved by applying distance-based localization, which however
deteriorates a posterior estimation of the leading mode by largely increasing
the variance. A possible remedy is instead of applying localization to use only
leading modes that are well estimated by ETPF, which demands a knowledge at
which mode to truncate