In this paper, we trivially extend Tempered (Localized) Ensemble Transform
Particle Filter---T(L)ETPF---to account for model error. We examine T(L)ETPF
performance for non-additive model error in a low-dimensional and a
high-dimensional test problem. The former one is a nonlinear toy model, where
uncertain parameters are non-Gaussian distributed but model error is Gaussian
distributed. The latter one is a steady-state single-phase Darcy flow model,
where uncertain parameters are Gaussian distributed but model error is
non-Gaussian distributed. The source of model error in the Darcy flow problem
is uncertain boundary conditions. We comapare T(L)ETPF to a Regularized
(Localized) Ensemble Kalman Filter---R(L)EnKF. We show that T(L)ETPF
outperforms R(L)EnKF for both the low-dimensional and the high-dimensional
problem. This holds even when ensemble size of TLETPF is 100 while ensemble
size of R(L)EnKF is greater than 6000. As a side note, we show that TLETPF
takes less iterations than TETPF, which decreases computational costs; while
RLEnKF takes more iterations than REnKF, which incerases computational costs.
This is due to an influence of localization on a tempering and a regularizing
parameter