  Data assimilation (DA) is widely used to combine physical knowledge and
observations. It is nowadays commonly used in geosciences to perform parametric
calibration. In a context of climate change, old calibrations can not
necessarily be used for new scenarios. This raises the question of DA
computational cost, as costly physics-based numerical models need to be
reanalyzed. Reduction and metamodelling represent therefore interesting
perspectives, for example proposed in recent contributions as hybridization
between ensemble and variational methods, to combine their advantages
(efficiency, non-linear framework). They are however often based on Monte Carlo
(MC) type sampling, which often requires considerable increase of the ensemble
size for better efficiency, therefore representing a computational burden in
ensemble-based methods as well. To address these issues, two methods to replace
the complex model by a surrogate are proposed and confronted : (i) PODEn3DVAR
directly inspired from PODEn4DVAR, relies on an ensemble-based joint
parameter-state Proper Orthogonal Decomposition (POD), which provides a linear
metamodel ; (ii) POD-PCE-3DVAR, where the model states are POD reduced then
learned using Polynomial Chaos Expansion (PCE), resulting in a non-linear
metamodel. Both metamodels allow to write an approximate cost function whose
minimum can be analytically computed, or deduced by a gradient descent at
negligible cost. Furthermore, adapted metamodelling error covariance matrix is
given for POD-PCE-3DVAR, allowing to substantially improve the metamodel-based
DA analysis. Proposed methods are confronted on a twin experiment, and compared
to classical 3DVAR on a measurement-based problem. Results are promising, in
particular superior with POD-PCE-3DVAR, showing good convergence to classical
3DVAR and robustness to noise.
