Sequential data assimilation in fine-resolution models using error-subspace emulators: Theory and preliminary evaluation

A novel technique for nonlinear sequential data assimilation in computationally expensive fine-resolution models is introduced. The technique involves basis function approximation for dimension reduction and Gaussian Process Modelling for simulation speedup. The basis function approximation is carried out via the Singular Value Decomposition (SVD) of the model ensemble. The Gaussian Process Models propagate the model solution in the error-subspace defined by a finite set of basis functions. The developed technique can also be considered approximate Particle Filtering with two classes of particles: model-particles representing an ensemble of computationally expensive model solutions, and emulator-particles representing an ensemble of fast and cheap model approximations. The algorithm was tested by assimilating synthetic data into a two-dimensional (one spatial dimension plus time) sediment transport model in an idealised vertically-resolved benthic–pelagic system. The assimilation algorithm updates 2 spatially varying state variables and 3 unknown parameters. Numerical experiments illustrate robust performance of the technique for a wide range of the assimilation settings. The capabilities and limitations of the approach are discussed, and further developments are outlined.