Continuous and discrete data assimilation with noisy observations for the Rayleigh-Bénard convection: a computational study

Abstract Obtaining accurate high-resolution representations of model outputs is essential to describe the system dynamics. In general, however, only spatially- and temporally-coarse observations states are available. These can also be corrupted by noise. Downscaling a process/scheme in which one uses coarse scale reconstruct solution states. Continuous Data Assimilation (CDA) recently introduced downscaling algorithm that constructs an increasingly representation continuously nudging large scales using observations. We introduce Discrete (DDA) as based on CDA with discrete-in-time nudging. then investigate performance DDA algorithms for noisy Rayleigh-Bénard convection chaotic regime. this computational study, set was generated perturbing reference Gaussian noise before them. The downscaled fields assessed various error- ensemble-based skill scores. shown converge towards faster than but at cost higher asymptotic error. numerical results suggest quadratic relationship between ℓ 2 error level both DDA. Cubic dependences expected errors spatial resolution were obtained, respectively.