2018/09/23 by Emine Çelik, Eric N. Olson, Celik, Emine +3 · 1 citation
Computer Science · Earth and Planetary Sciences · #35Q30 #37C50 #76B75 #93C20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Cryospheric studies and observations #Dynamical Systems (math.DS) #FOS: Mathematics #Meteorological Phenomena and Simulations
paper · pdf · doi:10.48550/arxiv.1809.08654
openalex publication_date 2018/09/23 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
We describe a spectrally-filtered discrete-in-time downscaling data\nassimilation algorithm and prove, in the context of the two-dimensional\nNavier--Stokes equations, that this algorithm works for a general class of\ninterpolants, such as those based on local spatial averages as well as point\nmeasurements of the velocity. Our algorithm is based on the classical technique\nof inserting new observational data directly into the dynamical model as it is\nbeing evolved over time, rather than nudging, and extends previous results in\nwhich the observations were defined directly in terms of an orthogonal\nprojection onto the large-scale (lower) Fourier modes. In particular, our\nanalysis does not require the interpolant to be represented by an orthogonal\nprojection, but requires only the interpolant to satisfy a natural\napproximation of the identity.\n