2019/09/11 by Roland Young, Young, Roland M. B., Roman Binter +7
Earth and Planetary Sciences · Environmental Science · #Atmospheric and Oceanic Physics (physics.ao-ph) #Chaotic Dynamics (nlin.CD) #Climate variability and models #Data Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Meteorological Phenomena and Simulations #Plant Water Relations and Carbon Dynamics #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.1909.05906
openalex publication_date 2019/09/11 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Shadowing trajectories are model trajectories consistent with a sequence of\nobservations of a system, given a distribution of observational noise. The\nexistence of such trajectories is a desirable property of any forecast model.\nGradient descent of indeterminism is a well-established technique for finding\nshadowing trajectories in low-dimensional analytical systems. Here we apply it\nto the thermally-driven rotating annulus, a laboratory experiment intermediate\nin model complexity and physical idealisation between analytical systems and\nglobal, comprehensive atmospheric models. We work in the perfect model scenario\nusing the MORALS model to generate a sequence of noisy observations in a\nchaotic flow regime. We demonstrate that the gradient descent technique\nrecovers a pseudo-orbit of model states significantly closer to a model\ntrajectory than the initial sequence. Gradient-free descent is used, where the\nadjoint model is set to \λI in the absence of a full adjoint model. The\nindeterminism of the pseudo-orbit falls by two orders of magnitude during the\ndescent, but we find that the distance between the pseudo-orbit and the\ninitial, true, model trajectory reaches a minimum and then diverges from truth.\nWe attribute this to the use of the \λ-adjoint, which is well suited to\nnoise reduction but not to finely-tuned convergence towards a model trajectory.\nWe find that \λ=0.25 gives optimal results, and that candidate model\ntrajectories begun from this pseudo-orbit shadow the observations for up to 80\ns, about the length of the longest timescale of the system, and similar to\nexpected shadowing times based on the distance between the pseudo-orbit and the\ntruth. There is great potential for using this method with real laboratory\ndata.\n