Publication Date:
2022-05-26
Description:
© The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Nonlinear Processes in Geophysics 24 (2017): 351-366, doi:10.5194/npg-24-351-2017.
Description:
The Lagrange multiplier method for combining observations and models (i.e., the adjoint method or "4D-VAR") has been avoided or approximated when the numerical model is highly nonlinear or chaotic. This approach has been adopted primarily due to difficulties in the initialization of low-dimensional chaotic models, where the search for optimal initial conditions by gradient-descent algorithms is hampered by multiple local minima. Although initialization is an important task for numerical weather prediction, ocean state estimation usually demands an additional task – a solution of the time-dependent surface boundary conditions that result from atmosphere–ocean interaction. Here, we apply the Lagrange multiplier method to an analogous boundary control problem, tracking the trajectory of the forced chaotic pendulum. Contrary to previous assertions, it is demonstrated that the Lagrange multiplier method can track multiple chaotic transitions through time, so long as the boundary conditions render the system controllable. Thus, the nonlinear timescale poses no limit to the time interval for successful Lagrange multiplier-based estimation. That the key criterion is controllability, not a pure measure of dynamical stability or chaos, illustrates the similarities between the Lagrange multiplier method and other state estimation methods. The results with the chaotic pendulum suggest that nonlinearity should not be a fundamental obstacle to ocean state estimation with eddy-resolving models, especially when using an improved first-guess trajectory.
Description:
Geoffrey Gebbie
was funded through the Ocean and Climate Change Institute of
the Woods Hole Oceanographic Institution. Tsung-Lin Hsieh
was funded by the Arthur Vining Davis Foundations Fund for
Summer Student Fellows through the Woods Hole Oceanographic
Institution.
Repository Name:
Woods Hole Open Access Server
Type:
Article
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