Optimal linearization trajectories for tangent linear models

Stappers, R. J. J. and Barkmeijer, J. (2012) Optimal linearization trajectories for tangent linear models. Quarterly Journal of the Royal Meteorological Society, 138 (662). pp. 170-184. ISSN 1477-870X doi: 10.1002/qj.908

Abstract/Summary

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/28437
Identification Number/DOI	10.1002/qj.908
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO) Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	adjoint model;tangent linear assumption;bilinear differential equation;quadratic nonlinear;forecast sensitivity;iterative relinearization
Publisher	Royal Meteorological Society
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