Title: Optimal linearization trajectories

Authors: Roel Stappers (KNMI)
Jan Barkmeijer (KNMI)

Nowadays linear models play an important role in various components of NWP, such as ensemble forecasting and variational data-assimilation. Nonlinear model behaviour, however, can have severe implications for the usefulness of these linear models. We show that many types of nonlinearity, such as advection, can be taken into account 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 for more than 200 days in a 3-level 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. As such, this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We will discuss the use of the optimal linearization trajectory in the context of data-assimilation and adjoint observation impact studies.

GMAO Head: Michele Rienecker Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: March 1 2011