Title: Jacobians of the GEOS5 Relaxed Arakawa-Schubert convection scheme

Authors: Dan Holdaway (GESTAR/GMAO, Goddard Space Flight Center)
Ron Errico (GESTAR/GMAO, Goddard Space Flight Center)

In order to solve the minimization problem that is inherent in 4D variational data assimilation the adjoint of the numerical forecast model is required. Moist convective processes in the atmosphere can exhibit highly nonlinear behavior, meaning the tangent linear model, and thus the adjoint, would not always provide a suitable approximation for use in the minimization problem. As well as the inherent nonlinear interactions that occur in convective plumes the numerical representation of convection generally consists of a number of nonlinear discrete switches. Due to the high degree of nonlinearity tangent linearizations of the complete convection schemes, as used in modern global forecast models, are generally deemed inappropriate; for the adjoint calculation a much simpler scheme is usually considered. The aim of these simpler schemes is to capture the residing behavior but in a way that can be accurately linearized. In order to quantify the nonlinearity in the RAS convection scheme that is used in NASA's GEOS5 model, and thus proceed onto constructing a suitable version of the parameterization for use in the assimilation, the Jacobians are examined. The Jacobians are obtained by comparing the difference between the output of the RAS scheme when perturbing the model state and the output when using a control model state. The Jacobian structure, eigenvalues and magnitudes are examined to gauge sources of sensitivity and nonlinearity in the scheme and provide insight into the ways in which the scheme may be suitably simplified for use in the 4D variational data assimilation.

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

Curator: Nikki Privé Last Updated: May 27 2011