Control Of Gravitational Oscillations in Variational Data Assimilation

Abstract

Abstract Variational four-dimensional data assimilation, combined with a penalty method constraining time derivatives of the surface pressure, the divergence, and the gravity-wave components is implemented on an adiabatic version of the National Meteorological Center's 18-level primitive equation spectral model with surface drag and horizontal diffusion. Experiments combining the Machenhauer nonlinear normal-mode initialization procedure and its adjoint with the variational data assimilation are also presented. The modified variational data-assimilation schemes are tested to assess how well they control gravity-wave oscillations. The gradient of a penalized cost function can be obtained by a single integration of the adjoint model. A detailed derivation of the gradient calculation of different penalized cost functions is presented, which is not restricted to a specific model. Numerical results indicate that the inclusion of penalty terms into the cost function will change the model solution as desired. Th...