Normal Mode Initialization with Elementary Surface Friction

Abstract

Various normal-mode initialization techniques are applied to a simple 12-level linear model with boundary layer friction, and results are compared to exact solutions of the model. It is found that Machenhauer's initialization scheme gives an approximate solution to the initialization of ageostrophic circulations due to friction; however, all or almost all vertical modes must be initialized and a moderate number of iterations are required. Second-order Baer-Tribbia initialization is found to be less effective than several iterations of the Machenhauer procedure. An iterative initialization based on bounded derivative theory and requiring the second time derivatives of the gravity modes to vanish gives excellent results, but a simple iterative scheme to achieve this diverges with moderate friction. The successful application of these procedures to the initialization of ageostrophic circulations due to friction in numerical weather prediction models will require careful utilization of, and possibly improved, iterative methods to achieve convergence and stability.