Implicit Normal Mode Initialization for Spectral Models

Abstract

Implicit nonlinear normal mode initialization schemes enable nonlinear NMI to be performed in models whose normal modes cannot readily be computed. Such schemes are algebraically equivalent to conventional (?explicit?) NMI based on the normal modes of a set of linearized equations which is slightly different from the usual choice. In this paper we apply implicit NMI to a barotropic spectral model whose normal modes are easily found, thus permitting a direct comparison to be made between conventional and implicit NMI schemes. Both first-order (Machenhauer) and second-order (Tribbia) variants of implicit nonlinear NMI are formulated for a spectral model and compared with their explicit counterparts. Experimental results show that the differences between explicit and implicit nonlinear NMI am insignificant except at the very largest horizontal scales. Besides validating the concept of implicit nonlinear NMI, this study suggests a practical approach to initializing very high resolution spectral models for which the normal modes require an inconveniently large amount of storage.