Variational Implicit Normal Mode Initialization on the Sphere

Abstract

Due to its prohibitive computational cost, variational nonlinear normal mode initialization has received little interest during the last 10 years. Recently, soon after the introduction of the framework now called implicit nonlinear normal mode initialization, an efficient reformulation of variational nonlinear normal mode initialization using the implicit technique was demonstrated in the context of a barotropic finite-element regional model. This scheme allowed full variation of the variational weights at a low computational cost. To complement this previous work, the same variational approach for a global spectral shallow-water model is presented here. Similar results regarding the controlling and balancing aspects of the scheme are illustrated. The special form taken by the variational scheme in the context of height-constrained initialization is reconsidered after establishing the relationship between the implicit schemes and quasi-geostrophic theory on an f plane. Possible extensions of the method are mentioned at the end of the paper.