Comments on Charron et al.'s three recent articles on deriving dynamically consistent equation sets. (19th October 2015)

• Record Type: Journal Article
• Authors: Staniforth, Andrew; White, Andy
• Is Part Of: Quarterly journal of the Royal Meteorological Society. Volume 141:Number 693(2015:Oct.)
• Page Start: 3425
• Page End: 3430
• Publication Date: 2015-10-19
• Subjects: conservation -- equation sets -- geopotential coordinates -- gravitational potential -- ellipsoidal coordinates -- tensor analysis; Meteorology -- Periodicals; 551.5
• DOI: 10.1002/qj.2571
• Languages: English
• ISSNs: 0035-9009

Abstract

Abstract : Charron and co‐authors propose the preservation of tensor covariance as the criterion for dynamically consistent approximation of the governing equations for global atmospheric and oceanographic flow. Earlier criteria, based on vector differential analysis, involve the preservation of individual conservation properties. Here, the two approaches are compared for the interested, but possibly perplexed, reader. Differences regarding terminology and some consistency issues relating to certain 'quasi‐shallow' models are discussed. However, the overall similarity of the results of the two approaches and of the variational approach using Hamilton's principle of least action is evident. Relevant aspects of an approximate global model that uses an analytically tractable ellipsoidal geopotential coordinate system are also discussed.