Open AccessThe Coupled Manifold*
Author(s) -
Antonio Navarra,
Joseph Tribbia
Publication year - 2005
Publication title -
journal of the atmospheric sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.853
H-Index - 173
eISSN - 1520-0469
pISSN - 0022-4928
DOI - 10.1175/jas-3345.1
Subject(s) - singular value decomposition , canonical correlation , subspace topology , manifold (fluid mechanics) , generalization , procrustes analysis , mathematics , realization (probability) , singular value , field (mathematics) , computer science , variance (accounting) , algorithm , statistics , mathematical analysis , artificial intelligence , eigenvalues and eigenvectors , pure mathematics , physics , mechanical engineering , accounting , quantum mechanics , engineering , business
A new method is presented to detect the portion of variability connected between two climatic fields. The method is a realization of the Procrustes problem, and it is a generalization of methods for analysis of variance such as the singular value decomposition (SVD) or canonical correlation analysis (CCA). The Procrustes formulation offers a general framework to link together variance analysis methods, and regression methods, including as special cases SVD and CCA. Using this approach two fields can be divided into a subspace where variations of one field are connected to variations of the other field, the coupled manifold, and a subspace where variations are independent, the free manifold. The unified approach can be applied to prescribed SST experiments, in which case it recovers consistent results with other methods designed to identify the forced portion of variance, but it can now be extended also to the coupled case or to observations. Some examples from prescribed SST simulation experiments and observations are discussed.