Characterization of Forecast Error using Singular Value Decomposition

Authors: Andrew Moore, Kevin Smith, Hernan Arango

Singular value decomposition is a powerful tool for identifying the structure of errors that grow most rapidly in a model. The focus of this talk will be on forecast error growth following model initialization by 4D-Var data assimilation. The appropriate choice of norms in this case are the inverse analysis error covariance matrix at initial time, and the forecast error covariance matrix at final time, which yield what are commonly referred to as the Hessian Singular Vectors. This idea has also been extended to errors in the surface forcing and errors in the model to yield what we refer to as Hessian Stochastic Optimals. Examples will be presented from a hierarchy of ROMS configurations to demonstrate that the resulting error structures are relatively insensitive to the temporal nature of the errors. A proposed general framework for the description of errors in weak constraint 4D-Var will also be presented.