Potential Vorticity Regression and Its Relationship to Dynamical Piecewise Inversion

Abstract

Hakim and Torn (HT) presented a statistical piecewise potential vorticity (PV) regression technique that uses flow-dependent analysis covariances from an ensemble square root filter to statistically infer the relationship between the PV and state fields. This paper illustrates that the PV perturbation effectively regressed by HT?s regression is the projection of the PV perturbation onto the ensemble PV anomalies that define the regression operator. It is shown that the piecewise PV inversion of this effective PV perturbation via the technique presented in Davis and Emanuel yields nearly identical heights to those from an HT regression performed in the subspace of the leading PV singular vectors.