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On the Identification of Nonstationary Factor Models and Their Application to Atmospheric Data Analysis

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  • 1 Institute of Mathematics, Free University of Berlin, Berlin, Germany
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Abstract

A numerical framework for data-based identification of nonstationary linear factor models is presented. The approach is based on the extension of the recently developed method for identification of persistent dynamical phases in multidimensional time series, permitting the identification of discontinuous temporal changes in underlying model parameters. The finite element method (FEM) discretization of the resulting variational functional is applied to reduce the dimensionality of the resulting problem and to construct the numerical iterative algorithm. The presented method results in the sparse sequential linear minimization problem with linear constrains. The performance of the framework is demonstrated for the following two application examples: (i) in the context of subgrid-scale parameterization for the Lorenz model with external forcing and (ii) in an analysis of climate impact factors acting on the blocking events in the upper troposphere. The importance of accounting for the nonstationarity issue is demonstrated in the second application example: modeling the 40-yr ECMWF Re-Analysis (ERA-40) geopotential time series via a single best stochastic model with time-independent coefficients leads to the conclusion that all of the considered external factors are found to be statistically insignificant, whereas considering the nonstationary model (which is demonstrated to be more appropriate in the sense of information theory) identified by the methodology presented in the paper results in identification of statistically significant external impact factor influences.

Corresponding author address: Illia Horenko, Institute of Mathematics, Free University of Berlin, Arnimallee 6, 14195 Berlin, Germany. Email: horenko@math.fu-berlin.de

Abstract

A numerical framework for data-based identification of nonstationary linear factor models is presented. The approach is based on the extension of the recently developed method for identification of persistent dynamical phases in multidimensional time series, permitting the identification of discontinuous temporal changes in underlying model parameters. The finite element method (FEM) discretization of the resulting variational functional is applied to reduce the dimensionality of the resulting problem and to construct the numerical iterative algorithm. The presented method results in the sparse sequential linear minimization problem with linear constrains. The performance of the framework is demonstrated for the following two application examples: (i) in the context of subgrid-scale parameterization for the Lorenz model with external forcing and (ii) in an analysis of climate impact factors acting on the blocking events in the upper troposphere. The importance of accounting for the nonstationarity issue is demonstrated in the second application example: modeling the 40-yr ECMWF Re-Analysis (ERA-40) geopotential time series via a single best stochastic model with time-independent coefficients leads to the conclusion that all of the considered external factors are found to be statistically insignificant, whereas considering the nonstationary model (which is demonstrated to be more appropriate in the sense of information theory) identified by the methodology presented in the paper results in identification of statistically significant external impact factor influences.

Corresponding author address: Illia Horenko, Institute of Mathematics, Free University of Berlin, Arnimallee 6, 14195 Berlin, Germany. Email: horenko@math.fu-berlin.de

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