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Origin of Non-Gaussian Regimes and Predictability in an Atmospheric Model

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  • 1 Department of Mathematical Sciences, Atmospheric Sciences Group, University of Wisconsin—Milwaukee, Milwaukee, Wisconsin
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Abstract

This study details properties of non-Gaussian regimes and state-dependent ensemble spreads of trajectories in a reduced phase space of an idealized three-level quasigeostrophic (QG3) dynamical model. Methodologically, experiments using two empirical stochastic models of the QG3 time series disentangle the causes of state-dependent persistence properties and nonuniform self-forecast skill of the QG3 model. One reduced model is a standard linear inverse model (LIM) forced by state-independent, additive noise. This model has a linear deterministic operator resulting in a phase-space velocity field with uniform divergence. The other, more general nonlinear stochastic model (NSM) includes a nonlinear propagator and is driven by state-dependent, multiplicative noise. This NSM is found to capture well the full QG3 model trajectory behavior in the reduced phase space, including the non-Gaussian features of the QG3 probability density function and phase-space distribution of the trajectory spreading rates.

Two versions of the NSM—one with a LIM-based drift tensor and QG3-derived multiplicative noise and another with the QG3-derived drift tensor and additive noise—allow the authors to determine relative contributions of the mean drift and multiplicative noise to non-Gaussian regimes and predictability in the QG3 model. In particular, while the regimes arise predominantly because of the nonlinear component of the mean phase-space tendencies, relative predictability of the regimes depends on both the phase-space structure of multiplicative noise and the degree of local convergence of mean phase-space tendencies.

Corresponding author address: Sergey Kravtsov, Dept. of Mathematical Sciences, Atmospheric Sciences Group, University of Wisconsin—Milwaukee, P.O. Box 413, Milwaukee, WI 53201. E-mail: kravtsov@uwm.edu

Abstract

This study details properties of non-Gaussian regimes and state-dependent ensemble spreads of trajectories in a reduced phase space of an idealized three-level quasigeostrophic (QG3) dynamical model. Methodologically, experiments using two empirical stochastic models of the QG3 time series disentangle the causes of state-dependent persistence properties and nonuniform self-forecast skill of the QG3 model. One reduced model is a standard linear inverse model (LIM) forced by state-independent, additive noise. This model has a linear deterministic operator resulting in a phase-space velocity field with uniform divergence. The other, more general nonlinear stochastic model (NSM) includes a nonlinear propagator and is driven by state-dependent, multiplicative noise. This NSM is found to capture well the full QG3 model trajectory behavior in the reduced phase space, including the non-Gaussian features of the QG3 probability density function and phase-space distribution of the trajectory spreading rates.

Two versions of the NSM—one with a LIM-based drift tensor and QG3-derived multiplicative noise and another with the QG3-derived drift tensor and additive noise—allow the authors to determine relative contributions of the mean drift and multiplicative noise to non-Gaussian regimes and predictability in the QG3 model. In particular, while the regimes arise predominantly because of the nonlinear component of the mean phase-space tendencies, relative predictability of the regimes depends on both the phase-space structure of multiplicative noise and the degree of local convergence of mean phase-space tendencies.

Corresponding author address: Sergey Kravtsov, Dept. of Mathematical Sciences, Atmospheric Sciences Group, University of Wisconsin—Milwaukee, P.O. Box 413, Milwaukee, WI 53201. E-mail: kravtsov@uwm.edu
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