Tropical convective transition statistics and causality in the water vapor-precipitation relation.

Cristian Martinez-Villalobos, Daniel J. Vimont, Cécile Penland, Matthew Newman, and J. David Neelin,

J. Atmos. Sci., , submitted 01/2018.
Preprint (762 KB).

Abstract The most commonly used version of a Linear Inverse Model (LIM) is forced by state independent noise. Although having several desirable qualities, this formulation can only generate long-term Gaussian statistics. LIMlike systems forced by correlated additive-multiplicative (CAM) noise have been shown to generate deviations from Gaussianity, but parameter estimation methods are only known in the univariate case, limiting their use for the study of coupled variability. In this paper we present a methodology to calculate the parameters of the simplest multivariate LIM extension that can generate long-term deviations from Gaussianity. This model (CAM-LIM) consists of a linear deterministic part forced by a diagonal CAM noise formulation, plus an independent additive noise term. This allows the possibility of representing asymmetric distributions with heavier-or lighter-than-Gaussian tails. The usefulness of this methodology is illustrated in a locally coupled 2 variable ocean-atmosphere model of midlatitude variability. Here a CAM-LIM is calculated from Ocean Weather Station data. Although the time resolved dynamics is very close to linear at a time scale of a couple of days, significant deviations from Gaussianity are found. In particular individual probability density functions are skewed with both heavy and light tails. It is shown that these deviations from Gaussianity are well accounted for by the CAM-LIM formulation, without invoking nonlinearity in the time resolved operator. Estimation methods using knowledge of the CAM-LIM statistical constraints provide robust estimation of the parameters with data lengths typical of geophysical time series, e.g., 31 winters for the Ocean Weather Station here.

Citation Martinez-Villalobos, C., D. J. Vimont, C. Penland, M. Newman and J. D. Neelin: Calculating state-dependent noise in a linear inverse model framework. J. Atmos. Sci., submitted 01/2018.


Acknowledgments. This work was supported by National Science Foundation Grant AGS-1463643 (CM, DJV and MN), and National Science Foundation Grant AGS-1540518 (CM and JDN).

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