Statistical Response of ENSO Complexity to Initial Condition and Model Parameter Perturbations
Marios Andreou & Nan Chen
Statistical Response of ENSO Complexity to Initial Condition and Model Parameter Perturbations
Marios Andreou & Nan Chen
Embedded Files
Marios Andreou & Nan Chen
Abstract
Studying the response of a climate system to perturbations has practical significance. Standard methods in computing the trajectory-wise deviation caused by perturbations may suffer from the chaotic nature that makes the model error dominate the true response after a short lead time. Statistical response, which computes the return described by the statistics, provides a systematic way of reaching robust outcomes with an appropriate quantification of the uncertainty and extreme events. In this paper, information theory is applied to compute the statistical response and find the most sensitive perturbation direction of different El Niño-Southern Oscillation (ENSO) events to initial value and model parameter perturbations. Depending on the initial phase and the time horizon, different state variables contribute to the most sensitive perturbation direction. While initial perturbations in sea surface temperature (SST) and thermocline depth usually lead to the most significant response of SST at short- and long-range, respectively, initial adjustment of the zonal advection can be crucial to trigger strong statistical responses at medium-range around 5 to 7 months, especially at the transient phases between El Niño and La Niña. It is also shown that the response in the variance triggered by external random forcing perturbations, such as the wind bursts, often dominates the mean response, making the resulting most sensitive direction very different from the trajectory-wise methods. Finally, despite the strong non-Gaussian climatology distributions, using Gaussian approximations in the information theory is efficient and accurate for computing the statistical response, allowing the method to be applied to sophisticated operational systems.
Significance Statement
The purpose of this work is to better understand how the El Niño-Southern Oscillation (ENSO) responds to changes in its initial state and internal dynamics or external forcings. A statistical quantification of this response allows for the comprehension of the triggering conditions and the effect of climate change in the occurrence frequency and strength of each type of ENSO event. Such a study also allows to detect the most sensitive perturbation directions, which has practical significance in guiding anthropogenic activities. The approach used to study the response in this work is through the framework of information theory, which allows for an unbiased and robust assessment of the statistical response that is not affected by the turbulent dynamics of the system.
Schematic diagram of the framework
A few indicative figures and results (some not included in the published paper)
Figure 1. Statistical response of the Central Pacific SSTa density to perturbations in the initial conditions along the most sensitive direction defined by the leading eigenvector of the corresponding Fisher information matrix. (The signal-dispersion decomposition formula is used, assuming a Gaussian approximation.)
Figure 2. Statistical response of the Central Pacific SSTa density to perturbations in the initial conditions along the most sensitive direction defined by the leading eigenvector of the Fisher information matrix associated with the Eastern Pacific SSTa density. (The signal-dispersion decomposition formula is used, assuming a Gaussian approximation.)
Figure 3. Statistical response of the Eastern Pacific SSTa density to perturbations in the initial conditions along the most sensitive direction defined by the leading eigenvector of the Fisher information matrix associated with the Central Pacific SSTa density. (The signal-dispersion decomposition formula is used, assuming a Gaussian approximation.)
Figure 4. Statistical response of the Eastern Pacific SSTa density to perturbations in the initial conditions along the most sensitive direction defined by the leading eigenvector of the corresponding Fisher information matrix. (The signal-dispersion decomposition formula is used, assuming a Gaussian approximation.)
Figure 5. Statistical response of the Central Pacific SSTa density to uniform 30% perturbations in the initial conditions, quantified using all formulae and approximations defined in the paper.
Figure 6. Statistical response of the Eastern Pacific SSTa density to uniform 30% perturbations in the initial conditions, quantified using all formulae and approximations defined in the paper.
Figure 7. Statistical response of the Central and Eastern Pacific SSTa bivariate probability density to uniform 30% perturbations in the initial conditions, quantified using all formulae and approximations defined in the paper.
Figure 8. Seasonal average of the statistical response of both the Central and Eastern Pacific SSTa univariate densities to initial-condition perturbations along the most sensitive direction defined by the leading eigenvector of the Fisher information matrix associated with the Central Pacific SSTa density. (The signal-dispersion decomposition formula is used, assuming a Gaussian approximation.)
Figure 9. Seasonal average of the statistical response of both the Central and Eastern Pacific SSTa univariate densities to model-parameter perturbations along the most sensitive direction defined by the leading eigenvector of the Fisher information matrix associated with the Central Pacific SSTa density, where for the time dependent parameters the perturbation is enforced at each simulation time step. (The signal-dispersion decomposition formula is used, assuming a Gaussian approximation.)
Figure 10. Seasonal average of the statistical response of both the Central and Eastern Pacific SSTa univariate densities to initial-condition perturbations along the most sensitive direction defined by the leading eigenvector of the Fisher information matrix associated with the Eastern Pacific SSTa density. (The signal-dispersion decomposition formula is used, assuming a Gaussian approximation.)
Figure 11. Seasonal average of the statistical response of both the Central and Eastern Pacific SSTa univariate densities to model-parameter perturbations along the most sensitive direction defined by the leading eigenvector of the Fisher information matrix associated with the Eastern Pacific SSTa density, where for the time dependent parameters the perturbation is enforced at each simulation time step. (The signal-dispersion decomposition formula is used, assuming a Gaussian approximation.)
Figure 12. Examples of perturbed regimes in the initial conditions of the zonal current velocity and zonal advection feedback (for the latter the perturbation is enforced at each time step), illustrating temporal effects on the discharge–recharge processes in the SSTa.
Figure 13. Examples of perturbed regimes in initial conditions and model parameters (for the latter the perturbation is enforced at each time step), illustrating dominant effects on the variance rather than the mean of the SSTas.
Figure 14. Time evolution of the density, skewness, and kurtosis of the Central Pacific SSTa in response to initial-condition perturbations along the most sensitive direction, defined by the leading eigenvector (at April 1992) of the corresponding Fisher information matrix, during a mixed Central and Eastern Pacific El Niño event.
Figure 15. Time evolution of the density, skewness, and kurtosis of the Eastern Pacific SSTa in response to initial-condition perturbations along the most sensitive direction, defined by the leading eigenvector (at September 1987) of the corresponding Fisher information matrix, during a moderate Eastern Pacific El Niño event.
Typographical Errors:
Typographical Error: The definition of β_E(I) should read 0.15 (2 – 0.2I)√ρ instead of 0.15 (1 – 0.2I)√ρ, matching the original reference. That is, there is a typographical error; the 1 inside the parentheses should be a 2.
BibTeX Entry
@article{andreou2024statistical,
title = "{Statistical Response of ENSO Complexity to Initial Condition and Model Parameter Perturbations}",
author = "Andreou, Marios and Chen, Nan",
journal = "Journal of Climate",
ISSN = "0894-8755",
publisher = "American Meteorological Society",
volume = "37",
number = "21",
pages = "5629 - 5651",
year = "2024",
DOI = "10.1175/JCLI-D-24-0017.1",
URL = "https://journals.ametsoc.org/view/journals/clim/37/21/JCLI-D-24-0017.1.xml"
}
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