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Reducing the Errors of the Solar and Climatic Indices on the Basis of a Hypothesis on Nonlinear Dynamic Sun–Climate Coupling

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Abstract

Confidence interval estimates for the average values of the solar and climate indices are important for both modeling and forecasting problems. The formal approach is based on the interpretation of the measured data as independent and identically distributed (iid) quantities. Such an approach can lead to an overestimation of the confidence intervals, in particular, due to the relationship of neighboring values (for example, when smoothing the seasonal cycle for climate with a sliding window or the 27-day rotation cycle for the Sun when analyzing 10–11 year cycles), a significant asymmetry of statistical distributions, and other factors. Here, we propose a new approach to estimating the confidence interval for the average values of empirical indices, based on the hypothesis of the existence of a nonlinear Sun–Climate relationship. Within this approach, we add Gaussian noise of various amplitudes to the time series of the total solar irradiance (TSI) and the El Niño climate index (Nino 3.4). We found that increasing the amplitude of the noise reduces the detectable statistical relationship. We propose to use this fact to estimate the true confidence interval. Based on our calculations, we conclude that the width of the confidence intervals given for the TSI and Nino 3.4 indices is significantly overestimated when they are calculated from observational data. Refinement of the width of confidence intervals will help clarify the error of models and forecasts.

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ACKNOWLEDGMENTS

We thank the authors, both solar scientists and climatologists, who maintain open databases, without which this work would not have been possible.

Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. The Central Astronomical Observatory at Pulkovo, Russian Academy of Sciences, St. Petersburg, Russia

    D. M. Volobuev

  2. Independent Researcher, St. Petersburg, Russia

    A. A. Skakun

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  1. D. M. Volobuev
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  2. A. A. Skakun
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Correspondence to D. M. Volobuev.

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Volobuev, D.M., Skakun, A.A. Reducing the Errors of the Solar and Climatic Indices on the Basis of a Hypothesis on Nonlinear Dynamic Sun–Climate Coupling. Geomagn. Aeron. 63, 1149–1153 (2023). https://doi.org/10.1134/S001679322308025X

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  • DOI: https://doi.org/10.1134/S001679322308025X

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