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arXiv · 2509.01540

Discrete Chi-Square Method discovers solar forcing in El Ni\~no time series: The Pacific Ocean as a bolometer measuring the solar dynamo light curve in real-time

Lauri Jetsu
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Abstract

Discrete Chi-square Method (DCM) can detect multiple signals superimposed on an arbitrary trend. DCM's backbone is Gauss-Markov theorem that Least Squares (LS) is the best unbiased estimator for linear regression models. DCM is robust because it computes numerous linear model LS fits. Discrete Fourier Transform and other frequency-domain methods have many application limitations. None of those limitations constrains DCM. Fisher-test provides signal significances and identifies the best DCM model, which is validated by Forecast-test. Simulations verify the Window Dimension Effect (WD-effect): "For any sample window $\Delta T$, DCM inevitably detects the correct $p(t)$ trend and $h(t)$ signal(-s) when sample size $n$ and/or data accuracy $\sigma$ increase". WD-effect "sees through time". DCM's model analytical solution is ill-posed. We present a computational well-posed solution. Mainstream considers El Ni\~no phenomenon chaotic. Usual forecasts are probabilistic, not deterministic. We use El Ni\~no time series to stress-test DCM. It detects the multi-periodic "Big wave" superimposed on global warming trend. This gives accurate El Ni\~no forecasts. Our real-time forecast outperforms those of official agencies. Only solar forcing, not chaotic ocean-atmosphere coupling, can cause the "Big wave" cooling the Pacific Ocean at sunspot minima. The ocean acts like a giant bolometer measuring the deterministic "Solar dynamo light curve". DCM detects multi-periodicity in the ocean and sunspot record. The mainstream stochastic dynamo cannot cause this. Planetary tidal forces may drive solar dynamo. Future El Ni\~no models must integrate astrophysical cycles with chaotic climatological fluid dynamics. Validating our analysis now can save trillions (USD) in El Ni\~no damages.

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Lauri Jetsu. 2025-09-01. Discrete Chi-Square Method discovers solar forcing in El Ni\~no time series: The Pacific Ocean as a bolometer measuring the solar dynamo light curve in real-time. https://arxiv.org/abs/2509.01540

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