Speaker
Description
One of the most promising approaches to predict the Kp index is to consider this index as a nonlinear dynamic system driven by input parameters from the solar wind. This system theory allows to develop the physically interpretable models to make a good-quality predictions.
It is proposed to use a NARX (Nonlinear AutoRegressive with eXogenous inputs) model, which is a simplified form of the NARMAX (Nonlinear AutoRegressive Moving Average with eXogenous inputs) model, excluding noise. Various coupling functions and their influence on future Kp index values were investigated. The primary input to the model is the solar wind velocity $V$ (km/s). The Kp index ranges from 0 to 9 and we explore response over this scale. When the Kp index reaches 5, the geomagnetic activity is classified as a geomagnetic storm level and is also measured on the Geomagnetic G-scale, which ranges from G1 (minor) to G5 (extreme). It's very important the forecasting model produced the same scale. Therefore it is proposed to use the logistic model with this scale as follows
$Kp(t+1)=\frac{9}{1+e^{-f[Kp(t),V(t)]}}$, where $-f[Kp(t),V(t)]=g[Kp(t),V(t)]$ is a polynomial function. To remove the critical values of the Kp index, the limit values are replaced with 0.00001 and 8.99999, respectively. This model is represented as a multiple linear regression as follows $$9=Kp(t+1)(1+e^{g[Kp(t),V(t)]});$$ $$9=Kp(t+1)+Kp(t+1)e^{g[Kp(t),V(t)]});$$ $$9-Kp(t+1)=Kp(t+1)e^{g[Kp(t),V(t)]});$$ $$\ln(9-Kp(t+1))=\ln(Kp(t+1)) +g[Kp(t),V(t)];$$ $$\ln \frac{9-Kp(t+1)}{Kp(t+1)}=g[Kp(t),V(t)].$$
The degree of the polynomial is determined by incrementally increasing its order (The Weierstrass approximation theorem) until an acceptable multiple R-squared value is obtained using the Ordinary Least Squares (OLS) method.
For training, hourly data from the OMNI2 database covering the 23rd solar cycle (a total of 105,937 hours) were used. From this, 8,811 unique examples were identified. A 12th-degree polynomial was found to provide the best fit, yielding a correlation coefficient of 0.93 on the training dataset, which is statistically significant at the 95\% confidence level. This model was also tested on historical data from 1965 to 2024, achieving a correlation coefficient of approximately 0.9.
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