Research Article

A new deep-learning approach to infer solar and geomagnetic parameters for the 1859 Carrington event

¹ Center for Solar-Terrestrial Research, New Jersey Institute of Technology, Newark, NJ 07102, USA
² Institute for Space Weather Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
³ Solar-Terrestrial Centre of Excellence – SIDC, Royal Observatory of Belgium, Ringlaan -3- Av. Circulaire 1180, Brussels, Belgium
⁴ Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B 3001, Leuven, Belgium
⁵ Division of Space Information Research, Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea
⁶ School of Space Research, Kyung Hee University, Yongin 17104, Republic of Korea
⁷ G-LAMP NEXUS Institute, Kyung Hee University, Yongin 17104, Republic of Korea
⁸ Institute for Space-Earth Environmental Research, Nagoya University, Nagoya 4648601, Japan

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 27 September 2025
Accepted: 10 March 2026

Abstract

In this study, we investigate the solar and geomagnetic parameters of the 1859 Carrington event using deep learning and empirical relationships. For this, we apply an image translation model, a popular deep learning method based on conditional Generative Adversarial Networks, to the generation of magnetograms from sunspot drawings. We train the model using pairs of sunspot data from Debrecen Photoheliographic Data and their corresponding Solar and Heliospheric Observatory/Michelson Doppler Imager (SOHO/MDI) and Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) magnetograms from 1996 to 2018, using data from January–July and December of each year for training and data from August and November for validation. To test the model, we compare actual magnetograms with artificial-intelligence-based (AI-based) ones for September and October. Our results show that the unsigned magnetic fluxes of AI-based magnetograms closely match those of the originals. Applying this model to Carrington’s full-disk sunspot drawing of 1 September 1859, we generate an AI-based magnetogram and estimate its unsigned magnetic flux. To estimate solar and geomagnetic parameters, we use the following empirical relationships: magnetic flux and flare peak flux, magnetic flux and coronal mass ejection (CME) speed, CME speed and transit time, CME speed and interplanetary coronal mass ejection (ICME) speed, and ICME speed and the Disturbance Storm Time (Dst) index to obtain upper-limit estimates for an extreme event. We find that the estimated Sun-Earth transit time is 16.7 h, consistent with the historical observations. The corresponding Dst value is about −1313 nT, which is broadly consistent with previous reconstruction-based estimates for the Carrington storm.