Forecasting the solar cycle using variational data assimilation: Validation on cycles 22 to 25

Context. Forecasting future solar activity has become crucial in our world today, where intense eruptive phenomena, mostly occurring during solar maximum, are likely to exert a highly detrimental effect on satellites and telecommunications. However, forecasting such events is a very difficult task owing to the highly turbulent flows existing in the solar interior. Aims. We present a 4D variational assimilation technique (4D-Var) applied for the first time to real solar data, consisting of the time series of the sunspot number and the line-of-sight surface magnetic field from 1975 to 2024. We tested our method against observations of past cycles 22, 23, 24, as well as the ongoing cycle 25. For the latter, we offer an estimate of the imminent maximum value and timing, along with a first forecast of the next solar minimum. Methods. We used a variational data assimilation technique applied to a solar mean-field Babcock-Leighton (BL) flux-transport dynamo model. This translates to a minimization of an objective function with respect to the control vector, defined here as a set of coefficients representing the meridional flow and the initial magnetic field. Ensemble predictions were produced to obtain uncertainties on the timing and value of the maximum of cycle n + 1, when the data on cycle n were assimilated. In particular, we have studied the influence of the phase during which the data were assimilated into the model and that of the weighting of various terms in the objective function. Results. Our method was validated on cycles 22, 23, and 24 with very satisfactory results. We found a particularly good convergence of our predictions (both in terms of accuracy and precision) when the assimilation window encompassed more and more of the rising phase of cycle n + 1. For cycle 25, predictions varied, again depending on the extent of the assimilation window; however, they were seen to start converging past 2022 to a solar maximum reached between mid-2024 up to the beginning of 2025, with a sunspot number value of 143.1 ± 15.0. Relatively close values of the maximum have been found in both hemispheres within a time lag of a few months. We also offer a forecast for the next minimum to occur around late 2029 (with significant error bars). Conclusions. The data assimilation technique presented here combines a physics-based model and real solar observations, offering promising results for future solar activity forecasting.