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

Forecasting future solar activity has become crucial in our modern world, where intense eruptive phenomena mostly occurring during solar maximum are likely to be strongly damaging to satellites and telecommunications. We present a 4D variational assimilation technique applied for the first time to real solar data. Our method is tested against observations of past cycles 22, 23, 24 and on the ongoing cycle 25 for which we give an estimate of the imminent maximum value and timing and also provide a first forecast of the next solar minimum. We use a variational data assimilation technique applied to a solar mean-field Babcock-Leighton flux-transport dynamo model. Ensemble predictions are produced in order to obtain uncertainties on the timing and value of the maximum of cycle $n+1$, when data on cycle $n$ is assimilated. We study in particular the influence of the phase during which data is assimilated in the model and of the weighting of various terms in the objective function. The method is validated on cycles 22, 23 and 24 with very satisfactory results. For cycle 25, predictions vary depending on the extent of the assimilation window but start converging past 2022 to a solar maximum reached between mid-2024 up to the beginning of 2025 with a sunspot number value of $143.1 \pm 15.0$. Relatively close values of the maximum are found in both hemispheres within a time lag of a few months. We also forecast a next minimum around late 2029, with still significant errorbars. The data assimilation technique presented here combining a physics-based model and real solar observations produces promising results for future solar activity forecasting.