On Predicting the Solar Cycle Using Mean-Field Models

Abstract

We discuss the difficulties of predicting the solar cycle using mean-field models. Here we argue that these difficulties arise owing to the significant modulation of the solar activity cycle, and that this modulation arises owing to either stochastic or deterministic processes. We analyse the implications for predictability in both of these situations by considering two separate solar dynamo models. The first model represents a stochastically-perturbed flux transport dynamo. Here even very weak stochastic perturbations can give rise to significant modulation in the activity cycle. This modulation leads to a loss of predictability. In the second model, we neglect stochastic effects and assume that generation of magnetic field in the Sun can be described by a fully deterministic nonlinear mean-field model -this is a best case scenario for prediction. We designate the output from this deterministic model (with parameters chosen to produce chaotically modulated cycles) as a target timeseries that subsequent deterministic meanfield models are required to predict. Long-term prediction is impossible even if a model that is correct in all details is utilised in the prediction. Furthermore, we show that even short-term prediction is impossible if there is a small discrepancy in the input parameters from the fiducial model. This is the case even if the predicting model has been tuned to reproduce the output of previous cycles. Given the inherent uncertainties in determining the transport coefficients and nonlinear responses for mean-field models, we argue that this makes predicting the solar cycle using the output from such models impossible.

A history of solar activity over millennia

“…Prospectives of this approach are also not clear because of the stochastic component, which drives the dynamo out of the deterministic regime, and uncertainties in the input parameters (Tobias et al 2006;Bushby and Tobias 2007;Karak and Nandy 2012). Some models, mostly based on precursor method, succeed in reasonable predictions of a forthcoming solar cycle (i.e., several years ahead), but they do not pretend to extend further in time.…”

Solar Weather Event Modelling and Prediction

“…-Is it at all possible to make predictions? Bushby and Tobias (2007) state that it is not possible to make any predictions by using a mean-field dynamo, because of poor physical understanding of the dynamo, uncertainties in determining the transport coefficients, and, also, because of the non-linear chaotic nature of the solar dynamo.…”

Multiple and changing cycles of active stars

“…For critical reviews of those methods see Cameron & Schüssler (2007), and Bushby & Tobias (2007). The knowledge of the cycle pattern of as many active stars as possible may yield improved insight on the solar activity seen in the context of stellar activity.…”