A Bayesian Approach to Forecasting Solar Cycles Using a Fokker-Planck Equation

TL;DR

This paper introduces a Bayesian forecasting method for solar cycles that integrates a Fokker-Planck model with additional data sources, enabling probabilistic predictions of sunspot activity and cycle characteristics.

Contribution

It presents a novel Bayesian approach combining a Fokker-Planck model with other data sources for improved solar cycle forecasting.

Findings

Forecasted cycle 24 maximum daily sunspot number of 166±24 in March 2013.

Predicted a small cycle with a smoothed maximum sunspot number of 66±5.

Demonstrated the method's ability to quantify forecast uncertainty and variability.

Abstract

A Bayesian method for forecasting solar cycles is presented. The approach combines a Fokker--Planck description of short--timescale (daily) fluctuations in sunspot number (\citeauthor{NobleEtAl2011}, 2011, \apj{} \textbf{732}, 5) with information from other sources, such as precursor and/or dynamo models. The forecasting is illustrated in application to two historical cycles (cycles 19 and 20), and then to the current solar cycle (cycle 24). The new method allows the prediction of quantiles, i.e. the probability that the sunspot number falls outside large or small bounds at a given future time. It also permits Monte Carlo simulations to identify the expected size and timing of the peak daily sunspot number, as well as the smoothed sunspot number for a cycle. These simulations show how the large variance in daily sunspot number determines the actual reliability of any forecast of the smoothed maximum of a cycle. For cycle 24 we forecast a maximum daily sunspot number of $166\pm 24$, to occur in March 2013, and a maximum value of the smoothed sunspot number of $66\pm5$, indicating a very small solar cycle.