The McNish and Lincoln Solar Activity Predictions: The Method and its Performance

Abstract: The McNish and Lincoln (ML) method, introduced in 1949, was one of the first attempts to produce mid-term forecasts of solar activity, up to 12 months ahead. However, it has been poorly described and evaluated in the past literature, in particular its actual operational implementation by NOAA. Here, we reconstruct the exact formulation of the method, as it was applied since the early 1970s, and we provide a full mathematical derivation of the prediction errors. For bench-marking the method, we also produce monthly predictions over the past 190 years, from 1833 (Cycle 8) to 2023 (Cycle 25), and develop statistics of the differences between the predictions and the observed 13-month smoothed sunspot number (SSN) time series, according to the phase in the solar cycle. Our analysis shows that the ML method is heavily constrained because it is primarily based on the mean of all past cycles, which imposes a fixed amplitude and length and suffers from a temporal smearing that grows towards the end of the solar cycle. We find that predictions are completely unreliable in the first 12 months of the cycle, and over the last two years preceding the ending minimum (around 130 months), and beyond this minimum. By contrast, in the course of the cycle (months 18 to 65), ML predictions prove to be reliable over a time range of up to 50 months (4.2 years), thus much longer than the 12-month conventional range used so far. However, we find that predictions then suffer from systematic under-(over-)estimates for cycles that have a higher (lower) amplitude than the base mean cycle. Overall, we conclude that although the ML method provides valid prediction errors, it suffers from strong limitations, with very little room for improvement, as it indifferently merges all past cycles into a single fixed statistics.