Abstract
AbstractThe McNish and Lincoln (ML) method, introduced in 1949, was one of the first attempts to produce midterm 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.
Funder
Sixth Framework Programme
Publisher
Springer Science and Business Media LLC
Reference23 articles.
1. Chatzistergos, T., Krivova, N.A., Yeo, K.L.: 2023, Long-term changes in solar activity and irradiance. J. Atmos. Solar-Terr. Phys. 252, 106150. DOI. ADS.
2. Clette, F., Lefèvre, L.: 2016, The new sunspot number: assembling all corrections. Solar Phys. 291(9–10), 2629. DOI. ADS.
3. Denkmayr, K., Cugnon, P.: 1997, About sunspot number medium-term predictions. In: Heckman, G., et al. (eds.) Proc of Solar-Terrestrial Prediction Workshop V, Hiraiso Solar Terrestrial Research Center, Japan, 103.
4. Dudok de Wit, T., Lefèvre, L., Clette, F.: 2016, Uncertainties in the sunspot numbers: estimation and implications. Solar Phys. 291(9–10), 2709. DOI. ADS.
5. Fessant, F., Pierret, C., Lantos, P.: 1996, Comparison of neural network and McNish and Lincoln methods for the prediction of the smoothed sunspot index. Solar Phys. 168(2), 423. DOI. ADS.