Spatial-temporal forecasting the sunspot diagram

Aims. We attempt to forecast the Sun's sunspot butterfly diagram in both space(i.e. in latitude) and time, instead of the usual one-dimensional time series forecasts prevalent in the scientific literature. Methods. We use a prediction method based on the non-linear embedding of data series in high dimensions. We use this method to forecast both in latitude (space) and in time, using a full spatial-temporal series of the sunspot diagram from 1874 to 2015. Results. The analysis of the results shows that it is indeed possible to reconstruct the overall shape and amplitude of the spatialtemporal pattern of sunspots, but that the method in its current form does not have real predictive power. We also apply a metric called structural similarity to compare the forecasted and the observed butterfly cycles, showing that this metric can be a useful addition to the usual root mean square error metric when analysing the efficiency of different prediction methods. Conclusions. We conclude that it is in principle possible to reconstruct the full sunspot butterfly diagram for at least one cycle using this approach and that this method and others should be explored since just looking at metrics such as sunspot count number or sunspot total area coverage is too reductive given the spatial-temporal dynamical complexity of the sunspot butterfly diagram. However, more data and/or an improved approach is probably necessary to have true predictive power.