Spatial-temporal forecasting the sunspot diagram

TL;DR

This paper explores forecasting the Sun's sunspot butterfly diagram in both space and time using high-dimensional non-linear embedding, demonstrating shape reconstruction but limited predictive power, and introduces structural similarity as an evaluation metric.

Contribution

It is the first attempt to forecast the full spatial-temporal sunspot diagram, extending beyond traditional one-dimensional time series prediction methods.

Findings

Shape and amplitude of sunspot patterns can be reconstructed

Current method has limited predictive power

Structural similarity is useful for evaluating forecasts

Abstract

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. 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. The analysis of the results shows that it is indeed possible to reconstruct the overall shape and amplitude of the spatial-temporal 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.