Causal Analysis of Influence of the Solar Cycle and Latitudinal Solar-Wind Structure on Corotation Forecasts

Abstract: Studying solar wind conditions is central to forecasting impact of space weather on Earth. Under the assumption that the structure of this wind is constant in time and corotates with the Sun, solar wind and thereby space weather forecasts have been made quite effectively. Such corotation forecasts are well studied with decades of observations from STEREO and near-Earth spacecrafts. Forecast accuracy depends upon the latitudinal separation (or offset $\Delta \theta$) between source and spacecraft, forecast lead time ($\Delta t$) and the solar cycle via the sunspot number (SSN). The precise dependencies factoring in uncertain- ties however, are a mixture of influences from each of these factors. And for high precision forecasts, it is important to understand what drives the forecast accuracy and its uncertainty. Here we present a causal inference approach based on information theoretic measures to do this. Our framework can compute not only the direct (linear and non-linear) dependencies of the forecast mean absolute error (MAE) on SSN, $\Delta t$ and $\Delta t$, but also how these individual variables combine to enhance or diminish the MAE. We provide an initial assessment of this with potential of aiding data assimilation in the future.