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

Abstract

AbstractStudying solar-wind conditions is central to forecasting the impact of space weather on Earth. Under the assumption that the structure of this wind is constant in time and co-rotates with the Sun, solar-wind and thereby space-weather forecasts have been made quite effectively. Such co-rotation forecasts are well studied with decades of observations from STEREO and near-Earth spacecraft. Forecast accuracy is primarily determined by three factors: i) the longitudinal separation of spacecraft from Earth determines the corotation time (and hence forecast lead time) [$\delta$ δ t] over which the solar wind must be assumed to be constant, ii) the latitudinal separation (or offset) between Earth and spacecraft [$\delta\theta$ δ θ ]] determines the degree to which the same solar wind is being encountered at both locations, and iii) the solar cycle, via the sunspot number (SSN), acts as a proxy for both how fast the solar-wind structure is evolving and how much it varies in latitude. However, the precise dependencies factoring in uncertainties are a mixture of influences from each of these factors. Furthermore, 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 nonlinear) dependencies of the forecast mean absolute error (MAE) on SSN, $\Delta \theta $ Δ θ , and $\Delta t$ Δ t , but also how these individual variables combine to enhance or diminish the MAE. We provide an initial assessment of this with the potential of aiding data assimilation in the future.