Theoretical Refinements to the Heliospheric Upwind eXtrapolation Technique and Application to in-situ Measurements

Abstract

The large-scale structure and evolution of the solar wind are typically reproduced with reasonable fidelity using three-dimensional magnetohydrodynamic (MHD) models. However, such models are difficult to implement by the scientific community in general, because they require technical expertise and significant computational resources. Previously, we demonstrated how a simplified two-dimensional surrogate solar wind model, the Heliospheric Upwind eXtrapolation (HUX) technique, could reconstruct MHD solutions in the ecliptic plane, given either an inner (or outer) radial boundary condition. Here, we further develop the HUX technique and apply it to a range of solar wind in-situ datasets. Specifically, we: (1) provide a thorough mathematical analysis of the underlying reduced momentum equation describing the solar wind. (2) Propose flux-limiter numerical schemes that more accurately capture stream interaction regions and rarefaction regions; and (3) Apply the HUX technique to a variety of in-situ spacecraft measurements, focusing on Helios (1 and 2) and near-Earth spacecraft (Wind/ACE), for which near-latitudinal alignments occurred. We suggest that this refined HUX tool can be used for both retrospective studies as well as real-time predictions to better understand and forecast the large-scale structure and origin of the solar wind.

Bayesian Inference and Global Sensitivity Analysis for Ambient Solar Wind Prediction

“…We set r max to be ACE's maximum radial distance from the Sun for the considered CR. We solve the equation using the first‐order upwind scheme, see Issan and Riley (2022) for more details about the numerical scheme and stability requirements. Figure 3e shows the coupling of PFSS, WSA, and HUX solar wind speed predictions in comparison to ACE's in situ observations for CR 2053, see Section 2.4.2 for more details about ACE.…”

“…In an effort to reduce simulation time (especially in operational settings), the space weather community commonly uses lower‐fidelity models based on reduced physics and empirical relations. A well‐established and widely used chain of lower‐fidelity models couples the Potential Field Source Surface (PFSS) (Altschuler & Newkirk, 1969; Schatten et al., 1969), Wang‐Sheeley‐Arge (WSA) (Arge et al., 2004), and Heliospheric Upwind eXtrapolation (HUX) (Issan & Riley, 2022; Riley & Issan, 2021; Riley & Lionello, 2011) models.…”

Predicting Solar Wind Streams from the Inner-Heliosphere to Earth via Shifted Operator Inference

“…It has also been used to map streams directly from in-situ spacecraft observations (e.g. Helios A/B) to Earth [23]. The HUX model is based on simplified physical assumptions of the fluid momentum equation.…”

“…The term Ω rot (θ) = 2π 25.38 − 2.77π 180 cos(θ − π 2 ) 2 is the angular frequency of the Sun's rotation, i.e., a function of latitude [48]. The analysis in [52,48,23] justifies neglecting the pressure gradient and gravity terms in Eq. ( 7) and only taking into account variations of the velocity in the radial direction.…”

“…We use the first-order conservative upwind method from [23], so to approximate the partial derivative of the flux function f with respect to φ by…”