High-Performance Flux Transport (HipFT)

The standard way full-Sun magnetic maps are constructed by solar observatories (so-called “synoptic” maps) is by projecting full-disk magnetograms onto the Carrington (latitude, longitude) frame over the course of a solar rotation. An important limitation of most present observations of B are that they are available only along the Sun-Earth line, so data incorporated into the map can be as old as 27 days (the solar rotation period as viewed from Earth), so standard synoptic maps are more appropriately described as diachronic - built up by averaging measurements made over time. However, the processes by which the magnetic flux on the Sun evolves have been studied for many years. Surface Flux Transport (SFT) models (Wang et al., 1991; Worden & Harvey, 2000; Schrijver & DeRosa, 2003; Upton & Hathaway, 2014b) incorporate these processes (primarily differential rotation, meridional flow, supergranular diffusion, and random flux emergence) and have been successful in predicting the evolution of photospheric magnetic fields. Assimilative SFTs (ESFAM, Schrijver & DeRosa, 2003); ADAPT (Arge et al., 2013) and AFT (Upton & Hathaway, 2014b) ingest magnetograms from available observatories to produce a continuous approximation of the state of the photospheric magnetic field, as a sequence of “synchronic” maps - maps that attempt to represent the state of the Sun’s magnetic field at a given instant in time.

In the jointly funded NSF-NASA Space Weather with Quantified Uncertainties (SWQU) program, PSI has led the development of the Open-source Flux Transport (OFT) model, as part of the University of Alabama Huntsville’s multi-institutional project "Improving Space Weather Predictions with Data-Driven Models of the Solar Atmosphere and Inner Heliosphere" (Pogorelov et al., J. Physics Conf, accepted, 2024). The SFT for this model is the High-performance Flux Transport (HipFT) code, which solves

$$ \begin{equation} \label{eq-SFT} \dfrac{\partial B_r}{\partial t} = - \nabla_{s}\cdot\,(B_r\,{\bf v}) + \nabla_{s} \cdot (\nu\,\nabla_{s}\,B_r) + S, \end{equation} $$

on a spherical surface, where \(B_{r}\) is the radial magnetic flux at the surface, \(\nabla_{s}\) are the surface (\(\theta,\phi\)) components of the operator, \({\bf v}\) is the surface flow velocity, representing the large scales (but also can include smaller scale flows if they are present in the model), and \(\nu\) is a diffusivity coefficient meant to capture the diffusion of the radial field by the turbulent convective motions. \(S\) is a source term that can represent the data-assimilative insertion of flux, as well as the addition of small-scale random flux. HipFT incorporates data assimilation, random flux emergence, and flow models (both supergranular flows and large differential rotation/meridional flow). HipFT employs high-accuracy methods, CPU/GPU parallelism, and can produce multiple realizations.