The Source Surface Height Through the Solar Cycle: A Path to Better Solar Wind Forecasts
| Nugget | |
|---|---|
| Number: | 531 |
| 1st Author: | Sandeep KUMAR |
| 2nd Author: | Nandita SRIVASTAVA |
| Published: | July 20, 2026 |
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Introduction
The potential field source surface (PFSS) model serves as the basis of many state-of-the-art space weather forecasting frameworks, as described in our Ref. [1]. Essentially PFSS takes the photospheric magnetic field, observable in detail by Zeeman effect spectroscopy, and uses it to extrapolate into the solar corona. This requires the assumption of just a single parameter: the radial distance of the "source surface", a fictitious sphere separating radial field of the solar wind, from the structured field of the photosphere. Mathematically any field induced by external sources can be represented by a fitting spherical harmonic functions at its boundaries. This is tractable but physically it may seem terribly wrong, since it ignores all coronal field sources (currents) within the volume itself. But it works surprisingly well, perhaps because the currents that we know to be present only make a minor perturbation of the basic potential field.
The nature of the source surface
The PFSS model contains only a single free parameter, the source surface height, at which magnetic field lines are assumed to be exactly radial. A value of 2.5 R⊙ for the source-surface height has traditionally been adopted in most studies. Optimizing the source-surface value significantly improves model forecasts of the solar-wind speed as observed at the L1 Lagrangian point, just upstream of Earth in the solar wind (Ref. [1]). This study employed two types ("HU STD" and "HU ZPC"] of ([https://en.wikipedia.org/wiki/Global_Oscillations_Network_Group GONG) synoptic magnetic field maps. The fidelity of these data was confirmed by comparing the extrapolated global magnetic field structures with the large-scale corona observed in the extended field of view of the PROBA2/SWAP images as shown in Figure 1.
The solar cycle
How must the PFSS model evolve through the solar cycle, during which the solar wind obviously changes substantially? In Ref. [3] we carried out one of the most comprehensive and long-term studies of SS height optimisation for solar wind prediction at L1, analyzing synoptic magnetograms from both space-based (SDO/HMI) and ground-based (GONG) observatories, across nearly three solar cycles, SC23-SC25. This optimization used the PFSS parameters in the model of Ref. [2] to compare with the wind-speed observations. Our main finding is that the optimal SS height varies systematically with the solar cycle: higher SS heights (≥2.5 R⊙) provide better solar wind speed predictions during solar minimum, whereas lower SS heights (<2.5 R⊙) perform better during solar maximum, suggesting a relationship between SS height and SC phase over long timescales. We also found that the optimized SS height depends on the choice of magnetogram, whereas the pattern remains similar for a given choice of magnetograms. The HMI and GONG "ZPC" magnetograms perform similarly, and both provide better forecasting than GONG "STD" maps, as shown in Figure 2. The results provide strong evidence that solar-cycle-dependent optimization of the PFSS source surface height is a practical way to improve solar wind forecasting, which serves as the foundation for heliospheric models.
Conclusions
Our adjusted PFSS radii clearly improve forecasts of the solar-wind speed. The study highlights an inherent limitation of the PFSS model, which assumes a spherical source surface. This simplifying assumption restricts further improvement in the correlation coefficient. We anticipate much greater improvements from future modeling frameworks outside that of spherical symmetry of the source surface.
References
[1] "On the role of source surface height and magnetograms in solar wind forecast accuracy"
[2] "On the role played by magnetic expansion factor in the prediction of solar wind speed"