Xudong Sun¹, George Fisher², and Todd Hoeksema³ (for the CGEM Team)

1. Institute for Astronomy, University of Hawaiʻi at Mānoa, Pukalani, HI 98768
2. Space Sciences Laboratory, University of California, Berkeley, CA 94720
3. W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305

The CGEM team identified and corrected two artifacts that had affected the electric field calculation for a small number of active regions.

The PDFI_SS software^[1], developed by the Coronal Global Evolutionary Model (CGEM) team, derives the photospheric electric field based on a time sequence of vector magnetic field and Doppler velocity maps. It has been applied to the Space-weather HMI Active Region Patch (SHARP) data archive: the electric field maps (cgem.pdfi_output) are now a routine product of the HMI pipeline. As of May 01, 2023, the electric fields have been calculated for 4972 active regions, with a total of 2.9 million snapshots. Details of the software and the data products can be found in ref. [1] and ref. [2].

In January 2023, the CGEM team fortuitously discovered two artifacts when inspecting the CGEM quick-look animations. The team subsequently identified the causes of these artifacts, and implemented the corresponding corrections.

Figure 1|Artifact as vertical bands in electric field maps. Top: Map of the meridional electric field, E_θ, with artifact corrected. This map has a CGEM number 101034, a nominal record time at 2012.07.10_10:42:00_TAI, and a dimension of 1873 × 1044. It corresponds to SHARP number 1034, and NOAA AR 11519, 11520, and 11521. Middle: Mean E_θ for each column (with strong-field regions masked). The black curve shows the values before correction, the red after correction. The light/dark bands in the background (128 pixels wide) align with the vertical bands in the bottom panel. Discontinuities are clearly visible in the black curve at the boundary of these bands, which disappear in the red curve. Bottom: Map of E_θ, before correction.

First, some electric field maps showed distinct vertical bands. As illustrated in the middle/bottom panel of Fig. 1, these bands are typically 128 pixels wide; the values in adjacent bands (in weak-field regions) sharply offset from one another at the boundaries. The pattern persisted throughout these regions’ transit across the solar disk. The artifact appeared to affect large SHARPs exclusively. We inspected the animations of all regions wider than 1400 columns (N_col). Most regions with N_col ≥ 1500 (80 in total, 1.6% of all) displayed the artifact, while none with N_col < 1500 columns did so.

Second, some electric field maps were filled with NaN/Inf despite having no NaN/Inf in the input magnetic field or Doppler velocity maps. A full query of the archive found 423 such records (1.5 × 10^-4 of all) involving 185 SHARPs (3.7% of all).

The vertical bands originated from the Poisson equation solver FISHPACK, which appeared to misbehave under the default 64-bit (double precision) mode when the input maps were too large. As shown in the top/middle panels of Fig. 1, the artifact completely disappeared when the code was compiled and run in the 128-bit (quad precision) mode. As a trade-off, the processing time became 10-20 times longer. For CGEM region 101034 (Fig. 1), the electric field inversion took 32 s and 373 s under the 64- and 128-bit mode, respectively (M1 Max Macbook Pro and gfortran). The team decided to re-write the FISHPACK and the PDFI_SS software, such that they would use the 64-bit solution for N_col < 1500 columns, and 128-bit solution otherwise.

The NaNs originated from the FLCT flow tracking step. In rare occasions, the output velocity map would contain a single pixel with abnormally large value. Because the HMI pipeline stores floating-value numbers as scaled integers, the number inadvertently got converted to NaN/Inf during the compression process, which led to all NaNs in the electric field solution. To address this, the team (1) updated the FLCT code to prevent output of NaN/Inf in velocity solutions, and (2) capped the FLCT velocities to 10 km s^-1 in the HMI pipeline such that the compression would not produce NaN/Inf. The team also decided to skip frames that contain off-limb pixels which were represented as NaNs.

As of July 2023, the HMI pipeline and the stand-alone PDFI_SS software have both been updated. The affected regions have all been reprocessed. We thank Jeneen Sommers, Keh-Cheng Chu, and Art Amezcua for their assistance with code compilation and data processing.

References

[1] Fisher, G. H., Kazachenko, M. D., Welsch, B. T., et al. 2020, ApJS, 248, 2
[2] Hoeksema, J. T., Abbett, W. P., Bercik, D. J., et al. 2020, ApJS, 250, 28