UCB-SSL Progress Report for the Joint CCHM/CWMM Workshop W.P. Abbett, G.H. Fisher, and B.T. Welsch

Overview: With additional support from NASA’s Heliospheric Theory, and SR&T programs, and NSF’s CISM, we have developed, tested and applied a new code, RADMHD, capable of simultaneously modeling the turbulent convection zone and solar corona within a single computational volume. With the additional support of NASA’s SR&T, and the NSF ATM program, we have developed, tested, and released (through the Open Source GPL v2.1) improved, more efficient versions of UCB’s Fourier Local Correlation Tracking (FLCT), and our platform independent Simple Data Format (SDF) software packages. With the principal financial support of CCHM, we have implemented an automated FLCT pipeline that determines photospheric flow fields from time series of MDI magnetograms. We have developed, and continue to test our local, spherical flux transport code. In the coming year, we intend to merge observed flow and magnetic data into the flux transport model in order to provide more physical boundary conditions to global models.

RADMHD: Simulation of Quiet Sun magnetic fields generated by the action of a convective dynamo (from Abbett 2007*). Left: Magnetic field lines drawn from points in the model chromosphere (only a portion of the domain is shown); Center: Zooming in on a flux submergence event; Right: Temperature fluctuations at the visible surface (top), and in the chromosphere (bottom). The domain extends from 2.5 Mm below the visible surface out into the corona. 8 node, 16 processor run. *Abbett 2007 ApJ Sept., in press.

Progress: We have successfully demonstrated the efficiency of the code by generating Quiet Sun magnetic fields in a combined convection zone-to-corona system via a surface dynamo. The simulations of Abbett (2007) spanned a 30 x 30 x 7.5 Mm domain distributed over 8 nodes of our local Beowulf cluster. Plans for the upcoming year: We were just awarded 520,000 hours on NASA’s Discover platform. We are extending our domain to active region spatial scales (including much more of the corona), and will emerge magnetic flux from below the surface into the corona. We will study the emergence and decay of the model active region as it interacts with convection. We plan to use the simulated datasets to test our inversion techniques, and our flux transport schemes, and will also use RADMHD to perform data-driven simulations of active regions. RADMHD:

FLCT / ILCT: σ=20 σ=5 From Fisher (2007) A description of the FLCT and ILCT techniques can be found in Welsch et al.(2004, 2007) & Fisher (2007). Briefly, FLCT is designed to treat the “optical flow” problem. That is, given two images, what 2D flow field when applied to the scalar field of the first image, most closely resembles the second image? Given a vector magnetogram, and an FLCT flow field, ILCT produces an “inductive flow” --- a 3D flow field consistent with both FLCT flows and the MHD induction equation. Progress: Since the beginning of CCHM funding, we have (1) improved the FLCT code by finding the peak of the cross-correlation function much more accurately; (2) added spatial filtering to cope with particularly noisy data (not doing this results in an under-estimate of the shifts); and (3) implemented much more accurate co-registration software to remove systematic global shifts between images.

MDI FLCT Pipeline: As a first step toward implementing a time-dependent lower boundary condition for a global MHD model, we have implemented an automated FLCT “pipeline” that determines photospheric velocities from time series of MDI magnetograms. Method: The cron-invoked pipeline script uses wget to check for new magnetograms on MDI's remote data servers. If new magnetograms are available, they are downloaded, and a batch-mode version of FLCT is used to perform the local correlation tracking. Output files --- including graphical flow maps (generated with IDL's z-buffer) and data files --- are automatically transferred to local web servers. Re-projecting the magnetographic data is an essential pre-processing step prior to tracking, since the FLCT algorithm requires regularly gridded data as input. The Mercator projection was chosen for this purpose, because it is a conformal mapping: it distorts length scales, but not directions, meaning the correlation will not bias one flow component relative to the other. Plans for the coming year: We will merge the flow and magnetic data into our global magnetic flux transport model, to provide a “4π” boundary condition.

Flux Transport Model: Progress over the past year: We have developed, and are in the process of testing and improving our spherical flux transport model. Plans for the upcoming year: 1.Develop methods for incorporating active region magnetic fields and flows within the global flux transport model 2. Improve the numerical scheme by incorporating some of the more sophisticated algorithms of RADMHD into the flux transport code 3.Test and validate the code (and the associated inversion techniques) against RADMHD simulations of a decaying active region 4. Test our implementation of the “active boundary” (our means of driving MHD simulations with magnetic fields and flows based on observational data) against RADMHD simulations of the sub-surface to corona system.

Summary: We have made substantial progress in our efforts to efficiently model the solar atmosphere from the visible surface (where magnetic field measurements are routinely taken), through the transition region (where the lower boundary of most global models of the solar corona necessarily resides), and out into the corona. We have tested and validated our inversion techniques, and substantially improved our Fourier Local Correlation Tracking algorithm. Our publicly available software is reasonably well-documented and can be found online at: REFERENCES: W.P. Abbett, “The Magnetic Connection Between the Convection Zone and Corona in the Quiet Sun”, 2007, ApJ, in press. B.T. Welsch, W.P. Abbett, M.L. DeRosa, G.H.Fisher, M.K. Georgoulis, K. Kusano, D.W. Longcope, B. Ravindra, and P.W. Schuck, “Tests and Comparisons of Velocity Inversion Techniques”, 2007, ApJ, in press. B.T. Welsch, G.H. Fisher, W.P. Abbett, and S. Regnier, “ILCT: Recovering Photospheric Velocities from Magnetograms By Combining the Induction Equation with Local Correlation Tracking”, 2004, ApJ, 610, G.H. Fisher and B.T. Welsch, “FLCT: A Fast, Efficient method for Performing Local Correlation Tracking”, 2007, American Astronomical Society Meeting Abstracts, 210, #92.11