1. Mapping the Solar Magnetic Surface (a la Worden & Harvey)
Carl J. Henney Institute for Scientific Research, Boston College Space Vehicles Directorate/Air Force Research Laboratory

2. Introduction: AFOSR support
This work is a part the ADAPT* model project:
AFOSR Proposal Title: Incorporation of a Generalized Data Assimilation Module within a Global Photospheric Flux Transport Model
Nick Arge (AFRL) - PI
Shawn Young (AFRL) - Co-I
Josef Koller (LANL) - Co-I
Carl Henney (ISR) - Co-I
Jack Harvey (NSO) – Collaborator
Alex Fay (NSO) – Data Processing Aide [paid by grant]
Rich Compeau (UNM/AFRL) – Space Scholar
*Air Force Data Assimilation for Photospheric Flux Transport

3. Introduction: Carrington Maps
Carrington maps typically:
remap line-of-sight full-disk magnetograms into heliographic coordinates with the assumption that the magnetic field is radial.
employ a “solid body” rotation rate of days. This blurs feature position & time as additional images are included in the synoptic map.
weight the merged data to minimize the spatial blurring. For example, cos4, to give more weight to the central meridian.
Time
Carrington rotation 1 starts from November 9, 1853.

4. Introduction: Worden & Harvey
Worden & Harvey (2000) evolving map model includes:
Differential rotation (synchronic) & meridional circulation
Supergranular diffusion
Random flux eruptions
New data merging
The Worden & Harvey flux transport code was originally written in IDL & C. The IDL sections were translated into C last summer by Alex Fay (NS0).
Currently utilizes VSM data, but soon will incorporate KPVT & GONG magnetograms.

5. Worden& Harvey (cont’d)
Differential rotation:
Sidereal rotation rate (based on Howard, Harvey, and Forgach 1990): ω(θ)= A + B sin2θ + C sin4θ [μrad/s], where A= 2.894, B= , C= , and θ denotes latitude.
Meridional circulation:
flow speed (based on Wang & Sheeley 1994): M(θ) = 8.2 |cosθ|0.3 |sinθ|0.1 [m/s], where θ denotes latitude.
peak poleward velocity of deg.
Supergranular diffusion:
uses random attractors (based Mosher 1977),1 per supergranule cell
diffusion coefficient: D = 520 km2/s, using a cell radius and lifetime of 13.4 Mm and 1 day respectively.
Random Flux Emergence:
add a total flux of 1.1x1023 Mx/day (using a Gaussian distribution with a zero mean and a mean absolute value of 1.8 G).
ADAPT mods include:
model parameters freed
hemispheres decoupled
emergence vs. latitude?
Countercell (Jiang et al.)?

6. ADAPT Mods (cont’d)
Blend the east-limb of new magnetograms with the evolving map: use a linear distance weighting between 40o to 70o east CMD. Plus, using cos2 weighting to the west.
New weighting
Worden & Harvey
ADAPT will use the data variance to determine data merging weights.

7. Sample movie

8. Current Activities: model metrics
Preliminary model “quality” metrics between the evolved and observed data include (for each ~10x10 degree region):
net flux, total flux, and % polarity [emergence & diffusion]
cross-correlation in latitude & longitude [diff. rot. & merid. flow]
2-D power spectrum [emergence & diffusion]
For strong & weak magnetic fields, the metric parameters will be compared for the past three solar cycles (beginning in 1977) on time-scales of 3 to 24 hours, along with 1 to 10 days, and 1 to 3 rotations.
Evolving map
New data to be merged

9. Evolving Map Data Format
The current fits data files include 7 frames:
Net flux evo-map at time tObs
Merged data observed at time tObs
Previous evo-map evolved to tObs
Data error map (all zeros currently)
Model difference: [frame 3] – [frame 2]
Merge weight map (non-zero pixels were merged)
Observed data coverage map
Near-Future addition:
Model metrics with error estimates

10. Evolving Map Data Format: frame 1
Evolving Map Net Flux (at tObs):
Example images from: svsm_m11lr_L3_e fts

11. Evolving Map Data Format: frame 2
Merged data observed at time tObs:

12. Evolving Map Data Format: frame 3
Previous evo-map evolved to tObs:

13. Evolving Map Data Format: frame 5
Model difference ([frame 3] – [frame 2]):

14. Evolving Map Data Format: frame 6
Merge weight map:

15. Evolving Map Data Format: frame 7
Observed Data Coverage:
rows represent the longitudinal coverage of the previous 179 days; row 180 is for the current map, and row 1 is the total of each column.

16. Future Activities Near-term Tasks:
Incorporate results from the model “quality” metrics and data assimilation analysis, to validate the model parameters.
Add the option to “de-transport” for intermediate cadence selections using the nearest observation (needed for KPVT & VSM magnetogram data) and to create retrospective “best estimate” maps by averaging de-transported maps (that is, without diffusion) with the original sequence for longitudes with poor data coverage (e.g., far-side sectors).
Incorporate KPVT, GONG, and SOLIS magnetograms into the evolving map pipeline to create maps since 1977.
Long-term Tasks:
Incorporate vector magnetogram & far-side activity data for active regions.