1. Efficient tracking of photospheric flows
BALLTRACKING
Efficient tracking of photospheric flows
H.E.Potts, D.A.Diver, R.K.Barrett
University of Glasgow, UK
Funded by PPARC Rolling Grant PPA/G/0/2001/00472
Efficient tracking method
Picture shows an overview of the method

2. The Why and The How Why? How?
Investigate small scale interactions between magnetic elements and photosphere
Contribution to magnetic energy budget
How?
Quite hard:
Typical diameter ~1 Mm
Granules only live for 5–15 mins
Typical supergranular velocity 500ms-1 , but much faster ‘random walk’
Only advected ~0.5 Mm by supergranular flow in lifetime
Need lots of data!
MDI continuum data
Sub pixel movements

3. Established Tracking Methods
Standard LCT (Simon 1988).
Excellent results but slow (approx 4 days for 8hrs MDI High Resolution data)
CST (Strous 1995)
Complex, and limited to high resolution images. Need to be careful about selection effects
Simulated data needed

4. What will Solar-B give us?
SOHO
Solar-B
Instrument
MDI
Michaelson Doppler Interferometer
BFI
Broadband Filter Imager
Max Resolution
0.6 arcsec
0.08 arcsec
CCD size
1024 x 1024
2048 x 2048/4096
Max image rate
60s
10s
10 – 20 times more data to process!

5. Balltracking 1: Filtering and derotation
Continuum data is dominated by p-mode oscillations
2D Fourier filter applied to remove all but granulation information. No time filtering used
Derotation
Minimal remapping – just rigid derotation. Any more sophisticated scaling done on processed data set
Much smaller dataset (eg. 6GB raw vs. 10MB processed)
Reduces interpolation errors
Done in Fourier space
Both done in a single operation for speed

6. Balltracking 1: Filtering and derotation
Raw Image
Filtered image
2D Fourier Transform
Mask
Phase adjust
Inverse transform
FILTER DEROTATE

7. Balltracking 2 : Tracking
Surface made from smoothed granulation data
Massy ‘balls’ dropped onto the surface.
Balls ‘float’ on surface and settle to local minima
Balls are then pushed around by travelling granulation patterns
Balls removed if too close to each other
Damping force for stability

8. Balltracking 3: Smoothing
Set of irregularly spaced ball trajectories
Smooth in space and time to get underlying velocity V(i,j):
V(xi,yi,t) : smoothed velocity
s : spatial smoothing radius
Dt : time smoothing interval
rn,t : distance from (xi,yi) to ball

9. How accurate is possible?
Random Velocity > Directed velocity
Estimate error in smoothed velocity:
But adjacent measurements are not independent:
Best possible, regardless of sampling frequency:
RS ,TS : Smoothing lengths
Dt, Dr : Sampling intervals
sv, su, : STD of smoothed
and random velocity

10. How smooth is smooth enough

11. Making Test data
Make uniform density array of randomly positioned cells
Assign a size and lifetime to each cell.
Specify velocity field v
Cell is advected by underlying velocity field, and repelled by surrounding cells
As a cells dies replace, with spatial frequency S :
S : local cell replacement rate
v : specified velocity field
t : mean cell lifetime
n0 : mean cell density

12. Results from simulated granulation

13. Real results - Supergranule evolution
4 hour average
2.5 × 2.5 arcmin
Passive flow tracers

14. Supergranular lanes 36h Quiet sun
Granulation pattern found from velocity field using a lane finding algorithm
Note differential rotation

15. Conclusions BALLTRACKING Very efficient and robust tracking method
Accuracy close to the maximum possible
Useful for tracking any flow with features at a characteristic spatial scale
Fast enough for automated, real time analysis of large data sets

16. Publications Balltracking method: Interpolation errors in LCT:
Potts HE, Barrett RK, Diver, DA Balltracking: An ultra efficient method for tracking photosperic flows. Submitted to A&A, November 2003
Interpolation errors in LCT:
Potts HE, Barrett R, Diver, DA Reduction of interpolation errors when using LCT for motion detection. Submitted to Solar Physics, June 2003