Efficient tracking of photospheric flows H.E.Potts, D.A.Diver, R.K.Barrett University of Glasgow, UK Funded by PPARC Rolling Grant BALLTRACKING
Jan 03, 2016
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
BALLTRACKING
The Why and The How
Why?• 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
Established Tracking Methods
• Standard LCT (Simon 1988). – Excellent results but slow (approx 4 days for 8hrs MDI
High Resolution data)
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dx,dy
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• CST (Strous 1995) – Complex, and limited to high resolution images. Need
to be careful about selection effects
• Simulated data needed
What will Solar-B give us?
SOHO Solar-B
Instrument MDIMichaelson Doppler
Interferometer
BFIBroadband 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!
Balltracking 1: Filtering and derotation
Filtering:• 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
Balltracking 1: Filtering and derotation
Filtered image
Inverse transform
Phase adjust
Mask2D Fourier Transform
Raw Image
FILTER DEROTATE
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
Balltracking 3: Smoothing
• Set of irregularly spaced ball trajectories
• Smooth in space and time to get underlying velocity V(i,j):
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V(xi,yi,t) : smoothed velocity
: spatial smoothing radius
t : time smoothing interval
rn,t : distance from (xi,yi) to ball
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
t, r : Sampling intervals
v, u, : STD of smoothed
and random velocity
How smooth is smooth enough
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
: mean cell lifetime
n0 : mean cell density
Results from simulated
granulation
Real results - Supergranule evolution
4 hour average
2.5 × 2.5 arcmin
Passive flow tracers
Supergranular lanes
• 36h Quiet sun • Granulation pattern found
from velocity field using a lane finding algorithm
• Note differential rotation
Conclusions
• Very efficient and robust tracking method• Accuracy close to the maximum possible• Useful for tracking any flow with features at a
characteristic spatial scale
BALLTRACKING
• Fast enough for automated, real time analysis of large data sets
Publications
Balltracking method:• 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