Efficient tracking of photospheric flows

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Efficient tracking of photospheric flows
BALLTRACKING

• H.E.Potts, D.A.Diver, R.K.Barrett
• University of Glasgow, UK
• Funded by PPARC Rolling Grant PPA/G/0/2001/00472

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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 515 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
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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

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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!
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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

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

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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
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How accurate is possible?

• Random Velocity gt 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
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How smooth is smooth enough
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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
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Results from simulated granulation
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Real results - Supergranule evolution
4 hour average 2.5 2.5 arcmin Passive flow
tracers
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Supergranular lanes

• 36h Quiet sun
• Granulation pattern found from velocity field
  using a lane finding algorithm
• Note differential rotation

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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

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Publications

• Balltracking method
• Potts HE, Barrett RK, Diver, DA Balltracking An
  ultra efficient method for tracking photosperic
  flows. Submitted to AA, 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