Dst Prediction from Solar Wind Conditions

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Dst Prediction from Solar Wind Conditions

• Review of Burton et al. paper by McPherron
• ESS293B Wed Jan 17, 2007

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DESSLER-PARKER-SCKOPKE DERIVATION
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THE DESSLER-PARKER-SCKOPKE RELATION
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The Burton Correction of Dst

• Let H be the horizontal component corrected for
  secular variation and quiet day variations
• The approximate defintion of Dst is then given in
  1st two lines
• Represent the disturbed and quiet fields as sum
  of effects of magnetopause and ring current
• Averaging is a linear operation so separate terms
• Rearrange to obtain the disturbed field due to
  ring current
• Define some new terms including the corrected
  Dsto
• Final equation for corrected Dst in terms of the
  measurements

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THE Dst INDEX, ITS CORRECTIONS AND POSSIBLE ERRORS

• Definition of Dst index

• Removal of background

• Disturbed contributions to H

• Definition of Dst index

• Quiet contributions to H

• Estimate secular variation and quiet day
  variations

• The corrected Dst index

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CONTRIBUTIONS TO THE VARIATION IN THE H COMPONENT
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Rewrite Burton Equation

• Substitute for Dst0 in Burton equation
• Rearrange terms
• Obtain an expression for rate of change of
  measured Dst index in terms of injection
  function, current Dst, square root of dynamic
  pressure and rate of change of dynamic pressure
• Problem is to determine the constants in this
  relation from measurements

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Determination of b

• These values translate to a modern value ofb
  15 nT/(nP)1/2

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Determination of c

• The Burton equation uses corrected Dst which
  asymptotically approaches zero when decay is
  constant without input

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Determination of a (1/t)

• During northward field the corrected Dst index
  decays towards zero with rate 1/a since there is
  no input
• Plot rate of change of Dst (nT/hr) versus Dsto
• Fit a line to the observed recovery rates to
  find t 7.7 hr

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Determination of Injection Function

• Find intervals without change in dynamic pressure
  and plot rate of decrease of Dst corrected for
  decay versus EyVBs
• Find no injection for northward field and a
  linear relation for southward field
• Slope of this line is 1.23 x 10-3 (nT/s)/(mV/m)
• This is 4.3 (nT/hr)/(mV/m)

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The Prediction Algorithm

• Note the use of a time delayed Ey
• Also note the use of a low pass filter
• Burton et al found that you must smooth the input
  with a 30 min filter to get a stable estimate of
  Dst
• This suggests the magnetopause is a low pass
  filter for solar wind electric field

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Example Prediction

• Plot inputs in top two panels
• Initial phase is caused by dynamic pressure pusle
• Main phase is caused by interval of southward IMF
• Recovery is a result of reduced input
• Note additional input keeps Dst down

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A Nonlinear Equation For Rate of Change of Dst

• The Burton et al. equation for ring current
  dynamics is derived from the DPS relation
• Assume that the ring current is driven by a solar
  wind coupling function depending on IMF Bz
• Correct the measured Dst for effects of
  magnetopause and incorrect base lines
• Obtain a first-order differential equation for
  Dst with two solar wind drivers that is nonlinear
  in the unknown parameters
• The equation is non-linear in the model parameters

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Parameters in the Burton Equation

• Assume the parameters in the Burton equation are
  constants
• Use the Burton et al. values and calculate the
  prediction efficiency
• Use non-linear inversion to obtain self
  consistent values for southward IMF
• Repeat for northward IMF
• The Burton parameters are far from optimum
  values!
• The self consistent decay time is different for
  IMF north or south, and are longer than Burton
• The self consistent pressure constant is only
  half as large as Burton
• The self consistent injection constant is lower
  than Burton because the decay time is longer