ESS 261 Topics in magnetospheric physics Space weather forecast models ____ the prediction of solar

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ESS 261 Topics in magnetospheric physicsSpace
weather forecast models____ the prediction of
solar wind speed

• April 23, 2008

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Methods

• Empirical methods
• Interplanetary scintillation (IPS) techniques
• Interplanetary scintillation (IPS) of cosmic
  radio signals has been employed to deduce the
  solar wind in regions beyond the ecliptic plane
  and near the sun, where spacecrafts have no
  access. IPS observations are performed at a
  frequency of 327 MHz using four radio telescopes
  at Toyokawa, Fuji, Sugadaira, and Kiso. This
  four-antenna system is able to observe the solar
  wind at distances of 0.1-1 AU from the sun.

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Potential field source surface (PFSS) model

• Principle the more slowly a coronal flux tube
  expands in areal cross-section, the higher the
  asymptotic wind speed along that flux tube. (The
  physical basis for this inverse correlation is
  the rapid increase in the mass flux density at
  the coronal base ___ hence decrease in the energy
  per particle ___ with increasing areal divergence
  rate.)
• The flux tube divergence rates will be calculated
  by applying a potential-field source-surface
  (PFSS) extrapolation to the observed photospheric
  flux distribution, in the form of monthly
  synoptic maps from the Wilcox Solar Observatory
  (WSO).
• In the PFSS model, the magnetic field is assumed
  to be curl-free in the region between the solar
  surface and a spherical source surface, where
  the tangential field components are constrained
  to vanish.

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Expansion factor

• For a flux tube that passes through a given point
  on the source surface,
• which is the factor by which the flux tube
  expands in solid angle between its footpoint
  location and the source surface.
• The expansion factor equals to 1 if the bundle of
  open field lines diverges as r2, but exceeds 1 if
  (as usually the case) the flux diverges more
  rapidly than r2.

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A modification to the PFSS model

• Arge et al. have applied a modification to the
  Wang-Sheeley model.
• The modification consists of deriving an
  empirical relationship between fs and solar wind
  speed at 2.5 Rs rather than L1.
• This empirical function was found by iteratively
  testing various mathematical relationships
  between fs and vsw, using it to assign the solar
  wind speed at the source surface, propagating the
  wind out to L1, and then comparing the results
  with observations.
• The procedure was repeated until a best fit was
  found.
• A simple 1-D modified kinematic (1-DMK) model,
  which included an ad hoc method to account for
  stream interactions, was used to transport the
  wind to L1.

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• Solar wind observations made at L1 must be mapped
  back to the Sun to compare with photospheric and
  coronal field parameters.
• WIND spacecraft observations was mapped from 1995
  back to 0.1 AU (i.e., 21.5 Rs) assuming constant
  flow speed, neglecting stream interactions, but
  accounting for solar rotation.

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• Schatten current sheet (SCS) model
• Representing the field configuration of the outer
  corona between 2.5 and 21.5 Rs.
• Others?
• 1-D modified kinematic model (1-DMK)
• Using this model rather than MHD model is mainly
  for simplicity
• For this particular study, the 1-DMK code is
  preferred over a more advanced 3-D MHD code, as
  it significantly reduces the time required for
  each new trial run.

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Parameters

• Expansion factor fs evaluated at 2.5 Rs
• Photospheric (or footpoint) field strength (Bph)
• The minimum (spherical) angular separation
  between an open field footpoint and
• Sub-earth point
• Current sheet
• Nearest coronal hole boundary.

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• First, search for patterns between solar wind
  speed and the above five photospheric/coronal
  parameters
• Second, deduce and empirical relationship for vsw
  involving one or more these parameters
• Third, assign vsw at the outer boundary of the
  SCS model, and then, for each daily updated map
  from 1995, propagate the solar wind out to Earth
  using a 1-D modified kinematic (1-DMK) code
• Fourth, directly compare predicitons with
  observations.

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To be continued by Morrisa