Alternative Model of the Ionospheric Critical Frequency Reduced by the Solar Zenith Angle

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Alternative Model of the Ionospheric Critical
Frequency Reduced by the Solar Zenith Angle
IRI-COST Workshop 10-14 July 2007, Prague, Czech
Republic

• T.L.Gulyaeva
• tamara_at_izmiran.troitsk.ru

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foF2 inversion procedure

• The solar zenith angle ? affects diurnal /
  seasonal variations of foF2 at a given location.
• These effects of foF2 changes in the Suns zenith
  angle can be removed with a factor deduced from
  the solar zenith angle ? (rad.) at a particular
  time and the local noon value ?0 (rad.)
• fnF2 foF2 z(?) / z(?0)
• where factor z(x) x2 - ? x ?,
• x? or x? 0, ? 3.54, ? 3.875.
• Coefficients ?, ? are obtained for
  0º???180º by least squares fit to variation of
  1/? at ? lt 1rad.

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Outcome of foF2 reduced by the solar zenith angle
to fnF2

• The inverted critical frequency fnF2 coincides
  with observed foF2 at noon but it is gradually
  reduced towards the midnight around the year.
• This particularly affects results for a local
  summer
• Correlations between fnF2 values at different
  locations and between the data of the same
  station at different seasons are improved
  compared with the source foF2 data (Gulyaeva and
  Gulyaev, 2007).

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Daily-hourly values of the critical frequency
foF2 observed and fnF2 reduced by the solar
zenith angle at Moscow during June 2006
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Database of topside sounding

• Data sets of 90,000 foF2 values are provided by
  ISIS1, ISIS2, IK19 and Cosmos-1809 topside
  soundings for the period of 1969-1987.
• foF2 is obtained from electron density height
  profile by exponential fitting to two lowest
  heights
• The foF2 values are reduced by the solar zenith
  angle to fnF2.
• Empirical model of regular foF2 fnF2 variations
  based on these satellite data is produced in
  terms of modified dip latitude, local time,
  season and solar activity.

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Data analysis

• The individual foF2 fnF2 value is characterized
  by
• year, month, day-of-year, local time / universal
  time,
• geodetic geomagnetic coordinates,
• the solar zenith angle calculated with IRI
  standard subroutine SOCO (McNamara, 1986
  Bilitza, 2001)
• modip latitude ? tan(?)(I/rad) / ?cos(?)
  (Rawer, 1963)
• solar radio flux F10.7 proxy index
• Fsp (Fs81F10.7p)/2 (Lei et al., 2005)
• geomagnetic kp index effects are neglected due to
  mixed positive and negative foF2 storm effects

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Solar activity trends of foF2 observed and fnF2
reduced by the solar zenith angle with 2? error
bars deduced from topside sounding database
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Comparison of variation of foF2 with the Fs proxy
radio flux from the topside database and IRI-CCIR
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The solar cycle - local time changes of foF2 and
fnF2
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Modip local time variation of fnF2 deduced from
the topside database at solar minimum
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Modip Local Time variation of fnF2 for 3
seasons deduced from the topside database at
solar minimum
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Model analytical functions

• Model coefficients define 9th order polynomial of
  modip, P(?)
• from the matrix of polynomials P(?) produced for
• (1) 4 selected local times (00, 06, 12, 18 h LT),
  
• (2) 3 seasons (winter solstice, equinox, summer
  solstice),
• (3) 2 levels of solar activity solar flux proxy
  index
• Fsp70 s.f.u. (LSA) and Fsp200 s.f.u.
  (HSA).
• Epstein exponential function is used for
  interpolation of foF2 model for given day-of-year
  (Epstein step-function between 2 embracing
  seasonal days-of-year) and local time (between 2
  embracing grid local times) at LSA and HSA.
• Model foF2 value for given solar activity proxy
  index Fsp is produced with linear interpolation
  between model results for LSA and HSA.

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Modip variation of foF2 for 4 selected local
times at winter summer solstices and equinox
for the solar minimum (LSA) fitted by 9th order
polynomials
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Model foF2 results Latitudinal / diurnal (LT)
variation at 0E for 3 seasons at solar minimum
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Conclusions

• The long-term topside sounder measurements
  onboard of ISIS1, ISIS2, IK19 and Cosmos-1809
  satellites during 1969-1987 have been used as a
  database for an empirical modeling of foF2
• The effects of changes in the Suns zenith angle
  have been removed by multiplying the critical
  frequency foF2 by a factor related with the solar
  zenith angle ? at a particular time and the local
  noon value ?0
• The model of regular foF2 fnF2 variations is
  produced in terms of local time, season, modified
  dip latitude and solar activity