Fig. 1. The slant TEC, as measured along the satellite–receiver line-of-sight. The majority of TEC is concentrated in the ionosphere shell, near altitudes of 350 km.
lute range errors associated with GPS signal propa- Ž
gation through the ionosphere as integrated along .
the path length : 40.3
40.3 Nd s s
TEC 5
Ž .
H
2 2
f f
path
where TEC represents the total electron content along a 1 m
2
column along the signal path. The majority of TEC is concentrated near altitudes of 350 km, where
Ž .
the largest electron densities are found Fig. 1 . The Ž
. dispersive nature of the ionosphere d nrd f 0 al-
lows direct calculation of the absolute TEC, if range measurements are available on two separate frequen-
cies:
1 1
1 TEC s
y PR y PR
6
Ž .
Ž .
1 2
2 2
ž
40.3 f
f
1 2
for the case of a dual-frequency GPS receiver, where Ž
. f s 1575.42 MHz herein referred to as L1 and
1
Ž .
f s 1227.60 MHz herein referred to as L2 . The
2
corresponding absolute ionosphere range delay can Ž .
be derived from Eq. 5 . Such range delays, along the slant line-of-sight through the ionosphere shell,
are referred to as slant range delays. For differential GPS applications, the decorrelation of slant iono-
sphere range delay depends directly on the distribu- tion of spatial irregularities in electron density. Such
irregularities can be significant in the auroral region.
3. Auroral region and substorm effects
The auroral oval is located at northern latitudes and is characterized by enhanced conductivity and
Ž energetic electron precipitation Fig. 2; Feldstein and
. Starkov, 1967 . This region is limited in latitudinal
extent, located between approximately 558 and 658 N Ž
geographic latitude nightside — North American .
Ž sector , with an average width of 5–78 Rostoker and
. Skone, 1993 . Dayside oval boundaries are f 108
higher; the oval being partially fixed with respect to Ž
both the Sun and the geomagnetic pole Akasofu, .
1968 . Auroral regions include much of Canada and
Alaska, in addition to parts of Russia and Northern Europe. Under active conditions, energy from the
solar wind is released into the auroral ionosphere via large-scale electric currents carried primarily by elec-
trons along terrestrial magnetic field lines. The pre- cipitating electrons collide with neutral atmospheric
constituents, resulting in emissions of visible and ultraviolet radiation. Localised intensifications of
Ž electrons result in the visible aurora
Northern .
Lights and variable TEC. Structured irregularities in TEC can be extremely localised, with horizontal
Ž scale sizes ranging from 20 to 400 km Coker et al.,
. 1995 . Significant decorrelation of TEC, and equiva-
lently, ionosphere range delay, can occur over short distances.
Such irregularities are characteristic of magneto- spheric substorms, which generally occur in the local
Ž .
time sector 1900–2400 magnetic local time MLT . The most volatile phase of substorm development is
the expansiÕe phase, which can last 30–60 min Ž
. Hargreaves, 1992 . During the substorm, auroral
oval boundaries may expand 5–108 southwards. Northern Lights have been observed as far south as
Ž Fig. 2. Series of ultraviolet images from the POLAR satellite, depicting auroral intensifications during the April 11, 1997 substorm courtesy
. of G. Parks, The University of Washington .
the southern United States during intense substorm events.
Sunspot activity is directly correlated with the emission of solar electromagnetic radiation and the
creation of solar flares, two phenomena that control the level of auroral activity. The solar activity under-
goes periodic variations over several time scales, the principal cycle having an 11-year period. A solar
maximum was last observed in 1989, with the next solar maximum being predicted for the year 2000
Ž .
Kunches, 1997 . At this time, an increase in the frequency and magnitude of magnetospheric sub-
storms will accompany the enhanced solar flare ac- tivity.
4. Sample substorm event — April 11, 1997
