Bernese GPS Software Version 5.0 - Bernese GNSS Software

Single layer
H
Receiver
R
α
z
z’
Sub-ionospheric point
Figure 12.3: Single-layer model.
12.3 Ionosphere Modeling
Satellite
Ionospheric pierce point
With the help of Figure 12.3, it can be easily verified that the geocentric angle α equals
z − z ′ .
The height of this idealized layer is usually set to the expected height of the maximum
electron density. Furthermore, the electron density E – the surface density of the layer – is
assumed to be a function of geographic or geomagnetic latitude β and sun-fixed longitude s.
The “modified” SLM (MSLM) mapping function includes an additional constant, α [Schaer,
1999]:
FI(z) = E
Ev
= 1
cos z ′ with sin z ′ = R
R + H
sin(α z). (12.9)
Best fit of Eqn. (12.9) with respect to the JPL extended slab model (ESM) mapping function
is achieved at H = 506.7 km and α = 0.9782 (when using R = 6371 km and assuming
a maximum zenith distance of 80 degrees). The resulting mapping function is used in the
ionosphere analysis at CODE. For computation of the ionospheric pierce points, H = 450 km
is assumed (according to Figure 12.3).
To map TEC, the so-called geometry-free (L4) linear combination (2.46), which principally
contains ionospheric information, is analyzed. The particular observation equations for undifferenced
phase and code observations read as
where
L4,P4
1
L4 = −a
f 2 1
1
P4 = +a
f 2 1
− 1
f2
2
− 1
f 2 2
FI(z)E(β,s) + B4
(12.10a)
FI(z)E(β,s) + b4, (12.10b)
are the geometry-free phase and code observables (in meters),
a = 4.03 · 10 17 m s −2 TECU −1 is a constant,
Bernese GPS Software Version 5.0 Page 259