Bernese GPS Software Version 5.0 - Bernese GNSS Software

11. Troposphere Modeling and Estimation
where n is the refractive index and N trop the so-called refractivity. The integration has to
be performed along the actual signal path through the atmosphere. According to [Hopfield,
1969] it is possible to separate N trop into a dry and a wet component
N trop = N trop
d
+ Ntrop
w , (11.4)
where the dry component (N trop
d ) is due to the hydrostatic and the wet component (Ntrop w )
is due to the non-hydrostatic part of the atmosphere. About 90% of the tropospheric path
delay stem from the dry component [Janes et al., 1989]. On the other hand, the path delay
originating from the wet component shows a much higher variability (see, e.g., [Langley,
1996]). Using the previous equation we may write
∆̺ = ∆̺d + ∆̺w = 10 −6
N trop
d
According to [Essen and Froome, 1951] we have
N trop
d,0
= 77.64 p
T
K
mb
and N trop
w,0
= −12.96 e
T
ds + 10 −6
N trop
w ds . (11.5)
K
5 e
+ 3.718 · 10
mb T 2
2 K
, (11.6)
mb
where p is the atmospheric pressure in millibars, T the temperature in degrees Kelvin,
and e is the partial pressure of water vapor in millibars. The coefficients were determined
empirically.
The tropospheric delay depends on the distance traveled by the radio wave through the
neutral atmosphere and is therefore also a function of the satellite’s zenith distance z. To
emphasize this elevation-dependence, the tropospheric delay is written as the product of
the delay in zenith direction ∆̺ 0 and a so-called mapping function f(z):
∆̺ = f(z) ∆̺ 0 . (11.7)
According to, e.g., [Rothacher, 1992] it is better to use different mapping functions for the
dry and wet part of the tropospheric delay:
∆̺ = fd(z) ∆̺ 0 d + fw(z) ∆̺ 0 w
. (11.8)
Nowadays, several different and well established mapping functions are available (and supported
by the Bernese GPS Software). It is worth mentioning, however, that to a first order
(“flat Earth society”) all mapping functions may be approximated by:
fd(z) ≃ fw(z) ≃ f(z) ≃ 1
cos z
. (11.9)
One of the most popular models to compute the tropospheric refraction is Saastamoinen.
It is based on the laws associated with an ideal gas. [Saastamoinen, 1973] gives the equation
∆̺ = 0.002277
cos z
1255
p + + 0.05
T
e − tan 2
z
, (11.10)
where the atmospheric pressure p and the partial water vapor pressure e are given in millibars,
the temperature T in degrees Kelvin; the result is given in meters. Be aware that the
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