Bernese GPS Software Version 5.0 - Bernese GNSS Software

11.4 Troposphere Modeling in the Bernese GPS Software
model described in Eqn. (11.10) implicitly contains a mapping function (zenith dependence).
[Bauerˇsíma, 1983] proposed special correction terms B and δR:
∆̺ = 0.002277
1255
p + + 0.05 e − B tan
cos z T 2
z + δR . (11.11)
The correction term B is a function of the height of the observing site, the second term δR
depends on the height and on the elevation of the satellite. Only the B-term is implemented
in the present version of our software.
The input values p, T, and e for a priori models are usually derived from a standard atmosphere
model. In this case, the following height-dependent values for pressure, temperature,
and humidity are assumed [Berg, 1948]:
p = pr · (1 − 0.0000226 · (h − hr)) 5.225
T = Tr − 0.0065 · (h − hr)
H = Hr · e −0.0006396·(h−hr)
(11.12)
where p, T, H are pressure (millibar), temperature (Celsius), and humidity (%) at height
h of the site; pr, Tr, Hr are the corresponding values at reference height hr. The reference
height hr, and the reference values pr, Tr, Hr are defined in the file ${X}/GEN/CONST. and
we do not recommend to change these values:
hr = 0 meter
pr = 1013.25 millibar
Tr = 18 o Celsius
Hr = 50 %.
(11.13)
The troposphere mapping function commonly used today in GNSS data analysis is from
[Niell, 1996]. They are given separately for the dry and for the wet component of the
troposphere. The coefficients of the continued fraction representation of the dry hydrostatic
mapping function depend on the latitude and height above sea level of the observing site
and the day of the year. The dependence of the wet mapping function is only on the site
latitude.
For ranging measurements the tropospheric delay is not dispersive. It depends on the wavelength
of the signal. For SLR applications the Bernese GPS Software provides the Marini-
Murray model [Marini and Murray, 1973]. The Laser frequency is hardwired in subroutine
${LG}/TROPOS.f to 532 nm (Neodym-Yag) for all stations except Zimmerwald (Station
ID 7810) for which 423 nm is used (Titanium-Sapphire) to compute the refraction correction.
11.4 Troposphere Modeling in the Bernese GPS Software
In this section we give a detailed overview of the troposphere representation used in the
Bernese GPS Software Version 5.0 . Let us therefore elaborate on the tropospheric refraction
term ∆̺i k from observation equations (2.34). It may be written down in a more sophisticated
way:
∆̺ i k (t,A,z) = ∆̺apr,k(z i k ) + ∆
a priori model
h ̺k(t)f(z i k ) + ∆
ZPD
n ̺k(t) ∂f
∂z cos Aik + ∆e̺k(t) ∂f
∂z sinAik ,
horizontal gradients
(11.14)
Bernese GPS Software Version 5.0 Page 243