Geoscience Reference
In-Depth Information
gravity acceleration, which can cause errors in the zenith hydrostatic delays of about
20 mm (Davis et al.
1985
).
3.1.2 Optical Zenith Hydrostatic Delays
The optical zenith hydrostatic delay can, just as for microwaves, be expressed as a
function of the surface pressure. The derivation is in principle the same and will not
be repeated here. The final expression is
p
0
1022
k
d
(ν)
×
L
h
=
10
−
6
Δ
0
.
h
0
)
.
(42)
f
(θ,
The above equation is slightly different from the one developed byMendes and Pavlis
(
2004
), which is expressed as
p
0
L
h
=
10
−
6
Δ
24
.
16579
f
h
(ν)
×
h
0
)
.
(43)
f
(θ,
Mendes and Pavlis (
2004
) derived their own dispersion factor
f
h
(ν)
based on
the modified dispersion formula in Eq. (
24
) for the wavelength of 0.532
m.
Equations (
42
) and (
43
) produce similar accuracy results if they are applied to real
SLR observations.
µ
3.1.3 Pressure Values
For the analysis of space geodetic techniques, there are three possibilities to obtain
pressure values at the stations: local pressure recordings at the sites, pressure values
from numerical weather models, or empirical models for the pressure (Böhm et al.
2009a
). For instance, simple empirical models are the ones by Berg (
1948
)
5
.
225
p
=
1013
.
25
·
(
1
−
0
.
0000226
h
)
,
(44)
with the pressure
p
in hPa and orthometric station height
h
in m, or the model by
Hopfield (
1969
)
T
k
−
α
g
R
d
α
h
p
=
1013
.
25
·
,
(45)
T
k
with the atmospheric temperature at sea level
T
k
= 293.16 K, the normal lapse rate
of temperature with elevation
= 4.5 K/km, gravity
g
at the surface of the Earth
(9.7867 m/s
2
) and the gas constant
R
d
= 0.287 kJ/K/kg for dry air. More sophisticated
empirical models are UNB3m (Leandro et al.
2006
) or Global Pressure and Tem-
perature (GPT; Böhm et al. (
2007
)). UNB3m is based on meteorological parameters
(pressure, temperature, humidity, temperature lapse rate, and water vapor pressure
α
