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Δ
Δ
where
L w are called the hydrostatic and wet delay, respectively. Com-
monly, the effect of bending, S
L h and
G , is by convention considered to be part of the
hydrostatic delay, i.e. the hydrostatic mapping function (see Sect. 4.2 ) includes the
bending effect.
In space geodesy it is common to refer the slant delays to the delays in the zenith
direction (using mapping functions, see Sect. 4.2 ). The zenith hydrostatic delay
L h
Δ
L z w are given by
and the zenith wet delay
Δ
10 6
h 0
L h =
Δ
N h (
z
)
d z
,
(29)
10 6
h 0
L z w =
Δ
N w (
)
,
z
d z
(30)
where h 0 is the altitude of the site.
3.1 Hydrostatic Delay
From Eqs. ( 17 ) and ( 29 ) we see that the hydrostatic delay only depends on
the total density and not on the mixing ratio of wet and dry parts. Following
Davis et al. ( 1985 ), the hydrostatic delay can be determined by using the hydrostatic
equation
d p
d z =− ρ (
z
)
g
(
z
),
(31)
(
)
where g
is the gravity along the vertical coordinate z , and integration of Eq. ( 31 )
yields the pressure p 0 at the height h 0
z
h 0 ρ (
g eff
p 0 =
z
)
g
(
z
)
d z
=
h 0 ρ (
z
)
d z
.
(32)
Instead of the height-dependent gravity g
(
z
)
, we introduce the mean effective gravity
g eff
h 0
ρ (
z
)
g
(
z
)
d z
g eff
=
h 0
,
(33)
ρ (
z
)
d z
and the inversion yields the height h eff which is the height of the center of mass of
the atmosphere above the site and can be determined with
h 0
ρ (
z
)
z d z
h 0
h eff
=
d z .
(34)
ρ (
z
)
Saastamoinen ( 1972b ) used the approximation for the effective height
 
 
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