TROPOSPHERE AND IONOSPHERE - GPS Satellite Surveying - page 196

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The first term of (6.6) expresses the sum of distortions of electron charges of the dry-
gas molecules under the influence of an applied magnetic field. The second term of
(6.6) refers to the same effect but for water vapor. The third term is caused by the
permanent dipole moment of the water vapor molecule; it is a direct result of the
geometry of the water vapor molecular structure. Within the GPS frequency range
the third term is practically independent of frequency. This is not necessarily true for
higher frequencies that are close to the major water vapor resonance lines. Equation
(6.6) is further developed by splitting the first term into two terms, one that gives
refractivity of an ideal gas in hydrostatic equilibrium and another term that is a
function of the partial water vapor pressure. The large hydrostatic constituent can
then be accurately computed from ground-based total pressure. The smaller and more
variable water vapor contribution must be dealt with separately.
The modification of the first term (6.6) begins by applying the equation of state
for the gas constituent i, (i

[19

= d,i = wv) ,

= ρ i R i T

p i Z i (6.9)

Lin
—
3.8
——
Nor
*PgE

ρ i is the mass density and R i is the specific gas constant ( R i =

where R/M i , where

R is the universal gas constant and M i is the molar mass). Substituting p d in (6.9) for
the first term in (6.6), replacing the

ρ d by the total density ρ and ρ wv , and applying

(6.9) for ρ wv gives for the first term

p d
T

R d
R wv

p wv
T

Z − 1
d

Z − 1
wv

= ρ d = ρ − ρ wv = ρ −

k 1 k 1 R d k 1 R d k 1 R d k 1 R d k 1 (6.10)

[19

Su bstituting (6.10) in (6.6) and combining it with the second term of that equation
gives

p wv
T

k 3 p wv k 2 Z − 1

wv

T 2 Z − 1

N = k 1 R d ρ + + (6.11)

wv

The new constant k 2 is

R d
R wv =

M wv
M d

k 2 =

k 2 − k 1 k 2 − k 1 (6.12)

Be vis et al. (1994) gives k 2 = 22 . 1 K/mbar.

We can now define the hydrostatic and wet (nonhydrostatic) refractivity as

p
T

N d = k 1 R d ρ = k 1 (6.13)

p wv
T

k 3 p wv

k 2 Z − 1

wv

T 2 Z − 1

N wv = + (6.14)

wv

If we integrate (6.6) along the zenith direction using (6.13) and (6.14), we obtain the
ZHD and ZWD, respectively,