Path Delays in the Neutral Atmosphere - Atmospheric Effects in Space Geodesy - page 78

is larger than the wet part, the wet refractivity is much more variable and difficult
to model. We will see in Sect. 3.1 that the effect of the hydrostatic refractivity on
the propagation of microwaves can be accurately estimated from just the surface
pressure, while the modeling of the wet part is more complicated.
It should be noted that in the literature sometimes a division of the refractivity
into a dry and a wet part is used (e.g. Perler et al. 2011 ). The dry refractivity will
be the part caused only by the first term of the righthand side of Eq. ( 15 ), while the
other two terms are designated as the wet part. It is important to remember that the
wet refractivity obtained in this case is not the same as the wet (i.e. non-hydrostatic)
refractivity obtained when dividing the refractivity into a hydrostatic and wet part
(Eq. 18 ). The division into dry andwet partsmakes sense in that it clearly separates the
contributions from the dry gases and water vapor (part of the hydrostatic refractivity
is caused by water vapor). However, there are practical advantages of using the
division into hydrostatic and wet parts, making it more commonly used. As shown
in Sect. 3.1 the propagation delay caused by the hydrostatic refractivity can easily be
inferred from surface pressure measurements.

2.2 Optical Refractivity of Moist Air

For optical frequencies, the coefficient k 3 in Eq. ( 11 ) is very small and can be ignored.
However, the frequency dependence of the k 1 and k 2 coefficients needs to be con-
sidered. Normally the refractivity is expressed as a function of the density of dry air
and water vapor (see Born and Wolf 1999 , pp. 95-103)

p d
T

p w
T

R
M d ρ d +

R
M w ρ w

Z − 1
d

Z − 1
w

N = k 1 (ν) + k 2 (ν) = k 1 (ν) k 2 (ν)

= k d (ν)ρ d + k w (ν)ρ w . (19)

k d (ν)

and k w (ν)

are the dispersions of dry air and water vapor components, respec-

tively. ρ w are the density of dry air and water vapor, respectively.

Similarly for microwaves, N can also be divided into a hydrostatic and a non-
hydrostatic (wet) part

ρ d and

N = N h + N w , (20)

where

N h = k d (ν)ρ t , (21)

N w = k w (ν)ρ w , (22)

k w (ν) = k w (ν) − k d (ν).

(23)

k d (ν)

and k w (ν) In the literature, the dispersion formulae for proposed by vari-

ous investigators such as Edlén ( 1966 ), Barrell and Sears (Jeske 1988 , p. 217),