Theory of GNSS Radio Occultation - GNSS Remote Sensing: Theory, Methods and Applications - page 102

expressed in terms of refractivity defined as N D ( n 1) 10 6 . The refractivity at
GPS frequencies contains contributions from four major components, i.e., the dry
neutral atmosphere ( N dry ), water vapor ( N vapor ), free electrons in the ionosphere
( N iono ), and particulates (primarily liquid water and ice water content, N scatt ) through
the following relationship (Kursinski et al. 1997 ;Hajjetal. 2002 ):

40:3 10 7 n e
f 2

C O 1
f 3

D 77:6 P

T C 3:73 10 5 P w

N

T 2

(5.1)

C 1:4W liquid C 0:6W ice

D N dry C N vapour C N iono C N scatt

(5.2)

where P and P w are total pressure and water vapor partial pressure in hectopascal
(hPa), T is temperature in Kelvin (K), n e is electron number density per cubic meter,
f is signal frequency in Hertz (Hz), and W liquid and W ice are referred to liquid water
content and ice water content in gram per cubic meter, respectively.
Dry refractivity is proportional to molecular number density and is dominant
below 60-90 km. The dry refractivity term is due to the polarizability of molecules
in the atmosphere, i.e., the ability of an incident electric field to induce an electric
dipole in the molecules. The moist refractivity term is due primarily to the large
permanent dipole moment of water vapor and becomes significant in the lower
troposphere, especially in the tropics and subtropics (Kursinski et al. 2000 ). The
ionospheric term in Eq. ( 5.1 ) includes a first-order approximation (1/ f 2 )tothe
Appleton-Hartree equation (Papas 1965 ), which is mainly due to free electrons in the
ionosphere and becomes important above 60-90 km. The second-order term (1/ f 3 )
is generally neglected (e.g., Kursinski et al. 1997 ). The scattering term given in Eq.
( 5.1 ) is due to liquid water droplets and ice crystals suspended in the atmosphere.
For realistic suspensions of water or ice, the scattering term is small in comparison
with the other terms and is therefore neglected in most RO applications.

5.2.2 Geometric Optics Approximation

At GNSS frequencies, it is convenient to assume that the refractive index is real
(i.e., zero absorption). For simplicity, we can further assume that the signals are
monochromatic, which is largely valid in the dry atmosphere. Because the wave-
lengths of the GNSS radio signals are generally small compared to the characteristic
scale of the atmospheric problem, the geometric optics (or ray optics) concept can
be applied to describe the GPS radio occultation measurements. The signals (light
waves) propagate in a direction orthogonal to the geometrical wavefronts defined as
the surface on which the signal phase is constant (i.e., stationary phase) (Born and
Wolf 1980 ). Lines representing these signal propagating trajectories are called ray
paths (e.g., black solid curve in Fig. 5.2 ).