Geoscience Reference
In-Depth Information
2.1 Refractivity N
As anomalous propagation is due to relatively small variations of the air refractive index
n
,
the magnitude known as refractivity
N
, defined as one million times
n-1
, is commonly used
in anaprop studies. As shown by Bean and Dutton (1968), or more recently in ITU (2003),
N
can be written as:
77.6
4810
e
6
Nn
(
) 0
p
,
(1)
T
T
where
T
is the air temperature (K),
p
atmospheric pressure (hPa), and
e
is the water vapour
pressure (hPa). According to ITU (2003), this expression may be used for all radio
frequencies; for frequencies up to 100 GHz, the error is less than 0.5%. This formula takes
into account only air gases and does not consider liquid water content (usually with
negligible effects), or free electron density (important for high atmospheric altitudes,
typically above 60 km).
Note that
N
is a dimensionless magnitude, though quite often the term “
N
units” is
employed.
N
is sometimes considered the sum of two different terms of (1): the dry term,
N
d
,
which depends only on
p
and
T,
and the wet term,
N
w
, which is also function of
e,
i.e. is
related to moisture content. Typical values of
N
of air at ground level are within the range
250 to 450.
2.2 Modified refractivity M
A magnitude related to
N
is the modified refractivity
M
, which is defined as:
z
MN
,
(2)
6
10
r
where
z
is altitude and
r
is the radius of the Earth, expressed in meters (m). Modified
refractivity is very useful to characterize propagation conditions as for constant
M
the
curvature of the ray path is that of the Earth's surface and, therefore, when there are
negative
M
vertical gradients the ray path may be bent towards the surface and then radio
waves get trapped like in a wave guide (ducting). Based on M gradients, Johnson et al.
(1999) suggested the use of a ducting index, with positive values proportional to the
probability of occurrence of ducting.
2.3 Propagation conditions
Propagation characteristics may vary largely, depending for instance on the type of air mass
(Gossard, 1977). When characterizing the radio propagation environment it is usual to
consider the vertical refractivity gradient (VRG) of the air of the first kilometre above
ground level to estimate propagation effects such as ducting, surface reflection and
multipath on terrestrial line-of-sight links. However, the effect on weather radar beam
refraction not only depends on the refractivity gradient of a layer but also on the angle of
incidence between the beam and the trapping layer considered or the frequency of the
electromagnetic wave (ITU, 2003). In the following paragraph, specific VRG values are given
for the propagation conditions described earlier qualitatively.
