Basic Principles of Surface-Based Remote Sensing - Surface Based Remote Sensing of the Atmospheric Boundary Layer - page 38

77.6 p

e
T 2 ,

10 5

N =

T +

3.73 · (3.4)

with the air temperature T in K, the air pressure p and the water vapour pressure
e in hPa (Bean and Dutton 1968 ). The interesting problem for the refraction of the
RADAR beam near the surface is whether the curvature of the beam is smaller
or larger than the curvature of the Earth's surface. For this purpose a modified
refractivity M is defined:

10 6 z M ( z ) =

R +

N = 157 z + N , (3.5)

with the height above the Earth's surface z and the Earth's radius R , both given in
km. If M(z) turns out to be constant with height z , then the RADAR beam follows
the curvature of the Earth's surface always having a constant height above ground.
If M(z) decreases with height, the RADAR beam is bended towards the ground. In
layers with a negative vertical gradient of M , RADAR beams are captured like in a
wave duct. Such ducts can occur underneath of strong inversions. Vertical gradients
of M between 0 and 78 km − 1 are called superrefraction. Such conditions appear
with stabile thermal stratification and a strong vertical decrease of moisture, and they
lead to enhanced maximum ranges of a RADAR because the height above ground
of the RADAR is only increasing slowly. Gradients of M between 78 and 157 km − 1
are defined as normal propagation conditions, and gradients above 157 km − 1 as
subrefraction. Under subrefraction conditions, the RADAR is bended upward more
than normally and the maximum range of the instrument is reduced because the
beam is too high above ground in larger distances from the instrument.
A RADAR is usually operated in scanning modes. Rotation around the verti-
cal axis while emitting the beam at a constant low elevation angle leads to circular
maps of the precipitation distribution with the position of the RADAR in the centre
of these maps. This mode is known as PPI (plane position indicator). Because the
RADAR beam is usually bended less than the curvature of the Earth's surface, the
height of the beam above ground increases with growing distance from the centre in
a PPI mode. An elevation angle of 0.5 ◦ leads to height of the beam above ground of
4 km at a distance of 200 km. Successive scans with varying elevation angles can be
used to compute circular maps, which artificially show the backscatter echoes from
a fixed height above ground (CAPPI, constant altitude plane position indicator).
A second scanning mode with constant azimuth and periodically varying elevation
angle is called RHI (range height indicator) and serves to obtain vertical cross sec-
tions through precipitation areas (e.g. rain clouds and fronts). The maximum range
of a RADAR is about 200 km.
The RADAR reflectivity Z in the RADAR equation depends on the size of the
drop radii D i in the measuring volume

V ,

V D i .

1

Z = (3.6)

If the drop size spectrum N ( D ) is known, this sum can be written as an integral