Page 64 - Radar Technology Encyclopedia

54 atmospheric refraction atmospheric refractive index

somewhat larger angle than the direct geometric path to the
target (Fig. A94). 1 2
h
0
3 5
a
4 4 4'
Target A Y 5'
h h h
A Y A
Radar (a) (b)
q
Dq
Figure A95 Propagation of radio waves under condition of
refraction (a) normal refraction, (b) superrefraction (beams 3,
Figure A94 Elevation measurement error due to refraction. 4, 4’, 5, and 5’) and subrefraction (beams 1 and 2).

While refraction may be troublesome in radar operations near
At the same time, an extra time delay is produced, giving
the horizon, and must be accounted for in accurate tracking
a larger range reading than the true range. Random variations
applications, it can often be neglected at elevation angles
in refractive index produce smaller, random errors in mea-
greater than 3 to 5°. PCH, SAL
sured coordinates. In the troposphere, three effects must be
considered: Ref.: Blake (1980), Ch. 5; Skolnik (1980), p. 447; Barton (1988); Van Nos-
trand (1983).
(1) Regular refraction, resulting in the gradual reduc-
tion in the refractive index with altitude, causing elevation The atmospheric refractive index n is the ratio of the veloc-
and range bias errors. ity of electromagnetic waves in empty space c to that in a
(2) Tropospheric fluctuations, resulting from random medium:
variations in local refractive index and causing slowly vary- n = c/v
ing errors in all measurement coordinates. In empty space n = 1, and in the lower troposphere
(3) Ducting, resulting from steep gradients in refrac- n »1.0003. It varies throughout the atmosphere, the major
tive index, usually near the surface, creating low-loss propa- variation being an exponential change with altitude in the tro-
gation paths to low-altitude targets beyond the normal radar posphere. In an atmosphere that contains water vapor, the
horizon and leaving gaps in the coverage for targets just refractive index for radio and microwave frequencies is
above the duct. expressed by
Numerically, atmospheric refraction is calculated using 5
6 77.6p 3.73 ´ 10 × e
´
models of the variation of refractive index n(h). The curved ( n – 1 ) 10 = ------------- + --------------------------------
T 2
ray path length for a specified elevation angle q to a height T
0
h above the surface can be found as
0 where p is the barometric pressure (mbar), e is the partial
pressure of water vapor (mbar), and T is absolute temperature
h 0
nh () (K). In the ionosphere, n depends on the electron density, N
(
R q h ) = ò -------------------------------------------------------- hd e
,
0 0
n cos q 0 and the radar frequency f according to
0
0 1 – -------------------------------------
(
nh () 1 + hr ¤ )
0
– 12
81N ´ 10
e
where n = n(0) and r is the radial distance of the initial point n = 1 – --------------------------------
0
0
2
from the center of the earth. f MHz
Depending on the gradient of the refractive index, the
following cases can be distinguished: The refractive index is also called the index of refraction.
(1) Normal [regular] refraction. The refractive index may be modeled, for radar applica-
(2) Superrefraction. tions as the function of altitude h. Two basic models are used:
(3) Ducting. the exponential model (which is often referred to as exponen-
(4) Subrefraction. (See PROPAGATION). tial reference atmosphere) and the linear model. The expo-
In the first three cases the refractive index decreases with nential model represents the refractive index as:
height, but in (4), which is rare, it increases (Fig. A95).
×
The effects of refraction on radar operation are nh )( = 1 + ( n – 1 )exp c – ( e h × )
0
(1) To change the radar coverage (accounted for through
where n is the surface value of refractive index (h = 0) and
range-height-angle charts for normal condition. (See 0
c is a constant:
CHART.) e
(2) Sometimes to extend coverage beyond the normal 1 æ dn ö
c = – -------------- ------
e
1 dh ø
horizon (See DUCTING; PROPAGATION, anomalous). n – è h = 0
0
(3) To introduce errors in angular and range measure-
ments (See ERROR, propagation).