Statistical Estimation and Tracking of Refractivity from Radar Clutter

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agation calculations. Due to the curvature of the Earth, an initially horizontally
propagating signal will be moving away from the surface. To take this effect into
account, the modified refractivity (M) has been introduced. N and M can be
computed as
N = (n − 1) × 10 6 = 77.6p
T
rh6.105 expx
e s =
100
x = 25.22 T − 273.2
T
+ e s3.73 × 10 5
T 2 (1.1)
( ) T
− 5.31 log e
273.2
(1.2)
(1.3)
M = N + h a × 106 (1.4)
M ≃ N + 0.157h, (1.5)
where e s is the partial pressure of water vapor, p is the barometric pressure in
millibars, T is the temperature in o K, rh is the percent relative humidity, h is the
height above the earth’s surface, and a is the radius of the Earth.
Classification of Atmospheric Conditions
Even though the fluctuations are on the order of part-per-millions, they
are sufficient to cause major changes in the tropospheric electromagnetic propagation.
Normally, the refractivity is a near-exponential function of the altitude. This
exponential can be linearized within the first kilometer or so of the atmosphere.
The slope of this linear function is –0.039 N-units/m or 0.118 M-units/m and it
usually is referred to as the “standard atmosphere”. Standard atmosphere will
result in a downward bending of the electromagnetic wave. However, this is less
than the curvature of the earth, effectively resulting in a wave that slowly moves
away from the surface. This type of propagation is called the normal propagation
condition and it occurs as long as N is between –0.079 to 0 N-units/m (0.079 to
0.157 M-units/m).
If N has a positive slope with respect to the altitude, the wave will further
bend upward creating the sub-refractive conditions, which only infrequently occurs