CRPL exponential reference atmosphere refraction exponent
Refraction Exponent as Function of Surface Refractivity
Compute the refraction exponents for surface refractivities equal to
313 N-units, and
srfrf = [200 313 450]; rexp = refractionexp(srfrf)
rexp = 1×3 0.1184 0.1439 0.2233
Radar Vertical Coverage Pattern
Compute and plot the radar vertical coverage pattern for a sinc antenna pattern. Specify a frequency of 100 MHz, an antenna height of 10 meters, and a range of 100 km. Assume the surface is smooth, the antenna is not tilted, and the transmitted polarization is horizontal.
frq = 100e6; anht = 10; rng = 100;
To specify the effective Earth radius, assume a high-latitude atmosphere model and a winter-like seasonal profile. Use the
refractiveidx function to compute the refractivity gradient in N-units per meter using the Earth's surface and an altitude of 1 km.
alt1km = 1e3; [nidx,N] = refractiveidx([0 alt1km], ... LatitudeModel="High",Season="Winter"); RGrad = (nidx(2) - nidx(1))/alt1km; Re = effearthradius(RGrad);
Compute the vertical coverage pattern using the effective Earth radius and the radar parameters.
[vcpKm,vcpangles] = radarvcd(frq,rng,anht, ... EffectiveEarthRadius=Re);
Use the refractivity at the surface in N-units to compute the refraction exponent.
Ns = N(1); rexp = refractionexp(Ns)
rexp = 0.1438
Plot the vertical coverage pattern in the form of a Blake chart.
blakechart(vcpKm,vcpangles, ... SurfaceRefractivity=Ns,RefractionExponent=rexp)
Ns — M-length refractivity at the surface
M-length refractivity at the surface in N-units, specified as a real scalar.
rexp — Refraction exponent
nonnegative real scalar
Refraction exponent or decay constant in km–1, returned as nonnegative real scalar.
CRPL Exponential Reference Atmosphere Model
Atmospheric refraction evidences itself as a deviation in an electromagnetic ray from a straight line due to variation in air density as a function of height. The Central Radio Propagation Laboratory (CRPL) exponential reference atmosphere model treats refraction effects by assuming that the index of refraction n(h) and the refractivity N decay exponentially with height. The model defines
where Ns is the atmospheric refractivity value (in units of 10–6) at the surface of the earth, Rexp is the decay constant, and h is the height above the surface in kilometers. Thus
The default value of Ns is 313
N-units and can be modified using the
argument in functions that accept it. The default value of
Rexp is 0.143859 km–1 and can be modified using the
name-value argument in functions that accept it.
 Bean, B.R., and G.D. Thayer. "Central Radio Propagation Laboratory Exponential Reference Atmosphere." Journal of Research of the National Bureau of Standards, Section D: Radio Propagation 63D, no. 3 (November 1959): 315. https://doi.org/10.6028/jres.063D.031.
 Dutton, E. J., and G. D. Thayer. Techniques for Computing Refraction of Radio Waves in the Troposphere. National Bureau of Standards Technical Note 97. United States National Bureau of Standards, 1961, revised 1964.