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CRPL exponential reference atmosphere refraction exponent



rexp = refractionexp(Ns) computes the refraction exponent or decay constant of the CRPL Exponential Reference Atmosphere Model.


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Compute the refraction exponents for surface refractivities equal to 200 N-units, 313 N-units, and 450 N-units.

srfrf = [200 313 450];

rexp = refractionexp(srfrf)
rexp = 1×3

    0.1184    0.1439    0.2233

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], ...
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, ...

Use the refractivity at the surface in N-units to compute the refraction exponent.

Ns = N(1);
rexp = refractionexp(Ns)
rexp = 0.1440

Plot the vertical coverage pattern in the form of a Blake chart.

blakechart(vcpKm,vcpangles, ...

Figure contains an axes object. The axes object with title Blake Chart contains 14 objects of type patch, text, line.

Input Arguments

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M-length refractivity at the surface in N-units, specified as a real scalar.

Example: 313

Data Types: double

Output Arguments

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Refraction exponent or decay constant in km–1, returned as nonnegative real scalar.

More About

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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 SurfaceRefractivity name-value argument in functions that accept it. The default value of Rexp is 0.143859 km–1 and can be modified using the RefractionExponent name-value argument in functions that accept it.


[1] 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.

[2] 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.

Extended Capabilities

C/C++ Code Generation
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Version History

Introduced in R2021b