# refractionexp

CRPL exponential reference atmosphere refraction exponent

## Description

example

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

## Examples

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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], ...
LatitudeModel="High",Season="Winter");

Compute the vertical coverage pattern using the effective Earth radius and the radar parameters.

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, ...
SurfaceRefractivity=Ns,RefractionExponent=rexp)

## 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.

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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

$N=\left(n\left(h\right)-1\right)×{10}^{6}={N}_{\text{s}}{e}^{-{R}_{\text{exp}}h},$

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

$n\left(h\right)=1+\left({N}_{\text{s}}\text{\hspace{0.17em}}×{10}^{-6}\right){e}^{-{R}_{\text{exp}}h}.$

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.

## References

[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. https://doi.org/10.6028/jres.063D.031.

[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.

## Version History

Introduced in R2021b