## Atmospheric Effects On Propagation

1.3.1 Introduction

If a radio beam is propagated in free space, where there is no atmosphere (by definition), the path followed by the beam is a straight line. The transmission loss in free space was derived in Section 1.2.

However, a radio ray propagated through the earth's atmosphere encounters variations in the atmospheric refractivity index along its trajectory that causes the ray path to become curved (Ref. 6). Atmospheric gases will absorb and scatter the radio path energy, the amount of absorption and scattering being a function of frequency and altitude above sea level. Absorption and scattering do become serious contributors to transmission loss above 10 GHz and are discussed in Chapter 8. The principal concern in this section is the effect of the atmospheric refractive index on propagation. Refractivity of the atmosphere will affect not only the curvature of the ray path (expressed by a factor K) but will also give some insight into the fading phenomenon.

### 1.3.2 Refractive Effects on Curvature of Ray Beam

1.3.2.1 K-Factor. The K-factor is a scaling factor (actually assumed as a constant for a particular path) that helps quantify curvature of an emitted ray path. Common radiolinks, which are described as line-of-sight (LOS), incor-

rectly suggest that effective communications are limited by the optical horizon (i.e., K = 1). In most cases radiolinks are not restricted to LOS propagation. In fact, we often can achieve communications beyond the optical horizon by some 15% (i.e., K = 1.33). Figure 1.2 shows this concept in a simplified fashion, and Figure 1.3 shows the effects of various K-factors on the bending of the radio ray beam. This bending is due to angular refraction.

Angular refraction through the atmosphere occurs because radio waves travel with differing velocities in different parts of a medium of varying dielectric constant. In free space the group velocity is maximum, but in the nonionized atmosphere, where the dielectric constant is slightly greater due to the presence of gas and water molecules, the radio wave travels more slowly. In what radiometeorologists have defined as a standard atmosphere, the pressure, temperature, and water vapor content (humidity) all decrease with increasing altitude. The dielectric constant, being a single parameter combining the resultant effect of these three meteorological properties, also decreases with altitude (Refs. 7-9). Since electromagnetic waves travel faster in a medium of lower dielectric constant, the upper part of a wavefront tends to travel with a greater velocity than the lower part, causing a downward deflection of the beam. In a horizontally homogeneous atmosphere where the vertical change of dielectric constant is gradual, the bending or refraction is continuous, so that the ray is slowly bent away from the thinner density air toward the thicker, thus making the beam tend to follow the earth's curvature. This bending can be directly related to the radii of spheres. The first sphere, of course, is the earth itself (i.e., radius = 6370 km) and the second sphere is that formed by the curvature of the ray beam with its center coinciding with the center of the earth. The K-factor can now be defined as

the ratio of the radius, r, of the ray beam curvature to the true radius of the earth, r0, or r

where K is often called the effective earth radius factor and r is the effective earth radius.

1.3.2.2 Refractivity*. The radio refractive index is defined as the ratio of the velocity of propagation of a radio wave in free space to the velocity in a specified medium. At standard atmosphere conditions near the earth's surface, the radio refractive index, n, has a value of approximately 1.0003.

The atmospheric radio refractive index, n, can be calculated by the following formula:

where N, the radio refractivity, is expressed by

where P = atmospheric pressure (hPa)* e = water vapor pressure (hPa)* T = absolute temperature (K)

This expression may be used for all radio frequencies; for frequencies up to 100 GHz, the error is less than 0.5%.

For ready reference, the relationship between water vapor pressure e and relative humidity is given by

where H = relative humidity (%) t = Celsius temperature (°C)

es = saturation vapor pressure (in hPa) at the temperature t (in *C) The coefficients a, b, c, are as follows:

(valid between -20oCand +50oC, with an accuracy of ±0.20%)

(valid between -50oC and 0oC, with an accuracy of ± 0.20%)

Vapor pressure e is obtained from the water vapor density p using the equation e s ^ hPa <117)

*It should be noted that the World Meteorological Organization has recommended the adoption of hPa, which is numerically identical to mb, as the unit of atmospheric pressure.

where p is given in g/m3. Representative values of p are given in Recommendation 836.

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