(n-1) 106

400

FOR p=1000 MB

380

360

340

320

300

280

PER CENT RELATIVE HUMIDIT

100

80

60

40

120

260

FIGURE 18. Relation of n to temperature and relative humidity.

In order to compute M directly from temperature, relative humidity, and height data, the nomogram (Figure 19) has been constructed. Detailed instructions for its use are given.

The National Advisory Committee on Aeronautics [NACA] standard atmosphere commonly used in aeronautics assumes a sea level pressure of 1,013 mb (= 760 mm Hg) and a sea level temperature of 15 C, decreasing at a rate of 6.5 C per kilometer in the lower atmosphere. The NACA standard atmosphere is not concerned with the moisture content. In the actual atmosphere the moisture may vary between extremely wide limits, but as a typical value a relative humidity of 60 per cent may be assumed as the

By using this formula in conjunction with Table 1 it is easily shown that k% for the dry standard. atmosphere, and k=% for the standard atmosphere with a 60 per cent relative humidity. This value of k is the one commonly adopted in coverage diagrams corrected for standard refraction.

Because of the great variability of the moisture content of the atmosphere with season, geographical

location, etc., a moist standard atmosphere has a limited physical significance. The standard should rather be defined in terms of a fixed linear slope of

the refractive index, and for this purpose the value

k=% has been chosen.

17.2.2 The Measurement of Refractive Index

The lower atmosphere frequently is stratified by nonstandard distributions of temperature and humidity which vary rapidly and irregularly as functions of the height. The refractive index is then no longer linear but has a more complicated dependence on height, determined from equation (16). The stratification which is of particular importance in tropospheric propagation is found in the lower part of the atmosphere, that is, below about 4,000 to 5,000 ft and frequently in the lowest few hundred feet above ground.

Since the variation in the atmospheric pressure gradient is small, interest is mainly centered in the dependence of the modified refractive index M on the temperature and humidity distributions. Methods, useful in the field, have been developed for obtaining rapid determinations of temperature and humidity in the lowest levels of the atmosphere. The ordinary radiosonde (radiometeorograph) is not well adapted for this purpose since it is usually designed to give data at levels about 100 m apart, which often is not

close enough to reveal the significant details of the M curve. Consequently it has proved to be necessary to develop new instruments for this purpose.

Several types of instruments have been designed which can be placed on towers, or carried by slowflying airplanes or dirigibles or carried aloft by captive balloons or kites with wires connecting the temperature and humidity elements to measuring or recording equipment located on ground or aboard ship. Some such measurements have been made with instruments using electrical methods in which dry and wet electrical resistance elements are connected into a circuit to give "dry bulb" and "wet bulb" temperatures. Another electrical method uses the same "dry" temperature element but, in place of the wet bulb, obtains a relative humidity measurement by using an electrolytic humidity element of radiosonde. Hair hygrometers are definitely not the type employed in the U. S. Weather Bureau suitable for this type of work on account of their lag in adjusting themselves to changes in relative

humidity (of the order of 3 to 5 min for appreciable changes in humidity).

Measurements made from airplanes have the

advantage that it is possible to survey a compara

tively large area within a short time. This can be of great importance along coasts where conditions in the lowest levels of the atmosphere sometimes change rather rapidly with increasing distance from the shore. In the absence of suitable special equipment an ordinary psychrometer held out of the window of a plane will give quite satisfactory results in slowflying planes, providing care is taken to keep the wet bulb sufficiently moist. When measurements are made from an airplane the height above the ground is determined for each measurement by means of the plane's altimeter. Unless carefully done this introduces the possibility of considerable error.

In another method captive balloons, kites, ordinary radiosonde balloons, and, occasionally, barrage balloons have been used to carry the measuring elements aloft. Ordinary captive balloons will work in wind speeds up to about 8 miles per hour; in higher winds kites or, occasionally, barrage balloons are used. Kites can be flown from boats even at low wind speeds or in calm weather. With this type of equipment the electrical measuring elements aloft are connected to an indicating or recording instrument at the ground or aboard ship by means of fine insulated wires that are wound around the cable. holding the balloon.

For the standard atmosphere the M curve increases with height as shown in curve I. For nonstandard atmospheres, the M curves will take one or another of the forms illustrated in curves Ia, Ib, II, IIIa, and IIIb. Of particular interest are those curves in which M decreases with height for a range of altitudes. (This decrease is the result of a sufficiently sharp decrease in n with height as illustrated in Figure 15.) In this event an inversion layer is formed in the atmosphere.

Throughout the range of altitudes of decreasing M the curvature of the rays exceeds the curvature of the earth. Nearly horizontal rays which either originate in, or penetrate into, this layer are trapped, and, if the layer extends far enough, energy may be carried to distances far beyond the geometrical horizon. However, the region in which the waves or rays are trapped may have a thickness or depth exceeding that of the inversion layer. This region is known as a duct. Its precise definition may be taken from Figure 20. It is the strip between an upper minimum of the M curve and either the ground or the point where the vertical projection from the upper minimum intersects the M curve. There are two main types of ducts, the ground-based duct,

illustrated by curves II and IIIb, and the elevated duct, illustrated by curve IIIa.

The height in the atmosphere at which the variations in refractive index occur may vary from a few feet to several hundred or even a few thousand feet. These variations are likely to be found at fairly low elevations in cold climates and at the higher elevations in warm climates. The meteorological conditions which yield these various M curves are described in Section 17.3.

The opposite effect occurs when the M curve takes the substandard form (curve Ib in Figure 20). Here the lower portion of the M curve has a slope which is less than standard. In this event the rays in the lower atmosphere are bent downward to a lesser degree than in the standard atmosphere or may even be bent upward. Depending to some extent upon the elevation of the transmitter, the field strength in the substandard region may be reduced considerably below normal, even to the point of producing a radar and communication "blackout.” If the M curve is steeper than average in the lowest layers, the transitional case arises (curve Ia). Here a slight change in the temperature and moisture distribution might lead to a curve of type II and a duct.

17.2.4

Rays in a Stratified Atmosphere

Nonstandard vertical variations of refractive index occur frequently in the lower atmosphere. In addition there may be gradual variations in the horizontal direction. So far, the theory of propagation has not reached a stage where such horizontal variations can be taken into account. Unless otherwise stated it is always assumed that the stratification extends horizontally as far as the coverage of the transmitter and that the variation in the M curve is entirely vertical. Weather conditions often are sufficiently homogeneous horizontally to warrant this assumption, but there are exceptions, mainly near coasts (see Section 17.3).

Only those rays are affected by the vertical variations of refractive index in the lower atmosphere which leave the transmitter at a very small angle. Both theoretically and practically it has been found that the effects of nonstandard refraction are negligible for rays that leave the transmitter at an angle with the horizontal of more than about 1.5°. Rays that leave at an angle with the horizontal of less than 1.5°, and especially those emerging at angles

with the horizontal of 0.5° or less, are strongly affected by nonstandard refraction. This part of the transmitter radiation is of paramount importance in early warning radar and in communications. For such applications of radar as gun-laying or searchlight control the effects of nonstandard propagation are usually negligible because the rays which reach the target have emerged from the transmitter at a fairly large angle with the horizontal.

The progress of a ray through the stratified atmosphere is described by Snell's law, discussed in Section 17.1.4. When the angle a between the ray and the horizontal is small

variations of the modified index. Although this ray tracing method is only an approximation of the true solution of the wave equation, it can be used, subject to certain limitations, for computing quantitatively the strength of the field. The approximation breaks down when neighboring rays cross each other and form caustics.

αι

=

The method may be illustrated by the case of standard refraction with k = %. As shown in Figure 21, draw the M curve with a slope ka 4a/3. Let the subscript 1 stand for the transmitter level (of height h1). Pass a vertical line through the corresponding point M1 of the M curve. Lay off the distance a12/2 to the left of M1 for a particular ray, 1, which emerges from the transmitter at angle an with the horizontal. In order to make a and M comparable numerically, the factor 10-6 should be eliminated from equation (18) above. For this purpose a2 should be measured in the same unit as M, that is, in 10-6 radian. The distance between M and 1 at any height h then is equal to (M — M1) + α12/2, and by equation (19) the square root of twice this quantity is equal to the slope of the ray at height h. Hence, ray 1 starting downward from the transmitter is bent more and more toward the horizontal as h decreases. At point P this ray becomes horizontal and from there on increases in slope with increasing height.

Ray 1' starting upward from the transmitter at the same angle a continues to curve upward more and more rapidly as the height increases. Ray 2 is the