Influence of Meteorological Factors on Radio Wave Propagation

N. B. Barakan, Leningrad

The lower layers of the atmosphere that interest us—the first 10–12 km, the troposphere, where meteorological processes mainly occur—may be regarded as a medium that is a dielectric whose conductivity is insignificant and may be neglected in calculations. According to data from various authors, the density of charges of each sign here is relatively small and on the average does not exceed \(2—3 \cdot 10^3\) singly charged ions per \(1\ \mathrm{cm}^3\), while the mass of most ions is many thousands of times greater than the mass of electrons. Therefore, in order to characterize the ability of the troposphere to affect radio waves, it is sufficient to use the dielectric constant of air \(\varepsilon\), or the refractive index \(n\) depending on it, without taking conductivity and electric charges into account. The calculations of Pedersen¹, Hulburt², and other authors may serve as a sufficient basis for this.

The physical state of the air in the troposphere changes both under the influence of strictly periodic causes—for example, the height of the sun—and owing to the action of nonperiodic factors, in particular meteorological processes. Meteorological processes give rise in the atmosphere to various regions that differ greatly from one another in temperature, pressure, degree of humidity, etc. The character of these regions changes with time, and, moreover, they possess the ability to move.

Radio waves passing through the atmosphere, upon encountering the boundaries separating different layers or regions, will undergo reflection and refraction, which must to some extent affect the intensity of the electromagnetic field at the receiving antenna.

It should be expected that meteorological processes will influence radio waves as they pass through the troposphere, and also in the higher layers through the ionosphere, which is subject to the influence of these processes.

The study of the influence of meteorological factors on the propagation of radio waves is, of course, of great importance for communications, and this has chiefly prompted work on this question up to the present time. At present, however, there has arisen a natural desire to use data on the propagation of radio waves for the weather service, especially for weather forecasting.

The possibility of using radio for sounding also the lower layers of the atmosphere, for characterizing air masses and observing their movement, would be of exceptional importance for meteorology.

In the present article, in a somewhat systematized form, the results of works by various authors devoted, directly or indirectly, to this question are set forth.

The relationship between meteorological factors and the conditions of propagation of ultrashort waves

It may be assumed that a change in the physical properties of the atmosphere in the lower layers affects radio waves of different wavelengths in the same way. But in the case of short, medium, and long waves, rays reflected from the ionosphere, as well as those propagating along the earth’s surface, when superposed, mask the action of atmospheric factors. In addition, it is also necessary to take into account the relative dimensions of radio waves and of the regions of the atmosphere where gradients of temperature and humidity exist. For example, a warm band of air 10 m across will be large enough to deflect a 5-meter wave, but will not noticeably affect a 100-meter wave. Therefore attenuation from the tropospheric layers is easiest to detect and trace on ultrashort waves (u. s. w.).

Indeed, some studies show that, when u. s. w. propagate over relatively large distances, facts are observed that cannot be explained by the action of any constantly acting and unchanging causes. This includes the circumstance that, in the propagation of u. s. w. over distances exceeding the distance of geometrical visibility, electric fields are quite often observed that are many times greater or smaller than the expected values. In addition, the magnitude of these fields is, as a rule, subject to very considerable irregular changes lasting from several seconds to days.

The cause of this is the refracting action of the lower layers of the atmosphere, due to the change of the refractive index of air with height.

In this case the radio ray will bend, and its radius of curvature satisfies the relation

\[ \rho = - \frac{n}{\dfrac{dn}{dh}}, \]

where \(h\) is the height above the earth, and \(n\) is the refractive index.

The change of the refractive index with height in the troposphere may be caused by the change with height of: a) atmospheric pressure, b) temperature, c) the amount of water vapor.

Let us consider the influence of these factors.

As is known, the refractive index of a medium and its dielectric constant are related to each other by the following relation:

\(n=\sqrt{\varepsilon}\) (for \(\mu=1\)). The dependence of \(\varepsilon\) on the medium can be expressed for a gas in the following way\(^3\):

\[ \varepsilon - 1 = K \frac{p}{T}, \]

where

\[ K = 12.5 \cdot 10^{19}\left(a_0 + \frac{\mu^2}{3kT}\right) \quad \text{and} \quad \frac{p}{T} = 6237 \frac{q}{M}. \]

Here \(p\) is the vapor pressure in millimeters of \(Hg\), \(T\) is the absolute temperature, \(k\) is Boltzmann’s constant, \(a_0\) is the polarizability of the molecule, \(\mu\) is the electric dipole moment of the molecule, \(q\) is the mass density, and \(M\) is the molecular weight in grams.

With regard to the influence of pressure, Hulburt\(^2\), on the basis of calculations, concludes that the pressure gradients observed in the atmosphere are rarely so large (except in cases of hurricanes and tornadoes) as to cause noticeable refraction of long or short waves.

As for temperature, for the most part it decreases with altitude. But quite often, at certain altitudes, temperature inversions are observed, i.e., an increase of temperature with altitude. Scholz and Eggersdorfer\(^4\), comparing data from the German postal and meteorological services for 1935/1936, came to the conclusion that air layers with abnormal temperature gradients can both increase and decrease the range of ultrashort-wave transmissions.

According to Hulburt, the direct dependence of the refractive index on temperature has the form:

\[ dn = -5.5 \cdot 10^{-7} dt. \]

According to calculations by Vvedensky and Arenberg\(^3\), rays tangent (at departure) to the earth’s surface could remain rectilinear only if the decrease of temperature with altitude were \(0.0342\ \mathrm{grad}/m\).

With a larger temperature gradient the ray bends and turns its convexity toward the earth; conversely, with a smaller temperature gradient the ray turns its concavity toward the earth. The ray would follow exactly parallel to the earth’s surface if the air temperature increased with altitude with a gradient of \(0.1282\ \mathrm{grad}/m\).

Hall\(^5\), in a 5-meter transmission over a distance of \(143\ km\), observed that the strongest signals were obtained when the temperature increased upward; signals of especially high intensity were received when warm tropical air flowed over cold polar air.

The presence of water vapor in the air should also affect the refractive power of the air. Water vapor, owing to its polar molecules, has a large dielectric constant and, although constituting only a few percent of the total composition of the air, noticeably increases the dielectric constant of the atmosphere.

For air, in the above formula,

\[ K_{\text{air}} = 211 \cdot 10^{-6}, \]

for water vapor,

\[ K_{\mathrm{H_2O}} = 182 \cdot 10^{-6}\cdot\left(1+\frac{5583}{T}\right). \]

According to Zahn’s work\(^6\), it may be assumed that the law of additivity is applicable to a mixture of air and water vapor. Applying this law to moist air, one obtains

\[ K=\left[211+a\left(\frac{10159}{T}-0.298\right)\right]\cdot 10^{-6}; \]

here \(a\) is the ratio of the elasticity of water vapor to atmospheric pressure.

For comparison of the dielectric constant of dry air and the dielectric constant of water vapor at different temperatures, the following table\(^3\) may be used.

Table 1

In addition, it should also be taken into account that the curve of the negative gradient of the pressure of water vapor is usually steeper than that for air, especially in summer. Therefore it is natural to ascribe various phenomena with radio signals on short waves, similar to fadings, mainly to fluctuations in the elasticity of water vapor.

Almost half of the water vapor present in the atmosphere is contained in the space up to a height of 2 km, and, consequently, the influence of atmospheric water vapor on the propagation of radio waves will be most noticeable in the lower layers.

Since the elasticity of water vapor may either increase or decrease with height, water vapor may cause the radio ray to deviate either upward or downward. In this case, a decrease in the radius of curvature of the ray leads to an expansion of the horizon of audibility.

We shall also briefly dwell on the question of the influence of fog, clouds, and rain on the propagation of radio waves. Theoretically this question was examined in detail by Stratton\(^7\). The smaller the sizes of the droplets in comparison with the wavelength, and the smaller their concentration, the less the medium affects the scattering and absorption of radio waves. We give a table in which the scattering coefficients \(\sigma\) of electromagnetic waves, calculated by Stratton, are indicated for various meteorological conditions.

Here \(\sigma\) represents that part of the wave intensity which is lost in passing through a unit length of the scattering medium.

In the columns denoted by \(Z\), the distances in kilometers are given which the wave must travel for its intensity to decrease to \(1/10\) of its initial value.

From Table 2 it follows that the scattering of radio waves with wavelengths greater than 5 cm, produced by rain and fog, is very insignificant and practically does not occur.

Table 2

In addition, Pedersen¹, who likewise considered the influence only of droplet-liquid water, showed that the coefficient of reflection of radio waves from the boundary surface formed by a cloud or a fog wave is very small.

A number of experimental works have been devoted to the study of the influence of the lower layers of the atmosphere on ultrashort-wave transmission. Thus, Person and Ulrich⁸ found that the most stable reception of u.s.w., as a rule, occurred under established meteorological conditions at the earth’s surface; moreover, it did not depend on the numerical values of individual meteorological elements. A strong wind was also usually accompanied by comparatively stable reception. Sharp changes in meteorological conditions (temperature, humidity), however, were accompanied by fading of radio signals. These fadings are more sharply expressed in summer than in winter, and on hotter days they occur considerably more often than on cold days. The authors mentioned also observed that during the approach of a dense fog very rapid and deep fadings appear; after the fog has become established, however, reception becomes completely stable. But the effect on u.s.w. is due above all not to the air medium immediately at the surface of the earth, but to the state of the atmosphere in the nearest 2–3 km of height. Inhomogeneities encountered in the atmosphere with height change the path of the radio rays.

At the receiving point of u.s.w. a direct and a reflected ray may arrive simultaneously, which gives rise to an interference field. Since the paths of these rays do not coincide, a change in the physical properties of the air will affect each of the rays differently, as a result of which reception will prove unstable. The change in the phase of u.s.w. when they pass through moist air, in comparison with the case of propagation in dry air, is given by the expression:

\[ \vartheta = \frac{2\pi}{\lambda}\left(\sqrt{\varepsilon} - \sqrt{\varepsilon_0}\right) r; \]

here \(\varepsilon\) is the dielectric constant of moist air, \(\varepsilon_0\) that of dry air, and \(r\) is the distance.

As is evident from the formula, with shortening wavelength the change in phase increases. Substitution of numerical values gives ...

it should be noted that even in transmissions over short distances (1 km), a change in the moisture content of the atmosphere causes a noticeable phase difference. This phase difference between the direct and reflected rays, arising as a result of a certain distribution of moisture in the atmosphere, will be the more significant the more the paths of the rays differ from one another.

Englund, Crawford, and Mumford[^9] carried out many observations to study the influence of physical inhomogeneities of the atmosphere on the propagation of ultrashort waves. Conducting experiments with transmissions across the sea on ultrashort waves of length from 1.6 to 4.8 m over a distance of 112 km, they arrived at the following conclusions: records of the received strength of two waves of identical polarization, but of different length, received simultaneously, prove to be somewhat different from one another even in the case when their wavelengths differ by no more than 2%.

The shorter wave exhibited deeper fading.

If transmission was carried out simultaneously on radio waves of the same wavelength but differently polarized, then the records showed that the horizontally polarized wave always had deeper and faster fading than the vertically polarized one. In contrast to these fadings, which lasted 1–5 min., rapid oscillations, the so-called “twinklings,” were also observed on the recording curve; their number per 1 min. reached up to five.

A special check carried out by the authors showed that the observed fading has as its cause the interference structure of the electromagnetic field. Thus, in the reception of ultrashort waves, the resultant intensity of the arriving waves is composed of the intensities of several field components that interfere with one another. The cause of the appearance of these components, as the authors believe, is the inhomogeneity of the atmosphere.

Englund, Crawford, and Mumford[^10], beginning in July 1934, also carried out reception of ultrashort waves for two years over a water surface near New York at a distance of 112 km.

They transmitted on wavelengths from 1.6 to 5 m, throughout the entire day, in all types of weather.

On the screen of the cathode oscilloscope which they used there appeared more or less complex figures of standing waves, owing to the arrival, along different paths, of several components. For those cases when the number of components did not exceed two, it was possible to calculate the path difference for these two waves. Between the components there was a path difference ranging from several meters up to 550 m. A path difference of 550 m is equivalent to 5 km in height. All the reflecting layers lie below this height, and most of them below 2 km.

Using data from aerological observations carried out simultaneously and obtained from the Weather Bureau, the authors constructed a curve of the change of the dielectric constant with height for the time when they were receiving radio signals. In more than half the cases, the presence of discontinuities in the dielectric constant was thus recorded. The authors then marked the height of the reflecting layers in cases where the oscillograms formed—

were found with only two components. As can be seen from the figures presented (Fig. 1), both methods give consistent results both as to the presence and as to the position of the boundary surfaces.

Fig. 1. Location of reflecting layers according to aerological sounding data (left) and radio measurements (right)

England, Crawford, and Memford[^10], using data on North American air masses, calculated the effective radius

of the earth for different air masses, as well as the jump in the dielectric constant at the boundary between them. As the effective radius of the earth, which they use as a measure of the refracting power of the air, they take that radius of the earth for which radio signals would travel in a straight line if the atmosphere were homogeneous.

The results of the authors mentioned are given in Tables 3 and 4.

Table 3

\(^{1)}\) \(R\) = radius of the earth

A jump in the dielectric constant of \(10 \cdot 10^{-6}\) or more can create a reflected component of the ultrashort waves of the same order as the direct ray, and, thus, the method of using radio

Table 4

Jump in dielectric constant between air masses \(\Delta \varepsilon \cdot 10^{6}\)

waves for detecting air masses located at a certain height may be recognized as quite sensitive.

Vvedenskii and Arenberg\(^{2}\) point out that “in the future attention should be paid to clarifying whether the reception of ultrashort waves at great distances is a consequence not only of ‘lower’ rays tangent to the earth, but also of rays initially proceeding upward at some angle and encountering on their path in the atmosphere such physical inhomogeneities whose action is sufficient to return them to the earth.”

At the same time it must be assumed that the refracting and reflecting action of these inhomogeneities can exert a noticeable influence on the propagation of ultrashort waves, chiefly in links over great distances (in any case exceeding the distance of geometrical visibility). These considerations seem to be confirmed by the indications of some authors that, when the distance between transmitter and receiver was increased while passing beyond the limits of geometrical visibility, a weakening of reception was observed, which again became stronger with a further increase in distance.

Mimno^11 believes that observations of the range of propagation of waves of length 5 m may be used to study the displacement of air masses.

It is possible that the organization of simultaneous systematic observations of the propagation of ultrashort waves and of meteorological factors will provide a new method for weather forecasting. This would be especially valuable for regions and seas that are difficult of access.

*

The relation between individual meteorological elements and the layer of reception of long and broadcast waves

A number of works, especially from an earlier period, is devoted to clarifying the relation between the intensity of incoming radio waves of the broadcast and long-wave ranges and individual meteorological elements. Since it is rather difficult to trace the values of these elements along the entire path, and since they are moreover variable, the comparison was usually made with meteorological data obtained in the vicinity of the transmitting and receiving stations. A comparison of this kind was carried out by the Japanese Eitaro Yokoyama and Tomozo Nakai^12, who made use of observations of the transmissions of six stations located at various distances from 3,000 to 11,000 km and operating on wavelengths from 11,000 to 20,000 m. They came to the conclusion that the observed field intensity depended more on changes in meteorological elements in the vicinity of the receiving stations than in those of the transmitting stations. With a decrease in temperature and absolute humidity at the receiving station, the field intensity in daytime and nighttime reception increases and, conversely, falls as they increase.

The relation between field intensity and barometric pressure is less pronounced, but it nevertheless seemed that there was some direct dependence between them in summer and an inverse one in winter. These results were obtained by correlating both monthly means and diurnal variations.

The relation of intensity to weather proved to be weakly expressed. However, it was possible to observe an increase in signal strength when the weather changed from “cloudy” or “rainy” to “clear,” and a decrease in signal strength when the weather changed from “clear” to “rainy.”

A dependence of the same type was found by Jowett^13, comparing weather conditions with radio reception when receiving a wave 350 m long at great distances from the transmitter.

Austin^14 also noted that the field intensity varies inversely with the air temperature on the receiving side. He studied these phenomena over short distances of 281 and 251 km with daytime waves of length 13,600 and 15,900 m. The same was also found by Minohara^15, who observed daytime waves at 11,490 m over a distance of 6,400 km. However, Pickard^16 found, with nighttime waves of broadcast frequency over distances from 640 to 1,120 km, that the change in field intensity at night is directly related to the temperature and inversely related to the pressure on the receiving side.

The difference between this result and the preceding ones is possibly explained by the difference in wavelengths. But Pickard likewise found no relation between the temperature at the transmitter and the strength of reception.

In 1927, comparing nighttime reception in the broadcast range with the pressure gradient between the transmitter and the receiver, Pickard^17 was unable to establish the presence of any dependence.

There are still a number of works which indicate that a connection exists between the strength of radio reception and meteorological elements, in particular temperature and relative humidity. However, the work of Ralph Glover^18 compels one to treat such results with some caution. Over the course of a month this author monitored the sensitivity of a highly sensitive broadcast-band receiver. It turned out that the sensitivity of this receiver may undergo considerable changes even when the receiver is maintained under ideal conditions. Comparison with relative humidity showed that periods of high receiver sensitivity coincide with periods of low relative humidity, and vice versa. Such effects of relative humidity on the receiver may manifest themselves over the course of 1–4 days. These changes in sensitivity should be attributed to various kinds of losses arising in the high-frequency parts of the receiver.

It cannot, of course, be asserted that the results of the works cited above^12–17 were caused by reasons depending on the receiver circuit, but in any case they are subject to further verification with well-controlled apparatus.

Relation between weather and the strength of radio reception

In order to investigate the dependence of radio-wave intensity on barometric pressure, in recent years synoptic data on the passage of cyclones and anticyclones through the locations of stations have begun to be used for comparison. A considerable number of experimental studies have been carried out in this direction.

As early as 1924, Bureau^19 noted that the field intensity of received radio waves changes if the receiving or transmitting stations, separately or both simultaneously, are under the influence of an anticyclone, or when the stations are separated by a surface of discontinuity—the boundary of two different air masses.

Pickard^16 established that, in reception in the state of Massachusetts of transmissions from station WBBM, located in Chicago, the strength of reception

is affected by the passage through Massachusetts of the centers of cyclones and anticyclones. The intensity of the signals weakens before and increases after the passage of a low-pressure area, and, conversely, reception proves better before and worse after the passage of a high-pressure area.

The dependences he obtained are shown in Fig. 2, where the solid line gives the relationship between the change in reception strength and the passage of a cyclone, while the dashed curve gives the relationship between reception and an anticyclone.

Especially active in the use of data on radio-reception strength for weather forecasting is the American Colwell.

In 1927–1928 he received radio signals in Morgantown at a wavelength of 309 m from station KDKA in Pittsburgh, located on the same meridian as Morgantown, at a distance of 60 miles. His observations showed that the intensity of night signals was, on average, either equal to, less than, or greater than the intensity of daytime signals.

Fig. 2. Radio reception and the passage of cyclones and anticyclones through Massachusetts

Comparing changes in the intensity of radio signals received in Morgantown with meteorological conditions, Colwell discovered a number of interesting regularities. He found that an increase in the intensity of signals in the morning after a nighttime decrease signified for the weather a tendency toward rain, and, conversely, a further decrease in signal strength after nighttime weakening predicted good weather. If, however, the nighttime signal by morning remained on average unchanged in intensity, then the weather on the following day remained approximately the same as on the day when the curve was obtained (Figs. 3, 4, 5).

This made it possible for the author, on the basis of the calculated data, to predict weather conditions from the intensity of radio signals one day in advance (12–24 hours). Thus, he noted that an increase in intensity during the indicated time by 75–100% pointed to rain on the following day, while an increase in intensity by only 50% pointed to cloudiness on the following day. If the day of receiving signals with an intensity increased by 50% was itself cloudy with a tendency toward rain, then rain fell on the following day. A very strong increase in signal intensity after nighttime weakening almost invariably foretold the approach of a storm. Conversely, a 50% drop in intensity after a thunderstorm day predicted good weather for the following day.

From June 1927 to January 1928 Colwell obtained fifteen curves, and in only one case was the prediction not confirmed.

Thus, the degree of accuracy of the forecast is \(93\%\). This applies to both winter and summer months; only in March and April did the results prove less accurate.

In 1933 Colwell\(^{21}\) published an article in which, in developing this question, he sets forth the results of five years of work. He compared the change in the intensity of radio signals received from Pittsburgh at Morgantown during the transition from nighttime to daytime, with the passage through these cities of cyclones and anticyclones.

Fig. 3. 20/XI 1928. Increase in intensity after the nighttime drop. Indication that on November 21 there will be thunderstorm conditions

From several hundred curves obtained in the observations, it was established that an area of high pressure covering Pittsburgh and Morgantown, with its center north of Morgantown, causes the nighttime intensity to fall below the daytime one; at the same time, an area of low pressure occupying both cities, with its center north of Morgantown, causes the nighttime intensity to be somewhat greater than during the day.

An area of low pressure south of Morgantown causes reduced intensity at night.

Fig. 4. 18/XI 1928. Decrease in intensity after the nighttime drop. Indication of clear weather on 19/XI

Colwell’s data on the intensity of radio waves were used by West Virginia University to indicate the presence of cyclones and anticyclones, thus providing assistance in weather prediction. Over three years, from 1927 to 1930, the forecasts proved correct in almost \(90\%\) of cases.

To these observations of Colwell adjoin Ranzi’s\(^{22}\) studies on finding a connection between the troposphere and the \(E\) layer. From May 1931 to June 1932 he carried out, for 330 days, daily observations at short intervals of the reflection height of 100-meter waves. As is known about 100-meter waves, they are usually reflected from the \(E\) region in the daytime, and also for some time before sunrise and after sunset; at other times they are reflected from the \(F\) region.

Fig. 5. 9/X 1928. The intensity is the same as at night. Absence of changes in weather conditions

But reflections from the $E$ layer are often observed at unusual times and sometimes continue after sunset, even until midnight.

In other cases, after the disappearance of signals at sunset, the reflection appears again several hours later. Ranzi came to the conclusion that these increases of ionization in the $E$ region even after the action of ionizing solar radiation has ceased are accompanied by special isobaric situations characterized by the presence of barometric depressions at the place of observation or to the north of it.

Under anticyclone conditions, or under depression conditions to the south, reflection of 100-meter waves from the $E$ layer ceases within a short time, since from noon onward the ionization density then rapidly decreases. Of Ranzi’s 330 daytime observations, only 10 constituted exceptions to the indicated rules.

Colwell explains the relation he observed by the fact that the $E$ layer is subject to the influence of cyclones and anticyclones. In his supposition, the $E$ layer, present during the day over a certain extent (thickness) in the atmosphere as a result of the action of sunlight, completely disappears at night in an anticyclone and becomes many times stronger in the region of a cyclone. This circumstance affects the intensity of the received signals because the signals from Pittsburgh travel to Morgantown along two paths—by a sky wave and by a ground wave. During the day the ground wave is more intense, but the weak reflection from the $E$ layer slightly increases the received energy. At night, in the region of high pressure, there is no $E$ layer and, consequently, no reflection; therefore the night signal becomes somewhat weaker than the daytime one. In a region of low pressure the $E$ layer is very intense at night; as a result, there is a large increase in the intensity of radio signals after sunset.

As early as 1933, Colwell and Meers^22, while simultaneously carrying out observations of short waves (6140 kilocycles) from station W8XK and long waves—KDKA (980 kilocycles)—and comparing the results with synoptic charts, came to the conclusion that changes in barometric pressure affect only long waves, whereas the propagation of short waves does not depend on the weather. Since the propagation of long waves depends on the $E$ layer, and that of short waves chiefly on the $F$ layer, the authors express the opinion that only the $E$ layer lies within the region associated with changing pressures, whereas the $F$ layer is already outside this region.

All the above-mentioned authors express no considerations concerning the causes that determine the presence or absence of the $E$ layer at night as a function of particular meteorological formations.

It should also be noted (as Colwell also allows) that such dependences between signal intensity and meteorological conditions may turn out to be characteristic only for the given locality. A dependence sought under other geographical conditions, with ...

in a different mutual arrangement of the receiving and transmitting points and at other wavelengths may prove to be different both qualitatively and in sharpness.

More definite data concerning the connection between the ionization layers were published in 1937 by Leithauser and Beckmann[^24]. These data may possibly also serve to explain the results obtained by Colwell et al.

The authors suppose that, since in the region of the layers \(D\) and \(F\), situated comparatively low above the earth’s surface, the gases are still fairly dense, friction in the gases must still have an effect here. It is therefore possible that the upper air currents, in addition to other factors, also exert some influence on these layers, in particular on changes in their height. Since on the sunrise side the motion of the earth counteracts the diffusion of charge carriers toward the dark (night) side, at sunrise the appearance of meteorological influences will be less noticeable than at sunset. In this connection one should expect that a strong wind of westerly direction affects the displacement of charges differently than an easterly wind.

The closer the direction of the wind is to the westerly direction, the greater will be the quantity of ions that it carries with it into the region no longer illuminated by the sun, and the more slowly, in such a case, will the decrease of ionization and the apparent change in the height of the layers take place. With an easterly wind the opposite dependence should occur, i.e., the ionization should decrease more rapidly than in the case when there is no wind.

Thus, from observations of the layer \(F\) one may judge the processes that occur in regions located considerably lower. It should not, of course, be thought that the process which causes the change in the rate of ascent of the layers during the transition from day to night must also occur at an altitude of 200–300 km. This process may, however, affect the intermediate ionized regions that lie in the layers \(E\) and \(D\). For a change in the apparent height of a layer, two processes are possible: either a decrease of ionization in the layer \(F\) itself, with the observed point of reflection appearing to move upward, or a weakening of ionization in the lower layers, which will cause, upon measurement, an increase in the group velocity and, consequently, an apparent decrease in height. In particular cases the apparent height may remain unchanged as a result of the simultaneous action of both processes.

The observations made by Leithauser and Beckmann at the stations Pieskow and Schasmitzelsee were compared with meteorological data taken partly from the weather map and partly at the observatory in Lindenberg.

The dependence proposed by Leithauser and Beckmann between the course of the reflection curve (echo curve) and the winds at great heights was actually found. The authors established that, with strong westerly winds at great altitude, the rise of the layer in the transition from day to night almost always occurs more slowly than with easterly[^24]: Leithauser and Beckmann.

in the course itself. Fig. 6 shows the results for August and October 1936. Curve a gives the values of the steepness of ascent, expressed in arctangents, for the given days. Since here a process occurring in the evening is being considered, the points on the intervals of days are shifted to the right. Curve b gives the daily variation of the winds at an altitude from 3,000 to 4,000 m according to kite observations in Lindenberg (not far from the observation point).

Above the zero line are plotted the components of the easterly direction; below it, those of the westerly direction.

The dotted-dashed line gives the wind force measured in the morning, at 8 o’clock, and the dashed line at 17 o’clock. As can be seen from the figures, the curves

Fig. 6

a — steepness of ascent of the ionization layers, b — upper winds

a and b have almost the same course. The correlation coefficient obtained in this case for the steepness of the echo curves and the evening wind is six to seven times greater than its mean error.

As to the force and direction of the winds at the altitudes of interest (50–100 km), reliable data cannot yet be obtained, since pilot balloons reach only 30–40 km.

However, referring to the work of Peppler²⁵, Leithauser and Beckmann come to the conclusion that their work has established the fact of a dependence between the upper air currents and the observed change in the apparent height of the ionization layers.

If this point of view were confirmed, then, in addition to the fact that it would be possible to explain Colwell’s observations concerning the connection between baric formations and ionization in the upper layers of the atmosphere, this view could be made the basis of further investigations aimed at establishing a dependence between the propagation of radio waves and meteorological conditions.

It should only be pointed out that there is some divergence in interpretation between these authors and Colwell. Colwell believes that meteorological conditions can influence the layer \(E\), whereas the layer \(F\), in his opinion, remains beyond their influence. Leithauser and Beckmann, however, ascribe in this respect a large role to the layer \(F\).

Other works also confirm the existence of a dependence between the state of the ionosphere and meteorological processes. Thus, Appleton and Weekes\(^{37}\), following the behavior of the ionosphere, discovered phenomena of tides and ebbs in the upper layers of the atmosphere, caused by the influence of the moon; in doing so they were able to observe pressure oscillations with a relative amplitude \(\left|\dfrac{dp}{p}\right|\) of \(0.068\) at an altitude of \(110\) km.

Connection between thunderstorms and the ionosphere

There are a number of works in which the possible influence of thunderstorm phenomena on the propagation of radio waves is considered.

We shall examine those theoretical considerations which give grounds for expecting that thunderstorm activity must in some way affect the ionosphere and, consequently, the propagation of radio waves. This question was first considered by Wilson\(^{26}\) and analyzed in detail by Baro and Siam\(^{27}\).

According to Wilson’s conclusion, essentially confirmed by the most recent investigations of Simpson and Scrase\(^{28}\), the upper part of thunderclouds is positively charged, and between the cloud and the ionosphere an electric field is formed so strong that an electrical breakdown may occur directly beneath the ionized layers, where the pressure is much lower than near the cloud.

Appleton\(^{29}\) calculated that even when the field near the cloud amounts to only \(1/27\) of the breakdown voltage, at a distance of \(7\) km from the ionized layer it can already reach the breakdown value and cause the appearance of intense ionization currents and, consequently, an additional ionized layer.

From this point of view it is of interest from what maximum horizontal distance thunderclouds can influence the ionosphere at the point above the place of observation. According to Wilson, a thundercloud has an electric moment \(M\), which can be calculated by taking into account the moments from the upper and lower charges of the cloud and their corresponding images in the earth.

Fig. 7

\(O\) — position of the cloud, \(Q\) — place of observation, \(P\) — part of the ionized layer.

Such a cloud creates at a certain point at height \(h\) above the earth a field equal to

\[ \frac{2M}{h^3}. \]

If such a cloud is located above the point \(O\), at a horizontal distance \(d\) from the place of observation \(Q\) (Fig. 7), then the intensity of the vertical electric field at \(P\) from this cloud will be

\[ \frac{M}{(h^2+d^2)^{5/2}}(2h^2+d^2). \]

The value of the electric field at \(P\) from a thundercloud with electric moment \(M\), located at various horizontal distances \(d\) from \(Q_1\), is given in Table 5.

Table 5

Change of the electric field with distance

As the cloud recedes, the electric field produced in the region of the ionosphere above the place of observation gradually decreases. The composition and pressure of the air at an altitude of 80 km (the boundary of the Kennelly–Heaviside layer) are not sufficiently well known to determine the magnitude of the minimum electric moment that a thundercloud must possess in order to create an electric field of breakdown value at this altitude. But it is easy to calculate (see table) that if at the height of layer \(E\), directly above the thundercloud, the field does not exceed 30 times the breakdown-voltage value, then thunderclouds located beyond 200 km will produce no appreciable action in the ionosphere above the point of observation.

However, Pedersen\(^1\), who had earlier also considered this question, indicated that if one uses the value of the electric moment of a thundercloud given by Wilson,

\[ M = 3\cdot 10^{16}\ \mathrm{CGSE}, \]

then one can calculate that at height \(h\) above thunderclouds the field will be

\[ E=\frac{2M}{(10^5h)^3}=\frac{60}{h^3}\ \mathrm{CGSE}=\frac{18\,000}{h^3}\ \mathrm{V/cm}, \]

at an altitude \(h=60\) km, \(E=0.08\ \mathrm{V/cm}\). But since the mean free path of electrons at this altitude is 2 or 3 mm, an electric force of this magnitude is not capable of producing appreciable ionization even if \(E\) were ten times larger.

In addition, the displacement of ions and electrons will compensate this field. This compensation requires a surface density of \(2\cdot 10^{-5}\) CGSE per \(1\ \mathrm{cm}^2\), corresponding to \(5\cdot 10^4\) ions per \(1\ \mathrm{cm}^2\).

Since the volume density of ions at this altitude during the day and night is about \(10^4\) per \(1\ \mathrm{cm}^3\), compensation of such a field will require the displacement of ions over only 5 cm. Therefore Pedersen considers it impossible to recognize any influence of the charge in the troposphere on the ionization of the upper layers.

Wilson also indicated another process by which thunderclouds can cause enhanced ionization in the upper atmosphere. Electrons arising in clouds either as a result of radioactive processes or as a result of electric discharges, under the influence of a strong electric field, usually directed downward, will move upward. In doing so they should acquire energy rather quickly, because its increase exceeds the loss of energy due to collisions with particles. But the current of these upward-moving electrons, after passing the upper boundary of the cloud, must be drawn back under the influence of the electric field, which above the cloud is directed upward.

When a discharge occurs in the clouds the field is destroyed, and the flux of electrons rushes upward at high speed toward the ionosphere. Depending on their initial velocity they either are deflected downward by the earth’s magnetic field, or reach the \(E\) layer. In the latter case the moving electrons can intensify the ionization of the \(E\) layer.

If the effect of collisions with neutral atoms and molecules is neglected, then the force produced by the earth’s magnetic field is the only force that remains to act on these upward-moving electrons. Therefore the electrons will describe circles whose radius of curvature depends on their initial velocity.

The radius of curvature \(\rho\) of the trajectory of such a particle in a magnetic field \(H\) gauss, when it has an initial energy of \(v\) eV, is given by the expression:

\[ \rho=\frac{v}{300H}. \]

At atmospheric pressure, one high-energy electron creates about forty ion pairs per \(1\ \mathrm{cm}\) of path. For each pair 30 V is expended. A particle with a large initial energy therefore loses \(1200\) V of its energy for each centimeter of path. It has been found that electrons with an initial energy of less than \(2\cdot 10^9\) V do not manage to reach the earth and are absorbed in the region between the earth and an altitude of 20 km at distances up to 150 km from the center of the thunderstorm. The region where the electron trajectories end possesses intense ionization.

Electrons of such high energy as \(5\cdot 10^9\) eV move at a speed only a few meters per second less than the speed

light, so that their inertial mass becomes approximately two hundred times greater than the rest mass. Taking the intensity of the horizontal component of the magnetic field to be equal to 0.3765 gauss (which is the case for Calcutta, where Bar and Siam worked), one can see that the electrons with the greatest possible energy will describe circles with a radius of curvature of 100 km, which is the maximum limit. As the energy decreases, the radius of curvature decreases.

The frictional force due to collisions with oncoming molecules also tends to reduce the radius of curvature. On the other hand, the electrons must move along a circle with a minimum radius of curvature of 80 km in order to reach the surface of the layer \(E\).

It follows from this that the magnitude of the radii of curvature that must be taken into account lies within the limits from 80 to 100 km. Thus, after a simple calculation, it turns out that a thundercloud which, by means of the electrons it carries, can affect the ionosphere must be located at such a distance from the point of observation that some fraction of the electron trajectories passes through the point \(P\) or vertically above it. This distance, according to the calculations, lies within the limits from 160 to 40 km from the point of observation. If the cloud is closer than 40 km and farther than 160 km, then the electrons emitted by it deviate from \(P\) and will not affect the ionization state at this point.

To study the influence of thunderstorms on the ionization of the ionosphere, Bar and Siam\(^{27}\) undertook observations of the ionosphere in Calcutta in 1935. Bengal, as a subtropical region, is convenient for this purpose for the reason that here, almost regularly, at a definite time of day and year, intense thunderstorm activity occurs. At the same time, owing to the low latitude (\(22^\circ 33' \mathrm{N}\)), the influence of magnetic storms on the ionosphere should be considerably weaker here than at high latitudes.

The records of ionospheric observations were compared by the above-mentioned authors with data on thunderstorms. Proceeding from Wilson’s proposition, they came to the conclusion that in places where the inclination of the terrestrial field is small (in Calcutta \(1^\circ \mathrm{W}\)), electrons going upward into the ionosphere in the direction from the thundercloud should affect the ionization of that part of the ionosphere which is situated to the east of the thundercloud. Therefore, with respect to the ionization created by the electrons carried along, they considered only the thundercloud located west of Calcutta and lying within the limits from 160 to 40 km.

The observations made by Bar and Siam made it possible for them to establish that between the presence of thunderstorms and an abnormal increase of ionization in region \(E\) there is a connection with a correlation coefficient of 0.50.

Healey\(^{30}\) investigated the influence of a thunderstorm on the ionization density of layer \(E\), calculating the motion of electrons in gases under the action of electric fields. He established that during a day only less than \(1\%\) of lightning flashes causes a noticeable increase in ionization,

at night this fraction increases considerably. If, however, there is a constant electric field in the ionosphere of the order of \(0.5\ \mathrm{V/m}\), then such an increase should often be noticeable.

Carrying out observations, Lutkin\(^ {31}\) found a correlation coefficient of 0.75 between the ionization density in the \(E\) region and the intensity of atmospherics within 3,000 km of the observation site. Since it may now be regarded as established that atmospherics are caused by lightning, his results argue for the existence of a connection between thunderstorms and the state of the ionosphere.

Ratcliffe\(^ {32}\) likewise found a connection between the state of the \(E\) layer and thunderstorms.

Watson-Watt\(^ {31}\) attributes sudden local increases in electron density in the upper layers to the influence of local thunderstorm activity.

In Cambridge\(^ {11}\), before a thunderstorm, during the thunderstorm, and after it, transmission and reception were carried out at a wavelength of 86 m; the height of the ionized layers was determined at the same time.

Fig. 8 shows the curve of the height of the \(F\) layer, which is the mean of twenty-two records during a thunderstorm. The visible increase in the height of the layer during the thunderstorm can be explained by a decrease of the group velocity in the lower-lying layers through which the radio waves must pass. The curve for the \(E\) layer, constructed from three cases, is in complete agreement with the curves for the \(F\) layer, but shows the greatest delay of the echo at the moment when the thunderstorm begins.

Fig. 8. Activity of ionized layers and thunderstorms

Mimno believes that during a thunderstorm enhanced ionization of the upper layers of the atmosphere may occur, which often spreads downward and passes into the absorbing \(D\) layer. His observations showed an increase in the height of the \(E\) layer when a thunderstorm occurred. Here, apparently, a dependence on meteorological conditions is possible.

Minohara, Ito, and others\(^ {33}\) established that 67% of thunderstorm days in Japan in 1935 were accompanied by the sudden disappearance of reflected waves, with normal conditions then gradually restored. They express the opinion that lightning apparently causes a change in the distribution of electron density.

Kirby and Judson\(^ {34}\), who observed an increase in the density of the \(E\) layer that appeared, especially in summer, in the evening, attempted to correlate this phenomenon with local thunderstorms occurring within 100 and 300 km, but found no connection.

Chonland and Viljoen\(^ {35}\), studying the dependence under consideration, expressed doubt that penetrating radiation from thunderstorm clouds (by which they mean high-velocity electrons flying out from there) can have a noticeable effect on ionization.

On the other hand, Keirus^36, who studied the influence of thunderstorms on the ionization of the air at the earth’s surface, notes that observations made by him in the basin of the Amazon River led him to the conclusion that the effect on the ionization of the atmosphere from distant thunderstorms, although very small, nevertheless does exist. But thunderstorms located at a distance of less than 30 km already produced noticeable changes. Thunderstorms at a distance of less than 15 km showed no influence. Nor was any noticeable change in ionization observed for the majority of thunderstorms passing overhead. This author noted the important fact that thunderstorms to the west of the station produced a greater effect on ionization than thunderstorms to the east. This confirms to a considerable degree the hypothesis of electron drift.

From the several works enumerated, it follows that thunderstorms apparently influence the ionosphere and, consequently, the propagation of radio waves.

Up to now, investigations in this direction have not been of a systematic character; in particular, the connection between the displacement of the centers of frontal thunderstorms and the ionization state of the ionosphere has been insufficiently studied.

Thus, one may conclude that meteorological processes taking place in the troposphere influence the propagation of radio waves between two corresponding points. This influence manifests itself differently on waves of different lengths and depends both on the type of processes and on the extent and location of the region where they occur. The degree of influence also depends substantially on the geographical conditions of the locations of the transmitting and receiving stations.

The influence of meteorological processes manifests itself most sharply and noticeably only in certain particular cases; ordinarily it is veiled by the action on radio waves of other important factors (the earth’s magnetic field, solar activity, conductivity of the soil, etc.).

LITERATURE

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