OZONE IN THE STRATOSPHERE*

I. A. Khvostikov

INTRODUCTION

The study of the ozone layer in the stratosphere belongs among the most distinctive branches of the physics of the upper atmospheric layers. The profound and many-sided significance of the problem of atmospheric ozone became clear gradually. It becomes ever more certain the further research advances. In recent years new results of great importance have been obtained, and there has been general recognition of the need to investigate atmospheric ozone still more broadly; this has been reflected also in the program of the International Geophysical Year.

The amount of ozone in the air is very small, about \(4\cdot 10^{-7}\). For a long time it seemed that investigation of the ozone layer could have only “academic,” and in no way practical, interest. But gradually it became clear that this is not so. It is now quite evident that the study of ozone, and continuous observation of its behavior in the atmosphere, must become (and is already beginning to become) a powerful means of investigating fundamental processes, including weather-forming processes. The task is to learn how to use this means, and the first highly promising results have already been achieved.

The state of the upper layers of the atmosphere (especially the ionosphere) is almost completely controlled by solar radiation, primarily ultraviolet radiation. This also applies to the ozonosphere, since for the formation of ozone molecules \(O_3\) the presence of atomic oxygen is necessary, whereas in the lower layers of the atmosphere oxygen exists in the form of \(O_2\) molecules. In the upper layers reactions of oxygen dissociation are constantly taking place,

\[ \mathrm{O}_2 + h\nu \to \mathrm{O} + \mathrm{O}, \tag{1} \]

where the photon energy \(h\nu\) corresponds to the region of the solar spectrum \(\lambda < 2423\ \text{Å}\) (the dissociation energy of \(O_2\) molecules is \(5.116\ \text{eV}\)).

* This article is based on lectures on the ozonosphere delivered at the Faculty of Physics of Tbilisi University in December 1955.

The reaction of ozone formation

\[ \mathrm{O}_2 + \mathrm{O} + \mathrm{M} \to \mathrm{O}_3 + \mathrm{M} \tag{2} \]

requires the participation of some third particle, \(M\), which is necessary for the fulfillment of the conservation laws.

The ozone content in the stratosphere, its distribution with height, its dependence on latitude, etc., are determined by the nature of the illumination of the Earth’s atmosphere by the ultraviolet rays of the Sun. The problem of the ozonosphere is an important part of the “Sun—Earth” problem. The study of the ozone layer is of great importance for understanding the nature of solar influences on terrestrial phenomena, including ionospheric, geomagnetic, and other phenomena, which are so important not only in the theoretical but also in the practical respect.

The results of studies of atmospheric ozone and related questions have repeatedly been covered in Soviet literature \(^{1—20}\), including in the pages of this journal \(^{4—7,\ 12}\). Our review is devoted to works of recent years. The results of earlier investigations are mentioned briefly and only in those cases where the coherence of the exposition required it. To save space, the article often gives references to papers previously published in Uspekhi Fizicheskikh Nauk and to the recently published Russian translation of the book by the outstanding Indian geophysicist S. K. Mitra \(^{1}\).

METHODS OF INVESTIGATION AND SOME RESULTS OF MEASUREMENTS

1. Indirect methods. The history of the discovery of atmospheric ozone as the cause determining the sharp boundary of the spectra of the Sun (Fig. 1) and of all other extraterrestrial sources on the short-wavelength side (around \(\lambda = 2950\) Å) is instructive. One could not fail to find extremely interesting the fact that the atmosphere’s ability to protect all living things on Earth from the destructive action of the Sun’s ultraviolet rays is explained by the presence in the air of an insignificant “impurity” of ozone, in an amount of only a few \(\mathrm{O}_3\) molecules per \(10^7\) other molecules. When it turned out that ozone is distributed in the atmosphere not “as it should be,” but nonuniformly and in a very peculiar manner—its concentration increases with height and reaches a maximum in the stratosphere—the study of ozone attracted the close attention not only of geophysicists, but also of many physicists and astrophysicists.

For the study of atmospheric ozone, indirect (optical) methods are widely used, based on the characteristic features of the absorption spectrum of ozone (Fig. 2). Absorption in the Hartley bands is very great, which explains the complete absorption by atmospheric ozone of the ultraviolet rays of the Sun, despite the smallness of the \(\mathrm{O}_3\) concentrations. In the region 2950–3400 Å the magnitude of the absorption is relatively small; the solar rays are only partially absorbed in the Earth’s atmosphere. It is precisely this that makes it possible to determine the quantity

ozone in the atmosphere (using values of the ozone absorption coefficient known from laboratory measurements; see Fig. 2).

Fig. 1. Cutting off of the ultraviolet end of the solar spectrum by ozone: 1 — extra-atmospheric distribution of energy in the spectrum of the Sun (radiation of a black body at 6000° K); 2 — distribution of the energy of the solar rays at the Earth’s surface.

Fig. 2. Absorption spectrum of ozone in the ultraviolet and visible regions.

If all the ozone present in the atmosphere is collected into a layer of pure ozone under normal conditions, then the thickness of the layer \(x\) will be about 3 mm. The fluctuations of \(x\), depending on the season and the geographical latitude of the place, are quite considerable—from 1.5 to 4.5 mm. Usually an ozone maximum is observed in spring and a minimum in autumn (Fig. 3).

The amount of ozone \(x\) decreases as one approaches the equator; at any given point it may change over several hours (for more detail see § 7).

Fig. 3. Annual course of the total ozone content over Arosa (48° N) and over Tromsø (68° N).

An estimate of the mean height \(h_{\text{oz}}\) of that layer in which the greater part of the ozone is contained can be obtained by studying the edge of the solar spectrum at different zenith distances of the Sun \(Z\).

Fig. 4. For calculating the height of the ozone layer.

Let us imagine an observer situated on the Earth’s surface at point \(A\) (Fig. 4) and studying the solar ray \(ABC\), which forms an angle \(Z\) with the vertical \(h\). Let us further imagine that in the atmosphere there is an ozone layer of some thickness. This layer occupies a position, as yet unknown to us, relative to the Earth. Let us take two cases: when the layer directly adjoins the Earth’s surface and when it is located at some height \(h\). If the ray travels vertically (along \(h\)), then its path will be the shortest and, moreover, the same in both cases. But if the ray travels at some angle \(Z\), then the path of the ray through the ozone layer increases, and this increase occurs more rapidly in the lower layer, as is easy to see from the drawing: \(AB > CD\). Consequently, the higher the ozone layer lies, the more slowly the absorption should increase as the Sun approaches the horizon. By carrying out the complete geometrical calculation and comparing the results of the computations with the true daily course of absorption at the edge of the spectrum, one can determine the height of the ozone layer.

Under real conditions, however, ozone is distributed over a broad region (\(0\)—\(70\) km), and therefore the determination of the effective height of the ozone-

of the layer, becomes more complicated by the indicated method. For a long time the theoretical foundations of the method remained without rigorous substantiation. Moreover, in 1929 Roseland came to the conclusion that it was impossible to determine unambiguously the mean height of the ozone layer by this method[^23]. But this conclusion of Roseland’s proved to be incorrect, as was shown in 1934 by V. A. Ambartsumian[^3]. In this important work the possibility was rigorously proved of an unambiguous determination of the mean height of the ozone layer \(h_{\mathrm{oz}}\) from measurements of the ultraviolet end of the solar spectrum (or the spectrum of the Moon, of some star, etc.) at different \(Z\).

Fig. 5. Inversion curves for different ozone contents
(Mount Abu Observatory, India).
5.2.1952, \(x = 0.188\) cm \(\}\) (upper curves 3112 Å/3323 Å),
7.2.1952, \(x = 0.209\) cm \(\}\) (lower curves 3075 Å/3278 Å).

Another method for determining \(h_{\mathrm{oz}}\) from measurements of direct solar radiation was proposed in 1941 by Strong[^25]. This method uses, along with ordinary measurements of atmospheric ozone absorption in the ultraviolet region of the spectrum, also measurements of absorption in the far infrared region, in the ozone absorption band \(\lambda = 9.7\,\mu\). The method is based on the fact that absorption in the \(9.7\,\mu\) band depends on pressure, whereas ultraviolet absorption does not.

Interesting possibilities for studying the ozone layer are offered by the so-called reversal effect, discovered in 1931. The essence of the phenomenon is as follows. If, at different but not very large zenith distances of the Sun \((Z < 82^\circ)\), one measures the intensities \(I\) and \(I'\) of zenith light for two wavelengths \(\lambda\) and \(\lambda'\) at the ultraviolet end of the solar spectrum, then as \(Z\) increases the ratio \(I/I'\) (if \(\lambda' > \lambda\)) gradually decreases. This is quite understandable, since for \(\lambda\) the absorption by ozone is stronger than for \(\lambda'\). But if observations are continued up to \(Z \simeq 90^\circ\), then, beginning with some \(Z\), the dependence assumes the opposite character—the ratio \(I/I'\) increases with increasing \(Z\). Figure 5 gives an example (along the abscissa axis \(Z^4\) is plotted, and along the ordinate axis, \(\lg I/I'\)). The values of \(\lg I/I'\) at some point reach a minimum value (the reversal point), after which they increase.

According to Götz’s ideas, the position of the point (the moment of occurrence) of reversal on the reversal curve must be unambiguously connected with the height \(h_{\mathrm{oz}}\), while the shape of the reversal curve must be connected with the form of the curve of the vertical distribution of ozone.

Let us explain what has been said by means of illustrative examples. Suppose first that the spectrometer is directed at the Sun. If one assumes that the attenuation of the solar rays on their path through the atmosphere is due only to molecular scattering of light (as if there were no ozone layer), then the quantity \(\lg I/I'\) would vary with \(Z\) as shown in Fig. 6 by the line “Sun, no ozone” (in this diagram[^84] the zero position of the ordinate scale has been chosen in accordance with the condition that the extra-atmospheric intensities \(I_0\) and \(I'_0\) measured by the given instrument are equal to one another, i.e., that outside the atmosphere \(\lg I_0/I'_0 = 0\)). If, on the contrary, one takes into account the presence of ozone and assumes its amount \(x\) to be equal to

Fig. 6. Diagram illustrating the influence of the height of the ozone layer on the form of the reversal curve.

0.2 cm, then the change in \(\lg I/I'\) would occur approximately as shown by the line “Sun (ozone 0.2 cm).”

Let us now point the spectrometer at the zenith of a clear sky. The course of \(\lg I/I'\), actually measured under real conditions, is approximately as shown by the dashed line “20 km”; the point of reversal occurs at a value of \(\sec Z\) lying between 3 and 4. A rough calculation shows that in the absence of ozone the quantity \(\lg I/I'\) would vary with the Sun’s zenith distance as shown by the dashed line “Zenith light” (no ozone); and if it is assumed that all the ozone, in the amount \(x = 0.2\) cm, is concentrated in a thin horizontal layer, then the course of \(\lg I/I'\) depends on the height of the layer. If the layer is at the Earth’s surface, then the instrument readings will correspond to the curve “Ozone at the Earth, zenith light”; \(\lg I/I'\) depends little on \(Z\). If the ozone layer is placed at the upper boundary of the atmosphere, then the quantity \(\lg I/I'\) will change rapidly as a function of \(Z\), almost as for direct sunlight (in this case the effective scattering layers for both wavelengths, for all \(Z\), remain below the ozone layer). These were two limiting cases. For intermediate positions of the ozone layer the course of the curves will also have an intermediate character (for \(h_{03} = 5\) and 20 km the course of the curves is shown in the diagram). With an arbitrary distribution of ozone with height the calculations become complicated. When \(\sec Z\) is small (approximately 1.0–1.5), the vertical distribution of ozone has little influence; the course of the quantity \(\lg I/I'\) is determined mainly by the total ozone content \(x\) and \(h_{03}\). At large values of \(\sec Z\) (approximately those beginning from which the curve “20 km” departs sharply from the line “ozone at the upper boundary of the atmosphere”), the determining factor becomes the distribution of ozone in the upper part of the ozonosphere.

Fig. 7. Toward the calculation of the vertical distribution of ozone from the reversal curve.

The transition from such visual representations and rough estimates to quantitative calculation is associated with serious mathematical difficulties. Several years of effort by many authors were required before a satisfactory procedure was developed for the approximate calculation of the vertical distribution of ozone from the reversal curve. In 1934 Götz, Mees, and Dobson proposed two variants of such computational methods, calling them methods “A” and “B.”

Let an observer be located at \(C\) (Fig. 7), in whose zenith the point \(B\), at height \(h\), is illuminated by the solar ray \(AB\) (with wavelength \(\lambda\) and extraterrestrial intensity \(I_0\)). Along the path \(AB\) through

the atmosphere, this ray will be weakened by a number of times equal to

\[ 10^{-\int_h^\infty \left(k'\varepsilon+\frac{b\rho}{\rho_0}\right)\sec Z\,dh}, \]

where \(k'\) is the absorption coefficient of ozone, \(\varepsilon\) is the concentration of ozone in the atmosphere (depends on height), \(b\) is the coefficient of molecular scattering of light by air having the normal density \(\rho_0\), \(\rho\) is the (variable) density of air at one height or another; the zenith distance of the Sun \(Z\) has different values (owing to the sphericity of the Earth) at different points of the ray \(AB\); at point \(B\): \(Z=Z_0\).

The intensity of the light scattered at \(B\) by the atmospheric layer \(dh\) vertically downward will constitute a fraction of the incident intensity equal to

\[ \frac{b\rho}{\rho_0}(1+\cos^2 Z_0)\,dh. \]

This intensity along the path \(BC\) will be weakened by

\[ 10^{-\int_0^h \left(k'\varepsilon+\frac{b\rho}{\rho_0}\right)\,dh} \]

times.

Taking into account primary scattering, we obtain the total intensity of zenith light \(I\), falling at the point \(C\), by integration over the entire thickness of the atmosphere:

\[ I=\frac{b}{\rho}(1+\cos^2 Z_0)I_0 \times \]

\[ \times \int_0^\infty \rho \left[ 10^{-k'\int_h^\infty \varepsilon\sec Z\,dh -k'\int_0^h \varepsilon\,dh -\frac{b}{\rho_0}\int_h^\infty \rho\sec Z\,dh -\frac{b}{\rho_0}\int_0^h \rho\,dh} \right]dh. \tag{1.1} \]

The sum of the first two integrals without the factor \(k'\) is nothing other than the ozone thickness \(\mu x\) along the path of the ray \(AB+BC\), and the sum of the last two is the optical thickness of the air \(m\tau\) along the same path. Therefore equation (1.1) may be rewritten in the form

\[ I=\frac{b}{\rho_0}(1+\cos^2 Z_0)I_0\int_0^\infty \rho\,10^{-\mu x k'-m\tau}\,dh. \tag{1.2} \]

The ozone thickness \(\mu x\) depends not only on the amount of ozone \(x\), but also on its vertical distribution, which, in the opinion of many authors\(^{26}\), opens up the possibility of using formula (1.2) to compute this distribution from observations of zenith light. The calculation is carried out by approximate methods, for which purpose the ozonosphere is divided into a certain number of layers, in each of which the ozone

is considered uniformly distributed with height. The number of layers is often taken to be five, which makes it possible to ascertain the ozone distribution only in broad outline, while increasing the number of layers makes the problem extremely complicated.

Methods “A” and “B” for processing Umkehr curves differ from one another in the number and arrangement of the layers into which the ozonosphere is divided (for more details see Mitra¹ and Prokof’eva²).

The approximate processing methods used are not rigorously substantiated. Thus, in 1933 Pekeris, on the basis of a mathematical study of equation (1.1), came to the conclusion that the function \(\lg I/I'\) cannot have an extremum for any distribution of ozone with height³⁰. This result was obtained by Pekeris also when secondary scattering of light was taken into account. However, Pekeris’s work met with objections, first of all from Götz.

The nature of the Umkehr effect cannot be regarded as definitively established. Investigations by S. F. Rodionov show that the phenomenon may be produced by selective absorption by a layer of atmospheric aerosols⁸. This conclusion was reached as a result of many years of study of the phenomenon of anomalous transparency of the atmosphere, discovered by S. F. Rodionov, E. N. Pavlova, and N. N. Stupnikov⁹. The results recently published by Sh. A. Bezverkhnii¹⁰⁸ also speak in favor of this supposition. According to observations in Alma-Ata in the summer and autumn of 1952, the Umkehr effect is not always found; on some days it is absent. This fact is easily explained if one assumes that the Umkehr phenomenon is caused by the effect of anomalous transparency, which must be characteristic of the atmosphere only under certain meteorological conditions. Unfortunately, the method of measurement used by Sh. A. Bezverkhnii was not sufficiently rigorous (an electrophotometer with 3 filters, the transmission maxima of which corresponded to wavelengths of 3200, 3600, and 3900 Å). It would be desirable to repeat these observations with the aid of a spectrograph or monochromator. The question as a whole must be regarded as open. Regular application by many authors (for example, on four

Fig. 8. Vertical distribution of ozone over Delhi (India) for different amounts of ozone.

at observatories in India^24) of the method of curves of circulation for estimating the vertical distribution of ozone makes it possible to obtain results which, in broad outline, agree with other data. In Fig. 8 two curves are given for the vertical distribution of ozone concentrations over Delhi (India^24) (the concentration $\varepsilon$ is given in microns of thickness of the reduced layer of ozone, referred to an air layer of 1 km). The curves correspond to small and large (for the tropical zone) ozone content $x$.

In recent years, the method of lunar eclipses has been applied with great success to the study of the vertical distribution of ozone.

1. The method of lunar eclipses. During lunar eclipses, luminous phenomena caused by solar rays that have passed through the Earth’s atmosphere can be observed on the disk of the Moon. These phenomena make it possible to “see” the terrestrial atmosphere in a somewhat unusual way and to obtain valuable information about its structure.

The Moon is almost four times smaller than the Earth in diameter. Although the Earth’s shadow narrows and becomes conical, nevertheless, at the distance from the Earth at which the Moon is located, the Earth’s shadow is 2.7 times larger than the Moon (Fig. 9), and the latter, during the full moon, can enter completely into the Earth’s shadow; the resulting lunar eclipse can then last a long time, up to 1 hour 40 minutes.

Fig. 9. Diagram of a lunar eclipse.

The Moon does not completely disappear during a total eclipse, but continues to shine with a dim red light of a brownish hue. The character of this glow can vary greatly from one eclipse to another, which is caused by the action of the Earth’s gaseous envelope: solar rays that have undergone refraction in the terrestrial atmosphere penetrate into the cone of the Earth’s shadow. The red color of the Moon, like the red color of the Sun at sunset or sunrise, is caused by the preferential absorption (scattering) in the atmosphere of short-wave radiation, in accordance with Rayleigh’s law of light scattering. The brightness and color of the Moon during a total eclipse are affected by the weather in those parts of the Earth where these rays pierce the terrestrial atmosphere, i.e., along the circumference of the Earth if one looks at the Earth from the Moon. High cloudiness in these places on Earth will hold back the rays passing through the deep parts of the atmosphere. In this case the rays will pass only through the upper layers of air and will be refracted more weakly; the Moon will be dark. There have been cases when the Moon during a total eclipse became almost invisible. Conversely,

OZONE IN THE STRATOSPHERE

in clear weather on the Earth the rays can pass almost through the entire thickness of the air and the Moon will be brighter and redder.

Photometric investigation of the Earth's shadow on the lunar disk makes it possible to determine the absorption and scattering of light at different heights of the Earth's atmosphere and, as was first shown in the works of Fesenkov \(^{15}\) and Link \(^{27}\), can serve for the quantitative study of the high layers of the atmosphere. One of the interesting applications of the method of lunar eclipses is the detection and measurement of gases present mainly in the high layers of the atmosphere. Atmospheric ozone, as we know, belongs precisely to such a case. The possibility of clearly revealing ozone absorption by means of photometric observations of the disk of the eclipsed Moon was shown by Fesenkov \(^{15}\).

Let us consider two recent works by the French astrophysicists Barbier, Chalonge, and Vitrú \(^{28, 29}\), who investigated the visible region of the spectrum of the eclipsed Moon and developed an approximate theory for interpreting spectrophotometric data from lunar eclipses as applied to ozone measurements.

Let \(E_{0\lambda}\) denote the illumination of some portion of the lunar surface on which, outside eclipse, solar rays of wavelength \(\lambda\) fall, and let \(E_\lambda\) be the illumination of the same portion of the surface during eclipse. The quantity

\[ \Delta_\lambda = \lg \frac{E_{0\lambda}}{E_\lambda} \]

will be called the density of the shadow (the optical density of the Earth's shadow).

To calculate the attenuation of light in the atmosphere caused by absorption and scattering, it is convenient to use the equation of atmospheric absorption, on the basis of which the following relation may be written for the illumination before and during eclipse:

\[ \lg E_{0\lambda} - \lg E_\lambda = k'_\lambda x\mu + \tau_\lambda m + \tau_a m_a, \tag{2.1} \]

where \(x\mu\) denotes the reduced thickness of the ozone layer, calculated along the path of the ray \(yy'\) (Fig. 10), and \(m\) and \(m_a\) are the air masses of the clean atmosphere and, respectively, of the aerosol layer, also calculated along \(yy'\). The presence of other causes of selective change in \(E_\lambda'\), besides those taken into account by equation (2.1), can be revealed in the following way: having determined \(x\mu\) and \(m\) and having measured the shadow density \(\Delta_\lambda\) from spectrograms, one must compute the difference \(\Delta_\lambda - (k'_\lambda x\mu - \tau_\lambda m)\) for different \(\lambda\). In the presence of other factors of selective attenuation, these differences prove to be different for different \(\lambda\).

Fig. 10. On the calculation of atmospheric absorption in observations of a lunar eclipse.

I. A. Khvostikov

Let the reflectivity of the sighted portion of the lunar surface be equal to \(A\). Then the magnitude of the luminous flux \(\Phi_\lambda\) entering the telescope, which is directed at the given element of the Moon’s surface, taking into account the weakening of the flux in the atmosphere on the path from the Moon to our instrument, must satisfy the equality

\[ \lg \Phi_\lambda = \lg A E_\lambda - (k' x + \tau_\lambda + \tau_a)\sec Z, \]

where \(Z\) is the zenith distance of the Moon. For two spectra obtained before and during the eclipse, the following relations hold:

\[ \lg \Phi_{0\lambda} = \lg A E_{0\lambda} - (k' x + \tau_\lambda + \tau_a)\sec Z_1, \]

\[ \lg \Phi_\lambda = \lg A E_\lambda - (k' x + \tau_\lambda + \tau_a)\sec Z_2, \]

whence

\[ \lg \Phi_{0\lambda} - \lg \Phi_\lambda = \]

\[ = \lg E_{0\lambda} - \lg E_\lambda - (k' x + \tau_\lambda + \tau_a)(\sec Z_1 - \sec Z_2). \tag{2.2} \]

The value of the quantity \(E\) in equation (2.1) is determined from the results of observations—these are \(\Phi_{0\lambda}\), \(\Phi_\lambda\), \(Z_1\), and \(Z_2\); the absorption coefficient for ozone is known from tables. In order to determine the magnitude of the density of the shadow \(\Delta_\lambda\), it is necessary also to find the values of \(x\) and \(\tau_\lambda + \tau_a\). For this purpose, during the same night several spectra of a suitable star are taken at different \(Z\). For each spectrum one may write relations analogous to those considered above. If \(I_{0\lambda}\) and \(I_\lambda\) are the brightness of the star for wavelength \(\lambda\) outside the atmosphere and, respectively, at the level of the Earth, then

\[ \lg I_\lambda = \lg I_{0\lambda} - k'_\lambda x \sec Z_1 - (\tau_\lambda + \tau_a)\sec Z. \]

For two spectra obtained at zenith distances \(Z_1\) and \(Z_2\), we find:

\[ (\lg I_\lambda)_1 - (\lg I_\lambda)_2 = k'_\lambda x(\sec Z_2 - \sec Z_1) + (\tau_\lambda + \tau_a)(\sec Z_2 - \sec Z_1) \]

Photometric processing of the spectra makes it possible to find the numerical value of the left-hand side of the equation; choosing such a region of the spectrum where ozone absorption is equal to zero, we find \((\tau_\lambda + \tau_a)\), and then, using the region where \(k'_\lambda\) is large, we determine \(x\).

In Fig. 11 (curves IIId—Ve) the values of \(\Delta_\lambda\) are shown as functions of wavelength for various points of the Earth’s shadow, according to measurements of the lunar eclipse of May 2–3, 1942 (Barbier, Chalonge, and Vigrux\(^{28}\)). To facilitate identification of the absorption bands, in the same Fig. 11 there is given the curve of the optical density \(\Delta_\lambda\) of an ozone layer of thickness 10 cm at a temperature of \(-50^\circ\) (the temperature of the stratosphere), and the absorption bands of water vapor and oxygen are indicated schematically. Curve X represents the differences of the optical densities of the atmosphere

Fig. 11. Change in shadow density as a function of wavelength for different points of the Earth’s shadow.

for air masses 5.06 and 16.86, measured from the spectra of Sirius at the Jungfraujoch International Scientific Station (height 3457 m above sea level).

The curves in Fig. 11 clearly reveal ozone absorption (the Chappuis band) as the most remarkable feature of the eclipsed Moon spectra. The curves show maxima of ozone absorption at 6020, 5750, 5340, 5050, 4800, and 4600 Å. On curves IIIa and IIIb these maxima are more noticeable than on the calculated curve for 10 cm of ozone.

Another feature of the spectra is the presence of a well-defined oxygen $\alpha$ band (at 6280 Å). This band appears the more distinctly the closer the photometered point is to the center of the Earth’s shadow, i.e., the lower the solar ray illuminating this point passes through the atmosphere. The water-vapor bands do not show themselves noticeably. The increase of $\Delta_\lambda$ toward shorter wavelengths is due to the weakening of the solar rays on their path through the atmosphere by Rayleigh scattering.

Starting from the curves for $\Delta_\lambda$ (Fig. 11), Barbier, Chalonge, and Vigroux approximately calculated the vertical distribution of ozone. Their calculation reduces to the following. Consider a beam of solar rays incident on the lunar surface after passing through the upper layers of the atmosphere. Let us take into account the refraction of the rays on their path through the atmosphere; in view of the small values of the density gradient in the high atmospheric layers, the magnitude of the refraction is small. If the atmosphere only deflected the rays, without absorbing them, then the illumination $E_\lambda$, produced by radiation of wavelength $\lambda$ reaching the point of the Moon under consideration, would be proportional to the illumination $E_{0\lambda}$ of this point of the Moon outside the eclipse: $E_\lambda=aE_{0\lambda}$, where $a$ is a constant that may be regarded as independent of $\lambda$.

The account of atmospheric absorption can be simplified if the spectral region of oxygen absorption (the $\alpha$ band) is excluded from consideration, and if, for weakening by scattering, only molecular scattering $\sim \lambda^{-4}$ is taken into account. The latter condition may be justified to some extent by reference to the circumstance that the lower layers of the atmosphere, where the scattering of light has a certainly more complex character, do not take any noticeable part in illuminating the disk of the eclipsed Moon, since the solar rays passing through them are weakened by a factor of $10^3$–$10^5$. Therefore, for $E_\lambda$ one may write the equation

$$ \lg E_\lambda=\lg aE_{0\lambda}-0.004m\lambda^{-4}-k'_\lambda x\mu, $$

where 0.004 is the coefficient in Rayleigh’s formula. Hence we obtain the expression for the shadow density:

$$ \Delta_\lambda=\lg\frac{E_{0\lambda}}{E_\lambda}=0.004m\lambda^{-4}+k'_\lambda x\mu-\lg a \tag{2.3} $$

Considering any curve in Fig. 11, one can write equations similar to (2.3) for a number of points on the curve and, using the method of least squares, obtain the values of \(m\) and \(x\mu\). For example, for the Ve curve it was found that

\[ m = 10.0 \pm 0.3 \quad \text{and} \quad x\mu = 7.5 \pm 0.2. \]

Figure 12 shows the experimental points of the Ve curve, as well as

Fig. 12. Curve representing equation (2.2) for \(m = 10\) and \(x\mu = 7.5\), and the experimental points of the Ve curve (Fig. 11).

the curve representing equation (2.3) for \(m = 10\) and \(x\mu = 7.5\). There is satisfactory agreement between the points and the curve, except for the region near \(5750\ \text{Å}\), where excess absorption occurs.

Table I gives a summary of the results of processing the spectra of the eclipsed Moon[^28]. The second column gives the angular distance of the recorded region from the center of the shadow \(\bar{\omega}\), and the last gives the values of the optical density of oxygen (the \(\alpha\) band). As the distance from the center of the Earth’s shadow increases (increase of \(\bar{\omega}\)), the mass \(m\) decreases (the solar rays passed through higher atmospheric layers), and the oxygen absorption also decreases. As for the amount of ozone \(x\mu\), it first increases and begins to decrease only in higher layers of the atmosphere.

From the data of Table I, graphs have been plotted of the dependence of \(x\mu\) and of the optical density of oxygen in the \(\alpha\) band on \(m\) (Fig. 13). Despite the scatter of the points, caused by the complexity of the measurements, by

from the graph it can be established that the ozone thickness has a maximum value (about 11 cm) for the traversed air mass \(m \simeq 20\).

Fig. 13. Relation between the air mass \(m\), the ozone thickness \(x_\mu\) (crosses), and the oxygen thickness \(a\) (circles) traversed by the solar rays on their way to the eclipsed Moon.

Fig. 14. Dependence of the air mass \(m\), traversed by the ray \(y'y\) (Fig. 10), on the height \(h\).

Attention should be paid to the conditions under which the maximum ozone thickness \(x_\mu = 11\) cm occurs. This value is 50 times greater than the mean amount of ozone in the vertical air column \(x\), but in this case \(m = 20\), i.e., under conditions of a lunar eclipse observations can be made at \(\mu = 50\), while the air mass \(m\) then has a value 2–3 times smaller. Such conditions are very favorable for detecting ozone absorption against the background of the general attenuation of rays in the atmosphere caused by other causes. In observations of a star (including the Sun) near the horizon (and many determinations of atmospheric ozone are based on such observations; see § 1), the conditions are less favorable, since the corresponding largest values are \(\mu \simeq 10\) and \(m \simeq 40\), and therefore the weakening of light caused by scattering

Table I

Results of the processing of spectra of the eclipsed Moon (eclipse of March 2–3, 1942)

Spectrum No.	\(\bar{\omega}\)	\(m\)	\(x_\mu\), cm	\(a\)
IIId	\(15'\)	45,2	2,9	0,16
IIIe	\(20'\)	37,0	3,5	0,15
IIIf	\((20')\)	33,0	3,5	0,11
IIIc	\((22')\)	33,0	5,3	—
IVd	\(26'\)	—	—	0,08
IIIb	\((28')\)	26,8	9,5	—
IVe	\(33'\)	—	—	0,06
IIIa	\((33')\)	16,5	10,3	—
IVf	\(36'\)	6,9	8,9	0,05
Ve	\(39'\)	10,1	7,8	0,05

and absorption by other gases, screens the ozone absorption to a much greater extent. Such favorable circumstances are created by the features of the vertical distribution of ozone. Spectrophotometric studies of lunar eclipses are in general very promising with respect to detecting gases that may be present in the high layers of the atmosphere.

In observing the lunar eclipse of January 29–30, 1953, at the Haute-Provence Observatory (France), Vassy used a more powerful spectrograph and obtained spectra corresponding to still larger values of the ozone thickness \(x_\mu\) (more than \(15\) cm) traversed by the solar rays\({}^{29}\) (Table II and Fig. 15). The height \(h\) is the small—

Table II

Results of processing the spectra of the eclipsed Moon
(eclipse of January 29–30, 1953)

Spectrum No.	\(m\)	\(x_\mu\), cm	\(h\), km	\(\varphi_0\)	Spectrum No.	\(m\)	\(x_\mu\), cm	\(h\), km	\(\varphi_0\)
I	9.5	13.5	14.8	46°	VIII	11	8.5	14.2	6°
II	16.5	15.6	11.6	48°	IX	8.2	9.0	16	4°
III	29	15.8	7.8	71°	X	7.5	8.9	16.6	3°
IV	35	13.1	6.4	44°5	XI	6	9.4	18	2°
V	26.5	11.8	8.5	17°	XII	4.4	8.3	20	1°5
VI	20	9.3	10.4	14°	XIII	3.7	7.8	21	0°5
VII	15	8.3	12.2	9°

est distance of the solar ray illuminating the given point of the Moon from the Earth’s surface (Fig. 10), calculated from the values of the mass \(m\) (from the curve in Fig. 14).

In addition, Table II gives the values of the geographic latitude \(\varphi_0\) of that point on the Earth from which the given solar ray passes at the smallest distance \(h\). During the eclipse the latitude \(\varphi_0\) changes over wide limits, and all the spectra can be divided into two groups: I–III (taken before midnight) and IV–XIII (taken after midnight). The spectra of the first group reflect the properties of the ozone layer at middle and high latitudes, and those of the second—in the vicinity of the equator.

Omitting the exposition of the calculation of the vertical distribution of ozone from the values of \(x_\mu\) known for different \(h\) (it leads to Abel’s integral equation, solved by numerical methods),

we shall indicate the final results. In Fig. 16 a curve is given, constructed from the spectra of the second group. For \(h>21\) km the curve is extrapolated approximately exponentially, with the calculation made so that the values \(x_\mu\) (Fig. 15) for \(h\) from 50 to 60 km correspond to the ozone data obtained by rocket measurements. Let us consider the left-hand part of the curve in Fig. 15. Spectra VII–XIII correspond to \(\varphi_0\) from \(9^\circ\) to \(0^\circ.5\); taking into account that \(x\), and hence \(x_\mu\), depend on geographic latitude and have a minimum at the equator, Vigroux believes that the corresponding values of \(x_\mu\) refer practically to a single vertical. But for spectra VI and V

Fig. 15. Values of the ozone thickness \(x_\mu\) for different \(h\), according to measurements of the lunar eclipse of January 29–30, 1953.

the latitude \(\varphi_0\) is equal to \(14^\circ\) and \(17^\circ\), i.e. is still too small to account for the rapid increase of \(x_\mu\). Therefore two variants of interpretation of the curve are possible: either the ozone distribution on the night of the eclipse was normal and at an altitude of about 14 km there is a minimum of the concentration \(\varepsilon(r)\), located between two maxima (variant \(B\)), or else the considerable increase of \(x_\mu\) at relatively small latitudes was caused by a descending current which brought polar air richer in ozone (variant \(A\)). For variant \(A\), Vigroux, beginning with spectrum VII, i.e. for \(h<12\) km, extrapolated the curve as shown by the dashed line in Fig. 15. The results of calculations of the ozone distribution for both cases—variant \(A\), without a minimum, and variant \(B\), with a minimum—are given in Fig. 16. For the ozone content in a vertical atmospheric column, curve \(A\) gives the value \(x=1.92\) mm.

Since we interpret the curves in Fig. 16 as the vertical distribution of ozone near the equator, it is necessary to take into account the latitudinal effect and somewhat reduce the value of \(x_\mu\) corresponding

Fig. 16. Vertical distribution of ozone near the equator according to measurements of the lunar eclipse of January 29–30, 1953.

Axes in the figure: Altitude (km); \(150\, [[unclear: unit label]]/\text{km}\). Curve labels: \(A\), \(B\).

Fig. 17. Vertical distribution of ozone in the north according to measurements of the lunar eclipse of January 29–30, 1953.

Axes in the figure: Altitude (km); \(150\, [[unclear: unit label]]/\text{km}\).

reduced to the V spectrum. In this case the resulting distribution is approximately that which corresponds to curve \(B'\).

Spectra I–III provide some material for calculating the distribution \(\varepsilon(r)\) in a considerably more northerly region. Using these three points, and for the region of 25 km also using the same data from which curve \(A\) was calculated, Vigroux\({}^{29}\) obtained a new curve (Fig. 17). The maximum of the ozone concentration \(\varepsilon(r)\) is located at an altitude of about 14 km, i.e., lower than at the equator, while the concentration \(200\,\mu/\mathrm{km}\) itself is appreciably greater than the equatorial one. This distribution gives, for the zenith, the value \(x = 3.54\) mm, which agrees with what is known from other sources for these latitudes and seasons.

Fig. 18. Vertical distribution of ozone near the equator according to measurements of lunar eclipses (Petzold): 1 — September 14, 1932; 2 — September 29, 1941; 3 — March 2, 1942; 4 — August 15, 1943.

The method of lunar eclipses has repeatedly been used for studying the ozonosphere by other authors as well. Fig. 18 gives a summary of many years of investigations by Petzold,\({}^{31}\) who also determined the vertical distribution of ozone in the stratosphere from observations carried out at middle latitudes (Institute of Stratospheric Physics in Weissenau, Germany; \(48^\circ\) N latitude). The four curves shown, referring to different years, give the distribution with height not of the ozone concentration \(\varepsilon\), as was the case in Figs. 16–17, but of the ozone/air ratio (by volume). We shall return to the interpretation of these curves in § 11.

3. Direct methods. The concentration of ozone in air can be determined by methods of chemical and electrochemical analysis.\({}^{33,34}\) Important results at one time were obtained by the method of fluorescent analysis, developed in 1935 by M. A. Konstantinova-Shlezinger.\({}^{17,18}\) A reaction was found in which, owing to interaction with ozone, a fluorescent substance is produced, and moreover in a concentration proportional to the amount of ozone,

entered into the reaction. The fluorescence intensity in this case is a measure of the amount of ozone that has reacted. The reaction used was the oxidation by ozone of dihydroacridine into fluorescent acridine. \(0.00115\) mg of ozone increases the concentration of acridine by \(4.35 \cdot 10^{-6}\), which raises the luminescence intensity of the solution by more than \(2 \frac{1}{2}\) times. The sensitivity limit of the method depends entirely on how small luminescence intensities can still be measured. For these purposes the so-called quenching method, developed by S. I. Vavilov[^32], is used. In the quenching method, the eye, adapted to darkness, is used to measure the intensity.

Thanks to its combination with photometry by the quenching method, the Konstantinova–Schlesinger method has a high sensitivity exceeding that of chemical methods. To determine the ozone concentration it is sufficient to pass only 1 liter of air through an alcoholic solution of dihydroacridine.

The method of fluorescent analysis was used for systematic measurements of ozone concentrations at different altitudes; for this purpose air samples delivered from the slopes of Elbrus, and also from the stratosphere[^19], were used. The following dependence[^18] of ozone concentrations \(\varepsilon\) on altitude \(h\) was obtained:

\(h=\)	\(0.1\)	\(\ldots\)	\(2.2\)	\(4.3\)	\(9.6\)	\(13\)
\(\varepsilon=\)	\(9.2\)	\(\ldots\)	\(26.8\)	\(34.0\)	\(40.4\)	\(45.5\)

\(\varepsilon\) can be measured quite accurately from the absorption of ultraviolet radiation in the Hartley band. For this purpose V. V. Balakov, V. G. Vafiadi, and S. S. Krivich[^16] in 1935 photographed, at different altitudes (on the slopes of Elbrus), with a slitless astigmatic spectrograph, the spectrum of a quartz mercury lamp raised to the same altitude as the spectrograph and placed several kilometers away from it. At an altitude of \(4.5\) km they obtained \(\varepsilon = 42\ \mu/\mathrm{km}\).

Photoelectric installations with continuous automatic recording of the value of \(\varepsilon\), developed in recent years, are based on a similar optical principle (for example, the installation of the U.S. Bureau of Standards[^35]). Chemical methods with automatic recording of ozone concentration have also been developed[^128].

The most widespread way of using the optical principle for measuring the amount of ozone by direct methods is one in which the Sun serves as the source of ultraviolet radiation. The spectrograph is raised into the stratosphere by means of a stratospheric balloon, balloon sondes, or a rocket. The spectrum of direct solar rays or of solar rays reflected from a white screen is photographed at different altitudes. From a photograph obtained at altitude \(h\), one can determine the amount of ozone contained in the atmosphere above the level \(h\). Dividing successive photographs taken at different altitudes, one obtains the distribution of \(\varepsilon\) with altitude.

At present the method of the sonde spectrograph is being systematically applied in two places: at Weissenau, near Ravensburg (FRG), by the Max Planck Institute for Stratospheric Physics, and at Albuquerque (New Mexico, USA), where an aerological observatory is located (35° N lat. and 106.9° W long.), situated in the vicinity of the White Sands rocket range and connected with it by a joint program of regular investigations of the upper layers of the atmosphere (at this observatory, in addition to standard aerological investigations and ozone measurements, continuous observation of the state of the stratosphere is carried out by the method of searchlight sounding, as well as by studying anomalous zones of audibility; twilight-method observations are also conducted in this same region). Let us acquaint ourselves with the technique of the sonde spectrograph in its present state1.

Fig. 19. Sonde spectrograph: Стф—step filter, Щ—slit, Апд—aperture diaphragm, Обз—reflecting mirror, Пр—prism, Лк—camera lens, Бар—barograph, Ос—illuminator for the barograph.

To protect against impacts when the apparatus lands after flight, the spectrograph, together with auxiliary devices, is fastened inside a protective casing made in the form of a box, for which the optical scheme of the instrument has been adapted (Fig. 19). There is no collimator lens; the aperture angle of the beam passing through the prism is only 2°. The image of the slit, 3 mm high and 0.02 mm wide, is given at half scale by a simple plano-convex camera lens (relative aperture 1:15). In front of the slit there is a three-step platinum attenuator (transmission of the steps—100, 40, and 14%). The camera lens and the 60° prism (20 mm high, edge length 30 mm) are made of a special glass (homosil), transparent in the required spectral region (3180–2950 Å). The linear dispersion at 3000 Å is 80 Å/mm. The light source is a white disk illuminated by the Sun and coated with magnesium oxide. The instrument also contains elements for recording air pressure and temperature; the barograph device provides pressure measurement within the range 760–3 mm Hg with an error of ±0.2 mm, which corresponds to errors in determining altitude at the levels 30, 40, 45, and 50 km of 0.1, 0.6, 1.2, and respectively 2.5 km.

The weight of the described sonde spectrograph is 1 kg; regular ascents reach heights of 30–35 km, and the maximum “ceiling” attained is 38 km. Of 18 ascents, in only one case was the instrument lost. For checking the altitude values found by

OZONE IN THE STRATOSPHERE

in the barometric formula; during flights in clear weather the sonde is observed from the ground with a theodolite. The discrepancy between the heights found barometrically and geodetically does not exceed \(\pm 0.5\) km. The horizontal projection of the sonde flight trajectory obtained from geodetic measurements is used to compute the wind velocity in different atmospheric layers; the wind data are very useful for discussing variations in the ozone distribution (see § 8).

The spectrograms are processed as follows.

Let \(I_\lambda\) and \(I_{0\lambda}\) denote the intensities of monochromatic sunlight of wavelength \(\lambda\) at height \(h\) and, respectively, outside the atmosphere; \(\tau\) is the optical thickness of the pure (Rayleigh) atmosphere; \(m\) is the air mass traversed by the solar ray at the zenith distance of the Sun \(Z\); \(k'\) is the absorption coefficient of ozone. Then

\[ I_\lambda = I_{0\lambda}\cdot 10^{-(k'x\sec Z+\tau m)}, \tag{3.1} \]

which is a simplified equation of atmospheric absorption, written under the following assumptions: 1) it is assumed that in the stratosphere the aerosol attenuation of light may be neglected; 2) refraction is neglected; 3) the curvature of the atmospheric layers is neglected (according to the author’s estimate\({}^{31}\), for \(Z \le 70^\circ\) this gives an error of less than 2% and can be significant only in winter observations).

In processing the spectrograms, only the relative distribution of energy in a narrow spectral region near 3000 Å is taken into account, and the reference wavelength is taken as \(\lambda_0 = 3179\) Å, which corresponds to the Fraunhofer line \(R\), for which the absorption coefficient is \(k'_0\). Introducing, instead of the wavelengths \(\lambda\), the corresponding values of the absorption coefficient \(k'\), and denoting by \(I'(k')\) the intensity measured on the plate, while \(R(k', k'_0)\) and \(S(k', k'_0)\) are correction terms accounting for the action of Rayleigh scattering of light and the selectivity of the apparatus (spectrograph, white screen, aluminized turning mirror Obz, platinum stepped attenuator) and the photographic plate, we obtain from (3.1):

\[ \lg \frac{I'(k')}{I'(k'_0)} = \lg \frac{I_0(k')}{I_0(k'_0)} + R(k', k'_0) + S(k', k'_0) = F(k'), \tag{3.2} \]

\[ F(k') = -\sec Z\cdot x\cdot (k' - k'_0), \tag{3.3} \]

where \(x\) is the reduced thickness of the ozone layer above the spectrograph at the moment of photographing the given spectrum. Since for this moment the quantities \(\sec Z\) and \(x\) are constant, the values \(F(k')\) found from processing the spectrogram must be linearly related to the value of the difference \(k' - k'_0\). From the slope of the straight lines,

constructed from equation (3.3), the sought value of \(x\) is directly determined.

For measurements at high altitudes the term \(R(k', k'_0)\) has little influence, while the term \(S(k', k'_0)\) is determined by laboratory studies of the apparatus and photographic plates using a standard (hydrogen) continuous spectrum.

The determination of the term \(\lg \dfrac{I_0(k')}{I_0(k'_0)}\), which takes into account the extra-atmospheric distribution of energy in the spectrum of the solar rays, is more complicated. Using data from rocket measurements of the solar spectrum \(^{12}\),

Fig. 20. Ozone curves measured by a sounding spectrograph at Weissenau:
\(a\)—spring and summer; \(b\)—autumn and winter.

Petzold encountered the following fact. In the spectral region \(3180\)—\(3060\) Å, i.e. from \(k' = 0.5\ \text{cm}^{-1}\) to \(k' = 2.5\ \text{cm}^{-1}\), individual measurements lie well on the straight line \(F(k')\), and the values of \(x\) for the Earth’s surface determined from them satisfactorily agree with the values measured 100 km from Weissenau, at the Arosa Observatory (Switzerland), by a standard Dobson spectrograph. However, for \(\lambda < 3060\) Å there are systematic deviations from the data of the American rocket sounding. In connection with this, Petzold determined in this spectral region, for each ascent, such a distribution \(\lg \dfrac{I_0(k')}{I_0(k'_0)}\) as would agree with the straight line \(F(k')\). From a large number of such determinations a “standard” energy distribution was found, which was used in processing all soundings. The error in determining \(x\) at the maximum altitudes is 1—2%.

In Fig. 20 are presented the results of 17 ascents belonging to different seasons31 (separately for spring–summer and autumn–winter). The vertical distribution of ozone \(\varepsilon(h)\) is obtained from the integral curves \(x(h)\) by differentiation. The error in determining \(\varepsilon\) is, naturally, greater than for \(x\). Petzold estimates it at \(\pm 1\cdot 10^{-3}\), \(0.5\cdot 10^{-3}\), \(1.3\cdot 10^{-3}\) cm/km for heights of 5, 25, and, respectively, 30 km. Two curves \(\varepsilon(h)\) for Weissenau36, 37 are given in Fig. 21 (two other curves were constructed from measurements in Albuquerque; see below).

Fig. 21. Characteristic cases of the vertical distribution of ozone according to sounding results by direct methods

Line style	Date	Site
solid line	25.2.1950	Albuquerque
dashed line	18.4.1950	Albuquerque
dotted line	18.2.1950	Weissenau
crosses	18.4.1952	Weissenau

At the observatory in Albuquerque, instead of photographing spectra of sunlight, an electrophotometer developed by Koblenz and Stair38–40 (Bureau of Standards, USA) is used. The instrument consists of a cadmium photocell and a photocurrent amplifier. The photocell has a maximum sensitivity near \(\lambda = 2850\) Å and is not sensitive in the region \(\lambda > 3250\) Å. Light filters were used, owing to which the instrument recorded the integral intensity of ultraviolet solar radiation \(\lambda < 3132\) Å, strongly absorbed by ozone. The instrument as a whole was constructed as a radiosonde. It included a radio transmitter, whose signals were recorded by a ground receiving station. After amplification, the photocurrent acted on the transmitter, modulating oscillations in the generator circuit. Alternately with the ultraviolet-intensity signals,

radiation, pressure signals (for determining altitude) and temperature were transmitted. The instrument, weighing 2.3 kg, was raised into the stratosphere to an altitude of 26–29 km by balloons filled with hydrogen. In Fig. 21 two curves measured in Albuquerque are presented.

Since 1946 a new remarkable technique—rockets—began to be used for investigating the high layers of the atmosphere, including the ozonosphere; with their aid it proved possible to raise scientific apparatus to altitudes of 100–200 km, and in individual cases even higher. Thus the beginning was laid for a new, exceptionally important stage in the development of the study of the high layers of the atmosphere.

For photographing the spectra of the Sun, spectrographs with a diffraction grating were used. Until 1949 this was a spectrograph in which, in order to ensure the capture of direct solar rays, the slit was replaced by a ball of fluorine lithium $^{41}$ (type A), and in recent years, in addition, a spectrograph of an improved design with a slit of a distinctive construction, formed by a pair of mirror plates inclined toward one another $^{42}$ (type B). Spectrographs of both types and the method of measurement have already been described $^{5,6,12}$ in the pages of Uspekhi Fizicheskikh Nauk.

Fig. 22. Vertical distribution of ozone according to rocket data.

In Fig. 22 the curves of the vertical distribution of ozone obtained by means of rocket sounding are shown.

The most substantial result of investigations of the ozonosphere by means of rockets concerns the highest part of the ozone layer (above 50 km), where the concentration of this gas is vanishingly small, while at the same time obtaining the most accurate possible data is of great theoretical importance (refinement of the photochemical theory of the formation of the ozone layer, the theory of the temperature regime of the atmosphere

in the region of 50–100 km, theories of the luminosity of the night sky, etc.). For a long time this part of the ozonosphere remained inaccessible to investigation. Indirect (optical) methods could not provide information about it because of the screening action of the lower layers of air, which contain more ozone. The ceiling of direct methods, too, as we know, was limited to lower altitudes until rockets began to be used. But even with the aid of rockets, for a long time it was not possible not only to exceed, but even to reach, the altitudes up to which the structure of the ozone layer had previously been repeatedly determined by indirect methods. The rocket curves of the vertical distribution of ozone (Fig. 22) broke off at an altitude of 45 km. Because of the small ozone content in the air (of the order of 1 μ/km and less), absorption of light by atmospheric ozone became so weak that measurements at still greater altitudes proved impossible.

To overcome this difficulty, rocket launches were organized at a time of day when the sun was near the horizon. In this case the path of the rays through the atmosphere is considerably lengthened and, correspondingly, the absorption of sunlight by ozone increases. By this method it proved possible to measure the ozone concentration up to an altitude of 70 km.

The first such ascent was carried out on June 14, 1949, at the White Sands range. The Aerobee rocket was launched from the point 32°24.4′ N lat., 106°20.4′ W long. at 19 hours 03 minutes local time, when the Sun was at an altitude of about 1° above the horizon. Having reached an altitude of 112 km, the rocket fell 34.8 miles north and 3.4 miles west of the launch site. During the flight more than 200 spectra of the Sun were obtained, covering the altitude region 19–110 km. Some of the spectra proved unsuitable for use. In the processing, the curvature of the Earth’s surface (and, consequently, of the ozone layers) was taken into account, since the Sun was near the horizon[^5]. However, the spectra of the Sun near the horizon taken in flight, even without photometric processing, make it possible to detect the presence of ozone up to an altitude of 65–70 km. In Fig. 23 several spectra obtained with a slit spectrograph are reproduced. The spectra taken from altitudes above 50 km—there are three of them in the figure—show a noticeable shift of the short-wavelength boundary as the altitude of the exposure changes. Thus, the edge of the spectrum taken from an altitude of 64.0 km is shifted by more than 100 Å relative to the spectrum corresponding to 60.4 km, which directly indicates the presence of ozone in the layer 60.4–64.0 km. Let us note that the upper spectrum covers the region of maximum ozone absorption near 2500 Å (see the ozone absorption curve in Fig. 2). From λ = 2500 Å toward shorter wavelengths the coefficient of ozone absorption decreases; however, on the spectrogram this radiation is absent (the energy of solar radiation in this region rapidly decreases toward decreasing λ).

The computed values of \(\varepsilon\) are given in Table III and in Fig. 24, on which the upper part of the curve \(\varepsilon(h)\) (for \(h > 50\) km) is plotted

Fig. 23. Solar spectra taken from a rocket by a slit spectrograph with the Sun at the horizon.

on a scale 100 times larger than the lower part. Fig. 25 presents the vertical distribution of the relative ozone content

Table III

Vertical distribution of ozone up to \(h = 70\) km according to rocket measurements of June 14, 1949

Altitude, km	Ozone concentration, \(\mu/\text{km}\)	Altitude, km	Ozone concentration, \(\mu/\text{km}\)	Altitude, km	Ozone concentration, \(\mu/\text{km}\)
20	91	38	25	56	0,51
22	96	40	16	58	0,36
24	99	42	12	60	0,30
26	108	44	9,4	62	0,19
28	103	46	6,4	64	0,12
30	89	48	3,2	66	0,065
32	75	50	2,2	68	0,038
34	57	52	1,3	70	0,025
36	39	54	0,74

Fig. 24. Vertical distribution of ozone up to an altitude of 65–70 km according to rocket measurements on June 14, 1949, and January 25, 1950.

Fig. 25. Vertical distribution of the relative ozone content in the air according to rocket measurements on June 14, 1949.

in the air (the number of ozone molecules in 1 cm\(^3\) relative to the number of air molecules).

Knowing the distribution \(\varepsilon\) along the vertical, one can, by summation, compute the total amount of ozone \(x_0\) contained in the vertical column of air above a given level. The dependence of \(x_0\) on \(h\) is shown in Fig. 26. As is evident from this graph, the amount of ozone above the level 70 km is less than \(0.1\mu\). In the same figure the cross marks the value \(x_0 = 1.9\) mm, obtained from measurements from the earth’s surface on the same day and at the same point. Simultaneous measurements carried out at a mountain station situated at an altitude of 2760 m above sea level, about 70 km from the rocket-launch site, gave \(x = 1.76\) and \(1.86\) mm. Both these values agree well with the extrapolated portion of the rocket curve, shown by the dotted line.

Fig. 26. Total amount of ozone above a given level on June 14, 1949. (Solid line—according to rocket measurements; cross—according to measurements from the earth’s surface).

The measurements described, made on June 14, 1949, were carried out by the U.S. Naval Research Laboratory. Another scientific center in the U.S.A., where considerable work is being done on the study of the atmosphere and solar radiation with the aid of rockets, is the Johns Hopkins Applied Physical Laboratory. The results of measurements of ozone content up to \(h = 65\) km, carried out by this laboratory on January 25, 1950, are shown in Fig. 24. Comparison with the curve of June 14, 1949, indicates close agreement of the data in the upper part of the ozonosphere (above 50 km); in the middle and lower parts, however, there are large differences, caused, as we shall see below (see § 11), by the influence of meteorological processes in the troposphere and stratosphere.

THEORY OF THE OZONOSPHERE

4. Nature of the ozone layer. The ultraviolet radiation of the Sun plays a dual role with respect to ozone: it promotes the formation of ozone and destroys its molecules. Radiation of 1220–1759 Å (the Schumann–Runge continuum, see Fig. 27) is absorbed by oxygen, causing its dissociation and thereby creating the prerequisites for the formation of ozone. The same effect is produced by absorp-

radiation in the Herzberg continuum, beginning at \(\lambda = 2423\) Å. But radiation of \(2200\)—\(3100\) Å is absorbed by ozone and causes dissociation of its molecules:

\[ \mathrm{O}_3 + h\nu \to \mathrm{O}_2 + \mathrm{O}. \tag{4.1} \]

These two opposite processes must, evidently, balance each other at some concentration of ozone.

Elementary considerations make it possible to understand why ozone exists in the atmosphere in the form of a layer at a certain altitude. In the upper

Fig. 27. Absorption spectrum of oxygen \(\mathrm{O}_3\).

layers there should be little ozone: because of the high intensity of rays with wavelengths \(2200\)—\(3100\) Å, rapid destruction of ozone molecules takes place there. But this radiation penetrates into the lower layers weakened; the intensity of ozone destruction decreases, and the ozone content increases. In the still lower layers of the atmosphere, there is a decrease in the content of atomic oxygen, due to the fact that the short-wave radiation producing it is absorbed in higher layers. A decrease in the number of oxygen atoms slows the formation of ozone. In addition, in the higher layers of the atmosphere there are very few \(\mathrm{O}_2\) molecules (as a result of significant dissociation of oxygen), and therefore the probability of an encounter of O atoms with an \(\mathrm{O}_2\) molecule is small. Thus the ozone layer arises.

The processes of dissociation of molecules (1) and (4.1) can lead to the formation of excited atoms and molecules. Figs. 28 and 29 show schemes of the energy levels of the oxygen atom and molecule (the numbers near the arrows indicate the wavelengths of the spectral lines in Å). For \(O_2\) the electronic levels are given, while the vibrational and rotational levels are omitted.

Fig. 28. Energy levels of the oxygen atom.

The Schumann–Runge absorption system, caused by the transition of the molecule from the ground level \({}^{3}\Sigma_g^{-}\) to the level \({}^{3}\Sigma_u^{-}\), consists of a large number of closely spaced bands. The system extends\(^{43}\) from \(\lambda = 2010\) to \(\lambda = 1759\) Å. Near \(\lambda = 1759\) Å the band system converges, passing into a continuous absorption spectrum. The Schumann–Runge continuum continues to \(\lambda = 1220\) Å.

Fig. 29. Energy levels of the oxygen molecule.

The Herzberg band system \((2600\text{—}2423\ \text{Å})\) is associated with the transitions \({}^{3}\Sigma_g^{-} \to {}^{3}\Sigma_u^{+}\). The bands seem to pass into a continuum\(^{43}\) at \(\lambda = 2423\) Å, extending to 2010 Å. Absorption in the Herzberg region is very small; its quantitative study is associated with difficulties.

The transition \({}^{3}\Sigma_g^{-} \to {}^{3}\Sigma_g^{+}\) corresponds to the atmospheric bands, which are located in the visible region and are seen as absorption bands in spectra of the light of the sky (Fraunhofer bands \(B\), \(a\), \(A\), and \(Z\)).

The presence in the stratosphere of excited oxygen molecules \(O_2^*\) affects the process of ozone formation. The collision of an excited molecule with an unexcited one may lead to the formation of ozone:

\[ O_2^* + O_2 \to (O_2 + O) + O \to O_3 + O. \tag{4.2} \]

This reaction means that, simultaneously with the dissociation of the molecule, one of the oxygen atoms combines with an \(O_2\) molecule. The reaction may be the result of the absorption of solar ultraviolet radiation by molecular oxygen in the region of the Herzberg bands,

Graph labels: vertical axis—“molecular absorption coefficient \((\mathrm{cm}^{-1})\)”; horizontal axis—“wavelength \((\text{\AA})\)”; right-side arrow—“onset of the Schumann–Runge bands.”

Fig. 30. Absorption coefficient of oxygen in the Herzberg continuum: \(\odot\)—according to A. Vassy’s data \(^{50}\); \(\times\)—according to Buisson’s data \(^{49}\); — curve adopted by Nicolet and Mange \(^{43}\).

although it must be borne in mind that these bands are very weak (they are due to forbidden transitions). Laboratory experiments have shown \(^{44}\) that irradiation of oxygen with light of \(\lambda 2530\) leads to the formation of ozone. Quanta corresponding to this wavelength cannot cause dissociation of \(O_2\). In the Herzberg region, dissociation is produced by absorption in the continuum at \(\lambda < 2423\ \text{\AA}\), with \(O_2\) dissociating into two neutral atoms in the \({}^3P\) state. Fig. 30 gives a curve showing the dependence of the absorption coefficient

oxygen on the wavelength in the Herzberg continuum ^45, ^46, ^47–51 (the values of the coefficients in \(\mathrm{cm}^2\) are referred to one absorbing molecule ^43).

Upon absorption of \(\lambda 2530\), excitation of the oxygen molecule occurs,

\[ \mathrm{O}_2 + h\nu \to \mathrm{O}_2^*({}^3\Sigma_g^+), \]

and then the excited molecule enters into reaction (4.2)

\[ \mathrm{O}_2({}^3\Sigma_g^+) + \mathrm{O}_2 \to \mathrm{O}_3 + \mathrm{O}. \tag{4.3} \]

Absorption in the Schumann–Runge bands (2010–1759 Å) produces a somewhat different effect. Absorption of light here also first leads to excitation of the oxygen molecule, but the character of the excited state of the molecule is such that after a certain time it can ^52 spontaneously break up into two atoms (predissociation). The absorption coefficient in these bands has not yet been

Fig. 31. Potential-energy curves of the \(\mathrm{O}_2\) molecule.

determined accurately; according to some data ^53, in an oxygen layer \(20\ \mathrm{cm}\) thick under normal conditions, radiation \(\lambda 1860\) is attenuated to \(1/3\), and for the longer-wavelength bands the absorption is somewhat greater ^1.

Both the excited \(\mathrm{O}_2\) molecules and the O atoms formed as a result of light absorption in the Schumann–Runge bands can react with a normal \(\mathrm{O}_2\) molecule, forming ozone—reactions (4.3) and (2).

Absorption in the Schumann—Runge continuum (1759–1220 Å) leads to the dissociation of oxygen molecules, and (see Fig. 31) one of the atoms is produced in an excited state:

\[ \mathrm{O}_2+h\nu \rightarrow \mathrm{O}(^3P)+\mathrm{O}(^1D). \tag{4.4} \]

This reaction occurs upon absorption of light with \(\lambda \leq 1759\) Å, but upon absorption with \(\lambda \leq 2423\) Å the molecule breaks up into two unexcited atoms\({}^{43}\):

\[ \mathrm{O}_2+h\nu \rightarrow \mathrm{O}(^3P)+\mathrm{O}(^3P). \tag{4.5} \]

Absorption in the region under consideration is extremely strong. Figure 32 gives the values of the molecular absorption coefficients according to the measurements of Ladenburg and Wourchis\({}^{55}\) and the values,

Fig. 32. Oxygen absorption coefficient in the Schumann—Runge continuum: from 1333 to 1667 Å—according to the measurements of Ladenburg and Wourchis\({}^{55}\); from 1667 to 1759 Å—extrapolation by Penndorf\({}^{56}\), Bates and Nicolet\({}^{57}\), Moses and Yu Ta-Yu\({}^{58}\).

obtained by graphical and theoretical extrapolation\({}^{56–58}\). A layer of oxygen only \(0.0014\ \text{cm}\) thick under normal conditions attenuates the radiation by a factor of two. Figure 33 shows the results of more recent measurements by Watanabe, Inn, and Zelikoff\({}^{59}\), obtained with the aid of a one-meter vacuum monochromator and a photomultiplier with a fluorescent screen of sodium salicylate. The shape of the continuum is not symmetric; its maximum is located at 1420 Å.

Thus, there are three spectral regions in which absorption, directly or through subsequent processes, can lead to the dissociation of oxygen. However, the absorption features in each of the three regions make their participation in ozone-formation reactions unequal\(^{60,61}\). Absorption in the Herzberg bands, which causes reactions (4.2), falls in the region of strong ozone absorption and therefore cannot play a large role. The role of reaction (4.4) must also be secondary, since absorption in the Schumann—Runge continuum is so strong that solar radiation of these wavelengths is completely expended on the dissociation of oxygen at altitudes above 80 km. The main reaction of ozone formation (2) requires the participation of a third partner, but the probability of triple collisions decreases with altitude faster than the probability of double collisions. The probability of triple collisions at altitudes above 80 km proves to be negligibly small. As was pointed out as early as 1930 by Chapman\(^{65–68}\), the founder of the theory of the ozone layer, the lowest pressure at which triple collisions still play a noticeable role is \(10^{-2}\) mm Hg. Such a pressure corresponds to an altitude of 80 km. At greater altitudes, triple collisions occur so rarely that even at high concentrations of oxygen molecules the formation of ozone through reaction (2) becomes negligibly slow.

Fig. 33. Absorption coefficient of oxygen in the Schumann—Runge continuum according to the measurements of Watanabe, Inn, and Zelikoff\(^{59}\).

In the most favorable position are the Schumann—Runge bands. Absorption by oxygen in this region is sufficiently small that it does not prevent solar radiation from penetrating into lower layers. Thus, radiation with \(\lambda 1860\) can reach the 45 km level, being comparatively little (by a factor of two) attenuated and therefore capable of

produce here a large number of excited molecules \(O_2\). Radiation of \(\lambda 1930\) reaches the level of 35 km, likewise having an intensity of about \(1/10\) of the initial one\(^{54}\). The excited \(O_2\) molecules that are formed can, as we know, react with a normal \(O_2\) molecule, forming ozone (reaction 4.3). In addition, the oxygen atoms arising in this reaction and as a result of the predissociation of excited \(O_2^*\) molecules form ozone molecules according to reaction (2). Owing to the sufficiently large pressure at altitudes \(h < 45\) km, the probability of triple collisions here is relatively high.

Thus, the formation of ozone in the stratosphere must occur predominantly as a result of the absorption of the Sun’s ultraviolet radiation by oxygen in the region of the Schumann–Runge bands.

As we already know, simultaneously with the formation of ozone molecules their destruction continually takes place under the action of the Sun’s rays

\[ O_3 + h\nu \to O_2 + O^* \tag{4.1a} \]

and in collisions with oxygen atoms

\[ O_3 + O \to 2O_2^*. \tag{4.6} \]

The destruction of ozone molecules by light can occur under the action of red rays\(^{62}\) and even infrared\(^{69,70}\) radiation \(\lambda < 11340\) Å, but under atmospheric conditions photodissociation is caused mainly by absorption in the Hartley bands (2300–3100 Å). Reaction (4.1a) is intensified in the presence of water vapor, which acts as a catalyst. Laboratory experiments have established\(^{63,64}\) that the quantum yield of the reaction increases proportionally to the concentration of water molecules (this phenomenon has a large influence on the destruction of \(O_3\) molecules in the tropical troposphere; see § 12).

Attempts have repeatedly been made to calculate theoretically the vertical distribution of ozone, taking into account the processes considered above of the formation and destruction of \(O_3\) molecules. It has been possible to construct a theory that makes it possible, in general terms, to give a quantitative interpretation of many properties of the ozone layer. The starting point was Chapman’s work\(^{66}\). An account of the investigations carried out up to 1949–1951 can be found in the books by Mitra\(^{1}\) and Prokof’eva\(^{2}\). But in recent years new important results have been obtained, which we shall consider in § 5.

1. Theoretical calculation of the vertical distribution of ozone. The starting point of the theory is the assumption that the number of particles in \(1\ \mathrm{cm}^3\) of ozone molecules \(n_3\) in any layer of the stratosphere corresponds to photochemical equilibrium. This means that the concentration \(n_3\) is such that the number of ozone molecules being formed is equal to the number of molecules being destroyed by various methods in the same time and in the same volume.

If \(n\) is the total number of particles (of various kinds) in \(1\ \mathrm{cm}^3\) (concentration), \(n_1\) is the concentration of oxygen atoms, \(n_2\) is the concentra-

If the number of \(O_2\) molecules is denoted by \(n_2\), then the number of reactions forming ozone molecules (2) that occur per 1 sec in \(1\ \mathrm{cm}^3\) must be equal to the product \(k_{12} n_1 n_2\), where \(k_{12}\) is the constant of this reaction. The number of acts of photodissociation of \(O_3\) molecules, i.e., the number of reactions (4.1), is equal to the number of photons absorbed per 1 sec by ozone molecules contained in \(1\ \mathrm{cm}^3\). It can be represented in the form \(D_3 n_3\), where \(D_3\) is a coefficient equal to the number of acts of photodissociation (4.1) per 1 sec, referred to one \(O_3\) molecule. This coefficient is equal to \(D_3 = a_3 I_3\), where \(a_3\) is the molecular absorption coefficient of ozone (referred to one molecule), and \(I_3\) is the intensity of solar radiation in the absorption region of ozone (expressed as the number of photons per 1 sec per \(1\ \mathrm{cm}^2\)). The number of ozone molecules destroyed per 1 sec in \(1\ \mathrm{cm}^3\) by recombination with oxygen atoms (reaction (4.6)) may be expressed by the product \(k_{13} n_1 n_3\), where \(k_{13}\) is the reaction constant.

Generally speaking, the loss of ozone may also occur as a result of the reaction

\[ O_3 + O_3 \to 3O_2 . \tag{5.1} \]

The number of molecules destroyed in this way must be equal to the product \(2k_{33} n_3^2\), where \(k_{33}\) is the constant of this reaction. The coefficient 2 takes into account that as a result of each such reaction two ozone molecules disappear.

The condition of photochemical equilibrium of ozone may be written in the form of the equation

\[ k_{12} n_1 n_2 = D_3 n_3 + k_{13} n_1 n_3 + 2k_{33} n_3^2 . \tag{5.2} \]

The left-hand side of this equation takes into account the number of molecules formed, and the right-hand side the number destroyed.

If the constants \(k_{12}\), \(k_{13}\), and \(k_{33}\), the coefficient \(D_3\), and the total concentration of molecules \(n\) may be regarded as known in advance, then the concentrations \(n_1\) and \(n_2\) themselves depend on the processes of formation and destruction of ozone molecules, i.e., they must be determined from (5.2). Thus, equation (5.2) contains three unknown functions \(n_1\), \(n_2\), and \(n_3\), and two additional independent equations are required to determine them.

The necessary equations may be composed on the basis of considerations concerning the photochemical equilibrium of atomic and molecular oxygen and are analogous to the equation for ozone equilibrium (5.2). The equilibrium condition for atomic oxygen is

\[ 2D_2 n_2 + D_3 n_3 = k_{11} n_1^2 + k_{12} n_1 n_2 + k_{13} n_1 n_3 . \tag{5.3} \]

The left-hand side of this equation takes into account the formation of oxygen atoms by photodissociation of \(O_2\) and \(O_3\) molecules. The coefficient \(D_2\) is equal to the number of acts of photodissociation (1), referred to one \(O_2\) molecule, with \(D_2 = a_2 I_2\), where \(a_2\) is the molecular coefficient

absorption of oxygen, \(I_2\) is the intensity of solar radiation in the absorption region of the \(O_2\) molecule, expressed as the number of photons per 1 sec. per 1 cm\(^2\). In the right-hand side of the equation, reactions leading to the disappearance of atoms are taken into account: recombination of two atoms into a molecule in a triple collision, recombination of atoms with \(O_2\) molecules (also as a result of triple collisions), and the recombination reaction (4.6).

The equilibrium condition for molecular oxygen can be written in an analogous way:

\[ D_3 n_3 + k_{13} n_1 n_3 = k_{12} n_1 n_2 . \tag{5.4} \]

These equations, first formulated in 1930–1931 by Chapman \(^{65-68}\), are usually used as the basis for various versions of the photochemical theory of ozone. As the values of the coefficients of the equations and the total contribution of individual reactions to the process of photochemical equilibrium are refined, these equations are supplemented with new terms or, for the purpose of simplifying their solution, freed from those terms whose role in the overall balance is small. The works set forth in the books of Mitra \(^{1}\) and Prokof’eva \(^{2}\) are based on assumptions about the extraterrestrial radiation of the Sun in the ultraviolet region that existed before the rocket-research data were obtained; however, the latter substantially changed our ideas about this radiation \(^{12}\). Photographing the solar spectrum from high layers, repeatedly carried out since 1946 with rockets, revealed a large “deficit” of short-wave ultraviolet radiation of the Sun in the region where the dissociative absorption of oxygen and ozone molecules is concentrated. These new data were used in Petzold’s calculations in 1953.

Starting from the primary reactions (1) and (4.1) and the secondary reactions (2) and (4.6), Petzold \(^{69,70}\) obtained for the equilibrium concentration of ozone \(n_3\) an equation of the form

\[ n_3 = C n_2 n_1^{1/2} \sqrt{ \frac{k_{12}}{k_{13}} \cdot \frac{p_{O_2}}{p_{O_3}} \cdot \frac{D_2}{D_3} }, \tag{5.5} \]

where \(C\) is a factor depending on the choice of units of measurement. Using the experimental data of Eucken and Patat \(^{71}\), Petzold assumes for the ratio \(k_{12}/k_{13}\) the following temperature dependence:

\[ \frac{k_{12}}{k_{13}} = 3.5 \cdot 10^{-20} \sqrt{T}\, e^{\frac{6180}{RT}} . \]

The quantum yield \(p_{O_2}\) of the process of photodissociation of \(O_2\) molecules (1), depending on the absorption region and on the state of the dissociation products, varies over wide limits \(^{72}\), from 0.04 to the largest possible value 2 (two newly formed oxygen atoms correspond to one absorbed photon). To simplify the calculations, Petzold takes the averaged value \(p_{O_2} = 1\).

The quantum yield \(\rho_{O_3}\) of ozone photodissociation he takes to be equal to 1 (each absorbed photon dissociates an \(O_3\) molecule).

Fig. 34. Energy absorbed by oxygen (number of photons/cm\(^3\)) at different altitudes (four variants calculated by Petzold).

For estimating the extra-atmospheric intensity of solar radiation in the region \(\lambda < 3000\,\text{\AA}\), Petzold uses the published

Table IV

Extra-atmospheric distribution of energy in the solar spectrum
(number of photons per \(1\ \text{cm}^2\) per second falling within
a spectral interval of \(10\ \text{\AA}\))

Spectral region, \(\text{\AA}\)	Variant I	Variant II	Blackbody radiation \(6000^\circ\text{K}\)
1800—1850	\(8.4\cdot 10^{10}\)	\(3.3\cdot 10^{11}\)	\(6.0\cdot 10^{12}\)
1850—1900	\(1.3\cdot 10^{11}\)	\(5.3\cdot 10^{11}\)	\(7.8\cdot 10^{12}\)
1900—1950	\(1.8\cdot 10^{11}\)	\(7.2\cdot 10^{11}\)	\(9.7\cdot 10^{12}\)
1950—2000	\(2.6\cdot 10^{11}\)	\(1.0\cdot 10^{12}\)	\(1.2\cdot 10^{13}\)
2000—2100	\(4.4\cdot 10^{11}\)	\(1.7\cdot 10^{12}\)	\(1.7\cdot 10^{13}\)
2100—2200	\(1.4\cdot 10^{12}\)	\(3.0\cdot 10^{12}\)	\(2.4\cdot 10^{13}\)
2200—2400	\(4.0\cdot 10^{12}\)	\(5.0\cdot 10^{12}\)	\(3.5\cdot 10^{13}\)
2400—2600	\(8.5\cdot 10^{12}\)	\(1.0\cdot 10^{13}\)	\(5.9\cdot 10^{13}\)
2600—2800	\(1.8\cdot 10^{13}\)	\(1.8\cdot 10^{13}\)	\(8.9\cdot 10^{13}\)
2800—3000	\(5.5\cdot 10^{13}\)	\(5.5\cdot 10^{13}\)	\(1.23\cdot 10^{14}\)

in 1947, the results of rocket investigations[^73]. These data cover the wavelength region 2800–2200 Å and contain no information for the particularly interesting interval \(\lambda < 2100\) Å. In his calculations, Petzold takes two variants of the extra-atmospheric distribution of energy in the solar spectrum. For comparison, Table IV gives data on the radiation of a black body at a temperature of \(6000^\circ\) K. In addition, because of the absence

Fig. 35. Vertical distribution of equilibrium ozone concentrations calculated by formula (5.5) under different assumptions about the extra-atmospheric intensity of solar radiation (Table IV) and about the dependence of oxygen absorption on pressure (Petzold).

of definitive data on the dependence of the oxygen absorption coefficient on pressure, Petzold assumes two variants of this dependence: (a) the absorption coefficient is proportional to the air pressure \(p\) to the power 1.4; (b) the absorption coefficient is proportional to \(p\). In all, four variants of the calculations are obtained—combinations of variants I–II and a)–b): the first variant is Ia; the second is IIa; the third is Ib; the fourth is IIb.

The results of the calculations for these four variants are shown in Figs. 34 and 35. The first of them shows how much energy (how many photons) of solar radiation dissociating the \(O_2\) molecules (“ozonizing radiation”) is absorbed in \(1\ \text{cm}^3\) of air at a given altitude[^70]. Fig. 35 gives the calculated[^69],[^70]

according to formula (5.5), curves of the vertical distribution of equilibrium ozone concentrations (in $\mu/\mathrm{km}$).

These curves show that the height of the maximum ozone concentration depends little on the choice of variant and is close to the observed one. Photochemical formation of ozone cannot occur below the level of 10–15 km.

The indicated calculations were carried out by Pétjol’d for the solar zenith distance $Z = 45^\circ$ and under the assumption that the air temperature decreases uniformly with height in the region 0–16 km, in the layer 16–20 km it has a constant value ($-60^\circ$ C), above 22 km the temperature increases by $3^\circ$ for each kilometer, and above the level of 47 km it again retains a constant value $+15^\circ$ (variant $A$). However, the air temperature in the middle stratosphere is subject to large fluctuations, which may affect the magnitude of the equilibrium concentration of ozone $n_3$. In order to estimate the influence of temperature on the photochemical equilibrium of ozone, Pétjol’d, in addition to the variant $A$ indicated above, calculated the distribution of ozone for two more types of temperature regime of the stratosphere:

$B$. The temperature decreases uniformly from the Earth to $h = 22$ km, and above remains constant ($-60^\circ$ C).

$C$. The temperature decreases uniformly in the region 0–10 km, and above it remains constant ($-25^\circ$ C).

Fig. 36. Vertical distribution of ozone under different temperature regimes of the stratosphere (Pétjol’d).

The equilibrium concentration values calculated under these three assumptions (in $\mu/\mathrm{km}$) are shown in Fig. 36 (for variant Ia, $Z = 45^\circ$). The dependence of the vertical distribution of ozone on the solar zenith distance is presented in Fig. 37 (variant Ia, temperature distribution $A$). The values of $x$ (the total ozone content in the atmosphere) for the four calculation variants considered above and for different solar zenith distances (computed by integrating the function $\varepsilon(h)$, Fig. 35, over the height $h$) are given in Table V.

The influence of the temperature regime of the stratosphere and of the solar zenith distance on the ozone concentration, illustrated by the curves in Figs. 36–37 and Table V, to some extent characterizes the wi-

...linear dependence and seasonal variations of ozone, as they are obtained from the theory of photochemical equilibrium.

Table V

Ozone content in the atmosphere for different calculation variants
(in cm of reduced layer thickness)

Zenith distance of the Sun	Calculation variants	Calculation variants	Calculation variants	Calculation variants
	1	2	3	4
0°	0.46	0.57	0.23	0.44
45°	0.30	0.37	0.22	0.29
70°	0.15	0.19	0.09	0.12

An increase in the zenith distance of the Sun is equivalent to an increase in geographic latitude or to a transition from summer to winter. In this respect the results of the photochemical theory are in contradiction with observations. From Table V it follows that the total ozone content in the atmosphere should increase from high latitudes toward middle latitudes and, further, toward the equator. In fact, as we know (§ 1), the dependence of \(x\) on latitude is just the opposite. An analogous contradiction is obtained for latitudinal measurements of the vertical distribution of ozone.

Fig. 38 shows the schematic comparison, given in Petzold’s work \(^{74}\), of the averaged distributions of ozone with height observed at different latitudes with those calculated by the photochemical theory. The shaded areas between the curves show the “deficit” of ozone in comparison with the results of the photochemical theory. This deficit is almost entirely confined to the region of the ozonosphere located below the maximum of the curve, and increases toward the equator.

Similar results were obtained in 1956 by Dütsch.

The possible causes of such discrepancies will be considered by us later.

The presence of appreciable amounts of ozone at heights of 60–70 km, established by rocket measurements (see § 3), makes it necessary to examine specially this upper part of the ozonosphere from the standpoint of the theory of photochemical equilibrium. The corresponding calculation was publi-

Fig. 37. Vertical distribution of ozone at different zenith distances of the Sun.

... by Johnson, Purcell, Tousey, and Watanabe\(^{42}\) in 1952. They started from reactions (1), (2), (4.1), (4.6), and (5.1), and, in addition, took into account two more reactions:

\[ \mathrm{O}+\mathrm{O}+\mathrm{M}\to \mathrm{O}_2+\mathrm{M}, \tag{5.6} \]

\[ \mathrm{O}_3+\mathrm{O}_2\to \mathrm{O}+2\mathrm{O}_2. \tag{5.7} \]

These authors believe that, for layers situated above 50 km, where the relative concentration of atomic oxygen increases above the ozone layer, there is a transition layer “\(\mathrm{O}_2-\mathrm{O}\)”—a transition from almost undissociated oxygen \(\mathrm{O}_2\) to almost completely dissociated oxygen; see, for example, Mitra\(^{1}\); it is impossible to neglect the oxygen recombination reaction (5.6), as was done by many authors for the main part of the ozonosphere\(^{72,75,76}\). The equations for the rates of change of the concentrations of O atoms and \(\mathrm{O}_3\) molecules are written in the form

\[ \frac{dn_1}{dt} = 2D_2 n_2 + D_3 n_3 -2k_{11}n_1^2 n -k_{12}n_1 n_2 n -k_{13}n_1 n_3 +k_{23}n_2 n_3, \tag{5.8} \]

\[ \frac{dn_3}{dt} = -D_3 n_3 +k_{12}n_1 n_2 n -k_{13}n_1 n_3 -2k_{33}n_3^2 -k_{23}n_2 n_3. \tag{5.9} \]

Fig. 38. Schematic comparison of averaged curves of the distribution of ozone with altitude, observed at different latitudes, with those calculated from the photochemical theory: \(a\)—equator; \(b\)—47° N lat.; \(v\)—70° N lat. Solid line—observations; dashed line—theoretical calculation; dotted line—second maximum observed in spring at temperate and high latitudes.

In the calculations, the numerical values of the parameters entering equations (5.8) and (5.9), shown in Table VI, were adopted. The quantities \(D_2\) and \(D_3\) were taken from Craig’s work\(^{76}\), who calculated them

Ozone in the Stratosphere

Table VI

Numerical values of the parameters in equations (5.8) and (5.9)

Altitude, km	\(T\ ^\circ\mathrm{K}\)	\(n\)	\(k_{11}\cdot 10^{32}\)	\(k_{12}\cdot 10^{35}\)	\(\dfrac{k_{12}}{k_{13}}\)
30	225	\(4.2\cdot 10^{17}\)	1.8	6.8	\(4.5\cdot 10^{-19}\)
40	265	\(8.5\cdot 10^{16}\)	2.0	7.4	\(5.6\cdot 10^{-20}\)
50	280	\(2.3\cdot 10^{16}\)	2.0	7.6	\(3.1\cdot 10^{-20}\)
60	260	\(7.5\cdot 10^{15}\)	2.0	7.3	\(7.0\cdot 10^{-20}\)
70	215	\(2.0\cdot 10^{15}\)	1.8	6.7	\(9.0\cdot 10^{-19}\)
80	190	\(4.5\cdot 10^{14}\)	1.7	6.3	\(5.4\cdot 10^{-18}\)
90	225	\(1.0\cdot 10^{14}\)	1.8	6.8	\(4.5\cdot 10^{-19}\)

Altitude, km	\(k_{33}\)	\(k_{23}\)	\(D_2\)	\(D_3\cdot 10^3\)
30	\(2.5\cdot 10^{-32}\)	\(1\cdot 10^{-34}\)	\(2.0\cdot 10^{-11}\)	0.6
40	\(1.1\cdot 10^{-28}\)	\(2\cdot 10^{-30}\)	\(8.0\cdot 10^{-10}\)	4.5
50	\(1.4\cdot 10^{-29}\)	\(5\cdot 10^{-29}\)	\(1.2\cdot 10^{-9}\)	8.2
60	\(4.0\cdot 10^{-29}\)	\(9\cdot 10^{-31}\)	\(1.8\cdot 10^{-9}\)	8.7
70	\(2.5\cdot 10^{-33}\)	\(5\cdot 10^{-36}\)	\(3.3\cdot 10^{-9}\)	8.8
80	\(6.4\cdot 10^{-36}\)	\(6\cdot 10^{-40}\)	\(6.0\cdot 10^{-9}\)	8.9
90	\(2.5\cdot 10^{-32}\)	\(1\cdot 10^{-34}\)	\(1.0\cdot 10^{-8}\)	9.0

taking into account rocket measurements \(^{77}\) of the Sun’s ultraviolet radiation on October 10, 1946. The data for \(n\) and \(T\) were obtained by simple averaging of the results of a number of rocket measurements \(^{78}\); \(n_2\) was calculated under the assumption that at all altitudes oxygen is present in an amount of 21%. The ratio \(k_{12}/k_{13}\) was taken from the work of Eucken and Patat \(^{71}\), the values of the coefficients \(k_{11}\), \(k_{33}\), and \(k_{23}\) from the work of Dütsch \(^{75}\), and the coefficient \(k_{12}\) from the work of Schreier \(^{72}\).

Equations (5.8) and (5.9) were simplified by omitting terms containing the coefficients \(k_{33}\) and \(k_{23}\), which throughout the region of the atmosphere under consideration are very small in comparison with the principal terms of the equations. Accordingly, the equations of photochemical equilibrium were used in the form

\[ 2D_2n_2 + D_3n_3 - 2k_{11}n_1^2n - k_{12}n_1n_2n - k_{13}n_1n_3 = 0, \tag{5.10} \]

\[ - D_3n_3 + k_{12}n_1n_2n - k_{13}n_1n_3 = 0. \tag{5.11} \]

From these equations one can obtain an expression for \(n_1\):

\[ n_1=\frac{D_2 n_2}{k_{11}n_1 n+k_{13}n_3}, \tag{5.12} \]

and then equation (5.11) can be written in the form

\[ n_3=\frac{k_{12}n_1 n_2 n}{D_3+k_{13}n_1}. \tag{5.13} \]

The last two formulas served for the calculations of \(n_1\) and \(n_3\) in the region 30–90 km. The results of the calculations, together with the observed ozone concentrations, are given in Table VII and in Fig. 39.

Fig. 39. Comparison of ozone concentrations in the upper part of the ozone layer, obtained by rocket measurements (curve 1) and by calculations based on the theory of photochemical equilibrium; 2 — Johnson et al.\(^{42}\); 3 — Wulf and Deming (A); 4 — Wulf and Deming (D); 5 — Bates and Nicolet; 6 — Dütsch; 7 — Craig.

The agreement between the results of measurements and calculations is good. Fig. 39 gives curves calculated by other authors. The results of Craig and Dütsch do not agree with the experimental data. Johnson et al.\(^{42}\) see the reason for this in the fact that both Craig and Dütsch neglected triple collisions (5.6). On this basis they did not include the term \(2k_{11}n_1^2 n\) in equation (5.8), putting \(k_{11}=0\), which greatly simplified the problem and made it possible easily

solve equations (5.12) and (5.13) with respect to \(n_3\). However, this simplifying assumption is not justified for the region above 60 km, for which both terms in the denominator of equation (5.12) are of the same order of magnitude. Bates and Nicolet\(^{57}\) took into account reaction (5.6), but used somewhat different values of the constants. Their curve approximately coincides with the calculations of Johnson, Purcell, Tousey, and Watanabe.

Table VII

Concentration of O atoms and O\(_3\) molecules
in the ozonosphere

Altitude, km	Measured \(n_3\)	Calculated \(n_3\)	Calculated \(n_1\)
30	\(2.5\cdot 10^{12}\)	\(6.7\cdot 10^{12}\)	\(1.7\cdot 10^{9}\)
40	\(4.6\cdot 10^{11}\)	\(4.8\cdot 10^{11}\)	\(2.0\cdot 10^{10}\)
50	\(5.5\cdot 10^{10}\)	\(4.3\cdot 10^{10}\)	\(4.4\cdot 10^{10}\)
60	\(7.3\cdot 10^{9}\)	\(7.0\cdot 10^{9}\)	\(1.0\cdot 10^{11}\)
70	\(6.0\cdot 10^{3}\)	\(1.2\cdot 10^{9}\)	\(1.9\cdot 10^{11}\)
80	\(\ldots\)	\(7.6\cdot 10^{7}\)	\(2.7\cdot 10^{11}\)
90	\(\ldots\)	\(5\cdot 10^{6}\)	\(3.3\cdot 10^{11}\)

Thus, in the opinion of these authors,\(^{42}\) the experimental data should be regarded as direct confirmation that triple collisions (5.6) are significant for the ozone balance in the upper part of the ozone layer (above 60 km).

Wulf and Deming\(^{79-81}\) considered five variants with different numerical values of the ratios \(k_{12}/k_{13}\) and \(D_2/D_3\). They assumed that the distribution of energy in the solar spectrum corresponds to blackbody radiation at a temperature of \(6000^\circ\) K, which gives overestimated values in comparison with the quantities established by rocket measurements. Their extreme variants \(A\) and \(D\) are shown in Fig. 39.

According to the latest calculations of Dütsch,\(^{133}\) the concentration of O\(_3\) molecules in the upper part of the ozone layer is \(7\cdot 10^7\) (at an altitude of 80 km), \(1\cdot 10^9\) (70 km), \(6\cdot 10^9\) (60 km), \(3.4\cdot 10^{10}\) (50 km), and \(8.5\cdot 10^{10}\) (40 km).

THE PROBLEM “OZONE—WEATHER”

6. Ozone content as a conservative property of air. In the preceding paragraph, in calculating the equilibrium concentration of ozone, we did not consider the question of the time required for the establishment of photochemical equilibrium. Meanwhile this question is very important for understanding the role of ozone in the principal atmospheric processes. In a number of works in recent years an attempt has been made

an attempt to estimate the rate of restoration of the disturbed equilibrium. Nicolet \(^{82}\) proceeded from the equation

\[ \frac{dn_3}{dt}=2D_2n_2-\frac{2}{3}\frac{k_{13}}{k_{12}}\frac{D_3n_3^2}{n_2^2}, \tag{6.1} \]

in whose right-hand side the first term determines the rate of formation of ozone molecules, and the second—the rate of their destruction. It is clear that the rate of return to equilibrium depends on the power of the absorbed solar radiation. The time \(t\), calculated from (6.1), which is required for the restoration of photochemical equilibrium, depends on the altitude \(h\):

\(h\) (km)	32	25.5	19	12
\(t\) (sec.)	\(10^3\)	\(2\cdot10^3\)	\(10^6\)	\(10^{10}\)

According to these data, in the layers of the ozonosphere situated above 25 km, photochemical equilibrium obtains; its disturbances are rapidly restored. Below 20 km the disturbances are eliminated so slowly that the distribution of ozone with height must be determined mainly by the character of these disturbances, and not by photochemical reactions. The 25 km level is, as it were, transitional from one mechanism regulating the vertical distribution to another (the “critical level”).

Other investigators have also arrived at analogous conclusions; however, estimates of the level of the photochemically equilibrium ozonosphere do not always coincide. Thus, according to Schröer \(^{72}\), photochemical equilibrium is reached only above the level 33–35 km. According to his calculations, the time required for the formation (from zero) of the equilibrium concentration (if the photodissociation of ozone is neglected) is:

\(h\) (km)	45–50	40–45	35–40	30–35	25–30	20–25
\(t\) (sec.)	\(8\cdot10^3\)	\(2\cdot10^4\)	\(7\cdot10^4\)	\(5\cdot10^5\)	\(10^7\)	\(10^8\)

Values close to these were also obtained by Petiold \(^{69,83}\). According to his calculations, the time for the establishment of photochemical equilibrium is 20 days at an altitude of 30 km and increases to three years at an altitude of 20 km. Regener gives the following values \(^{37}\): below the 25 km level, photochemical equilibrium is reached in weeks and months; at an altitude of 35 km this process requires days; and in the 45–50 km layer, on the order of an hour. According to Wulf and Deming, the time during which the equilibrium concentration has time to become established by half is days at an altitude of 30 km and minutes at an altitude of 60 km. Normand \(^{84}\) summarizes the available data as follows: the equilibrium state of ozone is fully realized only above 35 km. Below 35 km the time for restoration of equilibrium rapidly increases, reaching weeks at an altitude of 27 km. According to the most recent calculations by Dütsch \(^{133}\) (1956), the “half-restoration” time is \(4\cdot10^3\) sec (at an altitude of 50 km), \(3\cdot10^4\) (40 km), \(10^5\) (35 km), \(5\cdot10^5\) (30 km), \(4\cdot10^6\) (25 km), \(2\cdot10^7\) (20 km), and \(2\cdot10^8\) sec at an altitude of 15 km.

Despite the divergence in the results of estimates of the rate at which the equilibrium concentration of ozone is restored, obtained by different authors (especially Nicolet), they make it possible to draw several important conclusions. Photochemical equilibrium is fully realized only in the upper part of the ozonosphere, above 30–35 km, where any disturbance of the equilibrium is rapidly (within a day or less) restored by the action of solar radiation. At lower altitudes the time required for the restoration of equilibrium becomes very large; beginning at a level of approximately 27 km it reaches such a large value (about a month and more) that any significant disturbance of the equilibrium is, in practice, no longer subject to noticeable restoration. As a result, ozone, regarded as an “impurity” in the air, acquires a new quality: the main mass of ozone may be considered “conservative” in the sense that, in the process of even slow displacements of air masses, the percentage content of ozone in a given portion of air remains practically unchanged. Accordingly, the problem of ozone acquires great meteorological significance, in particular for the study of the general circulation of the atmosphere. In recent years a new direction has taken shape in the study of atmospheric ozone—a meteorological one—with which we must become acquainted.

From the data given above on the rate of restoration of the equilibrium concentration, one may also conclude that ozone located below the 50 km level (and in this region almost all atmospheric ozone is found) apparently does not have time to respond to an increase (flare) of ultraviolet solar radiation during eruptions on the Sun, since even in the 45–50 km layer the process of establishing a new equilibrium concentration lasts for hours.

Significant fluctuations in the distribution of \(O_3\) molecules with altitude, especially in the lower part of the ozone layer, cannot be caused by photochemical reasons. Discussion of this question, widely developed in works of recent years, shows that the fluctuations are, basically, of a dynamic and circulatory nature.

For understanding the mechanism of ozone transport, the existence of a connection between the character of the vertical distribution of ozone and its total amount in the atmosphere is essential. Figure 40 presents one example of such a connection—typical curves of the distribution of ozone with altitude for small, medium, high, and very high contents of it (according to Geits\({}^{102}\)). This diagram also shows lines of equal percentage content of ozone in the air, which may be considered analogous to lines of equal water-vapor content in the air on tephigrams. At those altitudes where the ozone content is a conservative property, non-turbulent vertical displacements of the air must be described by motion along a line of equal ozone content. The process of mixing (exchange) of air must be accompanied by an equalization of the percentage content of ozone. The presen-

tion of ozone in the troposphere is, possibly, due to its influx from the stratosphere as a result of turbulent mixing \(^{85-87}\). In view of the conservative character of the percentage content of ozone in the air considered above, it should be pointed out that in the lower layers of the atmosphere this conservativeness is somewhat disturbed by processes of ozone destruction. Ozone has a high oxidizing capacity and is readily destroyed by readily oxidizable particles of organic origin suspended in the air. According to E. Regener \(^{85}\), the process of ozone destruction proceeds especially rapidly at the surface of the soil owing to the action of readily oxidizable organic substances.

Fig. 40. Typical curves of the vertical distribution of ozone at different amounts of it (according to Götz): --- low ozone content (Arosa, Umkehr effect), \(x = 0.20\ \text{cm}\); \(+++++\) average ozone content (Stuttgart, Regener sonde), \(x = 0.26\ \text{cm}\); — high ozone content (Tromsø, Umkehr effect), \(x = 0.34\ \text{cm}\); -·-·- very high ozone content (Tromsø, Umkehr effect), \(x = 0.40\ \text{cm}\); fine dotted lines—lines of equal percentage content of ozone in air.

The destructive action may also be exerted by solar radiation corresponding to the long-wave region of absorption of the \(O_3\) molecules; such action is intensified in the presence of water vapor. In the troposphere there is a convective flux of ozone directed, on the whole, downward \(^{88}\); its source is the “parent” ozone layer (the layer of photochemical formation of ozone), situated above \(20\ \text{km}\). According to Petzold’s estimate \(^{83}\), on the Earth over 1 year the vertical flux of ozone carries from the “parent” layer

$10^9$ tons of ozone. All the oxygen present in the atmosphere passes through the ozonized state once every $10^6$ years.

In the lower layers of the atmosphere there also occur processes of ozonization of air under the action of thunderstorm electrical discharges and the radioactivity of the soil (and also, perhaps, the radioactivity of aerosol particles suspended in the atmosphere).

7. Connection of ozone with the near-surface baric situation. As early as 1929 Dobson^89 drew attention to the existence of a connection between day-to-day changes in ozone content and weather conditions (the synoptic situation). On the basis of observations in the region of the British Isles he showed that to the west of the center there is a tendency toward an increase in ozone content, while inside an anticyclone there is a decrease in the content of $\mathrm{O}_3$. In the following years, through the works of Dobson^7, as well as Tönsberg and Langlo^92, who summarized extensive observational material in Scandinavia, the problem “ozone—weather” was considerably advanced by conclusions concerning fluctuations of ozone near frontal systems. Then, as material accumulated, mutually contradictory results^84 began to appear, as often happens in such cases. But the subsequent expansion of aerological investigations and the clarification of the synoptics of the higher layers of the atmosphere led to the problem acquiring sufficient definiteness, and very substantial facts were gradually clarified.

The numerous works published in recent years on the question under discussion may be divided into five groups:

1. Consideration of the meteorological conditions determining the ozone content in the near-surface layer of air.

2. Comparison of variations in the total amount of ozone in the atmosphere $x$ with ground-based meteorological observations.

3. Comparison of variations of $x$ with data from aerological investigations.

4. Analysis of the variability of curves of the vertical distribution of ozone up to great heights (30–50 km), taking account of aerological data.

5. Theoretical study of the possible influences of advective and dynamic processes in the atmosphere on the amount of ozone $x$ and its distribution with height.

We shall hardly touch upon the first group of works (see, for example,^88). In the second group, the many-year investigations by Dobson and a number of his collaborators in the region of the British Isles are of primary importance; a detailed account of these may be found in Dobson’s article^7, published earlier in Advances in the Physical Sciences. Here it should only be pointed out that works carried out in subsequent years in other countries confirmed Dobson’s main conclusions. From the many-year observations of Tönsberg and Langlo^92 in northern Norway it also follows that a low ozone content $x$ is found in the warm sector and in the region embraced by the warm

front, with a decrease in \(x\) often preceding the warm front by several hundred kilometers. Studying variations of ozone in connection with the movement of individual cyclones, they came to the conclusion that there exists a dependence of the rate of change of \(x\) on the speed of movement of cyclones. Tönsberg and Shalonzh \(^{91}\) as early as 1936 established a significant increase of ozone during the passage of a cold front, which was fully confirmed by subsequent observations in Norway \(^{92}\).

Fig. 41. Changes in the amount of ozone \(x\) at different distances from the center of an anticyclone. The arrow indicates the direction of movement of the anticyclone (Japan).

Processing of analogous materials for Japan, obtained during the period January 1951–September 1952 at the observatory of the Meteorological Research Institute in Tokyo (35°42′ N, 139°39′ E), led Miyake and Kawamura \(^{93,94}\) to the following conclusions. In the region of a moving anticyclone, positive deviations (an increase) of the ozone content from the mean value are observed in a zone extending 1000 km ahead of the center of the anticyclone and 300 km behind it. These data can be illustrated by a diagram (Fig. 41), on which the abscissa axis gives the distances between the observation point and the center of the anticyclone, as determined from the surface weather map; the arrow indicates the direction of movement of the anticyclone.

The conclusion of Dobson regarding an increase in ozone content after the passage of a cold front is confirmed. A large part of the observations pertains to baric systems (on surface weather maps) of the type shown in Fig. 42. The low-pressure area indicated at the top is localized in the Sea of Okhotsk or near Sakhalin, while the low-pressure area indicated on the left corresponds to an anticyclone advancing from the continent.

Fig. 42. Changes in the amount of ozone near the center of a typical cyclone (for the meaning of the circles see Fig. 41).

However, some differences are also noted in the character of these phenomena on the Asian coast of the Pacific Ocean as compared with what was established by Dobson for Europe. From observations in Shanghai, Lejay found that, when the center of the Siberian anticyclone passes through the observation point, positive deviations of the amount of ozone from the mean norm are usually observed, while near the pressure minimum in a cyclone, negative deviations are observed. Meanwhile, in Europe minimum amounts of ozone are observed in the rear of an anticyclone[^89]. Haurwitz attempted to remove this contradiction[^95]; he assumed that both the anticyclone extending over China and the rear of the cyclone over Western Europe have above them a trough of low pressure situated in the higher layers of the atmosphere.

In the works of Miyake and Kawamura[^93],[^94] it is also noted that the relation observed over Tokyo between ozone variations and the surface baric situation is more similar to the relation established in Shanghai than to the regularities in Europe. Miyake and Kawamura established, for a typical surface weather map in Japan (Fig. 42), that in the territory between two cold fronts a decrease in the amount of ozone \(x\) is observed and sometimes a minimum occurs near the center.

As for the equatorial region, as was established by observations of the Kodaikanal Observatory, interdiurnal variations of ozone there are barely expressed and no connection of them with weather has been detected[^84].

Fig. 43. Smoothed curves of changes in the amount of ozone \(x\), tropopause height \(h_{mn}\), and thickness of the 500–300 mb layer in the winter months over Oxford.

8. Ozone and circulation processes. Comparisons of variations in the amount of ozone in the atmosphere \(x\) with data from aerological investigations made it possible to establish the existence of a fairly clear correlation between the ozone content \(x\), the tropopause height \(h_{mn}\), and the thickness of the 500–300 mb layer \(Th_{400}\). In Fig. 43, as an example, smoothed curves are given for changes in \(x\),

$h_{rn}$ and $Th_{400}$ during the three winter months of 1950–1951 over Oxford (England). In this graph the vertical scale for $h_{rn}$ and $Th_{400}$ is oriented from top to bottom. Owing to the smoothing of these curves, long-period oscillations of the three elements, occurring, in general, in mutual agreement, are clearly revealed in them. But the correlation is not complete; in individual cases the agreement between changes in $x$, $h_{rn}$, and $Th_{400}$ is disturbed. For the three-month period under consideration such a case occurs in the week whose middle falls on January 9, 1951. Otherwise the course of the curves is identical.

A connection of this kind between $x$ and $h_{rn}$ is found in many other geographical regions. For example, from Johansen’s observations$^{96}$, carried out over $3\frac{1}{2}$ years (May 1941–October 1944) in Tromsø, the dependence shown in Fig. 44 was obtained. These data

Fig. 44. Mean annual course of the amount of ozone $x$ and of the tropopause height $h_{rn}$ over Tromsø (Johansen).

cover 941 determinations of $x$ and $h_{rn}$. Johansen processed them statistically and calculated the correlation coefficient $r(x,h)$ between the deviations $\Delta x$ and $\Delta h_{rn}$ from the mean curve of the annual course. The mean value of the correlation coefficient for Tromsø is

\[ r(x,h)=-0.54. \]

For Oxford, according to the initial investigations of Mees$^{57}$,

\[ r=-0.56. \]

There are grounds for believing that the relationship considered between the amount of ozone and the height of the tropopause has a circulation-related nature. From this point of view, the investigation by Sh. A. Bezverkhny is of great interest; using observational material from Alma-Ata (70 ozone measurements in 1953), he showed that the amount of ozone depends on the type of circulation$^{58}$. For his analysis he used charts of absolute baric topography (AT) up to heights of the 300-mb surface, and for greater heights, sounding data at individual points—

In order to characterize the synoptic situation, circulation macrotypes developed at the Kazakh Hydrometeorological Institute by M. Kh. Baidal2 were taken. Table VIII gives the characteristics of three types, summarizing 7 varieties. The result of the comparison is shown in Fig. 45, from which it is evident that substantially different ozone contents correspond to different types.

In addition to such a general comparison, trajectories of the motion of air particles over the course of three to seven days were constructed for all cases. The trajectories were constructed from pilot-balloon observation data plotted on \(AT_{500}\) charts. Comparison of the trajectories with the amount of ozone confirmed the conclusions. Three characteristic trajectories corresponding to the three selected circulation types are given in Fig. 46. Analysis of \(AT_{500}\) charts and of upper-level baric topography data for the 300 and 200 mb surfaces showed that the baric centers determining types II and III, on days with good correlation, move coherently at the indicated levels.

Fig. 45. Mean daily ozone content over Alma-Ata for three circulation types (Sh. A. Bezverkhnii).

However, there are dates for which such a relation is not obtained. One reason for this may be a substantial change in the mass along its path as a result of vertical displacement. Some judgment about this may be formed from the values of turbu-

Table VIII

Macrocirculation types according to M. Kh. Baidal

Type	Name of type	Characteristic of the type
I	Latitudinal	Movement of baric systems and air masses in a west–east direction with speeds greater than for the other types.
II	Meridional—C	Advection of heat from the south into Kazakhstan. The principal surface and upper-level maxima are located over Western Siberia and Kazakhstan.
III	Meridional—E	Inflow of cold air either directly from the north, or with some latitudinal component.

lence, or by the vertical component of velocity at the corresponding heights. Vertical motions of air in the stratosphere could have been measured with the aid of radiosondes^100, but it proved impossible to trace this quantity along the entire trajectory of motion of the mass because the station network lacked the observations needed for this purpose^98. Some conclusions, however, were obtained on the basis of qualitative judgments about convective motions in the air mass from the stratification of the given layer, determined for the corresponding dates and points along the path of the mass.

Fig. 46. Trajectories of motion of air particles toward Alma-Ata at a height of 500 mb above the surface (for masses that arrived in Alma-Ata: I — 14.9.1953; II — 4.9.1953; III — 9.4.1953).

It turned out that in those cases when the ozonometric observations do not fit the scheme (Fig. 45), phenomena that contribute to a change in the ozone content of the air mass along its path of motion are very probable (mixing of layers, considerable turbulence, etc.). For example, on 2.7.1953 in Alma-Ata an ozone amount of not less than \(x = 0.307\) cm was measured, although type-I circulation was present. The vertical temperature gradient for Aktyubinsk (29.6, 17 hours), Balkhash (1.7, 06 hours), and Alma-Ata (2.7, 06 hours) at heights of 10–15 km (there is evidence that in this layer the percentage ozone content is subject to especially large fluctuations, and the change in ozone concentration here is considerably greater than the percentage change of the total ozone in the atmosphere^90) reached 7.5 deg/km. With such large gradients, intensive vertical mixing can arise, as a result of which some quantity of ozone from the overlying layers, where the ozone concentration is greater, could have been carried into the layer under consideration. For the dates

with a well-defined connection the picture looks different. For heights above 11 km one usually has gradients \(\gamma \leq 0\).

Normand studied the causes of fluctuations in the amount of ozone over Oxford from height charts of the 300-mb surface[^84]. In Fig. 43 data are given relating to the winter months; we shall examine a separate large fluctuation of ozone that began on 8.12.1950. In Fig. 47

Fig. 47. Height charts (300-mb surface) on days with low and high ozone content over Oxford, corresponding to a long-period oscillation in the upper layers in December 1950.

are given the charts for December 8, 14, 15, and 19. On these days there were observed, respectively, low, high, high, and again low ozone contents (the amount of ozone in thousandths of a centimeter is indicated on the charts). The low ozone content coincides with the passage over Oxford of an upper-level ridge, and the high content with the passage of a trough. In general, this case is an example of a completed long-wave process in the upper-level current. The source of ozone-rich air on December 14 and 15, as also on December 4, is apparently located in the region of the winter Arctic.

Another illustration (Fig. 48) of the altitude conditions in winter consists of maps for January 21, 28, and 31 and February 6, 1951 (low, high, again low, and correspondingly high ozone content). This period covers two large oscillations on the curve in Fig. 43. Here an analogous picture is visible: the high ozone content on January 28 and February 6 is associated with an upper trough, while the low content on January 21 is associated with an upper ridge over southern England. The map of baric

Fig. 48. Maps of upper topography (300 mb) for days with low and high ozone content over Oxford during the period of a double long-wave oscillation in January–February 1951.

topography corresponding to the small amount of ozone on January 31 shows a more complex situation: the presence of a ridge advancing upon a trough, or, perhaps, the right edge of an emerging jet stream. In the Oxford region there is a ridge, and although a low-pressure area is situated not far away, on the maps published by the Meteorological Service of England the arrangement of the isobars is strictly and unquestionably anticyclonic.^84

In Fig. 49, constructed in the same way as the diagram in Fig. 43, data are given for the spring^84 (February 11–May 30, 1951). It has long been established that spring is the time of greatest ozone activity: the maximum in the annual course of the total amount of ozone in the atmosphere \(x\),

becomes greatest, the latitudinal gradient \(x\) is especially large, and fluctuations of \(x\) also become greater. This last point is also evident in Fig. 49.

Examination of these curves shows that, with few exceptions, in spring there is great similarity between the three curves. Analysis of maps of high-altitude baric topography leads to the same conclusions as in winter. An increase or decrease in the amount of ozone coincides with the direction of the wind, indicating more northerly or, respectively, more southerly sources. On days with a very high ozone content over Oxford, a trough of low pressure passes through (at the 300 mb level), while on days with very small content there is a high ridge.

Fig. 49. Smoothed curves of changes in the amount of ozone \(x\), the height of the tropopause \(h_{mn}\), and the thickness of the 500–300 mb layer over Oxford (spring).

As an example, let us consider the double oscillation between March 22 and April 9. Four maps (Fig. 50) correspond to days with low, high, again low, and high ozone content, and make it possible, without hesitation, to associate small values of \(x\) with an anticyclone and large values with an area of low pressure.

Similar conclusions follow from the analysis of the Oxford data for summer and autumn \(^{84}\).

The mechanism of the connection between the amount of ozone \(x\) and circulation processes in the stratosphere was clarified by observations of the temperature regime of the stratosphere. Sh. A. Bezverkhnii established \(^{98}\) that there is a correlation of atmospheric ozone with the temperature in the stratosphere \(t\). For Alma-Ata the best relation occurs at an altitude of 13 km, where the correlation coefficient \(r(x,t)=0.88 \pm 0.03\). The author concludes that nonperiodic changes of temperature are connected with circulation processes, and ozone, as a conservative characteristic of the air mass carrying it, may serve as a measure of the connection of temperature with advection in the stratosphere \(^{98}\). It is noteworthy that a satisfactory correlation occurs only in the comparatively thin layer 11–14 km. The connection between the amount of ozone and the temperature of the lower layers of the stratosphere may shed light on the correlation, discussed above, of the amount of ozone with the height of the tropopause (see Figs. 43, 44, 49, and 50), since changes in tropopause height, as is now well known, are usually accompanied by variations in tempe-

…temperatures of such a kind that a lowering of the tropopause corresponds to warming of the lower layers of the stratosphere and cooling in the upper layers of the troposphere. Therefore let us consider several other studies of the relation between ozone and the temperature of the stratosphere.

Extensive material was obtained by Johansen \(^{96}\) for northern Norway (Tromsø), who compared ozone variations with changes—

Fig. 50. Maps of high-altitude topography (300 mb) for days with low and high ozone content over Oxford during the period of a double long-wave oscillation in March—April 1951.

in temperature at altitudes of 6 and 12 km (the tropopause height over Tromsø is \(^{101}\) on the average 9.4 km, with a mean annual variation of 1.5 km). To eliminate the influence of annual variations, instead of successive changes the daily deviations from the smoothed curve of the annual cycle were considered. The data (1135 cases in all) were divided into 6 groups, with 4 months in each. The correlation coefficients obtained in this way for the altitude of 6 km (mean value \(r(x,t_6)=-0.56\pm0.03\)) indicate an increase in the amount of ozone with decreasing temperature. For the temperature \(t_{12}\) at an altitude of 12 km the correlation with ozone is positive. The mean value for the period February—September is \(r(x,t_{12})=\)

\(= 0.53 \pm 0.04\), which agrees well with the value for Oxford\(^97\) \(r(x, t_{12}) = 0.56\).

Johansen\(^96\) also studied the relationship of variations in the amount of ozone \(x\) with temperature and pressure and with the potential temperature \(\theta\) at altitudes of 6, 9, 12, and 15 km for the period April–September. The correlation coefficient \(r(x,\theta)\) of ozone with potential temperature is close in magnitude to \(r(x,t)\) and varies with height in approximately the same way. The values for Oxford are somewhat higher and show a tendency to increase with height\(^97\). For the altitude of 18 km at Oxford a very close correlation was obtained (\(r=+0.70\)). To determine whether such a tendency exists under the conditions at Tromsø, Johansen additionally studied sounding materials that reached an altitude of 18 km, although there were few such cases and they belonged to June–August of different years. The results of the processing show that the highest correlation pertains to the 12–14 km level. This conclusion is in good agreement with the results for Alma-Ata (the closest correlation of ozone with temperature at an altitude of 13 km, \(r=0.88 \pm 0.03\)).

Approximately this same altitude (the 100 mb level) is associated with the highest correlation of the total ozone amount with air temperature in the stratosphere over Japan\(^93\) (Tateno Aerological Observatory, \(36^\circ 03'\) N, \(140^\circ 08'\) E). However, this is true only for spring (February–April). In the period October–January the region of the closest correlation rises above the level of 19.4 km (60 mb).

The conclusion obtained for Alma-Ata by Sh. A. Bezverkhnii\(^98\), concerning the greatest ozone content under the type of circulation in which air enters from the north (see Table VIII and Fig. 45), and Normand’s analogous conclusion for Oxford\(^84\), is confirmed by observations in Japan, where the westerly wind in the stratosphere does not affect the ozone content, while the northerly wind causes it to increase. The best correlation (\(r=0.60\)) was found by Miyake and Kawamura\(^93\) for the layer located 5 km above the tropopause, which corresponds, depending on tropopause fluctuations, to an altitude of 15–18 km above sea level.

1. The role of advection. The phenomena considered above show that fluctuations in the total amount of ozone \(x\), depending on weather conditions, are the result of the constantly occurring spatial redistribution in the atmosphere of air masses with different ozone contents. One of the causes of redistribution is advection, i.e., the horizontal transport of air. On average, \(x\) increases with the geographical latitude of the observation point. A wind from the north, i.e., polar air masses, brings more ozone than tropical air from the south. For a time, advection was regarded as almost the sole cause of interdiurnal variations of ozone. But the gradually accumulating factual material forced this view to be changed.

From this point of view, the regularities of the latitudinal distribution of ozone are of great interest. In the first 15–20 years of syste-

matical observations of ozone, an approximate picture was established according to which the amount of ozone \(x\), at least on the average, increases with latitude over the entire range of latitudes from the equator to the pole. But in 1949–1951 an analysis of all the accumulated observational material compelled this picture to be substantially refined. In Fig. 51 is shown a diagram of isopleths constructed by Götz \(^{102, 103}\), showing the latitudinal dependence of \(x\) for each month of the year. The arrangement of the isopleths shows that the presumed dependence of the amount of ozone on latitude occurs only in spring, while in the other parts of the year the ozone maximum falls in the zone \(60^\circ\) N. lat. Kreig \(^{76}\) came to the same conclusions by 1950.

Fig. 51. Seasonal and latitudinal variations of ozone (after Götz).

In 1952 Langlo \(^{104}\) indicated that the mean annual dependence of ozone on latitude along the meridian of western Europe differs by a remarkable feature—constancy between the parallels \(70^\circ\) and \(45^\circ\) N. lat. According to monthly data, the change of \(x\) with latitude is large only from February to May, while in other seasons the gradient of \(x\) along the meridian is small. For September and October Langlo found a surprisingly small difference in the values of \(x\) between \(70^\circ\) N. lat. and the equator.

During the greater part of the year, advection, at any rate in the meridional direction, cannot exert a substantial influence on the ozone content in the air. Only in the spring months is the ozone gradient in the north–south direction large and able effectively to affect the spatial distribution of ozone.

Generally speaking, in addition to the principal ozone gradient in the north–south direction, a zonal gradient can also exist and exert its effect. Langlo \(^{104}\), comparing the mean distribution of ozone along a meridian with 24-hour variations of ozone at latitude \(62^\circ\), came to the conclusion that the zonal distribution of ozone may exert a greater influence on the diurnal variation of \(x\) than the meridional one. This question was also studied by Oksanen \(^{96}\). He compared the annual course of the correlation coefficient between the total amount of ozone and the height of the tropopause and the temperature at heights of 6 and 12 km (the characteristics of this correlation were given above) with the annual course of the horizontal ozone gradient between two points differing more in longitude than in latitude (Donbass, \(62.1^\circ\) N. lat., \(9.1^\circ\) E. long., and Tromsø, \(69.7^\circ\) N. lat., \(18.9^\circ\) E. long.). The greatest positive ozone gradient was found in the period February–May, and the horizontal gradient reaches its maximum value

in April. This is in good agreement with the annual course of the correlation coefficients, the largest values of which also pertain to April–May. However, during the period June–November the horizontal ozone gradient proves to be small, while the magnitude of the correlation coefficients indicates the presence during this period of an undoubted connection between ozone and the indicated characteristics of the state of the upper layers of the troposphere and the lower layers of the stratosphere.

All this compels one to suppose that, during the greater part of the year, the principal role in the spatial redistribution of ozone must belong not to advection, but to some other processes.

The nature of these processes may at present be regarded as clarified at least in general outline. Among them, vertical transport in the atmosphere is of great importance—turbulent mixing and ascending or descending currents.

10. Vertical currents in the atmosphere. Miyake and Kawamura\({}^{93,94}\) studied the relation of ozone to high-altitude baric topography on the basis of observations in Japan. They used charts of the absolute topography of the 500-mb surface and came to the conclusion that at the front of a trough at this level there exist ascending currents, and in the rear—descending currents; in the lower stratosphere the direction of the currents is the reverse. Proceeding from this, they investigated the relation between vertical motions and ozone variations. It turned out that when the front or rear of a trough at the 500-mb level passed over a station, positive and, respectively, negative deviations of the amount of ozone were observed. This conclusion is illustrated by the diagram (Fig. 52), in which \(H\) denotes the center of low pressure on the 500-mb surface, and the curved line indicates the position of the trough

Fig. 52. Distribution of deviations of the total amount of ozone in the atmosphere \(x\) from the norm near a typical trough on the 500-mb surface (Japan).

(its front is on the right), while the circles denote deviations of the amount of ozone from the norm. From these data Miyake and Kawamura conclude that the total amount of ozone in the atmosphere, \(x\), determined at the ground, increases in the presence of descending currents in the lower stratosphere.

These conclusions correspond to considerations expressed earlier concerning the possible influence on the magnitude of \(x\) of large-scale vertical motions and the dynamic processes associated with them in the atmosphere.^95 Nicole^82 and Dütsch^75 calculated the influence on the amount of ozone of horizontal convergence or divergence accompanying large-scale vertical motions. A calculation carried out by Reed^105,106 showed that these processes may be the cause of such changes in the total amount of ozone in the atmosphere as amount to about half the magnitude of the observed ozone fluctuations. Comparing the results of ozone measurements at New York University with upper-air weather charts, Reed established that cases of large positive changes in \(x\) are associated with well-pronounced descending currents at the levels of 10, 13, and 16 km, the rate of descent being greatest at the lowest of these heights and gradually decreasing with height.

Johansen^96, comparing fluctuations of atmospheric pressure at the levels of 0, 3, 6, 9, and 12 km and the height of the tropopause with variations in the amount of ozone, came to the conclusion that in an ordinary cycle moving eastward, fluctuations of surface pressure may be regarded as the result of two mutually compensating processes occurring below and above the nondivergent level. If the upper-level divergence is so intense that in its effect it exceeds the convergence in the lower layer, then surface pressure falls, and conversely. Redistribution of air masses in the lower layers of the atmosphere has no influence on the distribution of ozone, whereas convergence and divergence in the layers situated below the tropopause and above it cause changes in the amount of ozone in accordance with the results given by the calculations of Nicole^82, Dütsch^75, and Reed^106. The horizontal distribution of the amount of ozone \(x\), caused by these processes, is characterized by high values of \(x\) over the territory where surface pressure is rising, and by small \(x\) in the region of falling pressure. Correspondingly, the horizontal distribution of ozone must be more or less symmetrical with respect to upper-air waves, which is indeed observed.

Fig. 53 presents an example of a close connection between the amount of ozone and upper-air pressure waves.^96 These curves illustrate long waves of upper-air pressure over Tromsø, spreading from west to east, and show that the amount of ozone is large during the passage of an upper cold trough and small during the passage of an upper warm ridge. As was to be expected, proceeding from the existence of a large influence of dynamic processes

Fig. 53. Variations in the mean 5-day values of atmospheric pressure and temperature at an altitude of 6 km and in the total amount of ozone.

Legend: solid line — pressure; thin line — temperature; dashed line — ozone.

Months: February, March, April, May, June, July, August, September, October.

in the atmosphere on ozone variations, the greatest change in \(x\) is observed in spring and autumn, when baric systems are especially intense. The conclusion that convergence and divergence in the upper layers of the troposphere and the lower layers of the atmosphere influence variations in the amount of ozone was confirmed by Johansen by comparing ozone fluctuations with isopleths of potential temperature\({}^{96}\). The arrangement of isentropes indicates ascending motions along the surface of a warm front and descending motions along a cold front. In the stratosphere the isentropes change almost parallel to the tropopause. Periods of decrease in the amount of ozone are characterized by vertical compression of the isentropes and, correspondingly, by horizontal divergence. Periods of increase of ozone correspond to the reverse changes of the isentropes, i.e., vertical expansion and horizontal convergence.

1. Transformation of curves of the vertical distribution of ozone. Important information on the mechanism of the spatial redistribution of ozone can be obtained from considering the variability of the vertical distribution of ozone. In § 6 typical distribution curves for different amounts of it were considered (Fig. 40). The transformation of one ozone distribution with height into another as a consequence of vertical displacements of air may be represented, for example, in the following form\({}^{84}\). Let us consider the transition from the curve of high (\(x = 0.34\) cm) to very high (\(x = 0.40\) cm) ozone content (Fig. 40). Such a transition does not require vertical displacements above the level of 25 km. It requires a descent by 1 km at the 20 km level and by 2 km at the 15 km level, while near the 8 km level there again should be no noticeable vertical movements of air. The air column between the levels of 25 and 15 km must undergo downward stretching and occupy the space between the heights from 25 to 13 km. Such a current must obviously be accompanied by lateral compression (horizontal convergence). This question will be considered in more detail in § 13.

Of course, advection can also influence the character of the vertical distribution of ozone. This can be explained by the example of one of the most powerful ozone fluctuations characteristic of spring. According to English studies\({}^{84}\), on certain days the ozone distribution over Oxford corresponds to an average ozone content (\(x = 0.26\) cm), while at the same time over Iceland the amount of ozone is large (\(x = 0.34\) cm). The air current directed in the stratosphere from Iceland to the southeast reaches Oxford after a few days. On the way, owing to vertical divergence or stretching, the ozone distribution is transformed into one corresponding to its very high content (\(x = 0.40\) cm). As a result, over Oxford an increase in ozone content of \(0.40 - 0.26 = 0.14\) cm is observed, including an increase of \(0.34 - 0.26 = 0.08\) cm caused by advection, and of 0.06 cm caused by

OZONE IN THE STRATOSPHERE

Fig. 54. Distribution of ozone by altitude and paths of air arrival at Vienna at an altitude of 16 km.

18.2.1950 ———; 17.7.1951 — — —;
25.4.1951 ·······; 2.8.1951 — · — · —.

vertical divergence. Other, sufficiently numerous observations of the distribution of ozone with height also confirm the influence of advection, but only under certain conditions. Figure 54 gives a comparison by Brewer^107 of four curves of the vertical distribution of ozone with the trajectories along which the air at an altitude of 16 cm approached the observation point (Weissenau, Federal Republic of Germany). The ozone-distribution curves were obtained by direct methods (lifting a quartz spectrograph on balloons; see § 3). The trajectories of air motion make it possible to judge its “origin,” i.e., the place from which it arrived. This judgment is approximate, since the trajectories of air at an altitude of 16 km, naturally, do not provide information about air motion at greater heights. Nevertheless, a certain dependence of the form of the distribution curves on the origin of the air is revealed. Both left-hand ozone-distribution curves have a sharp maximum at a height of 23 km; in both cases the air came from the region of the Azores. The lower right-hand curve shows a broad maximum of ozone content below 20 km and a second, weakly expressed one at a height of almost 30 km. The first of these is clearly of advective origin. The trajectory of the air motion indicates a path from North America. In the case corresponding to the upper right-hand distribution curve, the air at an altitude of 16 km arrived from Greenland; the distribution of ozone with height differs in that, along with a sharply expressed maximum at the 23 km level, an astonishing constancy of the amount of ozone is observed over the broad altitude interval 12–22 km.

Let us return to consideration of the vertical transport of ozone arising as a result of turbulent exchange, as well as descending or ascending motions of air and the corresponding compression or expansion of ozone. Petzold^83 processed 35 measurements of ozone concentrations in the stratosphere, made by direct methods (with the aid of spectrographs raised in different years and in different countries into the stratosphere on balloons and rockets), and obtained the seasonal variation of concentrations at different levels (for middle latitudes). His results are presented in Fig. 55, where the ordinate indicates the thickness (in fractions of a centimeter) of the reduced ozone layer lying within the altitude ranges indicated on the graph. Despite the large scatter of points, features of the seasonal variation at different levels are discernible, and in the sum a satisfactory agreement of amplitude and phase is obtained with the many-year mean course of ozone from ground-based measurements. Below 20 km a spring maximum is observed, while in the 20–25 km layer there is a minimum in summer. Above 30 km, on the contrary, there is a summer maximum. Petzold indicates four principal factors regulating the seasonal variation of ozone concentrations at different heights and its total amount^36,83.

1. The spring maximum between the heights of 10 and 20 km is caused by high-altitude advection of polar air. The amount of ozone in this layer averages 0.04 cm.

1. The ozone maximum at the beginning of summer in the region of the stratosphere located above 30 km has a photochemical origin. Here, as is known, photochemical equilibrium is established, the level of which must follow the annual course of solar illumination.

2. The summer minimum between 20 and 25 km is very probably connected with the fact that in summer turbulent exchange is appreciably intensified, as a result of which a large amount of ozone is transported into the lower layers of the atmosphere.

In the layer between 25 and 30 km, as is seen from Fig. 55, there are no appreciable seasonal changes in the amount of ozone. This is evidently due to the fact that for photochemical effects this layer is situated too low, and for convective effects too high.

1. If the three factors indicated above are compared with one another, it turns out that, in order to explain the annual course of ozone, a fourth factor is also necessary, namely the compression of ozone in late autumn and its expansion in late spring—processes accompanying descending or, respectively, ascending motions of the air.

Fig. 55. Seasonal course of ozone at different heights (after Petzold).

On this last question it is necessary to dwell in greater detail. To determine the influence of vertical motions of the air it is more convenient to use not the absolute concentrations of ozone in the air ($\varepsilon$ in $\mu/\mathrm{km}$) at a given height $h$, but the ratio “ozone/air,” i.e. the ratio $\varepsilon/\rho$, where $\rho$ is the density of the air.

It is quite obvious that the process of vertical exchange of masses is accompanied by an equalization of the ozone/air ratio up to the establishment of a constant ratio with height, whereas vertical flows cannot affect the shape of the curve of the distribution with height of the ozone/air ratio.

In Fig. 56 the curves of the distribution of ozone with height over Weissenau are presented, according to measurements by direct methods[^83] in the autumn of 1953. It is known that the seasonal course of the latitudinal distribution of ozone is such

Fig. 56. Vertical distribution of ozone in autumn over Weissenau:
1 — 8.9.1953; 2 — 28.9.1953; 3 — 23.10.1953; 4 — 28.10.1953 (according to Petzold).

that in autumn the gradient of the total amount of ozone along the meridian is the smallest. Therefore the influence of advection at this time of year should be expressed especially weakly. Curves 2 and 3 in Fig. 56, b, reaching a height of 37 km, indicate the presence, at a height averaging about 25 km, of a first flat maximum, and at about 29 km—a minimum. The results of rocket sounding of the ozone layer make it possible to assume the presence of a second maximum at a height of approximately 40 km. It is striking that the first maxima and minima on the two curves under consideration lie at substantially different heights. The same state of affairs can also be seen on another pair of curves, 1 and 4, which reach only a height of 30 km, and also on curves measured by different methods (with the aid of spectrographs raised on balloons—sondes and rockets, and by the method of lunar eclipses) in other seasons. Analysis of the material shows[^83] that the course of the curves can be determined up to a height of 50 km, and moreover constantly

OZONE IN THE STRATOSPHERE

a recurrence of the form of the curves is observed. All this points to the influence of vertical currents. Their velocity, according to Petzold’s calculations[^83] (he proceeded from the data of Fig. 56, b and took into account the time required for the establishment of photochemical equilibrium), on the average has a value of the order of 1 cm/sec at a level below 35 km and approximately 10 times greater—at an altitude of 50 km.

It is hardly accidental, too, that in all cases the curves of the vertical distribution of the ozone/air ratio intersect at an altitude of about 20 km, as can also be seen in Fig. 56, b. In Petzold’s opinion, this means that at this level both descending and ascending motions of air disappear, and that the directions of motion above and below the indicated level are mutually opposite[^83].

The phenomenon as a whole, in the simplest case, may be imagined as a kind of oscillation, whose amplitude above the 20-km level is at least 10 km. In this way one can quite simply explain the alternation of flat and sharp ozone maxima, examples of which may be seen in Fig. 56, a. It is scarcely possible to interpret this alternation as the effect of vertical turbulent exchange of masses of variable intensity.

From the facts considered one may also draw the conclusion that in the stratosphere, from time to time, large masses of air are transported upward to an altitude of 50 km and more. This important conclusion must in the future be checked on more extensive observational material.

To explain the seasonal variations of ozone, in addition to the three factors indicated above (the annual course of photochemical processes, seasonal changes in advection, and turbulent exchange), it is also necessary to assume the presence of descending air motions in spring and ascending ones in autumn. According to Petzold’s estimate, based on consideration of the seasonal course of the ozone/air ratio at different altitudes, the velocity of the vertical currents should be approximately 0.1 mm/sec. The seasonal changes of these vertical motions should occur parallel to the seasonal course of the tropopause height[^83]. The variations of \(x\) produced by them (as a result of compression or expansion of ozone) have the same quantitative connection with changes in tropopause height as has already been established for the correlation of day-to-day changes in the amount of ozone with tropopause height, namely: a lowering of the tropopause by 1 km corresponds to an increase of ozone content by 0.011 cm, and conversely[^97].

Let us next consider some questions relating to the redistribution of ozone with height as a result of turbulent exchange of masses.

1. Turbulent exchange. The nature of the influence of turbulent exchange on the distribution of ozone with height was indicated at the end of § 6. Vertical exchange is especially intense in the tropics; therefore we shall consider separate phenomena characteristic of the tropical zone.

Let us acquaint ourselves with the results of observations carried out in recent years in India at latitude 24°26′ N (the observatory on Mount Abu, longitude 72°43′ E, altitude 1200 m above sea level) and at the observatories in Delhi, Pune, and Kodaikanal.

Interdiurnal variations in the amount of ozone at low latitudes are weakly expressed. In the northern part of India, in December–April, when active western disturbances pass through the country, the fluctuations have the same character as at extratropical latitudes, but they are observed more rarely and have a smaller amplitude^24.

The vertical distribution of ozone was determined on Mount Abu, as at the other observatories in India, by the inversion method (see § 1). It has characteristic differences from the distribution of ozone in more northern regions. Chief among them is the extremely low ozone content in the troposphere and the lower part of the stratosphere (up to 18 km). In the 0–9 km layer there is so little ozone that it is often not detected at all by the inversion method. In the 9–18 km layer there is very little ozone; its amount in this layer increases somewhat with an increase in the total ozone content \(x\). The amount of ozone above the level of 27 km decreases somewhat on those individual days when the value of \(x\) is anomalously high. A high correlation is observed between \(x\) and the amount of ozone in the 18–27 km layer, as may be judged from Fig. 57, which presents observations at the Abu observatory in October 1951–November 1952 and, for comparison, gives mean data for Delhi and Kodaikanal. The high correlation makes it possible to suppose that the air currents and convergences associated with the low-pressure centers of western depressions sometimes penetrate high into the stratosphere^24.

Fig. 57. Amount of ozone in the 18–27 km layer as a function of the total ozone content in the atmosphere \(x\) (India observatories). \(A\times\) — Abu (February–March); \(AO\) — Abu (remaining months); \(\Delta D\) — Delhi; \(K\square\) — Kodaikanal.

Table IX gives data on the mean distributions of ozone with height, grouped according to different values of \(x\) for

of a number of Indian stations. In the second column of the table the number of observations in the given group is indicated in parentheses.

Table IX

Mean distributions of ozone with height for different amounts of ozone
(group averages) for Abu, Delhi, Poona, and Kodaikanal (India)

Station	Amount of ozone, cm	0–9	9–18	18–27	27–36	36–54
		\multicolumn{5}{c}{Ozone content (cm) in layers at different heights}
		\multicolumn{5}{c}{height in km}
Abu	0.153 (4)	0	0.009	0.060	0.068	0.015
Abu	0.159 (11)	0	0.009	0.068	0.068	0.015
Abu	0.172 (8)	0	0.011	0.076	0.070	0.018
Abu	0.180 (6)	0	0.010	0.086	0.060	0.019
Abu	0.195 (4)	0	0.011	0.106	0.057	0.018
Abu	0.209 (1)	9	0.014	0.111	0.064	0.012
Delhi	0.155 (1)	9	0.015	0.049	0.069	0.013
Delhi	0.075 (3)	9	0.018	0.063	0.072	0.013
Delhi	0.200 (1)	9	0.023	0.091	0.073	0.013
Delhi	0.217 (1)	9	0.027	0.094	0.0?2	0.015
Poona	0.169 (8)	1	0.013	0.065	0.065	0.025
Kodaikanal	0.175 (4)	0	0.006	0.053	0.099	0.017

In discussing these results it must be taken into account that in the tropics the tropopause is constantly located at a great height (16–17 km). In a certain sense it may be considered that the low ozone content constantly observed in the tropics (usually \(x < 0.2\) cm) confirms the negative correlation, established for middle and high latitudes, between the height of the tropopause and the amount of ozone \(x\). Remarkable is the almost complete absence of ozone in the tropical troposphere. Ramanathan and Kulkarni explain this fact by the oxidizing or catalytic action of water vapor and other substances transported from the lower to the upper layers of the atmosphere by convective currents, which causes the destruction of ozone throughout the entire thickness of the tropical troposphere[^24]. These authors also suppose that the indicated process of destruction may be intensified by the action of solar illumination, which is very intense in the tropics. In favor of this view, in their opinion, are such facts as the rapid disappearance of episodic intrusions of ozone into the subtropical troposphere and the gradual decrease in the amount of ozone in late spring and summer in the atmosphere of middle and high latitudes.

Ramanathan and Kulkarni consider, in addition, a number of phenomena that further explain and substantiate the judgment about the active effect on ozone of intense turbulence and convection and of large-scale vertical motions. Over centers of cold, such as the polar regions and large continental areas in winter, where the tropopause is already low, masses of stratospheric air can sink into the troposphere and be located above inversions, retaining their high ozone content for a long time. Emert’s ozonometric observations from an aircraft clearly revealed such cases^24. However, ozone disappears as soon as it enters a convectively active region. Further, as Langlo noted, on the annual average the amount of ozone remains almost constant from Tromsø to Arosa and is about 0.235 cm, but at latitude \(25^\circ\) it drops abruptly to 0.190 cm. This sharp change occurs parallel to a change in the mean height of the tropopause. The indicated phenomenon may be compared with the fact that in northern India noticeable fluctuations of ozone are observed only during the season of western atmospheric disturbances, and during this period the frequent appearance of a complex (multi-tiered) tropopause is noted.

In addition, Ramanathan and Kulkarni note that, on average, the height of the tropopause varies with latitude within the limits from 17 to 9 km, with a very sharp jump or break between 16 and 12 km and another break near the polar front. Although the air between 9 and 16 km is strongly stratified, large-scale motions occur here, both vertical and horizontal, especially in the region between \(20^\circ\) and \(60^\circ\) N, associated with the conditions of extratropical weather.

All this indicates, in the opinion of Ramanathan and Kulkarni, the existence of a definite mechanism of large-scale but slow vertical air motions between 8 and 25 km, transporting ozone from the upper layers to the lower ones, where it mixes with water vapor and oxidizing particles and is thereby destroyed.

The problem of atmospheric ozone and its variations thus becomes a problem of large-scale turbulence and circulation in the upper layers of the troposphere and the lower part of the stratosphere. The ozonosphere may be conceived as consisting, as it were, of three parts. The upper part lies above 27 km—this is the “mother layer,” the region of photochemical formation of ozone. Beneath it is the middle part, the “refuge” of ozone, which is bounded below by the tropopause or the upper part of the troposphere, depending on the development of convective motions. Here the ozone content is to a high degree a conservative property of air masses; in this region ozone is protected from above (by ozone itself) from the action of the Sun’s ultraviolet radiation, and from below—from the destructive action of water vapor and atmospheric pollution. The lower part of the ozonosphere is ...

area of ozone destruction. The interaction between the indicated elements of the ozonosphere is effected by processes of large-scale turbulence and circulation.

13. Theory of the question. In §§ 7–12 we have repeatedly touched upon the theoretical interpretation of one or another of the processes leading to a change in the amount of ozone in the stratosphere. In concluding the discussion of the “ozone—weather” problem, we shall once more consider it from the theoretical point of view, trying to present clearly the question as a whole, insofar as the present degree of study of the complex and varied phenomena under consideration permits.

A theory taking account of the influence of advection is based on the fact that, in general, the ozone content in the atmosphere \(x\) increases toward the north; consequently, advection from the north over an observation point should lead to an increase, and from the south—to a decrease, of \(x\). A theory considering the action of vertical motions proceeds from the compressibility of the atmosphere: a given portion of air becomes

Fig. 58. Ozone concentration \(\varepsilon\) as a function of height before lowering of the air (curve I) and after lowering (curve II).

denser as it descends. For those atmospheric gases whose density usually depends on height, vertical mixing does not cause local changes in concentration. But the concentration of ozone in the stratosphere usually increases with height; therefore descending motions lead to an increase of the concentration at a given level, and ascending motions—to a decrease.

Such changes were calculated in 1945 by Nicole\(^{82}\) and in 1946 by Dütsch\(^{75}\). Subsequently these calculations were continued and refined by Reed\(^{105, 106, 115, 117}\), whose works we shall follow in the further exposition. Let us begin with vertical motions.

The ozone concentration $\varepsilon$, specified in $\mu/\text{km}$, is equivalent to density. Because of the compressibility of the atmosphere, it is necessary to take into account the horizontal divergence accompanying vertical displacements of air. But if one uses the dimensionless ratio ozone/air, then the divergence need not be taken into account. Let us examine the method of calculation by an example. Curve I in Fig. 58 gives the assumed$^{106}$ initial distribution of ozone with height in the region 5–20 km (from Götz’s curves, obtained by observations of the reversal phenomenon$^{86}$). Of the total amount of ozone in the atmosphere, $x = 0.320$ cm, here $0.132$ cm is contained. The ozone maximum at a height of about 13 km is the second maximum; the principal maximum was located at a height of 26 km.

Fig. 59. The “ozone/air” ratio as a function of height before the descent of the air (curve I) and after it (curve II).

Curve I in Fig. 59 gives this distribution in units of the ozone/air ratio. In the same figure, arrows show the distance by which the air presumably descended at one height or another. Recalculating this curve into units of concentration $\varepsilon$, we obtain curve II in Fig. 58: the amount of ozone in the layer 5–20 km increased by $0.024$ cm and now amounts to $0.156$ cm.

To calculate the positive deviations $+\Delta x$ during descents of air and the negative deviations $-\Delta x$ during its ascents, it is necessary to find the distance by which an air particle can practically descend or ascend relative to its normal level. For this purpose various methods have been proposed that use high-altitude weather maps. Let us consider one of them, applied by Reed. This method is based on a simple and visual analysis of the temperature field in the lower part of the stratosphere.

In winter, north of 40° N latitude, the horizontal temperature gradient is on average very small$^{116}$. Therefore the often encountered at

on high-altitude synoptic charts (for example, at the 200 mb level), the strongly expressed temperature contrasts can almost entirely be attributed to the action of adiabatic heating and cooling accompanying descending or, respectively, ascending currents in the stratosphere. Following this conception, one can obtain the greatest possible displacements of air particles \(\Delta h\) by comparing mean aerological data for the season under consideration with individual aerological soundings distinguished by particularly low or high temperatures over a broad height interval. The height differences of interest to us can in this case be determined from the points of intersection of the dry adiabat with two selected temperature soundings.

An estimate by this method gives, for the greatest displacement \(\Delta h\), approximately \(1.5\) km. In the example considered above (Figs. 58 and 59), the greatest displacement adopted was \(1.4\) km; the other factors entering into the calculation were also chosen so as to give large values. Thus \(\Delta x = 0.024\) cm must be regarded as a quantity close to the upper limit of possible changes in \(x\) caused by descending motions. It can be shown that other methods of calculation cannot give, for \(\Delta x\), values larger than that indicated above.

From this one may draw a conclusion about the relative role of vertical motions and advection in the intermediate variations of ozone. It should be borne in mind that the greatest negative changes in \(x\) (caused by ascending motions) are smaller than the positive ones, since the initial values of \(\bar{\varepsilon}\) are smaller. An analogous calculation gives, for negative changes, \(\Delta x = 0.017\) cm. In all we obtain \(\Delta x = 0.040\) cm. There are grounds for considering this value maximal for the conditions of the greatest variations in middle latitudes in late winter and early spring, when, as is known, ozone fluctuations are most markedly expressed. But we know that observations give for \(\Delta x\) values reaching \(0.120\) cm. Consequently, vertical displacements can be the cause of approximately one third of the observed fluctuations; the rest must be caused by other reasons, primarily advection. At high latitudes, where ozone fluctuations are more strongly expressed, the share of vertical motions must be correspondingly smaller.

Proceeding from the data considered, one may picture the mechanism of the “ozone—weather” connection.

Pressure troughs in the lower part of the stratosphere are usually observed in warm air, and ridges in cold air. These warm and cold regions move with the speed of the pressure system, which differs from the wind speed—as a rule, they advance much more slowly than the component of the wind in the direction of motion of the system. In other words, the high-altitude wind blows through the features of the pressure and temperature field associated with it. It follows from this that warm and cold regions can be created

dynamically, as a result of subsidence or, respectively, ascent. Maxima of warmth or cold in troughs or, respectively, ridges indicate that descending and ascending displacements are greatest precisely in these regions. Thus, through the action of vertical motions, maximum positive anomalies are produced in upper-level troughs and maximum negative anomalies in ridges.

At the same time, owing to the approximate coincidence of trajectories and isobars in the upper layers, air moving through a stratospheric trough is displaced farthest to the south from its initial position, whereas air in a ridge is displaced in the opposite way. Since, on average, the ozone content in the atmosphere \(x\) increases toward the north, displacement toward the south in a trough gives an addition to the normal value of \(x\), i.e. creates an additional positive anomaly \(+\Delta x\) in this region; in an analogous way, advection toward the north in ridges creates negative anomalies. The effects of vertical motions and advection add together; jointly they create positive ozone fluctuations in upper-level troughs and negative ones in upper-level ridges.

The connection between ozone fluctuations and surface weather is a natural consequence of the observed relation between upper-level and surface baric systems. In general, upper-level systems are shifted toward the rear of surface systems. Therefore positive ozone fluctuations should arise in the rear of a surface cyclone, and negative ones in the rear of a surface anticyclone.

The idea set forth is explained in Fig. 60. The assumed initial state with a north–south ozone gradient and east–west currents is shown in Fig. 60, \(a\). Let us suppose further that a disturbance has occurred, caused by the zonal flow, so that air is displaced toward the south in troughs and toward the north in ridges. In Fig. 60, \(b\), the thin solid lines represent the new distribution of ozone and, in rough outline, give the scheme of flows and isobars. The values of \(x\) are indicated at these lines, but it should be noted that only the part of the quantity \(x\) pertaining to the ozone contained in the lower layers of the stratosphere is subject to change. Having made the necessary conclusions about the upper-level meteorological situation connected with this disturbance, we obtain the schematic temperature field indicated in the figure (dashed lines) and the position of the tropopause (heavy line) at the 200 mb level.

So far we have made no estimates of the influence of vertical motions. They may be judged from Fig. 60, \(c\), which shows the distribution of anomalies \(\Delta x\) (in \(10^{-3}\) cm) corresponding to the temperature field in the preceding figure.

If the changes \(\Delta x\) indicated in Fig. 60, \(c\), are added to the values of \(x\) as they are given in Fig. 60, \(b\), then we obtain the ozone distribution shown in Fig. 60, \(d\). This distribution may

Fig. 60. Schematic diagrams explaining the “ozone—weather” relationship.

to be regarded as the final result of the combined action of advection and vertical motions.

In conclusion, one may point to Fig. 60, d, which shows the upper-level baric situation (solid lines), the surface baric situation (usual symbols), and the total magnitude of the ozone fluctuation \(\Delta x\) (dashed line). This last quantity was obtained by graphically subtracting the values of \(x\) corresponding to the normal distribution for the given season (Fig. 60, a) from the values of \(x\) obtained as a result of the disturbance considered (Fig. 60, g). There is satisfactory agreement between this theoretical picture and some of the empirical data considered earlier.

The large role of advection that follows from these calculations must be accepted with caution. In § 9 data were presented indicating that under certain weather conditions the role of advection apparently becomes quite insignificant. In particular, the sharply expressed north–south gradient of ozone, taken by Reed \({}^{106}\) (Fig. 60, a) as the basis of the calculation set forth above, is by no means always and everywhere present.

In 1951 Reed and Julius \({}^{115}\) carried out a quantitative analysis of the two most frequently assumed mechanisms of vertical ozone transport, namely meridional circulation and turbulent mass exchange. Their principal conclusion was that existing ideas about the physical characteristics of the atmosphere give grounds for doubting that either of these two mechanisms could by itself satisfactorily explain the variations in ozone distribution known from observations. Although this conclusion cannot be considered final, in 1953 Reed undertook a search for other processes that might play an important role in the vertical transport of ozone \({}^{117}\). He investigated large-scale vertical vortex flows at the level of the tropopause, in which, as elements of turbulence, broad descending and ascending currents associated with cyclones and anticyclones (or troughs and ridges) operate.

The amount of ozone transported through a horizontal area per unit time can be expressed by the product \(q w\), where \(q\) is the ozone density and \(w\) is the vertical velocity. Applying the usual method of analysis, we may write

\[ q=\overline{q}+q', \qquad w=\overline{w}+w', \tag{13.1} \]

where the overbar denotes averaging over 1 month, and the prime denotes “instantaneous” deviations from this mean.

Averaging the product \(qw\) with respect to time, we obtain:

\[ \overline{qw}=\overline{q}\,\overline{w}+\overline{q'w'}. \tag{13.2} \]

The physical meaning of equation (13.2) is that the averaged vertical transport may be regarded as consisting of

two parts. The first, \(\bar q\,\bar w\), gives exchange by means of vertical motions and meridional circulation. The second, \(\overline{q'w'}\), denotes a flux caused by large-scale vortical motions. Let us consider the second term in more detail.

From the definition of the quantities under consideration it follows that

\[ \overline{q'w'}=\sigma(q)\sigma(w)r(q,w), \tag{13.3} \]

where \(\sigma\) denotes the standard deviation of the given quantity, and \(r\) is the correlation coefficient between them. Therefore the upper limit for the magnitude of the large-scale flux can be found directly, if one assumes the existence of a direct strict dependence between \(q\) and \(w\). This estimate can show whether the process under consideration, in terms of the magnitude of its action, deserves further study.

The following calculation pertains to the flux near the 10 km level and to winter conditions in middle latitudes. On the basis of measurements of the vertical distribution of ozone carried out by Tönsberg and Olsen \(^{92}\), Reed \(^{117}\) takes the value \(\sigma(q)=5\cdot 10^{-11}\ \text{g}/\text{cm}^3\). From Fligel’s study \(^{118}\) one may conclude that for \(\sigma(w)\) one should take the value \(1\ \text{cm}/\text{sec}\). For \(r=1\), equation (13.3) gives

\[ \overline{q'w'}=5\cdot 10^{-11}\ \text{g}/\text{cm}^2\cdot\text{sec}. \]

From the same curves of Tönsberg and Olsen \(^{92}\) one can obtain a rough estimate of the mean increase of ozone in the troposphere (below 10 km). The calculation gives the value \(5\cdot 10^{-12}\ \text{g}/\text{cm}^2\cdot\text{sec}\), which directly indicates the effectiveness (under favorable conditions) of the process under consideration. To interpret the ozone flux into the troposphere observed at the tropopause level, it is sufficient to take \(r=0.1\).

But how high is the correlation between \(q\) and \(w\) in reality, and does it exist at all? A direct answer to this question cannot be given, since simultaneous measurements of both quantities do not exist. However, if one starts from an idealized physical model corresponding to the empirically known connection between the synoptic situation and the vertical velocity and the amount of ozone, then one may try independently to calculate the vortical flux without using any values of the correlation coefficient. Let us formulate the conditions which our model must satisfy.

1. Over a given point in middle latitude, upper-level ridge–trough systems pass once every four days. If we assume that the rate of displacement of the trough is such that in one day it moves by 10 degrees, this corresponds to a wavelength of 40 degrees.

2. The vertical velocity is equal to zero at the bottom of the trough and at the top of the ridge, and is maximal midway between them.

3. The positive and negative ozone deviations extend beyond two degrees to the west of the trough line and correspond-

...respectively, of the ridge. This assumption is based on the statistics of Mizama[^97], who established that the maximum positive ozone deviations \(\Delta x\) are observed approximately \(200\) km west of the high-altitude ridge.

1. The vertical velocities and ozone deviations vary sinusoidally in time at a given point.

The latter can be expressed mathematically as follows:

\[ \left. \begin{aligned} q'&=Q\sin{\frac{\pi}{48}}(t-20),\\ w'&=W\sin\frac{\pi t}{48}, \end{aligned} \right\} \tag{13.4} \]

where \(Q\) and \(W\) are the amplitudes of the variations. In integral form \(\overline{q'w'}\) may be written as

\[ \overline{q'w'}=P^{-1}\int_0^P q'w'\,dt. \tag{13.5} \]

Here \(P\) is the period of oscillation, expressed in hours. Then from (13.4) we obtain:

\[ \overline{q'w'}=\frac{QW}{96}\int_0^{96}\sin\frac{\pi t}{48}\sin\frac{\pi}{48}(t-20)\,dt. \tag{13.6} \]

After the corresponding trigonometric transformations, integration of equation (13.6) gives

\[ \overline{q'w'}=\frac{1}{2}QW\cos\frac{5\pi}{12}. \tag{13.7} \]

For a sinusoidal distribution, the amplitude values exceed the standard deviations of the variables by a factor of \(\sqrt{2}\). Therefore one may write that

\[ \overline{q'w'}=\sigma(w)\sigma(q)\cos\frac{5\pi}{12}. \tag{13.8} \]

Substituting the previously indicated values for \(\sigma(w)\) and \(\sigma(q)\), we finally obtain:

\[ \overline{q'w'}=1.5\cdot10^{-11}\cdot0.26=1.3\cdot10^{-11}\ \text{g}/\text{cm}^2\cdot\text{sec}. \]

This result confirms that the correlation between \(q\) and \(w\) is sufficiently high (\(r\) has a value between \(0.2\) and \(0.3\)) to ensure the necessary ozone flux.

Thus, the analysis shows that large-scale vortex flows may play an important role in the transport of ozone from the stratosphere into the troposphere.

THE THERMAL BALANCE OF THE OZONOSPHERE

14. The role of ozone in the thermal balance of the Earth. As is known, the distinction between the troposphere and the stratosphere—two air shells constituting the lower and middle parts of the atmosphere—is based on a temperature criterion (the nature of the vertical distribution of temperature). In the troposphere (Fig. 61) the temperature \(t\) rapidly decreases with height \(h\) (on the average \(\dfrac{dt}{dh} = -6 \ \text{deg}/\text{km}\)); the stratosphere, by contrast, is a region whose lower part is characterized by isothermy, and whose higher part by an increase of temperature with height. The transition from the troposphere to the stratosphere corresponds to a transition from one factor that mainly regulates the temperature of the air to another—namely, from convection to radiation. The temperature of the stratosphere approximately corresponds to a state of radiative equilibrium, in which the air is heated by the absorption of radiant energy to such an extent that the losses of heat through emission become equal to its supply through absorption.

Fig. 61. Air temperature in the troposphere and stratosphere.

The greater part of the energy in the spectrum of the Sun lies in the visible and near-infrared regions of the spectrum, for which the atmosphere is to a high degree transparent. Therefore solar radiation is only slightly absorbed by the atmosphere and is expended mainly on heating the ground. But the counter-radiation of the Earth is concentrated in the far-infrared region (maximum—about \(\lambda = 10\mu\), see Fig. 62), in which the atmosphere has such strong absorption that the counter-radiation is almost entirely retained in it.

This “greenhouse” action of the atmosphere, which has such great significance for the thermal balance of the Earth and, consequently, for the conditions of life on our planet, is determined not by the principal constituents of the atmosphere, but predominantly by gases present in it in small, sometimes negligible amounts: water vapor, carbon dioxide, and ozone.

The temperature of the stratosphere depends strongly on the absorption of the counter-radiation of the Earth’s surface and the troposphere. For a long time it was believed that the principal role here belonged to water vapor. It could be supposed that the more water vapor contained—

would be found in some layer of the stratosphere, the higher its (equilibrium) temperature would be. The study of atmospheric ozone and its radiative properties forced a fundamental change in this view. If one calculates the equilibrium temperature of some gas, which it must reach if only this gas is present and only it absorbs the outgoing radiation, then it turns out that

Fig. 62. Approximate distribution of energy in the spectrum of outgoing radiation at the level of the lower layers of the stratosphere.

for H$_2$O it is approximately 190°, for CO$_2$ about 200°, and for O$_3$ approximately 250° K. Consequently, an increase in the relative content of water vapor in the stratosphere should lower the temperature, whereas an increase in the fraction of ozone should be accompanied by a rise in temperature$^{7}$. One may point, for example, to the temperature distribution in the stratosphere calculated by Gowan$^{109,110}$ from the equation of radiative equilibrium for summer at latitude 50° N, under the assumption that the amount of ozone in the atmosphere is $x = 0.28$ cm, while the relative humidity has various values, from 0 to 100%.

Altitude in km	11—15	15—20	20—25	25—30	30—35	35—40	40—45	45—50
Humidity 0	290	285	285	290	295	335	480	535
» 40%	225	230	240	245	260	290	370	395
» 100%	200	195	220	235	245	260	310	315

One may judge the amount of energy absorbed by ozone from Fig. 62, in which the curve drawn with a thick line shows the distribution of energy in the spectrum of the back radiation of the earth and the troposphere that has reached the level of the lower stratosphere. The absorption bands of H\(_2\)O, CO\(_2\), and O\(_3\) are constructed so that the area bounded by each curve is proportional to the energy absorbed in the given band from the flux of back radiation. The value of ozone absorption in the band at \(9.7\,\mu\) is especially large because it falls in the region in which the other constituents of the atmosphere are transparent.

Thus, the rapid increase of air temperature with height, beginning at the level of 30–35 km (see Fig. 61), is due to the presence of ozone. The ozonosphere is a region of warm air in the stratosphere.

In recent years it has been possible to establish that the temperature regime of the stratosphere depends on the absorption by ozone not only of back infrared radiation, but also of direct solar radiation (primarily in the ultraviolet region). This fact is important for the “Sun—Earth” problem.

1. Heating of the ozonosphere due to absorption of solar rays. A number of studies have been devoted to this question, but investigations carried out before 1952 (for these see Mitra’s book\(^{1}\), ch. 4) were based on an ozone distribution obtained from observations of the Umkehr phenomenon (see § 1), which do not allow ozone to be detected above 50 km. The presence of ozone in these higher layers, established by rocket measurements (see § 3), considerably changes the picture of the temperature regime at a level of about 50 km, i.e. precisely near the maximum of the thermal action of ozone. In 1953 Johnson\(^{111}\) calculated the heat balance of the ozone layer on the basis of rocket data on ozone concentration up to an altitude of 70 km and on the distribution of energy in the solar spectrum. He calculated the magnitude of the energy of the solar rays absorbed per day by ozone in the ultraviolet and visible regions of the spectrum (Fig. 63), and the diurnal variations of temperature (Fig. 64) at different altitudes, assuming the heat losses through infrared radiation to be constant. The maximum absorption (\(10^{-5}\) calories in \(1\ \text{cm}^3\) per day) occurs

Fig. 63. Energy of solar rays absorbed by ozone per day at different altitudes.

to an altitude of 30 km, and the maximum daily temperature variation is 5.3° (the highest daytime temperature exceeds the lowest nighttime temperature by 5.3°) at an altitude of 47 km (Fig. 64). In 1955, Pressman \(^{112-114}\) calculated the seasonal and latitudinal changes of the daily temperature variations associated with the absorption of solar radiation by ozone. He arrived at the following conclusions.

1. Below 30 km and above 58 km the daily temperature variations are small (less than 1.5°).

2. The greatest daily variations amount to 5–6° (at an altitude of approximately 45 km).

3. The seasonal and latitudinal dependence of this effect proved unexpectedly small; it begins to appear only at high latitudes (75° N).

Fig. 64. Daily temperature variations at different altitudes.

It would be interesting to compare these theoretical data with the results of observations of the actual temperature variations of the ozonosphere. Unfortunately, there is as yet an insufficient number of measurements for this purpose. The stream of regular aerological soundings with radiosondes is inadequate, while rocket and acoustic measurements of the stratospheric temperature are still carried out too rarely. The only thing that can be used is information on the mean temperature of the ozone layer, obtained from observations of the absorption of solar rays (or of the light of the Moon and stars) by ozone in the ultraviolet and infrared regions of the spectrum (for these methods of measuring temperature see, for example, Prokof’eva \(^{9}\)).

According to the measurements of Häge \(^{119,120}\) in Kabul (Afghanistan) in 1951, made by the absorption method in the ultraviolet region, the mean temperature of the ozone layer changes during the day by tens of degrees (Table X). It must be borne in mind, however, that the accuracy of such measurements is hardly sufficient for discussing the causes of the excess of the observed temperature variations over the calculated ones. A faster method is the measurement of infrared absorption by ozone (the band at \(9.7\mu\)), with which one can carry out many dozens of separate measurements during the day and thereby increase the accuracy of the determinations. Since the summer of 1953 this method has been systematically applied by Eidel in the USA (Research Laboratory in Flagstaff, Arizona). He detected \(^{121}\) fluctuations of the mean temperature of the ozone layer of several-

types: 1) sudden warming by several degrees in 10–15 minutes; 2) irregular changes by several degrees over the course of hours or days; 3) at times sinusoidal variations are observed with a double amplitude of about 12° and a period on the order of

Table X

Average temperature of the ozone layer (°C) from observations in Kabul ^120

Date	9 h 30 min	10 h 30 min	14 h	15 h
3 January	−15°	5°	12°	0°
25 February	−6°	10°	20°	1°
26 February	−29°	0°	6°	−37°
19 September	−3°	20°	16°	7°
2 October	11°	30°	—	5°
23 December	0°	—	15°	9°

two weeks; 4) prolonged damped sinusoidal variations with a maximum double amplitude of about 7° and a period on the order of 11 weeks; 5) the mean monthly values have an annual course with a maximum and a minimum in the period of the summer and, respectively, the winter solstice.

CONCLUSION

The results set forth above show that regular observations of changes in the ozonosphere have recently become an important means of studying many atmospheric processes. Of great significance in this respect is the persistence (conservativeness) of the degree of ozonation of the air in the lower layers of the stratosphere, discussed in § 6. The presence in the air of such a conservative property permits one to consider that the ozone method of studying atmospheric processes, in its possibilities, corresponds to some extent to the method of “tagged atoms,” which is so effectively applied today in many branches of science.

But, as we have seen, the role of ozone is not exhausted by its methodological significance, since this gas itself exerts a direct influence on the development of atmospheric processes. Ozone-conditioned phenomena include variations of the temperature of the ozonosphere, the energy balance in it, the entropy balance, and, to a certain extent, wind (thermally conditioned wind). Some of these questions were briefly considered above.

In the Introduction we emphasized that the ozonosphere is an important part of the “Sun—Earth” problem. Within the scope of the present article we are not able to dwell in greater detail on this aspect of the question.

and we shall merely mention some aspects of the problem under discussion that have remained outside our consideration.

The theory of the ozonosphere is inseparable from the problem of dissociated oxygen. Directly above the ozonosphere there is a “transition layer” of oxygen, in which a rapid change in the relative concentration of atomic oxygen takes place, from very small values to almost complete dissociation of the molecules of this gas. In turn, the presence of such a transition layer is of primary importance for the physics of the lower layers of the ionosphere. A detailed account of studies of atomic oxygen may be found in Mitra’s book ^1.

Less clear for the time being is a new direction, now only beginning gradually to take shape: it concerns the effects of solar activity on weather-forming processes. Recently, works have appeared that attempt to establish the existence of such effects (the earlier ones among them are discussed in book ^20, and among recent ones one may cite ^22, ^122, ^123, ^125, ^126, ^129, ^131, ^132, ^134). The main difficulties encountered by this important line of research may be characterized approximately as follows. The observed connections between particular characteristics of solar activity and the weather and its changes are still of a descriptive-statistical character; there are no clear ideas about the possible mechanism of the effects of solar activity on the weather. Weather is determined by processes occurring in the troposphere and partly in the lower layers of the stratosphere, whereas the direct effects of solar activity (the ultraviolet, X-ray, and corpuscular radiation of the Sun) are localized in the ionosphere and partly in the upper layers of the stratosphere. The possibility of transmitting these effects from the upper layers of the atmosphere to the lower ones remains unclear. The question of the connection between the general circulation of the atmosphere and solar activity, and in general the problem of the “Sun—troposphere,” were discussed comprehensively at the Joint Scientific Session held on March 28–29, 1955, at the Geographical Society of the USSR in Leningrad ^130.

The studies of the ozone layer that have expanded in recent years and have revealed, as we know, a close connection between the ozonosphere and the principal meteorological processes, provide some material for substantiating the supposition that the ozone layer plays the role of a transmission link between the upper layers, which are under the control of solar activity, and the weather-forming processes in the troposphere. It is now difficult to judge to what extent this supposition corresponds to reality; but if it is confirmed, then the role of ozone studies, the role of the ozone method of studying the atmosphere, will increase still further. In any case, there is now no reason to doubt the existence of close interaction between the ozonosphere and the troposphere, and the direct dependence of the state of the ozonosphere on solar activity is also gradually becoming clear. As an example, let us point to the work of Malurkar ^124, who discovered

OZONE IN THE STRATOSPHERE

... connection between geomagnetic variations and changes in the amount of ozone in the atmosphere \(x\). On the basis of data from two Norwegian observatories for 1941, 1942, and 1951, he compared the magnitudes of the daily amplitudes of changes in \(x\) with the daily sums of the \(K\)-indices of geomagnetic activity and found good agreement in the course of the quantities being compared when their values increased. Upon return to the normal state, the daily amplitudes of ozone decrease more rapidly in comparison with the more gradual decrease of the daily sums of the \(K\)-indices.

In order to form a sufficiently clear idea of the peculiarity and many-sidedness of the problem of atmospheric ozone, two further circumstances must be borne in mind.

The first of these concerns the biological role of ozone. Not a single species of plant, no living creature, and not even any species of virulent virus could exist without shelter on the Earth and in the lower layers of the atmosphere if the ultraviolet rays of the Sun were not intercepted by ozone in the high layers of the atmosphere.

Secondly, ozone is of special interest in connection with the problem of the origin of the Earth’s atmosphere. The most difficult question in the history of the formation of the atmosphere is the origin of free oxygen, which constitutes more than 20% of its composition. If there were no oxygen in the atmosphere, then not a single species of the vast kingdom of living beings that breathe oxygen would ever have had the opportunity to develop normally. Oxygen is still preserved in the Earth’s atmosphere thanks to the flora of the Earth, which inhales carbon dioxide and exhales oxygen. Was not flora the producer of the oxygen now present? It is precisely known that flora is capable of reproducing the oxygen consumed by fauna. The material equilibrium between gases acquired and expended by the Earth’s atmosphere has undoubtedly been maintained for hundreds of millions of years. Organisms that are entirely incapable of withstanding any significant changes in the composition of the gaseous medium surrounding them flourished many millions of years ago. But if we follow the idea of the origin of the oxygen that initially appeared, relying on the interaction of the processes of flora and fauna, then there is a danger of finding ourselves inside a vicious circle, since molecular oxygen \(O_2\) would have had to be present in the atmosphere in advance in order to create ozone \(O_3\), which in turn would have had to begin intercepting the ultraviolet solar radiation. Without the fulfillment of this preliminary condition, the first organisms could not have arisen. This difficulty compels us to return to the inorganic domain of pure geophysics. Perhaps a sufficient amount of primordial oxygen was formed by the direct decomposition of water vapor by the ultraviolet radiation of the Sun in the upper part of the atmosphere. At the present time the process mentioned...

decomposition is one of the sources of free oxygen. But this source is weak; and if, nevertheless, it is made the basis of an explanation, one has to assume that the appearance of water vapor and oxygen in the Earth’s atmosphere was separated in time in a certain way. In any case, it must be taken into account that at the present time almost all free oxygen is formed through the process of photosynthesis taking place in chlorophyll, which is contained in the green parts of plants (the plant world on Earth can completely renew atmospheric oxygen in a period not exceeding 6000 years).

In view of the great scientific and practical importance of systematic investigations of the ozonosphere, one cannot but regret that in the USSR work of this kind has not yet received the necessary development. Although Soviet scientists have made a major contribution both to the theory of the ozonosphere and to its experimental study, the excessively narrow scope of the work does not correspond either to the importance of the problem or to the high level of geophysical science in our country. There has been an underestimation of the prospects of the ozone line of work in atmospheric physics. It must be supposed that the preparation and conduct of the International Geophysical Year in 1957–1958 will help to eliminate the indicated lag.

There are grounds to suppose that in the near future ozonometry will find wide application in the weather service and will enter into the basic observation program of all aerological observatories. Data on the spatial redistribution of ozone will become as necessary for methods of weather forecasting as upper-air weather charts.

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