Scintillations of centimeter waves and the atmospheric irregularities from radio occultation data



[1] The analysis of field strength fluctuations of radio waves in the wavelength band λ = 2 cm of radio occultation measurements between orbital station MIR and a geostationary satellite is presented. Examples of field strength E dependences on altitude H0 of the ray path are given. We find two types of fluctuations connected to turbulence and stratified formations in the atmosphere. The RMS deviations of field strength are investigated as function H0 for both types. The frequency spectra of the field strength scintillation G(F) are analyzed to determine a spectral index n and characteristic frequency of fluctuations F0 for different minimum altitudes of the ray path H0. It is shown that the troposphere at H0 < 7 km in the high-frequency part of the spectrum is described by a function G(F) ∼ Fn, where the spectral index n on average is equal to 2.5, which corresponds to the theoretical value for the Kolmogorov spatial spectrum. In the stratosphere at H0 = 15–35 km the mean value n equals 3.6, and only in 13% of the cases there are spectra that are in agreement with the Kolmogorov law. At the basis of the analysis of the connection between the spatial spectrum of the refractive index fluctuations and the frequency spectrum of field strength fluctuations, we discuss the application of the radio occultation technique for investigation of the atmospheric inhomogeneities.

1. Introduction

[2] In order to find out the possibilities of the radio occultation method for monitoring the Earth's atmosphere, experimental research on decimeter and centimeter radio wave propagation from orbital station MIR to a geostationary satellite has been carried out in Russia between 1989 and 1998 [Vilkov et al., 1993; Matyugov et al., 1994; Yakovlev et al., 1995a, 1995b]. In the United States, since 1995 the satellite Microlab-1, receiving decimeter radio waves emitted by GPS satellites, has been used to refine this atmospheric research technique [Ware et al., 1996; Kursinski et al., 1996, 1997; Mortensen and Høeg, 1998]. The results of the first stage of the radio occultation measurements using this improved method indicate the possibility for obtaining altitude profiles of temperature, pressure and humidity and for studying stratified formations and turbulence of the atmosphere.

[3] The large potential opportunities of the global radio occultation monitoring of the atmosphere will show themselves in full at the creation of small satellite systems using millimeter, centimeter and decimeter waves. The radio occultation measurements on the satellite-to-satellite links will provide the altitude profiles of temperature, pressure, humidity and ozone content. In addition, atmospheric structures such as thin layes, clouds, waves, and turbulence are sounded with a high vertical resolution by the transmitted multifrequency waves of the satellite system. In this connection we have carried out systematic investigations of the opportunities of the centimeter radio wave application for the occultation monitoring of the atmosphere.

[4] The occultation technique for obtaining the altitude temperature profiles is well justified now [Ware et al., 1996; Rocken et al., 1997], and the determination of other atmospheric parameters by this method is now under development. Random variations of the temperature and the humidity in the atmosphere result in the appearance of refractive index inhomogeneities causing amplitude and phase fluctuations of radio waves. The detection of the regularities of the radio scintillation changes during the occultation, depending on atmospheric state, height, location, time, and so on, will extend the understanding of creation processes of atmospheric inhomogeneities. A preliminary analysis of the amplitude scintillations in radio occultation experiments has been carried out by Yakovlev et al. [1995b], who showed the possibility of studying the turbulence and atmospheric stratified structure.

[5] The purpose of this paper is to analyze further the amplitude scintillations of the centimeter band and to bring to light the possibilities for studying the atmospheric inhomogeneities with the occultation technique.

2. Radio Occultation Experiment Conditions

[6] The radio occultation measurements have been carried out using the satellite link from orbital station MIR to geostationary when the station was going in the Earth's shadow relative to the geostationary. The experiment geometry is shown in Figure 1. Shown in this figure by point O is the center of the Earth; its radius is denoted by the symbol a, and the position of the station MIR, which radiated a radio signal with wavelength λ = 2 cm, is denoted by point A. During radio occultation measurements the maximum-gain axis of the transmitting antenna of the station MIR was oriented tangent to the Earth surface in the direction of a geostationary satellite. On moving the station MIR the minimum height of the ray H0 at point C that is in the perigee of the ray decreased, which provided a “slit” of the atmosphere. The distortion of the ray AB because of the refraction in the atmosphere in Figure 1 is not shown. The radio waves, having passed through the atmosphere, were being received on the geostationary satellite at point B, which had the receiving antenna with high gain oriented in the direction of the station MIR. The received signal was amplified and retranslated without a phase distortion on the ground receiving station. The application of the gain antenna on the station MIR and on the geostationary satellite provided a high signal-to-noise ratio that increased the measurement accuracy of the signal amplitude.

Figure 1.

Geometry of problem. Phase screen and ray path.

[7] In the measurements, two geostationary satellites-retranslators (western and eastern) were used. The first geostationary satellite was over the meridian 16°W, and the second was over the meridian 95°E. The orbital plane angle of the station MIR equal to 52° allowed radio occultation measurements to be carried out in the Southern and Northern Hemispheres in the latitude range from 0° up to 52°. The research of the regions in the belt ±2.5° in relation to average meridians 60.5°E and 171.5°E was possible. The measurements have been realized over the Indian Ocean, over the northern part of the Pacific Ocean, and also over the territory of Kazakhstan. The meteorological conditions in these regions strongly differ, which results in the appearance of features in experimental dependences of the field strength E on the minimum altitude of the ray H0. In this paper, we, in general, analyze dependences E(H0) for the southern region of the Indian Ocean with latitudes from 40°S up to 52°S and the average longitude 60.5°E, where 24 radio occultation experiments have been carried out during 1997–1998.

[8] Let us give the main parameters essential for the analysis of the amplitude scintillation: distances from the station MIR and from the geostationary satellite up to the probed atmospheric area AC = L1 = 2100–2500 km and BC = L2 = 41,700 km, respectively; the radius of the first Fresnel zone r = [λL1L2/(L1 + L2)]1/2 ≈ 0.2 km.The frequency of the amplitude scintillations F depends on the crossing velocity of atmospheric inhomogeneities by a line AB and scales of inhomogeneities. The conditional atmospheric width along the line AB is L ≈ (2aHa)1/2 ≈ 600 km, where Ha ≈ 6 km is the scale height. As L1L, in the case of weak fluctuations the effect of the atmosphere on the radio wave can be considered in the approximation of the phase screen passing through points O and C perpendicularly to the line AB. This phase screen is shown in Figure 1 by the rectangle. The velocity vector of the station MIR V0 determines the velocity of the atmospheric irregularity crossing by the ray in the phase screen plane. Let us introduce the angle θ between the tangent to the point C trajectory in the phase screen plane and OC vertical. Depending on the angle value θ, different cuts of the atmosphere by the ray AB are implemented: at θ = 0 (vertical) and at θ = π/2 (horizontal) cuts of the atmosphere. In the coordinate system, in which point B is fixed, the velocity of the station is expressed by its components: V0 = (V12 + V22 + V32)1/2, where V1 is the velocity component in a plane AOB perpendicular to the straight line AB, V2 is the velocity component along the straight line AB, and V3 is the velocity component perpendicular to the plane AOB (Figure 1). Let us notice that θ = arctan (V3/V1) and the velocity of the atmospheric inhomogeneity intersection by the line AB at point C, without taking into account the refraction, V = (V12 + V32)1/2L2(L1 + L2)−1 ≈ (V12 + V32)1/2. During our measurements the values V0, V1, V2, V3 and θ were in the following limits: V0 ≈ 7.31 km/s, V1 ≈ 1.8–2.6 km/s, V2 ≈ 4.9–6.9 km/s, V3 ≈ 1.0–4.9 km/s and θ ≈ 23°–71°.

[9] The signal registration started about 8 min before the ray perigee reached the altitude H0 ≈ 40 km and finished after the termination of the signal. The changes of the signal amplitude due to the atmospheric influence were being observed for 60–90 s depending on the velocity value V1. The received signal was detected by the linear detector with a dynamic range 50 dB and time constant equal to 2 × 10−3 s. The readings of the potential difference Uj, appropriate to the received signal, were carried out with the frequency 150 Hz; an analog-to-digital converter digitized them.

[10] After termination of signal registration, measurements of the amplitude characteristics of the communication link between the station MIR–geostationary satellite–ground receiving station were performed. During these calibration measurements the receiving antenna of the geostationary satellite was directed to the ground measuring station. The transmitter with an antenna similar to those used on the station MIR mounted on the ground station transmitted the signal in the direction of the geostationary satellite. Furthermore, the received signal was relayed to the Earth, where its registration was established. Thus this signal passed through the same path as during the occultation measurements. Such a calibration by the stepping of emitted power of the transmitter similar to the one set on the station MIR was made over the range of signal level changes observed at the occultation. According to the calibration data obtained, the through gain characteristic of the communication link was determined, which was taken into account while processing the data of radio occultation measurements.

3. Primary Data Processing

[11] The signal U(t) registered by the ground receiving station corresponds to the changes of the field strength E(H0) in the location of the geostationary satellite while the station MIR is going in the Earth's shadow. At the first stage of the data processing the measurements U(t) were corrected with allowance for the through gain characteristic of the communication link. Then the dependences of the potential on time U(t) were transformed into the dependences of the potential on the minimal altitude of the ray U(H0). For the determination of H0, the minimum altitude of the ray path was evaluated with the use of the ephemeris data of the station MIR and the geostationary satellite. The refraction effect was taken into account on the basis of the model of the exponential altitude profile of the refractivity N(h), where h is the altitude from the Earth surface. The model N(h) parameters were selected with allowance for the available data about surface values of the refractivity. In our estimations the errors of altitude relation can reach ±1 km in the stratosphere and ±0.5 km in the troposphere. On the measurement space appropriate to altitudes H0 = 50–70 km the mean value of potential U0 proportional to the field strength in the free space E0 was determined. The normalization of the Uj readings was effected further to the value appropriate to the radio wave propagation in the absence of refraction Ej = Uj/U0. So the field strength normalized to the level of the radio wave propagation in the absence of refraction E(H0) = Ej/E0 was determined; therefore E(H0 > 40) = 1. During the analysis of the E(H0) changes the altitude dependences of the fluctuation dispersion σ2 and the spectra of the field strength fluctuations G(F) (here F is the frequency of amplitude scintillation) were determined.

[12] The field strength fluctuation variance was calculated as

equation image

where Ej is a measured value, 〈E〉 is its average, and m is the number of samples. In the determination of σ2 the number of Ej value indications depended on the time interval Δt. The time interval was selected under the condition that the minimum ray altitude varies on ΔH0 = 2 km in the Δt time. At ΔH0 = 2 km the number of samples, m, at the σ2 calculation varied from 150 (at stratosphere probing) up to 2000 (at the troposphere bottom probing). The spectrum of the scintillations G(F) was determined according to the program of the fast Fourier transform; thus the data observed at the intervals Δt ≈ 2–4 s, appropriate to the altitude intervals ΔH0 ≈ 3–5 km, were used. The regular decrease of the field strength average level at the Δt intervals was taken into account in the σ2 and G(F) determination using a linear approximation. The obtained values of spectral density G(F) were smoothed by the rectangular window, whose width ΔF meets the condition FF = 2.

[13] The typical dependences of the field strength E on the ray altitude H0 are shown in Figure 2. Curves 3 in Figure 2 show a fragment of typical measurements of the signal amplitude at the altitude interval from 50 up to 85 km, where the atmospheric effect was absent; they give a representation of small E fluctuations due to equipment factors. When the station MIR is going in the Earth's shadow, the field strength mean value decreases, and the scintillations due to the atmosphere start to show themselves simultaneously. The E(H0) dependences in Figure 2 represent a typical pattern of the radio wave fluctuations with strong spikes (focusings) and deep fadings. The decrease of an average 〈E〉 level is determined by refractive attenuation and absorption of centimeter radio waves; these effects were analyzed earlier [Matyugov et al., 1994; Yakovlev et al., 1995b], and therefore they are not considered here.

Figure 2.

Typical dependences of field strength from the minimum altitude of ray path.

[14] In view of the diversity of meteorological conditions in different regions we have conditionally divided the E(H0) dependences into two qualitatively different groups. The first group included occultation events in which the sharply expressed regular E(H0) change is observed in the region of the tropopause, i.e., in the interval of the altitudes H0 ≈ 9–13 km. Curve 1 in Figure 2 belongs to this group, where the vertical arrow indicates strong E change in the region of the tropopause. In Figure 3 the examples, typical of the first group, of the E(H0) dependence are shown in the region of the tropopause; the stretched horizontal scale allows us to see a thin structure of the E change in this area. In Figure 3 the E = 1 values correspond to the condition of the radio wave distribution in the absence of the refraction, when the atmospheric influence is absent, and E = 0.5 corresponds to the average refractive attenuation for H0 = 9–14 km are visible. Sharp changes of the field strength from E ≈ 0.2 up to E ≈ 1.5–2 due to focusing by thin stratified inhomogeneities of the refractivity are seen in curves 1 and 2 in Figure 3. Layered structures of the refractivity are observed owing to a high resolution in the case of the centimeter radio waves. The reason for the frequency of the beginning of such a structure around the tropopause and its importance for meteorology are unclear to us at present. The absence of the influence of the obviously expressed stratified structures is characteristic of the second group of dependences E(H0) not only in the interval of 10–13 km but also in the troposphere at altitudes lower than 7 km. The occultation events with a higher level of random fluctuations at altitudes more than 13 km and the absence of a strong focusing effect in the region of a tropopause were ganged together in the second group. The dependence E(H0), shown in Figure 2, curve 2, represents this group.

Figure 3.

Examples of field focusing by layered formations to the tropopause.

4. RMS Amplitude Fluctuations and Level of Atmospheric Turbulence

[15] At first we shall consider dependences of the RMS amplitude fluctuations on a minimum altitude of the ray σ(H0). In Figure 4, values σ obtained at the processing of the dependences E(H0) for six occultation events of the first group are shown by different symbols. In this figure there is a strong variance of the values σ on the altitudes from 0.5 up to 13 km, connected with the fact that both random oscillations and regular spikes and fadings E contribute to σ. In the stratospheric area at H0 > 15 km the values σ are not large, and they decrease with increasing altitude H0. Figure 5 gives the dependence σ(H0), obtained according to the data of six events included in the second group. The regular increase σ with decreasing H0 from 35 down to 14 km, a relative persistence of fluctuation intensity in the altitude interval from 14 down to 8 km and the decrease of σ in the troposphere at decreasing H0 from 8 down to 0.5 km are characteristic for this group. In occultation events, shown in Figure 5, the main contribution to the field strength scintillation is made by random inhomogeneities of the refractive index, and the contribution of stratified structures is negligible here. By comparing Figures 4 and 5, the second group of events has a higher intensity of amplitude fluctuations in the stratosphere. For example, at H0 = 20 km for the first and second groups the values σ are equal to 0.14 and 0.23, respectively.

Figure 4.

RMS amplitude fluctuations as a function of altitude H0 for first group of measurements: pluses, 26 September 1996, 45°S, 58.2°E; solid circles, 11 March 1998, 50.8°S, 59.6°E; open squares, 12 March 1998, 41.7°S, 62.1°E; open triangles, 17 March 1998, 52.0°S, 59.2° E; open diamonds, 16 July 1998, 46.3°,60.8°E; solid squares, 17 July 1998, 49.1°S, 60.3°E.

Figure 5.

As in Figure 4, but for second group of measurements: solid circles, 28 November 1997, 47.9°S, 61.2°E; open squares, 1 December 1997, 48.4°S, 61.2°E; open triangles, 2 December 1997, 43.2°S, 62.3°E; open diamonds, 3 December 1997, 46.5°, 61.7°E; solid squares, 4 December 1997, 40.1°S, 62.9°E; pluses, 5 December 1997, 44.1°S, 62.3°E.

[16] Let us analyze the dependences σ(H0) and reveal the features that can be used in the estimation of the atmospheric turbulence level by the radio occultation technique. Two factors, not connected with the turbulence immediately, affect the dependence σ(H0). They are the mean altitude profile of the refractivity N(h) and the refractive attenuation of the field strength X. We shall take into account the influence of the first factor, N(h), considering relative fluctuations of the refractivity ΔN/N. The values 〈E〉 differ from X only by radio wave absorption; therefore it is possible to consider that 〈E〉 = X at H0 ≥ 5 km. From the wave propagation theory in a random medium it follows that σ is proportional to RMS deviation ΔN; therefore relative discontinuity of the environment in our problem can be characterized by the factor ΔN/N ∼ σ/N [Ishimaru, 1978]. It is the second factor, i.e., the influence of the refractive attenuation on the scintillation intensity, that we shall take into account [Woo et al., 1980b; Gurvich, 1989]. According to the results of these papers, in the case of the isotropic Kolmogorov spectrum the refractive attenuation decreases the intensity of the fluctuations as follows:

equation image

Here σ1 is the RMS values of the amplitude scintillations which would take place if a statistically isotropic medium without refraction were present instead of the real atmosphere with a strong refraction, X being the refractive attenuation of the field strength. The experimental dependence σ(H0), shown in Figure 5, confirms this theoretical conclusion. In fact, the decrease of the fluctuation intensity of the field strength with dropping of the altitude H0 is observed for H0 < 8 km. The same tendency is also seen in Figure 4, though the effect of stratified inhomogeneities of the troposphere results in a strong dispersion of experimental values of σ. Thus, as the characteristic of the turbulence degree of the atmosphere at radio occultation monitoring one can take the dependence

equation image

To describe Φ(H0), we use our experimental dependences σ(H0) and X(H0) and the known altitude profile of the refractivity N(H0). In Figure 6 the results of the determination of the Φ(H0) dependence are presented: Curve 1 corresponds to average values of σ according to the data of Figure 5, and curve 2 is obtained for σ in Figure 4. While making use of the dependence σ(H0), the averaging of the σ values at the altitude intervals ΔH0 = 1 km was realized.

Figure 6.

Typical dependences of value Φon altitude H0.

[17] From the comparison of curves 1 and 2 in Figure 6 it follows that the values of the atmospheric inhomogeneity characteristic Φ for the first and second event groups for the stratospheric area differ widely. For the second measurement group, when there is no explicitly defined focusing or decreasing of the field strength caused by the stratified structures, when they are destroyed by the increased atmospheric turbulence, Φ(H0) has an increased value in the stratosphere, i.e., at the altitudes of 22–30 km. In this interval of altitudes, Φ does not depend on H0, but at H0 < 20 km the monotonous decrease of Φ is seen with the decrease of the altitude H0. The fast decrease of Φ while the altitude changes from 30 up to 23 km, small values at H0 = 22–24 km and, practically, the persistence Φ in the interval of altitudes H0 = 13–22 km are peculiar to the first group of occultation events. Apparently, rather weak atmospheric turbulence was at the altitudes of 18–24 km in this case. For H0 < 13 km in the first group, Φ has a greater value than it has in the second event group. This is connected with the fact that the stratified structures present in the first group give a considerable contribution to the experimental values of σ. Thus the characteristics σ(H0) or Φ(H0) for H0 < 13 km do not give any objective information about the atmospheric turbulence in this case. In the case of the stable atmosphere, when the turbulence is not strong and the inversion stratified structures appear, one should eliminate the contribution of such structures to σ and, therefore, to the characterization of the turbulence Φ(H0).

5. Amplitude Temporal Spectra and Spatial Spectra of the Refractive Index Fluctuations

[18] We shall consider the behavior of the amplitude scintillation spectra G(F) for different altitudes H0. In Figure 7, examples of spectra G(F), observed at the occultation events in two regions, are shown, where F is the scintillation frequency. The conditions of the measurements in these events were approximately similar. The angle of setting θ was equal to 63.4° in measurements above Kazakhstan, and the values of vertical, horizontal and complete velocity of the inhomogeneity transfer without taking into account the refraction were V1 = 2.02 km/s, V3 = 4.04 km/s and V0 = 4.47 km/s. For occultation events in a region of the Indian Ocean we had θ = 65.4°, V1 = 1.94 km/s, V3 = 4.22 km/s and V0 = 4.60 km/s. Spectra 1, 2 and 3 correspond to the average altitudes H0 = 7, 22 and 26 km. Vertical segments in Figure 7 show 90% confidence intervals.

Figure 7.

Examples of amplitude scintillation spectra: 1 − H0 = 7 km; 2 − H0 = 22 km; 3 − H0 = 26 km.

[19] From the wave propagation theory in random media with a power law of the refractive index spectrum it follows that the spectrum G(F) can be described by the characteristic frequency F0 and by the law of spectral density change GFn at FF0 [Ishimaru, 1978]. The frequency F0 is a boundary between two areas of the dependence G(F). In the first area at F < F0 the spectral density of fluctuations depends slightly on F, and in the second area at F > F0, G decreases as GFn with the increase of F. The frequency F0 is determined as a cross point of a low-frequency asymptote G(F → 0) for the first area and a high-frequency asymptote G(FF0) for the second area. For the turbulent medium with a power law of spatial spectrum of the refractive index fluctuations, the theory [Ishimaru, 1978] of the approximation of weak fluctuations yields the following relations:

equation image
equation image

where p is the spectral index, V is the velocity of inhomogeneity intersection by the ray, L = L1L2 (L1 + L2) −1 and γ is a coefficient of the order of unity.

[20] The atmosphere cannot be considered as a homogeneous isotropic medium at radio occultation events on the satellite-to-satellite link. The vertical gradient of the refractive index results in a form deformation of the first Fresnel zone and in the decrease of the transverse velocity of ray moving in the atmosphere. It is also known that the refractive index inhomogeneities are strongly horizontally prolated in the stratosphere. These reasons should result in the change of the radio wave fluctuation spectra. The analysis of the effect of regular refraction and inhomogeneity anisotropy at occultation events was carried out by Woo et al. [1980a]. Let us further examine the results of this work. According to Woo et al. [1980a] the regular refraction and inhomogeneity anisotropy do not change the spectrum form in the high-frequency area for F > F0, where GFn, which allows one to determine the values of the index n and, according to (5), the spectral index p from the experimental dependences G(F). At the same time the effect of defocusing and anisotropy of irregularities give rise to the change of value F0 depending on the setting angle θ.

[21] We shall consider the dependences n and p on the altitude. The n and p values have been determined using the results of the analysis of 214 amplitude fluctuation spectra obtained for different regions while changing the minimum altitude of the ray H0 from 35 down to 0.3 km. The mean values of the coefficient n (left axis of ordinates) and spectral index p (right axis of ordinates) for different altitudes H0 are shown by points in Figure 8. Each point in Figure 8 has been obtained as a result of data averaging for 15–18 spectra, and the vertical segments characterize a RMS deviation of n, connected with variations of this value in the investigated regions, the dashed line describing the averaged experimental dependence n(H0). Three intervals can conditionally be selected in this dependence. In the troposphere at H0 ≤ 7 km the index n undergoes slight changes with the altitude, and its average value n = 2.5 ± 0.2 corresponds well to the spectral index of the Kolmogorov spectrum p = n + 1 = 11/3. In the stratosphere at H0 = 15–30 km, experimental n = 3.5 ± 0.2; it practically does not depend on the altitude. The spectral index p = 4.5 ± 0.2 appropriate to this n differs essentially from the theoretical value p = 11/3. At altitudes from 7 up to 15 km, values of n, according to the measurement results in different regions, vary over a wide range, which is in general caused by a different altitude of the tropopause in these regions. The linear dependence n(H0), shown in Figure 8, for this altitude interval is conditional. The difference between meteorological conditions in the investigated regions and the errors of defining n stipulate a random character of the index n changes with the same H0 value. In this connection we shall consider empirical probability density functions of n values, shown in Figure 9. In Figure 9, values n are indicated on the horizontal axis, and a relative observation frequency of the n value in the interval Δn = 0.3 expressed in percentage is shown on the vertical axis. The width of an interval Δn, shown in the figure by horizontal segments, corresponds to an empirical error of n determination estimated by us. In Figure 9a the n distribution in the troposphere is shown by the results of the analysis of 86 amplitude scintillation spectra obtained for altitudes H0 from 0.3 up to 8 km. The distribution of n values in the stratosphere constructed according to the data of the 96 spectra obtained at the mean H0 values in the interval from 15 up to 35 km is shown in Figure 9b. From Figure 9 it follows that distribution of the index n in the troposphere and stratosphere differ essentially. For the troposphere in 50% of the cases n = 2.5 ± 0.5, and the spectral index p = n + 1 = 3.5 ± 0.5, appropriate to this value, is close to p = 11/3, describing classical turbulence obeying the Kolmogorov law. For the stratosphere in 50% of the cases n = 3.6 ± 0.5; besides, an additional maximum is observed at n = 2.7 in the n distribution. Thus values n, corresponding to the Kolmogorov spectrum, are observed only in 13% implementations.

Figure 8.

Dependence of average value of exponent n and spectral index p on the minimum ray path altitude.

Figure 9.

Distribution of exponent n (a) for the troposphere and (b) for the stratosphere.

[22] Let us consider the other parameter describing the amplitude fluctuation spectrum, i.e., frequency F0. The range of the F0 variations at the occultation events at altitudes from 0.3 up to 35 km constitutes from 1.2 up to 30 Hz with the changing of the inhomogeneity intersection velocity V by the ray at point C (Figure 1) from 2.5 up to 5.2 km/s. The evaluations according to relation (4) for such measurement conditions give the range of F0 change from 4.7 up to 10 Hz. The reasons for experimental and theoretical difference of F0 values are explained by the following factors. The spectra G(F), in which the experimental values F0 are more than theoretical ones, are observed in the troposphere, when RMS fluctuations of the field strength σ ≥ 0.3. In this case, amplitude fluctuations cannot be considered weak any more, and, as it follows from Fante [1975], the spectrum G(F) broadening occurs, and the characteristic fluctuation frequency F0 does not meet relation (4). At σ < 0.3 the experimental F0 values obtained by us are equal to or less than theoretical ones. Woo et al. [1980a] show that the atmospheric inhomogeneity anisotropy and regular refraction change the value of F0. The inhomogeneity anisotropy is characterized by anisotropy coefficient η ≥ 1, determined as the ratio of a characteristic horizontal scale of the irregularities to a vertical scale. The calculations made by Woo et al. [1980a] show that in the specific case η = X−1 the shape of the spectrum G(F) will be the same as one at the isotropic irregularities of the refractive index; nevertheless, the characteristic frequency of fluctuations F0 thus varies. The change of F0 occurs because of a size decrease of the first Fresnel zone in the vertical direction

equation image

and a decrease of the transverse ray path velocity at a point C (Figure 1) due to refraction effect

equation image

The difference between V* and V (formula (4)) is due to the regular refraction effect.

[23] Let us discuss the relation between the spectrum G(F) and the spatial spectrum of the refractive index fluctuations W. The frequency spectra G(F) can be converted into one-dimensional spatial spectra of refractive index fluctuations W(æ), where æ = 2π/l = 2πF/V* is a spatial number, l is the scale of inhomogeneity, on the basis of the “freezing” hypothesis, assuming that while cutting the area containing inhomogeneities by the ray, their spatial distribution does not vary. In this case the one-dimensional spatial spectrum of refractive index fluctuations is possible to present as

equation image

where V* is determined according to equation (7). If the inhomogeneities of the refractive index are statistically isotropic, the spatial spectra W(æ) should not depend on the angle θ (Figure 1). The dependence of spectra W(æ) on θ is observed in our measurements. In the case of the inhomogeneities, strongly elongated on the horizontal, i.e., stratified structures, the frequency spectra of the amplitude scintillations G(F) should, in general, be determined by vertical velocity V1, and the spectra measured will be similar while converting them to vertical wave numbers æ1 = 2πF/V1. In this case the one-dimensional spatial spectra W1) along the vertical are also determined by equation (8) while substituting V* = X2V1 into it, i.e., the vertical velocity with allowance for the refraction.

[24] In Figure 10, examples of spectra W1), obtained from measurements 01.12.1997 (dark symbol) and 26.05.1998 (light symbol) are shown. The values of the vertical scale of inhomogeneity l1 = 2π/æ1 are laid out as abscissa and the W1) value as ordinates. In Figure 10, spectra W1) observed on the average altitude H0 = 20 km are marked by squares, those at H0 = 25 km are marked by triangles and those at H0 = 30 km are marked by circles and diamonds. In spite of the difference of climatic conditions, coordinates, time of day and trajectory, on which “slit” of the atmosphere was made, the spectra W1) in Figure 10 demonstrate a good recurrence. The spectra W1) have a maximum spectral density at sizes l1 = 2π/æ1 = 300–800 m in the stratosphere in the altitude range from 15 up to 35 km. At sizes l1 ≤ 200 m the spectral density W1) decreases as æ1−4.5, at least to l1 ≈ 40 m.

Figure 10.

Spatial spectra of refractive index fluctuations for the stratosphere related to vertical spatial scales.

6. Conclusions

[25] In this paper we tried to reveal the features permitting one to study the turbulence of the atmosphere from the surface up to an altitude of ∼35 km. The observation results of star flickers at their occultation by the atmosphere, obtained on the station MIR [Aleksandrov et al., 1990; Gurvich and Kan, 1997; Grechko et al., 1997], have shown the efficiency of this method for studying the stratospheric turbulence at the altitudes of 20–50 km. The comparison of our radio occultation data and observations of star flickers [Gurvich and Kan, 1997] indicates the agreement of the results of a turbulence parameter determination in the region of overlapping experimental data. It is necessary to note that atmospheric inhomogeneities are anisotropic and separating them into classical turbulence and atmospheric “layering” is conditional. This difficulty is detected in the radio occultation measurement of the atmosphere, where the separation of the field strength fluctuations, caused by turbulence, from amplitude fadings and spikes because of thin regular strata is subjective. The analysis of field strength fluctuations of centimeter radio waves in the radio occultation events has shown the possibility of studying statistical irregularities of the refractive index. Thus the spectral index p of a spatial spectrum of inhomogeneities is determined for the height interval from 0.3 up to 35 km. In the troposphere, at altitudes lower than 7 km, p is close to the value 11/3, corresponding to the Kolmogorov spectrum of the turbulence in ∼50% observations. In the stratosphere, at the altitudes more than 15 km, p = 4.6 in ∼50% of the cases and p ≈ 11/3 only in 13% of observations. The characteristic frequency of amplitude fluctuations F0 varies in range from units up to tens of hertz. The maximum values F0 are observed at a radio occultation measurement of the atmosphere at the level of the tropopause and below, when the amplitude scintillations can be large, which results in fluctuation spectrum broadening.


[26] This work was supported by the Russian Foundation of Basic Research, grant 01-02-16002. The authors are grateful to A. S. Gurvich and A. I. Efmov for helpful comments on the manuscript.