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BETTER ECHO-

Higher Statistical Moments of Vertical Sounding Signal Intensity Variations

 

N.A. Zabotin, Rostov State University, Rostov-on-Don, 344090 Russia

J. W. Wright, 1915 Spruce Avenue, Longmont, Colorado, 80501 USA

G.A.Zhbankov, Rostov State University, Rostov-on-Don, 344090 Russia

ABSTRACT

This work has been provoked by earlier investigation of the time series of the intensity of the vertical sounding signal [J.W. Wright, J. Atmos. Terr. Phys, vol. 36, pp. 721-740, 1974]. It has been shown there that statistics of the intensity scintillation index (second statistical moment) and skewness (third statistical moment) manifests an interesting feature: both quantities determined for E and F layer reflections often significantly exceed 1. According to standard phase screen theory large values of the intensity indices correspond to focusing conditions.

Now we confirm that result using intensity scintillation data obtained with modern digital techniques at fixed radio frequency. In addition the effect is treated by theoretical means. Basic features of the experimental data have been reproduced using a numerical model of interaction of the sounding signal with large (larger than Fresnel scale) irregularities. A multiple ray tracing technique was applied to the layer of the ionospheric plasma with two-dimensional disturbances. Influence of the refraction both on ray path shape and on echo intensity was taken into account. It has been found that focusing effects always occur in the multibeam reflection (glint interference) regime. Corresponding conditions easily arise under relatively small irregularity level (less than 0.1% for the scale length 20 km).

 

a --------------------------------------------b

Figure 1

 

Figure 2

Figure 3

What are scintillation indices?

Two dimensionless statistical quantities are meant that characterize the time series of the intensity of the vertical sounding signal. They are given by the following classical expressions:

Experimental data

Fig. 1 represents the data obtained with two kinesondes, at Bierre-les-Semur in France (1970) and near Plattville, Colorado (1972). The hardware kinesonde was a prototype of today's dynasonde's 'kinesonde mode', dedicated to multifrequency time series observations. The recordings were made on up to 6 frequency-pairs simultaneously, of several minutes' duration. The scintillation parameter estimates were a preliminary step in a more extensive time-series analysis, leading through the FFT's of the complex-amplitudes for each frequency/antenna channel, through their (optionally complex or real) time-lagged auto- and cross-correlations, to "moving pattern" velocities. In the preliminary steps, the phases were strung and linearly detrended; optional real or complex high- and low-pass "RC" filters were applied for better detrending and noise reductions if needed (the same data were often re-analysed many times, before one got these choices "right"). The scintillation indices were computed using the classic expressions. The summations were done: - over each antenna channel separately - over first/last halves of each channel separately (to judge stationarity) - over all channels lumped together; these were the values most used and published. Namely those are shown in Fig. 1. Panel a relates to the E-layer reflections, panel b - to the F-layer ones. Though only mutual distribution of the , is shown here, one can see that values of both indices less than 1 were rare.

Figs. 2-3 present results of our modern analysis done using recording obtained 26 October 1985 starting at 1130 UT by the TromsЬ dynasonde. This recording has 1000 time steps for each of 8 complex-amplitude channels; the channels correspond to 4 receiving antennas, each sampled in a certain cyclic pattern at 4.000 and 4.008 MHz. The present (new) results use measurements made at 'single TOAs', in fact 50 of them, equally spaced at 10 microsecond (1.5 km) TOA intervals. The , calculations are done for each TOA independently.

Fig. 2 plots vs. TOA the average intensity AVE; the average deviation from the mean AVD/10; and the standard deviation SDV/100 on the left (log) axis. , and are on the right (log) axis. There are 8 data points at each TOA, for each quantity, corresponding to the 8 antenna/deltaf channels. The lowest three TOAs are just noise. is satisfyingly small there. Near the peak of the main echo, at TOA=243 km, there is a definite minimum of and , and there are weaker minima near other predominant echo peaks. In between the peaks, however, where glint interference occurs, we get maxima of and . Fig. 3 plots vs. for each channel separately. Something resembling patterns from Fig. 1 can be seen, but unlike it, there are many values for > 1.5, and fairly small (<10). One distinctive feature of the new data is absence of the values less than 0.6. Evidently it is connected with sufficiently high level of the irregularities during those several minutes when this recording was done.

Numerical modeling technique

 

We assume that ionospheric layer contains mid-scale (10-100 km) irregularities of the following kind:

,

where is the unperturbed (background) altitude dependence of the electron density in the ionospheric layer, and are the amplitude and spatial period of irregularities. The density wave is propagating along the horizontal axis with phase velocity . Qualitatively new feature of radio propagation in the presence of mid-scale irregularities consists in the multibeam reflection phenomenon. The angular spectrum of radio waves coming back to an observation point becomes discrete. The signal on the Earth's surface is a result of interference of several rays following along separate paths:

  Figure 4

The trajectory and amplitude of each ray is determined by means of numerical solution of an extended set of the geometrical optics equations.

Phases of separate rays coming to the measurement point are considered statistically independent quantities uniformly distributed in an interval . It corresponds to the phase dispersion >1, that is to sufficiently high level of small-scale irregularities causing those phase variations. This assumption has nothing to do with instrumental phase distortions.

The algorithm simulating a reflection of sounding signal from the ionosphere looks as follows. Values of the phase of the model large-scale electron density perturbation (1) are set sequentially. For each of determined so positions of the perturbation the trajectories of a great many of rays outgoing from one point on the ground surface are calculated sequentially. These rays in the aggregate simulate the ionosonde radiation. If one uses the isotropic plasma model, only rays at the plane of propagation of the density wave (that is at the plane) are of interest. Only such rays have chance to return to the point from which they were radiated (see Fig. 4). Thus dimensionality of the problem is reduced by unit that enables to use simple algorithm of return reflection searching.

From the trajectory calculation data the rays returning into the observation point, which interference just gives the registered signal, are found.

Refraction (both regular and irregular) is very important in the considered problem. Our analysis shows that number of rays which are emitted and return back to the sounder by different paths tends to 50% when is increased. It means that reflection regime is not like with rippled mirror.

For each group of interfering rays several sets of independent random values of the phase are sequentially generated by the random-number generator and the total field parameters are determined by means of vector summation of the separate contributions. The waves reflected from the ground are also taken into account (see Fig. 4). Their amplitudes are determined using usual lows of reflection.

Obtained by such means values of the total field amplitude are used for study of statistical properties of this parameter.

Calculation results

a) F-region

The reflection level height was set equal to 250 km, sounding frequency 5 MHz.

In our calculations multibeam regime arose under very low disturbance level:

 

 

 

Table 1

Disturbance
scale length, km
value under which multibeam regime arises, for F layer, % value under which multibeam regime arises, for E layer, %
10 <0.05 0.2
20 0.1 0.8
30 0.3 1.7
40 0.4 3.0
50 0.6 4.4
75 1.2  

 

 

 

  Figure 5

Fig. 5 shows dependence of mean wave envelope amplitude on the disturbance level for several different disturbance scale lengths .

  -------

Figure 6 --------------- ----------------Figure 7

Figs. 6 and 7 show the same dependence for scintillation indices and correspondingly.

 

 

 

  Figure 8

 

 

Fig. 8 is an analog of the experimental plots from Figs. 1b, 3. This is mutual variation of vs . This plot looks much like experimental ones and is consistent with the phase theory results.

 

b) E-region

Our model calculations for the E layer conditions differ by choice of the parameters characterizing the reflection level (100 km) and sounding frequency (2 MHz).

First of all, calculations show that multibeam regime arises under slightly larger values of (see the Table 1).

  Figure 9

Fig. 9 shows dependence of mean wave envelope amplitude on the disturbance level for several different disturbance scale lengths . It is seen that the main maximum is located in this case also under larger values of . For the irregularity scale lengths 30-50 km it even does not get into the interval <10%.

Figure 10 -----------------------------------Figure 11

Figs. 10 and 11 show the same dependence for scintillation indices and correspondingly.

It turns out that location of the first pike in each graph of Figs. 6-7 and 10-11 coinsides with values in corresponding column of the above Table 1. First maxima locations (more presizely, locations of their left slopes) indicate arizing of multibeam interference regime.

  Figure 12

Fig. 12 is analogous to experimental Fig. 1a. This is mutual variation of vs . The difference from experimental plot is very small and relates primarily to the band . The calculations are deterministic for the range <0.2. By comparing Fig. 10 and data in the Table 1, we see that this is region of absence of multibeam regime. But there is known general feature of such reflections: "focusing prevails defocusing". Due to this feature distribution of the intensity must be asymmetric. The skewness coefficient must show that. The rest parts of the plot from Fig. 12 look like were taken directly from the experimental one.

The group time spread

When vertical sounding of the ionosphere, both in kinesonde and dynasonde P-mode, pulses are used. For multibeam interference to have possibility to occur the difference between group ranges of separate rays must not exceed the pulse length (~ 60 mks).

 

Figure 12

Fig. 12 shows the dependence of group range dispersion on the and . It is seen that dispersion is increased quite slowly with growth what must favour multibeam regime within broad range of .

Another criterion can be obtained when considering the maximum group range deviation for glints which intensity exceeds some threshold value. In Fig. 13, instead of r.m.s. values, group ranges of all rays are shown by points for each value. The density of points is proportional to number of echoes.

  Figure 13

The sharp limiting of group delay for a given on the upper and lower sides, and the linear increase of this limit with , are very striking and obvious. One can see that echo spreading comparable with the pulse length is achieved only under sufficiently large values. Note that every time when the first pike in and occurs, dispersion of group range is still very small and it means that namely multi-beam interference takes place.

 

Detailed investigation of the spike regions

Let us consider case of E-region reflections, for =20 km, and of 0.8, where the Table 1 states that the multibeam regime begins. The and graphs (Figs. 10 and 11) also show large spikes at the same , as it has been pointed out above. And Fig. 9 shows a very small value of there, with almost no peculiarities at nearby values of . On the other hand, there is region of the main maximum of the plot (near ~7%). One our purpose was to investigate the distribution of the signal intensity peculiarities causing such behavior of the statistical moments.

As before, instead of random irregularity field generation we use deterministic wave-like model. This wave (with fixed value of its amlitude ) moves over the sounder with some step. In our detailed calculations this step was 6 times smaller than before and corresponded to 360 positions of the disturbance per its spatial period . We also carried out these calculations for series of more close values of (the step over was 0.02% instead of old 0.1%). This 'breakage' of the deterministic calculation parameters influences the statisics also because it assists to more precise hits to the points where focusing and multibeam reflections take place. One can see that old and new dependencies have very close qualitative features. It relates to general shape of vs dependence and to locations of the first maxima in , . The maxima height appear different due to more precise hits to the points where focusing and multibeam reflections take place.

More detailed investigation of the region in our plots where the first spike in and occurs leads to interesting conclusion. It appears that simultaneously with multibeam regime rise the individual echoes appear that have amplitude about ten times as large than the mean one. It may be appraised only as manifestation of focusing. The conditions for focusing are already matured when multibeam regime arises.

Detailed investigation of the second region of interest (near ~7%) does not notice any qualitative jumps there. The multibeam regime has been developed already (about 5 echoes per pulse on the average, as can be seen from trajectory calculations). The pike region is characterized by frequent cases of focusing (many individual echoes have amplitudes above A/A0~2). One can make conclusion that more frequent focusing causes pike in the .

Why focusing occurs under low irregularity level?

Let us consider the wave-like disturbance of the kind

,

where , is the plasma frequency, is regular linear ionospheric profile and is irregularity amplitude. The reflecting surface shape is determined by the condition what gives

.

Using general expression for the