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Дата изменения: Fri Feb 2 12:02:01 2007 Дата индексирования: Mon Oct 1 21:46:40 2012 Кодировка: Поисковые слова: южная атлантическая аномалия |
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 |
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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 curvature radius of a line one can get in our case
.
The influence of the irregularity shape
manifests itself by numerical factor : if estimation was done for the spherical
reflection surface (instead of sinusoidal one), the factor would
be equal to 1/4.
Minimum corresponds to sin equal to 1. Maximum
corresponds to sin
equal to 0 and is always equal to infinity. For
=0.0076,
=20 km, H=20
km we obtain Rmin ~ 67 km. Thus, in our case
(reflection from the E layer, altitude about 100 km) focusing is
quite possible already when multibeam regime arises. If Rmin
is less than 100 km, always the position of the irregularity over
the sounder can be found when R coincides
with distance from the sounder to the reflection point.
Why focusing is connected with multibeam reflection?
The following three sketches (Fig. 14) show how events are developed with the irregularity growth.
Figure 14
Conclusions
We can state that experimental results with
large and
is evidence
of presence of multi-beam interference.
Our calculations show that multi-beam regime
arises easier for the F layer conditions (under equal irregularity
level of and the
same irregularity scale length
).