Determination of the characteristics of inversion reflecting layers in the troposphere on changes in the signal intensity on the near-earth over-thehorizon routes in the middle latitudes

 1 VV
  min max (8) 
 1 VVmin max
and the reflection coefficient from the layer is obtained using experimentally 
obtained data on the values of the attenuation factor. 
 Theoretically expected estimates of the reflection coefficient from a layer with a 
stepwise change in the refractive index by can be obtained using the relation [4]: 
 (9) 
which is true for small, but still greater than the angle of total internal reflection 
angles of meeting with the layer  n defined by the ratio: 
 Viewing angles corresponding to total internal reflection √ 
where - Expressed in N units, and - In milliradians. 
 The above relations make it possible to determine the reflection coefficients from 
the layer from the logged interference structure of the signal on the OTH route, the 
hop of refractive index and the characteristics of dynamics of its height changes. 
Journal of Military Science and Technology, Special Issue, No.72A, 5 - 2021 15 
 Electronics & Automation 
 3. EXPERIMENT RESULTS 
 Experimental studies in the mid-latitudes (Ukraine) of signal levels of TV 
stations on OTH routes made it possible to establish that interference phenomena 
in the received signal can be associated with multipath in the propagation 
channel. The most frequent it is observed from late spring to early fall. The 
measurements carried out during the spring-summer period (from May to 
August), when the presence of inversion layers is most likely. During 
observations, deep interference fading or received signal amplitude fluctuations, 
with a constant period were observed. 
 As an example, the characteristic behavior of the signal in the presence of 
inversion reflecting layers on the over-the-horizon propagation path is shown in 
fig.2. There is characteristic deep fading (up to 30 ... 40 dB) with a period of up to 
several hours. 
 In approximately 3% -5% of cases, 
in the morning hours of the summer 
months after sunrise, the level of the 
received signal decreased significantly 
below the average value. This, 
apparently, is due to the fact that the 
corresponding points: the transmitting 
one in Belgorod (height 175 m) and the 
receiving one in Kharkov (height 30 m) 
are located on different sides relative to 
the inversion reflective layer. The Fig. 2. Behavior of the VHF signal on 
analysis of the data show that in the the over-the-horizon route in the 
mid-latitudes the inversion reflective presence of inversion layers: signals 
layers are located, as a rule, at heights during: 1-st, 2- nd and 3-rd November. 
of 50 ... 650 m, have a difference in the 
refractive index from -0.33 to -0.105 N-units. Moreover, the speed of their vertical 
movement is from units to several hundred meters per hour. Interfering with a 
direct signal, they lead to the appearance of fading from a depth of 3dB to 23dB. 
 Experimental studies were carried out in the middle latitude (Ukraine). Their 
goal is to show the possibility of using the proposed approach to analyze the case 
when inversion reflective layers are present in the troposphere, which manifests 
itself in periodic signal fading on the over-the-horizon path. 
 Studies have shown that the characteristics of the troposphere are slightly 
influenced by 12-year cycles of solar activity - fig. 3. However, trend changes in 
the refractive index do not exceed 1% for middle latitudes. Fig. 4. shows its 
behavior on an interval of more than 7 years. 
 Comparisons of the behavior of the refractive index for the middle latitudes and 
Vietnam [4] show that they have both general regularities (daily and seasonal 
changes) and differences (a larger spread of refractive indices for middle latitudes - 
in summer, and for the tropical zone - in winter). 
16 N. X. Anh, , T. H. Trung, “Determination of the characteristics  the middle latitudes.” 
Research 
 Fig. 3. The behavior of the refractive index for Ukraine. 
 As an illustration, figs. 4, 5 show the changes in the refractive index for the 
middle latitudes and for the tropical zone, Ukraine and Vietnam. 
Fig. 4. Seasonal change in the refractive index for Kharkiv city (steppe zone) over 
 several years. 
 Similarity of refractive index behavior makes it possible to use the methods 
developed and tested in the middle latitudes (Ukraine) to study the tropospheric 
features for the tropical zone (Vietnam). 
Fig. 5. Seasonal change in the mean values of the refractive index after smoothing 
 over 30 days: 1- Hanoi; 2-Ho-Chi-Minh. 
 Fig. 6 shows the histograms (b) and the distribution functions (a) of the gradient 
of the effective refractive index in the layer the radio wave is propagated (1) 
reflection coefficient of the layer (2), the depth of signal fading (3), the altitude of 
the inversion reflecting layer (4) and its speed of movement (5). The integral 
distribution functions are given on a scale linearizing the normal distribution law. In 
this case, the value of the process (abscissa) is centered and normalized to rms value. 
Journal of Military Science and Technology, Special Issue, No.72A, 5 - 2021 17 
 Electronics & Automation 
 (x-m)/ 
 -18-16-14-12-10 -8 -6 -4 -2 0 2 4 6 8 10 20
 18
99,5
 98 16
 ) 14
 90 
 12
), % ), 70
 10
 50
 30 8
 p((x-m)/ 1 
 10 6
 4
F((x-m)/ 2
 0,5 2
 0
0,01 -20-18-16-14-12-10-8 -6 -4 -2 0 2 4 6 8 10
 (x-m)/
 (x-m)/
 -14-12-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 10
99,5
 98 8
 )
 90 
), % ), 6
 70
 50 4
 30
 p((x-m)/ 2 
 10 2
F((x-m)/ 2
 0,5 0
 -14-12-10-8 -6 -4 -2 0 2 4 6 8 101214
0,01 (x-m)/ 
 (x-m)/
 -14-12-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 12
99,5
 98 10
 )
 90  8
), % ), 70
 50 6
 30 4 3 
 10 p((x-m)/
 2
F((x-m)/ 2
 0,5
 0
0,01 -14-12-10-8 -6 -4 -2 0 2 4 6 8 101214
 (x-m)/ 
 (x-m)/
 -10 -8 -6 -4 -2 0 2 4 6 8 10 14
99,5 12
 98
 10
 90 )
), % ), 
 
 70 8
 50
 30 6
 10 4 4 
 p((x-m)/
F((x-m)/ 2 2
 0,5
 0
0,01 -10 -8 -6 -4 -2 0 2 4 6 8 10
 (x-m)/
 (x-m)/
 -6 -4 -2 0 2 4 6 8 10 12 14 16 12
99,5 10
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 
), % ), 70
 50 6
 30 5 
 4
 10
 p((x-m)/
F((x-m)/ 2 2
 0,5
 0
0,01 -6 -4 -2 0 2 4 6 8 10 12 14 16
 (x-m)/ 
 a) b) 
 Fig. 6. Characteristics of the inversion layers and the signals reflected from it 
propagating on the OTH path: distribution functions (a) and histograms (b) of the 
gradient of the effective refractive index of the layer (1), reflection coefficient from 
the layer (2), fading depth (3), and the altitude of the inversion reflective layer (4) 
 and its speed of movement (5). 
 It is seen, that if the distributions of fading, reflection coefficient, and layer 
18 N. X. Anh, , T. H. Trung, “Determination of the characteristics  the middle latitudes.” 
Research 
heights are satisfactorily described by the normal distribution law, then the 
distribution of its displacement velocity differs significantly from the standard 
model. The results of the statistical processing of the data are given in table 1. 
 Table 1. Numerical characteristics of reflective inversion layers according to 
 experiment. 
 
 +
 h t,
 
 , dB ,
  
 , m , /
 s
 +
 V, dB V,
 
 
 h
 N
 g
 Drop
 mph
 t, t, hour
 uration
 height height
 Relative Relative d
 reflection reflection
 Reflection Reflection
 Parameter half period
 layer lifting lifting layer
 layer height layer
 coefficient, coefficient,
 at 1 am h am at 1
 speed speed
 Mean gradient
 increment, increment,
 coefficient
 max/min max/min
 Mean 10,35 369,64 -0,0529 0,5080 -24,08 67,32 2,03 38,41 
Standard. 
 0,81 34,15 0,0031 0,0301 0,720 12,75 0,141 6,81 
 error 
 Median 10 450 -0,048 0,5195 -24,021 35,02 2 24,87 
 Moda 7 450 -0,049 0,3825 -16,665 34,84 1,5 
 RMSE 4,74 180,7 0,0164 0,1757 3,8824 67,45 0,813 36,05 
Dispersion 22,43 32655,4 0,00027 0,0309 15,07 4550,2 0,662 1299,5 
 Excess 0,471 -0,541 5,924 -0,515 -0,518 6,376 -0,853 1,921 
Asymmetry 0,858 -0,389 -2,386 0,170 0,0487 2,592 0,374 1,684 
 Interval 19,5 600 0,072 0,669 14,474 258,69 3,25 131,95 
Minimum 3,5 50 -0,105 0,1987 -31,139 23,77 0,5 9,27 
Maximum 23 650 -0,033 0,8678 -16,665 282,46 3,75 141,22 
 Sum 352 10350 -1,532 17,2735 -698,4 1885,0 67,15 1075,568 
 Score 34 28 29 34 29 28 33 28 
 The results of processing of the received signals of a HF (175 MHz frequency) 
TV channel (the Belgorod – Kharkiv OTH route with a length of 71 km) according 
to the developed method, as well as data of aerological sounding of the height of 
the inversion layer location made it possible to establish that fading with a depth of 
more than 10 dB is observed in less than 40% of cases, and over 20 dB no more 
than 5%. The height of the reflective inversion layer in approximately 85% of 
cases does not exceed 0.5 km. In this case, the differences in the refractive index in 
the layer are, as a rule, 6-14 N units. The range of variation of reflection 
coefficients from inversion layers ranged from -20 dB to -32 dB. Moreover, the 
most probable (with a probability of about 0.6) values of the relative reflection 
coefficient ranged from 0.4 to 0.8. The estimates obtained are in satisfactory 
agreement with the theoretically expected ones. The speed of change of the height 
of the inversion reflective layer obtained using ratios in approximately 70% of 
cases lies within 10-30 mph. 
 4. CONCLUSIONS 
 1. A technique is proposed for studying the characteristics of inversion layers in 
the troposphere from the characteristics of signal fading along the over-the-horizon 
path. It has been shown theoretically and experimentally confirmed that the 
Journal of Military Science and Technology, Special Issue, No.72A, 5 - 2021 19 
 Electronics & Automation 
selected spectral components of fluctuations of the signal received on the over-the-
horizon path make it possible to estimate the relative reflection coefficient from the 
layer, and hence the difference in the refractive index in it, as well as the altitude of 
its location and the speed of its vertical movement. This approach, based on the use 
of spectral analysis of the signal structure on over-the-horizon paths to study the 
structure of layers in the troposphere, was proposed for the first time and for the 
first time made it possible to obtain their characteristics (number, frequency of 
occurrence, average altitude and speed of its vertical movement, as well as the 
difference in refractive index in the layer) for the middle latitudes. A similar 
approach can be successfully used to study the characteristics of layers in the 
tropical zone of Vietnam. 
 2. Experimental studies carried out in the middle latitudes using the radiation of 
TV centers made it possible to establish that in most cases the number of inversion 
layers does not exceed 2 with a difference in the refractive index at the layer 
boundary of 6 ... 14 N units. The height of their placement for mid-latitudes, as a 
rule, does not exceed 1 km, and the lifting speed of several hundred meters per hour. 
 3. A standard Gaussian model can be used to describe fading statistics, 
reflection coefficients, and altitudes of inversion layers. At the same time, the 
distributions of the effective gradient of the refractive index in the layer, which is 
essential for the propagation of radio waves and the velocities of the inversion 
layers, differ from the Gaussian models. 
 4. The features of the behavior of the signal on the over-the-horizon path, which 
are characteristic of various states of the troposphere, were established, and 
classification criteria were formulated that would allow the signal behavior to 
diagnose the refractive state of the troposphere and study the frequency of 
occurrence of various situations. The obtained quantitative estimates are typical for 
the middle latitudes and will be different for the tropical zone, however, the 
formulated classification criteria will make it possible to use the approach 
proposed by the authors to study the features of the troposphere of the tropical 
zone using emissions from television centers and VHF broadcasting stations on 
over-the-horizon routes, which opens up new opportunities for studying the radio-
climatic features of Vietnam. 
 Acknowledgment: This work was supported by the National Academy of Sciences of Ukraine 
and the Ministry of Industry and Trade of Vietnam. 
 REFERENCES 
[1]. Anh N.X. “Estimation of Atmospheric Parameters Using Radio Occultation 
 Method” / N.X. Anh, P.L. Khuong, V.A. Kabanov, V.I. Lutsenko, I.V. Lutsenko, 
 V. B. Sinitsky // J. Geology, Series B.-2008.-No. 31-32.- P.60-66. 
[2]. Lutsenko V. I. “On the possibility of determining the characteristics of 
 reflecting layers in the troposphere above land from variations in the levels of 
 VHF signals on horizontal lines”. / V.I. Lutsenko, I.V. Lutsenko, E.N. Belov, 
 S.I. Khomenko // "Visnyk of V.N. Karazin Kharkiv National University Series 
 "Radio Physics and Electronics".- 2002.- No. 570.- P. 203-204. 
[3]. A.G. “Arenberg Propagation of decimeter and centimeter waves”. M .: “Sov. 
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 radio ".1957.-298p. 
[4]. Anh N.X. Radioclimatic features of Vietnam / Anh N.X., Popov I.V., 
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 TÓM TẮT 
 XÁC ĐỊNH ĐẶC ĐIỂM CỦA LỚP PHẢN XẠ NGƯỢC TRONG TẦNG ĐỐI 
 LƯU DỰA TRÊN CƯỜNG ĐỘ TÍN HIỆU THEO ĐƯỜNG TRUYỀN DẪN 
 GẦN CHÂN TRỜI TẠI CÁC VĨ ĐỘ TRUNG BÌNH 
 Phương pháp xác định sự thay đổi độ cao, vận tốc nâng và hệ số phản xạ 
 của lớp phản xạ ngược trong tầng đối lưu được nghiên cứu dựa trên kết quả 
 quan trắc tín hiệu VHF theo đường truyền gần chân trời. Ước tính vận tốc 
 nâng và hệ số phản xạ của lớp phản xạ ngược dựa trên kết quả đo đạc mức tín 
 hiệu VHF ở gần vùng che khuất hình học trong khu vực vĩ độ trung bình và dữ 
 liệu bóng thám không thu được. 
Từ khóa: Hệ số phản xạ; Lớp phản xạ ngược; Tầng đối lưu; VHF; Dữ liệu khí tượng. 
 Received Oct 07th 2020 
 Revised Dec 04th 2020 
 Published May 10th 2021 
Author affiliations: 
 1Institute of Geophysics, VAST, Vietnam; 
 2A.Ya. Usikov Institute of Radio Physics and Electronics of NAS of Ukraine (IRE NASU), 
 Ukraine; 
 3Kharkov Machine Building Design Bureau named after A.A. Morozov (KMDB), Ukraine; 
 4Vietnam Research Institute of Electronics, Informatics and Automation (VIELINA), 
 Hanoi, Vietnam; 
 5Graduate University of Science and Technology, VAST, Vietnam; 
 6Faculty of Electrical and Electronic Engineering, University of Transport and 
 Communications (UTC), Hanoi, Vietnam. 
 *Corresponding author: nxuananh05@gmail.com. 
Journal of Military Science and Technology, Special Issue, No.72A, 5 - 2021 21