1.
Department of Radio Engineering Devices and Antenna Systems of
National Research University
“Moscow Power Engineering Institute”
valerypermyakov@yandex.ru
Doctor of Physical and Mathematical Sciences, Professor Valery A. Permyakov
Ph. D. Mikhail S. Mikhailov
Ph. D. Mikhail V. Isakov
and Postgraduate Andrew M. Makhalov
St. Petersburg — 2017
PIERS
Progress In Electromagnetics Research Symposium

2.
ABSTRACT
The method of parabolic equation is
used to calculate the radar range in the
presence of the evaporation duct
Excitation of the evaporation duct at
variations in the refractive index of the
troposphere is analyzed

3.
The First Documentation
The first person to record the phenomenon
of super refraction of electromagnetic waves
was Gerrit de Veer, a member of Willem
Barentsz's expedition into the North Polar
Region in 1596–1597. Trapped by the ice, the
party was forced to endure the polar night on
the archipelago of Novaya Zemlya. On January
24, 1597, De Veer claimed to have seen the
Sun appear above the horizon, two full weeks
prior to its calculated return.

4.
Optical illusion
“Flying Dutchman”
The same is connected
with anomalous refraction

5.
Anomalous refraction
in the inversion layer
Humidity inversion
Evaporation duct
Temperature inversion
Near-surface duct
15m: 100m:

6.
Paulus–Jeshke model:
where x is altitude (height above ocean), hw is
evaporation duct height, and x0 is an aerodynamic
parameter equal to 1.5∙10-4
m,
and M(0) = (n-1)∙106
is the modified refractive
index at the sea level
Paulus, R.A. Practical application of an evaporation duct model / R.A. Paulus // Radio
Science. 1985. V. 20. № 4. – pp. 887–896
Jeske, H., Die Ausbreitung elektromagnetischer Wellen im cm-bis m-Band fiber dem
Meer unter besonderer Berficksichtigung der meteorologischen Bedingungen in der maritimen
Grenzschicht, in Hamburger Geophysikalische Einzelschriften, De Gruyter, Hamburg, 1965.
( ) ( ) 0
0
0 0,13 ln ,w
x x
M x M x h
x
 +
= + × − × 
 

7.
Paulus–Jeshke model:
(0) 315M =
15wh m=
M profile−
,x m
modified refractive index

8.
The radar range is limited by:
• the loss in the clean air
• the loss in the hydrometeors
• the scattering of electromagnetic waves by
sea waves
• the scattering of electromagnetic waves by
the turbulent troposphere
• the perturbations of the evaporation duct
refractive index in both vertical and
horizontal directions

9.
Loss in the clean air,
hydrometeors and by seawaves
range, km range, km
range, kmrange, km
-Lossless; -Loss in the clear air; -and hydrometeors
15
5
a
t
h m
h m
=
=

10.
Calculations were performed for
the following parameters:
• the length of the electromagnetic wave is 3 cm
• the mean power of the signal Pm = 15 W
• the antenna gain is 30 dB
• the antenna radiation pattern is described by the
function sin(x)/x
• the width of the main lobe is 5° in both planes and
is directed toward the horizon
• The target's effective scattering area is 10 m2
• heights of the antenna and the target are 5–7 m

11.
Reasons of this study:
• at tropic latitudes evaporation ducts arrive
with a probability of 100%
• profile reconstructed from the measured
meteorological parameters agrees with the
theoretical Paulus–Jeshke profile
• But! There are no the results of
measurements of the refractive index profile
at the seaside
Kenneth D.A. The RED Experiment. An Assessment of boundary Layer Effects in a
Trade Winds Regime on Microwave and Infrared over the Sea. // Bulletin of American
Meteorological Society, Sept.2004.–pp.1355–1365

12.
Reasons of this study:
• at middle latitudes the probability of the
existence of the evaporation ducts is high in
the middle of the day in summer months
• variations in the profile at the seaside are
substantially different from the P–J profile and
have higher variability in time
• variations in the evaporation ducts height
with distance from and along the seaside
Frederickson P. Improving the Characterization of the Environment for AREPS
Electromagnetic Performance Predictions / Weather Impacts Decision Aids (WIDA)
Workshop. 15 March 2012, Reno, NV

13.
For example:
(0) 347,5M =
3wh m=
M profile−
,x m
modified refractive index

14.
[ ] [ ] [ ] [ ] [ ]
3
2
77,6 373 10
,
P e
M
T T
P e mb T K
= + ×
= = =

15.
Parameters of numerical simulation
• the standard scalar parabolic equation was used.
• initial condition set at a distance of 100 m
• zero boundary condition was set at the sea level
• the range increment is 1–10 m
• the height increment is 0.05 m
• the maximum height is ~200 m
• the absorbing layer was introduces in an interval
of heights of 160–200 m

16.
Perturbations of the vertical profile
• Let us consider perturbation of the
evaporation duct by a segment of the normal
troposphere with positive gradient of the
refractive index situated directly above the
sea surface

17.
Perturbations of the vertical profile
thickness of the NT layer

18.
seaside 150km
20wh m=
5wh m=
Vertical and horizontal variations

19.
Vertical and horizontal variations
Antenna’s
heights is 7m
1st mode
2nd mode
3rd mode

20.
Vertical and horizontal variations
Antenna’s
heights is 20m
1st mode
2nd mode
3rd mode

21.
seaside150km
20wh m=
5wh m=
Vertical and horizontal variations

22.
Vertical and horizontal variations
Antenna’s heights is 7m
1st mode
2nd mode

23.
Transition region
Normal
troposphere
Transition
region
Evaporation
duct
z, kmz1 z2seaside
( ) ( )
( )
( ) ( ) ( ) ( )
( ) ( )
1 1
1 2 2 1
1 2
2 1
2 2
, 0
,
,
M x z M x at z z
M x z z M x z z
M x z at z z z
z z
M x z M x at z z
= < <

× − + × −
= < <
−
 = >

24.
Transition region
1 0z =
2 3z km=
2 30z km=
2 40z km=
on condition

25.
CONCLUSION
• The effect of variations in the refractive index in the
transition region from the seaside to the beginning of the
regular evaporation duct has been shown
• Perturbations of the duct parameters at the horizon
boundary and beyond have the effect of radar range
• The obtained results to be important for experiment on
observation of radio waves propagation above the sea
• In future, for operation of a radar station, it is expedient
to supplement the radar complex with a facility for
measuring the M profile at the radio horizon with the‒
help of sensors installed on buoys, ships, or pilotless
vehicles and a computer program for calculation of
radio link by the method of parabolic equation

26.
Thank you for attention!
This work was supported by the Ministry of
Education and Science of the Russian
Federation (project no. 8.3244.2017/PCh)
ACKNOWLEDGMENT