Proceedings of Annual Conference of China Institute of Communications
Optical Turbulence in the Marine Atmosphere Surface
Layer of Different Wavelength
Xichuang REN, Jiang’an WANG, Ronghua WU
Electronic Engineering College, Naval University of Engineering, Wuhan, China
Email: [email protected]
Abstract: A model used to estimate the optical turbulence in the marine atmosphere surface layer of different
wavelength is developed based on the similarity theory, and some numerical analyses are done. It is found
that value of the optical turbulence varies with the air-sea temperature difference, the humidity of the air, and
the sea surface wind speed. When the optical wavelength changes, the effects of the optical turbulence are
similar. But for infrared frequencies, the value is larger than that for visible and near infrared frequencies.
The optical with the wavelength of 1.55and 10.6  m are commonly used in free space optical communication,
and in this paper, the simulations of the optical of these two wavelengths are developed.
Keywords: optical turbulence; refractivite-index structure parameter; marine atmospheric surface layer
measurements of temperature, pressure and humidity, for
visible and near infrared frequencies (0.36-3  m ), the
atmosphere refractivity nv can be expressed as follows
[3]:
1. Introduction
The characteristics of laser atmospheric transmission
mainly contain absorption, scattering, refraction and turbulence effect. The atmospheric turbulence is directly
related to atmospheric refractivity. The propagation of a
light beam through the atmosphere is affected by random
fluctuation in the refractivity of air and it is these fluctuations or discontinuities that cause turbulence. The
refractivity index structure parameter, Cn2 , is usually used
to evaluate the atmosphere refractivity. Since direct
measurements of Cn2 over the sea are difficult and expen-
106 (nv  1)  m1( )
(1)
where P is atmospheric pressure, T is the temperature, q
is the specific humidity,  =0.622,   1  0.61q ,m1 and
m2 are empirical functions of wavelength:
6839.397 45.473

 m1( )  23.7134  130-λ -2  38.9-λ -2

-2
-4
m2( )  64.8731+0.58058λ -0.0071150λ (2)

+0.0008851λ -6


sive to obtain, it is useful to estimate C from indirectly measured environmental parameters. Some experiment has been done at marine surface environment.
Similar researches have been done by Paul A. Frederickson, Stephen Doss-Hammel and Dimitris Tsintikidis
[1,2], etc. The infrared scintillation has been obtained by
the American space and naval warfare systems center
and Naval Postgraduate School along a propagation path
over San Diego Bay in 2005.
For free space optical communication and infrared detection over the sea surface, the wavelength of
1.55  m and 10.6  m are extensively used. So the
characteristics of the optical with these two wavelengths
are important for infrared application near sea surface.
They were not detail represent in previous researches.
The main work of this paper is to determine how the laser beam with different wavelengths performed in marine
atmosphere, focused on the wavelength of 1.55  m and
10.6  m , to find the similarities and differences of the
two wavelengths.
2
n
And for infrared frequencies (7.8-19  m ), the atmosphere refractivity ni can be expressed as follows [4]:
106 (ni  1)  m1( )

p
qP
 m1( )
T
T 
qP Q(T ,  )
 S ( )]
[
RdT  H (T ,  )
(3)
where
Q(T ,  )  957-928y 0.4 ( x  1)
(4)
H (T ,  )  1.03y 0.17  19.8x 2  8.2x 4  1.7x8
(5)
S ( ) 
3.747  106
12499  x 2
(6)
and x  10 / y , y  T / 273.16 , Rd is the ideal gas constant
of dry atmosphere.
The refractive index structure parameter Cn2 is re-
2. The Refractivity Model
The refractivity of atmosphere can be determined from
978-1-935068-10-5 © 2010 SciRes.
P
qP
 [m 2( )  m1( )]
T
T 
376
Proceedings of Annual Conference of China Institute of Communications
lated to the atmospheric refractivity, and is defined as:
for humidity ( q ) are expressed as follows [7]:
[n '(0)  n '(r )]
(7)
r 2/3
where n’(0) and n’(r) are the turbulence fluctuation values of n at two points separated by a distant r along the
wind direction. Cn2 can also be expressed in terms of
u  ku ( z )[ln( z / z0 )  u ( z / L)]1
2
Cn2 
T  k[T ( z )  Ts ][ln( z / z0t )  t ( z / L)]1
q  k[q( z )  qs ][ln( z / z0 q )  q ( z / L)]
where k=0.4, u(z),T(z) and q(z) are the speed of the wind,
the temperature and the specific humidity at the height of
the z, the parameters z0 , z0t and z0 q are roughness
the structure parameter for temperature CT2 ,specific humidity Cq2 ,and the cross-structure parameter CTq , as
lengths of wind speed, temperature and specific humidity,
respectively. And the  functions are the integrated
dimensionless profile functions, can be expressed as follows:
follows:
Cn2  A2 CT2  2ABCTq  B 2 Cq2
(8)
for visible and near infrared frequencies,
A
nv
nv
,B 
T
q
4.7z / L, z / L  0

 t ( z / L)   q ( z / L )  
1  (1  9z / L)1/2
2l
n[
], z / L  0

2

(9)
and for infrared frequencies,
A
ni
ni
,B 
T
q
(14)
(10)
Once the T , q ( q( z )  qs ) and u are known, the value
of Cn2 can be calculated.
3. Parameters Near the Sea Surface
4. Simulations and Results
The structure parameter for temperature ( CT2 ), and spe-
There are four input file records (input cards) that contain
the wavelength and meteorological data for the
CN2model calculation.
The specific humidity is defined as [8]
cific humidity ( Cq2 ), and the cross-structure parameter
( CTq ) can be expressed in terms of the surface layer scaling parameters for temperature ( T ) and for humidity
( q ), as follows [5]:
C ( z)  z
2
T
2 / 3
CTq ( z )  z
q
T fT ( z / L)
2 / 3
2
rTqT q fTq ( z / L)
es mw / ma RH
m L 1 1
exp[ w * v (  )]
100
P
R T0 T
(15)
where es=6.1078 mbar is the saturation vapor pressure at
0℃; mw and ma are the molecular weights of water vapor
and of dry air, respectively; Lv  2.5008106  2.3103T
(T in degrees Celsius) is the latent heat of vaporization;
R is the universal gas constant; and RH is relative humidity in percent.
Several results of the model are presented graphically.
In Figure 1, the wavelength of laser is set to 1.55  m ,
the temperature of the sea surface is set to Ts  20 ℃,
the speed of the wind is set to u  10m / s , different
values of the relative humidity of the atmosphere are set
to RH=30 ,80, respectively, the value of log( Cn2 )at the
height of 10 meters above the sea surface versus air-sea
temperature difference is plotted. It is shown that when
the air-sea temperature difference (ASTD) is near to zero,
the value of log( Cn2 ) is sensitive to the humidity of the
atmosphere .When the temperature of the air is low to the
sea surface, the value of log( Cn2 ) is more sensitive to the
humidity of the atmosphere than that the temperature of
the sea surface is low to the air.
In Figure 2, the wavelength of laser is set to 1.55  m ,
(11)
Cq2 ( z )  z 2 / 3 q2 f q ( z / L)
where rTq is the temperature-specific humidity correlation
coefficient, L is the Monin-Obukhov length scale, z is the
height above the surface ,the functions fT ( z / L) ,
fTq ( z / L) and f q ( z / L) are dimensionless in terms of
z/L as follows [6]:
fTq ( z / L)  fT ( z / L)  f q ( z / L)
5.9(1  8z / L) 2/3 , z / L  0

2/3
5.9[1  2.4( z / L) ], z / L  0
(13)
1
(12)
and when T / q  0 ,the value of rTq is about 0.8,
when T / q  0 ,the value of rTq is about 0.5, where
T  Ta  Ts , q  qa  qs , Ta is the temperature of the
atmosphere, Ts is the temperature of the sea surface,
qa and qs are the specific humidity in terms of Ta and Ts .
According to the Monin-Obukhov similarity theory, the
scaling parameters for speed ( u ), temperature ( T ) and
377
978-1-935068-10-5 © 2010 SciRes.
Proceedings of Annual Conference of China Institute of Communications
marine atmosphere surface layer of different wavelength
is developed based on the similarity theory, and the
simulation of the optical with the wavelength of
1.55  m and 10.6  m has been done. It is found that
value of the optical turbulence varies with the air-sea
temperature difference, the humidity of the air, and the
sea surface wind speed. When the optical wavelength
changes, the effects of the optical turbulence are similar,
but for infrared frequencies, the value is larger than that
for visible and near infrared frequencies, and the wind
speed has a negative effect to the value of the turbulence.
the temperature of the sea surface is set to Ts  20 ℃,
the value of the relative humidity of the atmosphere is set
to RH=50, the speed of the wind is set to u =10m/s,
20m/s, respectively, and the value of log( Cn2 )at the
height of 10 meters above the sea surface versus air-sea
temperature difference is plotted. It is showed that the
turbulence is reduced when the sea surface wind speed
increases.
Figure 1. Effects of the relative humidity on the estimating of optical turbulence for 1.55  m
Figure 3. Effects of the optical turbulence for 1.55  m and 10.6  m
Acknowledgments
This work is supported by the National Natural Defense
Advanced Research Foundation of China.
References
[1]
[2]
Figure 2. Effects of the sea surface wind speed on the estimating of
[3]
optical turbulence for 1.55  m
In Figure 3, the temperature of the sea surface is set to
Ts  20 ℃, the value of the relative humidity of the atmosphere is set to RH=50, the speed of the wind is set to
u  15m / s , the laser wavelength is set to1.55  m ,
[4]
[5]
10.6  m , the value of log( Cn2 )at the height of 10 meters
above the sea surface versus air-sea temperature difference is plotted. It is showed that the value of optical turbulence is larger with the optical wavelength
 =10.6  m than the  =1.55  m . When the air-sea
temperature difference ( T ) is negative, the difference
of value with the two wavelengths is more apparent.
[6]
[7]
[8]
5. Conclusions
The model used to estimate the optical turbulence in the
978-1-935068-10-5 © 2010 SciRes.
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