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Evaporation Duct Model A Analysis
Tian Bin1, Cha Hao1, Li Jie2,3, Zhou Mo1 1. Institute of Ocean
Electromagnetic Environment, Naval University of Engineering,
Wuhan, China
2. Unit 61741 of PLA, Beijing, China 3. Institute of
Meteorology, PLA Univ. of Sci. & Tech., Nanjing, China
Abstract: Owing to sea evaporation and air-sea mutual effect,
many kinds of atmospheric refractivity profiles may oc-cur. The
evaporation duct is one kind of profiles, which is nearly always
present above oceans, it is a layer of air just above the sea
surface which can trap wireless energy. The duct is created by the
rapid decrease of humidity with height just above the sea surface.
Because of it, the path of wireless wave is changed remarkably, the
wireless detection range will be increased. This paper uses actual
atmospheric data measured in recent years to study the
characteristic of evapo-ration duct Model A in condition of low
wind speeds, which was mainly proposed by Babin coming from JHU/APL
(The Johns Hopkins University Applied Physics Laboratory). The
conclusions offer some help for understanding Model A in depth.
Keywords: radar engineering; evaporation duct; atmospheric
refractivity; Model A
1 INTRODUCTION
Evaporation duct is a kind of typical anomalous pro-files of
atmospheric refractivity, it is formed just above the ocean surface
by strong vertical humidity gradients[1]. Turbulent transport
results in water vapor pressure de-creasing with height in about a
logarithmic function. Eva-poration duct can guide radio waves to
distances far be-yond the horizon with less attenuation, and for
radar sys-tems, the extensions of detection range will occur[2,3].
Many researchers use propagation models, such as PE[4], to predict
radar detection performance, and vertical pro-files of atmospheric
refractivity are used as input data to these propagation models.
Since the atmospheric refrac-tivity profiles are very hard to be
measured above the ocean surface, a variety of evaporation duct
models[5,6] were developed to obtain the evaporation duct height
and atmospheric refractivity profiles.
A new evaporation duct model called Model A (also called BYC
model) was mainly proposed by Babin from JHU/APL (The Johns Hopkins
University Applied Phys-ics Laboratory). The most prominent
characteristic of Model A is that it uses the work of Godfrey and
Beljaars to extend the validity of MOS (Monin-Obukhov Similar-ity)
theory to low wind speeds. In this paper, the charac-teristic of
Model A is studied by using actual data meas-ured in recent
experiments.
2 THE BASIC THEORY OF MODEL A[7]
Model A uses 6m air temperature, relative humidity, wind speed,
pressure and the sea surface temperature as
inputs. Water vapor pressure e is related to specific hu-midity
q by:
q
qpe)1(
(1)
Where ε is the ratio of the gas constant for dry air to that of
water vapor (0.62197), and refractivity N is given by:
)))1((
48101(6.77qT
qT
pN
(2)
Then we have
zqC
zBA
zN
(3)
Where
2
2 3
/
2 3
22
77.6 4810 77.60.011
1 77.6 2 4810 77.61
77.6 2 4810 77.61000 1
4810 77.61
a pa
a
pa
R c
qA gT T q
g p e qc T T q
p pBT T q
pCT q
qp
In the formulas, ρa is air density (kg/m3), cpa is the dry air
specific heat (1004.07J/(kg·K)), Ra is the dry air gas constant
(287.05J/(kg·K)).
The values of z and q z are calculated using MOS, and other
quantities, such as L (Mo-
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nin--Obukhov) length, θ* and q* (Monin-Obukhov scal-ing
parameters), φθ and φq (nondimensional Mo-nin-Obukhov profile for
temperature and moisture) are all calculated through the algorithm
which can be obtained at
http://www.coaps.fsu.edu:80/coare/flux_algor/. Finally, for the
evaporation duct height δ, 157.0/ zN , and we then have:
0.157 A B qCk k
(4)
For stable and neutral conditions, the analytical value is
given:
* *
* *
( )5( 0.157) (
B Cq
k A B CqL
)
(5)
For unstable conditions, the functional form of φθ is such that
the following must be solved iteratively, since φθ is a function of
δ/L, and the iteration continues until the new value of δ is within
0.0001m of the old value.
* *( )( 0.157)B Cq
k A
(6)
3 THE CHARACTE RISTIC SIM ULATION OF MODEL A IN LOW WIND
SPEEDS
The model’s characteristic in low wind speeds is analyzed
through simulation, the following measurements are assumed: sea
surface temperature 15 oC, 25 oC , the
Figure.1 Model A results
Fig.2 Model A results
corresponding 6m atmospheric pressure 1020hPa, 1010hPa, 6m wind
speed 0.5m/s, 1.5m/s, 6m relative hu-midity (RH) 60% , 90%, the
results are given:
From Fig.1 and Fig.2, it can be seen that various meteorological
factors have different effects on Model A results. Firstly, for
ASTD<0, some reasonable values could be obtained through the model,
but for ASTD≥0, many unreasonable values would be evaluated. The
rea-son is that the model uses different equations for different
ASTD conditions. Secondly, larger relative humidity would make the
model get lower duct height results. Thirdly, model results are
sensitive to wind speed, the larger wind speed is, the greater
result is. Lastly, in the same RH, ASTD, and wind speed, higher air
temperature and sea surface temperature can make model results
greater.
4 THE CHARACTERISTIC ANALYSIS OF MODEL A IN LOW WIND SPEEDS
Experiments were carried out to acquire actual evaporation duct
height data, and the model’s characteris-tic in the low wind speed
condition could be studied. Model A input data are offered by a
maritime automatic meteorological instrument (Fig.3), according to
the model rule, its sensors are fixed at 6m above the ocean.
The actual evaporation duct data, which are used as reference
results, are obtained by the kytoon (Fig.4). It has the sensors
which can measure air temperature, rela-tive humidity, air
pressure, wind speed, etc, and the data are used to evaluate actual
evaporation duct heights.
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http://www.coaps.fsu.edu/coare/flux_algor/
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Figure.3 maritime automatic meteorological instrument
Figure.4 The kytoon
But the inaccuracies of the kytoon’s sensors could
affect calculated altitude results and modified refractivity
values deeply, Fig.5 shows the influence. The dashed line
represents a profile of modified refractivity without noise, and
the solid line represents a profile of modified refrac-tivity with
noise. The inaccuracies of sensors can result in air temperature,
relative humidity, and air pressure errors, finally a distorted
profile of modified refractivity would be obtained, so the kind of
noise must be removed.
Figure.5 signal without noise and signal with noise
In data process, db wavelet is used to denoise the-signal with
noise, which results from the inaccuracies of the kytoon’s sensors,
and then a least-squares curve fit is applied to the denoised data.
This curve is based on a log-linear function given by:
0 1 ln 0.001 2M f z f z f (7) The coefficients f0 , f1 and f2
are calculated for a
least-squares best fit. The height of the function is used as
the actual evaporation duct height. In this paper, actual duct
height data, which are corresponding to maritime automatic
meteorological instrument’s wind speeds (<2m/s), are chosen. The
plot of comparison between Model A and pseudo-refractivity model is
given:
Figure.6 comparison between two evaporation duct models
Pseudo-refractivity model, which is widely used in-
land, was proposed by Liu Cheng-guo, and this model is based on
Monin-Obukhov Similarity theory, so it could not perform better in
low wind speeds. The conclusion is shown in Fig.6. Owing to the
work of Godfrey and Beljaars, the difference is smaller using Model
A in low wind speeds. In Fig.6, some cases show that there are also
great differ-ences for Model A, the reason may be that large
changes in sea surface temperature occurred in small experimental
areas, an average sea surface temperature is used as a sub-stitute
temperature as input in Model A, and in the charac-teristic
simulation of Model A at low wind speeds, it can be seen that ASTD
has an influence on Model A results, so an average sea surface
temperature may have an effect on Model A height results and
differences.
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5 CONCLUSION
Pseudo-refractivity model is based on MOS theory, and adheres to
this theory faithfully, so it is not feasible in very low wind
speed conditions. Model A uses the work of Godfrey and Beljaars,
which offers a method of ex-tending MOS theory to very low wind
speeds, therefore Model A performs better than pseudo-refractivity
model in low wind speed conditions. Though it can be seen that
there are still large diff erences for Model A in Fig.6, the reason
may not be the model itself, but large changes in meteorological
factors (sea surface temperature, etc) oc-curred. In a word, it had
better to use Model A at very low wind speeds.
ACKNOWLEDGMENTS
The authors would like to express gratitude to Ding Ju-li of
Institute of Meteorology, PLA Univ. of Sci. &
Tech., and also thank Liu Cheng-guo of Wuhan Univer-sity of
Technology.
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