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/

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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[3] Tian B, Cha H, Wang Y Q, et al. The influence of the evapora-tion duct on the detecting range of radars [J]. CONTROL & AUTOMATION, 2007, 1: 145-146.

[4] Shi J W，Cha H，Lin W, et al. A study of evaporation duct to carrier radar coverage range with APM [J]．CONTROL & AUTOMATION，2006，22: 147-148．

[5] Liu C G, Huang J Y, Jiang C Y, et al. Modeling evaporation duct over sea with pseudo-refractivity and similarity theory [J]. ACTA ELECTRONICA SINICA, 2007, 29(7): 970-972.

[6] Paulus R A. Practical application of an evaporation duct model [J]. Radio Science, 1985, 20(4): 887-896．

[7] Babin S M，Young G S，Carton J A．A new model of the oceanic evaporation duct[J]．Journal of Applied Meteorol-ogy，1997，36: 193-204．

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