Model ot rathowaves dispertion in atmosphere.
Yuri M. Galaev Institute of Radiophysics and Electronics, Academy of Sciences of Ukraine,
Kharkov 310085, Ukraine

l_ AE3STRACT

Physical aspects of dispersion (dependence of refraction factor value from frequency) emergence in case of radiowave propagation in atmosphere with nonlinear dependence of atmosphere refraction factor value from coordinates have been considered. Dispertion phenomenologic model proved by results of nature measurements in surface millimeter range
direct visibility radiuline has been put forward.

2.IN TRODUCTION

'Fh disperlion of itmnsphere (dependence of atmosphere rehaction .ta:tur 'i from frequency
is a fundamuttal cause limiting communication systems passband, location systems
Of)e[aIIUfl accu[acy, etc. ihe must urgent dispersion data is iclated to the millimeter radiowave
range. A number investigations are known to be devoted to the development of the model of
atmosphere dispertion in wide frequency hand. That was also reflected in a number of
overview papers related to centimeter and millimeter waves propagation

But recently during experimental investigation of millimeter range surface communication line band properties it has been discovered that in some cases the atmosphere shows properties
of a dispersion media, and the value and variability of the dispertion sufficiently exceed theoretic eslimations and cannot be explained by th.e known phenomena . The measurements have been carried out in 1 GHz frequency band near 37 GHz carrier frequency on 13 km long
surface direct visibiJ.ity path. Dispertion effects having no direct relation to atmospheric gases polarisation or hydrometeors and underlayer surface influence have been found. The revealed
dispertion may sufficiently limit the operation of wide band communication lines 2 and high resolution systems. The measurements have been carried out by the phase invariant method in wich the measured value of phase invariant t p is dispersion measure and is equal.

2

— p.

O-8194-1526-X/94/$6.OO

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where

are phases of received modulated sensing sigadi disctete spec Ii urn cinnponerit,

corresponding to the following frequencies: — to the carrier irequency.,

to

the lower side component and

+

to the upper side component (c. is modulation

frequency). Phases included into (1) are

where 1= 0,1,2 are indexes corresponding to the frequencies of signals making sensing signal

spectrum; is a distance between a transmitter and a receiver. : is a velucily of light in

vacuum. it follows from (I) and (2) that in absence of dispertion

0. The measurements

carried out under the conditions of clear weather (in abcsence of Ii ydrorn eteors) revealed the

presence of daily and seasonal variations of

quantities and consequently the dispersion

value. in Fig.l average seasonal diurnal variations are presented. The x axis is the time of

day in hours. The y axis is

value measured in degrees. Curves corresponding to winter

deg.
4
0 -4
-8

Fig.l Average seasonal diurnal phase
invariant variations

Fi.2 L' VdU&'; nira;uiunt iult.;

ri :de l iai; il1 u it

0 - —

ui old front rrintion

spring. autumn and summer seasons are marked by the number i234. A cnnsIdetahe growth

of , , values up to '20...'30° has been observed duiing tire rain fall out in warm season and

with the motion ot cold atrno'pheric fronts in c:uld season. In results in case of rainfalls in summer and cold front motion in

Fig.2 typical measurements
wintei are presented

Temporal position of rains are marked by rectangIes Extreme

values were measured in

winter with the motion of cold atmospheric front ( '64°) and in the beginning of sum mci

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under 5tabIe clear weather with the air ternptrature up to +30uC

24U) These results

appeared to be unexpected as they could not be described within the known dispertion models.
Thus1 estimation of irtolecular oxygen and steam absorption lines influense under the air temperature of 3OC have shown that in the frequency range used in h phase invariant in

experimental commumication line does not exceed ÷O.16u. Direct influence of the earth surface

on the measuiements accuracy have been determined experimentally in paper and

estimatedat

The aim of this paper is to ascertain physical ieasons fur earlier revealed disperlion effects III ciise of millimeter wave piopagatiori n surface direct visibility channel and to develop dispeTtinn model describing tht effects found in experimental communication line.

3. PHF.NOMENOLOGY
The phenomenological model of groundbased channel of radio wave propagation of mm wave range in line-of-sight range, which explains dispersion effects, measured in ', is presented hi the paper. The known data about the spatial structure of groundbased atmos phere and radiowave propagation lie in the model basis.
it has been shown in the papers and some others, that regular nonlinear dependence of IV value on Ihe altitude Ii over the ground surface is inherent to groundbased atmospheric layer.
This nonlinear structuze of JV(h.) vertical pio files, is caused by the distinctions of meteorological elem ents distribution and is subjected to regular 24-hourly and seasonal
variations 24-hourly variations of JV(k.iprofiles in the layer with altitude up to A' lOOm, averaged over the seasons (for summer and winter) and typical for Russia, are plotted in Pig.3. The profiles were constructed by the experimental data from paper

Fig,3 4 hourh varialiorts f N(h) profiles, average over the season of the year

— — -— — 6 am.,----—------------ p.m., .

p-

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j/frr unit is connected with N value by relation iV. ( iV 1

' I I

oTder to stress ftc

profiles' characteristic feature, which is isscritial to our analVsis. the profiles were constructed

from the point h -• 25 m. in this case only time variations of index refractivity gradients values

K &Y / M' in the corresponding atmospheric layers were taken into account. Therefore the

horizontal axis has no graduation as to value of JV Jt ic essential that, the curves which

represent the "summer type of the piofile /V(ñ..) are concave and the curves which represent
' the "winter' ones are convex, i.e. these profiles have different signs of the second derivatives
d 2 ,, ,• dh It also follows from Fig.3 that for groundbased channels of radio wave

propagation of mm wave range in the line-of-sight range it is characteristic the situation, when

the scale of regular nun-linear variations of media properties. which is transverse to the wave

propagation direction is comparable with the Fresnel zones dimensions. For example, in 8 -

mm wave range the diameter of Fresnel zones d

is equal by the order to 10 in eters,

here A denotes radiation wave tength.

Let's consider the mechanism of dispersion advent over radio wave propagation in the atmosphere with nonlinear /Y('h./ profile. The qualitative behaviour of the propagation media in dependence on 1V"h) profiles type and signal trquency is plotted in Fig. 4. Fig. 4a corresponds to the "summer type of the profile and Fig. 4b corresponds to winter" one.

Ii

Summer

die

N
a)
N1

121($) I

4' tt
1 02

Fig.4 Atmospheric index refractivity variations in dependence on flu nlinear pruhk N ( h) type
arid signal frequency.

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L&t the axis of the space domain. wbich is essential under radio wave propagation passes

' through the point 4 . The diam eters of the sum e nato e Fresnel zones are denoted by indexes

iD, d1. t2

zones according to presented in

values, coirespood to signals with frequencies

measurement method of phase invariant
, 02 The average values of variation

ranges of A' values within these 6flOS for "summer" and "winter" profiles aie denoted by 'V0.

1) 2o ibVy1$.thjVe2$vekritnidcIaVl.a.U.rar)owIVs

iv
marked

, cnrre!pondingly. by digits 0, 1. 2, it

F or vizuali?ation, in the bottom of each figure is shown the location of these average values

along the IV axis. Inasm uch the dimensions of th same name F resnel zones are not coincide

with each other on different frequencies, the ranges of IV values variatioit within such zones

are not equal to each tither and owing to nonlinearity of jV(',J profiles these ranges and their average values are shifted as to each other. Therefore, in this case signals with different

frequencies propagate in the medias with different IV values, i.e. the dispersion, caused by

non-linear structure of JV('h.) profiles occurs, or one can say about the dispersion, caused by

the spatial truc1ure of atmospheric ground-based layer. One can see from the Fig. 4 that with increase of the profiles nonlinearity rate (i.e. their second derivatives d 2 jv dh 2 the

:dispersion va1u will increase and in the case of linear JY(h) dependence (i.e. d2 11// dh 2 ) such dispeisiun doesn't occur. This circumstance is connected with the fact, that the ranges

of IV values variation within the same name Fresnel zones are not shifted as to each other and

their average values coincide by the value and are deterruined f. rom well known class.ic represerttat,ion

equal 11 at

to iV(.& 1 — the alt.itu0de k

.

index
It is

refractivity, obvious that

similar effects will be observed in the case of non-linear distilbution of IV values in horizontal

direction (for example, in cloud cover).

Thus, if the paiameters of propagation media vaiy in dependence on coordinates in the directions, transversed to the direction of wave propagation, such media is a dispersive one.

Fo distinguish the above mentioned dispersion advent mechanism from other known causes, which induce it's appearance, we shall use for this mechanism the term "spatial dispersion".
Presented phenomenology enables to determine some properties of spatial dispersion and to
show it's place in the geneiai pioblem of wave propagation, and also to explain the
eKperilnental results, considered in 2 In the futher development we shall take into account the
spatial variations of Al value only in veitical direction, inasm uch fur ground--based atmos-
pheric layer. where the radio links ci line-of-sight range are located, dependence of IV value on the altitude is most essential

4. SPATIAL DISPERSION PROPERTIES.

Consider some spatial dispersion properties, which may essntially effect on the radio wave propagation in the ground based atmospheric Iaye.
It follows from phenornenology that the spatial dispersion occurs only in the case of non" linear dependence ci pupagation media Index refractivity value on coordinates, lransversed to

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the direction of propagation. In application o wave propagation in the groundbased atmospheric layer this spatial dispersion piopefty exhibits under non linear disitibution of iV values along altitude h.

An important spatial dispeision property is the dependnnce of it's bthavioui on Ib€ type tif

vertical profilts A/ç'h) nonlinearity. In the case of "summer" profile (Fig. Ia). the relation

between average index refractivity values on frequencies .

one can desciibe by the

inequality:

Iv1 S '° 1

- '2. 2

which represents anomalous character of the dispeisiun ( N decicases with the increase uf

i.e.

'o ' '2 In the case of winter profile JV(h) (Fig. 4b) corresponding inequality has

a form

, Jv1,t: )- "';( WI: )' i';,(cu?

and represents normal character of the dispersion (N increases with the increase of ). Thus, over wave propagation iii the atmospheiic ground based layer the spatial dispersion may b
' either normal of anomalous, according to type of non-linear dependence or atmospheric index
refractivity on the altitude h over ground suiface. It is well known I see, for example / . that non-linear dependence of ii value on coordinates is peculiar to earth atmosphere and this

cicumstance especially exhibits in the ground and sea-based layers, in cloud cover. in atrsios-

pheric frontal partitions and in some other cases. One can contend that the spatial dispersion

effects are inherent to the phenomena of radio wave propagation in the atmosphere. Thus, over

the radio wave propagatiøn description the effective frequency dependent index refractivity

Irveeflrf(aact')ivmityu,sdtebteermusineedd.

This
from

index refiactivity
well knowit classic

IV () iine can represent as a
orfefpresentation N1(1) (see, for

sum of index example ),

and the additional term, which appears owing to dispersion "spatial mechanisrri' /'(x)

iV.jiJj w

-- A't./'

)

-

iv i:I

),

(.L•)

it follows frn1L Fig. 4a that, in the case of anomalous patiai dispersion, the additional teims

A'() to A'() value, which one can treat here as N(JQ.) value, e positive, i.e. the

anomalous spatial dispersion leads the case of normal spatial dispersion

to the increase of u/0() value in respect (Fig. 4b) the additional terms N(0) are

ntoega./t/i(vce4a. rIind

lead to decrease of JV1() value in respect to !Y() It follows from Fig. 4, that with the

increase of , other things being equal, a contribution of N() into

value will

decrease, owing to decrease of Presnel zone dimension. This property of spatial dispersion one

can represent as follows

urn! .7 (, j _-O

()

p

The qualitative variations of

values in dependence on signal frequency and spatial

dispersion character are plotted in Fig.5. The dependence of iV1(o) is depicted by solid line.

By the same line we shall depict the dependence of A'1() in the case of linear profile A'7i5)

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because for this profile i1() 0 . 13y the dash line we shall depict M11() dependence,
when the effects of anomalous spatial dispersion occur over radio wave propagation. The
dependence JV011(1) in the case of norrnalspaLialdisperion is fiown by dash-dott line.

From the considered phenomenniogy it follows such evident property of the spatial

dispersion, as IV value dependence on the range ' of radio wave propagation in the atmos-

ph.re. Inasm uch,over the decrease of value the Presnel's zone dimension also decreases,

the contribution of IV value will decrease (Pig. 4). Note that N1 value in the expression (5)

doesn't depend on the range ; an d is

determined by the composition and the

state of the atmosphere in measuring

opnoifnrteqaunednicnyge4nieiral case also depends

N

Thus, the spatial dispersion

phenomena is inherent to radio wave

—

propagation in the atmosphere and in

•

particular to propagation in ground-

and seabasad layers. This dispersion

may be either normal or anomalous.

cr

The contribution of the spatial
dispersion to general atmospheric

Fi5 IV depndetice in tite case of

— — — - ano;ni1uu and —

noirnal spatial

diperiort.

'c1 () dependence

dispersion decreases with the signal frequency increase and decrease of
radio wave propagation channel
extent.

5. MEASUREMENTS RESULTS AND DISPERSION MODEL
The esperimental investigations, which were carried out on a ground--based line-of--sight range path in 8-mm wave range, confirmed the phenomenniogy of spatial dispersion, presented in this paper. The results of mesurements are presented in . It is shown that the brought out effects essentially impact en the band width of the radio link. The main results of above mentioned measurements from paper 2 are plotted in Pig. I and Fig. 2 for convenience of the
explanation of these experiments. Let's show the connection between the changeability of measured values of phase invariant
(expression (1)) and the spatial dispersion properties. Let is an increment of index refractivity with signal frequency increase from to (Pi84), then index refractivity increment decrftases with the signal frequency decrease from to , owing to nonlinearity
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of N(h) profiles one may write as A , where A ' 1. Let's e.Kprss N inI ;Y vaurc by the

increments and 1t 3 relatively to . F roni relations ( 1) n.id (2.) on can obtain that in the

case of anomalous dispersion (F ig. 4a)

values, with accuracy up to coefficients. are

equal:

J : 3 ( I 1- ) ,

(7 )

and take negative values (1 1) In the case at normal dispersion (F 1g. 4h) one can obtain

A=5(i--1'

(8)

In this case n are positive (I I) . Besides, it follows from lig. 4 and relations (7) and (8),
' that with increase of the profiles nonlineazity rate, the spatial dispersion value will increase. i.e.
6 and f values, and therefore 1 I will also increase.

Thus, positive values of phase invariant correspond to the normal dispersion and negative to anomalous one. Greater phase invariant absolute value corresponds to greater dispersion.

The characteristic feature of experimental data, presented in Fig. 1. is the presence of

extremums, located within the interval between 3 and 4 o'clock p.m. 24 hourly variations of

phase invariant p values, averaged for winter season, occupy the region of positive values and for summer season, conesponding values occupy the region of negatives. In spring and

autumn A p measured values are close to zero. Let's compare these data with 24-hourly

variability of iV('A) profiles (Fig. 3), which are also averaged over the seasons of the year.

According to phenomenoingy of spatial dispersion advent it is shown that atmospheric ground-
-based layer with profile A'(2) (Fig. 3, Fig. 4a), which is characteristic for summer clear

weather is a media with anomalous spatialdispersion and

measured values aic negative

(see, Fig. I, curve 4). In the case of JY(h) profile (Fig. 3, Fig. 4b), which is characteristic for

winter clear weather, the ground--based layer is a media with normal dispersion (see Fig. 1,

curve 1). In spring and autumn the ground- -based N(h) profiles are close to linear ones
' tAs it was shown in the case of linear N"h) dependence the spatial dispersion is absent and =- 0 . This fact is confirmed by the measurement results (F 1g. 1, curves 2,3). when

measured values

are close to zero. 24-hourly variations values

are connected

with 24hourly variations of the profiles )V'h,./ by the next manner. In summer afternoon

profile JV('/i.) (Fig. 3, solid line) has more expressed nun-linear structure than in the morning

or in the evening. By that spatial dispersion and consequently I

I have greater values

, (Fig. I, curve 4). In winter one can observe the inverse situation. In the afternoon non--linear
properties of profile JV'&,.) (Fig. solid curve) are more pronounced than in the morning or in

the evening. Smaller spatial dispersion and smaller values of phase invariant correspond to this

time. This fact occurs in the measurement results presented in Fig. I (curve 1).

Thus,pxopused spatial dispersion advent mechanism permits to explain on a qualitative

level a 24-hourly and seasonal variability of measurement results, obtained under clear

weather. The peculiarity of measurement results which carried out over the rainfalls in

summer (Fig. 2. solid curve) is a time delay (near 50 minutes) of the moment of measured

I

I value change from negative to positive relative to the beginning a rain and further

increase of this value to ÷20 0

0 In the framework of proposed spatial dispersion advent

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mechanism it can be epIained as follows. It is well known (hat 4,10,12 . atmospheric ground-

based layer afttr i'ailkfall th* summer type of profile JV(h) (Fig. 4a) Iransforms to winter one

(Fig. 4b). This tact occurs uwing to compensation of humidity deticit in the atmospheric upper

layers by the intensive evaportation from humid and heated surface. According to spatial

dispersion phenomnology this tact leads to changing at spatial dispersion character:

' anomalous dispersion changed into normal and correspondingly negative values of measured

value I d 'p 1 change to positive ones. By that, value I

I is determined by nonlinearity

rate of new profile

. The vertical velocity of water vapours turbulence diffusion (near I

In Cf minute 12 and radio waves propagation channel altitude over ground surface (near 50 m 2 can easily explain the reason and value (near 50 minutes) of time delay changing

moment of value from negative to positive relatively to rain beginning.

Thus, expeiimentally obtained change iii the character and value of dispeision at rainfall in atmospheric ground-based layer may be explained in the framework of proposed spatial dispersion advent mechanism. The proposed michaiiism allows tn show both of qualitatively and quantitatively dynamics of physical processes in the atmospheric ground-based layer.

Under the conditions of cold atmospheric fronts motion sufficiently non-linear winter type profiles JV('4J (Fig. 4b) up to inversion ones have been established 48,t0 According to

phertomenology of dispersion advent atmosphere with the profile of such type is a media with

normal spatial dispersion. Positive values of measured value correspond to that dispersion.

The greater profiles i'V(4} nonlinearity rate in a frontal partition causes a greater value of

spatial dispersion and correspondingly greater values of phase invariant relative to the standart

atmosphere. Such variaibiiity of values

which follows from. phenomenology of spatial

dispersion and processes in ground-based atmosphere under cold atmospheric fronts motion is
prove to be true by Ike measurement results 2 In Fig. 2 dolt line represent the typical

measurement recuIti nf t value under cold atmospheric fronts motion in winter. Usual for

winter clear weather i values from interval -'4 p0 increased up to 320 under cold

atmosphere front motionS In the powerful cold fronts this increase reached --64 , according

Thus, the results of experimental investigations carried out in winter with cold atmospheric fronts motion are explained in Iht fracnewoik of propos&d spatial dispersion advent mechanism of radio wave propagation in grnundhased itrnuspheric Iaynr.

From considered phenomenology the spatial dispersion phenomena and its properties

confirmed b peiimenta! investigations one must use effective index refiectivity while

discribiitg radio waves propagation. This index refractivity - has a form (5). The second term in

this relation is undefined. It
conditions of experimental work

turns out
2 may be

that dependence iV ( )
aproximated by the function

in the framework of

r4ff C w = () 14

)

-

(9)

According to representation (5) the second term describes the value iV( ) variability via

measured L values and frequency - This variability according to (6) is described as to

maximal frequency

in the sounding signal spectrum. used in ( co 37.5 GIJz ). This fact

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constrains frequency interval of expression (9) I* n the framework at known modtIs of atmospheric.

adpisp'pleicrsai.boinlitIyi

The and

dveafl.runeesAriA' (l

) is calculated
in dependence

on of atmosphere gases composition and state with due regards Lu impact of dielectric

permeability rotation part of water steam and magnetic molecular oxygen permeability. The

rotation part depends on . Expression (9) qulitatively and quantitatively describes dispersion effects wich were discovered in . iY11(co) calculated values satisfy to measurement results

A phenomenology which explains the reasons of spatial dispersion advent and relation (9)

which describes frequency dependence of index refrectivity of experimental lineo1sighl range radio link iii millimeter wave range we shall consider as phenomertulogical model of radio

waves dispersion in atmospheric ground-based layer.

In response of investigations carried out were shown the reasons of advent of radio waves dispersion effects in milimeter wave range over propagation in the 1ineuf-sight range ground based channei All these effects were discovered experimentally. It was shown that if in directions transversed to radio wave propagation direction the media parameters depend on coordinates in non-linear form, then such media is dispersive. The variability of nonlinear spatial structure of atmosphere leads to variability of observed spatial dispersion effects. In the framework of this phenomenology next facts are explained: seasonal and 24-hourly variations of dispersion; effect of atmospheric fronts and rainfalls; the reasons of spatial normal and
anomalous dispersion advent ; the dependence of spatial dispersion advent on signal frequency and radio waves propagation range. II was proposed phenomenological model of dispersion of experimental radio link This model was confirmed by measurement results.

All these investigations can be a base for radio wave propagation theory development and
methods of attenuation adverse influence of atmosphere effects on the wide range
comm unication systems performance, system state determination. etc.

The results of these investigations can be useful in acoustics. hydroacoustics. optics, where dispersion problems of propagation media are actuaL

6. REFERENCES.
1. R.K.Crane. 'Fundamental limitations caused by propagation", f?oc: JEA VoL 69, pp.
196--209, 1981
2. F.V.Kivva and Y.M.Galaev. 'Dispersion effects in frequency windows of milimeter range
radio waves', in: A/rnzvh#ik F ta/ion Tt'cbimiJ Imge' !:ea1,. Orlando, Florida,
USA, p.p.509-517, April 1993.
3. V.A.Zverev. "Modulation method of ultiaourtd dispersion measurement", PLt' A/V SR, Vol. 91, No. 4. pp. 791 794. 1953 (in Russian) 4. 1ean B.R. and Dulton E.J. 'Radio meteorology'S. Dover Publications, Inc. New York,

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1968.

5. Rukina AN. "Investigations of air index refractivity in th* lower, up to 300 m altitude, atmospheric layer in Ka1yzkaj region", Moscow. 1972, 18 p.(Preprint IRE AN USSR No 8Xiu Russian)

6. Vyaltseva E.E. "Atmospheric index refractivity variability for UHF radio waves in the
boundary layer". 4&'ioi z'd i''k'; No 2. p. 8I4, 1972 (in Russian)

7. Vyaltseva E.E. "Atmospheric index refractivity variability within the layer up to 300 in altitude for UHF radio waves in winter". if/k/p JEA 6(44). p. 99-- 105. 1974 (in Russian)

8. Vyaltseva E.E. "Air index refractivity horizontal inhomogenity for UHF in atmospheric fronts". Trudjr lEA'!, 10(53), p. 8085, 1975 (in Russian)

9.1. ipatov G .N., .Aksakuva OYa. "Some fealures of 24-hourly development and index

refractivity vertical profile in lower, up to 500 m atmospheric layer". JYwd.'

9, p.7l-

78, 1977 (in Russian)

10. Matveev L.T. "General Meteorology. Physics of the Atmosphere", Gidrometeoizdat, 640 p., 1976 (in Russian)

I II. Zhevakin S.A., Naumov A?. "The lower atmosphere refraction factor on millimeter and

submillimiter radio waves". 1diihmk

Y'cfron: Vol. 12, No 6, pp955- -964., 1967 (in

Russian)

12. Berlyand M.E., Solomatin LI. "24hourly humidity and air temperature oscillations in ground--based atmospheric layer". Leningrad, Gidrometeoizdat, Trudy 000, 123, p. 62--69., 1961 (in Russian)

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