NPIL Report 6766

Attenuation of Microwave Radiationfor Paths Through the Atmosphere

00 R. A. LEFANDE

Satellite Communication BranchRadio Division

November 29, 1968

NAVAL EFARCH LABOlWMThAYWa~hingtn, tD.C.

n&This kowMMt h= b Awi"vWd ,, ,blwk rekam "'d ask. its dlation i* Utt*d.

'CL E/, tc IN•;G .- U 3•E

33,, ,,,

CONTENTEF

Abstract liProblem Status iiAuthorization ii

INTRODUCTION 1

ABSORPTION BY MOLECULAR OXYGEN 2

ABSORPTION BY WATER VAPOR 5

A3SORPTION LINE SHAPE FUNCTION 6

DETERMINATION OF CONSTANTS BASED ONPUBLISHED EXPERIMENTAL DATA 7

Oxygen 7Water Vapor 10

TOTAL ABSORPTION FOR PATHS THROUGHTHE ATMOSPHERE 11

ATTENUATION BY RAINFALL 16

CONCLUSION 22

SYMBOLS 24

ACKNOWLEDGMENTS 27

REFERENCES 27

14

ABSTRACT

Microwave radiation is absorbed by atmospheric oxygen and watervapor and is absorbed and scattered by rainfall. This report providesvalues of these losses in the freqoeticy decade from 10 to 100 GHz forpaths through the atmosphere at elevation angles from 0 to 90 degrees.

The theoretical expressions for oxygen absorption are assembledin explicit form. The resonant frequencies are taken from publishedlow-pressure measuremernts, and the entire absorption profile is fittedto published intermediate and atmospheric pressure results, with aconstant of proportionality and the absorption resonance line width usedas fitting parameters. The absorption line breadth is found to deviatefrom the accept.ed linegr pressure dependerce, increasing approximatelyas the square root of pressure for pressures above one-half atmospheric.

The results of similaz analyaies of wv'ter vapor absorption are as-sembled and combined with the results of oxygen absorption analysesto obtain the complite absorption ccefficients as a function of the at-mospheric parameters.

The total attenuation aue to absorption in the clear atmosphere iscomputed for a model atmosphere with various water vapor concentra-tions. Results are provided in graphical form, giving attenuation as afunction of frequency and elevation angle.

The prediction of rainfall attenuation is severely limited by theabsence of meaningful statistics on rain rate and storm structure.Rough estimates for rain attenuation are made for crude model stormswhich occur for 1, 0.1, and 0.01 percent of the time. Total values of theattenuation for the' model storms and the atmospheric absorntion areprovided.

PROBLEM STATUS

This i&. an interim report on one phase o! the pi oblems; work onother phases ib continuing.

AUTHORIZATION

NRL Problems R01-34 and R01-36Projects RF 14-222-41-4353 and XF 019-0204-11648

Manuscript submitted July 1. 1968.

1,

ATTENUATION OF MICROWAVE RADIATION FORPATHS THROUGH THE ATMOSPHERE

INTRODUCTION

The attenuation of microwave radiation in the frequency dtcade 10 to 100 GHz forpropagation paths through the atmosphere at all elevation angles is of great interest inthe analysis of experiments in radio astronomy and communications by satellite. Thepurpose of this report is to assemble the explicit theoretical expressions and measuredconstants used to compute the attenuation and to o:ovide the results oi such a calculationfor a typical model atmosphere. The computatnr, of attenuation for paths through theatmosphere requires a knowledge of the magnitude of the absorption by the atmosphericconstituents, the frequency dependence, and the spatial variation of the effect along thepath. The attenuation, in general, consists of two contributions that require quite differenttreatments. The first contribution is the absorption by the molecular oxygen and watervapor that controls the attenuation in the clear atmosphere and can be computed accu-rately. The second contribution is attenuation due to rainfall; this can be treated onlyqualitatively, but it is quite important to the communicator who is not always able tochoose ideal conditions.

Molecular oxygen and water vapor absorption resonances or lines completely domi-nate the absorption spectrum in the band from 10 to 100 GHz. A review of the existingtheoretical treatments and experimental measurements is made here to obtain expres-sions giving the coefficient of absorption as a function of frequency, temperature, andpressure. The total attenuation for paths of varying elevation angles is obtained for amodel atmosphere by integrating the semiempirical expressions along the path.

First, the theoretical analyses are used to obtain the general expression describingthe interaction of the incident radiation with the oxygen molecule. Then the variousterms in the expression are identified and reduced to the form to be used in the pathcomputations. In its final form, the expression determines the functional dependence ofthe absorption spectrum except for a function describing the shape of the resonances inthe frequency domain and a constant.

The expression obtained for oxygen is adapted to the essentially similar water vaporinteraction, and a semiempirical approximation of the contribution of resonances thatoccur beyond IOU GHz is introduced. The problem of obtaining a function to describe theshape of the resonance line is discussed, introducing additional pressure and temperaturedependence and another fitting parameter, the line breadth.

The constants which remain in the theoretical functions are obtained by fitting pub-lished experimental data. Evidence for a pressure dependence for the oxygen linebreadth different from the theoretical result is aiso derived )m the data. The totalattenuation due to absorption by oxygen and water vapor ir ,outed as a function of fre-

quency and elevation angle for the model atmosphere.

"The attenuation due to rainfall is considered in an approximate manner in the lastpart of this report. The theoretical values of the attenuation as a function of frequencyand rain rate are taken from published results. The severe limitations of the existingstatistical data on the spatial and temporal distributions of rain rate are discussed, andsome crude model storms are constru,'ted. Finally, the attenuations produced by the

i1

2 R. A. LEFANDE

rain for propagation paths through the model storms are computed and combined with tneattenuation due to oxygen and water vapor to obtain representative values of the totallosses.

ABSORPTION BY MOLECULAR OXYGEN

The absorption of microwave energy by oxygen results from magnetic dipole inter-actions with the incident radiation due to the oxygen molecule's permanent magneticdipole moment, which produces transitions between molecular fine structure levels vithe allowed rotational states. A detailed dliscussion of the theory of microwave spec-troscopy is beyond the scope of this report, and the various treatises (1-5) on which thiswork is based should 1e referred to for an exact exposition.

The actual amount of the incident radiation absorbed by a given transition in a gas of4 the molecules depends on the relative fraction (f, ) of the molecules which are in thelower energy state of the transition and on the square of the matrix element of the dipolemoment connecting the two states. The aiagnitude of the matrix element is a measure ofthe effectiveness of the radiation in producing the transition.

The complete expression as obtained by Van Vieck (4) for the absorption coefficientv of a gas of molecules having a series of transitions has the form

"y = (constant) vN _ [Iý,.2, s S , ) I !fi,, fsIt 44,

This expression consists of pairs of terms representing emission and absorption transi-tions between two states. The algebraic sum of the two terms is the net absorption andis dependent on the relative population of states of higher and lower energy. The sub-scripts t and j are labels representing states defined by a set of quantum numbers. Thefrequency of the incident radiation is P, and v,, is the resonant frequency of the absorp-tion line. The resonant frequency is the frequency of the quanta of radiation energyequal to the difference between the energies of the initial and final states of the transition.N is the number of molecules per unit volume, S (i ',. 0) is a function describing the ab-sorption line profile (i.e., the absorption versus frequency curve), ;,f, is the matrix ele-ment connecting states i and j. The constant is a combination of physical and mathe-matical constants and is given by the exact theoretical treatments. As the predictedvalue does not fit the data perfectly, the constant will be used as a fitting parameter, andany physical constants subsequently introduced in this discussion will be absorbed intothis term.

The energy level structure of the oxygen molecule with intervals in the microwaveregion is produced by interaction of the uncompensated electronic spin (total spin formolecule = 1) and the "end over end" rotational angular momentum of the molecule. Therotational levels (quantum number K) are split into levels corresponding to the allow-able ways of constructing the total angular momentum vector. This level structure ismodified further by the rotation of the molecule, the interaction between the processingcomponent of the electron orbital angular momentum, and the total spin and centrifugaldeformation of the molecule.

Symmetr y considerations allow the rotational quantum number A to take on odd in-tegral values 1. 3, ... , only. Corresponding to each K, two possible transitions,J = K- I - J = K and J - K - J =" K (J = total angular momentum quantum number), areallowed by the selection rules &I ! I , ALK-= 0. The frequency of the quanta absorbed oremitted can then be calculated from the difference in the energy levels. The fine struc-ture of oxygen results in an infinite series of lines grouped about 60 GHz, of which

NRL REPORT 0766 3

approximately 25 c.ir be detected in actual measurements. The energy levels have beencomputed by Schlapp (3) in fair detail, and Burkhaiter et al. ,6) have obtai;ned the fre-auencies of 25 lines, which could be fitted Wo the Schlapp theory with the additionl of em-pirical terms. The frequencies of additional lines too weak to measure can be obtainedfrom such semiempiricai f!i s.

The matrix elrements are derived through quantum vector addition and obtain theform

2 1 2 A'02K, 3)

"(,2 '+ I)''-I)

2 2, (A - )12k- 1)"PK '2K I'K

2 8•" . 2 K

2 A I)(2A - )"_Ae K, KA -- ')2At I)

where -0 is the Bohr magneion. It should be noted that oxygen has lines at z, 0 foreach rotational level, which result in a nonresonant contribution to - total. The subscriptsA'_ and K'. denote the transitions I - A - I -. J r A" and j J7 = AtI respectively, whileK. denotes the tionresonant term corresponding to that value of A'.

The fraction of molecules in the ith state can be expressed as

f ' . (= i .f.)l cp (- R'T).

Z E Y (%.r) f , ' ' .r) e+ Ej U

a Boltzmann distribution with statistical weight factors (w.f.) reflecting the more fre-quent occurrence of certain states due to degeneracies. Z is the partition function, k isBoltzmann's constant, T the absolute temperature, and F, the energy of the ? th state,which depends in general on all of the quantum numbers defining the state.

In detailed treatments (see, for example, Ref. 2), !, is expreosed as f,.( a I, (J. A'. if,in which each term has the form given above; f, is the fraction of states in a vibi'ationalstate defined by the principle quantum number n, and f, the fraction of states which arein a rotational state defined by J, A', and it. For the oxygen molecule, the lowest vibra-tional frequency is sufficiently high that f,. is nearly 1 for the vibrational ground state attemperatures experienced in the atmosphere, and f can be considered equal to f.

If the identityf) -f, f; i - , f,) is used, then the population difference is

f, - k) - - 1 "

For transitions between states of constant A.

(a n.)d f 2K- I

and

4 R.A. -EFANDE

orkr

[ -A k

and since > << k,

The dependence of > on 1" obtained by Van Vlezk (4) further assumes tne energy K' todepend cn AK oniy, and thus fI has the approximate form

EK A AT

/A - -i , kT(2141)

where

E = PK (A 1) and

I? = 2.862 x 10- 2 1 joule.

Since I,•,•-= 2 ands: - (see Eq. (3)), canoewritten

, -(cnst nt V 2 ( "' [f - f

and • becomes

If the atmosphere is assumed to be sufficiently dilute to be approximated by an ideal gasN = P','kT where P0o is partial pressure of oxygen, so that

Y = (Cons•tant) •T ] "t!l ,t!S(v jv f

h the pressure dependence introduced through S ,z, ,. v) is neglected for the moment,is directly proportional to partial pressure. At moderate temperatures, the energy lev-els are small compared to kT. K :, 0 053 UT, and the sum over all states in the denomi-nator of f, is approximately proportional to 2". At frequencies removed from the reso-nant frequencies, the temperature dependence is given by T 2 because many linescontribute to the absorption so that the sum of the exponentials in the numerator tendsio cancel that in the denominatcr (except for additional dependence Litroduced throughst t. z> ). At frequencies where one line dominates, the dependence is given by

-ep (-_/'A kT)

The form finally used in computing the absorption coefficients is

NRL REPORT 6756

[}(1 .TI'• o 21 , I) eM)(-A'," k?')t o J T , Lt ,J

[ ____ MA'i 3)K (P2K-II _;

2(K tA + 1) (2A'+ 1)i -,f r . '.N ( -. ,) j . ( - E; A . k 7 ) ( 2 )

> is one of the constants adjusted in this worLk to give the best fit to the 'Ixperimen-tal data at P,, and T"0 , the " K. are the frequency intervals or resonances of the spectrum,and

EA'k = (2 0731) AhA'' ) ( ' K)

The summation is over odd values of A' only and is cut off at A = 51, as the contributionof lines beyond this was found to be insignificant.. The z'. are taken from experimentalresults discussed in a later section for A' = 1 to 25 and from the semiempirical modelsfor A"=25 to51:*

•'A" (GIk) 59. 550 - 0. 252A' 9 30 A

(6 I,?) 59 790 - 0 252K - 9 10 A'

AA* ABSORPTION BY WATER VAPOR

The absorption of microwave energy by water vapor (4,7) results from electricdipole interactions, and the theoretical treatment takes the same general form as thatgiven for oxygen in the previous section.

The rotational level structure of water vapor is much more complex, consisting ofa multitude of levels spaced at intervals in the microwave regions. Fortunately, theselection rules that result from the symmetry properties of the molecular levels permitonly one transition in the frequency range of 10 to 100 GHz (at : = 22.254 GHz), whileseveral quite intense lincs occur in the far infrared (z > 100 GHz). The absorption bywatei- MoecleI. then takes the form of one term of the sum of Eq. (1) above plus an ad-ditional semiempirical term approximating the total contribution of the low-frequencytails of the higher frequency lines. The fraction of molecules in the i th state, f, , hasthe form " ,,p (- , AI'), where Z is again the partition function which, for the case ofwater- vapor, is a double sum over two quantum numbers with significant contributionsfrom many states. By numerical evaluation, it can be shown that z 1 -" within a 10-percent error for variations of about 120°K in temperature (4).

The mn'rnhPr density of water vapor molecules 1, is proportional to the mass den-sity . The water vapor absorption can be expressed in terms of the vapor densityand

0 LT. 1 7 p/o

where Y, is one of the constants adjusted to fit the experimental results.

*Adapted from the wave number rceult given in Table J of Ref. 4.

6 R..A. LEFANDE

The residual absorption of highe: frequency lines is given by a sum over the lineswith -, I.o(, *.) replaced by its li-..it at ',, >' '. The exact calculation of this term isunprofitable, as the result is found to be only one-fourth of the observed residual ab-sorption, probably due to the inadequacy of the theory of S( . in this limit. Thesemiempirical result of Van Vleck (5) adeouately describes the experimental results andwill be used for the present purpose:

"(constant) - ( . JI m S(:I

t) , L

ABSORPTION LINE SHAPE FUNCTION

The frequer.cy dependence of the absorption coefficients obtained as discussed pre-viously is Lai gely determined by the line shape function s t., The natural widths ofthe absorption resonances are very small (: 10-' Hz), resulting only from the growth ofthe amplitude of the vibrations upon absorption of the incident" quanta. The observed linewidths are of the orde: of 109 Hz at atmospheric pressure, and the absorption at fre-quencies removed from the resonant frequencies is completely controlled by this linebroadening.

In the case of atmospheric gases, the lines are broadened by collisions between themolecule2s. Van Vleck and Weisskopf (8) have treated this classically by assuming thecollisions to be sufficiently strong that the oscillator is stopped at the moment of colli-sion and later restarted, with its phase wiLi respect to the incident field determineL tythe condition that thermodynamic equilibrium exists between the ensemble of oscillatorsand the field. This requires that the time of the collision is much less than the meantime between collisions. The kinetic theory is applied to obtain the probability of occur-rence for collisions. The results are combined and averaged over all the molecules toobtain the susceptibility and thereby the imaginary part of the index of refraction, theabsorption coefficient.

The, t esult, known as the Van Vleck-Weisskopf shape factor, is

A ] (3)

where A; is the line breadth factor ,A ! 2-• (- is mean time between collisions), whichcan obtain values of the order of

The limit used tc describe the nonresonant absorption of oxygen is

l .m [Z.Stz. 3)] 21%,

The limit of S( ',. •) used to describe the absorption of the submillimeter water vaporlines is

S0,1. p. . (, o n. s tn t) v'A:

Others have treated the problem using the methods of quantum mechanics and haveobtained the same result when the same assumptions were made. There is, however,some question as to the validity of the simple assumption of strong collisions, and many

NRL REPORT 6766 7

of the possible intermolecular forces, some acting at. relatively long range, may affectthe profiles of the absorption lines. In experimental determinations of !%V, it is in gen-eral difficult to fit the entire profile with this line shape function for a single value of A I;for example, if %., is chosen to fit the region contiguous to the peak, the theoretical ex-pression does not fit tne tail.

Since the available empirical values of actual atmospheric absorption can be fittedto within their uncertainties by appropriate adjustment of the constants, the Van Vleck-Weisskopf line shape is usable in the present effort as a good model even though the the-oretical treatment may not be completely satisfying.

The line breadth factor depends on the total number of molecules per unit volume N,their velocity r, and the cross section for collision -: A. z The collision crosssection can be shown to be proportional to , -- ' '" ' , where n is the exponent of theintermolecalar force law (V -r'") and can assume values from 1 to 7. From kinetic the-ory, r is proportional to 7" 2, and from the ideal gas law \ T7, so that

Or, if V" is the line breadth measured at 70 , 7 , then

where r, the exponent of the temperature dependence at constant pressure, is

2(n- I

The simple linear pressure dependence of -% is tested on experimental data in thenext section and is found to hold only at lower pressures. Apparently at pressures of300 mm Hg and higher, the individual collisions become less effective ir broadening theline (possibly due to either an increasing number of multiple molecular collisions or thefailure of a molecule to regain equilibrium between collisions), with the result thatmeasurements in the range of 300 to 760 mm Hg appear to exhibit an approximately PI 2dependence.

The pressure and temperature dependence of the line breadth factor enters into thecomplct: expression for the absorption coefficient (Eq. (2)) through s ( ,... ', contribt...ing a further difference ii the pressure and temperature variation of .( :. T I') betwcenthat at frequencies adjacent to the resonant peaks and that at frequencies removed fromthe peaks. This simple behavior of the line breadth is further complicated by the de-pendence of the perturbing effect of the collisions on A. Measurements'on individuallines at low pressures show that the variation of effective wiath from line to line is lessLhan 10 pe,-cent of the width, so that using an average value weighted over line strengthresults in a small error (9).

DETERMINATION OF CONSTANTS BASED ONPUBLISHED EXPERIMENTAL DATA

Oxygen

The experiments that have beer conducted are of two general types: measurements* of y, the "A. or '., at reduced pressure and measurement of the actual effect of the

8 R. A. LEFANDE

absorption at atmospheric pressure on a signal -either in the laboratory or over atypical path through the atmosphere.

The determination of the frequency intervals of the absorption lines must be ob-tained in a laboratory experiment at low pressure so that the individual lines can beseparated. Determinations for K = 1 to 25 by three investigators are listed in Table 1.The results of the three measurements can be considered the same for the present pur-pose, and Burkhalter's (6) more complete results will be used 'n the computation of theattenuation.

The experimental determination of the constant , and the line breadth has beentaken in two ways: by direct measurement of each individual line profile at low pressui eand by use of Av as a parameter to obtain the best theoretical fit to the measured ab-sorption profiles at atmospheric pressure.

The results obtained for the line breadth at low pressure are consistently about

1.5 GHz/atm with consistent linear pressure dependence, while field measurements at

Table 1EExperimental Determinations of Absorption Line

Frequency Intervals and Line Breadths

1 Absorption Line Frequencies, Line Breadth Factors at Unit Pressure,,.K. (GHz) I P' (GHz/atm)

Series K -___ 1 - 6j1 ) -Burkhalter Mizusuhima(1 Gokhale Artman urkal khale1 Anderson

______ (6 1 1) (10) (, (10)ltr~o(9

25- 53.5922 53.5994 . ...23- 54.1300 54.1294 -13

21- 54.6725 - -- 0.63 0.9619- 55.2208 55.2216 - 46 - - 1.2317- 55.7841 55.7846 - 138 - - 1.34

1+ 56.2651 56.2656 56.2656 1.67 - 1.05 1.4915- 56.3628 56.3640 56.3642 1.51 1.44 -

13- 56.9687 56.9708 - 1.41 - - 1.4211- 57.6120 57.6114 57.6123 1.50 - 1.02 -

9- 58,3240 58.3232 58.3249 1.52 - 0.63 1.503+ 58.4462 58,4462 58.4463 1.69 - 0.84 1.307- 59.1634 59.1634 5c,1642 1.38 - 0.84 -

5+ 59.610 59.5914 - 1.49 --

5- 30.3064 60.3080 - 1.51 -- -- 1.147+ 60.436 60.4334 - 1.46 - - 1.569+ 61.120 61.1496 -- 1.47 ----

11+ 61.8002 61.7998 - _ 1.501+ 62.4117 62.4138 62.4129 - 0.65 0.75 -

3- 62.4861 62.4872 62.4862 -- 1.59 111 1.4615+ 62m910 62.9966 -< 1- -- 1.35S17+ 63.5683 63.5672 ...19+ 64.1276 64.1280 --- -1.2021+ 64.6789 64.6782 ...23+ 65.220 65.2242 ... 0.96

25+ 65.770 .1- -- 118.71ý505 ...

Pressure I mm I ! - -2 to 10T <.I =I to 6 =0 to 12(ram Hg)

NRL REPORT 6766

atmospheric pressure are consistently about 0.6 GHz/atm (12-15). The low-pressureindividual line observations are also summarized in Table 1. This apparent inconsist-ency has been notea by othe. s (4,16) and various theorios have been suggested - notablythat the effect (f all the absorption lines is not a simple sum.

Artman and Gordon's data (11) at intermediate pressures provides a basis for de-termining ., and the actual pressure dependence of the line breadth factor.

Best-fit values for ,, and ". are obtained separately for sets of data points at 1,0.5, and 0.25 atm pressure taken from Artman and Gordon's paper representing meas-uremnents of dry air. A least-squares-fit computer program is applied, assu-ning thatthe theoretical equations (Eqs. (2) and (3)) give at least the functional form of the profilecorrectly. The results* (for 7., 300'K) are:

" (amM Hg) -" (dB/km GHz) ,I'(GHz/atm)

760 0.01647 0.00076 0.873 ± 0.1951380 0.01790 0.00153 1.496 0.456

[___ 180 0.01742 ___0.00065 1.518 _ _ _0.200 ISince • should be constant, it can be fLxed at its mean value = 0.0173 and the best-

fit values of', 11 obtained:

[1 ,(mmiHg) " (dB/'km GRZ)] ". (GHz/atm)

760 0.0173 1 1.0791 0.0585380 0.0173 1.2987 . 0.1583190 0.0173 1.4995 0.1659

In each case the fit is of about the same precision, and without further .ta it will beassumed that . is indeed constant.t

The choice of . is quite important, sine the value largely determines the absorp-tion at frequencies removed from the resonant peaks, which is the region of greateztinterest for propagation purposes. The theory of the Aine broadening has been the subjectof many studies, but none has yet predicted, cactly the correct value or behavior withtemperature and pressure so that it is necessary to use a semiempirical approach usingthe magnitude f '. as a fitting parameter and a semiempirical model to give the pres-Gure and temperature dependence. Since the use of as acurve-fitting parameter becomesquite subjective when only a few data points are available as in some of the actual pathloss measurements (13,15), the model for ':I I- T) used in the present work is based onthe study of Artman and Cordon's data. The adopted model is

*•annu:zz (17) clamrns there is another related effect of the collision process in which thephase shifts induced by the collisions results in an effective displacementof the resonantfrequencies with increasing prefsure. He uses a pressure dependence of the fo,,rn

to obtazn a better fit to ineasurements obtained at pres,.ures above I aten usinc a singleline at , ot)O GHz to ,approximate the entire spectrum. In fitting Artman and Gordon'sdata, - %as used as aa additional parameter, allowing the resonant frequency of eachresonance to be shifted by an amount proportional to the pressure. The mean ralue of aobtained for the six fits is -0.04 * 0.27 MHz/mm. Without further evidence, this effectwill be neglected for the present purpose and - will be set equal to zero.

IThis value of ." is greater than the theoretical value of -, = 0.0145, which i. obtairedfrom the various constants and an assumed number fraction of oxygen (0.21).

10 R. A. L1EFANDE

0 001S1 (.11, P'(mna fig). I' 0

0 690 (,l !P(nain fIg) ;;0' 46.. P 1 '0

The values of (P) obtained in !itting ArtmanO nand Gordon's data and the resulting mouA1 of the

-- EXTRAPOLATED WW-s'WSUR* pressure dependence of ". are plotted in Fig. 1. ItSRE51UT (1I., GHZ/ATu)- E. 05 H TTE"J/TM is clear that A.> begins to depart from a linear dt-

pendence on P' for P > 300 mm Hg. The data pointsA FI( WiTH yo V.RIABIE are plotted with the semiempirical curves that re-C FIT T• wy, FIxOE pot eOfep•0 suit from this model in Fig. 2.

0 YCMELD MEASULT -MENT RIESULT The temperature dependence of . at constant

pressure has been measured by Tinkham andStrandberg (18) (,o. = 0.75) and Beringer and

Sol Castle (19) 0.87). A m ean value of o. 0.8,wil: be used.

Water Vapor

L Available mea.'u'ements of water vapor absorV-tion are less plentilul. The values of ,, .,and zfor the resonant water vapor absorption computed byVan Vleck (5) are found to satisfactorily describe

I the experimrelntal data of Becker and Autler:

00..860 0 0 Icco " mPRESSU-PE'ri H;,, 0. 1864kn --l

Fig. I - Line. breadth vspressure modeled toArtman E,6Kand Gordon's (11) data k

k29

The line breadth parameter has been measured by Becker and Autler (20) and is found todepend on the water vapor density.

"( (1 + 0 (I(,,P0

at constant T. This vapor density dependence is an experimental result which reflectsthe greater effectiveness of HO-HO collisions in producing line broadening comparedto H2 0-air collie'-ons. The value of A:4 0 'P obtained at 318 0 K and small , is

-at ('j• °T• --x% 2.61(;l-

For the temperature dependence of n, the computed result of Beredict and Kaplan

(21) will be used in the absence of experimental results: 'jo = 0.63.

"The residual absorption of the submiilimeter resonances is given by

J-1T

NRL REPORT 6766 11

14-' P & m*P 1 980 mm Hg14•,~ ~ - 19 Mm 1 4gn Q

612' T - 500*K

S10ý

zw4ý

,. -0-.

II

50 5z 54 56 58 C; 62 64 66 68 1-0FPIEWENCY (GK6

Fig. 2 - Aztrnan and Gordon's data (1;' with semi-empirical absorption curves, holding ). constant(0.0173 dB/krn GHz)

The value of i is found to increase with the water vapor density. Schulkin (22)has calculated rcr i, to fit Becker and Autler's data (20) using their result for theline breadth:

km Gilz'

The water vapor absorption curves are plotted with the oxygen curve in Fig. 3. Thecurves show that absorption by water vapor largely controls the total attenuation overthe decade from 10 to 100 GHz except the region of high attenuation due to the oxygenresonances.

TOTAL ABSORPTION FOR PATHSTHROUGH THE ATMOSPHERE

V• The absorption for a path through the atmosphere is given by

S.11:,f. la f , T/. 1, :,) dI .

t

where I is the distance along the path measured from the ground, and T and I' varywith altitude which in turn is a function of I and F, the elevation angle of the aateuna.

The variation of temperature and pressure with altitude is not readily measured, sothat a model is needed to represent typical or average conditions. The ARDC 1959 modelatmosphere (23) is used for this purpose. A water vapor distribution proportiot|aI to a10-year average distribution for the Washington, D.C., area (24) is also assumed. The

12 K. A. Lk.FANDE

io-S09?-

S06• ,

TOTALTOTAL H

05

004.

2/ 04 ;TOTALFC H'0

S03-

4/

ýSEMIEMPIRIC.AL 0,

0 1 - . - - S V U S W L L I M E TE hCCNTR;B.T-ON

HIO RESONAMI LiNE

0 10 2) 30 o 0 50 S0 70 Eo 0 90 It

FR£O;ENCY %GHmz,

Fig. 3 - Water vapor and oxygen dbsorvtioncoefficients vs frequency (T 15C = 60*F.11 = 7bO mrn Hg, . , r 7.5 g/m)

ARDC profiles and the av irage water vapor distribution are shown in Fig. 4. The alti-tude dependence of the abbc,',"tion coefficient (dB/km) that results from this model at-mosphere is :,nown in Fig. 5 The curves plotted in Fig. 5 illustrate the difference in thedependence on altitude icr frequencies close to the resonances of the absorption ke.g., 60GHz) and those well removed from the resonances (e.g., 50 GHz). This difference is dlieto the cancellation of the pressure dependence of the absorption for frequencies exactlyequal to that of the resonances. For thest frequencies the absorption coefficient remainsnearly constant to high altitudes, and for the nearby frequencies the decrease in the ab-sorption is controlled only by the narrowing of the line breadth. The discontinuities thatoccur above - 12 km are due to the arbitrary cutoff in the assumed water vapor diztri-bution.

The absorption profiles for various altitudes are three values of ground-level watervapor density (.,), and are shown in Figs. 6 through 8. The chosen density values of 7.5,15.0, and 22.5 g/m' correspond to 60-percent relative humidity at 60, 80, and 93°F, re-spectively. The curves show the rapid decrease with altitude of the absorption coefficientat frequencies away from the resonances and the nearly altitude-independent behavior atthe oxygen peaks. Although the plotter does not have sufficient resolution to reproducethe full height of peaks at the resonances, the line structure of the oxygen absorption isin evidence at the highest altitude.

In the actual calculations applied here, the atmosphere is divided into a series of110 spherical shells of exponentially increasing thickness to a height of 30 km. * Except

*Repeating the calculation with IOi layer! from 0 to 30 km having uniform thicknessesproduced essetia•'•y the same results.

:JRI REPORI bi66 13

10 290 I 01 C -

09 280 900

08 270 800,

ýý0 7 260 700-1.

05 {240 500-

134 ~230 '40

.03 220 3 "00,

02 2:0 200\

01 200 tLCý.

00 4 12 16 20 24 28 32

ALTITUDE (kmn]

Fig. 4 - Temperature and pressure profiles ofthe 1959 ARDC model atmosphere, and averagewater vapor distribution

400 0 ...

0 0G

Oi L \0 ýoo 620 28 3

I 1,

S400 -jz \ \

S0 4 a 12 !6 20 24 28 3 2

ALTITUT f (k(A)

Fig. 5 - Net altitude dependence of absorp-tion for the 1959 ARDC roodel atmosphere

.I

14 R. A. LEFANDE

I 2~~~~000~---- -

1001

00 2C 3b 40 5b ýO 70 6D 90 k ODFREQUENCY (WHO

Fig. 6 - Absorption profiles for various altitudesfor p, 7.5 g/m3 (60%/ RH at 60*F)

1000 T-

0 k

of,,

122k

0 10 0 30 40 50 60 "70 O0 90 100FfIDEKUY (GHz)

Fig. 7 - Absorption profiles for various altitudesfor p. = 15.0 g/m 3 (60% RH at 80*F)

2000 I I I I I I ~ i I 1

I

NRL REPORT 6766 15

1000. .. . . .

C 014 6.LL

_'I

- I

0001 -- I!---!.,----- "I

00

0 to 20 30 40 50 60 70 so 90 !00FREOUF.NCY MGHz)

7Fig. 8 - Absorption profiles for various altitudes 'fo r ' -- Z . g l (6 0 5c R H a t 9 3 "F ) .

i ~for single frequencies -zorresponding exactly to the resonances, the contribution of the /i ~attenuation from ,altitudes greater than 30 km is negligible.

+; ~The slant distance 1, thru the layer between the altitade .4., and altitude n.+, isS~ given by

where

h/, ,

I//

and a,. is the radius of the e-arth. En is the elevation angle of the ray path at the point. at•- which it enters the n th layer. For the first layer, •,is the antenna elevation angle and'•- the succeeding values of En are given by

001' ' t '"'! ]0:. :0 0 3 40-'-.• 50 60 : 80_0,0

where Nn is . F index of refraction at the foth altitude.

The integral is then approximated using the trapezoidal rule

.4(,.F 1- t- 2~" -

.

A1;(In-

16 R.A. LEFANDE

-*here the subscript n denotes the value computed for the , th altitude. Similar calcula-tions that do not allow for the bending of the ray pnth show that the attenuation is essen-tially the same for a given antenna elevation angle and that the only effect of refractionis to change the angle required for a given source.I The final results of the calculations giving the total attenuation due to atmosiP'?ric

oxygen and water vapor are shown in Figs. 9 and 10 as a function of frequency ior vari-ous antenna elevation angles and as a function of elevation for various frequencies inFig. 11. The effect of the altitude dependence has sharpened the peaks and has produceda steep increase in the total attenuation below 10 degrees elevation. The plot in Fig. 10shows on a linear scale the frequency and elevation dependence of total attenuation (lcssthan 20 dB) and emphasizes the extremely bteep frequency dependence near the oxygenS~ resonances.

leI /%

I I,1' ~ELEVATK)N4

90

0 o 20 30 4o0 0 o -0o s 9o ,ooMMEOENcy (GHO)

Fig. 9 - Total absorption vs frequency for patht;

through the atmosphere at various antenna ele-vation angles (p0 z 7.5 g/rn3 )

ATTENUATION BY RAINFALL

The attenuation due to rainfall is treated separately since the distribution of rainalong the propagation path is generally unknown and unpredictable, making the. 2sults ofrain attenuation calculations quite qualitative.

The theoretical treatment of rainfall attenuation is a,. exercise in classical electro-magnetic theory. The general solutions to the wave equation in expanskons of sphericalfunctions are known. An incident pcane wave, a scattered wave, and a transmitted waveare ex:pressed in the spherical functions, and the coefficients of the expanded solutions

NRL REPORT 6766 17

6- I

41- 40

2

0 ./\ I

0 J0 10 20 30 40 50 60 70 80 so 100

FREQUENCY (GWHO

Fig. 10 - Total absorption vs frequency for pathsthrough the atmosphere at various antenna ele-vation angle.- (p 0 = 7.5 g/m 3 )

100 Ij 1

I0'04-6

1000

40.

01 -- (G' --

0 13 2o 50 40 50 i0 70 80 90 100ELEVATION ANGLE (DEG)

Fig. II - Tota: absorption vs antenna elevationangle for paths through the atmosphere at vari-ous frequencies (ip0 = 7.5 g/rn 3 )

IF

18 R. A. L[ FFANDE

are fitted to the boundary conditions at the surface of a sp~ierical raindrop. The attenua-tion due to a single raindrop is obtained by comparing the absorbed and scattered ener-gies with the incident energy.

The total attenuation due to the rainfall is then reLated to the rainfall rate using anempirically based model of the drop size vs number distribution as a futiction of rainxate by summing the attenuation due to the various si,.e drops, neglecting the effect ofmultiple scattering.

The attenuation at frequencies from 4 to 100 GHz has been most recently treated byOguchi (25,26) and has been reviewed with reference to the experimental evidence byMedhurst (27) and Crane (28). These papers also contain the earlier background refer-ences, detailed discussions of the theoretical solutions, and choice of drop size vs num-ber vs rate distributions.

In attempting to estimate tie actual effect of rainfall on propagation along pathsthrough the atmosphere, the gi eatest difficulty is not in computing Li.e magnitude of theattenuation once the characteristics of the rain are known, but in predicting these char-acteristics. In examining the attenuation observed during a given storm, the dii -epancybetween the measured and expected values will in greater part be due to departures ofthe rate and rate vs drop size distributions from the average and to the vagaries of thespatial distribution models in both altitude and range. The results of Oguchi's calcula-tions are in good agreement with results of experiments in which the various rain param-eters are known, and thest, results may be used without adding significantly to the errorinberent in the assumptiop -f models for rainfall distribution. Curves of attenuation vsfrequency and rate interpolated from Oguchi's tabulated numerical results are given inFigs. 12 and 13.

100T-

OuhO

000 - -- -Q'17

00011- ----- *---0 10 20 30 40 50 60 70 or 90 100

FREOWNCY i GH6z,

Fig. lZ - Theoretical rainfall attenuation vsfrequency for various rain rates

NRL REPORT 6766 19

S ~FR.CQUL,,•*(GH•)

.251Z 40

'ý20j

15

0 10 20 3o 40 W 70 80 90 1o0RAINFALL RATE (mrn/hr)

Fig. 1 3 - Theoretical rainfall attenuation v3rain rate for various frequencies

Tc discuss rainfall attenuation on a general basis without reference to a particularstorm, it is necessary to use a statistical approach. A meaningful sampling of typicalrainfall effects may be obtained by considering values of rainfall rates which will beexceeded 1, 0.1, and 0.01 percent of the time corresponding to light, moderate, and heavy

Srain.

Statistical studies of rain rate as a function of the total time a specific rate wasexceeded over the time period of a year are available for various locations. The surveypapers of Weible and Dressel (29) and Medhurst (27) contain lists of references for thisand other types of studies that will be referred (o here.

The results of Bussey (30) for Washington, D.C., give the instantaneous rain rate asa function of the total itumber of hours per year during which the rate is exceeded. Therate exceeded 87.6 hours per year or 1 percent of the time is 3.05 mm/hr; 15.2 mm/hr

I iis exceeded 0.1 percent of the time; and 61.0 mm/hr 0.01 percent of the time.

Altnough it is known that light rains tend to fall over wide areas simultaneouslywhile heavy rains are generally due to intense, highly localized storms, studies givingthe relative rates as a function of the ground range from the observer at a given instantare not available. Rather, the observed quantities are given in terms of averages overtime or over collecting area. Such averages necessarily include the effects of stormS~translation and are difficult to interpret precisely in terms of momentary distributions.

Radar studies of individual storms (31) have suggested that a parabolic distribution is afair approximation of that observed:

R, (r) I for r < a

it.(' 1 0. f,,r r - a.

where if ,i is the rain late at ground distance r from center, relative to the rzte a, thecenter, and a is the radius of the storm (kin).1'

20 1.A. A.LEFANDE

The dependence of the rate on altitude based on model distributions of the variousparameters, is given by Valley (32). Valley's curves can be fitted for computationalpur-osps by the function

Rh(hi) 1 ( 04 1) CXp f-0 1 •I-, 1 ( 1 ' +

where Rh(h) is rate at altitude 1, (kin) relative to rate at ground.

In the absence of meaningful statistical studies of Lhe instantaneous rainfall di.;tri-butions, the following approximate models will be assumed:

Model Time Exceeded Peak Rate torm hadiiusNo.. '.) (mm/hr) a (kn)

1.0_______ 6.05 J 50

.•, 2 0. i 15.2 20

The cross sections -, these model storms are shown in Fig. 14a, b, and c. To illus-trate the coarseness o' models, the cross section of a real thunderstorm is repro-duced in Fig. 14d.

01

6-

03

t 05-12 U? '

0/ u7I

.50 -40 -30 -20 -I0 0 *10 -20 .30 *40 .50

RANGE (kim)

a. Model I: a = 50 km

I 0'

6--~ --

S - 0 0 *O -2 ! 0. -O0 3 6 8 0 1-'

4s 405 05 4 1/

I 24!

07 0IIL6~ 0 . '-20 -10 0 -10 *20 -10 0 *i0 02 4 68 10 124

RANGE (km1

RANGE ikin) RANGE (kmn)

b. Modcl 2: a 2 20 km c. Model 3: d. Real thunder-a = 10 km storm

Fig. !4 - Model rainstorms and a real thundersturm,showing contours of rel-tivw rain rate

NRL REPORT 676t 21

Since it is not possible to consider possible preferred azimuthal directions withoutprior knowledge of the synoptic conditions at a given site, it will be further assumed, asa coarse average over all directions, that the storm is centered on the site.

The range and altitude distributions may be combined to give an effective path lengththrough the storm as a function of elevation angle E.. The effective path lengLh is

1" (K) -f le, (I . l 4E ? . ).n" .' dl,

the distance through an equivalent storm of constant unit rain rate throughout, having thesame total attenuation as the model storm. The use of such an effective path length as-sumes that the attenuation coefficient has a nearly linear dependence on rain rate. Theapproximate attenuati-n contributed by the rairnfall can be obtained by multiplying thislength by the attenuation coefficient corresponding to the local rain rate and the operat-ing frequency;

.rit'.. ) /'II 1 1, IE ,

\ here

= attenuation due to rain (dB),

= atteaiuation coeffic:ent (dB/km), and

local rain rate (mm/hr).

Figure 15 shows the effective path length as a function of elevation angle for urins ofvarious radii based on the above models.

The rainfall attenuations computed in this way using the rough models should indi-cate at least the order cf magnitude of the effect likely to be enco¢untered. rhe attenua-tion values [or the three? model storms are added to the absorption due to oxygen and

25-

. 5 •0 kmn

C..

30

ELEVAiION ANGLE (DEG)

Fig. t3- Effective path length vsel,.vation for model storm,

RAiSCs€~

22 R.A. LEFANDE

water vapor and displayed as total attenuation in Figs. 16 through 18. It is clear that therainfall atteruation Is dorninant at the higher frequencies for any but the lightest rainstorm.

I mio~~ /LLEVATIOtN

Z kc7

0 to 20 3 0 5 0 T o 9 0

lO4 . .. . ...

,oI.. i-t

FREQUENCY (GHz4

Fig. 16 - Total attenuation, Model Storm I

CONCLUSION

The values of absorptio-i coefficients used here are computted in detail from the the-ory as; tempered by the available empirical evidence. They represent as accurately as5 possible the effect- of atmospheric oxygen and water v'apor on microwave radiation.

The values of total path attenuation, however, also depend on artificial, models forthe distribution of the atmospheric czonstituents, -ýnd the results must be viewed as rep-resentative of values likely to be encountered but not necessarily precise under all

conditions.

The results obtained for the rainfall attenuation are intended only as a qualitativeindication of the effect to be expected. Serious attempts to predict the rain losses mustrest on meaningful statistical studies of instantaneous rainfall distributions at the site ofinterest. Experimental evidence is limited, and determination of thte actual attenuationoccurring along atmospheric paths at elevation angles other than zero must be made torefine the computed results and to determine the spread of values under a range of oper-atn c

NRL REPORT 6766 23

IC +i"•` -- ---- - -

SI! ---t

'- i2

<'P

I100

0 10 20 30 40 50 6 80 9" IooMQIUNC•Y *GMz)

Fig. 17 - Total attenuation. Mode! Stirm 2

ANGLE

10 -

4" 0 .0 t0 2o !.5 40 50 60 70 80 90 100

F1RECINCY (GHkI

Fi,,. 18 - Total attenuation, Model Storm 3

I

- ~ ~ ~ ~ ý -- - ` 7 ` -r'ý-r -- c--

SYMBOLS (in order of appearance)

Fraction of molecules inj th energy state

SAbsorption coefficient

Frequency of radiation

SNumber of molecules per unit volume

,•, Quantum mechanical matrix element connecting th and , th molecularenergy states

f, Fraction of molecules in energy state

Resonant frequency of absorption line corresponding to the transition fromstate to state j

Line shape function

SAK Rotational quantum number

J Total angular momentum quantum number

-o The Bohr magneton

4A! Matrix eleL..2nt corresponding to transitions K- K. I (+ and A'- I - AK-

6(A. f.) Statistical weight factor

SEnergy of i th state

k Boltzmann's constant

T Absolute temperature

Z Partition function

f,.(n) Fraction of states in vibrational state defined by principle quantum number

f, ( J. K. it) Fraction of states in rotational states defined a set of quantum numbers J, A',and I1

i! Quantum number for the pTojection of J on the molecular axis

C Base of natural logai ithras

R A constant

h Planck constant

Po0 . Partial pi.•ssure of 02

24

NRL REPORT 6766 25

I' Total pressure

"•O Constant adjusted in this work to fit the theoretical expression for the absorp-tion coefficient to experimental values at pressure I,., temperature 1,

VK, Resonant frequency corresponding to allowed transitions K -. AK + i (+) and

A'- 1" K- A'

Dummy parameter

o Resonant frequency of water vapor absorption

Water vapor density

Water vapor density at 1'0. 70

Experimental constant fitted to resonant water vapor absorption

E, Energy of lower state of water vapor resonance transition at 22.254 GHz

Line breadth factor

Mean time between molecular collisions

Collision cross section

t, Intermolecular force

r Distance between molecules

SExponent of intermolecular force law

SMeasured line breadth at I,0 . T"

SExponent of temperature dependence of line breadth at constant pressure

-•dtm Atmosphere (pressure)

* Constant of suggested pressure dependence of resonant frequencies of absorp-

f tion lines

"Value of - for 0.

Value of -for 11,0

. • Experimental constant fitted to residual water vapor absorption

E Elevation angle of antenna

H,: .•.) Total attenuation at fx equency - and elevation angle F

Distance along propagation path

,, Distance along propagation path through the nth layer

IR-,rees Fahrenheit

De .,• r -c -, Kc'IVll

!I

26 R.A. LEFANDE

I, , ae

eA,, Height of nth layer

a, Radius of earth

i ,, Total absorption coefficient at height A,,

E,. Local elevation angle at the n th layer

N.,, Index of refraction at height h,,

R,(r) Relative rairfall rate at distance, from center of storm

Rh (A Relative rainfall rate at height A

a Radius of model rain storm

P, Effective path length

Ira in(v, ?o) Rainfall attenuation coefficient corresponding to frequency ,', rainfall rate ie,

R, Local rain rate (mm/hr)

A ra i,, Attenuation due to rain (dB)

I

2

ACKNOWLEDGMENTS

Figures 2 through 18 were produced by a Gerber A'atomatic Drafting Machine oper-ated by Mr. Stanley Kozloski of the NRL Engineerbig Services Division. Co'uputer sub-routines required to produce the punched paper tape for the drafting machine were writ-ten and furnished by Mr. A. T. McClinton of the NRL Atmosphere and AstrophysicsDivision.

Mr. J. P. Leiphart has reviewed this report and made many helpful suggestions.

REFERENCES

1. Mizushima, M., and Hill, R.M., "Microwave Spectrum of Oxygen," Phys. Rev. 93:745(f eb. 1954)

2. Townes, C.H., and Schawlow, A.L., "Microwave Spectroscopy," F,:w York:McGraw-Hill, 1955

33. Schlapp, R., "Fine Structure in the Ground Stat2 of Oxygen Molecule, and the

Rotational Intensity Distribution in Atmospheric Oxygen Band," Phys. Rev. 51:343(Mar. 1937)

4. Van Vleck, J.H., "Absorption of Microwaves by Oxygen," Phys. Rev. 71:413 (Apr.1947)

5. Van Vleck, J.H., "The Absorption of Microwaves by Uncondensed Water Vapor,"Phys. Rev. 71:425 (Apr. 1947)

6. Burkhalter, J.H., et al., "Fine Structure of Microwave Absorption Spectrum ofOxygen," Phys. Rev. 79:651 (Aug. 1950)

7. King, G.W., et al., "Expected Microwave Absorption Coefficient of Water and RelatedMolecules," Phys. Rev. 71:433 (Apr. 1947)

8. Van Vleck, J.H., and Weisskopf, V.F., "Shape of Collision-Broadened Lipes," Rev.Mod. Phys. 17:227 (Jul. 1945)

9. Anderson, R.S., Smith, W.V., and Gordy, W., "Line Breadths of Microwave Spectrumof Oxygen," Phys. Rev. 87:561 (Aug. 1952)

10. Gokhale, B.V., and Strandberg, M.W.P., "Line Breadths in 5 mm Microwave Absorp-tion of Oxygen," Phys. Rev. 84:844 (Nov. 1963)

11. Artman, J.O., and Gordon, H.P., "Absorption of Microwaves by Oxygen in Millimeter"Wavelength Region," Phys. Rev. 96:1237 (Dec. 1954)

12. Beringer, R., "Absorption of One Half Centimeter Electromagnetic Waves in Oxygen,"Phys. Rev. 70:53 (May 1946)

13. Lamont, H.R.L., "Atmospheric Absorption of Microwaves," Phys. Rev. 71:353(Dec. 1948)

14. Lamont, H.R.L., "Atmospheric Absorption Millimeter Waves," Proc. Phys. Soc.61:562 (Dec. 1948)

128A

"1 2$ I:. .\. II.\ I) "

15. Crawford. et al., "Millimeter Wave Research," Final Report 24261-15, Bell Tele..phone Laboratories, Contrac' Ncnr-687(00), Oct. 1955

16. Str;Adberg, M.W.P., Meng, C.Y., and Ingersol, J.X., "Microwave Absorption Spec-trum of Oxygen," Phys. Rev. 75:1524 (May 1949)

17, lannuzzi, M-, and Minnaja, N., "Pressure Effect on Microwave Absorption of Oxygen,"Npiovo 1'ii-neito 30:997 (Nov. 1963)

18. Tinkhaxn, M., and Strandberg, M.W.P., 'Line Breadths in the Microwawv MagpeticResonance Spectrum of Oxygen," Phys. Rev, 99:537 (Jul. 1955)

19. Beringer. R., and Castle, JG., Ji., 'Microwave Magnetic Resonance Spectrum ofOxygen," Phys. Rev. 81:82 (Jan. 1951)

20. Becker, G.E., and Autler, S.H., "Waer Vapor Absorption of ElectromagneticRadiation in Centimete-.- Wav.length Range," Phys. Rev. 70:300 (Sept. 1946)

21. Benedict, W.S., and Kaplan, L.D., "Calculation cf Line Widths in H20 - N2 Colli-sio•r," J. Chem. P, 30:389 (Feb. 1959)

22. Schulkin, M., "Determination of Microwave Atmospheric Absorption Using Extra-terrestrial Sources," NRL Report 3843 (Oct. 1951)

23. U.S.A.F.. 'Handbook of Geophysics," Rev. ed., New York:MacMillan, 1960

24. Blake, B.L., 'Curves of Atmospheric-Absorption Loss for Use in Radar RangeCalculations," NRL Report 5601, Mar. 1961

25. Oguchi, T., 'Attenuation of Electromagnetic Waves due to Rain with DistortedRaindrops," J. of Radio Res. Lab. (Japan) 7:467 (Sept. 1960)

S26. Oguchi, T., "Attenuation of Electromagnetic Waves due to Rain with DistortedRaindrops (II), J. of Radio Res. Lab. (Japan) 11:19 (Sept. 1964)

27. Medhurst, R.G., 'Rainfall Attenuation of Centimeter Waves: Comparison of Theoryand Measurement," IEEE Trans. AP 13:550, Jul. 1965

28. Crane, R.K., "Microwave Scattering Parameters for New England Rain." M.I.T.Lincoln Laboratory Technical Report 426 (ESD-TR-66-447). Oct. 1966

29. Weibel, G.E., and Dressel, N.O., "Propagation Studies in Millimeter Wave LinkSystems," IEEE Proc. 55(No. 4):497 (Apr. 1967)

30. Bussey, H.E., 'Microwave Attenuation Statistics Estimated from Rainfall and WaterVapor Statistics," IRE Proc. 38:781 (Jul. 1950)

31. Atlas, D.. and Banks, H.C., "TIle Interpretation of Microwave Reflections fromRainfall," J. Meteorol. 8:271, Oct. 1951

32. Valley, S.E., ed., 'Handbook of Geophysics and Space Environments," Ch. 5,"Precipitation, Clouds, and Aerosols," New York:McGraw-Hill, 1965

Sectinty Ct-assification OuE7NTGDT.&DOCUMENT4 CONTROL DATA

($S-¢u.ity Clas ift,'afton of till*, body of abs'ract .,.ýd tndemin/ k-,.otition &sult b1 siored ý'.1..i. o-ml,4 toor io

I C.IC,,ATING &C 'IV TV (Co•porate a ,ho., 2-. REPORT SEC.'RITY CL ASSIPCA• lO-4

Naval Retiearch Labotat ory LNC!.ASS&FIEDWashington, D.C. 20390

rEPORT T:TLe.

ATTE.NUATION OF MICROWAVE RADIATION FOR PATHS THROUGHTHE ATMOSPHERE

4 O•SCRIP.IVE N•TEST••),,•, opol"d ,ncltwd.l) An interim report on tlese problems; wor -onother phases is continuing.,

5 A J THORSl (First "awo, A, ddle Initi.l, last, a1'm.)

R. A. LeFande

e RE PORT DATE 7* TO r•I NO OF P •GES |?b NO CIP REFS

November 29, 1968 32 32$a CONTRACT OR GRANT NO Sa. ORIGINATOR'S REPORT NUMOERIS)

NRL Problems R01-34 and RO1-36Sb. PAojC T No NRL Report 676d

RF 14-222-41-4353; XF 019-02-04-C 11648 09. OTHER REPORT NOIS, (Any oth .. wnS.. ,. thtm.y be .... I•dthis repot*)

10 DISTRIBUTION STATEMENT

This document has been approved for public reltaae and sale; its distrib,,tion isunlimited.

11 SUPPLEME•ITARY NOTES 12 SPONSORING MILITARY ACTIVITY

Dept. of the Navy (Office of Naval Re-search and Naval Electronics Systems

13 __ABSTRACT Command), Washington, D.C. 20360IS AUOTRAC T

Microwave radiation is absorbed by, atmospheric oxygen and water vapor znd isabsorbed and scattered by rainfall. This report provides values of these losses inthe frequency decade from 10 to 100 GHz for paths through the atmosphere at eleva-tion angles from 0 to 90 degrees.

The theoretical expressions for oxygen absorption are assembled in explicitform. The resonant frequencies are taken from published low-pressure measure-ments, and the entire absorption profile is fitted to published intermediate and at-mospheric pressure results, with a constant of proportionality and the absorptionresonance line width used as fitting parameters. The absorption line breadth isfound to deviate f.om the accepted linear pressure dependence, increasing approxi-mately as the square root of pressure for pressures above one-half atmospheric.

The results of similar analyses of water vapor absorption are assembled andcombined with the results of oxygen absorption analyses to obtain the completeabsorption coefficients as a function of the atmospheric parameters.

The total attenuation due to absorption in the clear atmosphere is computed fora model atmosphere with various water vapor concentrations. Results are providedin graphical form, giving attenuation as a function of frequency and elevation angle,

(over)

DD NOV .01473 (G ) 29 JII_ III

S/N 0101.807-6801 Securitv Classification

-Securi'y ClassifLcatlon

14 -EY WORDS LIMK A LINK U LINK C

ROE WT | ROLF WTY ROLE WT

AttenuationMicrowave radiationAtmosphereAbsorptionOxygenWater vaporAbsorption line shapeRainfall attenuationModel rain stormsLine breadthPropagation 4

II

The prediction of raiafall attenuation is severely limited by the absence ofmeaningful statistics on z -.a rate- and storm-structure. Rough estimates forrain attenuation are made .r crude model storms which occur for 1, 0.1, and0.01 percent of the time. Total values of the attenuation for the model stormsand the atmospheric ý6bsorption are provided.

DD "*G"V*1473 (BACK) 30 i

(PAGE' 2) Security Classification

NRL Report 676)Change 1May 27, 1969

1. On p. 2, nine lines up from the bottom, the word-iprocessing" should read "precessing."

2. On pages 14 and 15, the caption for rig. 6 belongs

to Fig. 8, and vice versa.Rvproduc•ud b./ the

CLEARING HOUSE.fo, Fed'ýral Sceren: c & 1echncaiInfo~matlon Sprinqtoeld Va ?2151

NAVAL RESEARCH LABORATORYWASHINGTON, D.C.