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USASRDL Technical Report 2258

THEORETICAL CONSIDERATIONS

ON THE EFFECTIVENESS OF CARBON SEEDING

bylia Robert Fenn

* U. S. Army Signal Research and Development LaboratoryCY. Fort Monmouth, New Jersey

L.j and

Hansjorg Oser-. National Bureau of Standards

Washington, D. C.

March 1962

U. S. ARMY SIGNAL RESEARCH AND DEVELOPMENT LABORATORY -'

FORT MONMOUTH, NEW JERSEY

U. S. ARMY SIGNAL RESEARCH AND DEVELOPMENT LABORATORYFORT MODMOUTH, NEW JERSEY

March 196 2

USAMDL Technical Report 2258 has been prepared underthe supervision of the Director, Surveillance Department, andis published for the information and guidance of all concerned.Suggestions or criticisms relative to the form, contents, pur-pose, or use of this publication should be referred to theCommanding Officer, U. S. Army Signal Research and DevelopmentLaboratory, Fort Monmouth, New Jersey, Attn: Chief, AtmosphericPhysics Branch, Meteorological Division.

J. M. KIMBROUGH, Jr.Colonel, Signal CorpsCormwinding

OFFICIAL:H. W. KILIAMMajor, SigCAdjutant

DISTRIBUTION:Special

ASTIA Availability Notice

Qualified requesters may obtain copies of this report from ASTIA.

This report has been released to the Office of Technical Services,U. S. Department of Commerce, Washington 25, D. C., for sale to thegeneral public.

March 1962 USASRDL Technical Report 2258

THEORETICAL CONSDERATIONSON THE EFFECTIVENESS OF CARBON SEEDING

Robert FennU. S. Army Signal Research and Development Laboratory

Fbrt Monmouth, New Jersey

and

HansjSrg OserNational Bureau of Standards

Washington, D. C.

DA TAM NO. 3A99-27-005-03

U. S. ARMY SIGNAL RESEARCH ,NID DEVELOPMENT LABORATORY

FORT MONMOUTH, N. J.

ABSTRACT

Presented in the report are: some results of machine computa-tions of the scattering functions, the extinction-, scattering-, andabsorption-coefficients for pure absorbing carbon particles, and thecompound carbon particles with concentric water shell of varyingthickness; and an analysis of the absorption properties of varioussingle particles.

The scattering and absorption properties of single particles areused to calculate the absorptivity, transmissivity, and reflectivityof three cloud models: a pure carbon particle cloud, a cloud of waterdroplets and carbon particles, and a cloud of compound concentric carbon-water particles. All three clouds are 1,000 meters thick and near theground.

The temperature change of one particle caused by radiation absorp-tion has been computed, and the total energy for evaporation of a. cloudmass has been estimated.

From these calculations it can be concluded t at a total carbonmass of the order of several hundred pounds per km will be necessaryto evaporate a stratus-type cloud.

CONTENTS

Abstract i

INTRODUCTION i

DISCUSSION 2

Absorption and Scattering Properties of Single Carbonand Carbon-Water Particles 2Absorption of Radiation by Carbon Particles Suspendedin the Atmosphere 15

CONCLUSIONS 24

"77ERENCES 24

Figures

1. E:tiiction-, scattering-, and absorption- 4through coefficients for carbon particles of varying ater through7. shell thickness 7

8. Absorption coefficient for constant total particle 9size as function of water shell thickness

9. Total absorption cross section for const. b/aand increasing particle size 10

10. Absorption cross section for constant carbonl1. nucleus size as function of water shell thickness

12. Scattering function for carbon particle with13. size parameter cc = 0.6 and 1 13

14. Scattering function for water droplet andcarbon particle with size parameter <x= 50 14

15. Total absorption coefficient for a given totalcarbon mass per unit volume as a function ofthe size parameter 16

16. Computed transmitted energy (ED), absorbedenergy (EA) and reflected energy (ER) forthree cloud models, as function of sun zenithdistance 19

Table

1. Absorption coefficients for water droplets(r = 6.265 a) with carbon particles of a = 0.171,0.215, 0.368 and o.480 radius, and for purewater droplets 12

THEORETICAL CONSIDERATIONSON THE EFFECTIVENFSS OF CARBON SEEDI

INTRODUCTION

The first big step in artificial cloud modification was t~ken in 1946when, through experiments conducted by Schaefer 1 and Vonnegut, the artifi-cial stimulation of precipitation from supercooled clouds became feasible.The teghnique applied by the two experimentalists was based on Findeisen'stheoryO that in supercooled clouds the introduction of nuclei could initiatethe formation of precipitation particles. Schaefer1 found that small piecesof dry ice could form a large number of small ice crystals in such a cloud,and Vonnegut discovered that, also, tiny crystals of silver iodide would bevery active as sublimation nuclei. Many successful seeding experiments withsupercooled cumulus clouds as well as supercooled stratus clouds have sincebeen carried out.

However, both of the above-mentioned seeding methods are confined tothe application for supercooled clouds only, whose temperature is below O°C;and all attempts to find a reliable method for the dissipation of warmclouds and fogs have been unsuccessful. The principal difficulty with warm-cloud seeding is that there is no "latent energy" in the cloud availablewhich, after liberation, could carry on the dissipation process by itself.

In the case of supercooled clouds, this latent energy is the energy offusion which becomes free after seeding and which has been provided in anindirect way by the decrease of the entropy of the system by nature itself.Whatever energy for a precipitation process or evaporation process is neededin a warm cloud, therefore, has to be fully supplied from an outside source.As such an energy source, the radiation energy from the sun is, of course,the most apparent. There are other forms of energy which could possibly beused; for instance, electrostatic forces for dissipation of fogs and clouds.These, however, will not be discussed in this report.

Using the properties of carbon-black particles suspended in the atmos-phere, several attempts have been made to absorb and emit sunlight, thusinfluencing, artificially, the energy processes in the atmosphere andespecially in clouds. In recent years, several investigators have madeestimates of the energy, absorbed in carbon spheres and clouds of carbon par-ticles; and various hypotheses have been developed on the processes whichmight occur in carbon-seeded clouds. However, all these computations of theenergy absorbed by carbon particles have been based on the so-called bulkmethod which uses the equivalent solid-mass layer for its absorption calcu-lations, or they were based on very rough estimates of the absorption crosssection. Such results, of course, may be po~siderably different from exactsolutions of the formulas of the Mie theory.

Actual carbon-seeding experiments have been carried out by Van Straten,Ruskin, Dinger, and Mastenbrook 5 and by personnel of the Air Force GeophysicsResearch Directorate, but none of these experimental tests of carbon seedinggave a decisive answer to the question of the effectiveness of this method.It therefore seemed desirable to conduct some theoretical studies on the feasi-bility of carbon seeding, including an evaluation of the absorption propertiesof carbon-cloud elements according to the Mie theory4 and to find from this asound basis for future experiments.

DISCUSSION

Absorption and Scattering Properties of Single Carbon and Carbon-WaterParticles

As mentioned previously, for a comprehensive solution of the problem itis necessary to investigate the optical properties of pure carbon particlesas well as compound carbon and water particles. The compound carbon-waterparticle, a carbon sphere with a concentric water shell around it, will be anidealization to some extent and will probably occur, in this form, only inthe case of condensation of water around the carbon center. However, it isthe only combination carbon-water droplet which can be treated theoretically.The exact 9 ormulas for such compound particles ha~e been worked out by Aden.and Kerker0 and are an extension of Mie's theory. They consider three dif-ferent media separated by two boundary layers. With this theory, the absorp-tion and scatteri±ng properties of pure spherical homogeneous particles withcomplex refractive index, and also of spherical particles with concentricshell of varying thickness can be computed. The following notations will beused:

9 = Scattering angle (@ = 0 is forward scattering)a = Radius of the inner sphere (carbon particle)b = Outer radius of the shellj = Wavelength of the incident lightm = n (I - n'i) = complex refractive index

= 27T"a/Ak = size parameter for aIP = 2 Jb/A = size parameter for bb/a = Specific ratio.

6According to Mie's theory and from Aden and Kerker's treatment, the fol-lowing quantities are derived.

The cross sections for extinction and scattering,

Qe = 2 i (2n + 1) Re(an + bn) (1)

Qs (2n +1). (jar + bn (2)

1

2

• I I I2

The cross section for absorption,

= Qe - Qs (3)

The absolute intensities,

i 1 ,11 ~2 and =2 12 12 (4.)

with Ii (n + ) an Trn + bn'n (5)

I2= . n Ja n Ln +bnT'n. (6)

The functions an and bn depend on the refractive index and the size parame-ter(s); the rn and n are functions of the scattering angle only.

Numerical computations have been carried out for Qe, Qs, il, and i 2 forpure carbon particles, refractive index m = 1.59 - 0.66i (b/a = 1), and car-bon spheres with a concentric water shell (b/a variable) for size parametervalues t from 0.1 to 200. The computations have been carried out underSignal Corps contract on the IBM 704 computer of the National Bureau of Stand-ards, Washington, D. C.

In Figs. 1 through 7 the computed total extinction-, scattering-, andabsorption-coefficients for compound water-carbon particles for variousratios b/a from I to 0 are plotted as functions of the size parameter. Since,per definition, the Qe, Q6, and Qa give the ratio between an area with whicha particle interferes with the incident light and the actual geometricalcross section, it can be seen that the effective absorption cross section ofa pure carbon particle (Fig. 1) for 1 4a < 4 becomes almost 1 1/2 its geomet-rical cross section. For a / 0.5 the extinction is practically due toabsorptic only, and for a > 2 scattering and absorption coefficients areof the saue order of magnitude.

For absorbing particles, the Q-functions are very smooth and do not showthe oscillations which are so characteristic for the extinction coefficientof nonabsorbing particles. However, as the thickness of the water shellaround the carbon particle increases, more and more of the effect of thedamping of the imaginary part of the refractive index is lost, and the oscil-lations in the Q-functions become stronger (b/a = 1.1, 1.2, 1.5, 2, 5 and 10in Figs. 2 through 7, respectively) until for very large b/a ratios the Q-functions approach the values for pure water droplets.*

*The curves in Figs. 5 through 7 for values P > 10 do not contain enoughcomputed points to identify them unambiguously. Q. (p-) for b/a - 10 ispractically already equal to Qs (cx) for pure water.

• I I II I I I I I I I II I I3

It

Fig. 2

L':tinction-, scattering-, and absorption- coefficientsfor carbon particles of varying water shell thickness.

0.2% 0. 41 0S .72 1.2 2.4 1.4 .3 7.2 0.6 1 2. H U 72 lIv

Fig.3

I.~ 2 5 5 0 20 20-.I' 2

0.5

I-

I 2

II

.1..02 % 1 ' 20 -j

Fi

I . 0

O I

1.5 I .i

(1.5

0.1 r0.2 0.5 1.0 2 5 6 51 0 20 -@0.2 0.5 0.6 2 5I S 12 14 20 50 - 0'

Fig. 6

jBxtinction-, scattering-, anu absm'ption-coefficientsfor carbon particles of varying water shell thickness.

IQ

0,~ I )2 I O l .5 8. 2P I 6 S I0 PS .- O

Fig. 7. Extinction-, scattering, and absorption-coefficientsfor carbon particles of varying water shell thickness.

7

In Fig. 8, the absorption coefficient Q. (referring to a pure carbonparticle as 100 percent), has been plotted as a function of b/a for constanttotal particle size ()v = const). It can be seen from this graph that forlarger particles (,P, ;10) the absorption coefficient of a carbon particlewill be increased even by a thin water shell (b/a = 1.1). However, if b/aincreases further, the water shell begins to reduce the absorption effectof the carbon nucleus. This shielding effect of the water shell is thestronger, the smaller the total particle size parameter.

According to the definition for Q., the absorption cross section ofone particle is

Ca =r . Qa, (7)

where r is the radius of the outer shell; i.e., in the case of compoundparticles, b is used instead of r. From this it follows that the absorptioneffect Ca of a compound particle which grows bigger and bigger disappearsonly if Qa(b) decreases more than b 2 increases with increasing b. However,since Qa is a function of cC and 9-, or of either oc or )P plus b/a, differ-ent results are obtained for equation (7), depending on whether b/a or P'is kept constant. If M and 04 grow proportionally (b/a = const), the increaseof b2 will always be of higher order than the one for Q, and therefore Ca-+oo as A increases (Fig. 9). Whereas, if c4 is kept constant and thewater is allowed to grow around the carbon particle (i.e., b/a variable),(0) will decrease much more for increasing %' (Figs. 10 and 11). In Fig.it is seen that even the efficiency factor for absorption Qa itself increasesabove the one for a pure carbon particle if a thin water shell forms aroundthe carbon core. In Figs. 10 and 11 for oC = 0.1 and c( = 1, the functionCa = b T' Qab/a) has been plotted. A normalizing factor C has been addedso that C . b . 7r Qa(b/a = 1) = Q,(b/a . 1), or since in this case b2 = a ,C becomes 1/a2 , which is constant per definition. Ca increases to a peakvalue two to three times the Ca for a pure carbon particle, and then dim-inishes again. This means that the water skin acts in the direction toincrease the absorption effect of the carbon particle. The absolute valuesdecrease considerably if the size of the carbon particle itself gets smaller.Computations uE to specific ratios b/a of 150 show that the absorption crosssection Ca = b 7" Qa remains finite and its obsolete value stays constantaround the value for Ca(B/a = 20).

An investigation was made of the wavelength dependence of the absorp-tion coefficient of carbon particles. From Fig. 1 it can be seen that forC< 4 1.5 and for 3< d 20 the absorption for carbon particles of constantsize is wavelength dependent, and that forOL L 1.5 the absorption is thesmaller, the larger the wavelength. The opposite is the case for 34.(-4 20.The range OC4 1.5 corresponds for visible light to very small particles(r 4 0.1.A). Over the wavelength range 0.34 A10.7, Qa can vary by a fac-tor 2. This results in the phenomena that industrial smoke quite oftenappears red-brown in the transmitted light if the particles are uniformenough in size and very small. As the particles become less absorbing(Figs. 2 through 7), the slope of Qa becomes flatter and the wavelengthdependence gradually disappears.

2 0

Fig. 8.Absorption coefficient for constant total particlesize as function of water shell thickness.

Iq

tto

00

I4-

0

CNN

'I

Q(b1*)

0., 0,

OS

2.20 j.

.2 I-

,2 0 2

Fig. 10

III

a . 1.

AbsorpDtion cross section for constant carbon

nucleus size as function of water shell thickness,

The influence of water absorption in the infrared region on the totalabsorption of compound carbon-,r t-: .- rticles must also be studied. InTable 1 the computed Q are listed for a t.:tal particle size b = 6.265,/t(to be comparable with Shifrin's computation. 7 ) and for carbon-particle radiibetween a = 0.171 and 0.48 ^ for wavelengths from 1.35 to 10 microns. Theabsorption data for water in these computations have been.taken from Dietrich8

and Shifrin. 7 It can be seen that the contribution of the carbon particle tothe total Qa decreases with increasing specific ration b/a, and if b/a islarger than about 10, only about 10 percent of the total absorption will bedue to the carbon nucleus. In other words, with respect to absorption proper-ties, a compound carbon-water particle with large b/a can be treated in theinfrared like a pure water droplet without introducing a large error.

Table 1. Absorption coefficients for water droplets (r = 6.265 ,) withcarbon particles of a = 0.171, 0.215, 0.368 and 0.480 radius,and for pure water droplets.*

Qa, water and carbon Qa, pure water

b/a=Z6.6 b/a= 29.1 b/a= 17 b/a=13.5 b/a=ooa = 0.171 a = 0.215 a = 0.368 a = 0. h0

1.35 0.0051 0.0o62 0.0121 0.01l11.5 o.o427 0.44o 0.0493 0.05372.0 0.0790 0.0798 0.0851 0.08953.0 1.1846 1.1846 1. 1846 1.1846 o.8943.2 1.1910 1.1910 1.1910 1.1910

3.4 1.0143 I.Ol4,4 1.0153 i.0162 0.9254.5 0.5004 0.5005 0.5022 o.5o4 0.5005.47 0.3716 0.3719 0.3734 0.37546.0 1.1311 1.1311 1.1312 1.1313 1.1277.0 0.7374 0.7376 0.7384 0.7395 0.70410.0 0.5751 0.5753 0.5757 0.5763 0.575

In Figs. 12 through 14 the scattering functions have been plotted for apure carbon particle for oY. = 0.6 and ory = 1 and also cc = 50. As a compari-son, the scattering function for a pure water droplet of the same size hasbeen added. It can be seen that the angular distribution of the scatteredlight for small OC-values depends only slightly on the refractive index.However, the total amount of scattered light is larger for carbon than forwater particles. The scattering function for large-size parameter valuesis particularly interesting since, until recently, no exact computations forlarge cX-values were available. With increasing o<, the convergence of theinfinite series of the an and bn becomes very poor, and more and more termshave to be computed. In addition, the number of oscillations in the i 1and 12 increases proportionally to OC. As Van DeHulst 9 has shown, the

7*Values for water droplets (r = 6 .25,0) taken from Shifrin.

12

/

;/ / /

-el

to

l lca

14

0

-- r

- - " - C

/ / "

IfZ

0

C)j

- a- S

a 0

icc

CI Iu,

Fig. 14. Scattering function for water roplet andcarbon particle with size paameter OC 50.

CU QIr a-

I I i g I I

20 80 60 .80 1OO 120 1180 160

1011

103--

10

I I I I I J

20 40 60 80 0 120 140 160

-14

distance between two consecutive maxima becomes approximately 180/ o. Thishas been proved by computations of Giese1 0 for water drops (cX = 25, 50, 100).It is also interesting to notice that these oscillations for absorbing parti-cles become completely suppressed for angles 9 ) 500. The broad maximumbetween 1400 and 1450 for water droplets which indicates the fogbow is notpresent for absorbing particles. It is also important to notice that forsuch large particles most of the total scattered light is scattered into thenarrow forward direction of about zero to 20, the intensities per unit solidangle being 103 times the ones for back-scattering angles. This property isindependent of the refractive index and the same for all O above 25. Thephysical explanation for this is that for large particles the diffraction oflight occurs only in these very forward angles. For most measurements itcannot be distinguished from the direct light, and therefore the Q. for suchparticles can be aisumed as I instead of 2.

Absorption of Radiation by Carbon Particles Suspended in the Atmosphere.

Before studying the absorption properties of a carbon-particle cloud,the optimum combination of particle number and size with respect to absorp-tion for carbon particles must be found for a given total carbon mass.

The absorption coefficient of a particle cloud per unit volume is

= N . r 217Qa (e), (8)

where N = number of particles per unit volume. If the volume of one parti-cle is V = 41r r3/3 and the total mass M of particles Der unit volume-isVt 4 S = density), the number of particles per unit volume isF-Vt . 3/4Wr 3 -3Mt/4.Vr 3 .S. And A becomes

or with r =oC . A /2W7,

fa =31r2 1 Qa(~

ra cont -L Q, (10)C(

In ?ig. 15, the function Qa (c()/cr is plotted, and the graphical solutiongives max for o. = 0.6.

For sunlight with an intensity peak at A = 0.5 micron, c = 0.6 corres-ponds to a = 0.05 micron.

it should be mentioned here that carbon black of this size is commer-cially available; however, it is very likely that these small particles willform larger.cong1merates during the dispersion process. Laboratory experi-ments on this problem wiil be necessary.

15

Q

*IIV4

IC 0/ 0

IV 4

/ 4

CIO

!After all necessary properties of single particles were investigated,a s dy of the processes of such particles in a cloud was begun. The follow-ing 'onsiderations and computations are based mainly on a thesis by G. Korb(19I, University of Munich, Germany) whose studies were carried out onSignal Corps Contract EUC-1612. The object of this study was to calculatethe absorption, transmission, and reflection of radiation propagating througha cloud. In order to understand the significance of the results, a briefsummary is given of Korb's solution.

In order to include multiple scattering effects in the cloud, a solptionmust be found for the general radiation transfer equation (Chandrasekharll).Korb's approach is to solve the equation for 2 + 2 TWradiation fluxes--oneupward, one downward and 2 IF fluxes in the horizontal. This approximationreduces Chandrasekhar's equation to a system of linear differential equationswhose solutions give the absorption, transmission, and reflection of radia-tion. The absorption is given as the amount of energy absorbed inside thecloud by particles and water vapor. The method also takes into considerationthe absorption of radiation by water vapor above and below the cloud. Thesecomputations of the absorption, transmission, and reflection have to be car-ried out separately for narrow spectral bands of the sun spectrum (dependingon the spectral dependence of the particle parameters), and eventually haveto be added up to give the total values. If the albedo of the ground surfaceis += 0, the same procedure must be applied to so-called auxiliary fluxes, i.e.,the diffuse radiation fluxes reflected from the ground sueface; and the result-ing absorption, transmission, and reflection of the primary and secondaryfluxes must be added up.

The first part of Korb's study included the computation-of absorption,transmission, and reflection for three model clouds of pure water droplets--a low cloud, a high cloud, and a cloud with large vertical extent.

Korb's method was applied here to calculate the absorption propertiesof a pure carbon particle cloud, a cloud mixed of droplets and carbon parti-cles, and a cloud of compound concentric carbon-water droplets, all threeclouds having a vertical extent of 1,000 meters, with their base near theground surface:

(a) Pure carbon particle cloud. The carbon particle concentration is104 particles per nm3 , 0.1-micron-diameter size. This is equivalent to approxi-mately 20 pounds of carbon black per 1m 2 for a l,000-me er-thick cloud. Thewater-vapor content in the cloud is assumed to be2 . 1- g/cm3 ; the totalwater-Mapor content above the cloud (above 850 mb) is 1.5 cm ppw (accordingto an average distribution over middle latitudes for summer, Korb, et ali2).

(b) Mixed cloud. The cloud consists of droplets of 4 microns radius,

597/cm3, and 104 carbon particles/cm3 of 0.05 micron radius. The water-vapor content above the cloud is the same as before--l.5 cm ppw; the satura-tion water vapor density in the cloud is assumed to be 8 • 10-6 g/cm3 at about+7.50C, and the albedo of the ground is zero.

(c) Compound particle cloud. This is a cloud of particles which con-sists of a spherical carbon nucleus with a concentric water shell. Thetotal particle size again is four microns radius and the concentration is

17

597/cm3 . (This number results from a water content in the cloud of0.16 g/m .) All the carbon particles of the cloud in paragraph (a) willbe inside the droplets, which gives 10,000/600 = 16.7 carbon particles/droplet. The size of the combined carbon-particle nucleus becomes approxi-mately 0.125 micron radius, which gives a specific ratio b/a = 32. Thewater-vapor content in and above the cloud is the same as in paragraph (b).

The sun spectrum from 0.2 through 10 microns has been divided into17 bands, and for each band the following quantities were computed:

nTr2 Qa + Tw kw (A)Ke jnrr2 Qe + 5w kw (A)

and T = j -( A) • dh, the optical density of the cloud. (12)f

Then the intensity of sun radiation incident on the cloud, Eo (A)

was computed; and finally the absolute values of absorbed, transmitted,and reflected energy were obtained. All computations have been carried outfor zenith distances of the sun of 00, 30*, 60 ° and 800.

The results of the computations are plotted in Fig. 16. In the graphsfor a mixed cloud, the absorption curve for a pure water-droplet cloud(taken from Korb's report) has been added for comparison. Also added is thecurve for Eo, i.e., the intensity of energy incident on the cloud top afterpassing through the upper atmosphere. Approximately 0.2 • cal/cm2 min.are absorbed by water vapor in the upper atmosphere above the cloud, forvertical incidence. In the case of the pure carbon-particle cloud, the per-centage of absorbed and transmitted energy is almost equal, with very littleenergy (< 5 percent) reflected back from the cloud top. For very-low sunelevations, such a cloud absorbs around 80 to 90 percent of the incidentradiation, although the absolute amount of absorbed energy becomes very smallfor low sun elevations. If, as a comparison, the absorption in such a purecarbon cloud for single &c4ttering only is calculated applying Bouguer's law,

Ea ( - e-L), (13)

substitution is made for N r2 ,'a = 5.5 10-7 cm"1 , and thepath length for zenith distance z = 0 is lO5 cm. Then, Ea/E o = 5.5 percent.The absorption by water vapor in the cloud is approximately 2.5 percent.This would give a tctal absorption of about 7 percent, only one-sixth ofthe actual absorption.

The optical properties of the mixed cloud are considerably different.About 60 percent of the incident radiation is reflected from such a cloudso that only a small portion of tne radiation penetrates into the cloud.However, it can be seen that, because of the carbon particles, about threetimes more energy is absorbed thian in vie pure water-droplet cloud. Onlyabout 12 percent of the incident lignt is transmitted through this cloud.

i8

NIH ZWO 0 GD 40 0 w at I"!

CdO C; - - 0 0 0

F p

C!UC

rd

~0

Lwa m.4 41

C..V

aco

.44

0)

~' =- . - a--a

-W o

*1 -H d.

WINI

A very in~eresting result is tat the optical properties of the mixedand the compound cloud are almost equal, the absorption of the mixed cloudoeiag 9hout 2 to 2.5 percent (of E') higher than for the compound particlecloud. From tixz.i&.t can be concluded that the form in which the carbon par-ticles are disr-,buted in the water-droplet cloud--whether they are in between

the droplets, or inside, or on the surface--makes little difference in theabsorption coefficient so long as the total carbon mass is about the same.This result is not too surprising if one looks at the spectral distributionof the absorbed energy. About 45 to 50 percent of the total absorbed energy

is absorbed in the infrared between two and ten microns wavelength, althoughthere is only about 27 percent of the total incident energy in this wavelengthrange. This is because of the high absorption of water in the infrared. Thiswavelength region is therefore influenced very little by the carbon absorption.

In the visible rangeA Figs. 10 and 11 show that for large b/a the absorp-tion cross section Ca = bl Tr' Q remains rather constant and is only slightlyhigher than the one for the carbon nucleus without water shell. This resultis important because it is not actually known what happens to the carbon par-ticles in the cloud after seeding--whether they will attach themselves to thesurface of droplets, or whether most of them will remain suspended in the air.It can be assumed that the rather special case of concentric compound parti-cles will exist very seldom--probably only if condensation of water on thecarbon particles occurs, most likely by radiational cooling of the carbonparticles during nighttiame.

So far in these calculations it has been assumed that the albedo of theground surface is zero. This means that the upward-directed radiation fluxat the bottom of the cloud is zero. The more light there is reflected fromthe ground back into the cloud, the higher the total absorption in the cloudwill be. Korb has computed the absorption, transmission, and reflection ofpure water-droplet clouds for various albedo values between zero and 0.9, andfrom his data it can be estimated that in the case of a mixed and compoundparticle cloud the absorption would be increased by about 2 to 3 percent(of ) if the ground albedo were 0.9 inqtead of zero. The increase inabsorption is so small because, in addition to the ground-reflected radiation, agreat peruzs of radiatiqn is reflected down from the bottom surface of thecloua. jjiJ ircreases the traramissivity of the cloud considerably. For thecarbon particle cloud, of course, higher ground albedo would result in a muchhigher absorption. The denser a cloud, the less influence the ground albedohas on the absorption of the cloud.

For energy processes inside the cloud, the vertical distribution of thetotal absorbed energy within the cloud must be considered. From Korb's thesisit follows that for a cloud with optical thickness 30 km-1 (as in the compoundand mixed-cloud model), for zenith distance z = 300 and ground albedo As = 0and Ka/Ke = 0.003, 50 percent of the total absorbed radiation is absorbed inthe upper 300 meters of the cloud; whereby, for 2 4 CZ-30, the intensity ofthe downward-directed radiation flux almost follows a distribution of theform E = -a t + b. The denser the cloud, the greater the percentage ofabsorbed energy in the upper portion of the cloud.

If results of this study are compared with previous calculations byother investigators, the rather detailed study by Smith, et al15 should bementioned. They have computed the transmittance, reflectance, and absorption

20

of a mixed cloud of droplets and small absorbing particles, neglectig theabsorption in droplets and applying the two-flux model by S. Fritz.W Forhigh optical thicknesses the two-flux model gives about 10 percut lowertransmission values, according to comparisons in Korb's report. Usingcalculations of Smith, Wexler and Glasser, 13 a cloud transmission of about5 to 10 percent, and a reflectance of about 80 percent, a 10 to 15 percentabsorption is obtained for the compound-particle cloud. This is for verti-

cal incidence. Computations made under this study give about 25 percentabsorption, 60 percent reflection, and 15 percent transmission. It seemsthat the two-flux model overemphasizes the reflectance of a cloud. Fordetailed discussions of the accuracy and significance of data obtained withthe 2 + 2lrflux model, reference is made to Korb's thesis.

Finally, an estimate is made of how much cloud evaporation or dissipa-tion can be achieved with this absorbed energy. The radiation energy whichis absorbed within the cloud is used for heating of the total air mass andwater-droplet mass, and then for evaporation of the droplets. If it isassumed that the absorption and evaporation process occurs slowly enough sothat equilibrium conditions are close between all the components and theatmosphere, then, for the energy budget,

dq - Cpa • 9'a * dT + cw - w dT + L • w. (14)

cpa = specific heat of air for const. pressure, 0.24 cal/g °C

S a = density of air, at 7.50 and 900 mb = 1.12 g/cm3

Cw, fw = spec. heat and density of water;w = liquid water content of cloud g/m3,

L = latent heat of vaporization of water, 590 cal/g °C.

Substituting these values into equation (14),

dq = 269 + 0.155 + 87 (cal/m3 )=356 cal/mo for a 10C temperature increase.

Heating of the carbon particles has been neglected completely because theirmass is only about 1/100,000th of the water content and it is seen that eventhe energy required for the heating of the droplets is negligible. The tem-perature rise which is required to increase the saturation water vapor con-tent from the original 8 g/m3 to 8.15 g/m° is approximately 0.30C. Fromequation (14), therefore, is obtained the energy required to evaporate thecompound-particle cloud and to achieve the necessary temperature increase of0.30C to about 100 cal/m3 .

In the case of the mixed cloud and the compound-particle cloud, theabsorbed eergy for sun zenith distances between zero and 30' is about0.4 cal/cm min. The air column below 1 cm is 1 • 105 cm3 = 0.1 m3, whichgives an average absorbed energy of 4 cal/m3 - min. This would result in anecessary absorption time of about 25 minutes. For a sun zenith distance of600, the absorbed energy would be only about 0.2 cal/cm 2 min. and the absorp-tion time therefore twice as long--apprcximately 50 minutes.

2 I

Actually, it must be expected that the upper 100 meters of the cloud,where the absorption per unit volume is about twice the average absorption,will start to warm up and evaporate first. This will, again, allow moreradiation to penetrate into the lower layers of the cloud. However, as soonas the upper layer starts to warm up it will also begin to rise and cool offagain. It certainly will be necessary to provide more than the minimum energyfor a 0.30C temperature increase if the evaporation process is to be maintainedlong enough to evaporate the cloud completely.

Van Straten5 suggested as a hypothetical process for the cloud dissipa-tion an evaporation and condensation process between droplets. Droplets con-taining many carbon particles would heat up more than pure water droplets,and therefore moisture would evaporate from the warmer droplets with thecarbon particles onto the colder pure water droplets.

A droplet containing carbon particles will absorb energy and conse-quently its temperature will rise. This again will cause an energy loss byconduction and evaporation. The energy budget can be written in the follow-ing way:

dEa = c • m . dT + 471 r • K (T - TO) + 47r 2 L dr (15)dt dt

c = specific heat of water = 1 cal. degr.-l 9 1M= mass of dropletr = droplet radius -K = therTal conductivity of air = 5 • 8 - 10' cal. cm

sec- degr-1T = droplet temperature

To= air temperatureY = water density = 1 g • cm

3

L = latent heat of evaporization = 590 cal g-1 . degr- 1

whereby dr D D (9d-w) (16)dt •r

D = coefficient of diffusion of water vapor = 0.22S cm2 . sec.1

Sd, 5 w = vapor density of water at the droplet surface andfar away from the droplet, respectively.

fd is a function of T and r, according to Kelvin's formula:

?d = M - Pw(T) • exp( (17)d , T xrT

= specific surface energy of water = 74.5 cal - cm-2

M = molecular weight of water = 18R = universal gas constant = 1.98 cal • g-1 . degr 1 .

Substituting (16) and (17) in- (15),

E c * m - T + 41Tr K(T-To) + 4Fr D w (T 1 2 -,T• _ • • exp(2 ) = ~). (18)dt dt F R rT

22

As a first approximation, it is assumed that r is constant and thefollowing abbreviations are used:

Cc = c m =2.68 * lO" 1 0 ca l degr "3

= 4T rK = 2.96 10-7 cal degr "I • sea "I

= 4 rLD= 0.67 cal gcm 3 sec l

2fM = 0.082 degr.

dEa = q- = 215 10- 11 cal • sec"1

S60

with Qa = 0.002, Eo = 1.5 cal cm- 2 min-

We then get

q = Q dT + (3 (T-To) + w (T) eT "w (To)

dt k 3

or cT+ (3 T + (T)eT q + ( To + (To) (20)

c q ( gT + f (T ) is constant. The magnitude of each of the threequantitieg ?q = 2.5 • iO- I I , (dTo= 8 • 3 i0-5, and J'. fw(To) =

5.4 -lO ), shows that q will have to be 100,000 times bigger to be of anyinfluence on the result of th s equation. This ionfirms Smith, Wexler, andGlaser's conclusion1 3 that l0 particles per droplet would be necessary toachieve a sufficient rise of temperature in the droplet.

An analytical integration of equation (18) will be extremely difficult,if not impossible. However, since in this study there is not much interestin the transient phase, dT/dt = 0 is assumed and T is calculated only afterreaching equilibrium conditions.

T +g2S'w (T) eT - c = 0. (21)

The numerical solution gives T = 280.460K or 7.3*C. The temperature of theparticle has decreased by 0.21C from the initial temperature, To = Tair.From an assumed air temperature of 7.50C, evaporation .ue to the curvatureof the droplet was obtained. Also, from equation (18), it can be seen thatthe condensation term is of the order 10"7 and the evaporation term is ofthe order 10"5; and the first term, the internal energy increase, is of anorder /1 0-10, which means that most of the absorbed energy is lost by con-duction to the surrounding air. This loss of energy to the air will actuallybe even greater since the heat transfer does not occur only by conductionbut also by convection. Consequently, the air temperature will rise almostas fast as the particle temperature. It has been shown that for smallabsorption rates the particle temperature may be even below the air tempera-ture because of evaporation due to vapor-pressure difference. Most of tfe

23

evaporated water from the droplets will be needed to mainta!.n saturation inthe heated air, and only a very small portion would be available for conden-sation on pure droplets. Tiereforc, ±L ct.u l stated defiaitely that anevaporation-condensation process cannot be contidered as a possible cloud-dissipation process9 and therefore the only possiLle dissipation process forcarbon-seeded clouds will be evaporation due to heating of the total air masswhich, as has been shown, requires very large quantities of carbon black.

This report has been limited to absorption processes only, and no dis-cussion has been made of any emission effects from carbon seeded clouds.For more information on the energy budget in clouds, a study is certainlynecessary. As a result of the very encouraging results of the first partof Korb's study and the results reported here, the studies by the Universityof Munich, Germany, have been extended under Signal Corps contract to alsocover various models of pure and mixed carbon and water clouds to a mucha extent and accuracy than has been done in work reported here.This extena(-. 3tudy will also include energy losses due to emission from thecloud.

C0NCLUSIONS

A summary of the results indicates that for a model cloud of approxi-mately 600 droplets/cm 3, 4 micron radius, from ground to 1,000 meters alti-tude (stratus-type cloud), seeding with 20 pounds of 0.05 micron radiusOArbon particles will increase the absorption of sun radiation within theCloud from about 0.15 to 0.4 cal/cm2 . min for 0* to 30* sun zenith distance.

The absorption, transmission and reflection are almost equal for amixed cloud of water droplets and carbon particles and a cloud of compoundconcentric carbon-water particles. This indicates very strongly that forSbsorption studies it is not very critical to know in what form the carbonpirticles are distributed within the cloud, i.e., whether they are containedwithin the cloud droplet or attached to its surface.

From estimates of the energy required for evaporation of the modelcloud it is concluded that for realistic field experiments it will be nec-essary to use seeding rates of the order of at least 100 pounds of carbonblack per km2 during high sun elevations and for relatively stable cloudformations. The necessary seeding rate may go up to several hundred poundsper km2 under less favorable conditions.

An analysis of the energy budget in the seeded cloud yields that anevaporation-condensation process will not be possible, and that evaporationof a cloud due to heating of the total air mass will be possible only undervery favorable conditions.

IEFMRENCES

1. Schaefer, V. J., Science, 104, p 457 (1946).

2. Vonnegut, B., Jour. Appl. Phys., 18, p 593 (1947).

3. Findeisen, W., Met. Z. 55, p 121 (1938).

24

4. Mie, G., Ann. Physik, 25, P 377 (1908).

5. Van Straten, F., R. Ruskin, J. Dinger, H. Mastenbrook, NRL Ept.

5235 (1958).

6. Aden, A. L. and M. L. Kerker, jour. Appl. Phys. 22, p 1242 (1951).

7. Shifrin, K. S., Doklady AN SSSR. Nowaya Serija 94, No. 4 (1954).

8. Dietrich, G., Ann. d. Hydrogr., 67, P 411 (1939).

9. vn pay~lst, Light Scattering by Smll Particles, John Wiley,New York (1957).

10. Giese, R. H., Met. Rundschau (1961).

11. Chandrasekhar, S., Radiative Transfer, Oxford Univ. Press (1950).

12. Korb, G., J. Michalowsky, and F. Meller, Tech. Rpt. No. 2,

Contract AF 61(514)-1005 (1957).

13. Smith, R., R. Wexler, and A. Glaser, Final Rpt, Contract AF 19

(6o4)-3492 (1959).

14. Fritz, S., Jour. Met. Vol. 11, pp 291-300 (1954).

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