Radiant Energy in Relation to Forests - AgEcon...

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.' MICROCOPY RESOLUTION TEST CHART MICROCOPY RESOLUTION TEST CHART

NATIONAL BUREAU or STANDARDS1963.A NAlIONAl BUREAU OF STANDARDS1963A

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PREFACE

The eneq..'}' required for forest growth and the hydrologic cycle, in ,vhich forest C'O\'er pln;vs an important part, is c1eriwd from the sun. The forester usually bikes solar energy for granted-as immutable in source,

IV TECENICAL BULLETIN NO. 1344, U.S. DEPT. OF AGRICULTURE

mits radiant energy is also presented. Three aspects of the forestenergy relationship are discussed: Forest transpiration, snowmelt, and forest growth. These aspects 'were selected because of their general importance in forestry, and because th~ writers had some famlliarity with background literature.

A startling contrast exists between our considerable physical knowledge of radiant energy and its measurement and the scarcity of the application of this 1 ..now]edge to furthering our understanding of forest-radiation relationships. The physics of radi!ttion are (,1 ear, and instrumentat.ion for radIation measurement is available-it is time for this illstrumentation to be employed in well-executed studies of the close relationship between the forest and the energy that produces it. Certainly, research in this field should produce new knowledge useful to forest and watershed managers.

Reference to commercial products a:!l.t firms ill this publication is solely for necessary technical information. No endorsement or 'warranty by the U.S. Department of Agriculture is implied.

W.E.R. and H.W.L. 1965

CONTENTS

Page

Radiant energy________________________________________ _ 1The physical laws of radiation ___________________________ _ 3

Rate of radiatioD ___________________________ ,_________ _ 3Wavelength of radiation_______________________________ _ Pe!l.k radiation _______________________________________ _ 5 6

Absorptivity, reflectivity, and albedo ___________________ _ 7 Emissivity and absorptivity: Kirchoff's Law_____________ _ 0 Radiati

VI CONTE~S Page

Solar radiation on the forest _____________________ ._________ 63

The reflecting leaL__________________________________ 6'\

Under the canopy___________________________________ i5

The absorbing foresk _______________________________ .. __ 63

The absorbing tree _______________ ._ ____ ____ ___ _ _ _ __ _ 65

The absorbing leaL________________ .. _________________ 65

The reflecting foresL _ _ _ _ _ _ _ ______ ____ __ _ _ _ _ _ _ _ _ _ __ ____ 66

The reflecting tree __ _ _ _ _ _ _ _ _ _ _ _ _ _ ____ _ _ _ _ _ __ _ _ _ _ _ _ _ _ 66

The radiating foresL__________________________________ 68

The transmitting foresL_______________________________ 69

Hardwood and conifer shade__________________________ 70

Effect of stocking___________________________________ 71

Influence on forest moisture relation::; ___________________ ~__ 79

Transprration_________________________________________ 80

Transprration at the leaL_________________________ ___ 80

Sources of moisture__________________________________ 81

Factors influencing transpiration amounts_ _ _ _ _ _ _ _ _ _ _ _ _ _ 81

Evapotranspiration estimates from solar radiation. _ _ _ _ _ _ 82

Snowmelt. _ _ _ _ __ _ _ ______ ________ _ ___ ______ ___________ 84

Snow reflection and radiation_________________________ 84

Ripening and melting________________________________ 85

Canopy closure effects_ _ _ _____ ___ ___ _________________ 86

Radiation and snow accumulation, melt, and runoff ___ _ _ 88

Influence on fore::;t growth________________________________ 89

Wood-producing lighL__ __ _ _ _ _ __ ___ _____ __ _ _ ____ _ _ _ _ _ __ 89

Reproduction_ __ __ _ _ _ ___ __ _ _ ___ _ _ _ _ _ __ ____ _ _ __ ___ __ _ _ _ 90

Thinning::;____________________________________________ 92

The solar fores!..________________________________________ 93

Literature cited_____________________ .. __ _ _ ____ __ _ _ _ _ _ _ ___ 95

Appendix____ _____ ____ ___ _ _ ________ _ _ __ ___ __ ___ __ _____ __ 104

A. List of symbols used________________________________ 104

B. Manufacturers and suppliers of various radiation equip

ment___________________________________________ 104

C. Derivation of view factor for forest opening____________ 105

D. C~ara~teristics, costs, and sources for radiation-measur

lUg JI1struments_ _ __ __ ___ __ ______ __________ _______ 107

E. True solar time____________________________________ III

L\5~- \

.\.- \~A~\ U.S. Department of Agriculture ..-Forest Service

Washington, D.C. 20250 March 1966

ERRATA

Technical Bulletin 1344, "Radiant Energy in Relation to Forests," Dated December 1965

Page 3, paragraph 4, line 9

Reads: lute temperature, of.

Should read: lute temperature, oK.

Page 16, Equation 14

Should read: I=ft~ (sin cJ> sin a+cos

P.adiant Energy in

I1.elation to . Forests

BY 'LLIAM E. REIFSNYDER, Professor of Forest Meteorology, Yale

UniveIsity School of Forestry, New Haven, Conn.

AND -';; A

RADIANT ENERGY

Radiation is one of the three physicnl proc.esses by which energy is transf(',rrcd from one place to another. It is the process by which energy is :'propagfLted through free space by virtu~ of jOi!1t undulatory vltrilttions in the electric and mabl"Jletic fields in space." 1 The tmnsfl'!' (X'CUt'S at th(~ speed O'f light, does not depend on the pre6ence of matter, iLnd ItS a pr(){~ess exhibits both wlLVelike and particulate pht'>t10meniL, It, (){''(~\lI'S in high-fr('(lltfulcy cOEmi-c waves wiih waveh'ngths about one-billionth of a micron (1 micron = one-millionth of a metl't') to low.fl'equc([lt(>ncy (Ioltg-waV(~lengt.h) mdi:dion has less energy IWI' qUIlIltum than high-frcquoTley m,cliation. One mole of quanta (I einstein) of red light. with a w:tVelength of 0.67 microll ha.s an E'nprgy of l-~,O()O c:llot'ies, ",herea...,; I einst(,in of blue light with a. wfL\'elt~ngt h of ().47 micron has :m enelogy of (;0,000 c:t1orie.c;.

Fm' heal. t mnsf('.r purposes, radiation elm be measured in lLny convrnient Nll>t'gy unit. Tn PllginecI'ing pntetice, t.he usual measure of

~I'hls d('finition and otht>r qllot('d definitions in this bul1(>iin nn' from TTusehke. Ralph I'J. ('(I.). Ulossnry of IIIt'teorology. AlIIerit'nn }\[ph'orologienl RO('\t,ty, BostOIl. GaS pp, 1()-;m.

I

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01

2 TECHNICAL BULLETIN NO. 1344, U.S. DEPT. OF AGRICULTURE

BAND: RECOMMENDED BY THE

DUTCH PLANT I'lRADIATION COMMITTEE

B

i-----SOLAR RAOlll,TlON -------+i!---TERRESTRIAL RADIATION ---~

- L TfiAVIOLET, -+"' S...t,NE.R INFRARED ---1----- FAR INFR.RED ----~ ISLE \

10 20 50 '00 WAVELENGTH. MICROIlS

IfIGURE I.-Wavelength of solar and terrestrial radiation and spectral bands, as defined by Dutch Committee on Plant Irradiation (Brook::; 10Ci9).

radiant energy is the British thermal unit (B.t.u.: the amolUlt of heat required to mise 1 pound of water 10 F.; rates are usual1y expressed in terms of square feet. wd hours (B.t.u./ft.2-hr.).

In the metric system, the gram calorie is a convenient unit (252 gram calories = 1 B.t.u.) , and the usual area unit is the square centimeter. The langley is defined as 1 gram calorie per square centimeter (cal./cm.'), and the rate measure is langleys per second (1y./sec.) or per minute or per day. As a point of reference, at about 400 north latitude, the earth's surface will receive about 500 ly./day in the summer, and about 100 in the winter. To convert x ly./min. to B.t.u./ft.'hr., multiply x by 221.

Because of the importance of light to human life, a series of concepts and terms relating to the visible portion of the spectrum has been developed. The lux is the unit of illuminance, as Lhe langley is the unit of irradiance; that is, an illuminance of 1 lumen per square meter is defined as 1 lux. The corresponding term in English units is the foot-candle, an illuminance of 1 lULien per square foot. The foot-candle was originally defined as the illumination provided by a standard candle burning at a fixed rate on a I-square-foot surface that is everywhere 1 foot from the candle. The standard candle has now been superseded by a definition of source intensity in terms of a more reproducible Bhmdard. It is defined as one-sixtieth of the luminous intensity of 1 square centimeter of platinum at its solidification temperature (2, 0460 K.) .

Since radiation is It flow of energy from lOne place to another, it can be referred to as It flux. Radiant flux density is the rate of flow of energy through a unit area of specified surface. It may also be referred to as the irrndiance. The irradiallce is not a vector quantity

3 HAOIANT ENERGY IN RELATION TO FORESTS

since it refers to the sum of all radiant energy incident up~n a surface (or passing through the surface from one side) irrespective of the direction of the incoming rays.

The term "foot-candle" is widely used in illumination engineering. Full moonlight produces an illuminance of about one-fiftieth of a foot-caneUe. Dlumination of about 20 foot-candles is considered adequate for reading. Full sunlight with the sun at the zenith produces

an illuminance of about 10,000 foot-cancUes on a horizontal surface. Although it is impossible to convert langleys to foot-candles accurately because the latter !tpplies only to the visible portion of the spedrum, a rough conversion can be made. For full sunlight in a clolidleBs sky, multiplication of the solar radiation intensity expressed in langleys per minute by 6,700 will yield an approximation of the illuminance all a horizontal surface, expressed in foot-candles, "within 5 per(ent. Because of the difference in spectral distribution of short-wave energy on a cloudy day, the multiplier then is about 7,000 (Kimball 1924) .

THE PHYSICAL LAWS OF RADIATION Sen'l'ld physic:t1 laws dl'seribe the radiation processes. Study of

these laws not only will aid in the qualitati\'e understanding of radiation pl'oeesses, but also will provide the tools for many quantitative estimat.~s of ('aelia/ion effects impol'tant in forestry. Most of these laws express the I'l'latiol1::lhip of nU'ious aspects of radiation to temperature. .

Rate of Radiation

Anythin~ tlm.t is WRl'mpl' than absolute zero (-273.20 C.) radiates encI',g"},-and at it I'lLte proportional to tIle fourth power of the absolute tl'mpprattlll'. For any t"elllpernture there is tl theoretical maximum rate of encr~y thnt cl1n be emitted by a so-called blark body. (See p. S for It detailed dis('ussion of hlaC'k bodies.) The law is written:

(1)

whl'l'C lVlI is the ratp at whi('h radiallt PIlerg}' is emitted per unit time PP(' unit surfa('e area of the bln.ck body (ly./min.), a is the StefanBoltzmann eonstant (8.132X lO-n ly. 0](.--1 min.-1), :md T is the nbsolute temperature, of. (0('.+273") of the black body.23

The implication of this la,,' that ('\'l'ry existing body radiates energy bears emphasis. Thlls, a hlac'k body at the tl'mperature of sublimating dry iN (-lB.;)') C.) raciiai(>s pnel'gy ttt the rate of O.E~ ly./min. A blac-k bocly at room tl'rnpemtnre (2P C.) radhLtesO.61ly./min. 'rhe Hiln l'nilia/('s:lt a bla('k-IJOcly t('mperatul'(' of n(>lIl'ly (i,OO()" K., and thus emits 105 1y.lmin., mol'l' than HiO,()()O tinws that Qf the l'of.lrn-tl'mperatu!'l' objpd. _\ doublin{! of the uhsolute tl'lll pprH furl' (not the temperattll'l'e in ce.) I'I'",nIts in R sixtl'enfol

4 TECHNICAL BULLETIN NO. 1344, U.S. DEPT. OF AGRICULTURE 1.0

/ I ..

.. /

/V

/'V

V .' /

V/.l

-20 10 20 30 40 10-'0 '0 TEMPERATUR', ac.

FIGURE 2.-Black-body radiation.

Radiant energy is emitted iH !\ll directions from a flat radiating surface, not just in the direction perpendicular to the surface. According to Lambert's cosine In w, the radiant intensity (flux per unit solid angle) p.mitted in any direction from a unit "perfectly diffuse" 4 radiating surface varies as the cosine of the angle between the perpendicnlar to thesurfaceanc1 the direction of the radiation. Although the cosine law applies rigoronsly only to perfectly diffuse bodies, it applies reasonably well to m05t natural bodies. An incandescent sphere (e.g., the sun) will appear uniformly bright when viewed from a distance in ('onrormity with Lambert's law. Although the flux of radiation from a unit area on the side of the sphere is less toward the \Tiewer, the viewer sees more area in a unit solid angle of vision. The two effects compensate exactly, and the viewer appears to see a flat disk of uniform brightness.

The term "perfectly diffuse" refers to the property of rough surfaces to follow the cosine Jaw when Hluminated by light from any angle. A surface that re/leds such light according to the cosine law is called a perfectly diffuse surface. However, the term may also be applied to surfaces radiating by ,Irtue of their own temperature according to the cosine Inw.

5 RADIANT ENERGY IN RELATION TO FORESTS

Wavelength of Radiation

A black body emits energy at all wavelengths as l1escribecl by Planck's (Un:3) law:

(2)

wht>r~ H\ is the intensity of the emitted radiation of W!lyelt'llgth, A, pel' 1\l1it \\'an'It>l1gth PH unit Hl't'H of hlHek-body slIrface at temperatul'P 1',' and ('\ and r~ arp unin'l'!-ml ('onstants.n Figure 3, a plot of lL. for Sp\'pl'lll temperatures, itl(lkatps that bodies at high temperat m'ps not only mdialt' pnel'gy at a greater rate than those at low tt'Illperatnl'l's (arpa unr the C'lll'\'P), but also radiate the. bulk of their ellHgy at shortt'l' WH\'plpllgths, .\::; indicated by the dashed line, }lC'ak int('llsit h>s at higher (Ptlljlt'l'atllrp:-l arE' also at :-l\)ol'ter \\'a \'p1(' tlgtlll',

Solutiott of pquatiotl ~ is ratllPr [t'

.000


Peak Radiation

The reciprocal relationship between the wavelength at which the ra.diation curve peaks and the temperature of the radiating body is expressed by Wien's law:

A =2897 max. T (3)

where Amax. is the wiwelength in microns of maximum intensity per unit wavelength and l' is the absolute temperature in degrees Kelvin. Figure 4 is a pll)t of this relationship showing the wavelength of maximum emission for several representative temperatures. Objects at normal tetTestrial temperatures radiate in the infrared and are not visible by virtne of their own emis.'3ion. They can be seen only by reflected or transmitted light, and their color results from some wavelengths being reflected or transmitted more than others.

This expression for 'Vien's law gives the wavelength of maximum radiant energy per unitw!1velength: However, 've can also define the maximum in terms of unit frequency, in which case the law assumes the form :

5099A =-- (4)1lUU. T

Hottel (McAdams 1954) suggests the use of the wavelength that di,rides the emission spectrum i.nto two equal-energy parts. The displacement Jaw so defined is:

(5)

1.CW

SUN

i

iI

, i\

i\?

HOT GROUND SURFACE (150' F.)

MEAN TEMPERATURE OF THE EARTH (57'F.)'.000

tO~D GROU~D SURF7E (O'F.) Ir---Mi ,.:--:-==- ---FF I :1$jj;J I 8 10 12 '6 '8 WAVELENGTH. MICRONS

l


Hottel also presents, in the same reference, a universal diagram that permits quick calculation of the percent of total energy found below a specified wavelength, as a function of AT.

The color temperature of a body is "an estimate. of the temperature of an incandescent body, determined by observing the wavelenf,rth at which it is emitting at. peak intensity (lts color) and using that wlwelength in ,Vien's law." Thus, figure 4 may be used to determine the color temperature of a body if the peak wavelength is known or can be estimated. The cGlor temperature would equal the true temperature if the rac1iatol' were an ideal black body; fOl' actual bodies, the color temper'ature is an approximation. For example, the color temperature of the sun is about 6,100 0 K., about 100 0 or so higher than its blackbody temperature.

Opaque solids emiL radiation in a continuous spectrum, according to Planck's law. Although the slln is not an opaque solid, it radiates very nearly as It black body, with the vNtvelength of maximum emission of radiation ahout OA7 micron. All hut 0.1 peY'cent is emitted between 0.15 ancl4.0 microns. The earth also radiates, but its maximum lies neal' 10 microns, in the infrared region. More than 99 percent of the earth'!:; radiation is emitted between 4 and 100 microns; thus there is \Tel'y Ii We overlap between solar and tenestrial radiation. This permits ns to treat, the two independently. Solar radiation is frequently referred to as Sho7't-1Om'e radiation and terrestrial radiation as long-luave radiation. Figme 5 shows black-body spectra for objects radiating at the sun's temperature and the earth's temperature, adjusted to the same peak intensity. Actually, the area under the solar curve should be abont. 160,000 times that under the terrestrial curve, if l'mittpd l'a(liation is being considered. However, if solar radiation received at the earth's surface at noon on a cloudless day is being considered, the area under the solar curve should be only three to four times that. under the terrestrial curve.

Another useful temperature concept is the effective (radiational) fem.peral,m'e, that. temperature at which a perfect radiator (black body) w,'ilcl radiate at the same rate as t.he imperfect radiator in question. The sun's effective temperature is about 5,700 0 K.; that of the clear night sky may be about 250 0 K. (-230 C.). The effective temperature is always less than the true tempernture of a body; both would he equal for a perfectly radiating black body-something that does not exist in nature.

If all object SIllToUluled by radiating surfaces is in radiational equilibrium with these surfaees (i.e., it. is losing as much radiant energy as it is receiving), its temperature is known as the'I'Mrtn1'(fdiant tem.pera

.. hue. ",Yhen the mean radiant temperature of the surroundings and the object's aetual surface temperature are known, it will he underst.ood whether the object will gain or lose heat. by radiant exchange with tIle surroundings.

Absorptivity, Reflectivity, and Albedo

Natural opaque bodies absorb ollly a fraction of the radiant energy incident upon them. This fraction, the aO.w1'ptivity, varies between ofor a pedeet refledor and 1 for a perfect absorber-a black body.


The fraction reflected is the refiecti'vity, and for opaque materials the sum of the absorptivity and the reflectivity must equal 1.

The term "black body" is derived from the fact that materials that absorb all incident light appear black to the eye. However, the definition is not restricted to visible light, and black-appearing materials mayor may not be good absorbers of radiation in nonvisible wavelengths. Conversely, light materials may be good absorbers of nonvisible long-wave radiation. For example, new snow is a poor absorber of short-wave radiation, but a good absorber of long-wave radiation. However, galvanized iron absorbs solar 'wavelengths very well, but absorbs long wavelengths poorly. Moist earth is a. good absorber of both long and !:hort wavelengths; aluminum foil is a poor a.bsorber in both regions.

Absorptivity and reflectivity can be defined for single-wavelength (monochromatic) mdiation or for all-wave radiation. It is also possible to define a part-spectrum absorptivity or reflectivity, as appbed to visible light, solar radiation, or some other restricted band. The term "albedo" usually refers to the reflected portion of a specified spectral band, such as the entire solar spectrum or the visible portion, while the ter'm "refieetivity" is usually restricted to specified monochromatic refleetion. Past and present usage varies considerably, and literature referenees to albedo and reflectivity must be interpreted cautiously.

The physical proeess of absorption of radiation is rather complicated and depends on the atomic and molecular structure of the absorbing material. Sin('e radiRnt energy exists in discrete quanta of varying energies depending on wavelength, the absorption of these quanta im

, i:

0) .5 1,0 5 'MIVELENGTH, MICRONS

,"~lGURE ;i.-Comparison of solar and terrestrial radiation, arbitrarily adjusted to the same peak intenSity.

100

9 RADUL~T E~~RGY ~ RELATION TO FORESTS

parts varying increments of energ-y to the absorbing ~edium. Absorption of radiation always results in the transformatton of the energy to radiation of another wavelength or to some other form of energy.

~fost of the energ-y in solar and terrestrial wavele.ngths .absor~ed by matter il:l converted into thermal enerf.,ry that mamfests Itself In the temperature of the matter. Howe\-er, the absorbed energy does not go immediately into increased translational enerf.ry of the molecules or atoms (the energ-y that determines temperature); it goes first into vibrational or rotational energ-y of the atoms and molecules, and into internal energ-y assoclded with the binding- forces within the atoms or within the nucleus itself. Translational energy of the atoms and molecules, and thus the temperature of the absorbing medium, are increased by the con,ersion of rotlltional and yibrational motion by intermolecular collisions, and the deg-radation of internal energy.

In general, high-energy quanta, suell as gamma rays, are required to produce changes invoh-ing- the nudeus. Electrons close to the nucleus can be excited by absorbed X-rays. Le~s tightly bound valence electrons ('[In be raised to hig-her energy le,els uy quanta in the visible light region. Low-ener~ry quanta in the infrared reg-ion may induce higher vibmtional states ir. atoms ('ombined in molecules, while lower energy rotational changes are caused by even lower energy quanta of far-infrared radiation or longer mdio waYes.

Monatomic gases generally absorb radiation in \"ery narrow wavelength bands, corresponding- to quantum energ-ies nee


called the absorptivity (in this case the monochromatic absorptivity). In general, this monochromatic absorpti\-ity will vary with the temperature of the absorbing body and the w:\\-elength of the incident radiation. It is convenient, however, to average the spectral absorpth-ities to obtain an integrated value representing the ltverage absorpth'ity to black-body radiation corresponding to a particular source temperature. Of course, this average absorptn-ity will vary somewhat if the 50l:-,,'':e does not radiate as a black body. However, we can st.ill specify t~_ average absorptivity to radiation from a natural source, such as thesun, which does not radiate precisely as a black body. Also, for most opaque solids at terrestria.l tempf~ratures, the absorptivity shows a very weak dependence on receiver temperature, and no correetion for temperature variation is necessary.

The emissivity of natural bodies, as indicated previously, must also be less than unity since nothing radiates exactly [1.'3 a black'body. Any object with a temperature above absolute zero will radiate energy at various wavelength::. and one can determine the emissivity at each wavelength. As with absorytivity, one ca.n find all lwemge emissivity that ItppJies to a surface radIating at a particular temperature, whether or not the surface is emitting as a gray body (a hypothetical body that absorbs some constant fraction between 0 and 1 of an the radiation incident upon it). The emissivity ofa surface depends on its roughness as well as its temperature ..

Emissivity and absorptivity are directly related. Consider 11 body completely surrounded bya.n enclosure of uniform temperature with whirh the body is in thermal equilibrium. The body will gain heat by \-jrtue of its absorptivity and the incident radiation. It wi1llose heat by virtue of its emissivity and temperature. N ow if the absorptivity were larger or smaller than the emissivity, the body would experience a net gain or loss of heat. Since this is contrary to the second law of thermodynamics and is contradicted by experience, it may be concluded that at thermal equilibrium, the emissivity and ahsorpti\-ity of thebocly are the same. This is one form of Kirchoff's law, which may also be stated as follows: at thermal equilibrium (i.e., I;'quality of temperature of source and receiving surfa{:e), the ratio of the total flux. density from a surface to its absorpth-ity is the, same for all bodies, and is equal to the radia.nt flux density of a black body.

(6)

The often-quoted corollary of Kirchoff's Jaw that good radiators of energy are good absorbers needs the qualification of wll\'elength and temperature. Since we are concerned with terrestrial surfaces in a narrow range of temperatures, tlle primary qualification is that of wavelength. As notedearlier, fresh snow is a poor absorber of solar wlwelengths, but a good emitter (and absorber) of long wavelengths. In contrast, aluminum foil, an equally poor absorber of solar wavelengths, is also a poor emitter of long wavelengths.

For many purposes, then, it is adequate to consider the absorptivity and emissivity of terrestrial objects 1ll two broad \YIn-elength bands: the short-wave and the long-wave region. Objects at norma.] terres

http:radia.nt


trial temperatures may be assigned composite long-wave emissivities derh'ed from comparisons of measured. emittance to black-body emittanee. For incIdent radiation of the same spectral distribution, the band absorptivity will be the same as the emissivity. Radiation of a dift'erent spN.'tral distribution will not, in general, be absorbed in the same. proportions, so the band absorptivity will be different. But these dIfferences may not be great through the normal mnge of terrestrial temperatures and consequent long-wave radiations, and it is permissible t.'1 assign a single absorptivity (and identical emissivity) for objects in the long-wave region.

Significant amounts of solar wavelengths are not produced by objects at normal terrestrial temperatures; however, a tiny amount of 5hort-'\\'a'-e enerp:y is emitted. It is not necessary to consider shortw(we emission of terrestrial objects. However, these objects absorb to some degree the short-wave solar enerp:y incident upon tllem, and it is possible and useful to consider the absorptivity of terrestrial objects to solar radiation. (This absorptivity is, of course, equal to the emissivity of terrestrial objects at these wavelengihs but, as pointed out, the total emission of short-wave radiation by objects at terrestrial temperatures is so small as to be totally insignificant.)

Absorpti"ities and emissivities for several common materials are given in table 1.

TABLE l.-.r;,,'!lOrt-ll'fI/'f a7)80rptil'ity aM long-ware emi.~8it'ity of Mme ('ammon material.~ (11'071'1> B1'ooks 1959)

::.'.Iaterial Short-wave

absorptivity

Long-wave emissivity

New snow ... ________ _________________________ _ Dry sand. ________________ ___________________ _ \Vet sand_____________________________________ _

0.13 .82 .91

0.82 .90 .95+

~i~ 1~~~t==:=:: :=:::: _::::::::::::::::::====::Aluminum foiL ______ . ___________ ___________ .. __ Galvanizrd iron _. ~ __ ____ ________ ________ _

.68

.86

.15

.65

.90+

. 90.1

.05

.13

Radiation Emittance by Natural Materials

The :::itefan-Boltzmann J'elationship app1ies rigorously only to perfeet black bodies, whil'll do not exigt in nature. The radiation emitted bv any natural body is always less than black-body radiation because the emissivity of the material is always less than 1. Accordingly, the Stefan-Boltzmann law for natural materials becomes:

(7)

where is the appropriate integ-rated emissivity.


Transmissivity

So -far, we have considered only opaque bodies; that is, ones that absorb or reflect the radiation incident upon them. A large class of natural materia,ls, howeyer, transmits a portion of the incident radiation. Thus, we may define tl'an.rsmis.rsi:I.'ity as the fraction of radil!tion incident upon an objeet that is passed throug-h the object. For a particular object, such as a sheet of window glass, the sum of the three fraetions-absorptivity, refledivity, and transmissivity-must equall.

However, transmissi \'ity of a translucent Or nonopaque object depends on its thickness-energ-y is absorbed, reflected, or scattered as a beam of radiation passes through the object. In describing this absorption, it is conyenient to have a property value that is independent of the thickness of the material. Such a measure is the absorption coefficient, defined by Bouger's law:

(8)

where Ix is the. radiant. Jlux density (rate of energy transmission per unit area) at distance x from the source where the flux density is 10 , The absorption coefficient, Ie (sometimes called the extinction or attenuation coefficient), is usually defined for a single wavelength, although it can be generalized to include a band of some width. How8'.er, radiant energy is usually absorbed differentially by a partially transparent medium. For example, glass appears colored because some wavelengths are absorbed more than others.

Although fractional absorptivities and transmissivities are dimensionless ratios dependent on the thickness of a translueent medium, they are related to the absorption coefficient as follows:

(9)

where u>.(x) is the absorptivity of a slab of material of thickness x. and absorption coefficient, k>., for normally incident radiation of wayelength,\..

Radiation Received by a Surface From a Point Source

Radiation from a point source spreads out equally in all directions in It transpar('nt mf'diull1. Since the flux throug-h each concentric "phere surrounding- the point must remain the same-and spheres with larger radii have larger surface areas-the flux of radiation through areas of the same size \\'i)] d('crease as t11(' meli us of the sphere increases. Since the surfaee tu('a of n. sphere is proportional to the square of the radius, the fl ux throug-h lIll it tLreas wi 11 decrease i II the same proportion:

(10)

where 1(1 is the radiant flux measured 'at distance 1'" from the source. lf R is defined as the radius 'ector of the eaIth (the ratio of the


actual sun-earth distance to mean distance), then the radiation received by a surface outside the earth's atmosphere is:

(11)

where 10 is the solar ('onstant. Yalues of it ar"e tabulated for various dates of the year in the Smith

sonian :Meteorological Tables (List 1958). Variations in the. amount of solar radiation received by the earth because of this disbmce \"luiation are about -+-3 percent.

Direction of Incident Radiation

A su.dace perpendieular to a. beam of radiation wi11 have i.ncident upon it an tLlnount equal to the radiant flux density. Any other surface not perpendjcular to the beam wm receive less energy per unit ltrea boc[luse the radiation will ,be spread over a, larger area. This geometri(,ltl relation is expressed by the cosine la.w of illumination:

1,,=locos/3 (12) w'here

I. is the flux densit\" on the surface;

Jf) is the flux densi(v perpemlieulltr to the beam:

11ml/3 is the angl(' of incid(,llee of the be.am (i.e., the angle between

the beam and a perpendicular to the surface). Thus. if fiux density is known, the radiation in6dent on any smface may be ('lllculllted if th(' angle between the beam and the perpendicular to the surfaee is known.

The cosine law of illumination is superficially similar io Lamberfs cosine lttw (see p. 4). However, there is a fundamental difference: the cosine Jaw of illumination is it purely geometrical relationship, wberea:, Lambert's law is a property of matter.

THE SOLAR ENERGY THAT REACHES THE EARTH'S SURFACE

The Hun is the Singh.' noteworthy soun"!.' of heat for th(~ earth's atmphere. Out illto interIlianewry spa(e from this gigantie body, wbose diameter is more than 100 tiuws tiIP eartb~':! and whose surface is estimated to han' a temperature of more tlulll lO,OOOoP., streams a tremendous mas:; of radiant energy. ll'rom eacb SClllar.:' yard of the sun's !:mrfal"e is b(>ing nldiated energ~ e1:111i\'ai('nt to a'llout 100,000 hOl"lll:'power. Although the ('arth. n('arl~' !)3 million mill"s distant, intercepts le;.,'1:l than OBI' two-biUiontb 'part of tlIP soiar output, this fraction amoullt.~ (ontinuously to 2.3 trillion horsepower. The earth as a whole re1:eiyes e\'eLY minutf' Ull much en('rgy as mankind lltilil'A:'S in a y('ar. Y('t to this small per

14 TECffi.'\'"ICAL BULLETIN NO. 1344, U.S. DEPT. OF AGRICULTURE

The amount and distribution of the solar energy that reaches a particular spot on the earth's surface depends on the geometry of the earth's orbit !Lround the sun, the orientation of the spot (its slope and aspect), the attenuation of the solar beam imposed by the earth's atmosphere, and obstructions by local topography and vegetation. 1'he spectml distribution depends particularly on the composition of the atmosphere. In the discussion that foI10\\'5, the sun-earth relationships--negleeting atmospheric effects-are eonsidered first; the important effeet of t.he air imd its constituents is considpred later.

Geometry of the Earth's Orbit

The earth travels around the sun in an elliptical path, tracing out a plane called the plane of the ecliptic, in whieh the sun is loc~lted at one of the foci of the ellipse. It takes 365% days for the earth to rno\"t~ around the sun. The earth is doser to the SUIl on December 22 tlHLIl on .Jllne ~l (;llP. winter' and summer solstiees) and still closer on Man'h :Jl and Heptember 23 (the spring amI fall equinoxes) (fig. H). ~\s indicated previously, this variation in distanee accounts ror tt maximum ddferenee of about 3 percent in the amount of solar radiation r('(:eived by the earth. Latitude, tilt of the earth, and slope and aspect of its surfaee exert the major geometrical controls over the amount of energy received by a particular area.

Effect of Latitude

..:\s tIl(' earth folloW's this ellipse, it. spins one revolution every 24 hou/s. If the earth spun upright (i.e., its axis of rotation perpendicular to the plane of the ecliptic), then from any point on its surface. the sun would be obsenred to always follow the same eourse. At the Equator it would always be overhead at noon. At the poles it would travel in a complete circle split in half by the horizons. At latitude 45" N.-about the la.tituc1e of Bangor, Me., Minn~lpolis, and Portland, Oreg.-the noon sun would be 45 from the zenitll.

SEPTEMBER 23 ......-

DECEMBER 22 t JUNE 21

--MARCH 21

FIGURE G.-T.he eurth's orbit.


In Columbia, S.C., and Los Angeles-at latitude 34 N.-it would be 34 from the zenith.

This is actually the situation during the equinoxes; the earth's position iB such that th~ sun's ra:ys are perpendicular to the axis of rotation (i.e., to some point on the Equator), and just ~I:aze the poles. For the region between, the amout of radiation received per unit of horizontaJltrea is directly related to the eosine of the latitude. Thus, soh!' radiation striking the Equator would be distributed over an area at right angles to its incidence (fig. 7). But at Columbia, 8.(,., and Los Angeles, ;34 to the north. the same am01l11t of radiation would be scattered over a larget area becallse of its angle, and the radiation rereived pel' unit, area would be cos :3J O of the mdiation received at the Equatot !lC'('ol'dillg to the cosine Jaw of illumination (equation H). Thus, if 1.50 Jy./min. are l'eceiyetl at the Equator 011 March 21, then cos 31Q x Uj or 1.2+ ly./min. are received at. Columbia, S.C., and Los An.!!eles, and cos 45 x 1.5 or LO() ly.!min. nre received at Bangor, l\finnea po] is, ilnd Portland.

Effect of Declination

If the axis of rotation of the earth wet'e perpendicular to the plane of the ecliptic, the pattern of sunlight would be the same every day of the- year at a PltJ'licular place on the earth's surface. But the axis or the earth is tilted :28% from this perpendicular so pact of the year t.he North Pole is tilted toward the. sun, and palt of the year it is pointed away from the sun. On .June 21, the summer solstice, it is pointed directly toward the sun; on December 22, the winter solstice, It is pointed diredly away from the Sun. At the equinoxes, the axis

N

.. .. A.. "

: B..

.. s .. FlOURE 7.-'I'he effect of latitude on the incidence of solar radiation during the

f.'fIuinox: A, at 34 N. ;'B, at the Equator.

16 TECHNICAL BULLETL.'I" NO. 1344, U.S. DEPT. OF AGRICULTURE

points neither toward nor away from the Slln and the days are as they would be if the axis were perpendicular to the plane of the ecliptic.

It is the tilting that is responsible for our seasons. In summer, the Northem H('mi~phere is tipped toward the sun so that its rays bear on it more directly (fig. 8). In winter, the Xorthern Hemisphere is tipped away from the sun so that its rays strike less directly, and less energy is reeeived per unit area. Also, less solar eneqry is received in willter because the rays pass through a greater mass of air. But it iR the anglf' of the SUIl aboye the horizon that is of primary importance.

\J Columbia, S.C" and LOR Angeles at the summer solstice, the ltoon sun is 7n],{~" abo\'(' thE' horizon, and at thE' winter soJstice, 321./20 . \.t Bangor, )[ainf', Minneapolis, and POltland. Oreg., the rf'spective 'll1glf'R would bE' !ii'\lho and ~11'2'" At these latirudes about two to thrpp till1P~ liS l1lueh solar ellE'rgy ::> l'E'(,E'ive.d per unit of horizontal ,in'a OIl .J llllP :21 as on D('('E'mber ~~.

Obdoll:?]\" to (',deulat> the amount of solar radiation reeeh-ed at :tHy OIl(> pOInt on tIl(> Pluth's ,;ul'fa('(', one must cOllsider both latitude Ilnd th(' angle at. wldeh th(' earth is tipped f!'Om the sun. For example, ll! thp Eqwltor Oil .Tune ~l. the SUll at noon is ~:3%O to the 110rth of a dirp(tly O\'edH'lld position, and striking at this angle the radiRtion 1'('('Pin'd PPl' unit area will 1)(' equal to cos :2:r~,!!o times the perpendil'lllar nuliatiOll (fig. n).

If flip intensity of tlll' solar bpaJll (i.e.. the intensitr on :tn area pprp!'lHlil'lllal' (0 'the solar rn,ys--the direct-benm solar ritdiation) and thp angh' b(>twePIl the beam and a normal ereetpd on a horizontal re('phjug slIl'fne(> tue knowll, thpn the irmdianee of the surface can be l'alc'lIlatpcl by the cosine Ittw of illllmim~tioll (equation 12). N"egleeting tIlE' elreds of atmospherie attenuation, the direct-beam solar irraclianee can bp ealeulated from tIl!> following l'elati.{)llShips:

I.J=R2 cos Z (13) or

J=i2 sin fjJ Sill 8+cos fjJ cos 8 cos h (14)

4J

~ ON MARCH 21

ON JUNE 21 ~ ON DECEMBER 22 OR SEPTEMBER 238'

6D~ QB~ ..

J

17 RADIAl."'\'T ENERGY IN RELATION TO FORESTS

where If} is the solar constant; R is the radius vector ofthe earth; z is the sun's zenith distance (i.e., angle between sun and zenith) ; '" is the latitude; {) is the sun's declination; and It, is the hour angle of the sun.

The Smithsonian Meteorological Tables (List 1958) give graphical solutions of these equations (table 170) as well as calculated daily and annual totals of sohtr i.nadianee at the top of the atmosphere (tables i!32-13+). A graphical calculator to aid in calculating the sun's zenith distance has been desigy:ed by Libbey-Owens-Ford Glass Co. (App. B). ~H loc'al solar noon, the angle betwen the sun and the perpendicular

to a horizontal surface can be calculated from only the latitude and the sun's dec'lination (taken from a sohlr ephemeris). If north declination is taken as posith'e and south declination as negative, for latitudes north of 2:3V;' the declination should be subtracted from the latitude. Thus. on-December 22 at the latitude of Bangor-Minneapolis-Portland, tht' zpnith angle would be the latitude angle (45) minus thp negative sOllth declination of 23%. The appropriate angle IS thun ()H1 2 On ,June ~1, the zenith angle would be 45 minus 23Yz0. or ~l1ho. To fiJld the angle that. the sun's rays make with the horizontal. the;:;c nllues must or eOllI'se be subtt'acted from 90.

Effects of Slope and Aspect The amount of radiation received also depends on slope and aspect.

The slope that fac-es the sun most diredly will re('eiYe the most radiation. Obviously, Rt midlatitudes in the Northern Hemisphere, a south-faeing slope will receive more radiation at noon than a north slope. The effect of slope depends on the sun's position; the higher the sun] the less slope required to receive maximum radiation. For estimatmg the angle between the sun's rays and :L perpendi.cular to

~ ----EQUATOR----, ~

~231/2 ~--~----------------~------

.. ..

Ii'WC'RE 9.-Lutitude und tilt ure used to euleulate the amount of Holar radiation.

18 TECHNICAL BULLETL.'l' NO. 1344, U.S. DEPT. OF AGRICULTURE

slopes facing south or north, the hillside can be considered displ~.~ in latitude by the degree of its slope-subtracting the slope angle from the sun's zenith distance for south-facing slopes and adding it for north-facing slolles.

For precise calculations of the angle that a particular slope makes with the sun at any time of day or year, the azimuth of the sun as well as the zenith distance must be calculated. Then the angle between the soJar beam and the partieular slope C

19 RADIA~T ENERGY IN RELATION TO FORESTS

).. .1

....

..... It)

0

~ .7 t..J .... ~ 6 .....

~ . 5 ~

~ .4

~

'" .3 ~ l

l\:l o

COMPUTED SEASONAL 8WATERSHED LOCATIONS tEl ENERGY DISTRIBUTION (")

~ .... (")

N 1,100 J >t"' IJj

I 000 I-:-,~~.,~.~t--... /J C~' " . ...... ~ - .7 ,I t"' t:) ~1 II(.~, '.......... , I

" 900 ~.". ~......... .. I~. ~ W E j ~ '. ~ ' .....~ WS- I V )( sa

800 r'~ -~ f I ~- ...~ '\.y /' ~ .... o z i::: 1\ "(1 ,":' ~ 700 ',~ .' I I ....

c.> ~ Q:; ..'~, , --.... ~ /~ ,.... "'" s WS-13 600 " \. "1 I I "'"

..... I~~ p" cWS-6 ~ wS-6~1'.... ~ '. j ,....' ~ ltil r~ 1ft: ~ It') ~oo I. ,I

~ WS-13 ... \. ~ ~~/.' tEl "Cl

~ I ' '/ : I~ ." I . "...... ' -';1 '1 I I !"3 ~~:.WS-17 ~ HORIZONTAL ~I\1 --TI-' ~":IWS-17 i o ~ 300 I I I . , , I I ':j

I "';~:::::::" 1 .. .... >.-:::,". 200 I I I " ::0 t.?R. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC. JAN. FEB. MAR. APR. MAY 2

FIGURE n.-Theoretical solar energy on four Coweeta watersheds (Swift alJd vanBnyelJ961). t3 c t;j

..- ., r "'


o . a.1 LV./AlIN.SPECTRAL BANOS RECOMMENDED BY THE DUTCH PLANT IRRADIATION COMMITTEE

REMOVED BY ATioSPTRE

RGY RECEIVED AT EARTH'

o ,6 .1 .8 10 U '.2 t 3 1.4 1.5 1.6 1.7 J,8 1.9 2.0 WAVELENGTH, MICRONS

FIGURE 12.--:Energy in solar spectrum before and after depletion by atmosphere for solar altitude of 30. (See fig. 1, p. 2.)

However, in passing through the atmosphere, certain wavelengths of the solar spectrum are absorbed. As a result, the spectrum at the surface of the earth is considerably modified and appears as indicated by the white areas in figure 12. The diminution of wavelengths in the ultraviolet region ea,n be noted in particular: nearly nIl such wavelengths are absorbed by ozone at high levels. The region of peak energy is shifted toward the red end of the spectrum. Visible light in the blue wavelengths is scattered, rather than absorbed-producing the fammar blue ]ightin the sky.

This scattered radiation accounts for a significant portion of the total incoming radiation-on the average, about 15 percent. On days when the sun is obscured by clouds and/or haze, scattered radiation accounts for aU of the solar energy reaching the surface. As an Itbsolute amount, this mlLy be very little, 'but on hazy days with high, thin clouds, a large amount of solar radiation may reach the ground as scattered and diffuse radiation.

In addition to modifying the spectral dist.ribution of solar energy, the atmosphere also weakens the solar ray. Thus the amount of solar energy reaching the surface directly from the sun is less than that racei ved at the top of the atmosphere, and is dependent upon the length of the path of the sun's rays through the atmosphere. This path length, the so-called optical airmass, depends on solar altitude. Assuming a coefficient of transmission of 78 percent (corresponding approximately to an u;bsorption coefficient of 0.25-soo equation 8), the relationship of solar elevation and thickness of atmosphere to intensit.ies of solar radiation received at the earth's surface are given as follows by Trewartha (1954) :


Ertratmutr;,u intenritv on a IlUrface

Perptndicular Hor;umtalRdati.e path length ourface 6Utjace

Eltvation of oun (opticat airma4&) (percent) (percent)90 ________________________ _

80_________________________ 1.00 78 78

1. O!? 77 7670 __________ .' _____________ _ 1.06 76 7260 _____ .. __________________ _50 ________________________ _ 1.15 75 65 40 ________________________ _ 1. 31 72 55 30 ________________________ _ 1. 56 68 44 20 ________________________ _ 2. 00 62 31 10 ________________________ _ 2.92 51 17 5 ________________________ _ 5.70 31 5 0 ________________________ _ 10.80 15 1

45. 00 o o Altitude

As altitude "increases, the length of the path of the sun's rays through the atmosphere decreases and atmospheric transmission increases. Becker and Boyd (1957) have calculated the percentage increase of solar-rad.iation intensity with altitude for June 21 and December 21 at 40 N. latitude. Up to 1,000 feet there was no definite relationship. Beginning at 2,000 feet the percentage increases were as follows:

Altitude Dec. I! June 1 Altitude Dec. II June!12,000 __________ _ . 3 000___________ _~ 3,000___________ _ 7 13 217,000___________ _7 12 14 234,000~__________ _ 8, 000___________ _9 155,000___________ _ 15 24

11 18

Percentage increases for other times of the year can be estimated by interpolating between paired values.

Turbidity

Atmospheric dust, in which most particles cannot be seen under a powerful microscope, scatters incoming sunlight; consequently, it is partly responsible for the sunrise and sunset colors, and for dawn and twilight.

Smoke and dust over industrial areas reduce and scatter light. From December through February, Chicago receives only 55 percent of the solar energy recorded at Madison, Wis., a smaller and less industrial city (Trewartha 1954). A comparison of the direct, dif fuse, and total radiation received for a clear and industrial atmosphere is given in table 2 (Brooks 1959). Total radi&tion, at solar altitudes from 10 to 60, is reduced one-third to one-fourth by industrial pollution.

Smoke from forest fires reduces radiation over large areas. In September 1950, smoke from forest fires in western Canada cut off 54 percent of the expected solar radiation at 1Vashington, D.C., and had a poticeable effect in ,vestern Europe (Lull 1951).

Cloudmess

The etfects of various types of cloud cover on the percent of clear-day radiation received (t,aule 3) varies from 15 to 85 percent lor a range of opti('al airmasses (List 1958).

---------- ---------- ----------

RADIA-~T ENERGY IN RELATION TO FORESTS 23

TABLE 2.-Solar r'adiation Jor clear (};lui industrial atmo81>here, in langley/minute.

(Adapted from Brooks 1959)

Standard cloudless atmosphere Industrial cloudless atmosphere Solar

altitude, degrees Direct, Diffuse on Total on Dir&i~, Diffuse on Total on

perpendic- horizontal horizontal perpendic- horizontal horizontal ular ular

5. __ __ 0.30 O. 03 0.06 0.15 O. 04 O. 0510 ______ .56 .06 .16 .26 .08 .1320 ______ .89 .10 .41 .47 .14 .2930______ 1.06 .13 .66 .62 .20 .5140 ______ 1.17 .14 .89 .71 .24 .7050______ 1. 24 .15 1. 09 .78 .26 .8660_______ 1.28 .15 1. 26 .82 .29 1. 0070______ 1.31 .16 1. 39 .85 .31 1. 1180 ______ 1. 32 .16 1. 4690______ ---------- ---------- ---------1.33 .16 1.48

Two regions in the United States are cloudy more than 60 percent of the time: one lies mainly over the northern Great Lakes region and northern New England; the other lies in the extreme northwestern part of the country, along the Pacific coast. Areas of minimum annual cloudiness lie in southern Arizona and southeastern California (Liverance and Brooks 1943). The average annual number of clear and cloudy days for specific locations is given in figure 13.

Clouds scatter as well as reduce light. Scattered light can come from the entire sky; direct light from the sun's surface occupies only lho in the sky-vault. On a clear day, scattered light at noon varies from 0.07 to 0.10 Jy./min., less than one-tenth the energy received directly from the sun. Under a cloudy sky-but not under rain clouds-scattered light intensity will reach 0.3 to 0.6 Iy./min., or one-fourth to one-half of the noon intensity on a clear day.

Cloudiness can modify the intluence of aspect and slope. For instance, on a clear winter day a south slope may receive three times as much direct sunlight as a north aspect with equivalent slope; on an overcast day the two aspects can receive nearly the same amount of radiation, for on such days light scattered by the clouds strikes the slopes from all directions. The greater the ratio of scattered to direct light, the less the influence of aspect and slope (Geiger 1957).

24 TECHNICAL BULLETIN NO. 13,H,U.S. DEPT. OF AGRICULTURE

tr 0:... >0 '" 0 z .. ::>0 00 z ~ :! 0 .,t I l"' >-.. .. 0 0 0 0 z 0..

0 .. !! :! e e OrnfBillTIl

... .... ~

:Xl

~":;;;';')'7, ~ 8 l"j

~ :Xl

~ 51 :Xl l"j

5... ~

DAYS 8

D 0 UNDER 40 El 40-80 ~

:XlE32l l"j80-120 I 120-160 ~

IIIIIlIIIIl 160 AND OVER

FIOURE lS.-Average annual number of clear (top) and cloudy (below) days (1899-l988) (U.S. Department of Agriculture 1941). ~

---------- ---------- ---------- ---------- ---------- ----------

TABU; a.-Pel'cent 0/ clem'-day 1'adiatioll 1'cceived /01' 1Jal'ious optlcal ail' ma,~8(,8 and ol'crca.st clmld types (Source: List !f1(8)

Solar Cirro- Alto- Alto- Strato- Nimbo-Opticnl airmt\ss 1/1' nltitudc, Cirrus strntus cumulus stratus cumulus Strntus strntus Fog

degrees

Percent Percent Percent Percent Percent Percent Percent Percent1.1 _____________________ 65 85 84 52 41 35 25 15 171.5 _____________________ 42 84 81 51 41 34 25 17 172.0 _____________________ 30 84 78 50 41 34 25 10 172.5 _____________________ 24 83 74 49 41 33 25 21 183.G _____________________ 19 82 71 47 41 32 24 25 183.5 _____________________

4.0 _____________________ 16 81 68 46 41 31 24 ---- .. -,..--- 18 14 80 65 45 41 :n 184.5 _____________________ ---------- ---------13 30 195.0 _____________________ ---------- ---------- -----_ ... _-- ---------- ---------- ---------11 29 19

-

I m=opticnl airmass (1.0 for zenith).

t..:l 0)

8 t':l C

~ .... c ~

8 tc

f:" ~ Z ~ ... t.

01>.

cl ~ t:=' t':l "d !'3 o "'J

o :n

I > ....

"

http:ol'crca.st

, ..

RADIk~:r KNERGY L~ RELATION TO FORESTS 27

Solar Radiation Received The average amount of solar radiation received per day for the

entire year and country is ;300 langleys. The amount varies from 100 to 800 langleys dependin!T on season and region. The following tabulation gi\"es lLYerage dairy amounts of solar radiation received regionally o\-er the "Cnited States on a unit horizontal surface for elLch month of the year, as taken from maps (samples, p. 28) prepared by the r.s. ,Yeather Bureau (1964).

Narlhea.t Southta8t .\Iidwt Northw1 Soulhwut January._. __ . February. _... ____ _ .:'.Iarch. __ . __ . _. _ _ ApriL __ ___ . __ .. l\[ay. ____ .. _. ___ ._ Junc._. _____ _ Ju1y____ .. _...... _.

125 225 300 350 450 525 525

200 275 350 475 550 550 550

200 275 375 450 525 575 600

150 225 350 475 550 600 650

275 375 500 600 675 700 700

August ___ . Septemb(>r.. _", ___ ._ ()cto ber __ _

450 350 250

500 425 325

525 425 325

550 450 275

600 550 400

November._. _. ___ _ 125 250 225 17i5 300 December__ _.. ____ . _ 125 200 175 125 250

LatittHUnal etfeets are most pronounced in the fall and early winter; there is little \-ariation in the amounts received during the summer. The greater values for the Southwest result from the relatively sparse ('lolld ('oyer o\-er that area.

Beeause of the great impottanre of the 11mOlll1t. of solar energy reaching the Nuth's surfnce, many lmmmaries have been made of the relevant figures for specific loeations. For instan('e, ('rabb (1950) presented the normal pattern of daily radiation re('eind at East Lansing, )-fich., during the, year, from 15-day mO\'ing averages. An average of 5 years of reronl, when plotted, ga \-e a smooth rUTve in which daily "flriatiolls due to c1ou(iine!'1s were aWrll!!ed out.

~[eteorologieal..:\bstrarts and Bihliogi'llphy has published a l~O-jtem bibliography on solar radiation dtlta, for all parts of the world (Dordid( H);)1:). Th(\ r.s. ,Veather Bureau publishes current data on solar rildiation in its ('linvdolO[li('1l1 DahL National RU1n7lwry; it obtains this information from a nehvork of about 50 stations.

Several st-udies have been made of ways of estimating daily or monthly insolation based on ('loud-rowl' or sunshine duration values. Zoller and .Lellz (H)5R) found It significant correlation between per('enta.ge of maximum insolation per half day and the sum, expressed in tenths, of eloud \-alues either at 6 :~O a.m. and 1:2 :30 p.m. or at 12 :30 p.m. and (j :~o p.m.

Fr'itz and Ma('Donald (1!14!l), in estimating monthly amounts of !'olar ener'!!Y received, in('luded data for cloudy and cloudless days. They Ilse(1"tlw following equation : .

R !R,,=O.~:5+0.(jlS (1:5) where

R =::;olar energy inlangle)'S per day, including cloud:\T days; Ro=solar energy in langleys per day re('ei \'eel on eloudless days: S =numher of hours of sunshine l'e('ordecL di\-ic1ed hythe number

ofhoursofp0B.


1

I

(U.S. Weather Bureau, 1964)

L

~

"

RADIA..~T ENERGY IN RELATION TO FORESTS 29

R was calculated for 150 points in the Cuited States where sunshine data were amiJable, and RQ was obtained from pre"jously computed charts. The ('orrel[~tion ('oeffieJent between HI ito and I."" was 0.88, and the average error of estimating it Was about 4.5 percent of the observed yalue. -'laps were de\'eloped to show the average daily amollnts of solar radiation receivecl on a unit. 1lOrizontai surface O\'er the Cnited SULtes (ba:;i::; for tabulation on p. 27).

A graphintl method for con\'ertill~ the percent of possible sunshine into (hily Insolation was developed by Hamon, ",eiss, and "\Vilson (lD5J) for:::r:Ltiomdrom latitllde~Jo X. to j()~' X. TeRtillg the method Oil irH.tependent data, they found R l'orrelariOJl c'oefli('ient of 0.97 between estimat ed and obser\'(~d yalues. Gates (IP()~) has recently reviewed t11(' literature on the eil'ect of doudiness on the amollnt of ener'gy rp('Pi \'ecL Iloting thllt 1)I'edid ion forllJ llias wjlJ ghoe reasonably good est illlntes of the totnl amount of ener~ry re('eiYed during the day but wIll not gin' instantan('()l.1S \"[lItH'S.

III l>:;tiJJJating the solar radiation at any point, consideration of all fac'ton; ill\'ol\'PlI (such as latitude, time of year, time. of day, slope, aspect. and doudiness) would lead to an unwieldy tabulation. III addition, th('['(, f\,re sl'\'eral dependent nlrillbles that may be tabulated: InsolnxioJl ratp.'>; total daily, weekly, monthly, or yearly amounts; cal('ullltions for horizontal suriacps or tho>;e oriented perpendieular to the sun'R rays; day length: solar angiE's; et('.

Of "ours(', ('olllpilation of a nearly complete set of sueh data would bea trel1lPl\(lous problE'm. Ho\\'E' Y;r, there 1m \"e been many compilations 01' J'('f'tl'i('t.('d areas or ('omlitions. Table 4 lists the sources of s('.v(>I"[t1 of tl1('se, their ('()lllpillltions, and >;alient. features. Geiger (HliJ7, table :Hj; 10(il, p. 3(0) lists additIOnal sour('es of such tables, mostly from Germall pubUeat ions. Budyko (ID56) presents a, number of formulas wherl'by short-waye (and long-waw) radiation can be (>Rt illlatecl, ilnd dis('usses !'l1itablp IH'O{'edllres in detail.

C'alC'ulntiol\ of ilH'Oming solar' radiation can, at best, provide only approxilllatt' (ignr(>R. Th('re are numerous yariables such as sh."}' cover, doud thi('kness and h(>ight, atmospllPric turbidity, etc., that can only he, roughly approximatNl. ThuR, eakulatecl yalues will vary widely fmm fu'hra] or measured ndues, and this error will be lnrger for ::horter inl('l"\'llls. Gr'('at caution Blust be exercise.d in attaching signi/i('fUlC'P to ('alc'lliated mllt('s of solar radiation re('ei\'e

TAnLJ~. J.-Summar'y of rat/iutioll ('/lJruJaI01w ~ o

Disphty !-3--~'~~::~:------'---~:SiS == L~~~~~s~=l l~:~~l:~~,~~~t::bles [-~~pendl'nt variables SUIll nn~k' Qalcl1ltllor Theory _1280, 32, 36, 40", Dlltc, true solar time, Solm' Illtitllde, llzi- Grn phical Cll)

(Al'rolltlulicnl Services 44,48,52 N. latitude. HlIlth. ~ culntor.1051).

Listl058,table 170 __ . __ ...do.. __ .. 0",10",20,25, ___ .do. __ _ _....do.. ,. ........ . ~ Graphs.30, 35, 40", 45, ' OJ 50 55 60 65 I q 70; 80: \l00: '" I 8List 1955, t.ahlt' 17t 'I,,do...... 'I All, by 5" and 2 Dale,latitude... __ ., .. _, Duration of dtlyJight __ .1 Tables and intervals. ! grllphs. ~

Orclldol'lf J954.. _.,, ____ . ___ .do_____ ._ 40" Slop(' (0, 10, 20", 30, ToLnl duBy "clear sky" Graphs. Z 45",60,75, \l00). radiation (solar).

Aspect (360, COI\ Dircct, diffuse, all d Tables. ~ tinuous). total solar radiation, Dnto (months). nverage conditions. .....

to)l

31 RADIA:."\,T EXERGY IN RELATIOX TO FORESTS

Because the. sun is the primary sourc,e of radiant energy influencing microclimates, it is highly important to rocognize the presence of obstructions that may shade a particular spot from the sun during the day. Nearby builclinf.,TS, mountain rid::,res, and surrounding vegeta.tion may [1,11 rust shadows on the spot, thus reducing the amount of dirbCt-beam oola.r radiation received by that spot.

.:\ convenient way to determine these relationships is by photographing th(' entir(' upper hemisphere o\'er the. spot with a. special camera, and then plotting the. SllIl'S path on the phot.o for the. time or time.s of Year of interest. SHel'al eameras ha n~ been de\'i::NI to pennit the il;;e of thi;; method.

Broll'lI ('11710In) f'(l1!lR1'fl.-Th is camera utilizes a, combiTl!Ltion of a lells sy~tem and piuhole to photograph !11l entire hemisphere. It is baspd Oil tIll' !:'()-('alled photo('anopymetel' of ('odd (1059) and Clark (HHH J. COIlstnH'tion detail" and snggestions for use are given by BrowlI (1 !)fi~).

The opti('al system con:-;i:-;ts of two lens('s--a mpni!-;(,lls and a plano('OI1


one-to-one correspondence was obtained for a wide variety of sites and radiation conditions.

GlOoo8cope camel'a.-The Globoscope of Pleijel (1954) utilizes a parabolic mirror that can be viewed or photographed from above to produce nIl image covering the entire hemisphere. A small portion at the zenith, !t relatiyely small portion of the entire field of view, is obscured hy the camem itself~

The photographed image is a stereographic projection of the upper hemisphere; therefore, it can he used rendily with similar p"ojectiolls of solar paths to determine screening ('fleets of surroundinf{ yegetation and other objeds. Pleijel also discusses the constructIOn of an o\'erlay to simplify calculation of the "iew factor (dis('ussed on p. 3a) of any portion of the s.ky or surrounding objects with reference to a hor'izontal area, the plane of the film in the camera.

Long-Wave Radiation

Thp solar pn('q,ry iH of ('ourse important b(>(llul;e it irmdiatps plants with the waY'I(~lIgths of iIflI){lIt!lll(P to photoSYllthesis and furthennorl' ('ontrihutl's l'n(,rgy to all of till' IIYIIHllIk aud llfpgiyill::- pr()('ess('s Oil the plunpt parth. Hut if the thprmal ['adiation from the grouud !llld atmosphere were not present, then life Oil tliis plurwt would uot ;he' pos;;ibl' pith('r, for during thp nighttimp (,\'prything would gpt dpsfl'ratply eold. Sueh is the ('ondition on thl' moon wherp there is no atm()spll('r('--lJlllzing hot by day !lnd way below free'J:ing at night. '1'111' point that should he malle is tllllt all components of the enprgy rpgime lire illlport!lnt Ilnll til ('onsid('r on(', sudl as th(' solar, without considering th(' other:; is to f:1tudy oIlly fl fraglll('nt of the total pi('tur('. (G-'.lt('S 19(2).

As illdiPnted previously, all objects above absolute zero radiate enP"J!}' lJy virtue of their temperature and emissivity. At temperatures normaJly exhibited by mttural obje('ts at or n('ar the ('arth's surface, this radiation is almost entirely in tlle infrared region, from approximately -1 to 100 microns. At the tempC'l"llture of melting snow, blackbody radiation amounts to OAf) ly./min.; at a surface temperature of )-;fiC' F. (ao) ('.), it is (J.GD Iy./min. ; and at a hot surface tem perature of IJfI? F. (flO') C.). it. is un Iy./min. Actual emission rates depend, of ('OUl:;(" on tll(' E'miS'lh'ity of the radiating surface (see equation 7, p. 11). For' many naturnl ohjects, long-wave ('missivity is abo\'e 0.9 ly./min.; wpt surfa('C's such as leltves or moist ground haye even higher emissi"ities, O.D51y./min. or more (table 1).

Lon,g-wRve radiation from the earth's surface and the vegetation on it thus IH'(X'eeds continually, day and night. In fact, bee-a use of higher sm'facC' ternpemtllrl'S during the day, the outwnrcllong-,mve radiation from thC' sudaceis normally higher in the day than at night. Thus, the OCl'U1Tence of so-e-alled "radiation frosts" at night does not result from large values of outward radiation, but from small values of incoming long-wave radiation from the night sky.

This downward radiation from the sky occurs as a result of earbon dioxide, water vapor and droplets, und partieulate matter in the atmospl1l'1'l' radiating aJ theil' own temperatures and emissi,-ities. A low, thic'k cloud cove,' with a temperature very nearly that of the ground stu'face will mdiate downward ~Lt very nearly the same rate as the ground is radiating upward. Thus, the net ex('hange will be very neady zero, and the ground will not cl1Rnge temperature markl'dly. The c'loud ('o\'(>!' kl'l'PS the earth relittively wal'lner than it would be llnd('r a clear sky and thus freer from extremes of temperature.

.A

~ '.

RADlk.'lT ENERGY L~ RELATION TO FORES'r.S 33

If the clouds are warmer than the ground, the surface temperature may e,Ten increase as IL result of the exchange. Conversely, a clear night sky may radiate downward much less than the ground is radiating upward, and the ground will sustain a net loss of energ-y and consequently cool rapidly, 1?ossibly with formation of dew or frost. On the so-caneel "radiation mghts," incoming radiation is much less than outgoing radiation, and cooling ILt the surface is rapid.

Although the radiation from the sky is ('omplex, and occurs only in certain \Va Yl.'lengths as a result of selecti "1.' e-mission by water vapor and ('arbon dioxide, it ('an be considered as ('oming from it hlack body at thl> temperatun> appropriate to the amount of radiation emitted. This templ.'mttlrl.' (the etfectil'(' te'flL[H?-r(dUl'e, as previously defined) is sometimes known as the equil'fdnli Hh'Y temperature (Brooks H)59). By eomparing the I.'qui\'alent night sky temperature with the temperature of the gr'ound sudrL('e, we can immediately know whether the ground will ('001 ofl' or wal'ln up as a result of the radiation exchange.

Most of the clowneoming radiation from the ('lear night sky comes from watl.'r \'apor in the lowest few hundred feel. Therefore, the moist urI.' ('olltl.'nt of thl.' surface air layers ran bl.' used as a good (lstimato!' of nocturnal sky ntdiation. Goss and Brooks (1956) give thl.' I.'quation :

(16) where

R is the sky radiation in ly./min.; e 1:-; the 2 p.m. weather'-sheIter nlpor pressure in millibars, and T is the weather-shelter air temperature, OK.

This rrnpirieal rrlatiollslrip assumes that the 2 p.m. vapor pressure is a. good ('::i(imate of moisture ('olltent of the lowest thousand feet or so of the fltmosplll.'re.

ThE' \'al1l1.'8 giv(>11 are for total hl.'mispl1ere radiation, i.e., from the I.'lltir(\ vault of sky. HO\\'('\'er, bl.'canse the a.tmosphere is thinnest clir(>('tly o"erl\(?lHl, and thus contains less mass of water mpor than any other path, radiatioIl from the zenith is usually it minimum. Thicker layers of til(' atmosphere contribute to the incoming radiation at angles approaching the horizon, and the incoming radiation from these angles is ('o/'l'espon the radiat ing substances in the atmosphere are l1eated by till.' Sllll. Sauberer and Dirmhirn (1958), measuring downcoming l()n~-wa,1.' ntdiatioll at Yienna in mid::iummel', found daytime rates of about :\0 Iy./hl'. and Iloc(umal rates of 28 Iy./hr.

View Factor

As alrl.'ady statl.'d, in addition to c1irl.'C't-beam solar radiation, any objeet 011 the elll'th's surfaC'1.' l'ecei,-es diffuse alld reflected solar radiation, and long-waye radiation I.'mitted by ,-uriolls components of the atmospherl.' and by terrestrial objl.'cts. It is offen important to know how mu('h I.':teh portion of the "view" of the object eontributes to the

~ tot!Ll mdinJion re.cei \'eel by the objl.'ct. For example, It sm!LII spot on ~ the gl"Ol!lul in!L forest; opening receives on a clear night radiation from

the sky th:Lt may have a much lower' eH'edive temperature than the sllrl"Ouncling trees which are also mcliating to the spot. Since the spot


radiates outward at a rate that is dependent only on its own temperature, the radiation balance on the spot is detenTIined largely by the relative amounts of radiation it receives from "cold" sky and "warm" tree canopy,

The geometric concept that expresses this proportion is the view factor, or shape factor. It is defined as the fraction of the radiation Ie... ving a surface in all directions that is intercepted by another surface. Consider a small area, dA 1 (fig. 14) radiating to the hemisphere above it. A portion of the radiant energy is intercepted by area dA 2 , Because of Lamberfs cosine law, the amount leaving dA 1 in the direction of dA2 is proportional to dA 1 cos !31' The amount received by dA 2 is proportional to COS!32 (cosine law of mumination) and inversely proportional to the square of the distance, r'. If 11 is the intensity of radiation from dA 1 (in the direction of the normal to the surface), then the rate of radiation from dA 1 to dA2 is given by (McAdams 1954) :

dW ,( IdA. cos {3l dA 2 cos {32 (17)1~2 r2

The total radiation leavino dA! can be found by integrating equation 17 o\'cr the entire hemi~~lere above flA!, Similarly, the radiation receind by any portion of the hemisphere can be found by a suitable integration, The ratio of the received portion to that radiated to the ('ntiIp hpmispherc is the\'iew faetor, P 1~2' It follows that the view fn.ctol'sfor the various portions that make up the en6re hemisphere must add up to one. Because the relationship is reciprocal, the view factor of the first area rebti ve to the se(!ond is the same as that of the second rebti ve to the first.

In the example cited, the view factor of the sky relative to the spot on the ground together with the equivalent temperature of the sky p(,I'mits c:druIntioll of the amount of energy receivecl by the spot, from the sky. Similar ealelllations for other portions of the view permit raleuhttion of the total radiation recei ved by the spot.

'1'1)(' lIsl'fulne.':iS of the view faetor concept can be illustrated. A spot. in the middle of a forest. opening radiates to the entire hemisphere abov( it. However, it receiv('s mdiation padly 'from the sky and partly from fhe trel'S sunounding the opening. The proportion of th('. upper h('mi~phere occupied by the sky is a function of the diamelH of thl:' opening and the height of the surrounding trees. In terms of dinmetl'l', tI, of the opening, (Lnd the height, 71" of the trees, the fracti~)I1 of the radi(~tioTl received by that portion of upper hemisphere occu plNl by the sky IS

F=sin2 (arc tan :fn) (18) P, then, is the view faetor of the open sky relative to the spot; and by reeiprocity, the view Jartor of thespot relative to the open sky.s If the l'f}'edivl' sky tl'mperature and the tempemture of the surrounding trees :tn', known, the ineoming radiation to the spot can be calclliated by thl' Stdan-Boltzmann law. The funetion, F, for this simple ease is presented in figure 15.

CmnpJet('


FIGURE 14.-Radiation exchange between two elemental areas.

The view factor depends only on the ratio of the tree height t.o opening diameter. Therefore, where the net outward radiation to a clear, cold sky is the consideration, a large opening in a taU forest acts similarly to a small opening in a young forest with the same diameter-height rat.io.

View factors for a number of interesting and useful cases are contained in standard heat-transfer texts, such as McAdams (1954). The case for a free-standin~ tree in an incomplete forest canopy is treated by 'Waggoner and ReIfsnyder (1961).

Radiation Balance

RadilU1t enel'g)' streams to alid from the surface. of a leaf, the bark of a tree, or the ground surface itself. The magnitude of these atreams, their direction, their spectra,} composition, and their distribution through t.ime control the energy that is available for heating the surfaces, evaporating water, supporting photosynthesis, and, in general, for making life on earth possible, The sum of these streams

----36 TECHNICAL BULLETIN NO. 1344, U.S. DEPT. OF AGRICULTURE

1.0

~

~ ,9

/.8 -...,.7

"'I~

/ ~

~ /~ .6 ... ~ ~ I(t) .::. .5

I

.3 ,-

I I 'll /hjf~.

1_ 9 11 .2 f--

I I~ d ~I

I

/0 2 3 4 5 6 7

r/h = d/2h I I I I I I i I

0 Z 4 6 8 10 12 14

d/h

FIGURE 15.-View factor of differential area at center of forest opening to sky above.

..


constitutes the radiatio1/, oa2a:nce or mdiation o1tdget. The latter term is perhaps more precise, for it is the imbalance in the radiation budget that leaves energy excesses for keeping the atmospheric engine going.

In terms of the radiation fluxes discussed in previous sections, the budget is composed of the following terms (considering the balance on a horizontal portion of the earth's surface) : Incoming solar radiation (including the ultraviolet, visible, and infrared portions, and consisting of the direct solar beam plus the scattered radiation) ; incoming long-wave radiation from the sky; outgoing short-wave radiation (i.e., reflected solar radiation) ; and urnmrdlong-wave radiation from the ground (com;isting of radiation emitted from the. glotll1d and ref1ected long-wave radiation).

Because of the difJerences in origin of these streams, anel of t11eir physical n.nd biological effects, it is often necessary to measure and analyze eaeh one separately. The direct solar beam varies in It complex way because of astronomica.l motions and atmospheric and other obsC'urations. Diffuse solar radiation comes from the entire unobseured vault of sky, and varies within narrower limits than that of the. direet solar beam. Long-wave rtldiation from the sky depends on the amount, distribution, and temperature of ,vater vapor, Jiquid water droplets, carbon dioxide, and other aerosols. The amount. of short-wave radiation reflected from the ground (or other surface) depends on its albedo. And the amount. of long-wave energy streaming upward from the ground depends on its temperature, emissivity, and its refiectivity t.o incoming long-wave radiation.

If al1 of the radiation fluxes to and from a surface tlre added algebraically, with regard to sign (convention prescribes fluxes to a surface as positive), the remainder is the net mdiation fl1l'{J. This amount must be distributed to (or supplied from, if it is negative) other energy consuming or transferring processes. It may heat the body on which the radiation is ineident, he11t the iLir in immediate contaet with the surfaee, be tram;fonnecl into latent heat through evaporation, or converteel into chemical energy through photosynthesis. In any event, the energy rl'presentpcl by tl1e, I1Pt radiation must be aeeountecl for to Fatisiy the law of C'ollsPl"vation of pneq..,}'.

For NMth ..:\.mPrie!l, net mdiatiOIl ranges from 20.000 to (iO,OOO ly./ yr. (Budyko 195G). The largest valups of net. radiation are found over the or'eans IlPltr the coasts because at night the cloud cover is more prevalent than it is over tll~ C'ontillent; thus, the ocean surface loses less heaL The elifferl!llce between continenbt1 and oceanic net. radiation on our east coast is 20.000 ly./yr.

Development of simple cleviees (described subsequently) to measure net. radiation has stimulated many researellers to correlate such measnrements with many biological and phy~ical pro(~esses. Where energy eonsiderations alone ltre import-ant in relatively simple systems, this may be an adequate proceclUle. But often the origin and disposition of the various fluxes, and their relation to the physical pn.rameters of the environment. must be known in order to lIllderstand nature's Systems sufficiently well to permit extrapohltion and prediction. .

A snitllbleledp:er sheet for entering radirttion budgets has been


SHORT-WAVE LONG-WAVE RADIATION. ALL RADIATION RADIATION WAVELENGTHSDIRECTION ~ DIRECT * DOWNWARD FROM SPACE + -- - SHORT-WAVE(DIRECT SOLAR BEAM)

DOWNWARD FROM THE DOWNWARD TOTAL ATMOSPHERE + ~~6~i:WAVE* LONG-WAVE DOWNWARD UPWARD FROM THE REFLECTED UPWARO TOTAL EARTH'S SURFACE SHORT-WAVE LONG-WAVE UPWARD+

NET NET NETSUM SHORT-WAVE LONG-WAVE ALL-WAVE

* INSOLATION, AS THE JOTAL DIRECT SHORT-WAVE RADIATION PLUS DIFFUSE SHORT-WAVE RADIAlIO.I, IS MOST CO ....ONLY ..eASURED AS ONE lTEIoi.

JUNE AVERAGE

SHORT-WAVE LONG-WAVE RADIATION. ALL-~

RADIATION RADIATION WAVELENGTHS

DIRECTION

DOWNWARD FROM SPACE~ +248 -- - --- (DIRECT SOLAR 8EAM)

DOWNWARD FROM ATMOSPHERE

THE .. + 218 +728 +1i94 UPWARD FROM THE ..I - 93 -809 -902EARTH'S SURFACE

SUM, LY'/DAY +373 -81 +292

DECEMBER AVERAGE (SNOW)

SHORT-WAVE LONG-WAVE RADIATION. ALL

RADIATION RADIATION ~VELENGTHS

DIRECTION ~

DOWNWARD FROM SPACE+ +12 -- -- -- -(DIRECT SOLAR BEAM)

DOWNWARD FROM THE +39 +582 +623ATMOSPHERE ..

U~'WARD FROM THE -18 -62l -639EARTH'S SURFACE +

SUM, LyjDAY +33 -39 -6

I

-----

39 RADIL~T ENERGY IN RELATION TO FORESTS

desirned by Miller; 9 a variation of it is presented in figure 16. 'Yith SUdl a. ledger sheet, it is easy to see the source of the various fluxes and to keE'p them sepn.ratecl. The budget may be calculated for instantanE'OUS rates or -for any convenient time interval such as hours, days, or months. Examples of the radiation budget, for a. meadow in summer and in winter when snow covered, are given in figure Hi.

MEASUREMENT OF RADIATION Considering the. importance of solar enE'r~ry and the radiant energy

balance to life on earth, it is suqJrising that until l"ecently few instrumE'nts WE'l"P !wll,il!Lble fOI' routine radiation measurements. For !llanyye~lt" the E'(>plE'Y pydleliometer was the only~en~rally tlyailable lDstrument. and It measures only short-wttve radmtJOn. However, with i!l('l'ea~e(l intE'rE'st in E'nergy-lmclgN studies, new instruments httve ben dp\'plopE'd and havE' become iLvailable commerdally. Tlwse measure dill'prent pOltions of the spe('t rum, haw c1iil'erent optical and geometri(al chartlei(>ristit's, employ or requirh different modes of reeonling or 1'l.'adout, and are widely prieed.

The value of many e{'ologieal studil:'s depends on the quality of the enl:'rgy- and racliation-balanee. ml:'ttSlirements. Often these measurements ('an be obtained I'E'Jatively easily, but too often the studies have been llHllTE'd by inadequate radiatiOJl data. \Ye hope to eneoumge the researc'her to make suitable meaSllrE'lllents and to pro,,-ic1e him with some fundamental information on types of instruments and their uses.

Some of the questions that must be answered are: \Yl1at radiation d!tta uo I need '? \Yhere should. I take my measureml:'nts~ Are point measuJ'l:'rl1E.'nts adequate. or must I take numerous samples? Do I need (:ontinuous reconL'i, 1)1' are tjml:'-integrat~d values adequate ~ \Vhat instruments are ava,ilable? 'Yhat do they measure? How suitable are they fOI' field observl1tions?

What To Measure Obviously, the question of what radiation fluxes to measure can be

amnvl:'red on ly by !t ellrefuI delinl:'at ion of the, purposes of the investigation. This heal'S ell1piUlSis hl:'t'fttlse so Il1uc-h etrOIt. has been wasted measurine; thl:'. wrong fiux at the wron~ place (md time.

l~adiatLOn from natural solnr and lerrestI'ia] sources comprises a ('ontinuollS speetrum; wavele.nf.,rths extend from about (J.:~ to about 100 microns. _\5 indicated pre\'iollsly, for many pllrpOSI:'S it is adequate to :,rroup solnr wllyelengths into it short-wa\-e spectrum and terrestrial wavelengths into a. .long-wave spectrum. But the biological eil'ectiveness of wavelen,!..rths within these ~rr()lIps \'a1.'ies widely. The phot.ochemit'al efred of specific bands has been c1I:'St'ribed as follows by the Dutch Committee on Plant Irradiation (\Yassink ] (53) : Band J. (Jl'patrl' tJ/fm 1 mirron. No speeific effects of this radia.tion

IU'P known; as far as it is i1bsorbecl by the plant it is transfonned .into heat without. interferenee of biochemical processes.

The H('h(>nH' was propos('(\ by Dayid ll. :Miller in note;; for a eourse in eliIDlltO]Ogy gin'n nt the t'nin>rllity of WiHeonsin. It is prl'Selltl>d here with the I~rn.d;;~jon of t)1(' author, nnd with our gratitude to hillJ,

40 TECHNICAL B(;.LLETIN NO. l3 4.4 t U.S. DEPT. OF AGRICULTURE

Band 2. 0.1 to 1 min'on. The region of specific elongating effect on plants.

Bawl S, O.6J to 0.7 micron. Strongest absorption of chlorophyll and strongest photosynthetic activity. In many eases the region of stl"Onge.';t photoperiodic activity.

Ban~1 4. ()./il to 0.61 mir'l'on. Low photosynthetic efJ'ectiyeness, Band :J. 0.4 tf) fUji mir)'on. :-:;trollg ehlorophyll absorption and ab

Rorptioll hy ypllow pigrnenti'l, and strong photosynthetic activity in thE' blu('-\"io]eL

Bmul fl. fJ.:n!; to rq mit";'01l. Fluores(,l'nce and strong photographic Ilf'tion.

Blind 7. 028 to fJ.31fi micrOll, \ nt iraehiti(, and gel'm kidal It(,tion. Btlnd 8. r.f'.Y;,~ tlwn fJ28 mi,"roll, Belo\\' the tt1mosphprie trnmnllit

tall('e limit fOI" l-luIlshillP,

If photosynthesis is h('ing stuclied, it may be, adequate to mpasure t he \"J~iblp portion of tlip SPP('t rum. ffowenl', nwM light Ill(>ters do not r?~p()!lcl to till> pntil'P \"i:;ih]p SjW('trnUl: thi:-: may b(' an important ('onsic]erafion in phu'ps ",hpJ'(' lig-ht qual1ty has hePIl modified, as in plant :--had(), If pllOto[)('['io

RADlA.c~T ENERGY IN RELATION TO FORESTS 41

flux of radiation by an instrument exactly at ground ]e,'e1. Therefore, it is necessary to place the horizontal receptor at some distance abo,e the ground so that it can be as.'-Ulned that the ('nergy receiYed at the instrument is the same as that emitted by the gl'ound surface (fig. 17).

This assumption will be correct only under the following C'onditions: (1) The grolUld surface has completely uniform radiation characteristics (emisshrity, temperature, reflectivity, illumination, etc.) in al1 uirection~ to infinity; (2) there is no absorption or emission of mea.sured wan~leJlf!ths in the space between the radiometer and the ground surface (i.e., there is 110 radiative divergence between the ground SUl'fa(-e, and the level of the 1lll'tl.BUring instrument) ; and (3) the variation of absorptivity with angle of imidence of the radiometer receptor is the, same as the angula.r \'ariatioll of emissiyity of the ground surf:u'('.

FOI'short wavelengths, departure from these conditions is usually npglig-ib1l' ex('('pt in the ease of specular reflection from water surfaces at low HIll angles, and il\ situations where the f!round ;;;urface i::; nonuniformly illuminated. (The sampling pl'Oblem is eomiiderec1 in fl subsequent section.) Long-wave mdiation, howen.'!", will be absorbed tlIld ('mitted by watl'r vapor in the layers of air near the gronnd, and may pr()\'ic1e, a soul'('e. of signifir.ant error unless the reeeptor is within II f('w feet of the g-round surf:H'e. ..:\. method for calculating the radiative (livergenee near the ground is given by Funk (1961).

For some stuc1ieR a fiat horizontal rl.'('eptor may not be appropriate. ~rensllr('ment of c1ired-benTll solar radiation-that re(,l.'i,'ed bv a SlIrface perpelHlieuhtr to thE'. rays of tlll.' sUIl--1"equires that the l'eceptor he th:> sun. This ('an be ac('oll1 plishecl by mounting the radiometl.'r on Il motor-(lriven telese-ope mount. In this c'asp a deyjce Jor limiting thl'. view of tbe radiometer to the sun and OTllit! ing t hl' sky and ground must be provided.

Sphl'rical or hemispherieal l"e.('l'ptnrs will provide measures of the racl.iatiol1 r('('(,j"1.'(1 hy an pquint1('nt shape in nature. Thus, Owy might bp appropriate for studies of the radiation balance on an isotatpeI tr('(' (Shirh'y 1!):~5a), a ppndant fruit, or a grazing cow (Bond llmi Kplly H););. Tlwrp is no diree( way of transforming radiation 1'("('('i,'('(1 on :->uc'h a shapl'd rPsibll' to meaSlll'e radiat iOIl with nninstrument Ihat i" part of t hl' ~u rfa('l' Oil whi('11 IJw radial ion exchangl' is oecul"l,jng. l ~';lI!Lll\". llwaSIU'('llIl'llts lllll"t be taken by an instt'uml'ni" that is rl'll1ote [!'OIlI, illlt illtl'l"\"j:-;ihll' witll. the surfac'p: Thus, the pl'oblenl is partly 011(' of j!l'oJlIPtri(' opti['s aJld plutly 01lP of ;:;alllpling; tlle probll'm i:;

fa ('ompli('atpd by tlH' fact that SOIlW of tbp radiant l'lll'I'gy originatl's _ from u point ";Ot!t'C'l' (IIIP ;;(111). whprpa:-' Jlllwh of both IOllg- and shOlt

wan' ('Ilprgy originatl's f!"Om arl'll SOUI'('p,; (t rf'l'S, sky, and ground).


\ I RADIOMETER \ ~ , .,/./ SURFACE

~ /Il\'\

GROUND SURFACE\ \ t I ELEMENT

--~_./_- GROUND SURFACE

FIGURE 17.-Radiation fluxes on the radiomet.er surface compared with those on the ground surface element.

If the measurements ('annot be made on the surface, where should they belllade'~ .Most radiometers huxe n, receptor that is exposed to an entire hemisphere; others llll\'e a ('onical view of various dimensions. For hen.t-bulance measuren1('nt~, flat-plate receptors open to a hemisphere are commonly llsed, The farther the receptor is from an aretL SOt1n'!' of radiant enN'gy, the larger the area from which the bulle of the enet'goy iJleident Oil the re('eptor is ('omin[?i i,e" for a given pel'('entng:t:;ured, tllP l'adiolllet'er must be placed close enough to the plot so that most of the J1I('asul'e.cl radiation is C'Dl1ling from the plot and. Hot from th' ground outside tire plot. But if it is too dose, it will "see" its own shadow and be in etTOI'. Generally this is not impOltant. "\ ra


-~

~t.. 41) !o~ 60 )',;; 81)

DIAMETER OF THE SEEN AREA, FEET

FIGURE lS.-Vil'w fartor of a radiometer in relation to height.

.::\rea-source mdiution from the upper hemisphere measured from within [L plan!; stand (fot, eXillllple, under a forest canopy) ..."ill generally be different at different heights above the ground; i.e" the radiometer's view of the three-dimensional plant canopy will change as the ,,!tdiollll'tH is moved upward from the gl'ouncl. For example, thj:l angular diameter of all opening in the (:llJ10py will inel'ease as it is (lpprOHl'hed frOIll below. Also, as the proport.ioll of the plant stand below th(\ iU5truIllent in('re,ases, the more sohu' and sky radiation will be 1'1.'.('1.' j ved (see fig, Hi) ,

Measurl'llll'nts of sunli/!ht or solar radiation under plant canopies lLre espe,dally dillkult when complicated pattrns of light and shadow am present. Little is known about the variation, or of suitable methods of :-;ampling. Here again one must first determine the data, requirt'd: ~\dai1y Illean, noon vI1Iu(', s('asonal total, 01' other \'!11ues, ~\tkins (1(.):)7) report('d that fot.' it well-stocked 80-vear-old reel pine stand with It basal area of ILI)proximately :200 sqUllre. feet, reducing the nurnu('r of phot()('pli r('[l( ings in half-acre plots from 255 taken at 10-foot spacing to ali ft";'w as :20 at 40-foot intervals caused little \'Hrilttioll in mean nl nes. Some inrf'!.'ased \'ariation was noted in sp:u'S('r stands with a. bm;al ar('u of about 100 square, f('('t.

In It study of illumination und!>!' a hazel and dogwood understory tlu~t l'(,lllained aftRr an HO-year-old upland oak stand in IowI1 was..

44 TECHNICAL BULLETIN NO, 1344, U.S, DEPT, OF AGRICULTURE

nearly 1,200 measurements in the UIH'ut understory to be 95 percent cedilln of ,finding an ll\'erage wi,th a s.t:u:dllrd elTor of less thllll 10 perc-ent. I [cm:(,\'t'I', lIlueh of tl;n; \'arl.atlyn was tlI,Jpar('nt,l.r due to the IHetporologwal and astTol1()Jlllc'al \'(ll'latlOll of sunlIght (lus observations were taken at irregular interntls within 1 hour of noon !'puf'ed throughout a !'lIl1l1l1prj. The Illllllb(>r of olJsprnttion..; undoubtedly could h~t\'(\ bl'l'lI n'(III('('(l if t'ltl'h had bePIl t'xprt'ssed as a ]lPl'c-entage of asimuItam'(Jus oln';PITatioll in tllt' open.

In n. stml\' of spatial \'al'iability of ill('oming mdilltioll under e\'enagt'd lodW'iJOlp pille stallcb ill ('oloms of instllntan('olls IlWaSlll'ements; t1wl'efoJ'l', ronsi(jel,thlp (i nle,\' ane! in IlIP OPP)) in ol'dl'r to eOlllptU'l' light illtpn~itips lllldpr diti'l'I'Pllt ('anopies at various times of tin' yl'tll', ;\Jthough tlH'Y did not justify (lIPir ~('l('('ti()n of ~ii pail'S of obs('l'\'atiolls, PXtlllllUtllioll of t hpil'

Radiant Energy in Relation to Forests - AgEcon...

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