Solar radiation as a forest management tool: a primer of principles and application

8/8/2019 Solar radiation as a forest management tool: a primer of principles and application

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C;EXERAI. TKCIINICAI .R I P O R T PSW- 33


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SOLAR RADIATION AS A FOREST MANAGEMENT TOOLa primer and application of principles

H o w a r d G. Hal verson James L S mi th

CONTENTSPace

Introductm . . . . . . . . . . . . . . . . . . . . . . . . . . . . I Earth-Sun Relations . . . . . . . . . . . . . . . . . . . . . I

The Sun Affects Our Forests . . . . . . . . . . . . . . . . . . . I Polar Till Define-i Our Seasons . . . . . . . . . . . . . . . 2

Sun -Ea nh Energy Relations . . . . . . . . . . . . . . . . . . . . . .4 Energy Balance. . . . . . . . . . . . . . . . . . . 7 Local Energy Relations . . . . . . . . . . . . . . . . . . . . . . .8 Management Technique5 . . . . . . . . . . . . Example A management Problem . . . . . . . . . . . , , 10 Literature Cited . . . . . . . . . . 13

Pacific Southwest Forest and Range Experiment StationP.O. Box 245

Berkeley, California 94701Apr i l 1979


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0 9 b S , n n u . 9 M . ., I950) and Michigan Slate Lni>mwy(P h U m h>drolng>. 19541


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INTRODUCTIONhe sun isthe pr imary source ofenergy for theearthT.nd il-i atmosphere. Sola r ene rgy drives thebiologic, hydrologic. and atmospheric processes Thesecond largest energy source is the heat flux from the

solatmn > sused to comb~ne lem ~n tsound near [hesurface of the earth so that essential physiologicalprocesses necessary or forest grow th and ma turity canbe comnleted The sun alsodrives the hvdroloeic cvcle

logic c ycle because wo od and water are tangible prod-u cts o f f o r e ~ tand.We cannot manage or control the incident solarradiation received by large land areas: however, forestm a g e m e n t canexert significant effect on local insol-ation in small areas. Harvest and regeneration patternsa n be designed to increase or decrease !he radiationleve l at many sites The objectives of the managememplan can determine the level of insolation desirable.Pre>vmsly. managem ent o f such mailers as reproduc-

EARTH-SUNT h e Sun A f f e c t s Our Fo r e s t sSeveral pmpe rtie-.ofthe -.un helpexp lain theenergyrelations ot the forest The -.un I;. our most prominentneighbor in he solar \y il c m In relanon to the earth, 11

15 sta t~onary. owever . 11q p e m o trace A path x m sthe sky because the earth i s rocacing on if. axisTh e sun. which 45 ill the center ot our solar system.has ii diameter more than 100 times l~irgerhan that o ftheearth The sun 11.93 mi l l ion mi les 0 5 0 mi l l ion k m )o m he earth Th e solar radiation wh ich rcache-i thea r ~ hm#ve%m parallel rays b e c w ~ co i solar v z c anddistance I f he sun were umiiller than the earth. solard m u l d appear as diverging rays Bccawc thcray\ are parallel. shadow. appear as a direct image of

i o n and snow water yield considered solar radiationlevels broadly or qualitatively before any activitystarted. but made no specific plan based upon a de -tailed examination This paper discusses basic rela-tionships usable to m ore quantitatively evaluate howsolar radiation and shadows can be integrated atspecific si tes to achieve a managem ent goal.This paper summarizes some basic concepts ofapplied climatology and solar radiation, Although theprinciples are well known to those trained 11 m r r -meteorology, they may be less fam iliar to those wo rk-inginresourc e management andplanning. Anexa mplei i included to show how these princ iples can be used inr e management The paper i s designed to beu s t h a l e r eport Conlrolling .whir ight and1 2 m tn ~ t Jomrby ~ n o t r o ~ m ~ ( H a l ve r ~l ~ o d o w m ~ ~ r c ~ ~s o and Smith 19748). That repon has been supple-mented by as eriesoftableso na tree-shadow length for2" latitude m crementsspanning latitudes 3 V to 50" N.Requests for copies o f the earlier repon-ResearchPaper PSW -102-and o f the shadow-length tables~ h o u l dbe directed to Pacific Southwest Forest andRange Experiment Station. P 0 Box 245. Berkeley.California 94701. Alln. Puhltcat~onsDistribution.

RELATIONSthe source projected along the rays to the surface o f theearth P a r a l l d ~ mo f w l a r n d m m makc, 11 p q ~ h l cto c a l c ~ ~ l ~ t chddow lwmons, w n I o w t ~ o n ,and sunI wn h reasonable accuracyAlthough the sun look $ small because of earth-to-n -eparationcontains most of the masiofou rsol5ystem. about 99 percent. The sun generates energythrough nuclear fusion, creating helium from hydro^e n n the process ~co nve rtsso memaw toenergy at aa c l y onstant rate The sun should last abouto t h e r 30 b i ll ion years Muc h o f the nuclear rad ia tionm m e d b y the sun s screened b y distance and atmos-phere before it reaches the earth.The energy emitted from the sun arrives in p arallelrays. Because of the Fixed and predictable re lation o fearth to sun one may precisely determine the position


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anda nglea t w hich these rays will str ike any po rt iono ftheearth on any givend ay. as well astheenergy w hichi v e ' 1 at that point unless it has been modified bycloud cover. Arrangements or rearrangement of thespatial distribution of tree boles and crowns can pre-C t r o w ra dia tion re ach in g a ny spot o fground. Thu s. timber harvest and tree planting can be

n other ways

Polar Tilt Defines Our SeasonsThe earth rotates on an ax i s extending through thepolar latitudes and completes one rotation every 24

hours A variation o f about 2 seconds in day lengthdoes not significantly affect our purposes The polara s i t s 23'27' fro m norm al alinemcnt wi th the planeof the ell iptical orhn around the sun and this tdt 1sr e s p o n ~ b l cor the seasons.Summer occurs when ourhemisphere i s t ipped toward the -im. winter rewl t?when we arc angled away from the w r0 e l m toward or away from the wn 1se la ted to theear th 's loeatmnonan orb~ taro wd thes un

ifie I ) The earth completes one revolution every365.25 days, or each year The sun iippears displacednorth o f the equator during summer and south during

Figure 1 The earth rotates on its axis in an elliptical orbitround he sun The polar axis trlls23 27'from normal alsne-men1with !he plane of the ellipticalorbit around the sun

winter The angular displacement i s called the solardeclination. The points of m aximu m displacement arerefemd to as [he su mm er and w ~ n t e r s o l s ~ ~ c ~nd wcwahout June 22 and December 22. The vernal and a wtumnal equinoxe'i occur about March 22 and Septem-ber 22 when theearth's orb it crossesthe solar equator.The reference plane used to describe the declnmtmn o fthe sun i s defined b y the earth's equator As the earthrevolves abou t the sun. the solar disk appear7 to m ovebelow , south of theequator in winter, and above, northo f i t m summer The maximu m displacement 15 thesame as the t i lt of the earth's axis. 23- 27'. an d rsdef inedasposit ive on June 22 and negativeon Decem-be r 22 Latitude i s also defined by the same piamth o u gh the equator. The t ropics-Cancer andCapncom-are at the u m e lat~tu de s the mammumdeclination of the sun. the sun i s directly overhead onthe appropriate solstice. At the equinox, the s i n 17 mtheplaneoftheeanh'sequatoranddeclination iszero

As the canh progresses through one ro tamn on ~ t ?a v e r y 24 hours, the sun appeapi to trace a path i nthe sky and that path completes a circle around theglobe each day. This translates to 360' in 24 h o i m , orY p e r hour Thisquanmy. 15. isdef ined a*, t h e h o wn,elc. the spherical angle the sun posit ion mustt e r s e per hou rso that it w il l appear in the same place24 hours hence. I t i s referenced to noon. true solart when the sun s due south o f the observer, and rpositive before noon and negative after (I t i s moreprecise to say the earth mu st revolv e through an arc of15- per hour. but manner of presentation does notaffect the calculations of sun pov tmnThe locat ionofthesun in thes ky can bedescribed b ytwo angles when the declination, latitude, and hourangle are know n The following equations define thesun clcia non abovethe horizontal and thesina:,muchThe WI m m u l h 8, the arc o f the h o m m m e aw re dbetween south and the vertical circle passing throughthe center of the poin t o f observation and extending tothe \""

l e v a t i o n o f the sun i s given by the equation.n c = sin L sin d + cos I.CO T d cm h

e = aluiudeof the sun langularelevat ionabove thehorizon)L = latitude of the $it"d = decl~nat ion ngle of the sunh = hour anelc


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The azimuth o f the sun i s defined ascos d sin h$,"a =-0s en which a = azimuth of the sun measured eastward(+I or westward (-1 from south. The algebraic stgmi f he two t r igonometric funct ions in the variousquad-

rants are:F""c,,,>"- R,>"~L," D


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10 the fourth power o f the absolute temperature F I V ~y a m ater, in 1884, L udw ig Boltzmann proved the k won he bas is o f thermodynamics From the Bo ltzmm nxp en me nts we have the Stefan-Boltzmann equation'

m which o- i s the Stefan-Boltzmann con-itant (8 14 x1 0 l y ' T " ) T he sun lu x isequal to 56 x lOUly- ' d i v i d e d by the surface area o f the sun 16 093 x0 m So lving the equation and extracting thefourth root o f the temperature variable yields a radia-t o p e ra tu re o f 5 8 W K.

Black body radiation characteristics w m no t ex-plained by the wave theory of l ight I t remained forMax Planck (1858-1947). a theoretical physicist, todeterm ine that a ll radiant energy come, to u\ tn theo m f e lectromagnetic waves and on ly in "chunks"or diicre te e nergy packets These chunks are calledquansa Planck, in the early p an o f this century, d mcovered that the energy, I,emitted per second per unitarea per un it of frequency into a sphere was describedby the equation

, - 87rhv3c1 [;;]

c- I

in which h is Planck's mnsiant (6 6252 x 10 "ergc ) . ibfrequency ofradiation, ande i s the baseof thet og T he Boltzmann constant i s expressed 11om i s t en t un it s ( I 3805 x 10-'


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- S o l a r R a d i a t i o n T e r r e s t r i a l r a d i a t i o n -F a r i n f r a r ed -

I I l l l l l l I 1 l l l l0 0 5 0 0 1 0 0 0 5 0 0 0 1 0 , 0 0 0 1 0 0 . 0

W a v e l e n g t h , N a n o m e t e r sFlgure3.Aportionof theelectromagneticspectrum isshow n,separated intosolarandte rrestrialadiation Visible, ultraviolet,and infrared lightwaves do not represent all of the known kinds of electromagneticradiation Beyond thevisibleand infraredtoward longer wavelengths would be heat w ave s, beyond the shorter wavelength would be X-rays and gamma rays

s greater than absolute zero must radiate energy ins wavelength spectrum. Th is is true for terrestrialobjects whose temperature is much below that of solartemperature If we consider temperatures in the range273" to 335' Absolute KPC to 6Z0CI.we find the

d u g he yea r The wavelengths a re not v is ib le , arelonger than solar wavelengths and, by oonventcm , acedesignated longwave or terrestrial radiation Iffg,3).Gases like those of the atmosphere emit radiation asw e as d i d objects and vegeta tionWe h a w treated r a d ~ a t m rom sources of vanowtemperatures as discrete quantities, msum mg a c h

source is a perfect block bod\ which absorbs and e m uenergy as a function of temperature A perfect whitebody would absorb and emit nothing and, theoren-cally, would have a temperatureofabsolute zero Mostobjects fall somewh ere in between, that is, they dono tabsorb all incident energy, emit something less thanthe flux indicated by the Stefan-Boltzmann Law, andr e referred t o as gray bodies The ratio of actual totheoretical emission is called emi'ssivify Emissivny isw a y s l ess than unity Gray bodies react exactly asblack bodies, except that the radiation flux is loweredby a f a c t o r e q u a l t o e m i s s i v n y e q u a l l y in a llwavelengths The term gray body describes radiaimnpropertiesand not the visihlecolor that we see If these

imperfect absorbers and emitters also function differ-ently at different wavelenghts, that is, if they have aspectral response, they are called natural bodiesSpectral responses ar e usually measured in bands offrom 10 to oerhacs ICQ n a no m e er $ E m ~ w w t v17

If we speak of a comparatively narrow hand or singlewavelength, the property isusually terme dreflectwt,yA broader wavelength, such ast he ent ire visible band,h o w an integrated reflection called albedo The al-bedo of new snow in short wavelengths may exceed 9 0p e t o th er w ords, only a bo ut 10 percent of thesolar energy impinging on a snow surface is absorbedA o a r energy is absorbed, an object warms andemits an increasing flux of longwave energy Oneprocess that occurs naturally is the conversion of solarenergy t o ongwave energy by all the components ofthe eanh-atm osphere system . Since natural bodies aremperfec t emitters, the law of conservation of energymplies that some absorbed solar energy is used formo ther purpose, or transmitted through the body andnot emit ted . The Stefan-Boltzmam Ldw can beapplied to a gray body when modified by the emittance(61

Flux = e6TaThe Stefan-Boltzmann Law applies al w to natural


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twdic-.. hut ihc *;nelength or hanJ muit be i p f t i k dt h e actor c m3) l a r y indif ferent w.i i- .' .fngih h a du a l l y a ra te th ce n erg y s p e ct r u min n ~~ h nn a milon g wavelengths and use an integrated em isw ity .

Snow serves to po int out a nother interesting facet o fenergy relations Snow has a high albedo in shortwavelengths. However, in the long wavelengths i t actsI m o s t a*. a perfect black body. It absorbs and emuslongwave energy close to the theoretical value The

w n c may hold true for t t i r n i ~ iSgaition t)pe-. .indniher namr-il leaiure< 01 (he forest h e example ofs o u * p u t , cn.i the b r d h a n d spec tral nature t lu tmany natural radiation so urcesexhibit. When discuss-in g energy relations we should specify the wavelengthband of interest. Most natural emitters approximategray bodies over the total longwave spectrum Soils,vegetation, and snow p roperties ca n be approximatedwith the gray body equations.

ENERGY BALANCEOf the various energy sources for the earth, the

d m i i t one is the bun . Energy from the sun reachesthe earth as shortwave radiation, some i s converted tolongwave radiation withintheearth-atmosphere. Someenergy i s converted 10 another form within the bios-phere. through chemical reactions or transpiration.some in the atmosphere. through heating: and somewithin the hydrologic cycle, through snowmelt andevaporation. The energy, however, i s eventually re-leased w ith in theearthandatmosphere system becausethese reactions are all reversibleReasonably then. theea rthmus t loseasmuchenergyannually as i t receives from the sun. Otherwise theeanh and atmoiphere wo uld be getting ra pidly wannerc o l d e r . But theearth docs not get rapid ly wanner orcolder, at least not permanently. although episodessuch as the ice ages indicate there can be geological lyshort-tcnn alterations.The earth r e c a w about 263 kl v oer wa r at the too

k lvA Solar energy incident at the topof the atmosphere 263

Reflected by clouds 63Reflected by other atmosphere consumen ts 15Reflected from the surface o f the earth 16Tota l reflection (albedo) 94Absorbed by clouds 7Absorbed by other atmospheric constituents 38Absorbed by the surface of the earth 124To tal absorption 169

One o f the processes gomg on i s the conversion o fshortwave energy to longwave so that the earth ca nexist in an energy-balanced state. Therefore, we m ustlo-ie the equivalent o f 16 9 kl y per year in longwave

d o , An approximation of the loss is ,k1.v-ongwave radiation emitted

by the surface o f the earth 25 8Lost beyond the atmosphere 20Absorbed by the aimoiphere 238Longwave radiation emittedb y the atmosphere 355Lost beyond the atmosphere 149Reabsorbed by the earth's surface 206Sum o f radiat ion lost f rom the surfaceof the earth 52

Sum o f radiation lost from the atmosphere 117Total loss 169

So the earth enjoys an energy balance, emm ing asmu ch energy as i t receives This energy is not distnb-d evenly, however, and vanes by geographic loca-t o n anddate(dec1ination). Theenergy surplus in areaslik e the tropics i s transferred poleward by atmosphe rican d ocean currents to areas where deficits occur. Eachr e then. has a "typic al climate." Lo cal climaten y how s large annual variations-but these area s about a mean and not simply random totalchanges 1 1 c lmate

Although the earth as a whole i s in balance, theearth's surface and atmo sphere show an energy d wcrepancy E x a m ~ n s tm f annual radiat ion fluxesshow sthanh c earth'ssurface absorbs 124 kl y peryearand radiates 52 k ly so ihc earth's surface gains 72 kly .The mo wh ere ab so rbs 45 k lv and radiates 117 k lv ncr)CAI for a ncgainc halance nt 72 k l) Encrpy m~,! ki n s f e r re d fr im the ground to the


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LOCAL ENERGY RELATIONS~ U X C ,at ,,ngtc ,,tc mdy ",,IC X ~ C ~ I Y~ r g y ha).

anct d u m g a ~ h o n fo r exam-me span. one ~ c ~ w n ,ple Over ~ c v c r dyear,, hcnvcwr, a b ~ l a n ww d l occurw ch that energy received and energy I h t ar e equalTh e \un c \ w l l thc p n m q energy w w c e althoughhowont;d energy tramfcr hy at rn m ph er ~m o t m ando c c m u m m h n c c c w q to the cnwg y halance overt h c u r l h ' \ wf.m

t km o ~ m p o w h l e ,o mmdge fo re \& to m p m d


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Longwave radiation fluxes wcur when pans o f thew e ah\orh dircct mnwlat~on We a n a m some con-trol w e 7 Ikmgwwe rad mm n levels h y control l ing thevan, o r a ~ t eh c h are ex ws ed to 4~radra180n. Ingcncr8l. a w c e x po w d to \o la r r a d ~ m o n h ow \\econdary d fec l< indud ins mcrea \ed ~ 1 1c m p r d -lu re , m m m u m a r t e m p e r m r e , e v a pmmn , :and era-yx rm on . Heal f l u x ? are gr ea IN ;kt the ground w r-I n e , hut mm >mu m empm mre \ w(1I he a tu~~ neda1rt m m d m w ly a h w e the gro un d w htch ~ ~ r c c c w m gd l-at1011 rom h t h the a tm m ph m and the ground I fs lr cd m 5o rm o w a r e p r e w n t h c w d w r @ e m p r m r e nll

MANAGEMENT TECHNIQUES

1 r d l c c ~ d em ~ttedr e ~ e m w ~ l l y 1y the earth, \omcret;$imd and wed to drwe the variou\ phywdogicdm d h m lo g~ ca l mce\\c\ wtth n , h ~ h e are h m ~ l ~ a rhe WIW o r total mncldent radrdtton "01 WII u,!much ah ou $hc evel ofcnergy a1 f o m t \ i t m Tdh lc\ofw l x h e m ~ m d ia u o n re a \ a I a h l c fo r l he m ~ d -Iht8 tud e~ . oweve r Th c vahle, puhlm\hed hy Frank and

Let (19661 l i\ t the p m e m d w l u adnmon l m d ~o ~bMlOU< a


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Encwrwpg r e p m d u c t m IT 8 \ p e c i case, w ~ hhe~ ~ l v ~ c u ~ ~ u r deqummentso f lhede \# red \pc !es~e t t~ng

EXAMPLE: A MANAGEMENT PROBLEM\hadow table i\ a v a k ~ b l etn an earlier p u h l i ca t mIWdIvcnon and Smith 1974h). But wc need #"forma-t m on p m t ~ a l01a radmt#on. The l'ables b y F m n kand L ee (l9 66 ) l i ~ ~ o n l y d o ; l v ~ o t d ~n d w ~ l ln o t g ~ v c u \

h r m ~~ w i h ~ m o n the & tj. D n p m % y B uff0 andothers (19721. however. g~ v e ourly md ra mn fluxe5for a variety o f dales and dopes, so we d m d e to methese wbIc\. A, often happens, the solar r a d m l mlahIe$ do "01 Ih t the e x 8 a dale and q l q x of mtere\t,An d Bu ffo and other? I19721 assumed an ~ t m o ~ p h c c ~t m m m w i o n o f 0 9 T r a n sm m m o f m l w mdm11.m

I a m u d c ~ .atmmph& tcansmmm n usually vanesf ro m a b u t 0 . 5 l o 0.9 , w ~ t h n average nearO.6 Anatmmphenc tran sm m~ on f 0 9 mtght not k apphcd-h k for our p u p x e s k c a u s e o f u n u sm l l w d c oo di-t iom , such a%aw p l l u t ~ o n . ocal m e ~ e o m l o g ~ wd lk able to ~ p p l yn estmate o f alm mp hem !rammrs.s m n . D#fticult!eswe often encountered k c a u s e ofxhee x t m w e range of slops and numerous dates forwh xh t ran\m!won cw f f ia en ts would y ie ld an almostm f i n ~ t e u m kr o f co m hm m o n\ . I f the s~ t e s verycrmc& com ct ions would k equired. But for mostpurpose


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No n h13299

66-3 iSouth W w E a s03 Use I - h o w m t e w a l ~ ,mnmg at 05 78 houm,

w n m e , 10 17 78 hours , p t efore w m e t4 A-I" the d8 mm Ium n mdzcates he pomt 1 m the

Wc can check o ~ r c d l c ~ ~ l a t ~ ~ n sy m tm g that radra-tmn total at a p i n t e x p s ed a ll day, a b u t 540 ly , fa llswxhm the rmge gwen by Bu fh and others (1972)w h c h ~5Sffl fo r a dope o f 0 and 420 f o r 2 slope o f I 5percent. A l w , we need to note the u n w m m d ~ a t m nd ~ t r # h u t ~ o nwdent m the openmg or8ented e m andwe


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LITERATURE CITEDH . H u t i d h w i . Smilh

W e hadow length tahles fn r latitude W iwrlt. IS D AFwe! s c n , 4v " P.,',,,, ,,?t,,h-e\, IW C \ , .,"d Range E T ~S . lcrkrlr\. Cold

H m . tlna.iri! (1 ..mil lm-.. Smith'7-kl Shadow length l a h h for l i i ldudr 42 north. L > D A

1 7 8 Shadow length mhks for IalKudr 48 north . LSDAF*c\,Wc\, .,"d R4"W L


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The Pacific Southwest Forest and Range Experiment S tationri;prcsent\ th e research branch of th e Forcsi Service in Cal i forn ia ;and Haviai i .

Documents

Solar radiation as a forest management tool: a primer of principles and application