PACIFIC SOUTHWEST Forest and Range Experiment Station
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C;EXERAI. TKCIINICAI. RIPORT PSW- 33 SOLAR RADIATION AS A FOREST MANAGEMENT TOOL a primer and application of principles
Howard G. Halverson James L Smith
CONTENTS
Pace Introductm ...... I Earth-Sun Relations ...... I The Sun Affects Our Forests ...... I Polar Till Define-i Our Seasons ...... 2 Sun-Eanh Energy Relations ...... 4 Energy Balance...... 7 Local Energy Relations ...... 8 Management Technique5 ...... 9 Example A management Problem ...... ,,10 Literature Cited ...... 13
Pacific Southwest Forest and Range Experiment Station P.O. Box 245 Berkeley, California 94701 April 1979 . . 0 9 b S , n n u . 9 M , I950) and Michigan Slate Lni>mwy (Ph U m h>drolng>. 19541 INTRODUCTION
he sun isthe primary source ofenergy for theearth ion and snow water yield considered solar radiation T.and il-i atmosphere. Solar energy drives the levels broadly or qualitatively before any activity biologic, hydrologic. and atmospheric processes The started. but made no specific plan based upon a de- second largest energy source is the heat flux from the tailed examination This paper discusses basic rela- tionships usable to more quantitatively evaluate how solar radiation and shadows can be integrated at specific sites to achieve a management goal. This paper summarizes some basic concepts of solatmn >sused to comb~neelem~nts found near [he applied climatology and solar radiation, Although the surface of the earth so that essential physiological principles are well known to those trained 11 mrr- processes necessary for forest growth and maturity can meteorology, they may be less familiar to those work- be comnleted The sun alsodrives the hvdroloeic cvcle inginresource management andplanning. Anexample ii included to show how these principles can be used in r e management The paper is designed to be logic cycle because wood and water are tangible prod- uswth a lerreport Conlrolling .whir light and ucts of fore~tland. 12m tn ~tJomrby ~notro~m~~l~odowm~~rc~~ (Halver~ We cannot manage or control the incident solar soand Smith 19748). That repon has been supple- radiation received by large land areas: however, forest mented by aseriesoftablesona tree-shadow length for magement can exert significant effect on local insol- 2" latitude mcrementsspanning latitudes 3V to 50" N. ation in small areas. Harvest and regeneration patterns Requests for copies of the earlier repon-Research anbe designed to increase or decrease !he radiation Paper PSW-102-and of the shadow-length tables level at many sites The objectives of the managemem ~houldbe directed to Pacific Southwest Forest and plan can determine the level of insolation desirable. Range Experiment Station. P 0 Box 245. Berkeley. Pre>vmsly. management of such mailers as reproduc- California 94701. Alln. Puhltcat~onsDistribution.
EARTH-SUN RELATIONS
The Sun Affects Our Forests the source projected along the raysto the surface of the earth Paralld~mof wlar ndmmmakc, 11 pq~hlc to calc~~l~tc\hddow lwmons, wn Iowt~on,and sun Several pmpertie-.ofthe -.un helpexplain theenergy I wnh reasonable accuracy relations ot the forest The -.un I;. our most prominent Although the sun look$ small because of earth-to- neighbor in the solar \yilcm In relanon to the earth, 11 n ¥-eparationncontains most of the masÈiofoursol 15stat~onary.however. 11 qpemto trace A path xms 5ystem. about 99 percent. The sun generates energy the sky because the earth is rocacing on if. axis through nuclear fusion, creating helium from hydro^ The sun. which 45 ill the center ot our solar system. en In the process ~convertssomemaw toenergy at a has ii diameter more than 100 times l~irgerthan that of aclyconstant rate The sun should last about theearth The sun 11.93 million miles 050 million km) other 30 billion years Much of the nuclear radiation omthe earth The solar radiation which rcache-i the mmed by the sun is screened by distance and atmos- ar~ham#ve%m parallel rays becw~coi solar vzc and phere before it reaches the earth. distance If the sun were umiiller than the earth. solar The energy emitted from the sun arrives in parallel d mwuld appear as diverging rays Bccawc thc rays. Because of the Fixed and predictable relation of ray\ are parallel. shadow. appear as a direct image of earth to sun one may precisely determine the position andangleat which these rays will strike any portionof winter The angular displacement is called the solar theearth on any givenday. as well astheenergy which declination. The points of maximum displacement are ive'1 at that point unless it has been modified by refemd to as [he summer and w~ntersols~~c~and wcw cloud cover. Arrangements or rearrangement of the ahout June 22 and December 22. The vernal and aw spatial distribution of tree boles and crowns can pre- tumnal equinoxe'i occur about March 22 and Septem- Ctor owI radiation reaching any spot of ber 22 when theearth's orbit crossesthe solar equator. ground. Thus. timber harvest and tree planting can be The reference plane used to describe the declnmtmn of the sun is defined by the earth's equator As the earth revolves about the sun. the solar disk appear7 to move below, south of theequator in winter, and above, north of it m summer The maximum displacement 15 the n other ways same as the tilt of the earth's axis. 23- 27'. and rs definedaspositive on June 22 and negativeon Decem- ber 22 Latitude is also defined by the same piam Polar Tilt Defines Our Seasons though the equator. The tropics-Cancer and Capncom-are at the ume lat~tudeas the mammum The earth rotates on an axis extending through the declination of the sun. the sun is directly overhead on polar latitudes and completes one rotation every 24 the appropriate solstice. At the equinox, the sin 17 m hours A variation of about 2 seconds in day length theplaneoftheeanh'sequatoranddeclination iszero does not significantly affect our purposes The polar As the canh progresses through one rotamn on ~t? astits 23'27' from normal alinemcnt with the plane a very 24 hours, the sun appeapi to trace a path in of the elliptical orhn around the sun and this tdt 1s the sky and that path completes a circle around the respon~blcfor the seasons.Summer occurs when our globe each day. This translates to 360' in 24 hoim, or hemisphere is tipped toward the -im. winter rewlt? Yper hour Thisquanmy. 15'. isdefined a*,thehow when we arc angled away from the wr n,elc. the spherical angle the sun position must 0 e l m toward or away from the wn 1s terseper hourso that it will appear in the same place elated totheearth's loeatmnonan orb~tarowdthesun 24 hours hence. It is referenced to noon. true solar ifie I) The earth completes one revolution every t when the sun is due south of the observer, and r 365.25 days, or each year The sun iippears displaced positive before noon and negative after (It is more north of the equator during summer and south during precise to say the earth must revolve through an arc of 15- per hour. but manner of presentation does not affect the calculations of sun povtmn The locationofthesun inthesky can bedescribed by two angles when the declination, latitude, and hour angle are known The following equations define the sunclcianon abovethe horizontal and thesina:,much The WI mmulh 8, the arc of the homm meawred between south and the vertical circle passing through the center of the point of observation and extending to the \""
levation of the sun is given by the equation.
n c = sin L sin d + cos I. COT d cm h
e = aluiudeof the sun langularelevationabove the horizon) Figure 1 The earth rotates on its axis in an elliptical orbit L = latitude of the $it" round the sun The polar axis trlls23 27'from normal alsne- d = decl~nationangle of the sun men1with !he plane of the ellipticalorbit around the sun h = hour anelc The azimuth of the sun is defined as 2.The half-day length (HIatall but polar latitudesis 0sH = tan Ltan d. The half-dav leneth will be cos d sin h $,"a = - "0s e
n which a = azimuth of the sun measured eastward all but the polar latitudes. (+I or westward (-1 from south. The algebraic stgm 3. In polar latitudes cos L is 0. sin L is 1, and sm ifthe two trigonometric functions in the variousquad- a = ind. from theequation for solar elevation. rants are: Then the elevation angle of the sun at the poles -F""c,,,>" R,>"~L," D Figure 2.Atagiven latitude, relationshipsamongthe hourangle. zenith angle, and solarelevationcan beshown (R) = the endpoint of a line from the center of the earth (01 to the center of the sun (R). o = center of the earth, p = position of obe~er,lineopvistheverticalalthe~ositionofthcobsewer,r'= 1inelromobseweftosun.or'R = hnefromthecenterof theearthtothesun Thevariousanglesarez = zemh anglebetweencenterolthesuna~theverticalatthepositionofth beer,h = hour angle between NPS and NT'S,a = azimuth of the sun. and 90"-z = elevation of the sun have been modified also by political entities to place true solar time because the edge of the dar hemi- entire States within asmgle time zone Local time may sphereappears before thecenterofthe sunand becau~ a considerably from solar time in different regions. atmospheric refraction makes the solar disk appear Using solar time as a base avoids the necessity to slightlyearlier.Thesametwoeffectsalsodelaysin~~t. consider these variations, The dewamn Iht, ahout 4 mmutc\ at m~dlat~tude~. Solar time is referenced to the center of the solar and increases in time wnh increasing latitude disk Apparent sunnx occurs slightly before wnc~m SOLAR ENERGY RELATIONS The various laws which govern the generation and away from the sun The energy received per unit area flux of radiations are well established These law,, on a sphere with a radius equal to the average distance which we apply, date hack to the 19th century and from the sun to the earth is thw earlier, and reached their maturity during "the thirty years that shook physics." from 1900 to 1930 ' Be- e these laws are important to the manipulation of or radiation data for management purposes, they wnll be reviewed. The basic unit of energy is the 15- gram-calorie (cal). [his is the amount of heat required to raw the temperatureof 1 gram of water 1°C When thisenergy is expressed on an area basis the unit area i~cmz The langley (ly) ts Igcaloriecm >.The kilolangley (kly) is, depends on transmission lo-ises in the atmosphere and by convention, IOOOly The langley unit isconvenient the sine of the angle between the earth surface and the for use in forest science because processes wch a\ rays from the sun. Because of variations in energy evaporation and snowmelt use the calorie as the bas^ output from the sunanddiffcnngdiitancesofeanh-sun nt.Otherdisciplinesuseotherunits, such asthewatt. separation, the solar constant vane-, by about 1 5 per- erg, joule, or Brmsh thermal unit IBTU) These quaw cent around the man value value^ of the 4arcon- ties are all intcrchangeahle with conversion facton stant reported in the literature also vary between I.94 such a< and 2 ly mm 8. hut for most purposes, the value 2 ly One 15" g cçcm-I = I cal cm-l m 1s acceptable.l The emission and absorption of radiation by the wn = I ly 1000 ly = I kly ire described by a numher of fundamental relatmm is their absorbing powers, or they could never attam The addition of the time unit. minutes, conven-i the temperature equality Qualitatively, therefore, Kirch- erg1 ' . to fix Flux is thc quantity of radian! hoff's Law says that good absorbers ofeicrpy are also energy of all wavelengths (call crossmg a unit area of goodemitters A hlcukhodv IS an object that emits and surface lcm'l per unit tme (mi") Minute5 are chmm absorbs radiation in all wavelength\. The tern "black ratherthan second-i10 prevent negative exponents from body" isaphysical one-it may not dc-ic-nhe thecolor appearing with the equivalent energy quantities. that we -see. although generally, objects that appear Theenergy emitted from thesun isabout 56x 1V61y I to u realso good radiation abwrhers and emit- mm~',and theearth isa meand~mnceof I 5 x 10"m ters If the sun is assumed to be a black body we can calculate its radiation temperature In 1879, Josef Ste- fan 11835-1893) deduced that the total em~ssmnof a black body for all wavelength\ together isproportiowd 10 the fourth power of the absolute temperature FIV~ The number of quanta emitted in a large-scale proc- yamlater, in 1884, Ludwig Boltzmann proved the kw s,h a I d t s so great that individual on the basis of thermodynamics From the Boltzmmn quanta cannot be distinguished Such a process, there- xpenments we have the Stefan-Boltzmann equation' tore, appear-, to be continuous Planck's assumption, later proved correct, gave a method to determine the relative energy of radiation of different frequencies Black bodies radiate at several frequencies centered m which o- is the Stefan-Boltzmann con-itant (8 14 x butmmm. Wilhelm Wien 11864-1928) proved 10ly"'T") The sun flux isequal to 56 x lOUly hat m energy radiated by a hot body shifts to -'divided by the surface area of the sun 16 093 x he and shorter waves as the temperature rases. 0 m Solving the equation and extracting the The maximum in terms of frequency can be derived fourth root of the temperature variable yields a radia- from the relationship tomperature of 58W K. c Black body radiation characteristics wm not ex- " =- plained by the wave theory of light It remained for A Max Planck (1858-1947). a theoretical physicist, to Using the measured wavelength of maximum radw determine that all radiant energy come, to u\ tn the lion we can determine the absolute temperature of an omof electromagnetic waves and only in "chunks" object by solving the equation which approximates or diicrete energy packets These chunks are called When's Law In the general case, Wien's Law 15 quansa Planck, in the early pan of this century, dm covered that the energy, I,emitted per second per unit area per unit of frequency into a sphere was described by the equation A = wavelength , - 87rhv3 T = absolute temperature w = Wien's displacement constant c1 [;; ] An approximation of Wien's Law. with w determined c- I exper,menta11y 1, in which h is Planck's mnsiant (6 6252 x 10 "erg c).v ibfrequency ofradiation, ande is the baseof the Solving Planck's equation for each frequency 1s tI log The Boltzmann constant is expressed 11 tedious Using Wien's Law, however, we find that omistent units (I 3805 x 10-' This equation can he written also as E = nhv, 1" Terrestrial Energy Relations which n is a whole number and is called a qucinmn A l~ttlereflemon on the nature of Planck's work and unhcr and hv is called a quamum of mew. Wien's Law tells us that any object whose temperature -Solar Radiation Terrestrial radiation- Far infrared- I I llllll I 1 llll 00 500 1000 5000 10,000 100.0 Wavelength, Nanometers Flgure3.Aportionof theelectromagneticspectrum isshown,separated intosolarandterrestrialradiation Visible, ultraviolet, and infrared lightwaves do not represent all ofthe known kinds of electromagnetic radiation Beyondthevisibleand infrared toward longer wavelengths would be heat waves, beyond the shorter wavelength would be X-rays and gamma rays s greater than absolute zero must radiate energy in imperfect absorbers and emitters also function differ- s wavelength spectrum. This is true for terrestrial ently at different wavelenghts, that is, if they have a objects whose temperature is much below that of solar spectral response, they are called natural bodies temperature If we consider temperatures in the range Spectral responses are usually measured in bands of 273" to 335' Absolute KPC to 6Z0CI.we find the from 10 to oerhacs ICQ nanomeer$ Em~wwtv17 dugthe year The wavelengths are not visible, are If we speak of a comparatively narrow hand or single longer than solar wavelengths and, by oonventcm, ace wavelength, the property isusually termedreflectwt,y designated longwave or terrestrial radiation Iffg, 3). A broader wavelength, such astheentire visible band, Gases like those of the atmosphere emit radiation as how an integrated reflection called albedo The al- weas did objects and vegetation bedo of new snow in short wavelengths may exceed 90 We haw treated rad~atmfrom sources of vanow petn other words, only about 10 percent of the temperatures as discrete quantities, msummg ach solar energy impinging on a snow surface is absorbed source is a perfect block bod\ which absorbs and emu A oarenergy is absorbed, an object warms and energy as a function of temperature A perfect white emits an increasing flux of longwave energy One body would absorb and emit nothing and, theoren- process that occurs naturally is the conversion of solar cally, would have a temperatureofabsolute zero Most energy tolongwave energy by all the components of objects fall somewhere in between, that is, they donot the eanh-atmosphere system. Since natural bodies are absorb all incident energy, emit something less than mperfect emitters, the law of conservation of energy the flux indicated by the Stefan-Boltzmann Law, and mplies that some absorbed solar energy is used for re referred to as gray bodies The ratio of actual to mother purpose, or transmitted through the body and theoretical emission is called emi'ssivify Emissivny is not emitted. The Stefan-Boltzmam Ldw can be ways less than unity Gray bodies react exactly as applied toa gray body when modified by the emittance black bodies, except that the radiation flux is lowered (61 by a factor equal to emissivny equally in all Flux = e6Ta wavelengths The term gray body describes radiaimn propertiesand not the visihlecolor that we see If these The Stefan-Boltzmann Law applies alw to natural twdic-.. hut ihc *;nelength or hanJ muit be ipftikd wnc may hold true for ttirni~iSgaition t)pe-. .ind thetactor c m3) lary indifferent w.ii-.'.fngih had niher namr-il leaiure< 01 (he forest heexample of uallyqaratethcenergy spectruminn~~hnnami sou* put, cn.i the brdhand spectral nature tlut long wavelengths and use an integrated emiswity. many natural radiation sourcesexhibit. When discuss- Snow serves to point out another interesting facet of ing energy relations we should specify the wavelength energy relations Snow has a high albedo in short band of interest. Most natural emitters approximate wavelengths. However, in the long wavelengths it acts gray bodies over the total longwave spectrum Soils, Imost a*. a perfect black body. It absorbs and emus vegetation, and snow properties can be approximated longwave energy close to the theoretical value The with the gray body equations. ENERGY BALANCE Of the various energy sources for the earth, the d o , An approximation of the loss is, dmiitone is the bun. Energy from the sun reaches -k1.v the earth as shortwave radiation, some is converted to Longwave radiation emitted longwave radiation withintheearth-atmosphere. Some by the surface of the earth 258 energy is converted 10 another form within the bios- Lost beyond the atmosphere 20 phere. through chemical reactions or transpiration. Absorbed by the aimoiphere 238 some in the atmosphere. through heating: and some Longwave radiation emitted within the hydrologic cycle, through snowmelt and by the atmosphere 355 evaporation. The energy, however, is eventually re- Lost beyond the atmosphere 149 leased within theearthandatmosphere system because Reabsorbed by the earth's surface 206 these reactions are all reversible Sum of radiation lost from the surface Reasonably then. theearthmust loseasmuchenergy of the earth 52 annually as it receives from the sun. Otherwise the Sum of radiation lost from the atmosphere 117 eanh and atmoiphere would be getting rapidly wanner Total loss 169 colder. But theearth docs not get rapidly wanner or colder, at least not permanently. although episodes such as the ice ages indicate there can be geologically So the earth enjoys an energy balance, emming as short-tcnn alterations. much energy as it receives This energy is not distnb- The earth recaw about 263 klv oer war at the too d evenly, however, and vanes by geographic loca- ton anddate(dec1ination). Theenergy surplus in areas like the tropics is transferred poleward by atmospheric and ocean currents to areas where deficits occur. Each r e then. has a "typical climate." Local climate nl y shows large annual variations-but these are Aklv a s about a mean and not simply random total Solar energy incident at the top changes 11 clmate of the atmosphere 263 Although the earth as a whole is in balance, the Reflected by clouds 63 earth's surface and atmosphere show an energy dw Reflected by other atmosphere consuments 15 crepancy Exam~nstmof annual radiation fluxes Reflected from the surface of the earth 16 showsthanhc earth'ssurface absorbs 124 kly peryear Total reflection (albedo) 94 and radiates 52 kly so ihc earth's surface gains 72 kly. Absorbed by clouds 7 The mowhereabsorbs45 klv and radiates 117 klv ncr Absorbed by other atmospheric constituents 38 )CAI for a ncgainc halance nt 72 kl) Encrpy m~,! k Absorbed by the surface of the earth 124 insferred frim the ground to the ~~rgy~UXC,at ,,ngtc ,,tc mdy ",,I CX~C~IYha). anct dumg a ~honume span. one ~c~wn,for exam- ple Over ~cvcrdyear,, hcnvcwr, a b~lanwwdl occur wch that energy received and energy Iht are equal The \un c\ wll thc pnmqenergy wwce although howont;d energy tramfcr hy atrnmpher~motm and occm ummh1, ncccwq to the cnwgy halance over thc urlh'\ wf.m tkmo ~mpowhle,to mmdge fore\& to mpmd Albedo and emmwity wdl vav. therefore the tabu- hted vdum ahow are m the range ,ha( mqhe ex- pled Alhedo mcrease~aslhemtdm angle of nd~a- tmndccreme~.The valuesforalkdoassume the wnL? near muth, 50 alhedw m early morning and law aftw noon would he hyher Emmw~tydces not wry a5 much kcawe I, i?a propeny of the mdmmg body. Ern~wwy.however, may vary shghtly w~th~cmpera. tun- Thc cm~~v~tyvmam LS so shgh! lor a g~vm naluml had? tha 81 is uwatly pored. excep! when m. we can draw \"me general ~ondusmns Dmct wlw radmtm n the kst vmahle to manage kcawe dar Iw*~,""and flux are predlctahl" D,f- tuwd 'ol~rmdmtm a\ wattered downward from 811 pans of the sky and vegetalm managemen! would hwe ,mdl ~ff%"'. 8 Longwave radiation fluxes wcur when pans of the we ah\orh dircct mnwlat~on We anam some con- trol we7 Ikmgwwe radmmn levels hy controlling the van, or a ~tewhch are exwsed to 4~radra180n. In gcncr8l. a wc expowd to \olar rad~mon?how\ \econdary dfecl< indudins mcrea\ed ~11lcmprd- lure, mmmum artempermre, evapmmn, :and era- yxrmon. Heal flux? are greaIN ;kt the ground wr- Ine, hut mm>mumlempmmre\ w(1I he atu~~nedm a1r tmmdmwly ahwe the ground whtch ~~rcccwmgmdl- at1011from hth the atmmphm and the ground If slrcdm5ormow areprewn thcwdwr@emprmrewnll MANAGEMENT TECHNIQUES 1, rdlcc~dore~emw~lly em~ttedby the earth, \omc 1, ret;$imd and wed to drwe the variou\ phywdogicd md hmlog~calpmce\\c\ wtth n,h~hwe are hm~l~ar he WIW or total mncldent radrdtton "01 WII u, !much ahou $hclevel ofcnergy a1 fomt \itm Tdhlc\of wlx hem ~mdiauonare a\aIahlc for lhe m~d- Iht8tude~.however Thc vahle, puhlm\hed hy Frank and Let (19661 li\t the pmemd wluradnmon lmd~fo~ bMlOU< a EXAMPLE: A MANAGEMENT PROBLEM \hadow table i\ avak~bletn an earlier puhlicatm IWdIvcnon and Smith 1974h). But wc need #"forma- tmon pmt~al501a radmt#on. The l'ables by Fmnk and Lee(l966) li~~onlydo;lv~otd~andw~llnotg~vcu\ d~wih~monhrm~ the &tj. Dnpm%hy Buff0 and others (19721. however. g~vehourly mdramn fluxe5 for a variety of dales and dopes, so we dmde to me these wbIc\. A, often happens, the solar radmlm lahIe$ do "01 Iht the ex8a dale and qlqx of mtere\t, And Buffo and other? I19721 assumed an ~tmo~phcc~ tmmmwion of 0 9 Transmmm of mlw mdm11.m Iamudc~.atmmph& tcansmmmn usually vanes from abut 0.5 lo 0.9, w~than average nearO.6 An atmmphenc transmm~onof 0 9 mtght not k apphcd- hk for our pupxes kcause of unusml lwd coodi- tiom, such a%aw pllut~on.Local me~eomlog~wwdl k able to ~pplyan estmate of almmphem !rammrs. smn. D#fticult!eswe often encountered kcause ofxhe extmwe range of slops and numerous dates for whxh tran\m!won cwffiaents would yield an almost mfin~tenumkr of comhmmon\. If the s~te1s very crmc& comctions would k required. But for most purpose 66 - 33 i South Ww Eas 0 3 Use I-how mtewal~,mnmg at 05 78 houm, wnme,10 17 78 hours, pthefore wmet 4 A-I" thed8mmIumn mdzcates the pomt 1, m the Wc can check o~rcdlc~~lat~~nsby mtmg that radra- tmn total at a pint expsed all day, abut 540 ly, falls wxhm the rmge gwen by Bufh and others (1972) whch ~5 Sffl for a dope of0 and 420 for2 slope of I5 percent. Alw, we need to note the unwm md~atmn d~tr#hut~onewdent m the openmg or8ented emand we,, LITERATURE CITED H . Hut<; i d hwi1. Smilh WeShadow length tahles fnr latitude W iwrlt. ISDA Fwe! scn , 4v " P.,',,,, ,,?t,,h-e\, IWC\, .,"d Range ET~ S . llcrkrlr\. Cold H m . tlna.iri! (1 ..mil lm-.I. Smith '7-kl Shadow length lahh for liildudr 42 north. L>DA 178 Shadow length mhks for IalKudr 48 north. LSDA F<"N 5m .$9 p Pdc#,#c%>",I>*c\,i Wc\, .,"d R4"W L