PACIFIC SOUTHWEST Forest and Range Experiment Station \ \\ \ 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<xz:, equals the declination angle, 0-90 90 180 180-270 270-360 4 The day is always symmetrical about solar noon sm + * - - on a level surface, that is. sunrise and sunset coume - - + + wcur the sme number of houm before and after 1arnThe azimuth and elevation angles are Another angle frequently encountered incalculation the mefor equivalent numbers of hours before of sun position is the yniih angle (7.1, the angular and after solar noon. Also. the azimuth west of separation of the sun from vertical at the sue. There- south st sunset I? equmalmt to the sunme fore. azimuth east of south Calculations forthe firstor 7. = 90"-e second half of a day can be transposed across I on10 describe the remaining half day ndfrom trigonometric identities The calculations described are all based on me I rime-sometimes called sun time. Solar time 1s COS 7. = sin e calculated from solar noon. when the sun isdue south. The relationships of the variou'i angles can be dia- along the meridian, of the observer.