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MODELING LIGHT PEN A SLASH PINE (Pinus ETRATION THROUGH elliottii)CANOPY KEVIN SCOT MCKELVEY a DISSERTATION PRESENTED TO THE GRADUATE SCHOOL THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA .,ull(*Y This work is dedicated wife Madeleine, and daughters Adrienne Tara. ACKNOWLEDGEMENTS Much data this dissertation was the result work many: Collection of data on CO, assimilation, foliar biomass light absorption canopy were carried out as part a fouryear study slash pine funded National Science Foundation. In particular would like thank Henry Gholz Sherry Vogel analysis analysis biomass fluctuation, of assimilation data, Wendell Cropper Katherine Ewel long hours of consultation without which this work would not have progressed. there is good science here, should receive a great deal credit. TABLE OF CONTENTS ACKNOWLEDGEMENTS ABSTRACT S. INTRODUCTION MODELING HIERARCHICAL EFFECTS IN SLASH PINE a a. a 14 Characteristic Evaluation of of Sla Model sh Pine Approache * a a. 14 Light Penetration Modeling in Discrete Space . 23 A DISCRETE SPACE MODEL FOR SLASH PINE . . . 29 Data Model Model Acquisition Structure Results . . 29 *. . . a a 45 *. a . a . 53 MODELING MODELING SEASONAL LIGHT PE BELOW CANOPY NETRATION LIGHT WITHIN PENETRATION CANOPY * 62 Sa a *. 88 EVALUATING MODEL a a a a a a a a . 95 CONCLUSIONS a a . a a a a a a a a .a Discu ssion of Light Penetration Through Future Slash Research Pine Needs a a a a a a . . a a a . a a a LITERATURE CITED a a a a a a a a a a a a a a APPENDIX COMPUTER CODE FOR DISCRETE SPACE MODELING OF LIGHT PENETRATION BIOGRAPHICAL SKETCH Abstract of Dissertation he University Requirements MODELING A SLASH P of Florida Presented in Partial Degree LIGHT INE of Doctor PENETRATION (Pinus elliotti Graduate School Fulfillment of Philosophy THROUGH i) CANOPY Kevin Scot McKelvey August, 1990 Chairman: Major Katherine Department: Ewel School Forest Resources and Conservation Conifer canopies are a hierarchy of discrete objects: crowns, shoots, and needles. Light penetration through this hierarchy is controlled size arrangement, and opacity of objects at each level. If light penetration patterns crown are level, dominated relationship organization between the light shoot or the penetration and leaf area will be indirect. The crowns of slash pine are conic, and the foliage is clumped. A discrete shootlevel geometric model was created to determine the importance this structure on light penetration. Shootlevel parameters were measured the laboratory using controlled light. Light penetration data was gathered from sensor arrays placed above below the canopy. Seasonal foliage biomass patterns stand were derived from destructive sampling, litterfall, and needle elongation Light penetration through canopy was simulated full range sun angles azimuths. Azimuth was found to be an important controlling parameter light penetration, and model output reduced to a single multiple regression equation based on sun angle and biomass per shoot. This simplified model was used to simulate light penetration days. Data midsky simulated indicated on uniformly assuming that light overcas that emanated t days. diffuse primarily Diffuse light light from was emanated from 45degree angles of elevation. model duplicated observed patterns seasonal variation in belowcanopy light penetration and explained the daily variation in belowcanopy light penetration during a 2month period centered on the winter solstice. Light penetration within canopy, when simulated planar surfaces, was similar to patterns generated vertically stratified, horizontally homogeneous models. When light penetration the simulated shoot positions was modeled, however, the patterns diverged due to selfshade within crown. The model accurately tracked pattern light penetration over time and, once calibrated, could used predict seasonal changes in foliar biomass. Leaf area could nont however be accurately estimated directly from liaht penetration because proportion light interception to woody biomass was unknown. INTRODUCTION Photosynthesis only pathway which sun energy can enter an ecosystem be stored in a metabolically utilizable form. Ecosystem metabolism is dependent upon limited estimate photosynthetic of photosynthetic production. input Obtaining therefore an accurate essential any attempt to quantify energy or carbon flow through ecosystem. The actual measurement gross primary productivity (GPP) difficult due to photorespiration. For most practical purposes, however, rate of CO, ass imilation, which measurable , provides a good approximation carbon input into system. intensity photosynthetically active radiation (PAR) the leaf surface acts as a direct control on assimilation rates. Because canopylevel assimilation sum the assimilation rates of all leaves leaf assimilation can be scaled canopy level quantity foliage and light penetration patterns through the foliage are known. Over time, foliage position light penetration are coupled. shift A change light in foliage penetration distribution pattern. will shift cause in the light penetration pattern will turn cause a change foliage light distribution penetration component of either due to growth formulations static are or dynam abscission. therefore a nece ic physiological Accurate ssary models. Life is defined pattern, pattern exists at all levels of scale nature. In science in general modeling in particular, pattern is often ignored in favor mean values. Models based on mean values are simpler less data intensive, but there are dangers this approach if relationships between variables are nonlinear. In light foliage penetration is generally modeling assumed through to lack forest spatial canopies, pattern, mean values light penetration through canopy are used indirectly to derive a variety of parameters such leaf area index (LAI), photosynthesis , and evapotranspiration. Because these parameters are related to light penetration through nonlinear functions, heterogeneous foliage distribution can affect calculated examines value the these effect parameters foliage . This distribution dissertation patterns  I.a  a a a a a 'and mm m . . Traditional foliage light distribution penetration models homogeneous assume space and that that leaves are opaque. this assumption of opacity valid, probability of a beam light penetrating canopy is simply probability that it will pass through canopy without contacting any the leaves . If the leaves are randomly distributed, number of contacts follows Poisson distribution with contacts = exp(uz) where contacts = the probability that a beam passes through canopy without intersecting any leaves, = the average leaf area, and = the length path that beam must travel (OkerBlom 1986). a large number beams , Pno contacts becomes the average through proportion canopy. of light This beams equation, penetrating generally to depth known Beer s law, is often expressed o exp(kuz) where = the photon density at depth photon density above canopy, and = the ratio OkerBlom projected (1983) argues to measured that, leaf area. in conifers, shoots should be considered to be discrete entities. the shoots are randomly distributed opaque then equation 2 is valid shoots as well needles. this case, light penetration penetration through through shoots needles to t will differ extent tha front t the light density shoots differs from density needles (Carter Smith 1985). This concept can be expanded to include all potential distribution canopies patterns consist scales of a hierarchy of patterning. of discrete Conifer objects distributed space, from individual crowns down opaque particles within needles. At each level the distribution canopy of foliage is contained is discontinuous. within All individual the crowns foliage which are generally crowns, foliage conic or paraboloid is confined the in form. regions Within adj acent actively growing meristems (shoots), and within these shoots, foliage confined to volumes defined individual needles. These levels u . hierarchy ars i t srrata in which foliage can exist and where the probability existence volume zero. defined For branch crowns foliage length is confined inclination. Moving down through the hierarchy, each level is spatially bounded higher levels . Shoot position is confined within crown, needle position within shoot. For any discrete array of n objects space , the proportion light penetrating through array K array = Po + PiK, + P2K, PK, where Karray = the total light penetrating the array, = the probability that no object encountered, p1. pn = the probabilities that objects are encountered, K,.. .K = the proportion light penetrating the objects given that objects are encountered. If it is assumed that objects are identical, then defined average proportion of light penetrating through an individual object. Equation then eQmnlI fo KobJect l...n l...n K array + C PI. object If Kobject small (the objects are opaque), then Karray approximately equal to P entirely dependent stribution internal and structure density . If objects dominates, and then not light their penetration through canopy will be controlled the distribution pattern of objects canopy. Because discrete ob conifer jects canopies , equation are can composed o be applied f a hierarchy repeatedly each level to define overall light penetration through canopy: 0 Po + Pi.crown crown Crown P shoo i.shoot Ki shoot 0 + Pi,1eaf leaf leaf ~lcel1 When the canopy is viewed in terms these equations it i possible to define the precise effect of each level cell i; P Kcanopy K ahoot canopy potential errors involved in assuming homogeneity any level. Any level hierarchy homogeneous density distributed objects . If that average define density level , Object evenly of integer order , then homogeneity can be defined as a special case of equation : all light beams encounter equal number of objects . As a system approaches homogeneity , all the terms series except the term defining mean number of encounters vanish, Pmean approaches , and the system collapses the next lower level the hierarchy. If Kobject approximately equal zero any level, then effects of all lower level will vanish. has traditionally been assumption light penetration through leaves . Equation Therefore, simply represents special case : Kleaf  "leaf , leaves are randomly distributed, homogeneity assumed higher level (shoot and crown) hierarchy. patterns above leaf level and are ignored, then light penetration through canopy will always underestimated primarily . The extent be a function underestimation magnitude will the terms because wi th n P hnmnnnna4n i nt lQQiimnIi nn C~hOh Ch rm ~ I 1 *" dominate their respective series, errors of omi ssion can large . If = 0.5 instance , with a stand random has a measured distribution = 4.0 leaf level and homogeneity calculated light shoot penetration crown (equation level vertical light .135*1 . If however foliage is held randomly distributed 4.0 and a projected shoots shoot a with an internal rea then leaf from area equation , the Kah~ anticipated light 2 0.37 + 0.37*0 penetration 18*0 0.42 .0182 case , three times as much light expected penetrate through random shoots even though the mean projected largely leaf due area the constant magnitude in both the cases. term Thi .37). equal to 1 .0 in homogeneous case, only 0.37 the canopy composed randomly placed shoots In a field crowns, crown structure and position will dominate light penetration crowns are widely spaced, no crown will approach ratio space between crowns crown diameter becomes large. For this reason, discrete and crown orchards model (Mann have et al been 1980 used to simulate Norman and row Well crops 1983; point therefore crown c shifts losure with and high increases t. For ve with rtical height. light crown entering an idealized closed stand composed of uniform conic crowns, Pno crown equals point crown closure and converges rapidly on 1 .0 with increasing height (Figure In species with conic or parabolic crowns, light penetration patterns in the upper crown may therefore dominated crown form even if homogeneity is a reasonable assumption light penetration the forest floor. Leaf area magnitude an important canopy level parameter physiological determining processes, is difficult measure directly. common practice sample light above below canopy and, assuming equation to be valid, to compute leaf area (Lang and Yuequin, 1986; Pierce and Running, 1988; Campbell and Norman 1989) inverting the function. The problem with this approach that, there canopy structure the shoot crown levels, then k loses definition ratio of projected to measured leaf area. leaves, k is generally close to 0.5, the theoretical value angular distribution leaves random (Campbell and Norman 1989) . This figure, or one very close, often used in equation to determine leaf area AI U U  w v ~,~,,, irrr r * ~ r* %o wn 4 Cod "4 H O C 4'O ui V HO) 4~VC CI~r >vrO ."LCW distribution and shape clusters and will be only indirectly related leaf area. In general, on light the penetration effects are di of various fficult scal to separate of at patterning the forest floor, and may have no clear geometrical interpretation. does not necessarily mean that Beer doesn 'work ' for stand, simply that there may uncertainty as to which level of hierarchy controlling parameters Mistakes in understanding these hierarchical effects can lead to a variety errors when using inver sion techniques. instance, example listed above (equation leaf area was unknown and the was assumed to be 0.5 calculated leaf area stand based on light penetration forest In(O floor .42)/0 would = 1.74 rather than the actual value of 4.0. Predictions based on inversion are prone to similar errors. The effects new foliage growth on light penetration, instance, depend impact new leaf production terms at each level the hierarchy it enters form new shoots of constant dimension then shoot area will be related to leaf area through a constant SIf cluster location is random, slightly modified Beer will approximate light penetration leaf densities =1 o exp( kuzq) where = a clustering constant interpretation of the with ratio geometrical of measured leaf area to projected cluster area (Campbell and Norman 1989) Spatial independence new foliage in conifers however, foliage biologically production improbable. occur Because exclusively both the branch branch and tips, new foliage will enter system at spatial locations determined largely the position the existing foliage. means that the position the new foliage space will be conditioned foliage, conditional position probabilities the will exi sting distort Poisson distribution. If constant shoot density assumed, increases in shoot size will translated into changes a S. a m .. * * i d assumed that shoots are spherical in form, then ratio of projected cluster area to projected leaf area will 2/ 4r3 = 3/4r where = the radius the shoot Other geometrical forms will have more complex relationships, and proj ected area will change with sun angle and azimuth, but, regardless the shape shoot or crown, equation cannot be considered to be valid model foliage growth associated with shoot elongation or enlargement Spatial heterogeneity of foliage can influence both the quantity Because pattern clustering of light can occur penetrating the level canopy. crown, shoot, or leaf, it i necessary to determine the extent which heterogeneity at each these levels affects light penetration before measured light below the canopy can reliably used to estimate leaf area. MODELING HIERARCHICAL EFFECTS IN SLASH PINE Characteristics Slash Pine In slash pine, carbon assimilation rate individual needles largely dependent on the light that those needles receive . Nearly measured variance of CO2 assimilation in needles can be accounted regressing ass imilation against photosynthetically active radiation (PAR) (Figure The crowns of slash pine are conic , and distribution of foliage spatially limited the volume defined branch length crown form (Figure , which . The turn canopy controlled therefore collection needle needles conic distribution exclusively units . Slash within each pine the having s (and area own other branc individual pines) or stem produce wood created during current season s growth. In slash pine, needle retention ess than years (Gholz and Fisher 1982), reason, need are restricted branch area immediately adjacent the actively growing ~n1 nztl marl 'PHI n~ 4torn r nrnnlHr'rn4 r f EtPm~ natt8m rraitag " nnn, O C) LsJ U) cnl * N 2 N 0 2t * m U) U)'k 00)1 k 04 04 Co owk rio a ) U) .p c ri) C 44C 000 4.4 C a)4Jr w. rlI COO 1) O rS Sn 1 ') N~ r / ~\ I I I St att at . foliated foliage region surrounding distribution in a slash stem pine (Figure stand The therefore spatially heterogeneous. The on light previous discussion penetration suggests the that impact light of heterogeneity penetration through a slash pine canopy should be influenced canopy structure. Given crown form and patterns foliage growth, several hypotheses can be posed: H1:Light penetration through a slash pine canopy differs in both pattern and quantity from light penetration through a homogeneous canopy. H2: For canopies made crowns of discrete dimensions, differences in spacing pattern will have a stronger influence on light than predicted homogeneous canopies. H3: If crowns are arrayed rows, the orientation rows will have a significant impact on light penetration on the timing of maximum penetration through Evaluation stand. of Model Approaches To explore effects of various levels ar 4a~ ..A a n ar a 4 J .. 3 !. ,I I L '1 * I 1 CO I I r , OHr 'C>' 0 r 4rt f od 0 cc v wC r 4IW'O r I 0r C:r a) HHW 4~C0 0 ) Wc, >4I tOWW 010 OCk 94044( 4. Z a2C f\A Il I L'k I I %LkI.\.Il penetration through a canopy with detail at both crown cluster level . In most common system modeling discontinuous canopies , subcanopies are represented as discrete geometric solids . In type modeling, the subcanopies are usually defined level of individual plants (Mann et al 1979, 1980 Norman and Welles 1983 Rook et al. 1985 Whitfield, 1986 Grace, 1988) or sometimes hedgerows (Charles Edwards and Thorpe 1976 Cohen Fuchs 1987) . In case foliage plant or hedgerow assumed to be confined within the volume solid and equation generally assumed to be valid within boundary . Thi type modeling called envelope modeling, because the leaf area of each subcanopy strictly confined 'envelope generally defined as an ellipsoid rotation. Envelope modeling very flexible because each envelope can be given individual transmission properties, envelopes simulate can foliated even and nes non inside foliated one portions another of a plant (Norman and Welles, 1983). an array of canopi the light reaching a given point can be described m P .. where = the extinction coefficients sub canopi 1... n, . .zZ = the chordal distances defined a beam of light as it passes through the array from a point source to a target. Light penetration calculating equation target surface 10 repeatedly computed a series of random locations on the surface and generating a statistical average (Norman and Welles, 1983). To compute must chordal be geometrically therefore simplicity present of form distances simple. As enormous turn efficiently lymmetries computational leads the crown difficult to a variety solids form . Thi of model artifices that may as severe those simple model that they are designed to replace . Vertical density patterns are easy to model in a homogeneous canopy but are very difficult to model using envelopes . Because constant foliage density envelope, generally vertical biomass assumed profile throughout each a crown the cross sectional area envelope as a function height . For many plants such as slash pine , foliage concentrated toward the top and the outside crown . .kn longitudinal (Generally plants are greater in height than in width To avoid artifice it i necessary nest envelopes envelope. problem . Not with does only lower not. does densities however nesting within really present each remove another subcanopy the level model the i complexity internal envelopes the p must roper position be based not and density on their actual attributes, but rather way in which they adjust crosssectional area outer envelope. Envelope modeling can be used to model canopies lower hierarchical levels such individual shoots . Many the problems associated with representing crowns ellipsoids of rotation vanish when modeling done the shoot level. The effects clumpiness on light penetration can be modeled, transmi ssion and crown properties form, per shoo foliage t can b placement e based and on data. Assumptions of uniformity in size density may also more valid the shoot level. Shoot level modeling also has the practical consequence of concentrating emphasis a unit of vegetation that properties that are measurable either in a laboratory or in a chamber field A great deal current phys biological work done . a. SI '' m II 1 work to be effectively scaled the crown and stand level, throughout it is necessary canopy. Ideally, to integrate light these penetratio processes n should also modeled the same unit on which physiological measurements are taking place. Modeling however, a stand requires of slash definition pine the the light shoot level, regime at several hundred target surfaces per tree generated light penetration through several thousand potential shade objects several that runs make will up the surrounding be needed to avoid stand. Fu artifices rthermore, due particular patterns of shoot placement. The problems associated with using an envelope model the shoot level primarily in computational expense. The modeling penetration single concepts through source. discussed a canopy Diffuse above light radiation compute emanating emanates light from a simultaneously from points dome. Computation of diffuse radiation involves integrating the light from entire sky: P(X,Y,Z) jQ(9S) ex SSg(e sin( A )nn~( A ~iAa    N ..  sin( )cos (11) ded (Norman and Welles 1983) D( sin( Al~nlF:(F3I where = the probability that diffuse light penetrates a point (X,Y,Z), = the light intensity function and, 9 and are angle of elevation azimuth respectively, s the density of foliage, and s the sum would pass the z distances through if its that point a light beam of origin lay along a vector starting the point (x,Y with a direction defined 8 and l. Numerically, this equation is difference into a series of direct Computing light computations diffuse radiation a grid patterns sky a sing locations. le point with an integration step of 5 degrees therefore involves computing 1300 direct light readings. Liaht Penetration ModelinQ in Discrete Soace Most computational burden envelope modeling lies the calculation chordal distances through each subcanopy . If, however, the subcanopies are small and uniform in dimension and light penetration properties, then each subcanopy can treated as if it were particulate canopy lies path of a beam. If it does, then it will remove a certain proportion light. To calculate the presence or absence of a spherical subcanopy in the path of a beam of light, a vector drawn normal the beam path from beam the center the subcanopy. magnitude vector is less than radius the subcanopy, the beam will pass through subcanopy; otherwise will not. This calculation is much simpler than computation a chord. first calculation can, step in computing however, further a chord.) The simplified the coordinate system itself aligned normal the beam path, with target point the origin, and scaled that one unit equals radius the subcanopy. presence or absence subcanopy in the beam path can then be determined rounding the center the subcanopy the nearest integer node. after rounding, the center subcanopy coordinates (0,0) the dimensions normal the beam path a magnitude greater than 0 in the dimension parallel beam, sub canopy will intersect the beam. If all subcanopies are the same size, then entire system can be scaled and rounded simultaneously, and the subcanopies that S  space, light penetration is computed in discrete integer space. If the target surface itself is composed a field system, of equalsized including simultaneously subcanopy points be scaled and units, then representing rounded. entire target, light can penetration entire target can then be determined through series row searches. In discrete dimension. space, dimension subcanopies only lose reflected explicit indirectly scaling factor. Subcanopies become points with light penetration properties defined average light penetration per unit area subcanopy. targets (and therefore light beams) are also restricted integer space, light penetration target point represents average light penetration to a gridsized area surrounding target. This discrete approximation keeps fundamental logic envelope model, modeling system as a series of subcanopies, but allows application on a much finer scale or on slower computers decrease in computational burden. Using technique, modeling on a cluster level can be accomplished on microcomputers. In discrete space, homogeneous medium of unit discrete nature space confines nodes to integer locations , causing raster effects similar those seen lowresolution computer graphi CS. A plane diagonal light source will be represented model as a series of smaller planes offset from one another one node. it i assumed that a Beer s law model is appropriate continuous shifts, system, light then, penetration as the r through elative sun system angle will decrease as a function relative angle: = I i  o exp(kdz/sin9) where = the relative angle between plane light source If kdz constant then equation 12 simplifies = I i o exp( k/sine) (13) where = a collapsed penetration constant normal describing the light plane.    this half one, same points leading system will is modeled be shaded to a predicted as a discrete points of 0.252*Io. entity, half this case prediction exponential error decline is less function than Because is uniformly convex, discrete model will always predict light penetration greater than or equal to a continuous model. The divergence however, not large. grid size decreases, system converges continuous representation. Modeling light penetration into a stand using discrete cluster level model involves five steps: Placing cluster into space ass signing light penetration properties to each cluster. Rotating shoots to align system with sun position. Rounding clusters nearest integer node. Searching presence of clusters between target nodes sun. Quantifying light attenuation caused shoots matching clusters with their specific light attenuation properties. To summarize , discontinuous canopies can be modeled creating geometric representations the stand t S  a i r . elipsoids however, in real this space. approach modeling is extremely shoot inefficient. level, Discrete space models offer a more efficient alternative therefore are a preferable approach shoot level modeling. A DISCRETESPACE MODEL FOR SLASH PINE Data Acquisition this study, a model was based on a stand plantationgrown slash pine. stand was approximately years. Total tree height was approximately 17 m and crown depth was approximately Stocking density was approximately 1200 stems*hal parameters used to model location of foliage space were based on a data derived destructively sampling trees August 1987 trees in August 1988 . Pertinent data obtained through sampling included number branch of branches length, non branch foliated position, branch 1 branch .ength angle total (length first live side limb), number needle clusters (shoots) per branch, biomass per branch. large one small branch were removed from each m segment down through crown. The segment began base terminal segments were marked down stem base crown. Crown depth varied   1I r i . clearly defined classes of branches exis within segment . If limbs were same size, limbs were classified large, only one limb from segment was sampled . Large small were therefore relative classifications . The point base terminal leader where top tree. segment terminal, began which was classified represented current year s growth, was treated as a branch was sampled . For each limb sampled, the position the base limb tip limb relative tree were recorded . From these data branch angles were determined using following formula AOEb = arcsin[(Dtop  Dbae.)/Lt] (14) where AOEb = the branch angle from horizontal, = the distance from branch tree, Dbame = the distance from base branch tree.  the total length branch. The bias due sweep limbs was minor was Foliage position was determined assuming that foliage was branch restricted first region foliated from bifurcation main branch. with Within equal this region, foliage probability, was needle assumed to biomass was occur therefore uniformly distributed. Using this technique, foliage was added to a standardized stem composed segments to build a vertical foliage profile stand. Because branches were angled between 50 and degrees branch towar angle shifted ertical the ca (Figure Iculated correcting position for foliage toward canopy (Figure . For m long branch with a nonfoliated length a Db.,e location m below tree and an AOEb of 50 degrees, this technique would allocate foliage m segment, foliage to 2 m segment, only to 3 m segment where branch originated. probably position Even placed . This after lower because adjustment, crown foliage however, than is assumed foliage actual to be evenly distributed within foliated region limb, when, in fact, most foliage concentrated toward *0  CD I NJ U, I3 4. 4. I I p  1~ I~ 0 in In I 4. I O 1 a) 0r) d4I space was possible due breakage that inevitably accompanied felling trees. each limb number needle clusters (apical growth meri stems) was counted. system used distribute foliage was also used to distribute clusters, with number of clusters per limb substituted dry weight biomass. Cluster distribution a random component, because number of clusters is discrete, sters are placed with equal probability along foliated limb rather than in equal proportion. horizontal distribution of foliage around stem was also determined using branch angle the foliated region limb. distance foliage from stem was rather determined than sine. cosine horizontal branch distribution angle was assumed to be uniform in regard to azimuth. model, two techniques can be used to place foliage model ( space. McKelvey, One, 1988), which used was the used in a preliminary vertical distribution biomass. this approach, needle clusters were assumed contain an equal quantity of biomass. Needle cluster position clusters was were therefore placed derived in vertical from biomass space data, a weighted random  placement was based on the branch length chosen height. second system distributing needle clusters uses vertical distribution clusters. this approach, determine foliage biomass extinction enters indirectly coefficient each is used cluster. This second method was used model presented here because it places emphasis on positioning clusters accurately heterogeneity space. The suggests previous that discussion changes position foliage should have more impact on light penetration than shifts in biomass cluster. slope exponential decline curve steepest values near and progressively flatter as values approach In a sub canopy model, where there are gaps in the foliage, model should therefore be most sensitive size gaps than properties foliage filling area between gaps. For purposes crown construction, rules placing clusters space create the gap structure, properties clusters define area between gaps. The priorities modeling should therefore primarily to position needle sters accurately space a . I . . I . direct light penetration is related to needle biomass per cluster, whether orientation cluster light source affects either penetration or projected area. To obtain these data Sa device was designed to allow controlled directional light to be directed onto clusters from a variety of angles (Figure . The device consisted of a light source, a collimation tube a light sensor which was held in a fixed position relative light source. Cor A 4 spot cm parabolic sensor, mirror eliminating focused angle light coverage on a Li effects to large between objects such sensor as branches. tube. Clusters The light were source placed was mounted on a stand with slip joints that allowed a full range cluster movement to remain three fixed dimensions. light This source allowed to be moved, allowing cluster to remain an orientation similar natural orientation tree. cluster was held in a movable stand (Figure . By moving cluster vertically horizontally through a series of fixed positions was possible to define a grid normal light source any sun angle. rotating cluster position clamp was possible to simulate any azimuth. LIGHT COLLI MATION TUBE SEHSOR Figure device used to determine light penetration through clusters. Figure Apparatus light pene horizontal for positioning needle clusters for tration measurements. Vertical and movement of the stand, coupled with generally angled toward branch tip. When viewed from branch clusters are circular, with a dense center defined apical meristem a maximum radius equal needle length. orientation, clusters are circular with a radius of 28 cm regardless of biomass. From side view, clusters are less similar in form. length cluster is a function growth rate over past season or two, depending on the time year. In April , the cluster holds one cohort of needles, October it holds two. In general, because new needles grow a very acute angle from the stem, region beyond limb forms a hemisphere defined the needle length. Below hemispherical end, there a portion indeterminate length that is cylindrical. At its base, this cylinder can terminate in a hemisphere needles are droop, or in triangle needles are young are still stiff angled toward branch tip. Light diverge from penetration greatest (parallel end projected extent when limb) cluster area cluster relative will is viewed side (normal limb). Light penetration through the cluster from other angles will encounter a form intermediate between these extremes. Measuring light penetration ~~~I  r I I mm a range of penetration area projection from potential sun angles. Needle clusters were sampled at 5 cm intervals over grid of 30x30 cm. With cm overlap caused parabolic mirror area covered was approximately 34x34 cm. This area is large enough encompass the end views needle clusters in their entirety. It encompassed side views of smaller clusters, but larger clusters cm long) projected beyond grid. Sample clusters were centered grid using apical meristem as the center end views midpoint cluster side views. Light penetration was calculated clusters from side results compared . The average light penetration values unit area these two views differed less than among clusters (average less light penetration from side). Rounded nearest compared using chisquare test of fit (Table Figure clusters showed no significant difference < 0.05) and four showed significant differences in pattern. Significant differences between side views were largely due increase in projected branch area when viewed from side. E C, 4' W U ~"4 S4)C ' Jr"4 Coa 4)cm, akooo Oo o "4 r CI) r4 3 4 00 'p4' %C(I 0rwSr Cr 2w C UU4U 04 )0 rC C "4 4)0 V a 3 r ~m~oc a) Dc 1 0~ t Oe v1 ~~~Or'0 WeOO O 0d r d C dlrlV S( Y ) ,O O CJC'Je. E 1 INW "4oc c ooc uc zr rr U I I Lao wo Z~ liW STI33 0 30 GlflN 0. a 0 ^vmmmigmm^I STI3 40 j36lAlN I C V04'd 0) rl I4. On 9 sf 4) .C0) ZO) 0k 0I) .0~ nr cxE z ID H C 0)0)0)0 043r4 1 $4e CH r O'ICV t 0 4' 4' $4l 0)*4W acV0)$ 0CC 0) Q0)0)4C) *rl 0)O uI ErI C~CCa coVdI~ o CCVQ~ $4 0, Ci 0)I >0 l #XXXXXXXXXXXXXXXXXXXXXXX~ 6WOWI[ll #XXXXXXXXXXXXXXXXXXXXXXX~ 4 DOOWWO~C~X1 #XXXXXXXXX~n ~owooow ~xxxxxxxx~o Ipxr~ I i r light source changes . The larger clusters are similar density will project as much as twice area when viewed from side rather than from end. This can lead to a disparity projected area between these modeled clusters area represent actual a significant proportion total cluster population. To determine proportion of proportion of large clusters canopy lengths of all the clusters were measured on five trees with stem diameters ranging from 15.8 cm to 25.2 cm in diameter at breast height (dbh 1.37 . Of 1585 clusters sampled, were less than cm in length were less than cm in length (Figure 10). Based on this sample, the maximum error estimated cluster area due the presence of large clusters was less than . At minimum biomass levels, canopy is primarily composed of clusters small enough to project equivalent assumption that area clusters density can from treated sun as points angles. with average area uniform penetration properties, necessary condition discrete clusterlevel modeling, therefore justified. A regression cluster penetration as a function biomass was constructed . For regression, light ~~~' A I a ^ _m r r O 0 f rn captures foliage regardless of cluster length, because orientation clusters tree suggests toward that light, view limb, dominates. which clusters represents grow change position meristem over time, must roughly parallel beams of light emanating from light source.) A log linear (exponential decline) curve, was chosen (Figure because same form exponential decline curve variables are analogous those used Beer s law modeling. The curve also stable properties when used to extrapolate beyond edge data set. Model Structure Cluster level modeling very flexible, a variety of configurations can be used to model stand. For results presented here, stand was modeled using following rules: trees were built using same procedure (Figure branch 12). foliage angles, branch quantity, lengths cluster were numbers, identical trees. parameters were mean values a 46 I , U)4r I C 4. 0o 0'I o (0 oo CJ h 4) t( 3 o 0 C) o I C, 0 a) V o El J 0 C.$ o 0 aa 0 4)C 0 BO H o Q.4a OO o l 0 r Cl I') 4 ID (0 F i 6 ci 6i c ci 6i OH I I I I I E~ 0 Hl riii\ MAD lfJlr2 *L urI, uI LOCATE TREE TOP MOVE DOWN ONE METER I COMPUTE BRANCH VECTOR N (ORE SECTIONS DONE Figure The rules building a tree in the cluster level PLACE CLUSTER RANDOMLY ALONG THE FOLIATED REGION OF THE BRANCH of clusters in both azimuth angle was random. trees were identical in height trees were evenly spaced on a grid aligned with cardinal compass directions. Rows columns ran exactly northsouth eastwest, respectively. the model, clusters are held as locations threedimensional space. Light penetrates system clusters determine obliquely light as a series penetration of parallel through beams. system, discrete that approximation coordinate technique system outlined be aligned above normal requires light source before scaling rounding. alignment accomplished rotating cluster positions around arbitrary origin until they occupy positions space that they would have they had remained fixed cartesian coordinate system been rotated. The process starts with an initial orientation in which the axes axis define is height. a plane initial parallel sun location ground and is at 0 degrees parallel X axis. Cluster rotation is always relative this initial configuration and is inverse movement light source. light source moves rinht I. I rlu S atsr nos i t ions are rotated down . t~ha . . axes with daily sun angles azimuths can be generated through t available rigonometric in the relationships, literature (Campbell, equations 1977 are ; Walraven, 1978 Gates, 1980). Rotation of points around an arbitrary origin requires several transformations . The point set must first centered on the origin, then scalar rotations are necessary. first aligns axes with the sun azimuth, second with AOE. This process can be accomplished efficiently through use transition matrices. Any rotation a group of points in Cartesian space can be viewed as a series of individual translations coordinate point. vectors, rotation each vector algorithm representing can therefore an individual be determined tracing translation of a single coordinate vector, through multiplication with a series transition matrices first I* translation can be written as C second ' * so forth can, however , be substituted in place of C second translation can therefore be expressed as ,,~ This process can be continued as many transition steps as are necessary to accomplish desired rotation. single transition matrix is created which product ,I A J AA Fri Ff r ,,',a  .4  Ir T2 ,  LI vector to its final position . The rotation process therefore always begins with same of initial coordinates, there no cumulative buildup errors during rotation. After rotation, each coordinate vector multiplied integer a scaling location. constant point rounded equidistant nearest between integers, coordinate is rounded the even integer. Once clusters have been rotated their positions rounded, be computed. amount If all of light penetrating clusters have target equal can transmission properties, light penetration point can be computed = Io exp(kn) (15) where = the number of clusters. transmission properties are different, then light penetration is computed 1 I o exp[ + k2d, +...kd.)] (16) where lr I, 1ho ~ ~ ~ ah nil nr an ran 4 1 an ~c' a 1 kd, L t tha C3V+I nrti an aan~ individual needle cluster, d,... d. = the densities. light penetration cluster is known (rather than computed through a Beer s law relationship), then this calculation collapses to a product series: n S I I i=l (17) if the penetration is identical clusters: = Io (18) With Cartesian coordinate system parallel solar radiation along X axis, task of searching shade becomes the search points that have same Z coordinates target larger X values. This search can potential coordinate accomplished shade clusters values. efficiently according array can first to either then sorting or Z be searched progressively. In certain cases may be beneficial sort first X coordinate to clip those points with X values less than target, because target is generally placed that maximum potential number shade clusters between it and the sun, this sort is not model was run angles azimuths representing one quarter dome. Light penetration was simulated AOE from to 85 degrees azimuths of 185 to 270 degrees at 5degree intervals. belowcanopy readings, target was a 5x5x1 m rectangular region below canopy containing measurement points at random locations. measurements within canopy, two target arrangements penetration were used. profile, To simulate a series of 5x5 a generalized xl m planar t light argets were placed at 1 m intervals within canopy. To simulate light penetration cluster surfaces, a target tree was used with each cluster acting as a measurement point. vertical position of each cluster was used to determine a light penetration profile surface clusters. modeling approach, an evenly planted stand, allows simulation from potential angles (above degrees) azimuths . The other three quarters dome can be filled in by assuming symmetry. The minimum sun angle that can modeled is dictated distance from target edge simulated stand depth canopy. question is whether a tree that is not modeled the potential to influence light environment at a target point. a field of conic crowns a target base canoov. distance edge the system necessary ensure that edge effects affect light penetration target (19) = tan(AOE)/ where = the distance edge system, = the depth canopy. This f breaks unction rather becomes sharply infinite below as AOE degrees approaches AOE. 0 and In Florida, direct light emanating from AOE greater than 30 degrees dominates solstice, daily sun i light s higher integral. than Even degrees winter a 5hour period midday. Florida, 30 degrees therefore a reasonable minimum angle. more northern latitudes, much light may emanate from AOE less than degrees. Model Results In a three dimensional model, asymmetries in foliage distribution may make light penetration strongly dependent on azimuth. a row crop, highest penetration through a~ ~ ~ ~~~~~~ a1 . L . a.h A n n. rt, .',,,,, ~1 rrnr~~r penetrates from an azimuth of 270 degrees (Figure 13). modeled tree configuration, an azimuth of 270 degrees is exactly parallel rows . Thi phenomenon however, only noticeable at low only occurs sun azimuth precisely aligned with row . An Azimuth of 185 with degrees, row instance, orientation. is only Azimuth degrees therefore of line not significant factor in belowcanopy light penetration . Thi means that light penetration curves can be created based sun angle, which simpler to generate than azimuth. Figure stand 14 shows with average light light penetration penetration per through cluster 2.88x2 m (1 trees hectare) spacing variance constant angles . For tree spacing biomass level, curve can be used directly generate light penetration patterns over time. The output cluster level model , in case Collapses single curve that can be used in simple light penetration model as a replacement exponential decline curves. Over course a year , needle growth abscission approximately doubles halves foliage canopy respectively . In model there are three ways to simulate doubling halving of foliage . The first to keep nr A1 A .n 71UT n Fnl(~na nllr alnr nrrmknr fhd aamn nar na nr  43 GOD cv>o 0 N CN 0 CM 0wD 00 tED 000 < < 000 nu,ca I 0 0D 00 00 0 0 4343 CCC 444 0000 Ca) SCI 04 0 i o t In CN 0)'.0W 0do\ m Ir45 >1I '44U ooC Cd .CG) OJ) .Cwo C cJ O0 OD Co D 000 CM o o0  a) ) 0) U, C40 r C Q0ld wa) HO Ed 0 airs 10 U) 1010 4J Cr ~Bos 433 Or O +s*9'4 w~ if La) aI) Wr ca co o (fl43 O a) o~ 0k ~ cW Ir ON O)C LL 0.0 a m~ O Jrl U) IC) to is roughly equivalent to dominance the side view clusters . The second to increase or decrease the penetration regression cluster (Figure 11). according This the equivalent developed t to dominance view. third possibility to increase decrease density trees. This not a real possibility within stand, but halving number trees approximate equivalent to a thinning operation, leaving wide holes foliage between individual eliminates crowns . Doubling betweentree gaps the and number eliminate trees s much effectively conic form canopy crown overlap. Together these three model runs tested importance cluster crown levels of hierarchy on light penetration through canopy. When these three possibilities were simulated There was little difference between light penetration patterns generated shifting cluster area shifting cluster density (Figure 15). differences that exist occur at high AOE . This suggests that, belowcanopy light penetration, sters were acting as if they were randomly because located position space. of each To a large cluster extent was they randomly were, chosen 41 QI iJ 004 III 004 C 4 4 4 N I I I I II II I I U' ~t 'C' C, U a I I Ii I I III I ff) OT  In 0 U, nIuJ w"d u. Z O 0 F 4 1L 0i 1~00 a W'w4r1 C4 vI ' 00rlu JJC44 ecl IAAd N I ~WI ITJI1J~d3 Pft'%lIJ*fl3IIl M13I. i ~n~lY~ ~111 nullu\rlllrn example of a Beer solution in which parameters are based on cluster rather than needle characteristics. There were, however, significant differences between light penetration patterns due to changes of biomass within crown changes due to changing number crowns (Figure 15). These data suggest that position trees is much more important to overall light penetration than internal structure crowns. Because model is insensitive to whether foliage enters system as additional area or as increased density within same area, changing biomass within canopy was constant modeled changing keeping the their light number of clusters penetration properties. view projection clusters dominates over side projection this view, area case, or if will then clusters change keeping are with cluster small, shifts area cluster in biomass. constant appropriate. Using cluster level regression (Figure 11), light penetration potential penetration curves biomass per can created quantities cluster sun simply across shifting range angles light of potential values. This produces a family curves (Figure  i A 0J ) S0, S0)0 ow tna I I II Ar a nt~~ .1*I N .c CJO om 10 L1a hia aL I ? h ~IU I h multiple regression. equation to model output m spacing .134 + 0.130*AOE  0.1834*B, .6E5*AOE2 (20) = 0.92 where = the fraction of light penetrating base the canopy, = a scalar producing varying between an average 2.0 and cluster light with penetration approximate median value cluster sample. A cluster level model was constructed slash pine. crown the 1 measured form ight under was determined penetration controlled through through conditions. destructive individual Model sampling clusters output was showed that azimuth was an important parameter controlling light behavior penetration was through captured canopy. in a regression Most equation model based biomass AOE. MODELING SEASONAL BELOWCANOPY LIGHT PENETRATION It is clear from equation that most dynamics threedimensional cluster level model can collapsed to a onedimensional form. This allows light penetration patterns over time to be modeled using a much simpler model. Other than using equation 20 rather than equation to a Beer to predict s law light model penetration, a horizontally a model identical homogeneous canopy can be used. Correct AOE can be generated through relatively simple entered, equations, model can biomass quantities be validated can matching model output with measured light penetration data through the canopy. Yearly biomass dynamics were derived from three sources of data: destructive sampling, litterfall, needle elongation rates. Foliage canopy any time mixture current year s cohort (new foliage) previous year s cohort (old foliage) . Over year period, the new foliage becomes falls the forest floor as litterfall. three consecutive years trees were a a a .6..! a a a I ...fl  a. a... 1.. a... __ 1a A. ,,,, 1 L,, LL, I 111 ? , both cohorts. In addition biomass estimates described at biweek earlier, Iv interv litterfall (weekly was collected during in litter peak traps litterfall period in November) . Needle growth was also measured need at biweekly interval throughout season active growth (weekly during spring break). these data , the destructive sampling was considered to be most accurate was used as a baseline biomass calculation . From these data biomass quantities were calculated both forward backward through time . The foliage dynamics were tracked through litterfall. Litterfall was assumed to be entirely foliage new foliage that fell into traps due to storm damage was separated . New foliage dynamics were based on needle elongation patterns . Biomass was then converted into sided leaf area using a geometric technique (Gholz et al. 1990) Based this analysis was found that the maximum foliar biomass was approximately times minimum (Figure that biomass pattern lagged the solar cycle approximately three months (Figure . In model, smoothed biomass curve shown in Figure was scaled a mean of 1 .0 and used as input for equation O c0, o 0 in 0 in 1 \% \J ^/ '0 I 0 I !  "I I c0 I 0 0 0 in o Io 0 Liu U) r4 'p>1 '. +T Ic' 4't HUV 00) mxII 00r Sr Ici I Y'~fl I1 kwII I I I  n~nlc ilu (S33 93G) 3J1NV NnS SA S __ rr~ Light penetration through canopy was measured with a seri of fixed sensor arrays . The arrays consi sted twelve linear response diodes mounted on aluminum beams m intervals . Each array consisted beams placed right angel on narrow triangular antenna towers . The arrays were level with ground . Two arrays were placed above the canopy, five were placed immediately beneath canopy were placed above shrub layer on the forest minute floor interval SReadings at each throughout the sensor day were taken at 5 an averaged value recorded was each hour . The sensors were calibrated to Li Cor spot sensors Three LiCor PAR spot sensors were also placed above canopy along with LiCor full spectrum time sensors. regressing system hourly was above checked canopy drift readings over from PAR spot sensors against abovecanopy diode arrays . An additional sensors ag check ainst was the made full regressing spectrum sensors PAR . The spot regression between PAR spot sensors abovecanopy diode arrays period starting on November , 1987 , through January 0.508 1989 was + 0.9286 (21) a 1% where = the mean abovecanopy diode arrays,  = the mean abovecanopy spot sensors There no indication of nonlinear behavior any light intensity level or any sign sensor drift. Because belowcanopy sensors were fixed space, possibility that readings were biased their specific locations . A check was therefore made regressing belowcanopy sensors against each other combinations on an hourly basi (Table . These regressions demonstrate that sensors, both below canopy above shrub layer tracked each other very well values ranged from 0.93 to 0 . Only three 36 combinations had an r value of 1 ess than . The slopes, ideally , ranged from to 1.31 with falling below 1.0 and 20 above . The average slope was .01. intercepts, PAR/m2*s . No ideally significant , ranged from difference was to 7 ( observed pmol between shrub level sensors belowcanopy sensors, suggesting that distance from canopy was not important influence on light readings. determining belowcanopy light, below a a a   ~  ~I _I~_ 3 JA i. Table Regression belowca 10, 1989 sensors nopy constants sensor arrays for hourly re from November . BC sensors were immediately were above the shrub layer. be ladings of pairs 6, 1987,to Octob neath the canopy, Model Slope + SE ( pmol/m2*sec) Intercept + SE (pmol/m2*sec) BC1 BC1 BC1 BC1 BC1 BC1 BC1 BC1 BC1 BC2 BC2 BC2 BC2 BC2 BC2 BC2 BC2 BC31 BC31 BC31 BC31 BC31 BC31 BC31 BC32 BC32 BC32 BC32 BC32 BC32 BC4 BC4 BC4 Rr4 = BC2 = BC31 = BC32 = BC4 = S1 = S2 = S31 = S32 = S4 = BC31 = BC32 = BC4 = S1 = S2 = S31 = S32 = S4 = BC32 = BC4 = Sl1 = S2 = S31 = S32 = S4 = BC4 = Sl1 = S2 = S31 = S32 = S4 = S1 = S2 = S31 =R ).90 ).86 ).85 ).88 ).88 ).82 1.89 1.86 ).85 1.88 1.88 .76 1.82 '.89 '.93 .90 .75 .89 .81 .81 .85 .92 .89 .77 .82 .83 .89 .92 .90 .80 .86 .81 .85 01' 1.81 '.97 1.86 .01 .16 .86 .01 .96 .17 .19 .99 .97 .31 .05 .22 .18 .08 .80 .93 .05 .80 .97 .91 .05 .02 .21 .96 .12 .07 .18 .06 .76 .93 OR ).005 ).006 ).005 1.006 1.006 i.006 '.005 .006 .008 .008 .007 .014 .011 .006 .006 .007 .017 .004 .008 .008 .005 .004 .005 .011 .008 .008 .005 .004 .005 .009 .007 .006 .006 rArn' ..79 ..61 ..60 ..40 ..36 ..80 ..35 ..53 ..50 ..35 .36 '.93 ;.85 ,.02 .75 .05 .90 .25 .68 .85 .56 .99 .20 .81 .82 .84 .50 .11 .25 .86 .44 .69 .47 rA j )er S figures were then divided into daily sum the average abovecanopy sensor arrays to obtain fractional belowcanopy 1987, light continuing penetration through daily March beginning 1989. November A period August 1988 is missing to a lightning strike several other days are also missing to equipment failure. Light estimates were made days potential days. With good data sets both belowcanopy light penetration biomass fluctuation, light penetration over time can modeled validated. To obtain accurate estimates of daily light integral, a simple model can used to generate sun angles approximate intensities (Campbell 1977). sinecorrected light impacting on a flat surface, SinAOE = sin(( sin(L) sin(Dec) cos cos (Dec) cos[15(tt)] ) where SinAOE = the sine AOE = the time of day in hours hour clock), = solar noon, = the latitude in degrees, *  LL , Sine corrected solar intensity on flat ground sea level can be approximated = sin[I., * T./SinAOE] where = the solar intensity on flat ground, = the solar constant, , = atmospheric transmissivity. determining proportional light penetration, can to 1.0, is dimensionless. is also dimensionless varies from on very clear days to 0.6 on hazy polluted days (Campbell 1977) Light penetration through canopy was calculated hourly intervals using equations and . To obtain daily time constant integrals, results duration were hour. assumed This to be integration technique is justified daily time integrals because, symmetry noon, integrated in angular light will distribution be underestimate around s d before olar noon overestimated after noon approximately equal amounts. time series extended from November , 1987 ha  .al ars.n n a  4 na M ~ Pn n I r I u u L I Ckn nrrrl h~ I.lh n A Ot~Ah A 41PS #MI a tree cluster spacing is assumed of 2.88x2.88 to be 70% light throughout penetration time series, simulation matches data until summer 1988 then diverges (Figure . Light penetration overestimated remainder time series. however, it is assumed that light penetration per cluster represents minimum biomass levels (March 1988), biomass is allowed to fluctuate over time according pattern shown in Figure is greatly improved (Figure 19). Diffuse light penetration canopy differs from direct beam radiation because it emanates directly from portions dome simultaneously. quantity diffuse light reaching target point within canopy will be decreased dome that an amount is obscured proportional surrounding area foliage light intensity those portions that are obscured. obscured portion dome, turn, related distance that shade object is from the target diffuse size modeling shade therefore object. One to compute approach dome coverage each target point. This approach used Norman Welles (1983) envelope modeling. Tha r fh Fa ,  nrhkl arn ck ck: n L~LIA~LII*A~CI~ LL 0 0 in) 4'0 Vt >1.( p4C OWu 'OW 0 o 1 o~m 0 C4 5I 4.) *4 OkW4 .Com g vowG 4)J 0 r 4JPIE 000E 4tQl( 2*4( r r4v U) H 4 tO Diffuse patterns are quite predictable when heavily overcast (Figure become very complex sunny days (Grant 1985). Diffuse light patterns are therefore difficult to simulate because they shift with weather cannot be generated through trigonometric techniques . In clear conditions, direct light dominates pattern of diffuse light is strongly anisotropic. Under heavy overcast, diffuse light is isotropic. uniformly overcast days, intensity per unit area dome is greatest the dome least horizon. greatest area, quantity however, of light is greatest therefore the emanates horizon. from mid region (Figure . Because azimuth was unimportant to light modeling penetration diffuse into light stand, assume a very that simple it all way emanates from midsky. premise that diffuse light enters stand primarily from midsky should have the result that, winter, days dominated diffuse light should have higher days. light This penetration because, i through n North canopy Florida, the than clear maximum AOE direct beam radiation winter solstice is 38 degrees. No direct light radiation enters canopy from I,~~~~~F *A t . * a L 1 ALI rr  .. 1'1 C 94 V 01 0: ni 0 'C CJ 0 Ct .I .Cw nO 0o a. a a aL a a   0 cs) QGIHO CSS) Sg crm~a, a~D be much more muted because a great deal direct light emanates from midsky. there a pattern, it should reverse from winter pattern because day direct light emanates from as high as 84 degrees. For a given sun angle, changes in abovecanopy PAR are to differences in atmospheric transmissivity. Decreased transmissivity, proportion of diffus to water e light or dust, (Campbell, increases 1977 the Spitters 1986). distributions, periods such with as exist similar sun around angle solstices , days with lowest integrated PAR should have highest proportion of diffuse light those with the highest PAR should have lowest. When a two month period surrounding each solstice was plotted against integrated PAR, patterns supported hypothesis that diffuse light emanated period solstice, primarily extending there one was from mid month a strong sky on either negative (Figure side 21). winter correlation between high abovecanopy PAR belowcanopy light penetration. period extending one month to either side summer solstice, there was a very weak positive correlation. Based this empirical support, diffuse light was aAJ~aA 4n 4l, A~ 2 nA I 1 .1 A.&. 1 A. 1 3'1 * (o o 0CC (0 0OVC .C a) ) 0)00 S00 ca i O) ah .1 WId AdONVO3AOBV J0 NOLLDOVY iVld AdONVO3AOSV IO NODLLOVUL days, randomly chosen were not sunny; split between direct diffuse light was purely random on those days (some would be partly cloudy) diffuse light emanated from degrees AOE. When these rules were applied annual light penetration constancy i model, n light patterns of winter penetration were d variance uplicated and with summer the exception of early summer variation (Figure 22). early summer measured data displayed higher variation than model predicted. This suggests that this approach to modeling diffuse light captures a great deal the impact of cloudy weather on canopy belowcanopy light penetration, belowcanopy that light pattern is caused of variation differences observed in system sensitivity to diffuse radiation rather than differences weather pattern. rules splitting days into diffuse direct light listed above were largely arbitrary. No attempt was made to match light penetration specific days. The proportion of clear cloudy days was, however, reasonably accurate. When total daily radiation days was compared with theoretical clear values, 75.4% days were within theoretical values . The C 4 ar. r r' avrn a 44 an a4,aa n a 1 A tfltwfA~l fl fn. l n~a hnrra 1 aC~nn khCltnnn aCrhnn ChC a 1 N N. r I NP FCC CCQ 0 LO 0 0 0 O 0 o O O r== N I Al 4 ^Q 0 I suggests that light penetration can be simulated on a daily basis if a rule partitioning total light into diffuse direct components based on daily abovecanopy can be derived The of diffuse simplest light pattern is a linear assume function that proportion of abovecanopy PAR. period covered in Figure 21a, was assumed that daily of 100 represented a uniform overcast day with 100% diffuse radiation of 800 represented in which light entered stand as direct radiation. When this linear pattern is modeled, simulation tracks pattern measured data, lower variation (Figure 23a) . This suggests that shift from direct to diffuse light is a nonlinear function daily take PAR the In its form most of a switch extreme where form, the this light nonlinearity pattern will shifts from entirely direct to entirely diffuse at a specific daily PAR. Campbell (1977) breaks diffuse modeling into a clear model, which allocates to 30% total radiation to diffuse (depending on the amount haze) a cloudy be diffuse. model in which In Campbell light s system, light is assumed is assumed dVd AdONVO3AOa:V JO NOIlOV ' dlVd AdONVD3AOV JO NOLLDVYL cn 1c:m exist. If a day high atmospheric transmissivity partly cloudy then, part day, clear conditions will dominate . Under these conditions there is a linear relationship between daily integrated light percent cloud cover (Spitters et al 1986) . Campbell models suggest that proportion of diffuse radiation will also be linearly dependent on the percent cloud cover. Frontal weather will produce either uniformly cloudy uniformly clear days, dynamics should be much more like with a switch. dynamics A sigmoid intermediate a simple between nonlinear a line function a switch, this pattern been shown to fit empirical data many sites (Spitters et al. 1986) . When a sigmoid function replaces linear dependency, model is improved (Figure 23b). When measured data are regressed simulation, both models account natural variation slope, ideally 1.0, is 1 linear model sigmoid model. Simple models diffuse radiation, when coupled with regression duplicate obtained observed through pattern cluster of light level modeling, penetration through canopy on both a seasonal a daily scale. Because output from cluster level model was n A.. A~ 4. aI :a 8.  i.' YIIILI CS m J identical input. Assuming constant foliage, only divergence at high sun angles (Figure 24). When biomass dynamics were included , the Beer s law model matched identically winter spring but was more sensitive biomass buildup during summer (Figure . Compared with measured light data, Beer s law model provided than a poorer cluster summer level model light (Figure penetration , in general, a sinecorrected Beer s model fits light patterns reasonably well. To determine extent to which difference between Beer' on the model presence cluster of clustering, level a modified model Beer was s law based model was constructed. this model, was assumed that clusters rather than leaves, were the basic unit. clusters were randomly positioned, light penetration through the clusters was based regression derived through direct measurement (Figure 11). When output from this model is compared with output from discrete cluster model, patterns are very similar 2.88 m spacing (Figure 27). This provided further evidence that, in the clusterlevel model, clusters were projecting randomly onto forest floor. close Ha +raa Inl nA .I i  CkA~~ ~ CI~ CI 1 ,'I JL 1 * * II Ur) UI) to N 0 U) 1F 6 0J) C 0Q .C r4 4.0 ilWr 0) OWd Sai WUH v,C 0a 4 to i, 44 4J4 4~J N4 Qaka O 0 Un 0 0 4 4.) S4 4)4 Co SH Sow m vw 1 d.C Q1 V0) CI "4 'a a SvlC WH 'C remE 20)k en 'C 0)0 C~a) wwO orC Coo Cd 0 r WW.C Q'W 'Cr4 HWQ. 1.40k V04C, 04l 4SW 0 0) Y(/0 U*) IC representation provided a numerically accurate picture light penetration. MODELING LIGHT PENETRATION WITHIN CANOPY Light penetration patterns through canopy are much more difficult to obtain than belowcanopy values are more important canopy physiology. The clusterlevel model is capable of simulating penetration either planar surface within canopy structure or to a target tree in which light penetration is calculated surface of each cluster. To obtain a rough estimate light penetration series of planes within canopy, five profiles were run on a uniformly overcast day (Figure 28). An overcast day was chosen to minimize variation within canopy. profiles were created hanging a small triangular antenna tower on the control plot swinging a line sensor in a circle approximately m in radius . Light readings were taken as much as possible at 15 degree intervals along arc. Each arc was therefore characterized individual readings which were then averaged to obtain a single reading representing arc. Arcs were spaced at 1m intervals from approximate I . a  5 .,   A S tl ~,,~,, U, UIn In CO In 4 U 00 to a depth of 7 The 7meter reading was entirely below canopy. When light profiles to a series of planar surfaces were modeled , the measured values fell between simulated curves 30 and degrees AOE (Figure 29). model therefore data a mid sky AOE, as is appropriate uniform overcast conditions. It is fair to question biological meaning of light penetration profiles based on a series of planar surfaces within the canopy. canopy, line sensor was primarily sweeping empty space , measuring holes between crowns. base canopy, was primarily measuring nonfoliated zone surrounding stem, an area that presumably does provide a favorable environment to support foliage. When was assumed that planes clusters, existed curves only at spatial looked quite locations different representing (Figure strong selfshade depression was indicated high AOE zone immediately below layer of maximum foliar biomass (Figure this region, crown was still narrow (Figure some self shading was inevitable. extent to which simulated self shade depression was accurate depends validity rules cluster nlnmC 1 a n4 a a A A 'I T Ik a) (00 Sa) CC C C C, r\ coS 0. 0 I cl 'C rIO Vt N\ cD in t LJ LW L. 000 000 000 MrO in . Co It, t rm, I I I I I I I p I 00 oa) F'w presumably can grow of each other s way. A selfshade depression should exist, is expected to be smaller than was simulated. Stratified Beer s law models were constructed both biomass profile adjusted branch angle unadjusted light profile penetration (Figure level 6). the When model belowcanopy based the adjusted biomass underestimated light penetration the upper canopy, model based the unadjusted profile provided a nearly perfect (Figure . Because unadjusted foliage profile sted is clearly above incorrect base assumed leader.), that this was largely fortuitous. Returning discussion heterogeneity dense in the near introduction, canopy. crowns no crown are small (equation will therefore should large underestimate computing (Figure light biomass unadjusted a homogeneous penetration. profile model method shifted foliage down from actual position served compensate underestimation of light penetration unit biomass. 