Virtual Geographic Simulation of Light Distribution Within Three-Dimensional Plant Canopy Models

International Journal of Geo-Information

Article Virtual Geographic Simulation of Light Distribution within Three-Dimensional Plant Canopy Models

Liyu Tang 1,2,*, Dan Yin 1,2, Shuwei Chen 1,2, Chongcheng Chen 1,2, Hongyu Huang 1,2 and Ding Lin 1,2 1 Key Laboratory of Spatial Data Mining & Information Sharing of Ministry of Education, Fuzhou University, Fuzhou 350116, China; [email protected] (D.Y.); [email protected] (S.C.); [email protected] (C.C.); [email protected] (H.H.); [email protected] (D.L.) 2 National Engineering Research Center of Geospatial Information Technology, Fuzhou University, Fuzhou 350116, China * Correspondence: [email protected]; Tel.: +86-0591-6317-9772

Received: 25 October 2017; Accepted: 15 December 2017; Published: 19 December 2017

Abstract: Virtual geographic environments (VGEs) have been regarded as an important new means of simulating, analyzing, and understanding complex geological processes. Plants and light are major components of the geographic environment. Light is a critical factor that affects ecological systems. In this study, we focused on simulating light transmission and distribution within a three-dimensional plant canopy model. A progressive reﬁnement radiosity algorithm was applied to simulate the transmission and distribution of solar light within a detailed, three-dimensional (3D) loquat (Eriobotrya japonica Lindl.) canopy model. The canopy was described in three dimensions, and each organ surface was represented by a set of triangular facets. The form factors in radiosity were calculated using a hemi-cube algorithm. We developed a module for simulating the instantaneous light distribution within a virtual canopy, which was integrated into ParaTree. We simulated the distribution of photosynthetically active radiation (PAR) within a loquat canopy, and calculated the total PAR intercepted at the whole canopy scale, as well as the mean PAR interception per unit leaf area. The ParaTree-integrated radiosity model simulates the uncollided propagation of direct solar and diffuse sky light and the light-scattering effect of foliage. The PAR captured by the whole canopy based on the radiosity is approximately 9.4% greater than that obtained using ray tracing and TURTLE methods. The latter methods do not account for the scattering among leaves in the canopy in the study, and therefore, the difference might be due to the contribution of light scattering in the foliage. The simulation result is close to Myneni’s ﬁndings, in which the light scattering within a canopy is less than 10% of the incident PAR. Our method can be employed for visualizing and analyzing the spatial distribution of light within a canopy, and for estimating the PAR interception at the organ and canopy levels. It is useful for designing plant canopy architecture (e.g., fruit trees and plants in urban greening) and planting planning.

Keywords: virtual geographic environment; three-dimensional model; light distribution; canopy structure; radiosity

1. Introduction The virtual geographic environment (VGE) aims to provide users with integrated tools to understand the world better, e.g., integrating urban green space typology into a procedural three-dimensional visualization for facilitating collaborative planning among stakeholders of different backgrounds [1]. Simulation is one of four components of a complete virtual geographic environment [2], and it has been regarded as a good approach for developing experiments [3,4]. Simulation has made the deductive process operable in scientiﬁc experiments related to research on

ISPRS Int. J. Geo-Inf. 2017, 6, 405; doi:10.3390/ijgi6120405 www.mdpi.com/journal/ijgi ISPRS Int. J. Geo-Inf. 2017, 6, 405 2 of 15 the real world beyond visualization [4], e.g., for interactively assessing the photovoltaic potential in urban areas [5]. In a VGE workspace, the user conducts computer-aided geographic experiments that correspond to the real world and its physical dimensions [6]. Light is a major ecological factor that influences plant growth and development [7]. The distribution of light within a plant canopy is a valuable research issue that is beneficial to our understanding of light propagation, light distribution, and even for urban green land micro-climates [8,9]. The light distribution within a canopy determines the energy availability for a large number of physiological processes (e.g., photosynthesis and transpiration). However, the effects of light on vegetation dynamics are poorly understood, and are expressed at a quantitative level. This is partly due to a lack of quantitative methods for evaluating light interception by individual plants [10]. Traditionally, the light distribution in a canopy is measured directly with radiation sensors. Field measurements are effective, but they are time-consuming and labor-intensive. Furthermore, it is difficult to obtain data with high spatial and temporal resolution. This method is suitable for shorter trees with a small canopy; hence measuring large, tall trees is laborious. Therefore, this method is not desirable in the present state of science and technology. Thus far, efforts have focused on modeling the radiation transfer within a canopy over time. The radiation transfer model relies on the representation of the canopy and the light transfer theoretical model, e.g., radiosity [11] and Monte Carlo ray tracing [12]. A turbid medium is usually used to describe the canopy [13]. This type of canopy model generally assumes that the leaves are small, and that they are randomly and uniformly distributed throughout the canopy. This model has achieved wide success. To account for the three-dimensional radiation transfer and computational efficiency, there are two popular crown simplification schemes [14]. The first scheme is based on a single ellipsoid or cylinders that represent the crown volume with respect to the location, size, and shape of the foliage, etc. [15,16]. The other scheme employs small cubic volumes as voxels to form a regular lattice that fills the entire tree crown volume [17]. These methods have been widely applied in inverse remote sensing due to the low associated cost of computing [18]. The light interception is then usually computed according to the area index (LAI) and the extinction coefficient [15]. Although these methods have provided good estimations of the total light interception within a canopy, they do not account for the effects of local light intensity and canopy heterogeneity on the light interception, according to a few authors [7,19,20]. The turbid medium describes the canopy structure using a statistical model that is not capable of accurately computing fluxes over individual organs [21]. Therefore, a detailed description of the canopy is required for overlapping foliage [20]. Three-dimensional canopy models can quantitatively and accurately describe the plant topology, geometry and organ position. Plant organs can be represented for each individual 3D unit, and the radiation transmission and interception among the units can be simulated with the Monte Carlo ray tracing model or radiosity algorithms. At present, a number of principles, methods, and tools have been developed for describing the canopy structure, including rule-based modeling [22,23], interactive parametric modeling [24–26], image-based 3D modeling [27], and 3D reconstruction based on measured plant structure data [28,29]. The use of radiosity was initially proposed to achieve a realistic scene [11] using computer graphic techniques. This method describes the scattering of light based on the Lambertian law. The model was later adapted to canopies [30,31] and incorporated into a 3D model, which developed into the radiosity–graphics modeling radiation regime (RGM) by Qin and Gerstl [32]. RGM took advantage of radiosity theory and the high accuracy of 3D models with the L-system. The nested radiosity model [21] was developed to simulate the distribution of light within a canopy at the organ level, and was incorporated into the OpenAlea platform [33] to analyze the light interception of herbaceous canopies [10]. Because light scattering within a canopy accounts for less than 10% of the incident photosynthetically active radiation (PAR) [34], several researchers have directly computed the uncollided propagation of direct solar radiation and diffuse sky radiation into the canopy using ray tracing [35,36], the projection Z-buffer algorithm [37], and a virtual camera based on ISPRS Int. J. Geo-Inf. 2017, 6, 405 3 of 15

OpenGL [38]. These simpliﬁed methods are useful for connecting to a leaf photosynthetic mode to estimate the canopy photosynthesis rates. However, light scattering in plant foliage is important for the photosynthesis of leaves under or within the canopy. The radiosity equation fully accounts for multiple scattering between facet elements, making it well-suited for calculating the radiation within a vegetation canopy [32]. In this paper, we focused on combining existing 3D morphological modeling approaches [25,39] and the radiosity algorithm. Radiosity was used to represent the interactions between the light and organs within a canopy. This research was undertaken with the following three objectives: (1) to construct detailed 3D Muluo loquat (Eriobotrya japonica Lindl.) models; (2) to develop a software prototype to simulate light distribution within a canopy; and (3) to simulate the light distribution within a loquat canopy at the organ scale, or even at small units (facets). The expected results will provide a useful approach for photosynthesis simulation, canopy light interception analysis, and the selection of ideotypes.

2. Materials and Methods

2.1. Measurement of Loquat Canopy Structural Parameters The loquat architectural parameters were collected from the natural germplasm resources of loquat nurseries in the Fuzhou National Fruit Gene Pool (26◦70 N; 119◦200 E). We selected a 7-year-old Muluo loquat that had never been pruned for the investigation. We measured and statistically analyzed the tree height, crown diameter, length and diameter of the central stem, length and thickness of the central shoot, the length and thickness of the lateral shoot, the location of the lateral shoot with respect to the father shoot, and the lengths and widths of the leaf blades. The number of shoots, the thickness variation along the branches, and the angle distribution range of each level of live branches from the father stem were counted and estimated. The tree height and crown diameter were 2 m and 4.4 m, respectively. The length and diameter of the central stem were 0.57 m and 0.08 m, respectively. The mean length and width of the leaf blade were 0.25 m and 0.11 m, respectively. Approximately 120 shoots were present on the whole tree. The number of leaf blades ranged from 15 to 20 on each shoot. The average leaf area of the leaﬂet was 63.24 cm2, as measured by hand-held Artec Eva laser scanner. The leaves were primarily distributed along the ends of the shoots. Table1 presents the canopy structural parameters of the loquat.

Table 1. The major structural parameters of a Muluo loquat.

Shoot Class Length (m) Thickness (m) Number of Shoots Angle (◦) Central shoot 0.85–1.06 0.11–0.12 4–6 30–45 Lateral shoot 0.51–0.90 0.09 2–3 30–60

2.2. Three-Dimensional Muluo Loquat Canopy Model Generation Detailed 3D architectural models provide the foundation for canopy radiation transfer and distribution simulation, and the precision of the 3D model has a direct impact on the accuracy of the radiation simulation [36]. As leaves are the major organs that affect light distribution and absorption, they are described explicitly. We focused on analyzing the light distribution in a Muluo loquat canopy. A 3D canopy model was constructed using the interactive parametric/individual 3D tree modeling tool known as ParaTree [25,39]. The basic element of the 3D canopy is a triangular facet. The process of building a 3D model of a loquat canopy has three key steps. (1) First, a detailed 3D leaf model is built, as shown in Figure1A,B using 3Ds MAX software. The leaf shape of the Muluo loquat is elliptical, and its mapping was initiated using the NURBS curve surface. Control points were then modiﬁed to make the length and width of the leaf close to the actual size, to make the size and shape of the triangular facet even, and to avoid long and narrow triangles, ultimately forming a leaf model. The leaf model is represented in a triangular mesh, in which each leaf blade consists of 20 triangles in ISPRS Int. J. Geo-Inf. 2017, 6, 405 4 of 15

ISPRSthe present Int. J. Geo-Inf. research. 2017, 6 To, 405 reduce the computational load, a single 3D leaf model is applied to the entire4 of 15 ISPRStree. Int. New J. Geo-Inf. shoot 2017 tips, 6, consist 405 of three leaf blades, as shown in Figure1C,D. (2) A trunk and branch4 of 15 andmodel using is created the interactive based on theparametric ﬁeld investigation individual mentioned 3D tree modeling above and tool using ParaTree. the interactive (3) The parametricleaf blade and using the interactive parametric individual 3D tree modeling tool ParaTree. (3) The leaf blade (leafindividual cluster) 3D model tree modeling is connected tool to ParaTree. the shoots (3) acco Therding leaf blade to their (leaf topological cluster) model relationship is connected and spatial to the (leaf cluster) model is connected to the shoots according to their topological relationship and spatial distribution,shoots according the texture to their is topological mapped, and relationship an entire and 3D spatialcanopy distribution, model with the46,221 texture triangular is mapped, facets and is distribution, the texture is mapped, and an entire 3D canopy model with 46,221 triangular facets is generated,an entire 3D as canopy shown model in Figure with 2. 46,221 The triangulartotal leaf facetsarea and is generated, LAI of the as model shown are in Figure 16.8 m2.2 The and total 1.7, generated, as shown in Figure 2. The total2 leaf area and LAI of the model are 16.8 m2 and 1.7, respectively.leaf area and LAI of the model are 16.8 m and 1.7, respectively. respectively.

Figure 1. Screenshot of the Muluo loquat leaf model. (A) A leaf blade wireframe model; (B) A leaf FigureFigure 1. ScreenshotScreenshot of of the the Muluo Muluo loquat loquat leaf leaf model. model. ( (AA)) A A leaf leaf blade blade wireframe wireframe model; model; ( (BB)) A A leaf leaf blade solid model; (C) A cluster leaf wireframe model; (D) A cluster leaf solid model. bladeblade solid solid model; model; ( (C)) A A cluster cluster leaf leaf wireframe wireframe model; ( D) A cluster leaf solid model.

Figure 2. The 3D Muluo loquat model produced by ParaTree. (A)Wireframe (B) solid and (C) image Figure 2. The 3D Muluo loquat model produced by ParaTree. (A)Wireframe (B) solid and (C) image ofFigure a real 2. loquatThe 3D tree Muluo by camera. loquat model produced by ParaTree. (A)Wireframe (B) solid and (C) image of of a real loquat tree by camera. a real loquat tree by camera. 2.3. Radiosity-Based Simulation of the PAR Distribution within a Canopy 2.3. Radiosity-Based Simulation of the PAR Distribution within a Canopy 2.3. Radiosity-Based Simulation of the PAR Distribution within a Canopy 2.3.1. Equation for Radiosity 2.3.1.2.3.1. Equation Equation for for Radiosity Radiosity The radiosity equation originated from computer graphics for the purpose of expressing the The radiosity equation originated from computer graphics for the purpose of expressing the globalThe illumination radiosity equationof a scene. originated The radiosity from equation computer describes graphics the for interactions the purpose of of radiation expressing based the global illumination of a scene. The radiosity equation describes the interactions of radiation based onglobal the illuminationassumption that of a the scene. surfaces The radiosity are Lambertian. equation The describes diffuse the radiation interactions flux at of all radiation the surfaces based can on on the assumption that the surfaces are Lambertian. The diffuse radiation flux at all the surfaces can bethe computed assumption by that considering the surfaces multiple are Lambertian. reflection The and diffuse transmission radiation processes flux at all [11]. the surfacesThe radiosity can be be computed by considering multiple reflection and transmission processes [11]. The radiosity equationcomputed is by as consideringfollows: multiple reflection and transmission processes [11]. The radiosity equation equationis as follows: is as follows: NN =+ρN = BBEiiijji= E + ρ B BFiF (i(= 1, 1,2,..., 2, . . . , NN )) (1)(1) BEi =+ρi i ∑ BFij ji ( = 1,2,..., N ) iiijjij=j=11 (1) j=1 where Bi isis the the radiosity of of facet facet ii inin a a scene, scene, namely, namely, the total light energy exiting facet i per unit area where Bi is the radiosity of facet i in a scene, namely, the total light energy exiting facet i per unit area per time. EEii isis the the emittance emittance of of facet facet ii;; at at present, EEii isis null null for for plant leaves leaves but but is is not null for light per time. Ei is the emittance of facet i; at present, Ei is null for plant leaves but is not null for light sources. ρii isis the the diffuse diffuse reflectivity; reflectivity; N isis the number of surfaces in the scene; and Fjiji isis the the form factor sources. ρi is the diffuse reflectivity; N is the number of surfaces in the scene; and Fji is the form factor between surface ii andand surface surface jj andand describes describes the the contribution contribution of of each each facet facet j toj to the the radiosity radiosity at atfacet facet i. i. between surface i and surface j and describes the contribution of each facet j to the radiosity at facet i. 2.3.2. Incorporation of Radiosity into a Three-Dimensional Model 2.3.2. Incorporation of Radiosity into a Three-Dimensional Model The simulation prototype system for light dist distributionribution within a canopy was implemented by The simulation prototype system for light distribution within a canopy was implemented by integrating the interactive parametric 3D individual treetree modelingmodeling systemsystem ParaTreeParaTree withwith radiosityradiosity[ [40]40] integrating the interactive parametric 3D individual tree modeling system ParaTree with radiosity [40] by using VC++ as as the the language language and and OpenGL OpenGL and and Visual Visual Studio Studio as as the the development platform. platform. by using VC++ as the language and OpenGL and Visual Studio as the development platform. Furthermore, thethe system system integrated integrated an astronomicalan astronomic parametrical parametric algorithm algorithm to estimate to estimate the light the intensity light Furthermore, the system integrated an astronomical parametric algorithm to estimate the light intensityat the top at of thethe canopy,top of consideringthe canopy, the considering light characteristics the light with characteristics respect to the with geographic respect location, to the intensity at the top of the canopy, considering the light characteristics with respect to the geographic location, direction, and time, because the light may vary temporally and spatially with geographic location, direction, and time, because the light may vary temporally and spatially with the height due to the movement of the sun. the height due to the movement of the sun. A 3D geometrical model of a Muluo loquat canopy was employed as the computational A 3D geometrical model of a Muluo loquat canopy was employed as the computational environment to determine the radiosity. The PAR distribution was simulated within the canopy. environment to determine the radiosity. The PAR distribution was simulated within the canopy.

ISPRS Int. J. Geo-Inf. 2017, 6, 405 5 of 15 direction, and time, because the light may vary temporally and spatially with the height due to the movement of the sun. ISPRSA Int. 3D J. Geo-Inf. geometrical 2017, 6, 405 model of a Muluo loquat canopy was employed as the computational5 of 15 environment to determine the radiosity. The PAR distribution was simulated within the canopy. The incidentThe incident radiation radiation primarily primarily comes fromcomes direct from solar direct radiation, solar radiation, and diffuse and radiation diffuse comes radiation from thecomes sky. Thefrom photosynthetically the sky. The photosynthetically active wave band active is generallywave band within is generally a range within of 400 a to range 700 nm. of 400 Based to 700 on datanm. fromBased the on literature, data from we the assumed literature, that PAR we accountsassumed for that 40% PAR of the accounts global solar for radiation40% of the energy. global Figure solar3 illustratesradiation energy. the process Figure of radiosity-based 3 illustrates the light process distribution of radiosity-based simulation withinlight distribution a canopy. The simulation primary stepswithin are a canopy. as follows: The (1) primary The zenith steps and are azimuth as follows: angles (1) of The the zenith sun are and calculated azimuth using angles the of astronomical the sun are parametriccalculated using algorithm the astronomical [41] according parametric to the geographical algorithm location [41] according of the plant to the (latitude), geographical the day location of the year,of the and plant the (latitude), time of day. the The day intensities of the year, of the and direct the time solar of PAR day. and The diffuse intensities sky PAR of werethe direct calculated solar hourlyPAR and using diffuse the radiation sky PAR transfer were modelcalculated for the hourly atmosphere using [the42]. radiation The geometry transfer and lightmodel properties for the couldatmosphere then be [42]. identiﬁed. The geometry (2) Triangles and werelight employedproperties within could the then 3D be canopy, identified. and the (2) form Triangles factors were computedemployed usingwithin the the hemi-cube 3D canopy, algorithm. and the (3) Basedform onfactors the opticalwere properties,computed theusing radiosity the hemi-cube equation wasalgorithm. solved (3) using Based a progressiveon the optical reﬁnement properties, algorithm; the radiosity the equation PAR was was then solved estimated using for a progressive individual leafrefinement units. algorithm; the PAR was then estimated for individual leaf units.

Geographical location of Meteorological Simulation time Architectural parameters product area conditions

Astronomical parametric algorithm Parametric tree modeling ParaTree Intensity at the top of the Zenith angle Azimuth angle canopy

3D Detailed canopy model The reference projection plane Direct Diffuse Simula definition -tion of solar sky PAR PAR PAR distrib- Computation of form-factors utions using hemi-cube in the Reflectance canopy Radiosity solution by progressive refinement algorithm

PAR three dimensional PAR intensity per leaf visualization

Figure 3. AA schematic schematic of of the the processing processing pipeline for a light distribution simulation in a canopy.

2.3.3. Definition of the Light Source 2.3.3. Definition of the Light Source The efficient sampling of the positions and the direction of incident radiation are key issues The efficient sampling of the positions and the direction of incident radiation are key issues [19]. [19]. The virtual environment was defined as consisting of the light source and the 3D tree canopy The virtual environment was defined as consisting of the light source and the 3D tree canopy model. model. Since the incoming radiation is partitioned into direct solar flux and diffuse flux, the light Since the incoming radiation is partitioned into direct solar flux and diffuse flux, the light sources sources include direct solar light and diffuse sky light. include direct solar light and diffuse sky light. The direct solar light source was described as a reference projection plane located above the The direct solar light source was described as a reference projection plane located above the canopy that was normalized to the direction of the light [36], and it was discretized into triangles. canopy that was normalized to the direction of the light [36], and it was discretized into triangles. The normalization of the plane is defined according to the zenith and azimuth angles of the sun, The normalization of the plane is defined according to the zenith and azimuth angles of the sun, and and the reference projection plane is perpendicular to the incident light and must be large enough the reference projection plane is perpendicular to the incident light and must be large enough for rays for rays originating from the plane to illuminate the entire canopy. The plane was first created as an originating from the plane to illuminate the entire canopy. The plane was first created as an infinite infinite plane at a certain distance from the canopy surface. Figure 4 shows that when the bounding plane at a certain distance from the canopy surface. Figure4 shows that when the bounding box box of the tree model was projected onto this infinite plane, eight vertexes were then projected onto the plane. The minimum parallelogram containing the eight points is regarded as the reference projection plane, i.e., to define the direct solar light source. The plane was divided into a number of identical parallelograms. Each parallelogram was subdivided into two triangles (Figure 4).

ISPRS Int. J. Geo-Inf. 2017, 6, 405 6 of 15 of the tree model was projected onto this inﬁnite plane, eight vertexes were then projected onto the plane. The minimum parallelogram containing the eight points is regarded as the reference projection plane, i.e., to deﬁne the direct solar light source. The plane was divided into a number of identical parallelograms.ISPRS Int. J. Geo-Inf. Each 2017 parallelogram, 6, 405 was subdivided into two triangles (Figure4). 6 of 15

ISPRS Int. J. Geo-Inf. 2017, 6, 405 6 of 15

FigureFigure 4. Schematic 4. Schematic diagram diagram for definingfor defining the the reference reference projection projection plane plane of of direct direct solar solar light. light. TheThe eight eight cyan points on the plane indicate the projection of the octree bounding box onto the plane, and cyan points on the plane indicate the projection of the octree bounding box onto the plane, and they they define the size of the plane. defineFigure the size 4. Schematic of the plane. diagram for defining the reference projection plane of direct solar light. The eight cyan points on the plane indicate the projection of the octree bounding box onto the plane, and Thethey diffusedefine the light size sourceof the plane. from the sky was described as the sky hemisphere over the canopy. The sampling diffuse light of the source sky hemisphere from the usually sky was relies described on a discretization as the sky in hemisphere solid angle overelements, the canopy.so The samplingthat theThe radiance diffuse of the lightwithin sky source hemisphere identical from solid the usually elementssky was relies desccan onberibed assumed a discretizationas the tosky be hemisphere constant. in solid Figure over angle 5the shows elements,canopy. the so that thecontinuousThe radiancesampling sky withinof hemisphere the sky identical hemisphere as a solid finite usually elements set of relies light can onsources. bea discretization assumed The hemisphere to in be solid constant. isangle large elements, Figure enough5 showstoso the continuousencompassthat the radiance all sky the hemisphere within canopy identical elements. as asolid finiteThe elements surface set of ofcan light the be sources.skyassumed hemisphere Theto be hemisphereconstant. was divided Figure isinto large5 showsa number enough the to ofcontinuous regions with sky equal hemisphere solid angle as asectors. finite setThe ofhemi lightsphere sources. is partitioned The hemisphere with the isreference large enough direction to encompass all the canopy elements. The surface of the sky hemisphere was divided into a number of ofencompass the meridians all the and canopy parallels. elements. The Thelight surface source offrom the thesky skyhemisphere was approximately was divided simplified into a number as a regions with equal solid angle sectors. The hemisphere is partitioned with the reference direction of numberof regions of withtriangular equal ligsolidht sources angle sectors. (Figure The 5). hemisphere is partitioned with the reference direction the meridiansof the meridians and parallels. and parallels. The light The source light source from thefrom sky the was sky approximatelywas approximately simplified simplified as a as number a of triangularnumber of light triangular sources lig (Figureht sources5). (Figure 5).

Figure 5. Schematic representation of the diffuse sky light source with a discretized hemisphere over the canopy that consists of a number of triangular facets. The light source consists of rays traveling from the light plane to the canopy. FigureFigure 5. Schematic 5. Schematic representation representation of theof the diffuse diffuse sky sky light light source source with with a discretizeda discretized hemisphere hemisphere over over the canopy that consists of a number of triangular facets. The light source consists of rays the canopy that consists of a number of triangular facets. The light source consists of rays traveling 2.3.4.traveling Computation from the of lightForm plane Factors to the canopy. from the light plane to the canopy. The hemi-cube algorithm is one of the major methods that is employed for computing the form factors2.3.4. Computation in radiosity of [40,43]. Form Factors The present research integrated this method to simulate the light 2.3.4. Computation of Form Factors distributionThe hemi-cube within aalgorithm canopy. Foris one each of theelement major of meth the odscanopy that model,is employed its center for computing is regarded the as form the Thecenterfactors hemi-cube of in the radiosity overhead algorithm [40,43]. hemi-cube. The is one presentThe of five the researchfaces major of theintegrated methods hemi-cube thatthis are ismethod divided employed to into simulate grids for computing with the 100light × the form100distribution factors elements. in radiositywithin Each solida canopy. [40 angle,43]. Forwas The each defined present element according research of the to canopy integrated each elemental model, this its methodarea center of the is to regardedface simulate and centeras the the light distributionofcenter the ofhemi-cube. within the overhead a canopy.Each hemi-cube. hemi-cube For each The face elementfive defines faces ofofa view the hemi-cube canopy volume model,to are define divided its which center into elementsgrids is regarded with of 100 the as× the environment are visible. The visible elements were projected onto each hemi-cube face, and the center100 of elements. the overhead Each solid hemi-cube. angle was Thedefined ﬁve according faces of to the each hemi-cube elemental area are dividedof the face into and gridscenter with approximateof the hemi-cube. form Eachfactor hemi-cube of the elements face defines was de atermined view volume by summing to define up which the area elements of the ofgrids the coveredenvironment by the are projection. visible. The visible elements were projected onto each hemi-cube face, and the approximate form factor of the elements was determined by summing up the area of the grids covered by the projection.

ISPRS Int. J. Geo-Inf. 2017, 6, 405 7 of 15

100 × 100 elements. Each solid angle was defined according to each elemental area of the face and center of the hemi-cube. Each hemi-cube face defines a view volume to define which elements of the environment are visible. The visible elements were projected onto each hemi-cube face, and the approximate form factor of the elements was determined by summing up the area of the grids covered by the projection.

2.3.5. SolvingISPRS Int. the J. Geo-Inf. Radiosity 2017, 6, Equation 405 7 of 15

The2.3.5. radiosity Solving equation the Radiosity is solvedEquation on the basis of a progressive refinement algorithm [40,44]. The algorithm process is as follows: (1) The initial exitance of each element in the environment is The radiosity equation is solved on the basis of a progressive refinement algorithm [40,44]. The determined. Only the light source elements have nonzero values for photon flux, and are determined algorithm process is as follows: (1) The initial exitance of each element in the environment is by the intensitydetermined. of the Only light the source. light sour Once the elements other hand,have nonzero the values values for thefor treephoton canopy flux, modeland are are all initializeddetermined to zero. (2)by the The intensity element of withthe light the source. greatest On amountthe other ofhand, photon the values flux tofor the the shoottree canopy is selected, and the exitancemodel are received all initialized by every to zero. other (2) elementThe element in the with environment the greatest isamount calculated, of photon adding flux theto the value to both unsentshoot exitance is selected, and and the the final exitance exitance. received The byshaded every other element element values in the areenvironment zero. (3) is After calculated, the photon adding the value to both unsent exitance and the final exitance. The shaded element values are zero. flux has been shot to each element, the unsent value is reset to zero. This element can shoot again only (3) After the photon flux has been shot to each element, the unsent value is reset to zero. This after receivingelement further can shoot photon again flux only from after thereceiving other furthe elementsr photon during flux subsequentfrom the other steps. elements (4) Steps during 2 and 3 are repeatedsubsequent until the steps. total (4) amountSteps 2 and of 3 photon are repeated flux variesuntil the by total less amount than a of given photon value. flux varies by less Figurethan6 showsa given thatvalue. when a given light source facet shoots a photon flux based on its initial state, only the visibleFigure elements 6 shows inthat the when environment a given light are source illuminated, facet shoots while a photon the restflux based of the on elements its initial in the environmentstate,remain only the shaded. visible elements The results in the change environment as more are illuminated, light source while facets the shoot rest of a the photon elements flux in and as the environment remain shaded. The results change as more light source facets shoot a photon flux more environmental elements receive the photon flux. These elements then become a secondary light and as more environmental elements receive the photon flux. These elements then become a source, shootingsecondary part light of source, the photon shooting flux part to of otherthe photon elements. flux to other elements.

Figure 6. Schematic representation of light distribution variations within a canopy based on the Figure 6. Schematic representation of light distribution variations within a canopy based on the number of light sources and iteration steps. The black triangles represent elements that have not number ofreceived light a sources photon flux, and whereas iteration the steps. bright yellow The black triangles triangles represent represent those receiving elements a photon that flux. have not receivedThe a photon brightness flux, corresponds whereas theto the bright irradiation yellow intensity. triangles (A) Ten represent light facets; those (B)receiving fifty light facets; a photon (C) flux. The brightnessone hundred corresponds light facets; to the and irradiation (D) two hundred intensity. light facets. (A) Ten light facets; (B) fifty light facets; (C) one hundred light facets; and (D) two hundred light facets. 2.4. Alternative Methods for Simulating the PAR Distribution within a Canopy Ray tracing and TURTLE [45] algorithms are alternative methods that are useful for a wide variety of radiation transport problems. They were integrated into ParaTree. The former is used for

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2.4. Alternative Methods for Simulating the PAR Distribution within a Canopy Ray tracing and TURTLE [45] algorithms are alternative methods that are useful for a wide variety of radiation transport problems. They were integrated into ParaTree. The former is used for computing the uncollided propagation of direct solar radiation, and the latter is used for computing the diffuse sky radiation into the canopy. The detail implementation can be found in [36]. Based on the ray tracing algorithm, a discrete number of rays were used to simulate the paths of a nearly continuous distribution of photons.ISPRS Int. The J. Geo-Inf. ray 2017 starting, 6, 405 point, as well as the direction and energy of each ray, determine8 of 15 the triangle of the canopy components that the ray intersects at the shortest distance from the starting point. Oncecomputing the trianglethe uncollided was found,propagation the of ray direct information solar radiation, was and stored the latter in the is used intersection for computing list and the the diffuse sky radiation into the canopy. The detail implementation can be found in [36]. Based on intersectedthe ray triangle tracing list.algorithm, The ray a discrete information number included of rays were the direction,used to simulate starting the location,paths of a intensity,nearly and intersections.continuous Thus, distribution the energy of photons. (direct solar The ray light) starting reaching point, each as well organ as the surface direction (triangle) and energy of the of canopy can be recursivelyeach ray, determine calculated. the triangle The diffuse of the skycanopy radiation components into thethat canopythe ray intersects was implemented at the shortest as follows. For eachdistance element from surface the starting (triangle) point. Once of the the canopytriangle was model, found, its the center ray information is regarded was as stored the centerin the of the overheadintersection sky hemisphere. list and the Theintersected hemisphere triangle list. was The divided ray information into many included regions the direction, with equal starting solid angle location, intensity, and intersections. Thus, the energy (direct solar light) reaching each organ sectors. If the ray from each region center intersects the projected element (triangle), then the region is surface (triangle) of the canopy can be recursively calculated. The diffuse sky radiation into the shadedcanopy by the was projected implemented element, as follows. and the For region each elem is notent viewable.surface (triangle) Otherwise, of the canopy the region model, is its viewable. The intensitycenter is of regarded a diffuse as the sky center PAR-reaching of the overhead element sky hemisphere. can be estimated The hemisphere by taking was divided the viewable into rate multipliedmany by regions the intensity with equal of the solid diffuse angle skysectors. PAR. If the ray from each region center intersects the projected element (triangle), then the region is shaded by the projected element, and the region is not 3. Resultsviewable. and Discussion Otherwise, the region is viewable. The intensity of a diffuse sky PAR-reaching element can be estimated by taking the viewable rate multiplied by the intensity of the diffuse sky PAR. In the case study, all the simulations were performed in Fuzhou (26◦70 N; 119◦200 E) on 21 June3. 2016, Results under and Discussion clear sky conditions. The intensity of the incoming radiation was computed from 6:00 toIn 18:00 the case in 13-hourlystudy, all the time simulations steps. Speciﬁcally, were performed the in radiation Fuzhou (26°7 intensity′ N; 119°20 was′ estimatedE) on June 21, at the top of the canopy.2016, under The clear PAR sky obtained conditions. at The the leafintensity level of wasthe incoming estimated radiation hourly was during computed the daytime.from 6:00 to 18:00 in 13-hourly time steps. Specifically, the radiation intensity was estimated at the top of the 3.1. Spatialcanopy. Distribution The PAR obtained of Direct at Solar the leaf PAR level in was the Canopyestimated hourly during the daytime.

Figure3.1. Spatial7 presents Distribution the 3Dof Direct spatial Solar distribution PAR in the Canopy of PAR within the loquat canopy, based on the incoming direct solar PAR at 12:00. The false color indicates the amount of received PAR. The daily Figure 7 presents the 3D spatial distribution of PAR within the loquat canopy, based on the −2 −1 mean intensityincoming perdirect leaf solar unit PAR of at direct 12:00. The captured false color solar indicates PAR wasthe amount 239.33 ofµ receivedmol·m PAR.·s The, and daily the mean −1 amountmean of direct intensity solar per PAR leaf captured unit of direct by the captured whole solar canopy PAR was was 4021.52 239.33 μµmol·mmol·s−2s−1, inand the the daytime. mean If the solar zenithamount was of direct larger, solar then PAR the captured directions by the of whole incoming canopy light was 4021.52 sources μmol·s would−1 in be the distributed daytime. If nearly vertically.the solar The amountzenith was of larger, irradiation then the captured directions by of the incoming outer (upper)light sources elements would ofbe thedistributed top canopy is greaternearly than the vertically. amount The captured amount byof theirradiation inner and capt lowerured by elements. the outer Due(upper) to the elements overshadowing of the top among canopy is greater than the amount captured by the inner and lower elements. Due to the the leaves,overshadowing the direct lightamong fractions the leaves, transmitted the direct light to thefractions foliage transmitted increased to the with foliage the foliageincreased height with within the canopy,the foliage and withheight the within distance the canopy, from and the with center the of distance the canopy. from the center of the canopy.

Figure 7. Direct solar PAR distribution within the virtual loquat canopy at 12:00 on June 21, 2016. Figure 7. Direct solar PAR distribution within the virtual loquat canopy at 12:00 on June 21 2016. The brightness corresponds to the irradiation intensity. (A) Overhead view and (B) profile view. The brightness corresponds to the irradiation intensity. (A) Overhead view and (B) proﬁle view. Table 2 shows the parameters obtained from the simulated results of the two methods. The amount of PAR captured within the canopy as determined by the ray tracing is approximately 6.7% lower than the value based on the hourly radiosity.

ISPRS Int. J. Geo-Inf. 2017, 6, 405 9 of 15 ISPRS Int. J. Geo-Inf. 2017, 6, 405 9 of 15 Table 2. Comparison of direct solar PAR parameters that were simulated hourly based on radiosity and ray tracing within the loquat canopy. Table2 shows the parameters obtained from the simulated results of the two methods. The amount Intensity of PAR (μmol·m−2·s−1) PAR Captured Per Second by the Whole Canopy (μmol·s−1) of PARTime captured within the canopy as determined by the ray tracing is approximately 6.7% lower than the value basedRadiosity on the hourlyRay radiosity.Tracing Radiosity Ray Tracing 06:00 22.04 20.89 370.31 350.96 07:00Table 2. Comparison95.14 of direct 83.36 solar PAR parameters 1598.60 that were simulated hourly based 1400.67 on radiosity 08:00and ray tracing178.46 within the loquat 161.54 canopy. 2998.72 2714.37 09:00 272.48 250.76 4578.52 4213.66

10:00 345.49 Intensity of PAR 325.04 (µmol ·m−2·s−1) PAR 5805.43 Captured Per Second by the Whole 5461.77 Canopy (µmol·s−1) Time 11:00 401.50 Radiosity 379.03 Ray Tracing 6746.55 Radiosity Ray 6369.01 Tracing 12:00 06:00425.74 22.04 401.04 20.89 7153.88 370.31 350.96 6738.92 13:00 07:00403.34 95.14 382.07 83.36 6777.48 1598.60 1400.67 6420.11 14:00 08:00350.84 178.46 333.22 161.54 5895.21 2998.72 2714.37 5599.30 09:00 272.48 250.76 4578.52 4213.66 15:00 10:00278.55 345.49 261.22 325.04 4680.57 5805.43 5461.77 4389.39 16:00 11:00192.25 401.50 178.34 379.03 3230.46 6746.55 6369.01 2996.72 17:00 12:00114.01 425.74 96.91 401.04 1915.80 7153.88 6738.92 1628.49 13:00 403.34 382.07 6777.48 6420.11 18:00 14:0031.43 350.84 29.32 333.22 528.20 5895.21 5599.30 492.59 mean 15:00239.33 278.55 223.29 261.22 4021.52 4680.57 4389.39 3752.00 16:00 192.25 178.34 3230.46 2996.72 17:00 114.01 96.91 1915.80 1628.49 3.2. Spatial18:00 Distribution 31.43of Diffuse PAR within 29.32 the Canopy 528.20 492.59 mean 239.33 223.29 4021.52 3752.00 Figure 8 shows the 3D spatial distribution of diffuse PAR within the loquat canopy at 12:00. The daily mean intensity per leaf unit of diffuse captured PAR was 38.14 μmol·m−2·s−1 in the 3.2. Spatial Distribution of Diffuse PAR within the Canopy daytime, while the mean amount of diffuse PAR captured was 640.94 μmol·s−1 by the whole canopy in theFigure daytime.8 shows A comparison the 3D spatial of Figures distribution 7 and of 8 diffuse with the PAR legend within shows the loquat that canopyunder clear at 12:00. sky −2 −1 conditions,The daily mean the intensityamount perof direct leaf unit solar of diffuse PAR capturedis much PARgreater was than 38.14 theµmol amount·m ·s of indiffuse the daytime, PAR. −1 However,while the meanthe distribution amount of of diffuse diffuse PAR PAR captured was more was uniform. 640.94 Thisµmol difference·s by the results whole from canopy the larger in the powerdaytime. of Aincident comparison direct of solar Figures radiation7 and8 withand the legendsingle-direction shows that incident under cleardirect sky solar conditions, light under the clearamount sky of conditions, direct solar and PAR the is much fact that greater the thandiffus thee amountsky light of remains diffuse PAR.nearly However, the same the all distribution day long becauseof diffuse it does PAR not was have more a uniform.privileged This direction. difference results from the larger power of incident direct solarTable radiation 3 shows and that the the single-direction diffuse light energy incident captur directed solar for the light loquat under based clear on sky hourly conditions, simulations and usingthe fact radiosity that the is diffuseapproximately sky light 26.2% remains greater nearly than the that same obtained all day using long the because TURTLE it methods. does not have a privilegedBased on direction. the simulation results for the direct and diffuse PAR within the canopy, which were calculatedTable 3at shows hourly that time the steps, diffuse the light average energy total captured PAR intensity for the per loquat leaf basedunit was on hourly277.47 μ simulationsmol·m−2·s−1 inusing the daytime. radiosity The is approximately average PAR 26.2%captured greater by the than whole that obtainedcanopy was using 4662.46 the TURTLE μmol·s−1 methods..

FigureFigure 8. AA screenshot screenshot of of the the diffuse diffuse PAR PAR distribution within the virtual loquat canopy at at 12:00 on June21 June 21, 2016.2016. TheThe brightnessbrightness correspondscorresponds toto thethe irradiationirradiation intensity.intensity.

ISPRS Int. J. Geo-Inf. 2017, 6, 405 10 of 15

Table 3. Comparison of diffuse sky PAR parameters simulated hourly based on radiosity and the TURTLE algorithm within the loquat canopy.

ISPRS Int. J. Geo-Inf.Intensity 2017, 6 of, 405 PAR (µmol·m−2·s−1) PAR Captured Per Second by the Whole Canopy10 ( µofmol 15 ·s−1) Time Radiosity TURTLE Radiosity TURTLE Table 3. Comparison of diffuse sky PAR parameters simulated hourly based on radiosity and the 06:00TURTLE algorithm 31.7644 within the loquat 23.4353 canopy. 533.749 393.793 07:00 45.4446 33.5285 763.624 563.393 08:00 45.4228 33.5123 763.257PAR Captured Per Second 563.122by Intensity of PAR (μmol·m−2·s−1) 09:00Time 40.9469 30.2100 688.048the Whole Canopy (μmol·s 507.632−1) 10:00 35.9087 26.4929 603.389 445.172 11:00 32.1965Radiosity 23.7542 TURTLE 541.011 Radiosity TURTLE 399.152 12:0006:00 30.7322 31.7644 22.6737 23.4353 516.405533.749 393.793 380.996 13:0007:00 31.8199 45.4446 23.4763 33.5285 534.682763.624 563.393 394.483 14:0008:00 35.2424 45.4228 26.0013 33.5123 592.192763.257 563.122 436.912 15:00 40.1698 29.6367 674.988 497.998 16:0009:00 44.9061 40.9469 33.1312 30.2100 754.574688.048 507.632 556.717 17:0010:00 45.9886 35.9087 33.9298 26.4929 772.765603.389 445.172 570.137 18:0011:00 35.3222 32.1965 26.0603 23.7542 593.533541.011 399.152 437.902 mean12:00 38.1435 30.7322 28.1417 22.6737 640.940516.405 380.996 472.878 13:00 31.8199 23.4763 534.682 394.483 Based on the simulation14:00 results35.2424 for the direct26.0013 and diffuse592.192 PAR within436.912 the canopy, which were 15:00 40.1698 29.6367 674.988 497.998 µ · −2· −1 calculated at hourly time16:00 steps, the44.9061 average total33.1312 PAR intensity754.574 per leaf unit556.717 was 277.47 mol m s −1 in the daytime. The average17:00 PAR45.9886 captured by the33.9298 whole canopy772.765 was 4662.46570.137µmol ·s . The simulated light18:00 distribution35.3222 is affected26.0603 by the accuracy593.533 of the 3D437.902 tree architectural canopy model, the optical propertiesmean of38.1435 plant tissues,28.1417 and the properties640.940 of solar472.878 light. Nevertheless, it is difﬁcult to measureThe simulated the 3D light canopy distribution architecture is affected accurately by the accuracy (e.g., of thethe 3D leaf tree position architectural and canopy leaf inclination) and light distribution.model, the optical Therefore, properties validationsof plant tissues, regarding and the properties the 3D canopyof solar light. radiation Nevertheless, transfer it is simulation results aredifficult poor or to almostmeasure non-existent. the 3D canopy architecture The PAR capturedaccurately (e.g., by the the whole leaf position canopy and basedleaf inclination) on radiosity was comparedand to the light results distribution. estimated Therefore, using validations the ray tracingregarding and the TURTLE3D canopy algorithmsradiation transfer [35, 36simulation]. Figure 9 shows results are poor or almost non-existent. The PAR captured by the whole canopy based on radiosity the differencewas compared between to the the simulation results estimated results using obtained the ray tracing using and the TURTLE two methods. algorithms The [35,36]. two Figure results exhibit a consistent9 shows variation the difference trend in between the daytime. the simulation In this re paper,sults obtained the ray using tracing the two and methods. the TURTLE The two algorithm did not accountresults exhibit for scattering a consistent among variation the trend leaves in inthe the daytime. canopy; In this therefore, paper, the the ray difference tracing and in the results may be due toTURTLE the contribution algorithm did of not light account scattering for scattering in plant among foliage the leaves in radiosity. in the canopy; The therefore, simulation the of direct difference in results may be due to the contribution of light scattering in plant foliage in radiosity. PAR distributionThe simulation within of thedirect virtual PAR dist canopyribution using within radiosity the virtual is canopy found using to be radiosity effective. is found The to PAR be captured by the wholeeffective. canopy The usingPAR captured radiosity by the is approximatelywhole canopy using 9.4% radiosity greater is approximately than that obtained 9.4% greater using the ray tracing andthan the that TURTLE obtained using algorithms. the ray tracing This and difference the TURTLE is close algorithms. to the This ﬁndings difference in is the close literature, to the which show the lightfindings scattering in the literature, within which a canopy show isthe less light than scattering 10% ofwithin the incidenta canopy is PAR less [than34]. 10% This of portion the of the incident PAR [34]. This portion of the irradiation is generally distributed along the inner and lower irradiationareas is generally of the canopy, distributed where the along leaves the are inner under and the lowerlight saturation areas of point. the canopy, For these where leaves, the an leaves are under theincreased light saturation PAR would point. obviously For theseenhance leaves, the net an phot increasedosynthesis PAR rate; wouldthus, multiple obviously scattering enhance in the net photosynthesisthe canopy rate; plays thus, a role multiple in plant scatteringgrowth. in the canopy plays a role in plant growth.

Figure 9. (A) Daily variation in the average hourly direct solar PAR intensity captured from the loquat, as simulated using radiosity and ray tracing; (B) The daily variation in the average hourly diffuse PAR intensity captured from loquat, as simulated using the radiosity and the TURTLE algorithm. ISPRS Int. J. Geo-Inf. 2017, 6, 405 11 of 15

Figure 9. (A) Daily variation in the average hourly direct solar PAR intensity captured from the loquat, as simulated using radiosity and ray tracing; (B) The daily variation in the average hourly diffuse PAR ISPRS Int. J. Geo-Inf. 2017, 6, 405 11 of 15 intensity captured from loquat, as simulated using the radiosity and the TURTLE algorithm.

3.3. Light Interception EfficiencyEfficiency The silhouette area to total area ratio (STAR) was used to analyze the light interception of the canopy. InIn thethe presentpresent study, study, the the silhouette silhouette area area refers refers to theto the leaf-captured leaf-captured light light directly directly from from the light the sourcelight source or the or leaf-scattered the leaf-scattered light, whichlight, which is different is diff fromerent the from definition the definition given in given [7]. In in previous [7]. In previous studies, thestudies, silhouette the silhouette area was area defined was defined as the leaf as the area leaf projected area projected onto a planeonto a thatplane is perpendicularthat is perpendicular to the projectedto the projected direction direction [7]. The [7]. STAR The value STAR is value calculated is calculated by comparing by comparing the silhouette the silhouette area to the area total to leafthe area.total leaf When area. only When considering only considering the direct solarthe direct light, solar the STAR light, value the STAR of the va wholelue of canopy the whole ranged canopy from 0.288ranged to from 0.609 0.288 during to the0.609 daytime, during withthe daytime, a daily mean with STARa daily value mean of STAR 0.492. value The model of 0.492. calculated The model the STARcalculated value the distribution STAR value within distribution a canopy within volume a canopy with a horizontalvolume with area a ofhorizontal 0.5 m × 0.5area m of and 0.5 a m height × 0.5 ofm 0.5and m. a height The canopy of 0.5 wasm. The discretized canopy intowas sub-volumes,discretized into and sub-volumes, the mean STAR and ofthe each mean sub-volume STAR of each was calculated.sub-volume The was size calculated. of the sub-volume The size can of be alteredthe sub-volume based on various can be requirements. altered based Figure on 10various shows therequirements. STAR value Figure distribution 10 shows within the STAR the canopy value atdistribution a certain moment. within the canopy at a certain moment.

Figure 10. The STAR value distribution within the virtual loquat loquat canopy canopy on on June 21 June 21, 2016. Warmer colors denote a higher STAR value, whereas cooler colors denote lower STAR values.values. (A) 10:00 and (B) 12:00.

As a light interception indicator, the daily mean STAR value was 0.492, which is higher than that of of a a previous previous report report that that demonstrated demonstrated a range a range from from 0.238 0.238 to 0.340 to 0.340 for two-year-old for two-year-old apple apple trees trees[7]. This [7]. difference This difference is partially is partially due to due the toinclusio the inclusionn of scattering of scattering among among leaves leavesin the present in the present study. study.In the literature, In the literature, estimations estimations of the silhouette of the silhouettearea [7] only area considered [7] only considered directional directionallight. Moreover, light. Moreover,the architecture the architecture of the apple of tree the and apple the tree loquat and theare loquatdifferent. are Figure different. 11 shows Figure that 11 showsthe maximum that the maximumSTAR value STAR was valueobserved was at observed noon, while at noon, the whileminimum the minimum STAR value STAR was value observed was observed at dusk or at early dusk ormorning. early morning. This finding This implies finding that implies the thatcanopy the has canopy a larger has aSTAR larger when STAR the when zenith the angle zenith is angle lower. is lower.This result This is result similar is similarto the finding to the findingin which in the which STAR the of STAR a shoot of avaries shoot with varies its withorientation its orientation relative relativeto the direction to the direction of the light of the [7]. light [7]. The relative photosynthetically active radiation (RPAR) was used to analyze the light interception of the canopy, which refers to the ratio of the PAR at an area in the canopy to the PAR at the top of the canopy. When the leaf RPAR in the canopy decreased to 30%, these leaves were called low-efficacy light areas in the canopy [46]. Figure 12 shows the distribution of the low-efficacy light area in the canopy at certain moments. The average low-efficacy light area accounts for 17.73% of the entire canopy during the daytime. As an evaluating indicator of the light distribution within the canopy, a high proportion of the low-efficacy light area in the canopy often means the light distribution within the canopy is uneven. Figure 13 shows that the proportion of the low-efficacy light area accounting for the whole canopy was less than 30% based on the RPAR. According to the statistical data, the proportion of low-efficacy light area accounting for the whole canopy ranged from 8.57% to 22.86% during the daytime. ISPRS Int. J. Geo-Inf. 2017, 6, 405 12 of 15

ISPRS Int. J. Geo-Inf. 2017, 6, 405 12 of 15

Figure 11. Daily variation in STAR for the loquat model at the whole canopy level.

The relative photosynthetically active radiation (RPAR) was used to analyze the light interception of the canopy, which refers to the ratio of the PAR at an area in the canopy to the PAR at the top of the canopy. When the leaf RPAR in the canopy decreased to 30%, these leaves were called

low-efficacy light areas in the canopy [46]. Figure 12 shows the distribution of the low-efficacy light area in theFigure canopy 11. atDaily certain variation moments. in STAR for the loquat model at the whole canopy level.

34.96° 61.68° 87.14° 36.94° ABCD

FigureFigure 12. The 12. The distribution distribution of theof the low-efficacy low-efficacy light light area area in in the the virtual virtual loquat loquat canopycanopy on 21June June 21, 2016. The yellow2016. The round yellow symbols round illustratesymbols illustrate the light the source, light andsource, the yellowand the linesyellow illustrate lines illustrate the direction the of the light.direction The of figure the light. in the The diagram figure in illustrates the diagram the illustrates elevation the angle. elevation The areaangle. with The red area leaves with red denotes leaves denotes the low-efficacy light area, whereas the area with green leaves denotes the active the low-efficacy light area, whereas the area with green leaves denotes the active light area. (A) 8:00 light area. (A) 8:00 (B) 10:00 (C) 12:00 and (D) 16:00. (B) 10:00 (C) 12:00 and (D) 16:00. ISPRS Int. J. Geo-Inf. 2017, 6, 405 13 of 15 The average low-efficacy light area accounts for 17.73% of the entire canopy during the daytime. As an evaluating indicator of the light distribution within the canopy, a high proportion of the low-efficacy light area in the canopy often means the light distribution within the canopy is uneven. Figure 13 shows that the proportion of the low-efficacy light area accounting for the whole canopy was less than 30% based on the RPAR. According to the statistical data, the proportion of low-efficacy light area accounting for the whole canopy ranged from 8.57% to 22.86% during the daytime.

Figure 13. The proportion of the low-efficacy light area to the whole canopy. Figure 13. The proportion of the low-efﬁcacy light area to the whole canopy. It is useful to design an ideotype canopy. To provide more detailed guidance for fruit farmers or gardeners regarding the manipulation of tree architecture, the net photosynthesis model should be employed to identify leaves with a negative net productivity (i.e., irradiance below the compensation point). If the maximization of the productive leaf area is the goal, then the pruning strategy should be based on cutting shoots with negative net productivity.

4. Conclusions The study of virtual geographic experiments involves the reconstruction of simple 3D scenes including a single tree and light source, as well as the simulation of light transmission and distribution within a canopy. In the current study, a quantitative analysis method for determining the light distribution within a canopy was developed based on the individual tree modeling software ParaTree and an integrated radiosity-radiative transport algorithm. A detailed 3D geometrical canopy model was built, which is more similar to the real architecture than the model achieved using the turbid medium-based approach. Each organ was divided into sufficiently small 3D facets; thus, the transmission and interception processes of light were simulated at the facet levels, allowing for direct scaling from organs to canopies without assumptions of local homogeneity. It is possible to accurately estimate the PAR intercepted by leaf elements at various scales, e.g., at the shoot or whole canopy scale. This model enables us to simulate the light distributed to individual organs (facets). The simulation outputs provide critical information for models of photosynthesis. In conjunction with leaf light–photosynthesis response models, the canopy photosynthesis rates can be estimated. Using the loquat as an example, we built detailed models and simulated the PAR distribution within the canopy, analyzing the light interception of the canopy. This portion of the radiation is generally distributed along the inner and lower areas of the canopy, where the leaves are under the light saturation point. For these leaves, an increased PAR would obviously enhance the net photosynthesis rate; thus, multiple scattering in the canopy plays a role in plant growth. Furthermore, the simulation of PAR distribution within a virtual canopy using radiosity is shown to be effective. This model can be used to evaluate light distributions, and to estimate the contribution of light scattering in plant foliage. Therefore, we believe that this model is useful not only for designing an ideotype canopy and manipulating fruit tree architectures, but also for studying other biophysical models (e.g., plants in urban landscapes), and for examining the effect of canopy environment parameters, such as the temperature, within a canopy.

ISPRS Int. J. Geo-Inf. 2017, 6, 405 13 of 15

It is useful to design an ideotype canopy. To provide more detailed guidance for fruit farmers or gardeners regarding the manipulation of tree architecture, the net photosynthesis model should be employed to identify leaves with a negative net productivity (i.e., irradiance below the compensation point). If the maximization of the productive leaf area is the goal, then the pruning strategy should be based on cutting shoots with negative net productivity.

4. Conclusions The study of virtual geographic experiments involves the reconstruction of simple 3D scenes including a single tree and light source, as well as the simulation of light transmission and distribution within a canopy. In the current study, a quantitative analysis method for determining the light distribution within a canopy was developed based on the individual tree modeling software ParaTree and an integrated radiosity-radiative transport algorithm. A detailed 3D geometrical canopy model was built, which is more similar to the real architecture than the model achieved using the turbid medium-based approach. Each organ was divided into sufﬁciently small 3D facets; thus, the transmission and interception processes of light were simulated at the facet levels, allowing for direct scaling from organs to canopies without assumptions of local homogeneity. It is possible to accurately estimate the PAR intercepted by leaf elements at various scales, e.g., at the shoot or whole canopy scale. This model enables us to simulate the light distributed to individual organs (facets). The simulation outputs provide critical information for models of photosynthesis. In conjunction with leaf light–photosynthesis response models, the canopy photosynthesis rates can be estimated. Using the loquat as an example, we built detailed models and simulated the PAR distribution within the canopy, analyzing the light interception of the canopy. This portion of the radiation is generally distributed along the inner and lower areas of the canopy, where the leaves are under the light saturation point. For these leaves, an increased PAR would obviously enhance the net photosynthesis rate; thus, multiple scattering in the canopy plays a role in plant growth. Furthermore, the simulation of PAR distribution within a virtual canopy using radiosity is shown to be effective. This model can be used to evaluate light distributions, and to estimate the contribution of light scattering in plant foliage. Therefore, we believe that this model is useful not only for designing an ideotype canopy and manipulating fruit tree architectures, but also for studying other biophysical models (e.g., plants in urban landscapes), and for examining the effect of canopy environment parameters, such as the temperature, within a canopy.

Acknowledgments: This work was supported by a program of the National Science Foundation of China (Grant No. 41471334) and the pilot project of Fujian Province, China (Grant No. 2016Y0058). The authors thank Jiang Jimou from the Pomology Institute, Fujian Academy of Agricultural Sciences, for his help with the structure inventory. We thank the other members of our research group for their help with the system development. Author Contributions: Liyu Tang conceived and designed the experiments, analyzed the results and wrote the paper; Dan Yin and Shuwei Chen developed the program, constructed the experiments and analyzed the results. Chongcheng Chen conceived and modified the paper. Hongyu Huang and Ding Lin constructed the experiments and modified the paper. Conflicts of Interest: The authors declare no conflict of interest.

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