ISPRS Journal of Photogrammetry and Remote Sensing 97 (2014) 195–203

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ISPRS Journal of Photogrammetry and Remote Sensing

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Modeling spatiotemporal patterns of understory light intensity usingairborne laser scanner (LiDAR)

http://dx.doi.org/10.1016/j.isprsjprs.2014.09.0030924-2716/� 2014 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved.

⇑ Corresponding author at: Huyang Building 316, Lanzhou University, Tian ShuiSouth Road 222, Lanzhou City, Gansu Province 730000, China. Tel.: +8613679458015.

E-mail address: nanzhr@lzb.ac.cn (C. Zhao).

Shouzhang Peng a, Chuanyan Zhao a,⇑, Zhonglin Xu b

a State Key Laboratory of Pastoral Agricultural Ecosystem, School of Life Sciences, Lanzhou University, Lanzhou 730000, Chinab College of Resource and Environmental Science, Xinjiang University, Urumqi 830002, China

a r t i c l e i n f o

Article history:Received 27 March 2014Received in revised form 29 August 2014Accepted 9 September 2014

Keywords:LiDAR3D raytrace modelForest-shaded areaSolar rayUnderstory lightQinghai spruce

a b s t r a c t

This study described a spatiotemporally explicit 3D raytrace model to provide spatiotemporal patterns ofunderstory light (light intensity in the forest floor and along the vertical gradient). The model was builtbased on voxels derived from LiDAR and field investigation data, geographical information (elevation andlocation), and solar position (azimuth and altitude angles). We calculated the distance (L, in meters) trav-eled by solar ray in the crowns based on the model, and then calibrated and verified the light attenuationfunction using L based on Beer’s law. L and the ratio of below canopy light intensity to above canopy lightintensity showed obviously exponential relationship, with R2 = 0.94 and P < 0.05. Estimated and observedunderstory light intensities were obviously positively correlated, with R2 = 0.92 and P < 0.01, and the esti-mated values were slightly lower than the observed values. The spatiotemporal patterns of the lightintensity in the forest floor were mapped with the respect to the solar position, and these patterns rep-resented the variations in the forest-shaded area. The spatial patterns of the light intensity along verticalgradient were also mapped, and they showed strong variations. We concluded that L could account forthe complex patterns of understory light environment with respect to the geographical and solar positionvariations. The 3D raytrace model can be integrated with ecological or hydrological models to resolveseveral issues, such as plant succession and competition, soil evaporation, plant transpiration, and snow-melt in the forest.� 2014 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier

B.V. All rights reserved.

1. Introduction

The understory light environment is a key determinant of veg-etation patterns and ecohydrological processes in forest floor(Martens et al., 2000; Leuchner et al., 2012), because of its effectson the micro-environment (e.g., solar radiation, soil temperature,and soil water content) (Martens et al., 2000; von Arx et al.,2012). The understory vegetation types and their competition, suc-cession processes, and soil water balance are closely related to theunderstory light environment (Sakai and Akiyama, 2005; von Arxet al., 2012). Moreover, the spatiotemporal patterns of understorylight are controlled by the overstory characteristics (i.e., coverage,openness, closure, and height of canopy), site characteristics (i.e.,slope, aspect, elevation, and latitude), and solar position (i.e.,

azimuth and altitude angles) (Martens et al., 2000; Sakai andAkiyama, 2005; Ameztegui et al., 2012; Alexander et al., 2013).These factors could produce complex understory light patternsthat express not only horizontal heterogeneity, but also the verticalvariation at any given time. Considering the complex patterns ofunderstory light, the light model is a useful tool to simulate thespatiotemporal distribution of understory light. Therefore, many2D and 3D light models have been developed (Ameztegui et al.,2012).

The 2D light models are easily parameterized to model theunderstory light environment because they only require severalsimple forest canopy parameters (e.g., crown size, canopy cover,canopy openness, and canopy closure) estimated from remotesensing data with high spatial resolution (Martens et al., 2000;Ameztegui et al., 2012; Bode et al., 2014; Espírito-Santo et al.,2014). Owing to the simplification of 2D light models, their outputsonly represent the understory light environment at an altitudeangle of 90� and not at any other solar position. Thus, they cannotaccurately estimate the energy budget in the forest floor; conse-quently, some phenomena corresponding to energy budget cannot

196 S. Peng et al. / ISPRS Journal of Photogrammetry and Remote Sensing 97 (2014) 195–203

be accurately explained, such as latent and sensible heat fluxes, soiltemperature and water content, and snowpack accumulation andmelting (Duursma et al., 2012; Musselman et al., 2013). To accu-rately simulate the spatiotemporal patterns of understory light,the solar position and 3D canopy structure of the forest shouldbe introduced in 2D models (Ross, 1981; Iandolino et al., 2013).The former can provide temporal patterns of forest light regimeand the latter can ensure spatial distribution of the understorylight in forest floor or along vertical gradient of forest stand.

Light attenuation in the forest stand can be expressed as a func-tion of distance traveled by solar ray through the forest canopy(Brunner, 1998; Martens et al., 2000; Groot, 2004). This functionoften obeys Bouguer’s law (also called Beer’s law). Beer’s lawdescribes the exponential attenuation of monochromatic radiationin a turbid medium (Brunner, 1998; Mahat and Tarboton, 2012),and is the foundation for 3D light models that simulate the under-story light environment (Duursma et al., 2012; Musselman et al.,2013). However, 3D light models are limited in acquiring 3D dataof the forest canopy structure. Although several researchers haveused plant architecture models, such as YPLANT based on allome-tric parameters (Duursma et al., 2012; Iandolino et al., 2013) andCORONA based on the configuration of tree crown as ellipsoid(Groot, 2004) to reconstruct single plant architecture, theseapproaches are not suitable for forest stand level applicationsbecause the collection of numerous allometric parameters isimpractical and reconstructed forest structure considerably devi-ates from the actual situation. Fortunately, with the developmentof airborne or terrestrial light detection and ranging (LiDAR), the3D structure of tree crown can be described by numerous voxelsfrom LiDAR data (Kato et al., 2009; Béland et al., 2011;Musselman et al., 2013; Lu et al., 2014), which can meet the 3Dmodels’ demand in the forest stand. In addition, LiDAR can gener-ate complex topographic data that can be used to represent thegeographical condition of forest stand. Based on the LiDAR data,several spatially explicit 3D light models have been developed toestimate the understory light environment. For instance, Leeet al. (2009) utilized LiDAR data to retrieve the forest canopy struc-ture and predict the amount of light received by the forest floorthrough defining a field-of-view function between the observerpoints just above the forest floor and the sun. Kobayashi et al.(2012) estimated the energy flux in the forest floor using a spatiallyexplicit 3D radiative transfer model based on LiDAR data.Musselman et al. (2013) estimated solar direct beam transmittanceof the canopy in forest floor using ray-tracing model and LiDARdata. Although the light distribution in the forest floor has beenaddressed in these studies, studies on the light distribution alongthe vertical gradient of the forest stand are still lacked. The lightintensities at different vertical gradients could influence thegrowth, competition, and succession of the forest community (deCastro and Fetcher, 1998; Latham et al., 1998; Bellow and Nair,2003; Hao et al., 2007).

The raytrace method can address the directionality of solar raytraveling along the forest crowns. Given the solar ray direction, thedistance could be calculated based on the canopy height, and thenlight intensity could be estimated using Beer’s law with the dis-tance. Using the 3D data of the forest canopy, the light intensitypatterns in the forest floor and along the vertical gradient couldbe simulated at the forest stand scale. However, to date, no studieshave accurately simulated these patterns with respect to solarposition at the forest stand scale. This study developed a spatio-temporally explicit raytrace model to provide accurate spatiotem-poral patterns of the understory light intensity. The objectives ofthis study are to (1) build a 3D raytrace model to estimate the dis-tance traveled by solar ray in the crowns; (2) calibrate and verifythe function of light attenuation using the distance based on themeasurements; and (3) estimate spatial patterns of the understory

light intensity in the forest floor and along the vertical gradientwhile considering the solar position.

2. Materials and methods

2.1. Experiment area and plots

This study was conducted in the Tianlaochi catchment locatedin the middle part of Qilian Mountains, Northwest China. Qinghaispruce (Picea crassifolia) is the dominant species and mainly dis-tributes on the north-facing slopes. The ground vegetation in theforest stand consisted of low herbs and moss with height of about15 cm above ground. Several shrubs appeared in the forest standwith low canopy closure. We selected a 169 m � 153 m experi-ment area (38.43�N, 99.93�E) in the Qinghai spruce forest (Fig. 1),in which we established 11 plots (2 calibration plots and 9 verifi-cation plots, see Fig. 1) for field measurements. The location of eachplot center was measured using differential Global NavigationSatellite Systems (GNSS). A Topcon Legacy 20-channel dual-fre-quency receiver that observes pseudorange and carrier phase ofGNSS was used as the rover equipment. Data collection lasted forabout 15 min to 30 min for each plot with 2 s logging rate. Theantenna height was approximately 4 m for all plots. Another iden-tical Topcon Legacy GNSS receiver was set as the base station. Thedistance between the plots and the base station was approximately100 m. Pinnacle version 1.0 post-processing software was used.Based on the positional standard errors reported by Pinnacle, theaccuracy of the planimetric plot coordinates ranged from <0.05 mto 1.2 m with an average of about 0.5 m.

2.2. Measuring and processing solar radiation

The solar radiation measurement for each plot was conductedusing nine solar pyranometers (TM-ZF, Yimeng Corp., China). Eachplot consisted of three points, and each point was set up with threesolar pyranometers. The recorded values from these three solarpyranometers were averaged for each time point, and the averagedvalue was referred to as sunlight intensity at the point. The solarradiation measurement over the forest canopy was performedusing a solar pyranometer (S-LIB-M003, Onset Corp., USA). The log-ging and sampling intervals for all solar pyranometers were set to10 min and 1 min, respectively. The measurement period was inJune 2013 and July 2013. Before measuring the solar radiation inthe plots, we calibrated the solar pyranometer made in China usingthe solar pyranometer made in USA. The calibration equation withR2 = 0.95 and P < 0.01 is expressed as follows:

SROnset ¼ 0:08933SRYimeng ð1Þ

where SROnset and SRYimeng (W/m2) are the solar radiations fromOnset Corp. and Yimeng Corp., respectively. Using Eq. (1), the solarradiation data measured by Yimeng Corp. was calibrated.

2.3. Canopy structure data acquisition

The LiDAR data for the experiment area were acquired by theALS70 airborne LiDAR system in August 2012. The laser beamdivergence angle was 0.22 mrad, with laser wavelength of1064 nm and pulse width of 3.5 ns. The relative flight height ofthe aircraft was about 800 m, and the average diameter of footprintwas about 38 cm. The average density of laser points in the studyarea was 1.2 points/m2 and the elevation accuracy of laser pointwas 0.1 m. The point cloud data of LiDAR was corrected throughthe GNSS. In this study, we used the TerraSolid software (TerraSol-id, Ltd., Finland) to classify the corrected point cloud data intoground and vegetation points. The digital elevation model (DEM)

Fig. 1. Location of experiment area, canopy height model (CHM), and distribution of calibration and verification plots.

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and canopy height model (CHM) with 0.5 m � 0.5 m resolutionwere obtained based on the ground and vegetation points,respectively.

To completely describe the forest canopy structure, we neededto acquire the under-branch height data of the forest, aside fromCHM. We divided the experiment area into 10 m � 10 m gridsand measured the under-branch height within the grid using ahand-held laser rangefinder. The locations of these grids weremeasured through the GNSS similar to the above 11 plots. Theaccuracy of the planimetric plot coordinates ranged from <0.02 mto 1.6 m with an average of about 0.4 m. We first averaged themeasured values in each grid, and then created an under-branchheight layer in the ArcMap software (version 9.2, ESRI, USA) basedon the average under-branch height in each grid. Finally, we chan-ged the layer spatial resolution to 0.5 m � 0.5 m in the ArcMap tomatch the CHM data.

2.4. Light attenuation function in forest stand

Beer’s law is often applied to study the light regime in the forest(Brunner, 1998; Richardson et al., 2009; Duursma et al., 2012;Cerasuolo et al., 2013). The light intensity under the forest canopycan be calculated as follows based on Beer’s law (Richardson et al.,2009; Cerasuolo et al., 2013; Luo et al., 2013):

I ¼ I0 expð�kLAIÞ ð2Þ

where I is the below canopy light intensity (W/m2); I0 is the abovecanopy light intensity (W/m2); k is the extinction coefficient deter-mined by a number of factors, such as leaf angle distribution, can-opy structure, and clumping level (Bréda, 2003); and LAI is theleaf area index that represents a structure parameter in the verticaldirection (Cerasuolo et al., 2013). LAI can only estimate the lightintensity of the forest floor in the vertical direction through the ray-trace method, not in any other direction. Suppose k is constantgiven a certain forest, then as the distance (L, in meters) traveledby the solar ray in the crowns increases, light intensity weakenstoward the forest floor. L can treat the directionality of solar raytraveling in the forest crowns and could be calculated based onthe canopy height at any solar ray direction. In this study, we

replaced LAI with L in Beer’s equation to estimate the light intensityin the forest stand considering the solar position. We fitted the lightattenuation model using the measurements as follows:

I ¼ I0a

bþ expðcLþ dÞ þm� �

ð3Þ

where a, b, c, d, and m are regression parameters, and c is equal to kin Eq. (2). As canopy-diffused light is measured using solar pyra-nometers in the forest floor, the light intensity is not zero when Lis infinitely large. Here, m represents the proportion of below can-opy-diffused light intensity over above canopy light intensity(Musselman et al., 2013).

2.5. Estimating spatiotemporal patterns of L

The framework of 3D raytrace model used to estimate thespatiotemporal patterns of L in the study was designed based onthe CHM, under-branch height, DEM, and solar positions. Given acertain solar position, estimation of the spatial pattern of L consistsof four steps:

(1) Searching the grids on the horizontal direction from a startgrid and calculating the horizontal length of the travelingsolar ray

Fig. 2 shows the projected line on the horizontal direction whenthe solar ray goes across the forest canopy. The grid with red pointis the start grid (Grid0). The horizontal line goes through numerousgrids (white-colored grids in Fig. 2), which are searched. Sevengrids were found, and we recorded the serial number from Grid1

to Grid7. A in Fig. 2 is the solar azimuth angle (A is clockwise andzero on due north) and grid size is gr � gr as obtained from theCHM data. For Grid1, line lengths from the center of Grid0 to thearriving point and to the leaving point were expressed as la andl1, respectively. la and l1 can be calculated using the followingformulas:

la ¼ ðgr=2Þ= sinð180� AÞ ð4Þ

ll ¼ ðgr=2Þ= sinðA� 90Þ ð5Þ

Fig. 2. Sketch map of the horizontally projected line (the arrow line) of a solar rayacross the forest canopy (white-colored grids represent the searched grids, exceptfor Grid0; red point represents the start point of the projected line; blue and greenpoints represent the arriving and leaving points of the line at Grid1, respectively;lengths from the center of Grid0 to the arriving and leaving points at Grid1 areexpressed as la and ll, respectively; gr is the size of the grid; and A is solar azimuthangle). (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)

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For each searched grid, la and l1 exist, and are calculated in amanner similar to that for Grid1.

(2) Calculating L traveled by solar ray in 3D space

All searched grids and Grid0 have two heights (canopy heightand under-branch height) that determine the canopy thickness.The canopy thickness of each grid was considered as a rectangularblock (i.e., voxel). Each rectangular block has an elevation valueobtained from DEM data. The heights of the upper and lower sur-faces and the elevation of the rectangular block over Gridi areexpressed as Hupi, Hlowi, and Elei, respectively.

Fig. 3 shows a solar ray traveling in 3D space. Point A is thestarting point of solar ray, and points B and C represent the arrivingand leaving points of the solar ray over Grid1, respectively. Theupper surface with point B and the lower surface with point C overGrid1 form a new rectangular block. The heights of the upper andlower surfaces of the new rectangular block are expressed as h1

and h2, respectively. Point G is at the ground of Grid0 and Z is thesolar altitude angle. Taking Grid1 as an example based on Fig. 3,we can first calculate h1and h2 as follows:

h1 ¼ Hup0 � la tanðZÞ ð6Þ

Fig. 3. Sketch map of a solar ray traveling in 3D space. Rectangular block with bluebold line is Grid0’s rectangular block. Rectangular block with blue dashed line isformed by the upper surface with point B (blue point) and lower surface with pointC (green point) over Grid1. (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)

h2 ¼ Hup0 � l1 tanðZÞ ð7Þ

Second, we could calculate the elevation difference betweenGrid1 and Grid0 using DEM data, and the elevation difference isexpressed as DH (i.e., Ele1 � Ele0). Finally, we could determine ifthe solar ray travels in the rectangular block of Grid1. If DH > h1,the solar ray would not arrive at Grid1 and the corresponding trav-eling distance of the solar ray over Grid1 is 0. Moreover, the solarray would only travel in Grid0’s rectangular block and its travelingdistance can be calculated using Eq. (14) or Eq. (15). If DH � h1, thesolar ray would travel in Grid1’s rectangular block and the corre-sponding traveling distance (d1) would have a different calculationformula because of different situations. The following six criteriaare needed to calculate d1 (see Fig. 4):

(1)

if ðDH þ Hlow1ÞP h1; d1 ¼ 0 ð8Þ

(2) if h2 < (DH + Hlow1) < h1 and (DH + Hup1) > h1, d1 isexpressed as

d1 ¼ ðh1 � DH � Hlow1Þ=sinðZÞ ð9Þ

(3) if (DH + Hlow1) P h2 and (DH + Hup1) 6 h1, d1 is expressed as

d1 ¼ ðHup1 � Hlow1Þ=sinðZÞ ð10Þ

(4) if (DH + Hlow1) < h2 and (DH + Hup1) > h1, d1 is expressed as

d1 ¼ ðh1 � h2Þ=sinðZÞ ð11Þ

(5) if (DH + Hlow1) < h2 and h2 < (DH + Hup1) 6 h1, d1 isexpressed as

d1 ¼ ðDH þ Hup1 � h2Þ= sinðZÞ ð12Þ

(6)

ifðDH þ Hup1Þ 6 h2; d1 ¼ 0 ð13Þ

After the above considerations and calculations, we could deter-mine if the solar ray would reach Grid1 ground. If DH P h2, thesolar ray would reach Grid1 ground and L at Grid1 would includetwo parts, namely, the distance of solar ray traveling in Grid1’srectangular block (i.e., d1) and the distance (d0) of the solar raytraveling in Grid0’s rectangular block. Calculation of the secondpart involves two criteria:

(1) if (Hup0 � Hlow0) P (tan(Z) � la), the solar ray would goacross the side of Grid0’s rectangular block, and d0 isexpressed as

d0 ¼ la= cosðZÞ ð14Þ

(2) if (Hup0 � Hlow0) < (tan(Z) � la), the solar ray would go acrossthe underside of Grid0’s rectangular block, and d0 could beexpressed as

d0 ¼ ðHup0 � Hlow0Þ= sinðZÞ ð15Þ

If DH < h2, the solar ray would go across Grid1’s rectangularblock and arrive at the next searched grid. We perform the sameprocedure applied in Grid1 for the other searched grids until thesolar ray reaches the ground of a searched grid. The serial numberof this grid and the corresponding L would be recorded.

(3) Obtaining complete forest shaded area

For Grid0, we partitioned its rectangular block into numeroussmall rectangular blocks along the vertical direction with a height

Fig. 4. Sketch map of six situations for calculating the distance of a solar ray traveling in Grid1’s rectangular block. Situations 1, 2, 3, 4, 5, and 6 correspond to Eqs. (8)–(13),respectively. Indications of blue and green points, red dashed line, and Z are noted in Fig. 3. Rectangular block with blue bold line is Grid1’s rectangular block. Rectangularblock with blue dashed line is the new rectangular block formed by the upper surface with point B and lower surface with point C over Grid1 (see Fig. 3). (For interpretation ofthe references to colour in this figure legend, the reader is referred to the web version of this article.)

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interval (Hi). Thus, numerous rectangular blocks with differentupper surface heights were located in Grid0. For these rectangularblocks over Grid0, we calculated the corresponding L as step (2).This process is the key in obtaining the crown-shaded area onthe ground, and Hi determines whether the forest-shaded area iscompletely represented. In this study, we set Hi as a dynamic valuewhen the L values are calculated at the searched grids. Hi is calcu-lated as follows:

Hi ¼ ðl1 � laÞ tanðZÞ=2 ð16Þ

The above calculation could ensure that when the travelingsolar rays stop at a searched grid, three solar rays would reachthe ground of this grid, and three L values would be obtained. Atthis grid, the averaged value of the three L values is the estimateof distance travelled by the solar ray in the crowns. Thus, the solarrays would start from different upper surfaces over Grid0 and forma shade line at several searched grids. In each grid, the correspond-ing averaged L value would be recorded.

(4) Estimating the spatial pattern of L

After finishing all calculations at Grid0, other grids in the exper-iment area would be considered as the staring grids and steps (1)

to (3) would be performed. Thus, numerous averaged L valueswould be recorded at several grids, and we would choose the max-imum L of each grid as the distance traveled by the solar ray in thecrowns. Accordingly, the spatial pattern of L would be estimated ata single solar position.

The temporal pattern of L could be determined by the variationof A and Z, which are related to the fundamental angles of latitude(lat), solar declination (ds), and local hour angle (hs) through thefollowing equations (Kreith and Kreider, 1978):

sinðZÞ ¼ sinðlatÞ sinðdsÞ þ cosðlatÞ cosðdsÞ cosðhsÞ ð17Þ

sinðAÞ ¼ cosðdsÞ sinðhsÞ= cosðZÞ ð18Þ

Solar declination is the angle between the direction of the sunand the plane of the Earth’s equator, and is given as follows(Duffie and Beckman, 1991):

ds ¼ 23:45 sinðBÞ ð19Þ

B ¼ 360365ð284þ NÞ ð20Þ

where N is the date of Julian day. The declination varies from23.45�S to 23.45�N. By convention, the values north of the equator

Fig. 5. Scatter plot of L traveled by solar ray in the crowns and f of two calibrationplots.

Fig. 6. Scatter plot of estimated (y) and observed (x) light intensities in the forestfloor at nine verification plots. Black line represents the fitting line. Gray dashed linerepresents the 1:1 line.

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are considered positive and those south of the equator are negative.The local hour angle describes how far in the east or west directionthe sun is from the local meridian. The local hour angle is zero whenthe sun is on the meridian and decreases at a rate of 15�/h. By con-vention, morning values are negative and afternoon values are posi-tive. Thus, the local hour angle could be calculated based on localsolar time (LST) as follows:

hs ¼ 15ðLST � 12Þ ð21Þ

LST is usually different from the local time (LT) because of theeccentricity of Earth’s orbit and human adjustments, such as timezones and daylight saving. LST could be calculated using LT andtime correction factor (TC) as follows:

LST ¼ LT þ TC60

ð22Þ

TC ¼ 4ðlat � LSTMÞ þ EoT ð23Þ

where LSTM is a reference meridian used for a particular time zone.In this study, the recorded time of the pyranometers referred to Bei-jing Time (GMT + 8 h) and its LSTM is equal to 120 E. EoT is anempirical equation that corrects for the eccentricity of Earth’s orbitand axial tilt, and is expressed as follows:

EoT ¼ 9:87 sinð2BÞ � 7:53 cosðBÞ � 1:5 sinðBÞ ð24Þ

Through hs, the time series of the sampled data from the pyra-nometers and L calculated from the 3D raytrace model can bematched within one day.

All of the above processes used to calculate L were conducted bya program developed in Python’s Integrated Development Environ-ment with Geospatial Data Abstraction Library. The input data con-sisted of the CHM layer, under-branch height layer, DEM layer, andsolar position file (azimuth and altitude angles).

3. Results

3.1. Calibration of light attenuation function

In all 10 min-interval records from the pyranometers, weselected the continuous records from clear days as the calibratedand verified data. A total of 114 records from clear-day conditionare present in the two calibration plots at July 2, and these recordswere used to calibrate Eq. (3). We calculated the spatial distribu-tion of L at the corresponding logging times using the 3D raytracemodel and extracted L values from the two calibration plots basedon locations. L and the fraction (f) of I over Io were exponentiallyrelated with R2 = 0.94 and P < 0.05 (Fig. 5).

3.2. Spatiotemporal patterns of the light intensity in the forest floor

Using the calibrated Eq. (3) and given the solar radiation overthe forest canopy, layers of CHM, DEM, and under-branch heightin the experiment area, we mapped the spatial patterns of the lightintensity in the forest floor at different times. Fig. 6 shows the scat-ter plot between estimated and observed light intensities in theforest floor at nine verification plots. The figure shows that inten-sities are positively correlated, with R2 = 0.92 and P < 0.01. In addi-tion, the estimated values are slightly lower than the observedvalues. Taking June 11, 2013 sampling date as an example, wemapped the spatial patterns of understory light intensity from1130 H to 1630 H of Beijing time at one-hour interval (Fig. 7).Moreover, we set L higher than 0 and obtained the forest shadedarea at different times (Fig. 8). Table 1 shows the shaded areaand its ratio to the experiment area. Evidently, the ratio is smallestwhen the time is 1330 H because this time is nearest to the 1200 Hof the local solar time in the experiment area.

3.3. Spatial patterns of the light intensity along the vertical gradient

As the study introduced the elevation as a parameter to deter-mine if the solar ray reached the ground, mapping the light inten-sity along the vertical gradient by altering the elevation values ofthe searched grids is extremely convenient. In this study, the spa-tial patterns of the light intensity at different vertical gradients(0.5, 2, 5, 10, 15, and 20 m based on the forest floor) were mapped.Fig. 9 shows the light intensity variations along the vertical gradi-ent at 1330 H of June 11, 2013 in the experiment area.

4. Discussion

Estimation of the spatiotemporal patterns of understory lightusing LiDAR data could supplement or even replace field-basedmethods. LiDAR-based L was shown to be an excellent predictorof the understory light environment (Fig. 5), and the below can-opy-diffused light intensity was about 0.15 times of the above can-opy light intensity when the L was greater than 10 m in theexperiment area (Fig. 5). Through field verification, the relationshipbetween the estimated and observed understory light intensitiesevidently showed a positive correlation (Fig. 6), which indicated

Fig. 7. Spatial patterns of the light intensity in the forest floor on June 11, 2013 from 1130 H to 1630 H of Beijing time at one-hour interval in the experiment area.

Fig. 8. Spatial patterns of forest shaded area in June 11, 2013 from 1130 H to 1630 H of Beijing time with one-hour interval in the experiment area.

Table 1Summary of shaded area at different times on June 11, 2013.

1130 H 1230 H 1330 H 1430 H 1530 H 1630 H

Shaded area (ha) 1.16 1.08 1.04 1.06 1.14 1.20Ratio of shade area to experiment area (%) 44.90 41.64 40.4 41.0 44.07 46.28

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that the integration between Beer’s law and L could estimate thespatiotemporal patterns of the understory light intensity. The lightintensity in the forest floor of the experiment area on June 11, 2013showed strong spatiotemporal variations (Fig. 7). On one hand, the

heterogeneity of forest structure caused spatial heterogeneity ofthe light intensity in the forest floor at one time point. On the otherhand, the solar position variations caused the forest shaded area toshift (Fig. 8), resulting in temporal variations of the light intensity

Fig. 9. Light intensity variations along the vertical gradient (from 0.5 m to 20 m based on the forest floor) at 1330 H of June 11, 2013 in the experiment area.

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in the forest floor with a given forest structure. The strong spatio-temporal heterogeneity of the light intensity in the forest floorwould not only rapidly vary latent and sensible heat fluxes, soiltemperature and water content, and snowpack temperature inthe forest stand (Duursma et al., 2012; Musselman et al., 2013),but could also determine the recruitment, growth, and successionof the understory in the shaded area (de Castro and Fetcher, 1998;Bellow and Nair, 2003). We calculated the ratio of forest shadedarea to experiment area at different times (Table 1). Resultsshowed that the ratio near noon was the smallest, indicating thatthe forest floor area received the most intense solar radiation atnoon. In addition, the light intensity along the vertical gradientshowed strong spatial variations at a certain time (Fig. 9), whichwere caused by the vertical heterogeneity of the forest structure.The higher gradient received more solar radiation (Fig. 9), whichwould determine the synusia structure and species competitionof forest community (Latham et al., 1998; Hao et al., 2007; Silvaand Pôrto, 2010).

To date, designs of other raytrace models are based on the pointin which the view is from ground to sun, and then the number ofLiDAR point returns along a ray path (Groot, 2004; Musselmanet al., 2013) or in a variable cone (Lee et al., 2009) is detected. Thesedesigns could accurately determine the canopy transmittance orlight environment in the forest floor, but cannot draw the forest-shaded area and predict the light environment along the verticalgradient. The basis of the calculation of L is that the traveling solarray (from sun to ground) and all rays are parallel, and this basis canaddress the above issues aside from estimating the light intensityin the forest floor. The calculation of L completely integrated thesolar position (azimuth and altitude angles) into geographicalinformation (elevation and location) and canopy structure (thecanopy and under-branch heights). Thus, L can be considered asa practical parameter for estimating the light regime in the forest.For different species, Eq. (3) should be calibrated when the modelis applied. The calibration approach could use the data from under-story hemispherical photos or photosynthetically active radiation,which could be rapidly obtained using a fisheye camera(Musselman et al., 2013) or TRAC and ACCUPAR (Majasalmi et al.,

2014), aside from the measuring instrument for solar radiationused in this study.

In step 3 for calculating L, a height interval that controls the pat-tern of shaded area and records how many solar rays arrive atevery grid in the shaded area exists. If the height interval is smaller,the shaded area is more continuous and more solar rays arrive atevery grid, thereby improving the accuracy of L. However, moretime would be needed for calculation. The spatial resolution ofthe input data also influences the accuracy of L because a high-res-olution CHM could better describe the actual canopy structure, andmore time would be needed for calculation. The measurement ofthe under-branch height in the study is coarse and an alternativeapproach is the utilization of terrestrial LiDAR (Béland et al.,2011; Seidel et al., 2012), which can accurately describe the canopystructure combining the airborne LiDAR. Moreover, we used thereal-time kinematic technology with GNSS to measure the plotcoordinates. However, the position data contained multi-patherrors and the average positioning accuracy was only 0.5 mbecause a part of plots were surrounded by tall canopies. Althoughthis average positioning accuracy is not adequate enough for aphotogrammetry project, it should be adequate enough for an eco-logical application as suggested in this study. Other studies inwhich higher positioning accuracy is necessary could utilize thetotal stations.

In this study, the estimation of understory light depended onthe above canopy solar radiation, which was obtained from a solarpyranometer near the experiment area (about 60 m). Therefore,the model application is limited. To remove this limitation, themodel can be integrated with solar radiation models, which canaccount for the above canopy solar radiation based on physical reg-ulations. An alternative integration approach is utilizing the AreaSolar Radiation module in the ArcGIS software because this modulecould spatially estimate the solar radiation. To date the develop-ment language in ArcGIS, Python language, could be used to permita seamless integration between the Area Solar Radiation moduleand the model. Moreover, the model could also be integrated withecological or hydrological models to resolve several issues, such asplant succession, soil evaporation, plant transpiration, and

S. Peng et al. / ISPRS Journal of Photogrammetry and Remote Sensing 97 (2014) 195–203 203

snowmelt in the forest (Belsky and Canham, 1994; Martens et al.,2000; Sakai and Akiyama, 2005; Ameztegui et al., 2012).

Acknowledgement

This work was supported by National Natural Science Founda-tion of China (No. 91025015 and No. 41361098). The authors wishto thank the editors and two anonymous reviewers for their con-structive suggestions to improve the quality of this article.

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