Xi Zhu
a,⁎, Andrew K. Skidmore
a,b, Tiejun Wang
a, Jing Liu
a,c, Roshanak Darvishzadeh
a,
Yifang Shi
a, Joe Premier
d, Marco Heurich
d,eaFaculty of Geo-Information Science and Earth Observation (ITC), University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands bDepartment of Environmental Science, Macquarie University, NSW 2109, Australia
cSchool of Science, RMIT University, Melbourne 3000, Australia
dBavarian Forest National Park, Freyunger Straße 2, 94481 Grafenau, Germany
eChair of Wildlife Ecology and Management, Faculty of Environment and Natural Resources, University of Freiburg, Freiburg, Germany
A R T I C L E I N F O
Keywords:
Terrestrial laser scanning Effective leaf area index Leaf angle distribution Clumping
Woody-to-total area ratio
A B S T R A C T
Leaf area index (LAI) has frequently been measured in thefield using traditional optical methods such as digital hemispherical photography (DHP). However, in the DHP retrieved LAI, there is always contribution of woody components due to the difficulty in distinguishing woody and foliar materials. In addition, the leaf angle dis-tribution which strongly affects the estimation of LAI is either ignored while using the convergent angle 57.5°, or inversed simultaneously with LAI using multiple directions. Terrestrial laser scanning (TLS) provides a 3-di-mensional view of the forest canopy, which we used in this study to improve LAI estimation by directly re-trieving leaf angle distribution, and subsequently correcting foliage clumping and woody effects. The leaf angle distribution was retrieved by estimating the angle between the leaf normal vectors and the zenith vectors. The clumping index was obtained by using the gap size distribution method, while the woody contribution was evaluated based on an improved point classification between woody and foliar materials. Finally, the gap fraction derived from TLS was converted to effective LAI, and thence to LAI. The study was conducted for 31 forest plots including deciduous, coniferous and mixed plots in Bavarian Forest National Park. The classification accuracy was improved by approximately 10% using our method. Results showed that the clumping caused an underestimation of LAI ranging from 1.2% to 48.0%, while woody contribution led to an overestimation from 3.0% to 31.9% compared to the improved LAI. The combined error ranged from−46.2% to 32.6% of the leaf area index (LAI) measurements. The error was largely dependent on forest types. The clumping index of con-iferous plots on average was lower than that of deciduous plots, whereas deciduous plots had a higher woody-to-total area ratio. The proposed method provides a more accurate estimate of LAI by eliminating clumping and woody effects, as well as the effect of leaf angle distribution.
1. Introduction
Leaf area index (LAI), defined as one-sided leaf area per unit ground surface area (Chen and Black, 1992), is one of the primary variables to characterize canopy structure (Chen et al., 1997). LAI influences many biological and physical processes, such as photosynthesis, respiration, transpiration, and light and rain interception (Asrar et al., 1984; Burstall and Harris, 1983;Chen and Cihlar, 1996). LAI plays a key role in the exchange of energy and mass between the canopy and atmo-sphere (Weiss et al., 2004) and is a key vegetation structure variable determining ecosystem functioning (Béland et al., 2011). Consequently it is regarded as one of the essential biodiversity variables capturing
major dimensions of biodiversity change (Pettorelli et al., 2016; Skidmore et al., 2015). Therefore, an accurate and efficient estimation of LAI is of key importance for physiological, ecological and climato-logical studies (Li et al., 2017).
There are two main categories of methods to derive in situ LAI: di-rect and indidi-rect ones (Jonckheere et al., 2004). Direct methods consist of leaf collection such as destructive sampling and litterfall collection, and point contact sampling (Jonckheere et al., 2004). Destructive sampling is dependent on extrapolation using allometric methods which are not easy in heterogeneous forests (Chen and Cihlar, 1995b). The use of litterfall collection is limited to deciduous forests (Neumann et al., 1989). The point contact method determines LAI from the mean
https://doi.org/10.1016/j.agrformet.2018.08.026
Received 28 March 2018; Received in revised form 16 August 2018; Accepted 25 August 2018
⁎Corresponding author.
E-mail address:x.zhu@utwente.nl(X. Zhu).
Available online 10 September 2018
0168-1923/ © 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
contact number of a thin probe that passes through the canopy at a known inclination and azimuth angle (Wilson, 1960). This method re-quires many insertions into the canopy, which is impractical in forest stands due to the height of the trees and the high density of leaves (Chen and Cihlar, 1995b). In addition, the application of direct methods is generally laborious and time-consuming (Eschenbach and Kappen, 1996). Indirect methods using optical instruments such as LI-COR LAI-2000, TRAC or digital hemispherical photography (DHP) have been widely used for the estimates of LAI (Chen, 1996;Chen et al., 2006; Jonckheere et al., 2004;Schleppi et al. 2007). These instruments and models are less laborious and can be readily applied across larger re-ference sites (Leblanc et al., 2005), and also the theories behind these techniques are mature (Chen et al., 2006;Weiss et al., 2004). Among them, DHP has the advantage of providing a permanent 2-dimensional record of canopy structure (Danson et al., 2007). Various studies have used DHP as validation for gap fraction and LAI measurements (Hopkinson and Chasmer, 2009;Korhonen et al., 2011;Morsdorf et al., 2006). However, the LAI directly obtained from DHP or other optical instruments is, in fact, a plant area index (PAI) which consists of both woody and leaf components. The differentiation between the green and non-green vegetation versus the background (sky or soil) is rather un-reliable, since the radiometric information from the images is affected by light and shadow conditions within a forest (Jonckheere et al., 2004). In addition, all these methods require information on the dis-tribution of leaf angles within the canopy to estimate LAI (Jonckheere et al., 2004). Different models have been used to estimate LAI by sim-plifying the leaf angle distribution (e.g. spherical distribution, plano-phile distribution), which may introduce errors when characterizing the whole plant canopy (Ma et al., 2017a).
Terrestrial laser scanners (TLS) are capable of yielding detailed 3-dimensional canopy structure information when data are collected with a high point density (Van der Zande et al., 2011). Because TLS is an active sensor, the data can be collected without sun illumination, and the shadow can be avoided (Woodhouse et al., 2011). In addition, non-photosynthetic materials such as trunks and branches can be di ffer-entiated (Ma et al., 2016;Zheng et al., 2016;Zhu et al., 2018), so LAI is retrieved instead of PAI. A number of studies have investigated the application of TLS to estimate LAI using different methodological ap-proaches (Danson et al., 2007; Hosoi and Omasa, 2006;Jupp et al., 2009;Moorthy et al., 2008). One group is based on voxelization of the point cloud (Béland et al., 2011;Hosoi and Omasa, 2006), another on point-based methods using data from a single scan (Danson et al., 2007; Jupp et al., 2009;Li et al., 2017). The main advantage of voxel-based methods is that no assumptions about leaf spatial distribution are re-quired, so underestimation caused by nonrandom foliage distribution can be avoided (Hosoi and Omasa, 2006). However, voxel-based ap-proaches are computationally expensive and convoluted by the voxel size which can significantly affect the results (Béland et al., 2014; Cifuentes et al., 2014;Li et al., 2017). In comparison, point-based ap-proaches are more efficient by avoiding data acquisition and registra-tion of multiple scans (Li et al., 2017).
In order to obtain LAI using point-based approaches, the penetration rate of the pulses through the canopy layer (gap fraction) needs to be converted using gap fraction theory based on the Beer-Lambert law (Nilson, 1971) as:
= −
P θ G θ LAI cos θ
ln ( ( )) ( ) e/ ( ) (1)
where P(θ) is the gap fraction at the viewing zenith angle θ, G(θ) is the fraction of the leaf area projected on a plane normal to the zenith angle θ (Ross, 2012), and LAIe is effective leaf area index. G(θ)/cos(θ) is
called the extinction coefficient, or k, which is determined by the di-rection of incoming beams and the foliage inclination angle distribu-tion.
The leaf area index derived optically from gap fraction was de-scribed as“effective LAI (LAIe)” (Chen and Black, 1992). The
conver-sion from LAIe to LAI is needed for two main reasons: (1) the gap
fraction theory for LAIe estimation is based on the assumption of a
random foliage distribution, (2) LAIe does not account for the
con-tribution of non-photosynthetic materials (i.e. stems, branches) (Moorthy et al., 2008). Therefore, this initial estimate of LAI needs to be corrected by taking into account the error caused by foliage clumping and the contribution of woody materials (Chen and Cihlar, 1996).Zhao et al. (2012)presented a method using TLS to retrieve the clumping index in a conifer forest which was correlated with that of hemi-spherical photos (R2= 0.866).Li et al. (2017)estimated the clumping
index of 35 deciduous trees and achieved a strong correlation (R2= 0.76) between TLS-based LAI measurements and destructively sampled LAI measurements. Zheng et al. (2016) separated photo-synthetic canopy components from non-photophoto-synthetic active nents using TLS. Their study showed that non-photosynthetic compo-nents contributed from 19% to 54% to LAI measurements depending on forest density. Zhu et al. (2018) developed a method based on the adaptive radius near-neighbor search to discriminate foliar and woody materials in a mixed natural forest. However, the influence of both foliage clumping and woody contribution on LAI measurements has not yet been explored.
This paper aims to improve the estimation of LAI from TLS in a mixed natural forest. Firstly, the leaf angle distributions of both de-ciduous and coniferous forests are estimated to derive the extinction coefficient k. Secondly, the clumping index Ω quantifying the effect of foliage clumping is calculated by adapting the gap size distribution method (Chen and Cihlar, 1995b) to TLS data. Lastly, the classification method (Zhu et al., 2018) was further improved by adding an addi-tional feature (viz. zenith angle) to obtain the woody-to-total area ratio.
2. Materials and methods 2.1. Study area
The study area is located in the Bavarian Forest National Park (BFNP) in southeastern Germany. The natural forest ecosystems of the BFNP vary according to altitude: there are spruce forests on peat bogs and cold depressions in the valleys, mixed mountain forests on the hillsides and mountain spruce forests in the high elevations (Heurich et al., 2010). Data from DHP and TLS were acquired in July 2016 for 31 plots consisting of 8 European beech (Fagus sylvatica) plots, 8 Norway spruce (Picea abies) plots and 15 mixed plots (Fig. 1). The land cover map with the classification of the deciduous, coniferous and mixed forest was provided by the BFNP (Silveyra Gonzalez et al., 2018).
At least 4 hemispherical photos in each plot at the height of 1.3 m were taken and processed using the Hemisfer software (Hemisfer, Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Switzerland, 2016). At the zenith angle of 57.5˚, the relationship be-tween LAI and gap fraction becomes insensitive to the leaf angle dis-tribution (Wilson, 1960). Hemispherical photos were stratified into 5 rings with a step of 13˚ so that the zenith of 57.5˚ was close to the midpoint of ring 5 (52˚-65˚). An automatic thresholding method was applied using the algorithm of Nobis and Hunziker (2005) after a gamma correction (γ = 2.2) (Moeser et al., 2014). The gap fraction was calculated as the proportion of sky pixels to total pixels within analysis rings, and LAIewas derived from the gap fraction based on a constant
extinction coefficient (Lang, 1987). The gap size distribution method (Chen and Cihlar, 1995b) was applied to estimate the clumping index (Ω) and the corrected value of LAI (Thimonier et al., 2010). DHP measurements were used as a comparison in this paper, although they do not necessarily represent the‘ground truth’.
2.2. Terrestrial laser scanning data
The terrestrial laser scanner RIEGL VZ-400 (RIEGL Laser Measurement Systems, Horn, Austria) is a time-of-flight scanner. It is equipped with a shortwave infrared (1550 nm) laser. The laser beam
has a footprint diameter of 7 mm as it leaves the device with a diver-gence of 0.35 mrad. At a distance of 30 m, the footprint is around 1.8 cm. The system has a range accuracy of 5 mm, an effective mea-surement rate of 122,000 meas./s, and a maximum range of 160 m at 20% reflectance. The data were acquired in its long-range mode with an angular step of 0.04˚. A single scan was carried out in the center of each plot. The zenith angle of the TLS was from 30˚ to 130˚, and the azimuth angle was from 0˚ to 360˚.
2.3. Leaf area index estimation
The model for calculating leaf area index in a given direction is (Chen, 1996;Nilson, 1971):
= − −
LAI (1 α)( ln P θ( ( ))) cos /( ( ) )θ G θ Ω (2)
whereα is the woody-to-total area ratio, θ is the laser zenith angle, P(θ) is the canopy gap fraction in directionθ, G(θ)/cos(θ) is the extinction coefficient k, where G(θ) is the fraction of the leaf area projected on a plane normal to the zenith angleθ (Ross, 2012), andΩ is the clumping index.
2.3.1. Point cloud preprocessing
The point cloud data were imported into LAStools (LAStools, ra-pidlasso, 2017) to classify ground returns from non-ground returns (LASground). Ground returns were used to produce the digital elevation model (DEM) to which all return heights were normalized. After nor-malization, the elevation value of a point indicated the height from the ground to that point. A threshold of 1.3 m was used to separate canopy returns and below-canopy returns to coincide with the height at which the hemispherical photographs were taken. Laser beams were stratified
into 3 zenith zones: 30˚-39˚, 39˚-52˚ and 52˚-65˚ to coincide with the rings of the hemispherical photographs. The gap fraction and LAI for the whole canopy were then calculated by averaging those of the 3 zenith zones taking into account of their solid angle.
2.3.2. Gap fraction estimation
A“weight all return” method which considers all returns in each pulse was used to approximate the gap fraction for each zenith ring (Calders et al., 2014,2018;Lovell et al., 2011).
= −∑
P θ NR
N
( ) 1 1/
total (3)
where P(θ) is the gap fraction at the viewing zenith angle θ, NR is the number of returns detected for each pulse from the canopy, and Ntotalis
the total number of outgoing laser pulses. 1/NR is a weighted sum of all returns from the canopy. It produced a near unbiased estimate of gap fraction (Armston et al., 2013).
2.3.3. Extinction coefficient estimation
The extinction coefficient k (θ) is expressed in terms of G(θ), which is the mean projection of a unit leaf area on a plane perpendicular to the direction of the laser beam (Weiss et al., 2004):
=
k θ( ) G θ( )/cosθ (4)
Assuming that leaves are uniformly distributed with respect to the azimuth, G(θ) can be expressed as (Hosoi and Omasa, 2006):
∫
= G θ( ) π g θ S θ θ dθ( L) ( , L) L 0 /2 (5) Where=⎧ ⎨ ⎩ ≤ − ⎡ ⎣ + ⎤⎦ > − − S θ θ θ θ for θ θ θ θ for θ θ ( , ) cos cos , cos cos 1 , L L π L L x x π π L 2 2( tan ) 2 (6) = −
x cos 1( cot cotθ θL) (7)
S(θ,θL) is the absolute value of the cosine of the angle between the
direction of the incident laser beam and the direction of the normal to the leaf surface, θLis the leaf inclination angle, and g(θL) is the
tribution function of leaf inclination angle. To measure the actual dis-tribution of leaf inclination angle, Eq.(5)can be expressed as (Hosoi and Omasa, 2006):
∑
= = G θ( ) g q S θ θ q( ) ( , ( )) q T L 1 q (8) where q is the leaf inclination angle class, and Tqis the total number ofleaf inclination angle classes. This method does not take into account the azimuth angle because it assumes that leaves are uniformly dis-tributed with respect to the azimuth (Hosoi and Omasa, 2006).
Following the method used byBéland et al. (2011), the leaf angle measurements were divided equally into 9 classes (q) of 10˚ each (from 0˚ to 90˚). For each class, the leaf inclination angle θLof class q is the
midpoint angle. g(q) is then the number of samples within the class centered atθLover the total number of samples.
Before estimating the leaf inclination angle, TLS data werefirstly gridded at a grid size of 0.02 m using the software“R” (Jakubowski et al., 2013;R Core Team, 2016). This grid size was large enough to maintain an approximately constant point density while small enough not to remove too many points (Ma et al., 2017b). For an average leaf size of 40 cm2, there were around 10 points on a single leaf. Deciduous
leaves were approximated as planes, and normals (normal vectors) to the planes were estimated (Hosoi and Omasa, 2007;Zhu et al., 2015). Then the distribution of leaf inclination angle was obtained from the angle between the normal and the zenith. The shoots of needles were also found to form planes as can be seen inFig. 2.Rochdi et al. (2006) evaluated a simplified flat shoot parameterization for radiative canopy modeling, indicating that the simpleflat leaf model can be substituted for the detailed shoot model when modeling the total bidirectional reflectance and the canopy hemispherical reflectance and transmittance within homogeneous canopies. Likewise, the leaf zenith angle can be estimated by using the simpleflat leaf model to approximate planes from the point cloud data. Therefore, the same method to approximate the leaves as planes was applied to needles leaves, and the leaf angle distribution at the shoot level was estimated accordingly.
2.3.4. Clumping index estimation
The gap size distribution method (Chen and Cihlar, 1995b)
developed for optical instruments has been adapted to TLS data at the individual tree level (Li et al., 2017). In this study, the gap size dis-tribution method was assessed at the plot level for both deciduous and coniferous trees. In order to apply the gap size distribution method, the point cloud data were first converted to the Andrieu projection (Andrieu et al., 1994; Zhao et al., 2011). This projection has been evaluated for eLAI estimation with a good accuracy (Zhao et al., 2011). The laser beams with returns and without returns were assigned values of 1 and 0 respectively.
The clumping indexΩ is calculated as follows (Chen and Cihlar, 1995a;Leblanc et al., 2002):
= ∙ − − Ω θ F θ F θ F θ F θ ( ) ln [ (0, )] ln [ (0, )] 1 (0, ) 1 (0, ) m mr mr m (9)
where Fm(0,θ) is the measured total canopy gap fraction, while Fmr(0,θ)
is the gap fraction for a canopy with randomly positioned elements (Leblanc et al., 2002). For a canopy with a random distribution, the theoretical gap size distribution function F(λ,θ) can be expressed as (Chen and Cihlar, 1995a):
= ⎡ ⎣ ⎢ + ⎤ ⎦ ⎥ − + F λ θ L θ λ W θ e ( , ) 1 ( ) ( ) p p Lp( )[1θ λ W θ/ p( )] (10) whereλ is the gap size, Lp(θ) is the projected LAI, which can be
esti-mated from -ln[Fm(0,θ)], and Wp(θ) is expressed as (Leblanc et al.,
2005;Li et al., 2017): = − ∂ ∂ = W θ ln F θ ln F λ θ λ ( ) [ (0, )] | [ ( , )]/ | p m m λ 0 (11)
The measured gap size distribution Fm(λ,θ) can be obtained by
sorting the measured gaps in the order of the gap size. A four-connected neighborhood components algorithm (Haralick and Shapiro, 1992) was used to detect all gaps in each zenith layer. The measured gap size distribution Fm(λ,θ) was compared with the first estimate of the
theo-retical gap size distribution function F(λ,θ) to remove largest gaps. Then an improved F(λ,θ) is obtained, and the same gap removal process was iterated until Fmr(λ,θ) is brought to the closest agreement with F
(λ,θ) (Chen and Cihlar, 1995b).
2.3.5. Classification of foliar and woody materials
Based on the method used byZhu et al. (2018)to separate the foliar material from woody material, the Random Forests algorithm (Breiman, 2001) was employed for classification which has been widely applied in forest applications (Bigdeli et al., 2015;Koenig et al., 2015), as it can handle high data dimensionality with highly correlated features and is both fast and insensitive to overfitting (Belgiu and Drăguţ, 2016). Both geometric and radiometric features were extracted from the point cloud data. The radiometric features comprised Rigel’s apparent reflectance (AP) and mean AP which was corrected for the range effect, Rigel’s deviation and mean deviation of local points. The geometric features consisted of the most commonly used height-related features (Koenig et al., 2015), and local dimensionality features (Li et al., 2018) ex-pressing how the local points were distributed (Chi-Keung and Medioni, 2002). To estimate the local dimensionality features, a local covariance matrix of each point was calculated. The eigenvalues (λ) were ordered so thatλ1>λ2>λ3. The following features were calculated to describe
the local dimensionality (Demantke et al., 2011).
= − = − =
α1D ( λ1 λ2)/ λ1,α2D ( λ2 λ3)/ λ1,α3D λ3/ λ1 (12)
whereα1D,α2Dandα3Drepresent the likelihood that the shape of the
local points of the given point is linear, planar and random, respec-tively.
In addition to these features, the inclination angle and mean in-clination angle of local points were also included as a feature in the classification, as leaves had different inclination angles from stems. Stems tend to have large inclination angles close to 90˚, whereas leaves Fig. 2. Image of point cloud data for a coniferous tree (left) and a deciduous
tend to have small inclination angles smaller than 90˚, especially for deciduous trees.
The validation was performed by randomly selecting 30 points per plot which were visually identified into two classes (viz. wood and foliage) (Ma et al., 2016;Zhu et al., 2018). Woody and foliar points can be easily identified in the point cloud visualization (Fig. 3). An overall accuracy was calculated for each plot to assess the classification. 2.3.6. Statistical analysis
The estimated variables were tested against the measured variables based on the coefficient of determination (r2), the root mean square
error (RMSE), normalized RMSE, and normalized bias.
= −∑ − ∑ − ′ r y y y y 1 ( ) ( ) i i i 2 2 2 (13) = ∑ − ′ RMSE y y n (i i)2 (14) = nRMSE RMSE y/ (15) =∑ − ′ nBias y y ny (i i) (16) where yiandyi′are the measured and estimated values for sample i, and y and n are the mean and the number of samples, respectively.
The error of LAI estimates of each plot caused by foliage clumping and woody material was calculated as:
= − ∙
Error LAI LAI
LAI 100
after before
after (17)
where LAIafteris LAI estimates after correction, and LAIbeforeis LAI
es-timates before correction.
In order to analyze the factor that contributes to the variation of the error, a linear correlation test was performed (Pearson, 1896).
3. Results
3.1. Gap fraction estimation
Fig. 4shows the correlation of DHP and TLS-derived gap fraction. The correlation between the two estimates was significant with an r2
value of 0.96 and an nRMSE value of 0.17. TLS underestimated the gap fraction compared to DHP with an nBias value of -0.12.
3.2. Effective leaf area index estimation
Estimates of effective LAI at 57.5 ˚ were compared between the TLS and DHP measurements (Fig. 5). A significant correlation ( r2= 0.76) indicated that TLS measurements were in a good agreement with DHP. Estimates of the inclination angle for deciduous trees (mostly European beech) are shown inFig. 6a. The stems and branches of the beech trees had large angles close to 90˚, while leaves were shown to have low zenith angles (i.e. leaves perpendicular (horizontal) to the stems with a classic planophile distribution). The planophile distribu-tion is confirmed inFig. 7a which shows the planophile leaf inclination angle distribution closely matches the map of the leaf inclination angle inFig. 6a.
Estimates of the inclination angle for coniferous trees are displayed inFig. 6b. Again, stems were shown to have large inclination angles close to 90˚. However, branches had much lower angles than those of deciduous trees, as they were growing in a horizontal direction, while shoots of coniferous trees had large inclination angles (erectophile). This demonstrated the effectiveness of the method for the inclination Fig. 3. Visual interpretation of foliar and woody points (red circle: woody
points, green circle: foliar points). (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article).
Fig. 4. Correlation of gap fraction derived from digital hemispherical photo-graphy and terrestrial laser scanner for the individual sample plots.
Fig. 5. Correlation between effective leaf area index at 57.5˚ between digital hemispherical photography and terrestrial laser scanner.
angle estimation. Fig. 7b shows that leaf angle distribution for con-iferous trees were erectophile with most of the points having large in-clination angles.
InFig. 8, LAIeestimated from DHP and TLS was compared. There
was a good agreement ( r2= 0.88, nRMSE = 0.15) between these two
measurements. On average, estimates from TLS were higher than those from DHP (nBias = 0.03).
3.3. Clumping index estimation
Estimates of the clumping index derived from DHP and TLS were strongly correlated, with an r2value of 0.89 (Fig. 9). On average, the
clumping index of coniferous plots was lower than that of deciduous plots for both TLS and DHP measurements.
A comparison of the PAI after correcting for clumping derived from DHP and TLS is detailed inFig. 10. A significant relationship between these two estimates was obtained with an r2 value of 0.84 and an nRMSE value of 0.15.
3.4. Classification of foliar and woody materials
Table 1details the relative "importance" of different features, based on the variance explained by each feature as calculated by the Random Forests algorithm. The newly derived feature 'mean zenith angle'
Fig. 6. Estimates of inclination angle for deciduous trees (a) and coniferous trees (b).
Fig. 7. Leaf angle distribution for deciduous trees (a) and coniferous trees (b).
Fig. 8. Correlation of effective leaf area index between digital hemispherical photography and terrestrial laser scanner.
explained the most variance when classifying foliar and woody mate-rials, followed by mean AP, mean deviation and two geometric features. The overall accuracy of the classification for each plot without and with using zenith angle as a feature is presented inFig. 11. For most of the plots, adding zenith angle improved the accuracy.
InFig. 12, it is further shown that compared to the method not including the zenith angle as a feature, our method improved the classification accuracy by 10% (median value), demonstrating the sig-nificance of zenith angle in separating woody and foliar components.
In Fig. 13 the final classification results for a deciduous and a coniferous plot are presented.
The median, the 25th and 75th percentiles of the woody-to-total area ratio of deciduous, mixed, and coniferous plots are shown in Fig. 14. Deciduous plots had a higher woody-to-total area ratio than mixed and coniferous plots.
3.5. Contribution of clumping and woody material to the estimation of leaf area index
Foliage clumping caused up to 48.0% underestimation of LAI, with a higher error for coniferous plots than deciduous plots (Fig. 15). Woody material contributed from 3.0% to 31.9% to the overestimation of LAI depending on the forest type (Fig. 16). Combining these two factors, the error of the LAI estimate ranged from−46.2% to 32.6% (Fig. 17).
A Pearson’s correlation demonstrated that both canopy cover and stand height had statistically significant effects on the woody-to-total area ratio and clumping index with a P value smaller than 0.05 (Table 2). Woody-to-total area ratio and clumping index increased with increasing canopy cover and stand height.
4. Discussion
In this study, we were able to show that the estimation of LAI using TLS on the plot level can be considerably improved by taking into ac-count foliage clumping and woody material. The combined errors of these two factors caused the error ranging from−46.2% to 32.6% at the plot level, with an overall mean of 5.4%. The foliage clumping alone caused an underestimation of 14.2% and the woody material led to an overestimation with a mean value of 17.1%. Moreover we show that the leaf angle distribution of both deciduous and coniferous plots can be estimated from TLS.
Fig. 9. Correlation of the clumping index between digital hemispherical pho-tography and terrestrial laser scanner.
Fig. 10. Comparison of plant area index between digital hemispherical photo-graphy and terrestrial laser scanner.
Table 1
Feature importance value derived from Random Forests (α1Dand α3D: the
likelihood that the shape of the local points is linear and random respectively).
Features Mean zenith angle Mean apparent reflectance Mean deviation α1D α3D All the other features Importance 0.34 0.19 0.16 0.09 0.05 0.17
Fig. 11. Classification accuracy for each plot without and with using zenith angle.
In order to obtain accurate estimates of LAI on a plot basis, it is important to calculate and analyze these two factors separately. The clumping index estimated from TLS was in a good accordance with that from DHP at the plot level. The clumping index of coniferous plots on average was lower than that of deciduous plots for TLS measurements. For the same LAI, deciduous forests intercept and reflect more solar
radiation than coniferous forests because deciduous forests are less clumped than coniferous forests (Chen et al., 2005). Regarding the woody contribution, deciduous forests had a higher woody-to-total area Fig. 13. Visualization of the classification results for (a) deciduous plot (b) coniferous plot.
Fig. 14. Boxplot of woody-to-total area ratio of deciduous, mixed and con-iferous plots.
Fig. 15. Underestimation of leaf area index estimates caused by foliage clumping.
Fig. 16. Overestimation of leaf area index estimates caused by woody material.
Fig. 17. Error percentage of leaf area index estimates caused by foliage clumping and woody material.
estimated. They main reason was that the clumping index of the two coniferous plots was rather low, and that of the deciduous plot and the two mixed plots was relatively high. The results show that canopy cover and the height of a plot had a positive correlation with woody-to-total area ratio and clumping index, indicating that as the stand becomes denser and taller, the woody area increases more quickly than leaf area, and leaves become more clumped. However, we noted that due to the occlusion and the angle limitation of the TLS, the top of the trees in the center of the plot had lower point density. The woody area could, therefore, be overestimated at the top of the trees, and this should be further investigated.
Our analysis showed that estimates from TLS were in a good agreement with those from digital hemispherical photography, which is considered the standard for estimating LAI (Jonckheere et al., 2004; Schleppi et al., 2007). Nonetheless, we do not have a real ground truth for validation, which gives us no choice but to use DHP. In spite of the drawbacks of DHP, we show that these very different techniques gen-erated similar results, especially LAIe (r2= 0.88), PAI (r2= 0.84) and
the clumping index (r2= 0.89), indicating that the TLS methods show a
high degree of robustness.
The difference between TLS and DHP is a relative value, which does not indicate one technique is more accurate than the other. DHP es-sentially is a 2D passive sensor, so it has its own intrinsic problems when estimating LAI. In term of image acquisition, it is affected by the exposure, the unevenness of the sky lighting, and unevenness of foliage lighting caused by shadow and direct sunlight (Rich, 1988). When there is direct sunlight, the plant materials cannot be differentiated from the sky which may cause significant underestimation of LAI. In addition, in 2D images, the problem of occlusion is more noticeable than with TLS. Errors could be further introduced by image processing, especially the threshold used to distinguish plants from canopy openings. The images in our study as well as many other studies were taken in different sunlight conditions from site to site. The use of the threshold to dif-ferentiate vegetation pixels from sky pixel becomes crucial in the classification. An automatic thresholding method by Nobis and Hunziker (2005)was applied in this study. It improved the accuracy of results, especially in comparison with single manual thresholding. Nonetheless, some errors could still be detected in the images. In comparison, TLS allows a clear distinction between the vegetation (return) and sky (no return). No threshold is needed. Moreover, as mentioned in the introduction, DHP requires information on the dis-tribution of leaf angles within the canopy to estimate LAI. The leaf angle distribution which strongly affects the estimation of LAI is either ignored while using the convergent angle 57.5°, or simultaneously in-verted with LAI using multiple directions (Ma et al., 2017a), while we have shown that using TLS, the leaf angle distribution could be ob-tained for both deciduous and coniferous trees in our study area. Therefore, we believe that TLS in theory provides a robust and probably more accurate estimation of LAI compared to optical instruments. However, further study is needed.
The classification from DHP is not reliable for validation since the radiometric information from the images is affected by the shadow and
2004).
TLS underestimated gap fraction by 12% compared to DHP. This result is due to the limitation of the TLS, the zenith angle between 0-30° could not be scanned. Thisfield of view usually has a larger gap frac-tion, which can be observed from thefirst rings in DHP. The first two rings had a larger gap fraction than the rest. This further caused the overestimation of the canopy cover and hence the underestimation of the gap fraction.
The underestimation of gap fraction consequently led to the over-estimation of LAIeby TLS. However, the normalized bias and r2value
were lower than that for the gap fraction. These differences can be attributed to the measurements of LAIe from two different methods
(Hosoi and Omasa, 2006;Thimonier et al., 2010). The estimation of LAIefrom DHP was based onLang (1987)who calculated LAI based on
a linear regression of mean contact number against zenith ring angle, while the estimation of LAIefrom TLS was directly calculated from gap
fraction and extinction coefficient (Zheng et al., 2017). The gap fraction and extinction coefficient were also estimated directly from TLS data.
Estimates of the inclination angle for European beech (Fagus sylva-tica) showed a clear distinction between foliar and woody materials. Leaves had much lower inclination angles than stems and branches, which was the reason why the mean zenith angle as a feature for classification accounted for 0.34 of the total importance. The leaf angle followed a planophile distribution (Fig. 5). This distribution was ob-served by Wagner and Hagemeier (2006)in their study of the same species.Pisek et al. (2013)also demonstrated that a planophile or a plagiophile distribution appears to be a more appropriate assumption for modeling radiation transmission through temperate and boreal de-ciduous stands. It was shown that stems of Norway spruce had large inclination angles. However, branches had much lower angles than those of deciduous trees, since they are growing in a horizontal direc-tion. By contrast, leaves had large inclination angles as they were dropping from the branches. The leaf angle followed an erectophile distribution, which is the typical observation of coniferous trees (Sandmeier and Deering, 1999a,b;Schlerf et al., 2007).
The 'importance value' of the Random Forests algorithm demon-strated that the mean zenith angle was the most important feature to differentiate foliar and woody materials. The analysis confirmed that the zenith angle significantly improved the classification accuracy by 10% (median value) compared to the adopted method for our sample plots (Ma et al., 2016; Zhu et al., 2018). Leaves and wood showed different zenith angles, especially in deciduous plots. For conifers, the differences of zenith angle were more prominent between shoots and branches, as shoots had a large zenith angle, whereas the differences between shoots and stems were not as distinguishable as those in de-ciduous plots. In mixed plots, either stems (dede-ciduous) or branches (coniferous) could be discriminated from leaves using zenith angle. Combined with the other features, especially the radiometric features and local dimensionality features, the woody material was effectively separated from the foliar material. However, leaf zenith angle as a feature for classification is clearly species dependent, even for different deciduous species, (Raabe et al., 2015;Wagner and Hagemeier, 2006),
and may in the future be used as a metric to further improve the classification accuracy of individual tree species. The stem angle does not vary between species, while the leaf angle varies, though it should be noted that some species have larger zenith angles in the upper layers (Béland et al., 2011).
The classification between foliar and woody components could be further improved by using a multi-wavelength laser scanner. In a recent paper, Li et al. (2018) showed value of dual-wavelength spectral scanning in separating foliar and woody components by combining geometric and radiometric attributes. Instead of the intensity of a single wavelength, a normalized ratio of two wavelengths could be obtained. The use of the combination of two bands could potentially tackle the most intractable problems caused by the variation of the incidence angle and partial hits, as long as the intensity of both wavelengths is similarly affected by these effects (Gaulton et al., 2013;Hancock et al., 2017).
Some of the methods used in this study may potentially be applied to airborne LiDAR data. Ma et al. (2017a) retrieved leaf angle dis-tribution from airborne LiDAR data. The leaf angles of coniferous trees were simulated by approximating individual shoots with a cylinder geometric model. TheMa et al. (2017a)model was not applicable to the coniferous trees in our study area, because the shoots clump together into plane shapes. However, their study demonstrated that airborne LiDAR could also be used to retrieve leaf angle distribution at the shoot or branch scale. The upscaling of the approach to estimate woody-to-total area ratio is more problematic, since most of the features for classification between woody and foliar material require many points on a single leaf, whereas the distance between two consecutive points from most current airborne LiDAR is usually larger than the size of a single leaf size. In addition, the footprint size of airborne LiDAR is also larger than the size of a single leaf, so the features for classification such as the zenith angle and the local dimensionality features cannot be estimated. Finally, an element clumping index may be estimated from airborne LiDAR, since the scale of element clumping is larger than the shoot (Chen, 1996). Exhaustive experiments and analysis with simu-lated and actual airborne LiDAR data are necessary to study the effects of point density and footprint size beyond conjecture.
Acknowledgements
This work was supported by the ITC Research Fund under Grant 93003245. We thank the Bavarian Forest National Park for supporting the data collection. We acknowledge the support of the “Data Pool Forestry” data-sharing initiative of the Bavarian Forest National Park. References
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