Mapping LAI in a Norway spruce forest using airborne laser scanning

Remote Sensing of Environment 113 (2009) 2317–2327

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Remote Sensing of Environment j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / r s e

Mapping LAI in a Norway spruce forest using airborne laser scanning Svein Solberg a,⁎, Andreas Brunner b, Kjersti Holt Hanssen a, Holger Lange a, Erik Næsset b, Miina Rautiainen c, Pauline Stenberg c a b c

Norwegian Forest and Landscape Institute, P.O. Box 115, N-1431 Ås, Norway Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, P.O. Box 5003, N-1432 Ås, Norway Department of Forest Resource Management, University of Helsinki, P.O. Box 27, FI-00014, Finland

a r t i c l e

i n f o

Article history: Received 7 November 2008 Received in revised form 8 June 2009 Accepted 8 June 2009 Keywords: LAI LIDAR Norway spruce

a b s t r a c t In this study we demonstrate how airborne laser scanning (ALS) can be applied to map effective leaf area index (LAIe) in a spruce forest, after being calibrated with ground based measurements. In 2003 and 2005, ALS data and field estimates of LAIe were acquired in a Norway spruce forest in SE Norway. We used LI-COR's LAI-2000® Plant canopy analyzer (“LAI-2000”) and hemispherical images (“HI”) for field based estimates of LAIe. ALS penetration rate calculated from first echoes and from first and last echoes was strongly related to field estimates of LAIe. We fitted regression models of LAIe against the log-transformed inverse of the ALS penetration rate, and in accordance with the Beer–Lambert law this produced a linear, no-intercept relationship. This was particularly the case for the LAI-2000, having R2 values N 0.9. The strongest relationship was obtained by selecting ALS data from within a circle around each plot with a radius of 0.75 times the tree height. We found a slight difference in the relationship for the two years, which can be attributed to the differences in the ALS acquisition settings. The relationship was valid across four age classes of trees representing different stages of stand development, except in one case with newly regenerated stands which most likely was an artifact. Using LAIe based on HI data produced weaker relationships with the ALS data. This was the case even when we simulated LAI-2000 measurements based on the HI data. © 2009 Elsevier Inc. All rights reserved.

1. Introduction There is currently an increasing interest in forests, for bio-energy production, concern for deforestation and other disturbances, and the role they play in the global carbon cycle. Leaf area index (LAI) is one key variable in forest mapping and monitoring, and is a much studied variable in remote sensing research. LAI is an important biophysical measure in modeling of the exchange of energy, water, and CO2, as the leaves represent the vegetation's interface towards the atmosphere and incoming solar radiation (Waring & Running, 1998). For example in forest health monitoring, LAI might serve as an alternative to subjective defoliation assessments (Smolander et al. 2000). At global and regional scales, LAI data are now available from lowresolution passive satellite sensors such as MODIS, AVHRR, POLDER-2, MERIS, AATSR, and CYCLOPES, where ground validation is carried out by point measurements that are scaled up by higher resolution imagery such as Landsat TM (Chen et al., 2002; Morisette et al., 2006). Vegetation indices such as NDVI, RSR and MSI from Landsat and SPOT are also correlated to LAI (Eklundh et al., 2003; Stenberg et al., 1994; Rautiainen, 2005). However, the passive sensors have problems such as confusing influence from ground vegetation, shading, clouds, saturation at high LAI values, and difficulties with sensor calibration ⁎ Corresponding author. Tel.: +47 64948000; fax: +47 64948001. E-mail address: [email protected] (S. Solberg). 0034-4257/$ – see front matter © 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2009.06.010

and atmospheric correction (Eriksson et al., 2006; Nilson et al., 2003). The problems are particularly severe in conifer forests with a high degree of within-tree clumping of foliage, and between-tree gaps having a well-developed ground vegetation that produces a strong vegetation signal in low LAI stands. Hence, with increasing LAI the reflectance generally decreases for both visible and near-infrared wavelengths, and the relationships with vegetation indexes are weak, curve-linear, saturating and even decreasing at high LAI values (Spanner et al., 1990; Häme et al., 1997; Turner et al., 1999; Eriksson et al., 2006). Synthetic aperture radar (SAR) represents an active sensor which has fewer problems of this kind, and LAI has been found to correlate to SAR backscatter intensity (Ranson & Saatchi, 1992), and to the VV/HH ratio using polarimetric data (Manninen et al., 2005). However, variable moisture conditions and rugged terrain may create problems for SAR data. Airborne laser scanning (ALS) represents an alternative to those methods, either for making spatially continuous maps, for sampling based inventories, or for up-scaling of point measurements for validation of satellite data. Examples of the latter use of ALS include measurement of above-ground biomass (Lefsky et al., 2005) and fraction of photosynthetically active radiation absorbed by the canopy (fPAR, Chasmer et al., 2008). Effective leaf area index (LAIe) is a widely used variable for nondestructive measurement methods, because it is mathematically related to gap fraction. It differs from the true LAI because leaves and

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needles are not randomly distributed in the canopy space but rather clumped within shoots (Stenberg, 1996) as well as on larger scales (branches, whorls, crowns) (Chen et al., 1997). Furthermore, LAIe includes the areas of branches and stems, and corresponds to the term “plant area index” (PAI) (Cescatti, 2007). According to the Beer– Lambert law, the LAIe might be derived for a given forest stratum from the penetration rate (P) of ALS pulses through the canopy layer as: LAIe = β⋅ lnðP

−1

Þ

ð1Þ

where β is a slope parameter to be estimated. This slope will vary both between forest strata depending on their foliage angle distribution, and with the technical property of the ALS penetration variable, i.e. its ability to penetrate the canopy layer. The foliage is distributed over various azimuth and zenith angles, and devices such as the LAI-2000 and a camera with a hemispherical lens providing gap fractions over the hemisphere are required in order to derive LAIe estimates regardless of what the foliage angle distribution is (Miller, 1967; Welles & Cohen, 1996). However, if the foliage angle distribution is fairly stable within a given forest stratum, then LAIe can be predicted from the gap fraction in one direction, e.g. vertically, if combined with hemispherical measurements at a number of points. If we assume that an ALS penetration variable is correlated to gap fraction, then LAIe can be derived if the slope β is estimated from a number of points having both field estimated LAIe and an ALS penetration rate. Various definitions exist for leaf area index, and we here use the hemisurface area, which is one half the total surface area of the canopy objects. This is convenient for several reasons, and it corresponds to the one-sided

area of leaves. We might expect β to take a value around 2, which would be the case if the foliage angle distribution is spherical and if P is equal to the vertical gap fraction. Mapping of gap fraction or LAIe based on ALS has been demonstrated using various penetration rate variables, i.e. the fraction of the echoes located below the canopy layer or below a given height (Lovell et al., 2003; Todd et al., 2003; Solberg et al., 2006; Richardson et al., 2009), or similarly a fraction of a full waveform return (Lefsky et al., 1999a,b). For an ALS based LAIe mapping to work, it is important that the penetration variable is sensitive to variations in gap fraction regardless of the size of the gaps. For example, a penetration rate based on the first echo of each pulse might be insensitive to small gaps, because the ALS footprints are too large to penetrate such gaps (Lovell et al., 2003). A strong relationship between the ALS penetration rate and the gap fraction would ensure that the method works, in particular if the penetration rate is unbiased against gap fraction. Because ALS is a promising method for ALS mapping, it is necessary to further document its suitability and to further develop ways for calibration from field measurements. The aim of this study was to test if ALS could be used for mapping of LAIe in a Norway spruce forest and to test various methods for calibration. The specific objectives were to (1) evaluate how strongly ALS penetration rate was related to LAIe, (2) compare alternative ALS penetration variables, (3) evaluate the stability of the slope parameter β for two different ALS acquisitions over the same area, and across different age or development classes of the forest, (4) compare different field based calibration methods, and (5) compare the ALS penetration rate with gap fraction.

Fig. 1. Map of LAIe with spatial resolution 10 × 10 m based on the ALS data set from 2003. The locations of the plots are laid atop the map. LAIe values are color coded from white to black in the range 0 to 14. For the purpose of visualization all LAIe values N5 were given black color. Lakes, forest roads, and clear cuts are white.

S. Solberg et al. / Remote Sensing of Environment 113 (2009) 2317–2327

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most commonly used devices (Chen et al., 1997), and LAI-2000 appears to produce the most reliable LAIe values in forests (Chen et al., 2006). All field measurements were done 1 m above ground. This height is convenient for the field work, and is also suitable for avoiding the influence of ground vegetation in the LAIe values. Correspondingly, this height was also used as a threshold for separating ground echoes from canopy echoes in the ALS data. The LAI-2000 instrument has an optical sensor which consists of five light sensors arranged in concentric rings (#1–#5) spanning the zenith angles 0–13°, 16–28°, 32–43°, 47–58°, and 61–74°, respectively. It measures radiation in the blue spectrum (320–490 nm), where scattering from leaves is low. We recorded readings both in the forest plots (“below canopy”) and simultaneously every 15 or 30 s with an identical reference instrument placed on top of a building in an open area in the forest (“above canopy”) with distances to the plots varying up to 1.6 km. This was the nearest suitable location. We synchronized and calibrated the two devices according to the LAI-2000 manual. The forest measurements were carried out at the plot centers and at four additional points 3 m away in the four cardinal directions (Fig. 2), and these repetitions were treated as plot replicates. The instrument's sensor was equipped with a 90° view restrictor in the direction of the sun which also blocked out the operator. A similar view restrictor was placed on the reference instrument, and this instrument was oriented similarly to the below canopy instrument and re-oriented as the sun position changed. The ratio of below- and above-canopy light intensity readings of the five rings represents below-canopy light transmittance, and this was recalculated into LAIe as described in the instrument manual (Anon, 1992). Median below-canopy transmittances for each ring were used to calculate one LAIe value for each plot and year. Ideally, all foliage objects should be black and the only light reaching the sensors should be diffuse light passing through canopy gaps. In reality, some of the light reaching the sensors will be light that has scattered from foliage objects, in particularly under sunny conditions causing some overestimation of gap fraction and underestimation of LAIe. Light scattering in the canopy often causes some 10–20% underestimation of LAIe when using LAI-2000 (Stenberg et al.,

2. Materials and methods 2.1. The forest and the plots The study was conducted in the Østmarka forest (Fig. 1) near the city of Oslo in south-eastern Norway (59° 50′N, 11° 02′E, 190–370 m a. s.l). The forest is dominated by Norway spruce (Picea abies (L.) Karst), with some Scots pine (Pinus silvestris L.), birch (Betula pubescens Ehrh. and pendula Roth.), aspen (Populus tremula L.), and rowan (Sorbus aucuparia L.) The ground vegetation in old stands was dominated by low vegetation such as bilberry (Vaccinium myrtillus L.) reaching about 20 cm above ground. In younger and more open stands the ground vegetation comprised a variety of species which extended higher; however, rarely reaching more than 50 cm above ground. We established 24 circular 1000 m2 plots (radius = 17.8 m) for field measurements, and placed them in order to minimize problems with steep terrain and stand edges for the LAIe measurements. The plots were assigned to four different development classes, i.e. (1) newly regenerated forest, (2) young forest, (3) intermediate forest, and (4) old forest (Table 1). The location of the plot centers was measured by differential Global Navigation Satellite Systems (dGNSS) with a Topcon Legacy 20-channel survey grade dual-frequency receiver, observing pseudorange and carrier phase of Global Positioning System (GPS) and Global Navigation Satellite System (GLONASS). The average accuracy of the plot coordinates was expected to be 10 cm with the applied Pinnacle version 1.0 software package (Anon., 1999b; Næsset, 2001). In order to characterize the plots we measured diameter at breast height on all trees and noted their species. Four non-suppressed trees on each plot were systematically selected for height measurements. They were selected among the non-suppressed trees, being the first tree found going clockwise around the plot after each cardinal direction. 2.2. Field estimates of LAI Point measurements for LAIe estimation were carried out in the field with both LAI-2000 and hemispherical images. These are the two

Table 1 Descriptive statistics for the 24 plots. Plot #

Age class

LAI 2003

LAI 2005

N ha− 1

Dbh cm

Spruce BA%

Pine BA%

Decid. BA%

Hm

cr_height m

cr_rad m

101 103 105 107 108 102 104 106 12 10 15 16 11 2 14 7 3 17 18 6 13 5 19 4

1 1 1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4

L L L L L L L L

L, HI L, HI L, HI L, HI L, HI L, HI L, HI L, HI L L L L L, HI L, HI L L, HI L, HI L L L, HI L, HI L L L, HI

1400 1410 1550 2050 1520 1930 2290 2560 1720 1020 1150 1950 1010 1040 1360 1270 940 1060 1110 1080 960 920 980 750

5.0 4.5 4.0 6.2 7.1 7.1 7.9 8.7 13.9 17.4 17.6 13.5 19.6 17.0 14.0 14.8 18.3 18.4 15.5 16.2 18.5 19.8 21.1 25.3

86 88 79 97 88 78 76 83 83 91 94 58 87 90 87 80 88 86 87 78 89 96 89 100

0 7 2 0 0 2 0 0 4 2 0 11 0 0 0 0 0 0 5 2 0 0 0 0

14 5 19 3 12 20 24 17 13 7 6 31 13 10 13 20 12 14 8 20 11 4 11 0

3.3 4.0 4.2 5.4 7.3 8.3 8.9 12.5 17.1 19.3 20.5 20.5 21.3 23.3 23.5 23.9 24.7 25.6 25.8 26.0 26.2 29.0 30.1 30.5

0.2 0.3 0.3 0.4 0.4 0.5 0.8 3.1 6.2 3.1 6.4 5.0 4.8 3.5 3.9 5.2 3.8 9.3 9.6 5.1 7.0 4.8 10.0 12.2

0.7 0.8 0.8 0.7 0.9 1.0 1.0 0.9 1.4 2.3 1.8 1.6 1.6 2.0 2.7 1.6 1.7 1.8 2.0 2.0 2.5 2.7 2.1 1.6

L

L

L L

The two LAI columns show which measurements were done (L = LAI-2000, HI = hemispherical photography). The other columns are number of trees (N), mean breast height diameter (Dbh), basal area fractions (BA%) for spruce, pine and deciduous trees, and finally height (H), crown height (cr_height), and crown radius (cr_rad) averaged over four sample trees per plot.

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Fig. 2. The sample scheme of a plot showing the positions of LAI-2000 and HI measurements. A circle with extracted ALS data for the calibration is indicated.

1994; Chen et al., 1997; Leblanc and Chen, 2001). Ideal sky conditions for LAIe measurements can be rare here, and it was not feasible to obtain these in this study. In 2003 only one half of the plots were measured, after discarding some days with inappropriate weather conditions. The weather during the field work on July 28th and 29th was sunny with partial cloud cover. In 2005, the cloud cover on June 21st and 23rd was more even, starting with an even, thin cloud cover gradually changing into blue skies and sunshine. The terrain was rugged, varying between ridges and valleys, and in many cases the terrain would come into the field of view of the optical LAI measurement devices and be confused with foliage, while downhill terrain might cause an overestimation of canopy gap fraction. The forest was generally heterogeneous over short distances with stands so small that stand edges and neighboring stands would often come into the field of view. These problems could not be completely avoided by careful positioning of the plots; however, the LAI-2000 manual recommends excluding the 5th ring in such cases. In the standard procedure for deriving LAIe from LAI-2000 the path, or observation, length for each ring through the canopy is set to L = 1/cosθ, where L is the canopy height and θ is the zenith angle, assuming a uniform canopy height. We carried out a quality check of the LAI-2000 data in order to evaluate this problem, by calculating the contact number, κ, for each ring. This is a measure of how often a long thin needle inserted through the canopy would get in contact with foliage (Warren Wilson, 1959), and can be derived from gap fraction data by the LAI-2000 as: −1

κi = lnðGFi

Þ = Li

ð5Þ

where i is the ring number 1–5 of LAI-2000, GF is the gap fraction, and Li is the path length relative to canopy height. As shown by Lang (1987), uniform canopies with different foliage angle distributions have a common property: their contact numbers vary smoothly with zenith angle along a sigmoid curve. Although this is strictly valid only in canopies with randomly distributed leaves (as assumed by the LAI2000), we used this theoretical dependency of contact number on leaf and view zenith angles to check whether data for the different rings exhibited a logical behavior. We also acquired hemispherical images. In comparison with the LAI-2000, the advantage of HI is that the images are stored and thus provide flexibility for later analyses in selection of spectral channels (RGB) and azimuth and zenith angles. Hemispherical images were acquired at 15 of the plots in 2005. Images were taken at the plot centers and at only two of the additional points located 3 m from the

center, i.e. in the northward and southward directions. The photographs were taken with a leveled Nikon Coolpix 4500 digital camera equipped with a Nikon FC-E8 fisheye converter. Exposure (shutter speed and aperture) settings influence LAIe estimates from hemispherical images, and automatic camera settings are normally not recommended (Zhang et al., 2005; Macfarlane et al., 2000; Chen et al., 1991). Nevertheless, we chose to use fully automatic camera settings because Solberg et al. (2006) obtained very strong relationships (R2 = 0.87) that way in a similar study on ALS penetration rate and LAIe. Also, selecting the most appropriate exposure would require additional measurements by external light meters to measure the brightness of the sky in the zenith direction (Clearwater et al., 1999; Olsson et al., 1982). We also allowed the camera's built-in software to perform some other automatic image modifications, including a gamma-correction that takes care of the nonlinear brightness perception of the human eye, an increased edge sharpening routine, and a JPEG 1:8 compression. We derived LAIe from the HI data in two ways. First, we used the Hemiview software (Anon, 1999a) where we separated background sky from canopy objects by using one brightness value selected by the operator for the entire image (“global thresholding”), and derived LAIe with the standard Hemiview procedure (Anon, 1999a). Second, we used the HI data to simulate the LAI-2000 by (1) excluding a 90° sector centered towards the position of the sun at the time the photograph was acquired in order to simulate the 90° sun mask used with the LAI2000 instrument, (2) averaging gap fraction data for the five zenith angle spans corresponding to the LAI-2000 rings, (3) using only the blue band of the image corresponding to the lens coating on LAI-2000, (4) using a local thresholding technique to separate background sky from canopy (Appendix), and finally (5) using these simulated LAI2000 gap fraction data to calculate LAIe in the same way as described in the manual of LAI-2000. 2.3. ALS data The two ALS data sets were acquired with different sensors and different acquisition settings (Table 2). In 2003 the Optech ALTM 1233 sensor was used, which has two separate receivers recording first and last echoes, respectively. These two receivers were calibrated against each other using an unobstructed and horizontal area outside the study area. The average difference in height between the first and last echoes was − 5 cm, and we therefore added 5 cm to all first echo heights. The ALTM 3100 used in 2005 has only one receiver which records up to four different echoes of each emitted pulse, and there is no need for calibration of these echoes against each other. Initial processing of the data was accomplished by the contractor (Blom Geomatics, Norway). Planimetric coordinates (x and y) and

Table 2 Sensor and flight specifications for the two airborne laser data acquisitions. Date of acquisition

October 9, 2003

June 18, 2005

Platform Sensor Pulse width (ns) Pulse energy (μJ) Peak power (kW) Wavelength (nm) Mean flying altitude AGL (m) Pulse repetition frequency (kHz) Scanner frequency (Hz) Half scan angle (deg.) Flying speed (ms− 1) Swath width (m) Mean pulse density (m− 2) Beam divergence (mrad) Footprint diameter (cm)

Huges 500 Helicopter Optech ALTM 1233 11 84 7.6 1064 600 33 50 11 35 230 5.0 0.30 18

Piper PA31-310 Optech ALTM 3100 16 66 4.1 1064 750 100 70 10 75 264 5.1 0.26 21

S. Solberg et al. / Remote Sensing of Environment 113 (2009) 2317–2327

ellipsoidal height values were computed for all echoes. One of the flight lines was flown perpendicular to the other flight lines and used in matching and correction for systematic errors between swaths. Ground echoes were classified using the progressive Triangular Irregular Network (TIN) densification algorithm (Axelsson, 2000) of the Terrascan software (Anon., 2004). For each acquisition, a TIN was created from the planimetric coordinates and corresponding heights of the laser echoes classified as ground points. The ellipsoidal height accuracy of the TIN model was expected to be around 20–30 cm (e.g. Hodgson & Bresnahan, 2004; Kraus & Pfeifer, 1998; Reutebuch et al., 2003). The heights of all echoes relative to the ground surface were calculated by subtracting the respective TIN heights of all individual echoes using a bi-linear interpolation. In 2003 there were 72 days between the field measurements and the ALS scanning (29 July and 9 October, respectively). It is likely that the amount of foliage decreased during this period due to autumnal senescence and some leaf shedding on the broadleaved trees; however, it is likely that this had only a small effect on LAIe. Broadleaved trees made up an average fraction of 13% of the stem basal area (Table 1), and if we assume that the leaves made up 70–80% of the LAIe in these trees (Chen et al., 1997), a worst case with a complete leaf loss on all broadleaved trees would represent a 5% decrease in LAIe. Needle fall in Norway spruce is normally small in this period. In 2005 the field measurements and ALS data were acquired almost at the same time (23 and 18 June, respectively). We extracted ALS data from within a circle around the plot centre and calculated ALS penetration rate through the canopy layer. The LAI-2000 and the ALS were not sampling the same canopy volume, seeing an upwards facing cone and a vertical cylinder, respectively. The volume of the cone would depend on the height of the canopy. Hence, it was not obvious which circle size to use for the ALS data selection. We tried five alternatives with a fixed radius (5, 10, 15, 20, and 25 m) and five alternatives with a radius proportional to tree height (0.5, 0.75, 1.0, 1.5, and 2 times the mean height of the four sample trees). We calculated two alternative penetration rates, based either on the first echo or the first and last echo of each pulse. In the first case the penetration rate (P) of the ALS data was defined as P = Ng = ðNg + Nc Þ

ð2Þ

where Ng is the number of ground echoes which was defined as having a height above ground (dz) of maximum 1 m, and Nc is the number of canopy echoes having dz larger than 1 m. When using both first and last echoes of each pulse we calculated penetration rate as follows: P=

NgO + 0:5ðNgF + NgL Þ NO + 0:5ðNF + NL Þ

ð3Þ

where NgO and NO are the number of “only” echoes, below canopy and in total, respectively. The NgF and NF are the number of first echoes, also below canopy and in total, respectively. For ALTM 1233 this means the “first” echoes while for ALTM 3100 it means the “first of many” echoes. NgL and NL are the number of last echoes, also below canopy and in total, respectively. For ALTM 1233 this means the “last” echoes while for ALTM 3100 it means the “last of many” echoes. The rationale for this equation was that we intended to assign an equal weight to each laser pulse, thereby taking the pulses as a systematic sample of the penetration rate. However, the ALS data sets in the present study only contained echoes without pulse identification. Hence, the denominator is an estimate of the number of pulses for a given spatial unit. The numerator expresses the amount of penetration. This formula works both for the ALTM 1233 that has two separate sensors and does not produce “only” echoes, and for the ALTM 3100 which records multiple echoes with one sensor. Three typical echo outcomes of laser pulses from the latter sensor are canopy-only, canopy-first-

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ground-last, and ground-only. These are assigned the penetration rates 0, 0.5 and 1, respectively, with Eq. (3). This formula is also robust against problems when the numbers of first and last echoes are not identical. This happens when some echoes are lost or filtered out during pre-processing of the data set. For example if a pulse hits a bird and creates a first echo far above the forest canopy, then the preprocessing may filter away this echo, and the pulse ends up with a last echo only. 2.4. Analyses Using the LAI-2000 data we first ran the model in Eq. (1) and then extended that model sequentially with two more effects to test if a common slope could be used for both ALS acquisitions and for all development classes, with the following model: −1

LAIe ði; jÞ = ðβ1 + β2i + β3j Þ lnðPi Þ + e:

ð4Þ

For hypothesis testing the three effects (β1; β2i; β3j) were entered sequentially in the order they appear in the model and tested by the Fvalue obtained from the increase in explained sum of squares. Hence, β1 is a slope parameter representing the overall relationship between LAIe and ALS penetration rate. It can be seen as a slope common for both acquisitions and all development classes that would be obtained if the two latter parameters β2i and β3j were discarded as non-significant effects in the model. The parameter β2i is a slope adjustment representing the effect of the differences between the two ALS acquisitions (i = 1,2), and β3j is a slope adjustment representing the effect of development class (j = 1,..,4), and e is a random error. We intentionally omit the inclusion of an intercept since it lacks a physical basis. Thus, there are five independent slope parameters estimated in the full model, and they can be combined into eight slope parameters for the two acquisitions and four development classes. We compared the LAI-2000 and HI data, and their usefulness for calibrating the LAIe model (Eq. (1)). The HI data were measured at fewer points than with LAI-2000, and for the comparison we always used measurements from the same points. In order to compare ALS penetration rate P with the near-vertical gap fractions GF, we used below-canopy light transmittance from the first ring of LAI-2000 as an estimate of gap fraction. The scanning angle of the ALS was 0–10°, which corresponds quite well to the angle span 0–12° of the first LAI-2000 ring. We fitted this relationship using the non-linear model: GF = P

c

ð6Þ

The parameter c was estimated from the log-transformed version of the model, i.e. ð7Þ

lnðGFÞ = c⋅ lnðPÞ

This non-linear model has the intuitively suitable property that it meets the requirement that the ALS penetration rate and the gap fraction should coincide at both ends of the scale, i.e., when gap fraction equals zero (a completely opaque canopy layer) and when it equals one (a clear cut, i.e. unobstructed sky), while in-between the relationship can be either straight- or curve-linear. For the no-intercept regression models in this study we calculated the coefficient of determination (R2) in accordance with the recommendations by Kvålseth (1985): n

2

∑ ðyi −ŷiÞ

n i=1 ⋅ R = 1− n−p n ∑ ðyi −yÞ2 2

i=1

ð8Þ

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Table 3 Descriptive statistics (mean, minimum, maximum and the number of observations) for variables acquired in 2005. Source

Variable

Selection

Mean

Min

Max

N

LAI-2000 LAI-2000 HI HI LAI-2000 HI HI ALS ALS

LAI LAI LAI LAI Gap fraction Gap fraction Gap fraction Penetration rate Penetration rate

Rings 1–5 Rings 1–4 Standard hemiview LAI-2000 simulated Ring 1 0–12° global thresholding 0–12° local thresholding First echo First and last echo

2.65 2.91 2.35 1.95 0.42 0.66 0.67 0.28 0.38

0.58 0.55 0.62 0.50 0.08 0.35 0.37 0.06 0.14

5.13 5.91 3.52 3.02 0.95 1.00 1.00 0.75 0.75

24 24 15 15 24 15 15 24 24

where n is the number of observations, p is the number of model parameters, ŷi is the model prediction for a given observation yi, and y is the mean of all observations. 3. Results An overview of the data obtained from 2005, which is the year with the most complete data set, is given in Table 3. Field estimates of LAIe ranged from 0.5 to almost 6. The values varied between the methods, with generally lower values obtained from HI data. For LAI2000 the LAIe values were generally higher when the 5th ring was discarded. Near vertical gap fraction spanned almost the entire range from zero to one, based on the 1st ring of LAI-2000. Corresponding values from HI data were considerably more restricted in range, with the lowest values at 0.35. The two ALS penetration rates had generally lower values than gap fraction; in particular this was the case when using first echoes only. There was a strong relationship between the field estimated LAIe and ALS penetration rate (Fig. 3a). The linear, no-intercept relationship as described by Eq. (1) was apparently a good representation. This relationship was obtained by selecting ALS data from within a circle with a radius of 0.75 times the tree height of the plots, which turned out to produce the strongest relationship (R2 = 0.92–0.93) (Table 4). This circle radius produced the strongest relationship for all cases, i.e. either using first echoes or first and last echoes, and either

using all 5 rings or only rings #1–4 of the LAI-2000. Almost equally strong relationships were obtained when using any circle with a radius in the range 0.5–1.5 times the tree height. If the circle radius was fixed, the relationships were weaker; however, fairly strong relationships were obtained with a fixed radius in the range 10–20 m. The quality checking of the LAIe data from LAI-2000 data indicated that the 5th ring should be discarded from the analyses. The contact number κ tended to increase with increasing zenith angle (towards horizontal view) (Fig. 4). According to this, the foliage angle distribution was slightly erectophile, i.e. with a dominance of vertically oriented foliage (de Wit, 1965), and this type of behavior is also generated by ‘vertically oriented’ narrow tree crowns. However, the contact numbers of the 5th ring deviated from a smooth and monotonously changing κ over zenith angle by being lower than what would be expected, except for the newly regenerated stands. When using only the first echoes the relationship was similar for the two ALS acquisitions and for the four development classes regarding the parameter estimate, with a common slope of 1.90. With this slope parameter we produced an LAIe map for the entire area in 2003, as a demonstration of ALS' ability to provide spatially continuous maps (Fig. 1). One common regression line represented the relationship. Extending the model with acquisition (or year) and development class, revealed that neither of these effects significantly improved the model (Table 5). The slope parameter was 1.83 and 1.96 for the two years 2003 and 2005 respectively, i.e. a 7% difference. This means that a given penetration rate would in 2003 have corresponded to a 7% higher LAIe value than the same penetration rate in 2005. Hence, the ALS pulses had a slightly lower ability to penetrate the canopy layer in the first year. However, according to the hypothesis testing this might be a result of random errors only. The slope parameter for the four development classes was 1.83, 1.98, 1.93, and 1.83 for the development classes 1–4 respectively. These values are very similar. No tendency towards a changing relationship with development was seen. The parameter estimates presented above were obtained as what the slopes would have been if the data set was balanced, i.e. with equal number of plots in the two years and each of the four development classes. When both the first and any eventual last echo of each pulse were used, an overall linear regression model described the relationship

1 2 Fig. 3. a. LAIe obtained from LAI-2000 plotted against ln(P− 1) from ALS, with the fitted model LAIe = 1.93 ln(P− F ) and R = 0.93 for 1st echoes. The data are from both years 2003 and 1 2005. On LAI-2000, rings 1–4 were used and ALS data were selected from within a circle with radius equal to 0.75 times the tree height. n = 36. b. LAIe plotted against ln(P− FL ) for first 2 1 and last echoes, with the regression model LAIe = 2.69 ln(P− FL ) and R = 0.92 (bold line) and regressions specific for the two years and the four age classes indicated (hatched lines).

S. Solberg et al. / Remote Sensing of Environment 113 (2009) 2317–2327 Table 4 The strength of the relationship between LAIe (LAI-2000) and ALS penetration rate given as R2 for the no-intercept model in Eq. (1) with various alternatives. Echoes

First First First + last First + last

LAI2000 rings

Fixed radius, m

1–5 1–4 1–5 1–4

.37 .40 .60 .61

5

10 .87 .86 .92 .91

15 .89 .88 .89 .89

Radius proportional to tree height 20 .88 .86 .87 .86

25 .86 .84 .85 .83

0.5H .88 .90 .86 .88

0.75H .93 .93 .92 .92

H .93 .92 .92 .91

1.5H .90 .89 .88 .88

2H .87 .85 .86 .85

The alternatives for LAI-2000 were using either rings 1–4 or all five rings, while the alternatives for ALS data were variable circle sizes. N = 36.

fairly well (Fig. 3b). However, there were now significant effects of acquisition and development class (Table 5). The slope parameters were 2.30 and 2.64 for 2003 and 2005 respectively, i.e. a 15% difference. Again, the penetration rate was lower in the first year. The newly regenerated plots deviated from the three older plot categories, while these three were similar to each other. The parameter estimates were 1.86, 2.69, 2.65, and 2.69 for the development classes 1 to 4 respectively. The LAIe obtained from the HI data was weaker related to the ALS penetration rate than LAIe from LAI-2000. With the standard hemiview method R2 ranged from 0.56 to 0.73, while with the LAI-2000 we obtained R2 values of 0.93 (Table 6). However, when we derived LAIe from the HI data by simulating LAI-2000, we obtained stronger relationships (R2 values 0.68–0.80). The parameter estimates for the relationship had always lower values than those obtained with LAI2000, because of the generally lower LAIe values derived from the HI data. A comparison between the LAI-2000 and HI data ring by ring revealed that the gap fractions of the most horizontally viewing rings (4th and 5th) were almost identical, having a Pearson correlation coefficient r = 0.98–0.99 (Table 7). However, with an increasingly vertical view the difference between LAI-2000 and HI gap fractions increased, i.e. the HI had systematically higher gap fractions than LAI2000, and the correlation decreased. The relationship between LAI-2000 gap fraction and ALS penetration rate was fairly stable over a wide range of circle sizes for selecting ALS echoes, both for fixed circle sizes and circles varying proportionally to tree height. The strongest relationship (R2 = 0.61) between the gap fraction of LAI-2000 and ALS penetration rate was obtained by using both first and last echoes, and by using a circle with 2.5 m radius

Fig. 4. Mean contact numbers from LAI-2000 measurements per development class (N = newly regenerated, Y = young, I = intermediate, and O = old) plotted against the mean zenith angle of the rings.

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Table 5 Analyses of variance for the model in Eq. (4), i.e. the relationship between LAIe and ALS penetration rate (P), with the effects of ALS acquisition and age class. Source of variation

Parameter DF First echo

ln(P− 1) Acquisition Age class Error Uncorrected total

β1 β2i β3j e

1 1 3 31 36

First and last echo F

Pr N F

SS

MS

332 0.24 0.32 4.07 336

332 2528 b.0001 0.24 1.79 0.19 0.11 0.80 0.50 0.13

F

Pr N F

SS

MS

331 1.12 1.05 3.19 336

331 3212 b.0001 1.12 10.9 0.0025 0.35 3.41 0.030 0.10

Rings 1–4 were used on LAI–2000 and ALS data were taken from a circle with a radius of 0.75 times tree height. The F-tests are sequential. RMSE = 0.36 and 0.32, respectively. DF = degrees of freedom, SS = sum of squares, MS = mean square, F = Fisher test statistics, Pr N F = probability of having a larger F-value by chance

around the plot centre for selecting these ALS echoes (Table 8). The parameter estimate here was 1.31, which means that the ALS penetration rate generally represented an overestimation of gap fraction. This was mainly the case at low gap fraction values (Fig. 5). There was one outlier in the data set clearly appearing in the graph, with an ALS penetration rate of 0.68 and a gap fraction of 0.08 for the 1st ring of LAI-2000. The most likely explanation for this outlier is that a small cloud passed directly over the plot during the measurements, while it did not pass directly above the reference sensor. We redid the regression analyses without this outlier, whereby the slope, c, changed only slightly to 1.28, while the R2 increased to 0.75. The penetration rate based on the first echoes was generally somewhat weaker relative to gap fraction as compared to using first and last echoes. This penetration rate tended to be lower than the gap fraction with parameter estimates c around 0.7–0.9. The relationship was very similar for the two acquisitions. 4. Discussion The major finding of this study is that LAIe in a Norway spruce forest may be mapped with ALS after calibration with field estimates of LAIe. This is in line with theory and results presented in previous investigations (Lefsky et al., 1999a,b; Lovell et al., 2003; Todd et al., 2003; Morsdorf et al. 2006; Solberg et al., 2006). Riaño et al. (2004) also found strong relationships between field estimates of LAIe and ALS data by relating LAIe directly to percent canopy echoes of the ALS data. The results are promising because the relationships were strong and because they closely followed the theoretical relationship from the Beer–Lambert law. The physical explanation of the results is that the vertical gap fraction is strongly related to ALS penetration rate, and also strongly related to LAIe. The latter relationship is in accordance with the Beer–Lambert law, but also results from a fairly stable foliage angle distribution. The gain obtained by moving from point based estimates of LAIe to using ALS is the ability to produce spatially continuous data. As shown in Fig. 1, LAIe varies a lot over small distances, which illustrates this gain. Because the ALS based method is based on near-vertical pulses rather than a hemispherical view, a high spatial resolution can be obtained. The limitations that are present with field estimates of LAIe with LAI-2000 are also present with the ALS based method. The variable obtained is LAIe rather than true LAI. For mapping or monitoring, this may not be a problem because the spatial and temporal variation will be obtained anyway. For applications where the true LAI is needed it may be necessary to introduce corrections. For deciduous trees one may remove the woody area by scanning both with leaf-on and leaf-off. Another problem is an underestimation of LAIe caused by light scattering which is transferred from the field measurements through the calibration. While this will cause random errors between plots in field estimates of LAIe, an ALS based method has the advantage that

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Table 6 Comparing the goodness of LAI-2000 and HI for calibration. Data source

Azimuth angles

LAI-2000 HI HI

90° sun mask All 90° sun mask

Zenith angles

Spectral bands B⁎

5 rings Hemisphere 5 rings

Thresholding – Global Local

RGB B

LAIe calculation

First echo

LAI-2000 Hemiview LAI-2000

First and last

Slope (β1)

R2

Slope (β1)

R2

1.76 1.59 1.33

0.93 0.56 0.68

2.48 2.27 1.89

0.93 0.73 0.80

Results of fitting no-intercept linear regression models to ground based LAIe against ln(P− 1) from the ALS data. Two HI methods are compared, i.e. the standard Hemiview method and a simulation of LAI-2000 with local thresholding for separating foliage from background sky. Data are from the 2005 data acquisition. N = 15. ⁎ Lens coating filter removes radiation with wavelengths larger than 490 nm.

this will be a constant bias over the scanned area. A number of correction methods have been developed for field based estimates of LAIe and these may be applied for correction of ALS based LAIe data as well. Corrections for clumping and light scattering may be achieved from the field inventory with the TRAC instrument (Chen and Cihlar, 1995) or along concentric circles in HI data (Chen et al., 2006), withinshoot clumping in conifers may be estimated from detailed shoot measurements (Oker-Blom and Smolander, 1988; Oker-Blom et al., 1991; Chen and Cihlar, 1995), and Leblanc and Chen (2001) demonstrated how the light scattering effect can be removed by regression analyses and radiative transfer modeling. We excluded the 5th ring of LAI-2000 for calculating LAIe. Too short distances to stand edges would cause the 5th ring to be influenced by less dense neighboring stands, and vice versa (Fig. 6). Some other problems may also have contributed to the difficulties with the 5th ring. In old and dense stands, de-branched tree trunks rather than foliage would have dominated in the 5th ring's field-of-view. Leblanc and Chen (2001) demonstrated by repeated measurements during sunny days that in high LAI stands the 5th ring is the ring with the potentially largest problem with overestimation of gap fraction due to light scattering from the foliage, because this ring normally has the lowest gap fraction among all the rings and even a small amount of scattering may have a relatively large effect. Taking into account that we often carried out measurements under sub-optimal sky conditions, including partly sunny conditions, this problem is likely to have been present. Exclusion of rings is commonly done with LAI-2000, and Leblanc and Chen (2001) demonstrated that the 4th ring may even be used alone. The relationships between field estimates of LAIe were strongest when ALS data were taken from a circle having a radius of 0.75 times the tree height; however, almost equally strong relationships were found over a range of circle sizes. This result was fairly consistent with Riaño et al. (2004), who compared a range of circle sizes and found the optimal radius to be equal to tree height. One aim of this study was to determine if the ALS penetration rates corresponded to gap fraction and were sensitive to gaps of any size, including small gaps. Using the first and last echoes produced the strongest relationship with gap fraction and was hence more appropriate than only using the first echoes. However, the first-andlast-echo penetration rate tended to overestimate gap fraction as obtained with the 1st ring of LAI-2000 (Fig. 5), and this bias may have been even larger than the results indicate because of the light scattering problem with the LAI-2000 data. In open stands the foliage

vertically above the LAI-2000 sensor easily reflects sunlight directly down to the LAI-2000 sensor (Leblanc & Chen, 2001). We believe, however, that this bias can be removed from the ALS based method, by a tuning of the penetration value assigned to ALS pulses having a canopy-first and a ground-last echo. We arbitrarily assigned the penetration value 0.5 to such pulses, and a lower value would reduce the penetration rate. This should be addressed in further studies. An alternative way to obtain unbiased estimates might be to change the acquisition settings of the ALS scan. In laboratory experiments, Parker et al. (2004) demonstrated that a LIDAR beam more easily penetrates through a large gap than through a small gap, indicating that narrowing the ALS pulse would make the scan more sensitive to small gaps. However, ALS scans of forests have shown less clear effects of footprint size upon penetration, and that the penetration rate depends on the interaction between footprint size and the peak pulse power (Nilsson 1994; Hopkinson 2007). This ability to detect small gaps may not be present when only using the 1st echoes (Lovell et al., 2003; Morsdorf et al., 2006). The present study indicated that the ALS penetration rate based on 1st echoes represented an underestimation of gap fraction. However, the relationship towards LAIe was equally strong as for the first-and-last echo alternative. The explanation for this is likely that between-tree gaps dominated the gap fraction in the present spruce forest, with a high degree of within-tree clumping of foliage. In line with this, Blair and Hofton (1999) demonstrated that the FLI-MAP first-return-only airborne laser scanner with a 10 cm-diameter footprint hardly produced any ground echo in dense parts of a tropical forest in Costa Rica, while the ground return was evident with the LVIS fullwaveform laser scanner. There is, however, one limitation in a method that uses multiple echoes: For today's commonly used laser scanners having one sensor only, there will not be enough time to separate a first and a second echo in low-canopy forest stands. Such stands will then obtain underestimated LAIe values in an ALS based mapping which is calibrated with taller trees. There were some differences between the two scans in the ability of the laser pulses to penetrate the canopy layer. The calibration factor, β, between ALS penetration rate and LAIe was lower in the first scan as compared to the second scan, which corresponds to a slightly lower ability to penetrate the canopy layer. The difference was 7% when using first echoes and 15% when using first and last echoes. According to the hypothesis testing the former difference could be a result of random errors. However, these findings are plausible and in line with other

Table 7 Pearson correlations and mean differences between LAI-2000 and HI gap fractions for each of the five concentric, hemispherical rings as used in LAI-2000.

Table 8 The relationship between near-vertical gap fraction of LAI-2000 and ALS penetration rate given as the slope of a log-log relationship and R2 (%) of the no-intercept model Eq. (7) with various alternatives.

Ring 1 2 3 4 5

Global thresholding

Local thresholding

r

r

0.87 0.92 0.95 0.99 0.98

Mean difference − 0.14 − 0.08 − 0.06 − 0.01 0.05

0.87 0.93 0.96 0.99 0.98

Mean difference − 0.15 − 0.12 − 0.10 − 0.05 0.01

Echoes

Fixed radius, m 2.5

First First First + last First + last

5

7.5

Radius proportional to tree height 10

12.5 0.25H 0.5H 0.75H 1H

Slope, c .72 .70 .78 .78 .78 .77 R2 .41 .54 .54 .53 .51 .51 Slope, c 1.31 1.14 1.14 1.11 1.10 1.22 R2 .61 .60 .55 .50 .48 .60

.75 .53 1.07 .49

.81 .55 1.12 .50

1.25H

.86 .89 .55 .52 1.17 1.20 .50 .48

S. Solberg et al. / Remote Sensing of Environment 113 (2009) 2317–2327

Fig. 5. Near-vertical gap fractions (GF) from LAI-2000 plotted against ALS penetration rates (P). The 1:1 line is indicated.

studies. In a study of the influence of different ALS sensors and flight configurations on height- and canopy-related metrics derived from the ALS data over a mature spruce forest, Næsset (2009) compared the same two sensors and obtained similar results: ALTM 1233 produced 5% lower penetration rates than ALTM 3100. Hopkinson (2007) demonstrated that ALS echo intensity was linearly related to the parameter “peak pulse power concentration”, which was calculated as peak pulse power divided by footprint area. That study suggested that this parameter is a major factor in determining penetration of ALS pulses into vegetation: A reduction in peak pulse power concentration would increase canopy penetration, because larger foliage areas would be needed in order to raise the backscatter energy above a required threshold for pulse detection. In the two acquisitions in the present study the peak pulse power concentrations were 299 and 118 kW/m2, respectively, for the 2003 and 2005 scans (Table 2). Hence, the 1st scan had a lower degree of canopy penetration and a higher peak pulse power concentration than the 2nd scan, which is in accordance with Hopkinson (2007). The minor difference in penetration rate based on the 1st echoes seems to be in line with other studies. The degree of canopy height metrics, which partly reflects canopy penetration, is only moderately influenced by sensor and acquisition settings when first echoes are used (Næsset, 2004, 2009). When two or more echoes are derived from each pulse there are likely to be larger effects between sensors and acquisition settings. One explanation for this is that the minimum time required to separate adjacent echoes will vary. Comparing ALTM 1233 and ALTM 3100 represents a special case, as the former had two independent sensors for detecting 1st and 2nd echoes, while the latter had one sensor for detecting multiple echoes.

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Hence, there was no required minimum of time for separating adjacent echoes in the first year. With the ALTM 3100 the minimum time required after the first echo before another echo can be detected corresponds to a few meters. We could not detect any clear difference in β between the development classes, which indicates that there were no clear differences in foliage angle distribution. In the 2nd scan with ALTM 3100 the newly regenerated stands obtained a clearly lower β than the three older development classes. An age-related change in foliage angle distribution in Norway spruce might be expected because the phenotypic branching pattern normally changes from the plate type to the comb or brush type (Hanisch & Kilz, 1990). However, it is more likely that the lower β slope for the newly regenerated plots was an artifact. The trees here were so small that most ALS pulses produced echoes of the category “only”, and these echo types were given too low weight in comparison with pulses having canopy-first ground-last echoes. The gap fraction would thus be underestimated, producing a lower β value. When using the first echoes there was no difference between the development classes. Crown shape in combination with spatial pattern of trees is another factor that could introduce variation in β. At similar LAIe, a forest with well separated deep narrow crowns would give a smaller β than one with horizontally extended crowns and higher canopy cover. The relationships between LAIe obtained from HI data and ALS penetration rate were fairly strong; however, still clearly weaker than those obtained with LAI-2000. The simulation of LAI-2000 data with HI data increased the strength of the relationship. This demonstrates that LAI-2000 might be a more suitable device for calibration because of its lens coating that transmits blue light only, the masking of a sector towards the sun, and the exclusion of the most horizontally viewing angles. However, the major factor is still apparently the parallel measurements, i.e. the below and above canopy measurements. The HI data produced generally lower LAIe values than LAI-2000, which might be a result of overexposure: this was most pronounced in the vertical direction, and with increasing zenith angle became gradually a smaller problem along with the decreasing sky brightness. This explains why the gap fractions of the most horizontally viewing angles were almost identical with those of LAI-2000 while they were clearly higher for more vertically viewing angles. 5. Conclusions We conclude that airborne laser scanning is suitable for mapping or monitoring of effective leaf area index of Norway spruce. We obtained strong relationships between ALS penetration rate and field estimates of LAIe. Using first and last echoes to derive the ALS penetration rate was apparently more sensitive to variations in gap fraction, and hence generally more appropriate, than using only the first echoes. However, the results indicate that partial penetration from pulses having a canopy-first and a ground-last echo should have been assigned a penetration value lower than the 0.5 value used here, and finding the appropriate value should be addressed in further studies. The penetration rate derived from first and last echoes suffers

Fig. 6. The effect of small stands on the fifth ring of LAI-2000. Cross section through the canopy surface around one of the plots (age class newly regenerated), including the outermost view of the fifth and the fourth rings. The nearby, older stand erroneously increases the LAIe value if the fifth ring is included.

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from a problem of underestimation in low vegetation because with today's most commonly used ALS sensors there might not be enough time for the sensor to separate two adjacent echoes. The best method for calibration of the ALS based LAIe data was to use LAI-2000, exclude its outermost ring, and select ALS data from a circle with a radius of 0.75 times the tree height. The relationship was stable across ALS data acquisitions and development classes of the trees. Acknowledgements The Research Council of Norway together with the Forest Owners' Fund (“Skogtiltaksfondet”), and the Royal Norwegian Ministry of Agriculture and Food are acknowledged for financing the REMFOR project, which has partly covered this study. The Norwegian Forest and Landscape Institute and the Norwegian University of Life Sciences are also acknowledged for their support. Stenberg and Rautiainen acknowledge support from the Academy of Finland (SPRINTER and COOLFUTURE projects). Appendix A. The local thresholding algorithm We used an algorithm based on an automatic detection of thresholds for individual pixels to convert hemispherical images of forest canopies from 256 grey levels to binary images. It is context sensitive, i.e. uses the brightness information from neighboring pixels in order to set a threshold. This algorithm overcomes the common problems of (1) subjective settings for thresholds (Nobis & Hunziker, 2005) and (2) a variation of thresholds between zones in the image that are due to uneven image brightness (Wagner & Hagemeier, 2006). In the first step of the algorithm, pixels located at edges between sky and foliage are detected and classified, typically about 10% of the pixels in the image. This is done in a similar way as in a standard unsharp filter. For each pixel, a mean brightness contrast is calculated against its eight surrounding pixels. Surrounding pixels were only used to calculate this mean if they had a contrast above a given minimum. This minimum contrast is lower for darker pixels than for brighter pixels, with a linear increase between a minimum and maximum contrast threshold. The minimum contrast threshold is calculated automatically based on the distribution of contrasts for the entire image and placed on the right side of the peak describing the majority of pixels with a low contrast. The maximum contrast threshold is set to twice the minimum contrast threshold. Mean contrasts above or below zero indicate that the pixel is located at the edge between darker and brighter zones. Pixels on the dark side of edges and pixels on the bright side of edges are classified during this step. This edge detection should retain even the smallest gaps open and preserve small branch structures. In the second step, the darkest and brightest pixels in the image are classified based on a brightness value distribution for the entire image. About 90% of all pixels are classified in this step. Thresholds are set inside the peaks describing the majority of pixels that are either very bright or very dark. In the third and final step, the remaining pixels (typically less than 1%) are classified based on the classification of neighboring edge pixels. In a spiral search around the pixel, the first five edge pixels are identified. Their majority determines the classification of the pixel. Canopy openness from locally thresholded images was calculated using 32,400 sections of the hemispherical image (Brunner, 1998). References Anon. (1992). LAI-2000 plant canopy analyzer. Operating manual. Lincoln, USA: LI-COR Inc. Anon. (1999a). HemiView user manual. Version 2.1.Cambridge, UK: Delta-T Devices 75 pp. Anon. (1999b). Pinnacle user's manual. San Jose, CA: Javad Positioning Systems. Anon. (2004). TerraScan user's guide. Helsinki: Terrasolid Ltd.

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