Effects of different flying altitudes on biophysical stand properties estimated from canopy height and density measured with a small-footprint airborne scanning laser

Remote Sensing of Environment 91 (2004) 243 – 255 www.elsevier.com/locate/rse

Effects of different flying altitudes on biophysical stand properties estimated from canopy height and density measured with a small-footprint airborne scanning laser Erik Næsset * Department of Ecology and Natural Resource Management, Agricultural University of Norway, P.O. Box 5003, N-1432 A˚s, Norway Received 9 February 2004; received in revised form 26 March 2004; accepted 27 March 2004

Abstract Canopy height distributions were created from small-footprint airborne laser scanner data collected over 133 georeferenced field sample plots and 56 forest stands located in young and mature forest. The plot size was 300 – 400 m2 and the average stand size was 1.7 ha. Spruce and pine were the dominant tree species. Canopy height distributions were created from both first and last pulse data. The laser data were acquired from two different flying altitudes, i.e., 530 – 540 and 840 – 850 m above ground. Height percentiles, mean and maximum height values, coefficients of variation of the heights, and canopy density at different height intervals above the ground were computed from the laser-derived canopy height distributions. Corresponding metrics derived from the two different flying altitudes were compared. Only 1 of 54 metrics derived from the first pulse data differed significantly between flying altitudes. For the last pulse data, the mean values of the height percentiles were up to 50 cm higher than the corresponding values of the low-altitude data. The high-altitude data yielded significantly higher values for most of the canopy density measures. The standard deviation for the differences between high and low flying altitude for each of the metrics was estimated. The standard deviations for the height percentiles ranged from 0.07 to 0.30 cm in the forest stands, indicating a large degree of stability between repeated flight overpasses. The effect of variable flying altitude on mean tree height (hL), stand basal area ( G), and stand volume (V) estimated from the laser-derived height and density measures using a two-stage inventory procedure was assessed by randomly combining laser data from the two flying altitudes for each individual sample plot and forest stand. The sample plots were used as training data to calibrate the models. The random assignment was repeated 10,000 times. The results of the 10,000 trials indicated that the precision of the estimated values of hL, G, and V was robust against alterations in flying altitude. D 2004 Elsevier Inc. All rights reserved. Keywords: Forest inventory; Laser scanning; Canopy height; Canopy density; Monte Carlo simulation

1. Introduction Airborne laser scanning systems offer an opportunity to determine biophysical properties of forest stands such as mean tree height, basal area, and timber volume (e.g., Holmgren et al., 2003; Magnussen & Boudewyn, 1998; Means et al., 2000; Næsset, 1997a,b), and practical largescale procedures have been developed to determine such stand-level characteristics based on small-footprint laser data and ground-based training data (Holmgren, 2003; Næsset, 2002a, Næsset & Bjerknes, 2001). Laser pulses of

* Tel.: +47-64948906; fax: +47-64948890. E-mail address: [email protected] (E. Næsset). 0034-4257/$ - see front matter D 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2004.03.009

small-footprint systems typically produce a roughly circular spot size on the ground with a diameter of a few centimeters up to a couple of meters. Laser scanning data are now being used operationally in commercial, stand-based forest inventories. Transitioning from research to operational use introduces a number of problems as the scale changes from local, scientific studies to regional inventories. Large-scale inventories now cover a wide range of forest types and topographic structures, with highly variable and not always optimal flying conditions. In areas with rough topography with steep slopes and deep valleys, the altitude of an airborne platform above the terrain will vary from one site to another within an inventory. Thus, different forest stands will be measured at different ranges, and if there is an overlap between adjacent stripes, there

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might even be a variation in ranges within a give site. The footprint size on the ground will vary according to alterations in ranges measured by the laser. In some of the early studies of airborne laser profiling and scanning of forest ecosystems, the effects of changing beam divergence and footprint size were investigated to see how they affected tree height derived from laser data (e.g., Aldred & Bonnor, 1985; Nilsson, 1996). It was concluded that the optimal footprint size was different for coniferous and deciduous species and that footprint size was not critical for stand height estimation of a given forest type (Aldred & Bonnor, 1985). However, certain differences in height estimation using different beam divergences were noted (Nilsson, 1996). Airborne systems in operational use are pulsed smallfootprint lasers (Baltsavias, 1999). It is likely that the penetration rate of pulsed systems is affected by footprint size. Since biophysical properties such as basal area and timber volume are determined partly from metrics characterizing canopy density, such as, for example, various measures of penetration rate, it is likely that footprint size will affect estimation of basal area and volume. Næsset (in press) analysed the effects of range differences between plots and range variability within plots on six estimated biophysical properties (mean height, basal area, volume, etc.). Only a few effects for certain combinations of forest type and biophysical property were found to be statistically significant. However, the analysis was based on relatively small, 233-m2 sample plots. With a laser sampling density of about 1 pulse/m2, the residual error for such small plots is relatively high and much higher than corresponding errors for entire stands of 1 ha or greater (Næsset, 2002a, in press). Since forest stands are the target unit of practical inventories, it is important to examine how alterations in range affect stand variables derived from laser data. In the practical procedures developed to inventory biophysical properties of stands and in other studies relating laser data to field-measured stand or plot properties (e.g., Lefsky et al., 1999; Lim et al., 2003; Magnussen et al., 1999; Means et al., 1999, 2000; Nelson, 1997; Nelson et al., 1988, 1997), laser-derived metrics used in the analysis include percentiles, maximum values, and standard deviation of the canopy height distributions and canopy density of different vertical layers. Thus, there are a large number of potential explanatory laser variables to predict forest biophysical properties, but many of them are highly correlated. In addition, if some subset of these potential, predictive laser measures is more sensitive to changes in flight altitude above ground level, then it would be best to select, as independent variables, those laser measures that are least affected by altitude changes. In this study, the differences between two different flying altitudes for selected laserderived variables were assessed. The operational forest stand inventory method utilizing airborne laser that is used in Scandinavia is based on a two-stage procedure (Næsset, 2002a; Næsset & Bjerknes,

2001). In a first stage, georeferenced sample plots with corresponding laser data are used to develop empirical relationships between various metrics derived from the laser data and biophysical properties measured in field. These relationships provide, in the second stage, corresponding predicted values for each stand from the laser data. If the basic laser-derived metrics are influenced by flying altitude, it is likely that also the resulting stand estimates of the biophysical variables will be affected. However, since the biophysical properties are predicted from equations that are combinations of several laser variables, the effect of changing flight altitude above terrain can hardly be assessed just from the altitude effects on individual laser metrics. The effect of variable flying altitude on stand estimates following the two-stage inventory procedure was therefore assessed in this research. The objective of this study was (1) to assess how laserderived metrics were affected by alterations in flying altitude and to examine how forest type influenced on these effects and (2) to assess how flying altitude affected stand estimates of three biophysical properties, i.e., mean tree height, basal area, and volume. The effects on these properties were analysed using Monte Carlo techniques to combine laser data from different flying altitudes over a sample of selected field plots and forest stands.

2. Materials and methods 2.1. Study area This study was based on data from a forest inventory in southeast Norway conducted in the municipality of Va˚ler (59j30VN, 10j55VE, 70– 120 m a.s.l.). The size of the inventory was approximately 1000 ha. As compared to average forest conditions in Norway, the terrain was considered as quite flat with gentle slopes. The main tree species were Norway spruce [Picea abies (L.) Karst.] and Scots pine (Pinus sylvestris L.). Further details about the study area can be found in Næsset (2002a). The inventory started with stand delineation accomplished by stereoscopic photointerpretation. Interpretation of aerial photography was used to classify the delineated stands according to criteria such as age class, site index, and tree species. The photointerpretation was used as prior information in designing the inventory. Two different ground reference datasets were acquired. (1) One consists of sample plots distributed systematically throughout the entire study area. They were used as training plots to establish relationships between biophysical stand characteristics and laser data in the first phase of the proposed inventory procedure. (2) The other one is a dataset with forest stands for which characteristics were predicted from the laser data. The ground reference stands were used to assess the effect of flying altitude on the practical inventory procedure. Both datasets were also used to analyse the effect

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of flying altitude on laser-derived canopy height and density metrics.

Table 1 Summary of sample plot reference dataa Characteristic

2.2. Sample plots As part of a related research project dealing with automatic tree height estimation by image matching (Næsset, 2002b), 133 circular sample plots were distributed systematically throughout the entire 1000-ha study area according to a regular grid. The plots were divided into three strata according to age class and site quality, i.e., (1) young forest (‘‘stratum I’’), (2) mature forest with poor site quality (‘‘stratum II’’), and (3) mature forest with good site quality (‘‘stratum III’’). The size of each plot was 300 m2 in stratum I and 400 m2 in strata II and III. Field data were collected during summer of 1998 (see Næsset, 2002b). Since the laser data were acquired in 2001 (see below), the plots were revisited in field in December 2001 to verify that none of them had been subject to any harvests or serious natural disturbances. However, it is likely that some natural mortality had occurred during the 3 –4 years period. On each plot, all trees with diameter at breast height (dbh)>4 and >10 cm were callipered on young and mature plots, respectively, which conforms to ordinary inventory practice. Basal area ( G) was computed as the basal area per hectare of the callipered trees. The heights of sample trees selected with probability proportional to stem basal area at breast height using a relascope were measured by a Vertex hypsometer. The number of sample trees per plot ranged from 2 to 17 with an average of 9. Mean height of each plot was computed as Lorey’s mean height (hL), i.e., mean height weighted by basal area. Total plot volume (V) was computed as the sum of the individual tree volumes for trees with dbh>4 cm and dbh>10 cm, respectively. Volumes of the individual trees were found by ratio estimation using the tree volume tariff method (Husch et al., 1993). First, volume of the sample trees were computed by means of volume equations of individual trees, which are based on height and diameter as predictor variables (Braastad, 1966; Brantseg, 1967; Vestjordet, 1967). Second, the tariff volumes of the same sample trees were computed from the volume equations for individual trees using measured diameters and heights estimated from standard height curves (Fitje & Vestjordet, 1977; Vestjordet, 1968). The ratio between tariff volume and actual volume for each sample tree was computed, and the average ratio for all sample trees by tree species was multiplied by the tariff volumes of all callipered trees. hL, G, and V were prorated by up to 3.8 years using growth models (Blingsmo, 1984; Braastad, 1975, 1980) to correspond to the date on which the laser data were acquired. These prorated values were used as ground reference. A summary of the ground-truth plot data is displayed in Table 1. Differential GPS and Global Navigation Satellite System (GLONASS) were used to determine the position of the

245

Young forest—stratum I (n = 53) hL (m) G (m2 ha
1) V (m3 ha
1) Tree species distribution Spruce (%) Pine (%) Deciduous species (%)

Range 7.3 – 22.3 11.2 – 44.8 48.8 – 519.4

14.5 27.4 207.2

0 – 100 0 – 97 0 – 69

53 34 13

Mature forest, poor site quality—stratum II (n = 34) hL (m) 11.6 – 21.7 G (m2 ha
1) 9.8 – 30.9 59.6 – 310.5 V (m3 ha
1) Tree species distribution Spruce (%) 0 – 89 Pine (%) 0 – 100 Deciduous species (%) 0 – 21 Mature forest, good site quality—stratum III (n = 46) hL (m) 11.8 – 26.7 13.0 – 50.7 G (m2 ha
1) V (m3 ha
1) 103.0 – 604.0 Tree species distribution Spruce (%) 0 – 100 Pine (%) 0 – 100 Deciduous species (%) 0 – 49 a

Mean

16.4 19.9 157.0 29 66 5

20.5 29.7 292.1 68 23 9

hL = Lorey’s mean height, G = basal area, V = volume.

centre of each sample plot. A Javad Legacy 20-channel dual-frequency receiver observing pseudorange and carrier phase of both GPS and GLONASS was used. Another Javad Legacy receiver was used as base station. The distance between the plots and the base station was approximately 19 km. Coordinates were computed by postprocessing in an adjustment with coordinates and carrier phase ambiguities as unknown parameters using both pseudorange and carrier phase observations. The estimated accuracy of the planimetric plot coordinates (x and y) ranged from < 0.1 to 2.5 m with an average of approximately 0.3 m. Further details are given by Næsset (2002b). 2.3. Stand inventory In total, 56 stands were selected for this study. They were selected subjectively among the stands delineated by photointerpretation in order to represent different combinations of age classes, site quality classes, and tree species mixtures. Field data were collected during summer and fall 1998 through intensive systematic field sample plot inventories within stands (Næsset, 2002a). The average stand size was 1.7 ha and the average number of plots per stand was 20. The stands were revisited in field in December 2001 to verify that none of them had been subject to any harvests. However, the extent of natural mortality was not assessed. For even-aged forest, the expected annual mortality rate for Norway spruce and Scots pine would be around 0.4– 0.6% (Eid & Øyen, 2003).

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The size of the individual plots in the young stands and the mature stands were 100 and 200 m2, respectively. On each plot, all trees with dbh>4 cm and dbh>10 cm were callipered in young and mature stands, respectively, and stand basal area ( G) was computed as basal area per hectare of the callipered trees. The heights of the sample trees selected with probability proportional to stem basal area at breast height were measured with a Vertex hypsometer. The number of sample trees per stand ranged from 24 to 87 with an average of 44. Lorey’s mean height (hL) was computed as the arithmetic mean of the sample tree heights. Stand volume (V) was computed from standard volume equations for individual trees and diameter – height relationships derived from the sample trees (see Næsset, 2002a for further details). hL, G, and V were prorated by up to 3.8 years using growth models (see above). The prorated values were used as ground reference. A summary of the ground-truth stand data is displayed in Table 2. 2.4. Laser scanner data Laser scanner data for this specific study were acquired on 16 and 17 July 2001 (leaf-on canopy conditions). The flying conditions were good. A Piper PA31-310 aircraft carried the Optech ALTM 1210 laser scanning system. On the average, the plane was flown approximately 530 –540 m Table 2 Summary of stand reference dataa Characteristic Young forest—stratum I (n = 22) Stand area (ha) hL (m) G (m2 ha
1) V (m3 ha
1) Tree species distribution Spruce (%) Pine (%) Deciduous species (%)

Range

Mean

0.8 – 4.1 10.8 – 20.6 17.4 – 40.0 110.3 – 382.9

1.6 14.4 26.0 184.7

9 – 100 0 – 86 0 – 30

Mature forest, poor site quality—stratum II (n = 17) Stand area (ha) 0.8 – 11.7 hL (m) 13.7 – 18.1 G (m2 ha
1) 13.3 – 31.4 V (m3 ha
1) 97.3 – 266.3 Tree species distribution Spruce (%) 4 – 76 Pine (%) 18 – 92 Deciduous species (%) 2 – 22 Mature forest, good site quality—stratum III (n = 17) Stand area (ha) 0.7 – 6.0 hL (m) 16.3 – 23.3 G (m2 ha
1) 19.3 – 41.8 V (m3 ha
1) 151.4 – 405.0 Tree species distribution Spruce (%) 44 – 90 Pine (%) 0 – 43 Deciduous species (%) 1 – 22 a

hL = Lorey’s mean height, G = basal area, V = volume.

48 39 13

2.0 16.2 19.9 152.8 31 62 7

1.5 19.6 30.2 280.8 70 20 10

above the selected field sites in the low flight and 840– 850 m above ground in the high flight (Table 3). In total, 33 parallel flight lines were flown at each altitude. The aircraft followed the same GPS tracks in both flights. The pulse repetition frequency was 10 kHz and the scan frequency was 30 Hz. Maximum scan angle was 16j. According to standard procedures, pulses transmitted at scan angles that exceeded 15j were excluded from the final dataset. The average footprint diameters at the ground were 16 and 26 cm for the low and high flights, respectively. The pulse density ranged from approximately 0.6 to 1.3 m
2 with an average around 0.84– 0.89 m
2 (Table 3). First and last returns were recorded. The mean rate of penetration through the tree canopy ranged from 11.1% to 33.0% for the first pulse data and from 37.7% to 60.1% for the last pulse data. Processing of the laser data was accomplished by the contractor (BN Mapping, Norway). Planimetric coordinates (x and y) and ellipsoidic height values were computed for all first and last returns. The last return data were used to model the ground surface. In a filtering operation on the last return data undertaken by the contractor using a proprietary routine, local maxima assumed to represent vegetation hits were discarded. A triangulated irregular network (TIN) was generated from the planimetric coordinates and corresponding height values of the individual terrain ground points retained in the last pulse dataset. Individual TIN models were made for each of the two flying altitudes. The ellipsoidic height accuracy of the TIN models was expected to be around 25 cm (Kraus & Pfeifer, 1998; Reutebuch et al., 2003). For each of the flying altitudes, four different datasets were derived from the first and last pulse data for further analysis. First, all first and last return observations (points) were spatially registered to the TIN according to their coordinates. Terrain surface height values were computed for each point by linear interpolation from the TIN. The relative height of each point was computed as the difference between the height of the first or last return and the terrain surface height. Thus, the two first datasets retained for analysis were geographically registered data for all transmitted pulses that were classified as first and last returns, respectively. Second, two datasets intended to represent the canopy were created. Since a large portion of both the first and last pulse data were expected to represent hits above the ground, both first and last return data were used to derive tree canopy heights. Observations with a height value less than 2 m were excluded from the two first datasets to eliminate ground hits and the effect of stones, shrubs, etc. from the tree canopy datasets (Nilsson, 1996). Thus, the two tree canopy datasets retained for analysis were geographically registered data on canopy height derived from the first and last returns, respectively. These datasets were spatially registered to the sample plots and stands measured in field. Pulses that hit outside these objects were excluded from further analysis.

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Table 3 Summary of laser scanner data Flight

Stratum

Sample plots Low I Low II Low III High I High II High III Stands Low Low Low High High High a

I II III I II III

No. of obs.

Beam range (m)

No of transmitted pulsesa (ha
1)

Penetration rate (%)

Range

Mean

Range

Mean

First pulse

Last pulse

53 34 46 53 34 46

505 – 576 506 – 560 505 – 573 822 – 894 817 – 878 810 – 891

539 530 539 850 844 852

6134 – 11128 6487 – 10913 6362 – 11014 6000 – 11832 6035 – 11491 6010 – 12698

8573 8433 8589 8578 8552 8579

11.5 32.3 14.5 11.1 33.0 14.2

38.9 60.1 39.3 38.0 60.1 37.7

22 17 17 22 17 17

515 – 559 513 – 555 512 – 568 824 – 872 824 – 867 818 – 884

535 533 538 847 846 849

7244 – 9634 7612 – 9871 7891 – 10339 7764 – 10667 6605 – 10828 6664 – 10933

8505 8740 8743 8755 8720 8902

17.1 29.5 16.7 16.7 29.3 16.6

44.2 56.2 41.4 43.0 55.2 40.5

Refers to first pulse data.

2.5. Computations The most commonly used canopy height-related metrics are the percentiles of the height distributions of laser pulses classified as canopy hits. In this study, height distributions were created from laser canopy heights (>2 m, see above) for each plot and stand inventoried in field. Separate distributions were created for the first and last pulse data, respectively, and percentiles for the canopy height for 10% (h10), 50% (h50), and 90% (h90) were computed. In addition, also the maximum (hmax) and mean values (hean) and the coefficient of variation (hcv) of the height distributions were computed. Furthermore, several measures of canopy density were derived. The range between the lowest laser canopy height (>2 m) and the maximum canopy height was divided into 10 fractions of equal length. Canopy densities were then computed as the proportions of laser hits above fraction # 0 (>2 m), 1, . . ., 9 to total number of pulses. The densities for fraction # 1 (d1), # 5 (d5), and # 9 (d9) were selected for further studies. To assess how flying altitude affected the laser-derived metrics, differences between corresponding metrics derived from high and low altitude were computed for each sample plot and forest stand. The standard deviations of the differences were also computed to assess the stability of the respective metrics. Separate comparisons between high and low altitude were carried out for first and last pulse data, respectively. To assess how forest type influenced on the effects of flying altitude on the laser-derived metrics, mean differences between high and low flying altitude of the investigated height and density-related metrics were compared for different strata by means of t-tests. Correspondingly, the variances of the differences between high and low altitude were compared for different strata by means of F tests.

In the comparisons of the nine laser-derived metrics for different flying altitudes within strata and in the comparison between strata, nine t-tests or F tests were accomplished simultaneously. In order to control the total Type I error, Bonferroni tests were applied (Miller, 1981). Thus, the level of significance for each of the nine tests was a/9. The effects of variable flying altitude on the estimation and prediction of biophysical stand properties as they would appear in an area with hilly terrain were assessed in a Monte Carlo simulation consisting of three steps in which the high and low-altitude laser data were combined according to a random procedure. In step 1, multiple regression analysis was used to create stratum-specific relationships between field measurements of the 133 sample plots and corresponding laser data. For each individual plot, a random number was generated from a uniform distribution to determine whether the high- or low-altitude laser data should be applied for that specific plot in the regression analysis. The estimation of regression models was based on the height- and density-related metrics derived from the first and last pulse height distributions as candidate explanatory variables. The use of such metrics to derive biophysical properties is in correspondence with previous research (e.g., Næsset, 1997a, 2002a, in press; Lefsky et al., 1999; Lim et al., 2003; Magnussen et al., 1999; Means et al., 1999, 2000; Nelson, 1997; Nelson et al., 1988, 1997). In the multiple regression analysis, multiplicative models were estimated as linear regressions in the logarithmic variables because such models were found to be suitable by others (Lim et al., 2003; Næsset, 2002a, in press; Næsset & Bjerknes, 2001; Næsset & Økland, 2002). The multiplicative model was formulated as b

b

b

b

b

b

b

b

b

b

b

b

b

b

b

b

b

3 5 6 7 8 9 10 1 2 4 Y ¼ b0 h10f h50f h90f h10l h50l h90l hmeanf hmeanl hmaxf hmaxl

b

 hcvf11 hcvl12 d1f13 d5f14 d9f15 d1l16 d5l17 d9l18

ð1Þ

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E. Næsset / Remote Sensing of Environment 91 (2004) 243–255

whereas the linear form used in the estimation was

and 90th percentiles of the mean differences and standard deviations, respectively, and the arithmetic mean value of the 10,000 mean differences and standard deviations. These values were compared with validation results obtained using either low-altitude data or high-altitude data for all training plots and test stands.

lnY ¼ lnb0 þ b1 lnh10f þ b2 lnh50f þ b3 lnh90f þ b4 lnh10l þ b5 lnh50l þ b6 lnh90l þ b7 lnhmeanf þ b8 lnhmeanl þ b9 lnhmaxf þ b10 lnhmaxl þ b11 lnhcvf þ b12 lnhcvl þ b13 lnd1f þ b14 lnd5f þ b15 lnd9f þ b16 lnd1l þ b17 lnd5l þ b18 lnd9l

3. Results ð2Þ 3.1. Height percentiles

where Y = field values of hL (m), G (m2 ha
1), or V (m3 ha
1); h10f, h50f, and h90f = percentiles of the first pulse laser canopy heights for 10%, 50%, and 90% (m); h10l, h50l, and h90l = percentiles of the last pulse laser canopy heights for 10%, 50%, and 90% (m); hmeanf and hmeanl = mean of the first and last pulse laser canopy heights (m); hmaxf and hmaxl = maximum of the first and last pulse laser canopy heights (m); hcvf and hcvl = coefficient of variation of the first and last pulse laser canopy heights (%); d1f, d5f, and d9f = canopy densities corresponding to the proportions of first pulse laser hits above fraction # 1, 5, and 9 to total number of first pulses; and d1l, d5l, and d9l = canopy densities corresponding to the proportions of last pulse laser hits above fraction # 1, 5, and 9 to total number of last pulses. Stepwise selection was performed to select variables to be included in these models. No predictor variable was left in the models with a partial F statistic with a significance level greater than 0.05. The standard least-squares method was used (Anon., 1989). In step 2, the estimated regression models were used to predict corresponding biophysical properties of the large test stands. This was done by first assigning high- or lowaltitude laser data to each individual stand according to the random process outlined above. All stands were then divided into regular grid cells with a cell size of 350 m2. Laser canopy height distributions were created for each cell from the assigned first and last pulse laser data, and the biophysical properties were predicted at cell level using the estimated stratum-specific equations and the derived laser metrics. Predicted values at stand level were computed as mean values of the individual cell estimates. In step 3, the differences between predicted values of the biophysical stand properties and ground-truth values were computed. The standard deviations of the differences were also estimated. The sequence of operations in steps 1 and 2 represents a complete procedure to inventory forest stands by laser scanning using field training plots. The entire sequence in steps 1 –3 was repeated 10,000 times to assess the effects of variable flying altitude on the inventory procedure. Thus, 10,000 estimates of the mean differences between predicted biophysical stand properties and ground-truth and corresponding estimates of the standard deviations of the differences were derived. The results of the 10,000 trials were presented by the fractiles corresponding to the 10th

First, differences between high- and low-flying altitude for the laser-derived canopy height and density metrics were computed for the 133 sample plots and the 56 test stands. For the first pulse data, none of the mean differences were found to be statistically significant. For the first pulse height distribution percentiles (h10, h50, and h90), the differences between high- and low-flying altitude ranged from
0.02 to 0.13 m (Tables 4 and 5). The differences were at the same level for plots as for large stands, and the differences were also of a similar magnitude for all the three investigated percentiles. The testing based on the stand material revealed that the differences across flying altitudes were of a similar magnitude for the three different forest types (strata I– III) (Table 6). The standard deviations for the differences of percentiles between flying altitudes ranged from 0.23 to 0.75 m for the sample plots (Table 4) and from 0.09 to 0.18 m for the stands (Table 5). None of the variances for the differences were found to be statistically significant ( p>0.05) when I made comparisons between forest types (Table 6). The degree of similarity between height percentiles of the first pulse data for highand low-flying altitude is illustrated for the test stands in Fig. 1. For the last pulse data, 6 of a total of 18 mean differences of percentiles between flying altitudes were found to be statistically significant. For the test stands, 5 of a total of 9 mean differences were greater than could be expected due to randomness. In all the percentile comparisons, the values of h10, h50, and h90 were larger in the high-altitude data than in the low-altitude data. The differences ranged from 0.04 to 0.52 m for the plots (Table 4) and from 0.03 to 0.50 m (Table 5) for the stands. For h10, the differences across flying altitudes differed significantly between mature forest dominated by pine (stratum II) and spruce (stratum III), respectively (Table 6). The standard deviations for the differences were in the range between 0.39 and 1.20 m for the sample plots (Table 4) and between 0.07 and 0.30 m for the test stands (Table 5). The variances for the differences of h10 differed significantly between the forest type dominated by mature pine (stratum II) and the forest types representing young and mature spruce (strata I and III) (Table 6). The comparison of high- and low-flying altitude for the last pulse data is displayed in Fig. 2.

E. Næsset / Remote Sensing of Environment 91 (2004) 243–255 Table 4 Differences (D) between high- and low-flying altitudes for laser-derived metrics of small sample plots and standard deviation (S.D.) for the differences for first and last pulse data, respectivelya Metricsb

D, first pulse Mean

D, last pulse S.D.

Young forest—stratum I (n = 53 sample plots) h10 (m)
0.01 NS 0.50 h50 (m) 0.01 NS 0.23 0.05 NS 0.31 h90 (m) hmax (m)
0.01 NS 0.86 hmean (m) 0.02 NS 0.17 hcv (%) 0.17 NS 1.77 0.15 NS 2.57 d1 (%) d5 (%) 0.85 NS 5.61 d9 (%) 0.37 NS 1.86

Mean

S.D.

0.31 NS 0.16 NS 0.09 NS
0.08 NS 0.20***
1.61* 1.41NS 2.02** 0.54 NS

1.09 0.40 0.40 0.86 0.32 3.55 3.80 3.90 1.68

Mature forest, poor site quality—stratum II (n = 34 sample plots) h10 (m) 0.06 NS 0.75 0.14 NS h50 (m)
0.02 NS 0.43 0.40 NS 0.01 NS 0.35 0.20 NS h90 (m) hmax (m)
0.20 NS 0.60
0.23 NS hmean (m)
0.01 NS 0.31 0.33* hcv (%)
0.05 NS 2.46
2.19 NS
0.47 NS 3.31 0.63 NS d1 (%) d5 (%)
0.08 NS 2.86 1.43* d9 (%) 0.74* 1.26 0.75*

0.85 1.11 0.44 0.67 0.57 4.68 2.98 2.47 1.32

Mature forest, good site quality—stratum III (n = 46 sample plots) h10 (m) 0.13 NS 0.59 0.52* h50 (m) 0.11 NS 0.39 0.23 NS 0.10 NS 0.31 0.04 NS h90 (m) hmax (m)
0.01 NS 0.75
0.03 NS hmean (m) 0.08 NS 0.23 0.32*** hcv (%)
0.19 NS 1.75
1.92** 0.30 NS 2.17 2.10** d1 (%) d5 (%) 0.88 NS 3.81 2.55*** d9 (%) 0.01 NS 2.13 0.05 NS

1.20 0.69 0.39 0.73 0.47 3.38 3.69 3.62 1.59

a

Level of significance (Bonferroni test, a/9): NS = not significant (>0.05). *< 0.05; **< 0.01; ***< 0.001. b h10, h50, and h90 = percentiles of the laser canopy heights for 10%, 50%, and 90%; hmax = maximum laser canopy height; hmean = arithmetic mean laser canopy height; hcv = coefficient of variation of laser canopy heights; d1, d5, and d9 = canopy densities corresponding to the proportions of laser hits above fraction # 1, 5, and 9, respectively, to total number of pulses (see text).

3.2. Height maximum, mean, and variability The maximum values of first as well as the last pulse canopy height distributions (hmax) did not differ significantly between the flying altitudes for any of the forest types. The differences did not differ between forest types either (Table 6). The mean differences between flying altitudes ranged from
0.20 to
0.01 m for first pulse data and from
0.23 to
0.02 m for the last pulse data (Tables 4 and 5). The standard deviations ranged between 0.60 and 0.86 m for the plots (Table 4) and between 0.33 and 0.83 m for the test stands. For the test stands, the standard deviations for the differences were greater for the maximum values than for the percentiles. Both the first and last pulse data indicated that the variances for the differences for the

249

test stands were significantly smaller in the pine-dominated forest (stratum II) than in the spruce-dominated forest (stratum III) (Table 6). The mean height values of the first as well as the last pulse data (hmean) showed similar patterns as did the height percentiles. For the first pulse data, the mean differences between high- and low-flying altitude ranged between
0.02 and 0.08 m for the plots as well as the test stands, but none of these mean differences were statistically significant ( p>0.05). For the last pulse data, however, all the comparisons indicated that the mean values of the highaltitude data were significantly different and larger than the low-altitude data ( p < 0.05). The differences ranged from 0.20 to 0.37 m (Tables 4 and 5). The differences across

Table 5 Differences (D) between high- and low-flying altitudes for laser-derived metrics of forest stands and standard deviation (S.D.) for the differences for first and last pulse data, respectivelya Metricsb

D, first pulse Mean

D, last pulse S.D.

Mean

S.D.

0.18 NS 0.29*** 0.03 NS
0.03 NS 0.21***
1.74*** 1.84*** 1.35 NS 0.06 NS

0.30 0.24 0.16 0.63 0.16 0.79 1.43 2.34 0.13

Mature forest, poor site quality—stratum II (n = 17 stands) h10 (m) 0.01 NS 0.13 0.07* h50 (m)
0.01 NS 0.13 0.47***
0.02 NS 0.09 0.08 NS h90 (m) hmax (m)
0.04 NS 0.33
0.08 NS hmean (m)
0.02 NS 0.09 0.25***
0.01 NS 0.47
1.59*** hcv (%) d1 (%) 0.13 NS 0.64 1.36*** d5 (%) 0.14 NS 1.05 1.20*** d9 (%)
0.02 NS 0.13
0.01 NS

0.07 0.19 0.13 0.33 0.13 0.72 0.73 0.84 0.11

Mature forest, good site quality—stratum III (n = 17 stands) h10 (m) 0.07 NS 0.16 0.29*** h50 (m) 0.05 NS 0.15 0.50*** 0.05 NS 0.16 0.10 NS h90 (m) hmax (m)
0.01 NS 0.80
0.02 NS hmean (m) 0.06 NS 0.13 0.37*** hcv (%)
0.24 NS 0.42
2.16*** 0.19 NS 0.94 1.75*** d1 (%) d5 (%) 0.52 NS 2.44 1.90** d9 (%) 0.08 NS 0.36 0.06 NS

0.23 0.23 0.19 0.83 0.14 0.65 1.26 1.81 0.28

Young forest—stratum I (n = 22 stands) h10 (m) 0.06 NS 0.13 h50 (m) 0.05 NS 0.17
0.01 NS 0.18 h90 (m) hmax (m)
0.12 NS 0.56 hmean (m) 0.03 NS 0.14
0.21 NS 0.49 hcv (%) d1 (%) 0.43 NS 1.04 d5 (%) 0.96 NS 3.01 d9 (%) 0.08 NS 0.18

a Level of significance (Bonferroni test, a/9): NS = not significant (>0.05). *< 0.05; **< 0.01; ***< 0.001. b h10, h50, and h90 = percentiles of the laser canopy heights for 10%, 50%, and 90%; hmax = maximum laser canopy height; hmean = arithmetic mean laser canopy height; hcv = coefficient of variation of laser canopy heights; d1, d5, and d9 = canopy densities corresponding to the proportions of laser hits above fraction # 1, 5, and 9, respectively, to total number of pulses (see text).

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Table 6 ¯ ) and standard Comparisons between strata of mean differences (D deviations for the differences (S.D.) between laser-derived metrics of forest stands from high- and low-flying altitudesa,b,c Metrics

¯I
D ¯ II D

¯I
D ¯ III D

¯ II
D ¯ III D

S.D.I
S.D.IId

S.D.I
S.D.IIId

S.D.II
S.D.IIId

First pulse h10 h50 h90 hmax hmean hcv d1 d5 d9

data NS NS NS NS NS NS NS NS NS

NS NS NS NS NS NS NS NS NS

NS NS NS NS NS NS NS NS NS

NS NS NS NS NS NS NS *** NS

NS NS NS NS NS NS NS NS *

NS NS NS * NS NS NS * ***

Last pulse h10 h50 h90 hmax hmean hcv d1 d5 d9

data NS NS NS NS NS NS NS NS NS

NS NS NS NS * NS NS NS NS

** NS NS NS NS NS NS NS NS

*** NS NS NS NS NS NS *** NS

NS NS NS NS NS NS NS NS *

*** NS NS ** NS NS NS * **

a

Roman subscript refers to stratum. Level of significance (Bonferroni test, a/9): NS = not significant (>0.05). *< 0.05; **< 0.01; ***< 0.001. c h10, h50, and h90 = percentiles of the laser canopy heights for 10%, 50%, and 90%; hmax = maximum laser canopy height; hmean = arithmetic mean laser canopy height; hcv = coefficient of variation of laser canopy heights; d1, d5, and d9 = canopy densities corresponding to the proportions of laser hits above fraction # 1, 5, and 9, respectively, to total number of pulses (see text). d Variance comparison by F tests. b

flying altitudes differed significantly between young (stratum I) and mature (stratum III) spruce forest (Table 6). The standard deviations for the differences in mean values between flying altitudes ranged between 0.32 and 0.57 m for the sample plots (Table 4) and between 0.13 and 0.16 m for the test stands (Table 5). These standard deviations tended to be smaller than corresponding standard deviations for height percentiles and maximum values, and they did not seem to differ between forest types. The variability of the first pulse canopy height distributions expressed by the coefficient of variation (hcv) was hardly affected by flying altitude. The mean difference between high- and low-flying altitudes ranged from
0.19% to 0.17% for the sample plots (Table 4) and from
0.24% to
0.01% for the test stands (Table 5). These differences did not differ significantly between forest types (Table 6). For the last pulse data, however, the variability of the height distributions derived from the low-altitude data was significantly different and larger ( p < 0.05) than the corresponding variability of the high-altitude data in five of six cases. The mean differences in hcv between high and low altitude ranged between
2.19% and
1.59% (Tables 4 and 5). The standard deviations for the differences between

flying altitudes were 3.38 –4.68% and 0.65– 0.79% for the sample plots and test stands, respectively. 3.3. Canopy density For the first pulse canopy densities (d1, d5, and d9), the mean differences between high- and low-flying altitude ranged from
0.47% to 0.88% for the sample plots (Table 4) and from
0.02% to 0.96% for the test stands (Table 5). Only 1 of these 18 mean differences was greater than what could be expected due to randomness. For the last pulse data, the estimated canopy densities were significantly larger for the high-altitude data for a majority of the comparisons. The mean differences in canopy density between flying altitudes ranged from
0.01% to 2.55%. However, the differences in canopy density across flying altitudes did not differ significantly between forest types in any of the 18 comparisons (Table 6). The standard deviations of the differences in canopy density between flying altitudes ranged from 1.26% to 5.61% for the sample plots and from 0.11% to 3.01% for the test stands. The variance for the differences across flying altitudes for each of the investigated densities seemed to be significantly smaller for stratum II than for the other strata in many of the comparisons (Table 6), which means that the variability in canopy density derived from first as well as last pulse data for the pine-dominated forest was less affected by alterations in flying altitude than the other forest types. 3.4. Simulations To assess the effects of variable flying altitude over a forest area on the accuracy of biophysical properties predicted at stand level following the practical inventory procedure proposed by Næsset and Bjerknes (2001) and Næsset (2002a,b), the inventory procedure was repeated 10,000 times using random combinations of different flying altitudes for each individual sample plot and forest stand. The average mean differences between predicted mean height (hL) and ground-truth mean height over the 10,000 trials ranged from 0.58 to 0.83 m in the three investigated strata (Table 8). These average mean differences were compared with the corresponding mean differences using only low-altitude data or high-altitude data. The mean differences for high- and low-altitude data ranged from 0.41 to 0.80 m. Correspondingly, the average over the 10,000 trials of the standard deviations for the differences between predicted mean heights and ground-truth values were 0.83, 0.40, and 0.99 m in strata I –III, respectively, whereas the standard deviations using only high- or lowaltitude data were 0.79 – 0.86, 0.35 –0.41, and 0.87 –1.11 m in strata I –III, respectively. The regression models that were selected when using only high- or low-altitude data are displayed in Table 7. None of the models comprised more than three explanatory variables and the coefficient of

E. Næsset / Remote Sensing of Environment 91 (2004) 243–255

251

Fig. 1. Laser-derived first pulse canopy height and density metrics of forest stands from low-flying altitude plotted against corresponding metrics from highflying altitude (n = 56 stands).

determination (R2) ranged from 0.75 to 0.94 for the three examined biophysical response variables. Similar patterns were found for basal area ( G) and volume (V) as for hL when the predicted values of the 10,000 trials were compared with values obtained using only high- or low-altitude data. For basal area, the average mean value of the trials ranged from
4.34 to
0.71 m2 ha
1, whereas the corresponding values using high- or lowaltitude data were from
5.16 to
0.01 m2 ha
1 (Table 8). Average standard deviations ranged from 2.40 to 3.26 m2 ha
1, whereas the standard deviations without combining

data from different flying altitudes ranged between 2.25 and 3.52 m2 ha
1. For V, average mean values of the differences and mean values of the differences for the two specific flying altitudes ranged from
18.8 to 1.9 m3 ha
1 and from
32.4 to 26.5 m3 ha
1, respectively. Average standard deviations and standard deviations for high or low altitude ranged between 20.2 and 31.7 m3 ha
1 and between 20.2 to 32.8 m3 ha
1, respectively. The 10th and 90th percentiles of the 10,000 estimated mean differences and standard deviations for hL, G, and V indicated small differences between most of the 10,000

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E. Næsset / Remote Sensing of Environment 91 (2004) 243–255

Fig. 2. Laser-derived last pulse canopy height and density metrics of forest stands from low-flying altitude plotted against corresponding metrics from highflying altitude (n = 56 stands).

trials (Table 8). Especially the standard deviations seemed to be robust against alterations in flying altitude.

4. Discussion and conclusions The major findings of this study indicate that: (1) First-return pulse measurements of height (e.g., h10, h50, and h90), height variability (e.g., hcv), and canopy density (e.g., d1, d5, and d9) are relatively stable

regardless of flight altitude/spot size, at least when spot size varies in the 16 – 26 cm range, i.e., by a factor of up to about 60%. (2) Last-return pulse measurements are significantly affected by changing spot size. Increasing spot size tends to increase the values of canopy height and canopy density derived from laser data and reduce height variability. (3) Stand type, i.e., spruce versus pine, makes a difference. Airborne laser measurements of canopy characteristics are more robust in stands with rounded crowns, e.g., pine, than in stands with conically shaped crowns, e.g., spruce.

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253

Table 7 Selected models for biophysical properties (response variables) from stepwise multiple regression analysis of the sample plots using laser-derived metrics from low- and high-flying altitudes as explanatory variables Response variablea

Low altitude

High altitude

Expl. variablesb

R2

RMSE

Expl. variablesb

R2

RMSE

Young forest—stratum I (n = 53 plots) ln hL ln h90f, ln hmeanl ln G ln h50f, ln d1f ln V ln h50f, ln d1f, ln d9f

0.90 0.90 0.94

0.08 0.11 0.14

ln h90l, ln hmeanl ln hmeanf, ln d1f ln hmeanf, ln d5l

0.89 0.90 0.94

0.08 0.12 0.13

Mature forest, poor site quality—stratum II (n = 34 plots) ln hL ln h90l ln G ln h50f, ln h10l, ln d1f ln V ln h10l, ln hmeanf, ln d1f

0.76 0.75 0.82

0.08 0.15 0.16

ln h90f ln h10f, ln h50f, ln d1f ln h10l, ln hmeanf, ln d1l

0.75 0.75 0.83

0.08 0.15 0.16

Mature forest, good site quality—stratum III (n = 46 plots) ln hL ln h90f, ln hcvf, ln d5l ln G ln hmaxl, ln d5f ln V ln hmeanf, ln d1f, ln d5l

0.86 0.84 0.91

0.06 0.12 0.13

ln h90f, ln h10l ln h90l, ln d1f, ln d5f ln hmeanf, ln d1f, ln d5l

0.82 0.85 0.91

0.07 0.12 0.13

hL = Lorey’s mean height (m), G = basal area (m2 ha
1), V = volume (m3 ha
1). h10f, h50f, and h90f = percentiles of the first pulse laser canopy heights for 10%, 50%, and 90% (m); h10l and h90l = percentiles of the last pulse laser canopy heights for 10% and 90% (m); hmaxl = maximum value of the last pulse laser canopy heights (m); hcvf = coefficient of variation of the first pulse laser canopy heights (%); hmeanf and hmeanl = arithmetic mean of first or last pulse laser canopy heights, respectively (m); d1f, d5f, and d9f = canopy densities corresponding to the proportions of first pulse laser hits above fraction # 1, 5, and 9, respectively, to total number of first pulses (see text); and d1l and d5l = canopy densities corresponding to the proportions of last pulse laser hits above fraction # 1 and 5, respectively, to total number of last pulses. a

b

(4) Biophysical stand characteristics derived from prediction equations—e.g., Lorey’s mean height, basal area, and volume—are not significantly affected by changing flight altitude/spot size. This finding is true even when the predictive equations include last-return laser measurements that are significantly affected by changing spot size.

Effects of beam divergence, and thus footprint size, on tree height estimation were analysed in some of the early studies of application of airborne systems in forestry. Nilsson (1996) did not find any significant effects of beam divergence on the height estimates obtained over a pinedominated test site even though he altered the divergence by a factor of up to 4. Some of the results obtained by Aldred

Table 8 Testing of the selected regression models for biophysical properties derived from high- and low-altitude laser data (Table 7) against ground-truth data from the test stands, and test results from the simulation study of estimating regression equations and predicting biophysical properties of the test stands by mixing laser data from high and low altitude by a random procedure using 10,000 iterationsa Response variableb

Low altitudec ¯ D

High altitudec

Simulation resultsd

S.D.

¯ D

S.D.

¯ jp10 jD

¯ jp90 jD

¯ Mean D

Young forest—stratum I (n = 22 stands) hL (m) 0.49*
2.86*** G (m2 ha
1) V(m3 ha
1) 26.5***

0.86 2.30 30.8

0.48**
2.66***
32.4***

0.79 2.49 29.0

0.42 2.48 4.6

1.09 5.16 34.4

Mature forest, poor site quality—stratum hL (m) 0.49*** G (m2 ha
1)
0.18 NS V (m3 ha
1) 3.7 NS

II (n = 17 stands) 0.41 0.59*** 2.25
0.01 NS 20.2 4.0 NS

0.35 2.32 20.3

0.40 0.05 2.5

Mature forest, good site quality—stratum hL (m) 0.41 NS G (m2 ha
1)
4.68*** V (m3 ha
1)
31.1**

III (n = 17 stands) 1.11 0.80** 3.52
5.16*** 32.8
14.2 NS

0.87 3.01 30.0

0.32 2.57 11.0

a

S.D.p10

S.D.p90

Mean S.D.

0.75
3.34 1.5

0.69 2.36 25.5

1.17 3.30 37.5

0.83 2.73 30.7

0.64 3.16 6.5

0.58
0.71 1.9

0.33 2.24 19.2

0.42 2.72 21.5

0.40 2.40 20.2

1.14 5.19 29.8

0.83
4.34
18.8

0.88 2.82 29.9

1.14 3.52 33.7

0.99 3.26 31.7

Level of significance: NS = not significant (>0.05). *< 0.05; **< 0.01; ***< 0.001. hL = Lorey’s mean height, G = basal area, V = volume. c ¯ D = mean difference between values predicted by the regression models and ground-truth data, S.D. = standard deviation for the differences. d ¯ ¯ | p90 = the fractiles corresponding to the 10th and 90th percentiles of the absolute value of the mean differences between predicted values | D | p10 and | D ¯ = the arithmetic mean value of the 10,000 mean differences (D ¯ ), S.Dp10 and S.Dp90 = the fractiles and ground-truth data for the 10,000 iterations, Mean D corresponding to the 10th and 90th percentiles of the standard deviations for the differences for the 10,000 iterations, Mean S.D. = the arithmetic mean value of the 10,000 standard deviations (S.D.). b

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and Bonnor (1985) indicated increased height estimates as the beam divergence increased, especially in deciduous forest, but this was not a general trend. However, typical for these early studies were that full waveform systems were used, and the canopy height was estimated as the difference between a certain threshold of the first peak and the last peak. Nilsson (1996) used a threshold value of 10%, whereas Aldred and Bonnor (1985) tested threshold values such as 20% and 50%. At least, Nilsson’s algorithm is probably quite close to what is considered to be the first pulse reflection of current commercial scanning systems. Thus, the results obtained for the first pulse data in the present study support what Nilsson (1996) found a decade ago. Furthermore, none of the previous studies can be compared directly with the last-pulse data analysed in the present experiment. The variability between flying altitudes for the canopy height and density metrics seemed to be of a similar magnitude for the first and last pulse data. For the height percentiles estimated for the large test stands, the standard deviations for the differences between flying altitudes was generally low, with values around 0.1 –0.3 m (Table 5). Although there might exist a systematic difference in laserderived canopy measures between repeated flight overpasses at different altitudes, the small standard deviations indicate a high degree of stability and repeatability of the investigated laser metrics. The second objective of this study was to assess how variable flying altitude may affect stand estimates of three important biophysical stand properties essential in forest planning, namely, mean height, stand basal area, and stand volume. The regression models estimated for each flying altitude separately indicated that the laser-derived explanatory variables selected in the final models were combinations of first and last pulse metrics (Table 7). A similar mixture of first and last pulse metrics was found to provide the ‘‘best’’ models in a study of six biophysical properties where variations in flying altitude ranged from around 430 to 960 m (Næsset, in press), which represents an even larger variation than in the present study. The precision of hL, G, and V predicted in the present study by combining laser data from different flying altitudes was also in accordance with the precision found in the same test field using laser data acquired from a stable flying altitude of about 700 m above ground 2 years earlier (Næsset, 2002a). The stability of the precision is illustrated by the 10th and 90th percentiles of the 10,000 estimated standard deviations, which are very close to the average values. The insignificant effect on the predicted biophysical properties of combining data from different altitudes is supported by results found by Næsset (in press). In a test field with large topographic variability, it was assessed how beam range variations affected the residuals in the regressions derived for biophysical properties. A total of 18 different models were estimated for different forest types, and beam range was found to be significantly correlated ( p < 0.05) with the residuals in only 1 of the 18 cases.

To conclude, the present study has indicated that flying altitude and thus footprint diameter may affect canopy height and density metrics derived from laser data. The effects are more pronounced for the last pulse reflection than for the first pulse reflection. If the sample of pulses is large, i.e., if the pulse density is high or the target object, such as a forest stand, has a certain size, the values of the laserderived metrics are stable from one flight overpass to another. Although the laser-derived metrics to some extent are affected by flying altitude, the precision of the applied two-stage procedure to inventory biophysical properties of forest stands are hardly affected by moderate altitude variations. In this study, the highest flying altitude was approximately 60% above the lowest altitude. As the repetition frequency of commercial small-footprint scanning lasers increases, there is an interest in elevating the platform altitude to provide the same sampling density on the ground with reduced flight time and thus reduced costs. The highest altitude considered in this study was about 850 m above ground, and there were no evident differences between the results revealed for the two flying altitudes. Thus, assuming a linear dependency of flight altitude, at least for moderate altitude variations, the results of this study may indicate that the flying altitude for forest inventories can be increased by, for example, 60% up to 1300– 1400 m above ground without any serious effects on the estimated stand properties.

Acknowledgements This research has been funded by the Research Council of Norway (research project no. 133303/110), the Forest Trust Fund (the Norwegian Ministry of Agriculture) (research project no. 150551/110), and the Borregaard Research Fund. Thanks to BN Mapping for collection and processing of the airborne laser scanner data. I would also like to thank the three anonymous reviewers for their constructive criticism.

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