A pseudo-waveform technique to assess forest structure using discrete

Author's personal copy Remote Sensing of Environment 115 (2011) 824–835

Contents lists available at ScienceDirect

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

A pseudo-waveform technique to assess forest structure using discrete lidar data Jordan D. Muss ⁎, David J. Mladenoff, Philip A. Townsend Department of Forest and Wildlife Ecology, University of Wisconsin-Madison, 1630 Linen Dr., Madison, WI, 53706, USA

a r t i c l e

i n f o

Article history: Received 23 June 2010 Received in revised form 23 October 2010 Accepted 7 November 2010 Available online 23 December 2010 Keywords: Lidar Airborne laser Intensity Forest structure Tree height Crown base height Canopy coverage

a b s t r a c t The use of airborne laser scanning systems (lidar) to describe forest structure has increased dramatically since height profiling experiments nearly 30 years ago. The analyses in most studies employ a suite of frequencybased metrics calculated from the lidar height data, which are systematically eliminated from a full model using stepwise multiple linear regression. The resulting models often include highly correlated predictors with little physical justification for model formulation. We propose a method to aggregate discrete lidar height and intensity measurements into larger footprints to create “pseudo-waves”. Specifically, the returns are first sorted into height bins, sliced into narrow discrete elements, and finally smoothed using a spline function. The resulting “pseudo-waves” have many of the same characteristics of traditional waveform lidar data. We compared our method to a traditional frequency-based method to estimate tree height, canopy structure, stem density, and stand biomass in coniferous and deciduous stands in northern Wisconsin (USA). We found that the pseudo-wave approach had strong correlations for nearly all tree measurements including height (cross validated adjusted R2 (R2cv) = 0.82, RMSEcv = 2.09 m), mean stem diameter (R2cv = 0.64, RMSEcv = 6.15 cm), total aboveground biomass (R2cv = 0.74, RMSEcv = 74.03 kg ha− 1), and canopy coverage (R2cv = 0.79, RMSEcv = 5%). Moreover, the type of wave (derived from height and intensity or from height alone) had little effect on model formulation and fit. When wave-based and frequency-based models were compared, fit and mean square error were comparable, leading us to conclude that the pseudo-wave approach is a viable alternative because it has 1) an increased breadth of available metrics; 2) the potential to establish new meaningful metrics that capture unique patterns within the waves; 3) the ability to explain metric selection based on the physical structure of forests; and 4) lower correlation among independent variables. © 2010 Elsevier Inc. All rights reserved.

1. Introduction The use of airborne laser scanning systems (lidar) to describe forest structure has increased dramatically since height profiling experiments nearly 30 years ago (Nelson et al., 1984). While studies continue to use lidar to estimate canopy height (Andersen et al., 2006; Hopkinson et al., 2006, 2008; Næsset, 2004; Næsset & Bjerknes, 2001; Nayegandhi et al., 2006), others focus on tree diameter at breast height (Gobakken & Næsset, 2004; Næsset, 2004), stand basal area (Nelson et al., 1997), aboveground biomass (Bortolot, 2006; Bortolot & Wynne, 2005), stand volume (Næsset, 2004; Nelson et al., 1997; Wallerman & Holmgren, 2007), stem density (Bortolot, 2006; Gobakken & Næsset, 2004; Wallerman & Holmgren, 2007), growth (Hopkinson et al., 2008; Véga & St-Onge, 2008; Yu et al., 2006), and habitat (Goetz et al., 2007; Hinsley et al., 2006). In general, strong relationships have been shown to exist between lidar data and forest structural descriptor variables, but there are caveats. First, many of these studies have been conducted in a narrow range of fairly homogeneous conifer stands, including Norway spruce (Picea

⁎ Corresponding author. Tel.: +1 608 265 6321; fax: +1 608 262 9922. E-mail address: [email protected] (J.D. Muss). 0034-4257/$ – see front matter © 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2010.11.008

abies), Scots pine (Pinus sylvestris), Douglas-fir (Pseudotsuga menziesii), Sitka spruce (Picea sitchensis), and ponderosa pine (Pinus ponderosa) (for example Andersen et al., 2006; Donoghue et al., 2007; Gobakken & Næsset, 2004; Lefsky et al., 2005). While these studies have found similar relationships between dependent and independent variables, each model must still be calibrated with local field data; consequently, reliable models that can be used independent of location or forest type are lacking. Another drawback of these forest-lidar studies is their use of a frequency-based approach, in which lidar data are binned into height quantiles to create predictor variables that are used in linear models. These quantile-based predictors make it difficult to formulate a priori hypotheses regarding the significance of model variables, or a posteriori explanations for the derivation of these models that are based on the physical structure of the forest. Moreover, models that use multiple height quantiles could be called into question because quantile-based metrics can be highly correlated, especially if the data have a symmetric distribution (Breidt, 2004; Groeneveld, 1998). Finally, frequency-based analyses of discrete lidar data often ignore a potentially significant element of data – the intensity of the return – that, if used, could enhance model robustness. The main argument against including intensity in data analyses has been the proprietary methods that commercial sensors use to report return

Author's personal copy J.D. Muss et al. / Remote Sensing of Environment 115 (2011) 824–835

intensity. These methods obfuscate the power of the original pulse, making it impossible to directly compare two returns. However a known set of factors influence return intensity, including the reflectivity of the target and the amount of the pulse that is incident on the target (Baltsavias, 1999; Lim et al., 2003), so it may be possible to make some inferences about the reflecting bodies using both the position of the return and its relative intensity. Recently, it has been suggested that intensity can be used to estimate forest structural characteristics (Lim et al., 2003; Pesonen et al., 2008), differentiate between dead and live trees (Kim et al., 2009), identify basic land cover types (Antonarakis et al., 2008; Reutebuch et al., 2005), or classify forests by species (Donoghue et al., 2007; Moffiet et al., 2005; Ørka et al., 2009). Lim et al. (2003) proposed that intensity could be used to filter ground and canopy surface returns from within canopy returns. They found that the inclusion of return intensity improved estimates of stand basal area, wood volume, and biomass, but it was not possible to explain this phenomenon without further knowledge about the factors responsible for return intensity. Similarly, Pesonen et al. (2008), found that intensity could be used to improve estimates of stand coarse woody debris volume, but they could not offer physical explanations for this phenomenon. Intensity has also been used to aid in the classification of land cover types such as water, bare ground, gravel river beds, and short herbaceous vegetation (Antonarakis et al., 2008). However, the results have been inconsistent when used to differentiate among tree species, with lack of radiometric calibration cited as the most likely cause (Moffiet et al., 2005; Ørka et al., 2009). While it would be ideal to have radiometrically calibrated intensity data, it has been demonstrated that uncalibrated data can be used to discriminate between live and dead standing biomass due to the spectral characteristics of foliage and wood in the near-infrared wavelengths commonly used by lidar systems (Kim et al., 2009). Kim et al. (2009) used wave-like density distributions, which may have reduced the variability inherent to uncalibrated intensity data that could be problematic to a more traditional frequency-based approach. In general, the resulting distributions were bimodal, with the low peaks correlating to standing dead trees without foliage and the high peaks to live trees. These were not the first simulated waveforms (or pseudo-waves) from discrete lidar data; Lovell et al. (2003) introduced the idea by fitting Weibull functions to the height and intensity of discrete lidar returns. Their results demonstrated that pseudo-waveforms could be used to approximate canopy profiles that were less likely to miss treetops or to be dominated by single tall trees. However, the tworeturn data that they used tended to generate exaggerated bimodal pseudo-waves that missed much of the internal canopy structure. More recently, frequency-based pseudo-waves have been used to estimate the leaf area of cottonwood trees using simple metrics that included maximum height of the wave and the height of its median energy (Farid et al., 2008). Meanwhile, intensity-based pseudo-waves have been created within pre-determined tree boundaries to detect canopy profiles (Popescu & Zhao, 2008). While these studies suggest great potential for the use of pseudowaves derived from discrete lidar data in forest analyses, it should be noted that the discrete nature of the source data prevents a complete recreation of continuous waveforms. Despite this, we suggest that true waveform reconstruction may not be mandatory to exploit pseudo-waves. Moreover, a set of wave-based metrics may prove superior to those traditionally used in discrete lidar analyses. Mindful of this, the goals of this study are: 1) to introduce a method to create pseudo-waveforms from discrete lidar data using a spline function to smooth gaps between measurements; 2) explore the differences between pseudo-waves generated from height frequency distributions and those created using total intensity by height; 3) introduce new metrics that are based on the physical characteristics of the wave rather than frequency-based statistics; 4) test and compare the

825

effectiveness of models created using pseudo-waves and wave-based metrics with similar models created using frequency-based metrics to derive forest physical characteristics. 2. Methods 2.1. Study area We conducted the study on the Bayfield Peninsula in northwestern Wisconsin, USA. (46°50′W, 91°10′N, Fig. 1). The Peninsula has rolling topography of glacial origin, largely outwash sands, that ranges in elevation from 182 m at the shores of Lake Superior to 433 m. The forests are dominated by early successional species including aspen (Populus spp.), jack pine (Pinus banksiana), and red maple (Acer rubrum), with sugar maple (A. saccharum) on heavier soils. Red pine (P. resinosa) plantations are common, and remnant pockets of white pine (P. strobus), white spruce (Picea glauca), hemlock (Tsuga canadensis), and northern white cedar (Thuja occidentalis) occur (Rhemtulla et al., 2009). 2.2. Field-based data We measured stands from nine forest types typical of the study area: aspen, oak (Quercus rubra and Q. ellipsoidalis), maple (red and sugar), red pine, white pine, white spruce, balsam fir (Abies balsamea), hemlock, and cedar. These represent both broad-leaved deciduous and coniferous species found in the Upper Midwest that have crown structures ranging from sparse/open (young aspen) to heavy/dense (mature hemlock). Five replicate stands were sampled for aspen, oak, and maple; four for red pine; three each for white pine and hemlock; and two each for spruce, fir, and cedar. Stands were sampled in the field during the summer of 2006 using variablesized plots with no fixed boundaries (Grosenbaugh, 1952; Townsend, 2002). This design varied sampling intensity according to stand density and tree basal area such that stands with larger and fewer trees per hectare had larger plots than younger, denser stands. Each stand had five replicate sub-plots arranged in a cruciform pattern, with centers spaced approximately 30 m apart. There were, however, four stands with fewer (at least 3) sub-plots due to stand size and configuration. In total, 148 sub-plots were sampled across 31 stands, all of which had level terrain. The location of the center of each sub-plot was recorded using a Trimble® Pathfinder® Pro-XRS GPS, with horizontal positional accuracy of 0.5 m after differential correction. Using a tenfactor cruising prism, live trees were tallied from the center of each sub-plot. They were then tagged with numbered aluminum tags, and their position relative to the plot center was measured using a Leica Disto-A5™ laser range finder and a Suunto compass. We also recorded the species and diameter at breast height (DBH; 1.4 m above the ground) for each tree. Additional measurements of canopy structure (Table 1) were made in all five sub-plots of nine stands (one of each forest type), and at the center sub-plot of each of the remaining 22 stands. These measurements included tree height (Top) and crown base height (CBH), which was identified as the lowest living branch that was beneath two consecutive live branches (Rautiainen & Stenberg, 2005). Hemispherical photos were acquired using a Nikon Coolpix 5000 digital camera with a 7.7 mm FC-E8 fisheye lens mounted on a tripod 1 m above the ground at each plot center during the summer of 2006. The photos were analyzed using GLA 2.0© (Frazer et al., 1999), and reports of sky and canopy pixels for the first 30° from nadir were used to estimate canopy coverage for each plot. Although this could cause canopy coverage to be overestimated by approximately 7% due to the planar projection of the spherical cap, we determined that this was an acceptable tradeoff for an increased sky view.

Author's personal copy 826

J.D. Muss et al. / Remote Sensing of Environment 115 (2011) 824–835

Fig. 1. Location of the study area in reference to the Upper Midwest, USA. The enlarged area is the Bayfield Peninsula, Wisconsin (46°50′W, 91°10′N). The bounding box delineates the area for which lidar data were collected, and the tree symbols are the plot locations where ground measurements of trees were made.

2.2.1. Plot-level and stand-level basal area and biomass estimates Basal area was estimated for each stand from field data (Grosenbaugh, 1952). We used DBH-based allometric equations to estimate total aboveground biomass and tree biomass components for each tree species encountered in our plots (Ter-Mikaelian & Korzukhin, 1997). Species-specific equations were chosen from studies that reported total aboveground, foliage, and branch biomass; had site climate and geophysical conditions that were comparable to ours; and included a range of tree diameters that overlapped our observations. 2.3. Lidar data Lidar data were collected by Ayres Associates (Madison, Wisconsin) on June 28, 2006, using a Leica ALS50 airborne laser scanner. Mean flight speed was 120 knots at a mean altitude of 2156 m AMSL. The scan rate of the laser was 32.00 Hz with a scan angle of ± 20°, but only data with scan angles between ± 15° were used. The scan rate, flight speed, and altitude produced a laser footprint of approximately 68 cm with a pulse spacing of approximately 2 m (~ 0.4 pulses m− 2). Scan rate and laser footprint are crucial because they control the laser pulse energy, which influences the depth that the laser penetrates into the canopy. A total of 21 flight lines were collected, resulting in 39% overlap, with up to four returns reported for each pulse. Return data included x-, y-, and z-coordinates and return intensity. The lidar contractor processed the raw data to remove spurious points and generate a digital elevation model (DEM) with 0.61 m spacing between points. These data were then transformed using the DEM and an inverse distance weighting method so that all lidar heights were reported relative to the ground rather than mean sea level. The transformed data were collected into 60 m radius footprints for each stand, seven different footprints (2, 5, 10, 15, 20, 25, and 30 m radii) for each sub-plot, and a variable radius footprint for each sub-plot. Footprint centers were established using the coordinates of sup-plot and stand centers. The large stand-level

footprints were used to make stand-wide estimates of basal area, mean stem diameter, and stem density, while the smaller footprints were analyzed to determine the smallest collection of returns that could be used to estimate forest structural variables at finer scales. The variable footprints were created using the maximum tree height within a plot and a 30° view angle. This method was chosen to mimic the view conditions of the hemispherical photos. For each footprint, we used the heights of individual returns to calculate common frequency-based metrics (Table 1) that included height bins by 10% and 25% quantiles, plus the 95th percentile (Q10,…,Q 95); the maximum return height (Htmax); mean return height (Htmean); and the standard deviation (HtSD); coefficient of variation (HtCV); measure of skewness (Htskew); and measure of kurtosis (Htkurtosis) of all return heights (Andersen et al., 2005; Hopkinson et al., 2006; Næsset, 2002). We estimated canopy coverage using canopy return ratio (CRR), which is the ratio of canopy reflections to total reflected lidar signal as described by Morsdorf et al. (2006), where canopy returns were defined as all returns greater than 1 m above the ground (the height of acquisition of the hemispherical photos). 2.3.1. Pseudo-wave creation Pseudo-waves were generated in four steps: 1) All returns within each footprint were collected and binned according to height above ground (2 m bins for this study); 2) Each bin was assigned a value that was either the sum of all intensities within that bin for intensity waves (IW) or the total number of returns in the bin (a height frequency distribution) for frequency waves (FW); 3) The pseudo-wave was then created using a cubic spline function. This function was chosen because it has the ability to capture multimodal distributions in contrast to more restrictive unimodal Gaussian or Weibull functions; 4) The final wave was normalized using its minimum and maximum intensity values.

Author's personal copy J.D. Muss et al. / Remote Sensing of Environment 115 (2011) 824–835

827

Table 1 Description of field-measured forest metrics, and frequency-based and wave-based metrics derived from the lidar data. Metric

Definitiona

Forest structure TopMax The highest point of the canopy within a subplot. TopMean The mean tree height measured within a subplot. CBH Crown base height. The average height of the lowest living branch for all trees within a subplot. CL Crown length. The length of the live crown, measured as the difference between the top of a tree and its lowest living branch. Crown length was averaged for all trees within a subplot. LCR Live crown ratio. The ratio of crown length to tree height. Live crown ratio was averaged for all trees within a subplot. Canopy The percentage of sky obscured by tree canopy. Coverage Lidar: Frequency-based Qxx Height of the xxth quantile as determined from all lidar returns within a footprint. Htmax The highest lidar return recorded within a footprint. Htmean The mean height of all lidar returns recorded within a footprint. HtSD The standard deviation of the heights of all lidar returns recorded within a footprint. HtCV The coefficient of variation of the heights of all lidar returns recorded within a footprint. Htskew The skewness of the heights of all lidar returns recorded within a footprint. Htkurtosis The kurtosis of the heights of all lidar returns recorded within a footprint. Lidar: Wave-based Max The highest point below which the intensity of a wave climbs. Mid The height of peak intensity of a wave. Min The height of the lowest wave minimum below Mid before intensity levels off or begins to increase again. AreaTotal The total area under the wave. AreaPeak The total area under the portion of the wave bounded by Min and Max. Mid:Max The ratio of Mid to Max. Min:Max The ratio of Min to Max. CRRXm The ratio of the sum of the intensities of all canopy returns to the total intensity of the pseudo wave, where X indicates the height used to differentiate canopy returns from non canopy returns. AWMHx The sum of the products of the area of each sub-peak within a wave and the height of Mid for that sub-peak, where x indicates whether AWMH is calculated for the complete wave, or just the peak bounded by Min and Max. AWMHx: The ratio of AWMHx to Max, where X indicates whether AWMH is Max calculated for the complete wave, or just the peak bounded by Min and Max. Complexityx The ratio of AWMHx to the number of peaks within a wave, where X indicates whether AWMH is calculated for the complete wave, or just the peak bounded by Min and Max. a

See text for more details.

Fig. 2. A pseudo-wave (solid line) and the height frequency distribution (2 m bins; gray bars) of discrete lidar height data for a maple plot. The dashed horizontal lines are drawn at locations of key inflection points; from the top are the first minima (Max), maximum amplitude (Mid), and second minimum (Min). Table 1 provides details on the metrics for pseudo-wave inflection points.

Canopy coverage estimates were examined using two versions of a variation on the CRR that was used with the point data. The wavebased CRR was defined as the ratio of the area of the portion of the pseudo-wave that represents the canopy to the total area of the wave. The two versions of the CRR differed by how the lower bound of the canopy was defined; we used the wave's minimum (CRRMin), and a 1 m base (CRR1m). The first method identified the base of canopy using the structure of the wave, and counted canopy returns above this point. The second method used the height of acquisition of the hemispherical photos (1 m) as the height above which canopy returns were counted. Our goals were twofold: first, to evaluate the use of pseudo-wave data versus point data, and second, to test two schemes to differentiate canopy from ground returns. Finally, we developed area-weighted mean height (AWMH) metrics to describe canopy complexity. The area-weighted metrics used the area of each peak to add weight to the height of that peak, and were calculated for the main peak and across the complete wave. The resulting values were then normalized by Max (AWMHwave:Max and AWMHcan:Max), total area of the wave (AWMHwave and AWMHcan), and the number of peaks within the wave (complexitywave and complexitypeak). The last two metrics describe the homogeneity (or complexity) of the wave.

Using this methodology, we created two sets of pseudo-waves for each footprint size for each plot — one using return height and the other using return height and intensity (Fig. 2).

2.4. Data analysis

2.3.2. Pseudo-wave metrics We developed a set of simple calculus-based metrics (Table 1) that used inflection points and area under the wave to analyze the pseudo-waves. The inflection points (points where the pseudo-wave undergoes major change) were identified using finite difference methods. We hypothesized that these metrics would be related to forest structural characteristics and estimates of biomass and stand basal area. We expected that the mean height of the canopy would be directly related to Max, crown base to Min, crown length to the difference of Max and Min, and live crown ratio to Min:Max. The wave area metrics were thought to be related to site biomass and canopy coverage.

Least-squares regression analyses were employed to relate subplot- and stand-level measurements of each biophysical variable to independent sets of frequency-based and wave-based lidar metrics. These metrics were analyzed for colinearity and were only included in a model if their correlation coefficient with any other variable in the model was less than 0.60. The only exception to this was the estimate for crown length, which by definition is the difference between the top of the tree and CBH, two highly correlated measures by nature. Logarithmic transformations were applied to the field measurements of basal area, stem density, and biomass, because these data had exponential distributions. All-subsets regression was performed using the leaps package (Lumley, 2009) in the R statistical language (R Development Core Team, 2009) to generate model

Author's personal copy 828

J.D. Muss et al. / Remote Sensing of Environment 115 (2011) 824–835

matrices from which we selected the most parsimonious models with the highest adjusted R2. These were vetted for covariance and significance of predictors (p values b 0.05) and validated using leave one out cross-validation. In this paper, we report final models with model coefficients estimated using the full data set, while adjusted R2 and root mean square error were calculated using the results of the cross-validation (R2cv and RMSEcv respectively). 3. Results We sampled plots ranging from young dense aspen stands with small stems to larger more mature hemlock stands (Table 2). Target species dominated the surveyed stands (in both stem density and basal area), with the red pine and spruce plantations nearly complete monocultures. 3.1. Footprint size For each set of models developed to estimate forest structural characteristics, we found that model fit improved dramatically as footprint radius increased between 2 and 10 m. There were only slight improvements at 15 m, but then model fit decreased as footprint size increased from 15 to 30 m (Fig. 3). Table 3 indicates that this pattern persisted for all canopy height models, which led us to use the 10 m plots for the biomass, basal area, and stem density analyses because they offered finer spatial resolution than 15 m plots without a significant reduction in model fit. 3.2. Variable correlations A high degree of correlation was observed among many of the frequency-based variables (Fig. 4). In particular, Q10 and Q 20 were the only quantiles that had correlation coefficients below 0.60 with any other height metric. Q10 met these criteria with Q 60 through Q 95, and Htmax, while Q20 only met this condition with Q 95 and Htmax. Coefficient of variation, skewness, and kurtosis were also highly correlated, probably because they all rely on sample mean and standard deviation. The pseudo-wave metrics had much less correlation among variables (Fig. 5). High correlation (r N 0.6) was typical of metrics that were subsets of another (i.e. AWMHwave:Max and AWMHcan:Max), but higher correlations were also observed among height-based metrics (e.g. Max and Mid). 3.3. Heights of canopy structures When we examined the wave-based models used to estimate the heights of canopy structural elements, we found no connection

between wave type and model formulation, fit, or RMSE (Table 4). Table 4 also indicates that the wave-based models performed comparably to or better than the frequency-based models in most cases, with the best results achieved by the models that estimated the mean canopy height (IW:R2cv = 0.80, RMSEcv = 1.88 m; IW:R2cv = 0.79, RMSEcv = 1.94 m). While many of the wave-based models (e.g. Topmax) included anticipated metrics, it is notable that the best model for estimating CBH was based on Max, Mid:Max, and CRR rather than the lower inflection point (Min), as was hypothesized (Table 4). The frequency- and wave-based models used to estimate crown length also presented some interesting results. We expected the crown length models to be a union of the models that estimate the top and bottom of the canopy, but this was not the case for either set of models. The frequency-based models that estimated the top and bottom of the canopy had most of their variation explained by Q 95, Q 80, and HtCV, but the crown length model dropped all of these variables and used a single lower quantile (Q70). A similar outcome was observed for the wave-based models, which replaced Max, Mid: Max, and CRRmin with Mid. Despite similarities on the information used by both sets of models, the wave-based models were much stronger (R2cv = 0.48, RMSEcv = 1.63 m) than their frequency-based counterpart (R2cv = 0.39, RMSEcv = 1.77 m). Although both the frequency-based and wave-based models for the canopy top, base, and crown length were statistically significant, neither method produced a significant model for live crown ratio. 3.4. Canopy coverage Of the three models tested for estimating canopy coverage, the wave-based model that compared the intensity peak to the total signal (CRRmin) had a moderate fit (R2 = 0.49 for 10 m footprints; Table 3). Using a 1 m cutoff, which approximated the height of acquisition of the hemispherical photos instead of the wave minimum, increased the fit substantially (R2cv = 0.79, RMSEcv = 0.05) and was comparable to that for the model based on frequency of returns (R2cv = 0.76, RMSEcv = 0.06). 3.5. Stem density and basal area Stem density and basal area had more variable results. In contrast to the models used to estimate heights of canopy structure, we observed differences between the IW and FW models that estimated mean stem diameter and total stand stem density. The IW model for stem diameter used Max, Mid:Max, and CRRmin (R2cv = 0.64, RMSEcv = 0.22) while the FW model achieved a comparable fit using only Max and AWMHcanoy: Max. In comparison, the IW and FW models for stem density had nearly identical structure, but the IW model outperformed the FW model (IW: R2cv = 0.63, RMSEcv = 0.34; FW: R2cv = 0.56, RMSEcv = 0.37). Despite

Table 2 Stand structure from data collected during the summer of 2006. Biomass is estimated using DBH and formulae in Ter-Mikaelian and Korzukhin (1997). Numbers in parentheses are standard error. Forest type

Field measurements Stem density (ha

Fir Maple Spruce Red pine White pine Aspen Oak Hemlock Cedar a b

Stem density. Basal area.

−1

2002 744 1128 665 789 2404 1031 679 2164

Biomass estimates Mean height

Mean DBH

Target (%) a

Mean BA b

−1

(2.5) (1.5) (3.2) (2.4) (2.2) (1.4) (1.4) (2.8) (2.7)

)

(m)

(cm)

SD

BA

(m ha

(269) (77) (373) (102) (91) (303) (81) (55) (214)

14.1 (0.4) 21.9 (0.4) 14.0 (0.5) 22.2 (0.3) 20.2 (0.4) 13.0 (0.5) 21.5 (0.4) 22.0(0.3) 15.7 (0.4)

19.5 29.9 22.7 30.3 32.1 13.9 27.9 39.2 24.7

56 64 91 88 63 72 63 75 64

50 56 96 89 67 70 70 79 50

32.6 29.6 25.9 30.7 34.4 20.4 34.3 52.4 59.1

(0.4) (0.4) (0.5) (0.3) (0.7) (0.5) (0.5) (0.6) (0.8)

Total

2

)

Branch −1

(Mg ha 59.6 166.5 72.9 110.0 128.4 25.5 193.0 286.7 153.7

)

(5.2) (12.1) (19.3) (9.8) (10.0) (5.6) (13.2) (14.3) (22.6)

(Mg ha

Foliage −1

6.6 (1.1) 37.7 (4.2) 20.3 (5.3) 18.0 (1.6) 12.7 (1.5) 4.3 (0.8) 36.6 (2.9) 58.8 (2.9) 19.7 (3.1)

)

(Mg ha− 1) 5.4 3.3 6.6 10.6 4.3 0.6 2.7 23.3 9.3

(0.3) (0.4) (1.7) (1.2) (0.1) (0.1) (0.2) (1.7) (2.0)

Author's personal copy J.D. Muss et al. / Remote Sensing of Environment 115 (2011) 824–835

829

Fig. 3. Variation in model fit (adjusted R2) by lidar plot “footprint”. All model-footprint plots had similar patterns; this figure shows models for maximum tree height (frequencybased: Topmax ~ β1Q 95 + β0; wave-based: Topmax ~ β1Max + β0).

the same, this was not the case for branch biomass. The FW model for branch biomass achieved the same results as its IW counterpart without the inclusion of CRRmin. Although, the performance of the frequency-based and wavebased models that estimated total aboveground, branch, and foliage biomass did not differ significantly, the structure of the individual models should be acknowledged. All of the frequency-based models relied on returns from higher within the canopy, while the wavebased models all used Max plus other metrics that described canopy structure, including CRRmin and Mid:Max. The resulting wave-based models had the strongest relationships with total and branch biomass (R2cv = 0.74 and 0.74 respectively). The models of foliage biomass were also significant, but with weaker prediction ability (R2cv = 0.35, RMSEcv = 1.09).

these differences, both models outperformed their frequency-based counterpart, which was a function of the variability of return heights and the difference between the upper and lower returns (R2cv = 0.45, RMSEcv = 0.42). It is noteworthy that the wave-based and frequency-based models for log-transformed total stand basal area had similar predictors, coefficients, and fit (frequency-based: R2cv = 0.46, RMSEcv = 0.24; IW: R2cv = 0.48, RMSEcv = 0.23; FW: R2cv = 0.47, RMSEcv = 0.24; Table 4). Moreover, the frequency-based models for mean stem diameter and stand basal area were functionally analogous. They both depended on higher returns (Htmax and Q 90) from highly correlated predictors (r = 0.95), and had comparable model coefficients. In contrast, the wave-based model for mean stem diameter differed from its basal area counterpart by the inclusion of AWMHcan:Max for the FW model and Mid:Max and CRRmin for the IW model (Table 4).

4. Discussion 3.6. Biomass 4.1. Footprint size It is evident in Table 4 that each pair of FW and IW models used to estimate biomass were equivalent in fit. While the structure within model pairs that estimated total biomass and foliage biomass fit was

For this study, we observed a consistent pattern in which fit increased with footprint size through 15 m, and then leveled off for

Table 3 Estimates of forest structure using frequency-based metrics and wave-based metrics. The values in the footprint column are adjusted R2 for each model using the full data set. All models were significant with p-value b 0.0001. Lidar “footprint” (m)

Frequency

Forest metric

Model

2

5

10

15

20

25

30

TopMax TopMean CBH CL LCR

Q 95 Q 95 + HtCV Q 80 + HtCV Q70 NS ∑RCanopy ∑RAll Max AWMHCanopy Min Mid Mid Max + Max −CRRmin Mid NS CRRmin CRR1m

0.10 0.14 0.12 0.05 NS

0.73 0.53 0.44 0.26 NS

0.88 0.71 0.72 0.42 NS

0.90 0.77 0.74 0.46 NS

0.83 0.75 0.73 0.47 NS

0.79 0.68 0.73 0.46 NS

0.78 0.66 0.72 0.46 NS

Variable footprint

0.77

0.20 0.32 NS 0.19 0.16 0.25

0.71 0.58 0.22 0.38 0.38 0.32

0.83 0.81 0.27 0.57 0.69 0.53

0.86 0.84 0.24 0.63 0.74 0.53

0.79 0.84 0.24 0.61 0.71 0.57

0.68 0.81 0.22 0.62 0.70 0.53

0.71 0.80 0.20 0.59 0.67 0.53

Variable footprint Variable footprint 5 39 10 63 20 95

0.49 0.81 161 255 394

378 563 824

378 887 1314

378 1192 1848

378 1496 2418

Canopy coverage Pseudo-wave

TopMax TopMean CBH

CL LCR Canopy coverage Min number of returns Mean number of returns Max number of returns

Author's personal copy 830

J.D. Muss et al. / Remote Sensing of Environment 115 (2011) 824–835

Fig. 4. Plot of correlations for traditional frequency-based discrete-lidar metrics: maxium return height (max), quantiles (Q#), mean return height (Avg), standard deviation (SD), coefficient of variation (CV), skewness (Skew), and Kurtosis. Red plots have correlation values N 0.6, yellow values are between 0.4 and 0.6, and green values are ≤0.4. Pearson correlation coefficients are posted in the bottom half of the matrix.

larger footprints. From these results, we determined that the optimal footprint size was between 10 m and 15 m. Likely causes for this include GPS errors, density of lidar returns, and within-plot variability. Of these, GPS-error from multipath (tree stems) and interference (foliage and branches) were likely major sources of error in the smaller plots. The GPS post-processing software reported plot center location accuracies of 0.5 to 1 m, making the possibility of registration errors between field and lidar data considerable for the 2 m and 5 m footprints. However, registration errors for the larger footprints would drop considerably for the 10 m through 30 m footprints.

Paucity of returns was another factor that likely contributed to the poor fit observed for the smaller footprints. This implies that a minimum number of returns are needed to create satisfactory pseudo-waves. We inferred from the results (Table 3) that between 250 and 500 returns are necessary for acceptable pseudo-wave creation. The leveling off of fit for the larger footprints was likely due to the variable-sized sub-plots, which could have resulted in undersampling of the larger area encompassed by the footprints. Indeed, increased return density would allow the creation of pseudo-waves with greater resolution between height intervals, which could improve model fit for the smaller footprints by capturing more

Author's personal copy J.D. Muss et al. / Remote Sensing of Environment 115 (2011) 824–835

831

Fig. 5. Plot of correlations for pseudo-wave metrics described in section 2.3.2. Red plots have correlation values N 0.6, yellow values are between 0.4 and 0.6, and green values are ≤0.4. Pearson correlation coefficients are posted in the bottom half of the matrix.

variability within the waves. These high return density footprints could then be used to improve the registration of pseudo-wave and plot centers beyond GPS's accuracy limitations by allowing the discrimination of individual trees (Brandtberg et al., 2003; Popescu & Zhao, 2008). 4.2. Intensity calibration It has been argued that the intensity information provided with discrete lidar data is of questionable utility because it lacks radiometric calibration, and because the proprietary nature of the

data collection and management processes employed by the system manufacturers makes it difficult, if not impossible, for post hoc calibration (Donoghue et al., 2007; Kim et al., 2009; Ørka et al., 2009). While this might be important for studies that attempt to classify objects using multi-temporal data, it is less so for single epoch data acquisitions such as ours. To understand why, the main factors that affect the intensity of the laser return must be examined. These include: the distance between the target and the sensor (range); the initial power of the laser pulse; the transmissivity of the atmosphere; the reflective properties of the target; and the proportion of the pulse's footprint intercepted by the target (Baltsavias, 1999). Of these,

Author's personal copy 832

J.D. Muss et al. / Remote Sensing of Environment 115 (2011) 824–835

Table 4 Final models selected to measure forest structure using lidar data and 10 m footprints. Adjusted R2 and RMSE are cross validated results. The methods of analyzing lidar data are traditional frequency-based (F), height and intensity pseudo-waves (IW), and height frequency pseudo-waves (FW). Forest metric

n

TopMaxa

67

TopMeana

67

CBHa

67

CLa

67

Canopy coverageb

ln(Total stand basal area)

148

c

31

ln(Mean stem diameter)d

31

ln(Total stand stem density)e

31

ln(Aboveground biomass)f

148

ln(Branch biomass)g

148

ln(Foliage biomass)h

148

Method

Model

Adjusted R2

RMSE

F IW FW F IW FW F IW

1.1Q95 + 1.7 Max + 2.0 Max + 2.0 0.9Q95 + 3.1HtCV − 2.0 0.8AWMHCanopy + 5.7 0.9AWMHCanopy + 5.7 0.6Q80 + 3.8HtCV − 2.9 Mid 0:5Max + 3:3 Max −5:0CRRmin + 1:7

0.88 0.82 0.82 0.70 0.80 0.79 0.71 0.65

1.73 2.11 2.09 2.29 1.88 1.94 1.52 1.67

FW F IW FW F

Mid −6:8CRRmin + 2:6 0:5Max + 3:4 Max 0.3Q70 + 2.4 0.3Mid + 2.6 0.3Mid + 2.6 ∑R 0:7 ∑ canopy −0:3 R

0.64 0.39 0.48 0.48 0.76

1.68 1.77 1.64 1.63 0.06

All

IW FW F IW FW F IW

1.2CRR1m − 0.3 1.6CRR1m − 0.7 0.06Htmax + 1.9 0.07Max + 1.9 0.07Max + 1.8 0.09Q90 + 1.5 Mid 0:07Max + Max −0:4CRRmin + 1:2

0.79 0.78 0.46 0.48 0.47 0.64 0.64

0.05 0.06 0.24 0.23 0.24 0.22 0.22

FW F IW FW F IW FW F IW FW F IW FW

0:07Max + 1:3 MaxCanopy + 0:8 0.05Htmax − 0.1Q10 − 0.5HtSD + 8.7 1.9CRRmin − 0.1Mid + 6.8 2.3CRRmin − 0.1Mid + 6.3 0.2Q95 + 0.03 Mid 0:2Max + 1:6 Max −0:8 Mid −0:9 0:2Max + 1:5 Max 0.2Q80 − 1.1 Mid 0:2Max−0:8CRRmin + 2:6 Max −3:6 Mid 0:2Max + 2:4 Max −3:0 0.2HtMax − 3.2 0.2Max − 1.4CRRmin − 1.7 0.2Max − 1.2CRRmin − 2.0

0.61 0.45 0.63 0.56 0.75 0.72 0.74 0.74 0.74 0.74 0.37 0.34 0.35

0.23 0.42 0.34 0.37 0.56 0.59 0.57 0.55 0.56 0.56 1.08 1.10 1.09

AWMH

The following are the units of measurements. a Height and length (m). b Canopy coverage (%). c Stand basal area (m2 ha− 1); Back transformed RMSE: F = 8.31 m2 ha− 1, IW = 8.12 m2 ha− 1, FW = 8.16 m2 ha− 1. d Stem diameter (cm); Back transformed RMSE: F = 5.97 cm, IW = 6.15 cm, FW = 6.16 cm. e Stem density (number of stems ha− 1); Back transformed RMSE: F = 551 stems ha− 1, IW = 544 stems ha− 1, FW = 600 stems ha− 1. f Biomass (Mg ha− 1); Back transformed RMSE: F = 70.42 Mg ha− 1, IW = 73.72 Mgha− 1, FW = 74.03 Mg ha− 1. g Biomass (Mg ha− 1); Back transformed RMSE: F = 13.72 Mg ha− 1, IW = 14.37 Mg ha− 1, FW = 14.73 Mg ha− 1. h Biomass (Mg ha− 1); Back transformed RMSE: F = 7.43 Mg ha− 1, IW = 7.33 Mg ha− 1, FW = 7.36 Mg ha− 1.

it can be assumed that during a four-hour data acquisition campaign, atmospheric transmissivity and laser power are essentially constant, with even less variability during the one or two second period in which the data for a 10 m radius footprint are collected. Indeed, contiguous returns from homogenous surfaces (e.g. asphalt roads, dirt roads, and flat rooftops) had comparable intensities. Range, however, is a potential problem. If all other factors are held constant, the intensity of a return pulse is inversely proportional to the square of the range (Baltsavias, 1999), thus changes in range will cause intensity to vary by the ratio of the squares of the ranges (i.e.   Range1 2 I2 ∼I1 ). Three factors will cause range-induced differences Range2 in return intensity: the ability to maintain constant altitude, variation in the heights of reflecting surfaces, and topography. Each of these must be considered in the context of the flight plan, stand characteristics, and methods used to create pseudo-waves in this study. First, current auto-pilot systems allow lidar contractors to maintain platform altitude within 10 m of that specified in the flight plan under calm conditions and 40 m if there is turbulence (Todd Thies, Ayres Associates, personal communication). From this we can estimate that the intensities of two returns from the same surface would vary by 1% to 4% for a sensor flown at a constant flight altitude of 2000 m. This difference could be much less for a 10 m footprint, in which data are collected during two seconds of flight time (96% of the

footprints used in this study were created from data collected in the same flight line). Next, the maximum tree height for the 1,118 trees measured in the field was 40 m, but 99.5% were less than 30 m. Finally, as we noted earlier, plot topography was level and site topography ranged between 182 m and 433 m amsl. Therefore, the maximum range difference between any two points in a footprint is 50 m, which would result in a possible measured difference in intensity between two identical reflectors of 6.7% at the lowest and 5.7% at the highest topographic points of the survey (11% and 9.4% if there is turbulence). We felt that this made it unnecessary to apply the height normalization method used in other studies (Donoghue et al., 2007; García et al., 2010; Luzum et al., 2004). The remaining sources of variability in intensity between any two returns are the reflective properties of the target and the proportion of the pulse's footprint intercepted by the target. If one of these variables is known, then inferences can be made about the other. But if both are unknown, specific conclusions cannot be made about either reflecting surface, e.g. whether the surface is foliage or woody tissue. Our method avoids this paradox by viewing intensity as the interaction of the two sources of variability, rather than handling them independently. Thus, the accumulated intensity at a point on the wave is a measure of the porosity of the canopy or density of plant tissue at that height. In other words, patterns of intensity distribution are examined, not the specific intensity of any single return. Therefore, the specific tissue or species composition

Author's personal copy J.D. Muss et al. / Remote Sensing of Environment 115 (2011) 824–835

of a footprint cannot be described, but structural differences between footprints can be related to observed differences in patterns among waves. 4.3. Height frequency-based pseudo-waves versus Intensity-based pseudo-waves Although recent studies have demonstrated the merit of using the intensity of returns in models that estimate forest structure, composition, and structural characteristics (Antonarakis et al., 2008; Kim et al., 2009; Ørka et al., 2009; Pesonen et al., 2008), we did not find any support for the inclusion of intensity in pseudo-wave creation. In all but three cases, the IW and FW model pairs were nearly identical in fit, RMSE, and formulation. Of the three outstanding cases, only estimates of total stand stem density were improved using the IW models. Moreover, the FW models for mean stem diameter and branch biomass were more parsimonious than their IW counterparts. Overall, these results suggest limited value for return intensity in pseudo-wave-based analyses. 4.4. Frequency-based versus wave-based analyses Differences in site conditions and methodology make it difficult to compare the results from this study with those from past lidar studies. Our conservative approach restricts auto-correlation among variables, resulting in lesser fits but possibly greater model robustness. For example, Andersen et al. (2005) report a near perfect relationship (R2 = 0.98, RMSEcv = 1.5 m) between tree height in conifer dominated stands and Htmax, Q 25, Q50, and Q75, but we have shown that these variables are all highly correlated. In light of this, we feel that our model, which only uses Q95, is more suitable. Similar relationships were seen between our models and those in other studies that focused on a narrow set of conifer species and site conditions, and used highly

833

correlated variables, such as for CBH (R2 = 0.77, RMSEcv = 4.1 m; Andersen et al., 2005) and stem density (R 2 = 0.60 to 0.81, RMSE = 0.13 to 0.25; Næsset, 2004). Our results demonstrate comparable fit and estimated error between frequency-based and wave-based models. When residuals were analyzed (see online appendix for all model residuals), no patterns were detected for most models or forest types. An exception was the frequency-based model for mean canopy height (Fig. 6), which underestimated the canopy heights for the hemlock plots and overestimated those for the cedar plots. A plausible explanation for this can be made after considering how stand structural characteristics (Table 1) can affect the variability of lidar return heights. Mature stands, such as those in which we established the hemlock plots, have large canopy gaps, which would have resulted in more lidar returns from below the canopy surface than would occur from a stand with trees of a similar size, but a closed canopy. The increased variability in return height would cause Q95 and HtCV to be lower than expected and lead to an underestimation of mean canopy height for mature stands. Likewise, stands with a mix of tall and short trees (the cedar plots had a few tall red and white pines interspersed among many shorter cedar) could cause Q95 and HtCV to be higher than the actual mean canopy height. In contrast, the wave-based models were stronger and more consistent because they related mean canopy height to a metric that captured canopy variability across a footprint by giving weight to all peaks within the canopy (AWMHcanopy). This limits the use of noncanopy returns in the model, while allowing for stratified or multiple canopies in a footprint. Perhaps the biggest drawback to using frequency-based methods to analyze lidar data for forest structural assessment is the difficulty in making meaningful statements about the relationships between lidar metrics and dependent variables. For example, one would expect Htmax to be a better estimator of the top of the canopy than Q95, but this is not the case. Although they are highly correlated (r = 0.97;

Fig. 6. Residual plots for the models created to estimate mean canopy height (TopMean). Models (Frequency: TopMean = 0.9Q95 + 3.1HtCV − 2.0; FW: TopMean = 0.9AWMHCanopy + 5.7; IW: TopMean = 0.8AWMHCanopy + 5.7) were created using 10 m footprints.

Author's personal copy 834

J.D. Muss et al. / Remote Sensing of Environment 115 (2011) 824–835

Fig. 4), it could be argued that Q95 performs better because it captures systematic errors in field-measurements which could underestimate canopy heights. The wave-based approach, however, offers a more plausible model based on a 1:1 relationship with Max, which is in agreement with findings from a study on Assateague Island using the EAARL waveform sensor (Nayegandhi et al., 2006). While the EAARL study had better model fit (R2 = 0.91), its overall error (RMSE = 1.93) was comparable to our model (RMSEcv = 2.08). If it is accepted that field errors (including those from GPS registration, tree top identification, and ground measurements) are well within this range, it would not be unreasonable to suggest that Max could be used as a universal estimator of tree height. Justification for frequency-based metrics is further hampered as more variables are added to the models or when unexpected relationships appear among models. This is evident in the models for mean canopy height and stand stem density. In the case of mean canopy height, it should be noted that the frequency-based model is a variation on the model for maximum canopy height, the main differences being the inclusion of HtCV in the mean height model and its performance relative to the maximum height model. While it is conceivable that canopy rugosity could correlate with variability in return heights, the overall similarity of the models and the reduced performance of the mean height model (R2cv = 0.70, RMSEcv = 2.29) relative to the maximum height model (R2cv = 0.88, RMSEcv = 1.73) raises uncertainties as to whether Q 95 is actually estimating the mean height of the canopy. It may be that the correlation between the mean and maximum heights of the canopy (r = 0.81) are too high for frequency-based metrics to discriminate between the two. We assert that the wave-based models for top of canopy and mean canopy height are more plausible; they each employ different variables for which more defensible physically-based justifications can be made. Consider the model for the mean canopy height in comparison to the one for the top of canopy. The latter model uses Max to estimate height while the former uses AWMHcanopy, the sum of the area-weighted heights of all peaks within the canopy (primary peak). In a simple unimodal pseudo-wave, this corresponds to Mid, which we suspect correlates with the greater reflectance of the upper surface of the canopy. For more complex multi-modal waves, this metric allows each peak to contribute information based on its size and position. The result is two distinct models that estimate different features of the canopy — its highest point and its general surface. The models that estimate stand stem density further demonstrate the advantage that wave-based analyses can have over frequencybased analyses, especially when relationships between variables and physical measurements are to be interpreted. The frequency-based model is the most complex model that can be created using frequency-based metrics while avoiding high levels of colinearity amongst variables, yet its fit is only moderate. Moreover, it is difficult to offer any satisfactory explanation as to why Htmax, Q10, and HtSD correlate to stand stem density. However, the wave-based models have much stronger relationships with stem density, suggesting that the variables in these models (CRRmin and Mid) are well suited to capture changes in canopy structure that coincide with stem density. Specifically, we argue that the higher stem densities that occur during aggradation will have fewer canopy gaps and longer crowns (Bormann & Likens, 1979), which will coincide with higher canopy return ratios and pseudo-waves with lower primary peaks. But as stands mature, mortality increases causing stem density to decrease and canopy gaps to open, resulting in lower canopy return ratios and pseudo-waves with higher primary peaks. Finally, the wave-based models for CBH and canopy coverage produced some unexpected results; specifically, we had hypothesized Min would be highly correlated with CBH, and that this relationship could be used to improve models that estimate canopy coverage. This was not the case. Our hypothesis had been based on the assumption that Min, the point where the number of returns (or intensity for an

IW) drops abruptly, would be the base of the crown (Popescu & Zhao, 2008), and that this could be used to separate canopy from ground returns. While the results of our wave-based model for CBH compared favorably to those from other studies (Popescu & Zhao, 2008; Riano et al., 2004), our best model did not directly include Min. It is possible that our definition of CBH in the field was too restrictive, and that Min was detecting either branches that we ignored, or the sub-canopy which we did not measure. Moreover, in order to relate lidar-based estimates of canopy coverage to ground-based estimates, it became clear that it is necessary to cut the pseudo-wave at the same height from which the ground-based estimates were made. Yet, this suggests that the coverage of different strata of the canopy can be estimated using lidar data if a legitimate cut can be established. However, further research would be required. 5. Conclusions We have demonstrated a method to create pseudo-waveforms from discrete lidar data and the potential to improve forest analyses using these pseudo-waves. We introduced a set of basic metrics that exploited the physical characteristics of the wave, and demonstrated that models created using these wave-based metrics performed comparably to, and in some cases dramatically better than, similar models created using traditional frequency-based metrics. Because the pairs of models had comparable fits and mean square error, we suggest that the advantages of the pseudo-wave approach are 1) the increased breadth of available metrics; 2) the potential to establish new meaningful metrics that capture unique patterns within the waves; 3) the ability to explain metric selection based on structural characteristics of forests; and 4) lower correlation among independent variables. While independent variables were selected based on a maximum pairwise correlation of 0.6, it should be noted that some high correlations amongst variables, such as Max, Mid, and Min, may not be accurate. For example, a correlation of 0.67 prohibited the inclusion of Min and Mid in the same model, but this correlation may be artificially high because Min can never be higher than Mid, which results in a lack of points below the 1:1 line (Fig. 5). This study uniquely compares wave-based and frequency-based methods of lidar analysis across several different coniferous and deciduous forest types that reflect a wide range of physical and structural variability. We believe this is the first application of this method to create pseudo-waves; that many of these metrics are novel; and that the use of this technique and these metrics are novel in forest-lidar analyses. The metrics introduced in this study were used to highlight the strengths of wave-based analysis of discrete lidar data in forestry studies. As such, there is great potential for other, perhaps better, metrics. Possible alternative metrics include those that stratify the pseudo-wave by inflection points, or those that capture both the nature of the wave and the x- and y-positions of the discrete returns. Acknowledgements Data were acquired and analyzed with funding from the Wisconsin Coastal Management Program and the National Oceanic and Atmospheric Administration, Office of Ocean and Coastal Resource Management under the Coastal Zone Management Act, Grant # NA08NOS4190431; the Wisconsin Department of Natural Resources Bureau of Science Services and Divisions of Water and Forestry; and through a graduate fellowship from the NASA/Wisconsin Space Grant Consortium. We would like to thank the Bayfield County Forestry Department for use of their forests in this study and supplying supporting stand information; and pre-submission reviewers: Faith Fitzpatrick (U.S. Geological Survey), Steve Loheide (UW Madison), and Jodi Forester (UW Madison). We thank Sudeep Samanta, Todd Hawbaker, Camilo Alcantara, and members of the Forest Landscape

Author's personal copy J.D. Muss et al. / Remote Sensing of Environment 115 (2011) 824–835

Ecology lab for their invaluable help in gathering field data as well as for insights and suggestions during this study. Appendix A. Supplementary data Supplementary data to this article can be found online at doi:10.1016/j.rse.2010.11.008. References Andersen, H., McGaughey, R. J., & Reutebuch, S. E. (2005). Estimating forest canopy fuel parameters using LIDAR data. Remote Sensing of Environment, 94, 441−449. Andersen, H., Reutebuch, S. E., & McGaughey, R. J. (2006). A rigorous assessment of tree height measurements obtained using airborne lidar and conventional field methods. Canadian Journal of Remote Sensing, 32, 355−366. Antonarakis, A. S., Richards, K. S., & Brasington, J. (2008). Object-based land cover classification using airborne LiDAR. Remote Sensing of Environment, 112, 2988−2998. Baltsavias, E. P. (1999). Airborne laser scanning: Basic relations and formulas. ISPRS Journal of Photogrammetry and Remote Sensing, 54, 199−214. Bormann, F. H., & Likens, G. E. (1979). Pattern and process in a forested ecosystem. New York: Springer. Bortolot, Z. J. (2006). Using tree clusters to derive forest properties from small footprint lidar data. Photogrammetric Engineering and Remote Sensing, 72, 1389−1397. Bortolot, Z. J., & Wynne, R. H. (2005). Estimating forest biomass using small footprint LiDAR data: An individual tree-based approach that incorporates training data. ISPRS Journal of Photogrammetry and Remote Sensing, 59, 342−360. Brandtberg, T., Warner, T. A., Landenberger, R. E., & McGraw, J. B. (2003). Detection and analysis of individual leaf-off tree crowns in small footprint, high sampling density lidar data from the eastern deciduous forest in North America. Remote Sensing of Environment, 85, 290−303. Breidt, F. J. (2004). Simulation estimation of quantiles from a distribution with known mean. Journal of Computational and Graphical Statistics, 13, 487−498. Donoghue, D. N. M., Watt, P. J., Cox, N. J., & Wilson, J. (2007). Remote sensing of species mixtures in conifer plantations using LiDAR height and intensity data. Remote Sensing of Environment, 110, 509−522. Farid, A., Goodrich, D. C., Bryant, R., & Sorooshian, S. (2008). Using airborne lidar to predict Leaf Area Index in cottonwood trees and refine riparian water-use estimates. Journal of Arid Environments, 72, 1−15. Frazer, G. W., Canham, C. D., & Lertzman, K. P. (1999). Gap light analyzer (GLA), version 2.0: Imaging software to extract canopy structure and gap light indices from truecolour fisheye photographs. Millbrook, NY: Simon Fraser University, Burnaby, B.C., and the Institute of Ecosystem Studies. García, M., Riaño, D., Chuvieco, E., & Danson, F. M. (2010). Estimating biomass carbon stocks for a Mediterranean forest in central Spain using LiDAR height and intensity data. Remote Sensing of Environment, 114, 816−830. Gobakken, T., & Næsset, E. (2004). Estimation of diameter and basal area distributions in coniferous forest by means of airborne laser scanner data. Scandinavian Journal of Forest Research, 19, 529−542. Goetz, S., Steinberg, D., Dubayah, R., & Blair, B. (2007). Laser remote sensing of canopy habitat heterogeneity as a predictor of bird species richness in an eastern temperate forest, USA. Remote Sensing of Environment, 108, 254−263. Groeneveld, R. A. (1998). A class of quantile measures for kurtosis. American Statistician, 52, 325−329. Grosenbaugh, L. R. (1952). Plotless timber estimates — New, fast, easy. Journal of Forestry, 50, 32−37. Hinsley, S. A., Hill, R. A., Bellamy, P. E., & Balzter, H. (2006). The application of lidar in woodland bird ecology: Climate, canopy structure, and habitat quality. Photogrammetric Engineering and Remote Sensing, 72, 1399−1406. Hopkinson, C., Chasmer, L., & Hall, R. J. (2008). The uncertainty in conifer plantation growth prediction from multi-temporal lidar datasets. Remote Sensing of Environment, 112, 1168−1180. Hopkinson, C., Chasmer, L., Lim, K., Treitz, P., & Creed, I. (2006). Towards a universal lidar canopy height indicator. Canadian Journal of Remote Sensing, 32, 139−152. Kim, Y., Yang, Z., Cohen, W. B., Pflugmacher, D., Lauver, C. L., & Vankat, J. L. (2009). Distinguishing between live and dead standing tree biomass on the North Rim of Grand Canyon National Park, USA using small-footprint lidar data. Remote Sensing of Environment, 113, 2499−2510.

835

Lefsky, M. A., Hudak, A. T., Cohen, W. B., & Acker, S. A. (2005). Patterns of covariance between forest stand and canopy structure in the Pacific Northwest. Remote Sensing of Environment, 95, 517−531. Lim, K., Treitz, P., Baldwin, K., Morrison, I., & Green, J. (2003). Lidar remote sensing of biophysical properties of tolerant northern hardwood forests. Canadian Journal of Remote Sensing, 29, 658−678. Lovell, J. L., Jupp, D. L. B., Culvenor, D. S., & Coops, N. C. (2003). Using airborne and ground-based ranging lidar to measure canopy structure in Australian forests. Canadian Journal of Remote Sensing, 29, 607−622. Lumley, T. (2009). Leaps: Regression subset selection. R Foundation for Statistical Computing. Luzum, B., Starek, M., & Slatton, K. C. (2004). Normalizing ALSM intensities. GEM Center Report No. Rep_2004-07-001. Gainesville, Florida: University of Florida. Moffiet, T., Mengersen, K., Witte, C., King, R., & Denham, R. (2005). Airborne laser scanning: Exploratory data analysis indicates potential variables for classification of individual trees or forest stands according to species. ISPRS Journal of Photogrammetry and Remote Sensing, 59, 289−309. Morsdorf, F., Kotz, B., Meier, E., Itten, K. I., & Allgower, B. (2006). Estimation of LAI and fractional cover from small footprint airborne laser scanning data based on gap fraction. Remote Sensing of Environment, 104, 50−61. Næsset, E. (2002). Predicting forest stand characteristics with airborne scanning laser using a practical two-stage procedure and field data. Remote Sensing of Environment, 80, 88−99. Næsset, E. (2004). Practical large-scale forest stand inventory using a small-footprint airborne scanning laser. Scandinavian Journal of Forest Research, 19, 164−179. Næsset, E., & Bjerknes, K. O. (2001). Estimating tree heights and number of stems in young forest stands using airborne laser scanner data. Remote Sensing of Environment, 78, 328−340. Nayegandhi, A., Brock, J. C., Wright, C. W., & O'Connell, M. J. (2006). Evaluating a small footprint, waveform-resolving lidar over coastal vegetation communities. Photogrammetric Engineering and Remote Sensing, 72, 1407−1417. Nelson, R., Krabill, W., & Maclean, G. (1984). Determining forest canopy characteristics using airborne laser data. Remote Sensing of Environment, 15, 201−212. Nelson, R., Oderwald, R., & Gregoire, T. G. (1997). Separating the ground and airborne laser sampling phases to estimate tropical forest basal area, volume, and biomass. Remote Sensing of Environment, 60, 311−326. Ørka, H. O., Næsset, E., & Bollandsås, O. M. (2009). Classifying species of individual trees by intensity and structure features derived from airborne laser scanner data. Remote Sensing of Environment, 113, 1163−1174. Pesonen, A., Maltamo, M., Eerikäinen, K., & Packalèn, P. (2008). Airborne laser scanningbased prediction of coarse woody debris volumes in a conservation area. Forest Ecology and Management, 255, 3288−3296. Popescu, S. C., & Zhao, K. (2008). A voxel-based lidar method for estimating crown base height for deciduous and pine trees. Remote Sensing of Environment, 112, 767−781. R Development Core Team (2009). R: A language and environment for statistical computing. R Foundation for Statistical Computing. Rautiainen, M., & Stenberg, P. (2005). Simplified tree crown model using standard forest mensuration data for Scots pine. Agricultural and Forest Meteorology, 128, 123−129. Reutebuch, S. E., Andersen, H. E., & McGaughey, R. J. (2005). Light detection and ranging (LIDAR): An emerging tool for multiple resource inventory. Journal of Forestry, 103, 286−292. Rhemtulla, J. M., Mladenoff, D. J., & Clayton, M. K. (2009). Legacies of historical land use on regional forest composition and structure in Wisconsin, USA (mid-1800s1930s-2000s). Ecological Applications, 19, 1061−1078. Riano, D., Chuvieco, E., Condes, S., Gonzalez-Matesanz, J., & Ustin, S. L. (2004). Generation of crown bulk density for Pinus sylvestris L. from lidar: Forest fire prevention and assessment. Remote Sensing of Environment, 92, 345−352. Ter-Mikaelian, M. T., & Korzukhin, M. D. (1997). Biomass equations for sixty-five North American tree species. Forest Ecology and Management, 97, 1−24. Townsend, P. A. (2002). Relationships between forest structure and the detection of flood inundation in forested wetlands using C-band SAR. International Journal of Remote Sensing, 23, 443−460. Véga, C., & St-Onge, B. (2008). Height growth reconstruction of a boreal forest canopy over a period of 58 years using a combination of photogrammetric and lidar models. Remote Sensing of Environment, 112, 1784−1794. Wallerman, J., & Holmgren, J. (2007). Estimating field-plot data of forest stands using airborne laser scanning and SPOT HRG data. Remote Sensing of Environment, 110, 501−508. Yu, X. W., Hyyppa, J., Kukko, A., Maltamo, M., & Kaartinen, H. (2006). Change detection techniques for canopy height growth measurements using airborne laser scanner data. Photogrammetric Engineering and Remote Sensing, 72, 1339−1348.