Estimation of forest resources from a country wide laser scanning survey and national forest inventory data

Remote Sensing of Environment 119 (2012) 148–157

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Estimation of forest resources from a country wide laser scanning survey and national forest inventory data Thomas Nord-Larsen ⁎, Johannes Schumacher University of Copenhagen, Forest and Landscape, 23 Rolighedsvej, DK-1958 Frederiksberg C, Denmark

a r t i c l e

i n f o

Article history: Received 2 September 2011 Received in revised form 20 December 2011 Accepted 23 December 2011 Available online 26 January 2012 Keywords: LiDAR Model Basal area Volume Biomass

a b s t r a c t The demand for renewable energy has raised a need for efficient mapping of forest fuel resources in Denmark. Airborne laser scanning may provide a means for assessing local forest biomass resources. In this study, national forest inventory (NFI) data was used as reference data for modeling forest basal area, volume, aboveground biomass, and total biomass from laser scanning data obtained in a countrywide scanning survey. Data covered a wide range of forest ecotypes, stand treatments, tree species, and tree species mixtures. The four forest characteristics were modeled using nonlinear regression and generalized method-of-moments estimation to avoid biased and inefficient estimates. The coefficient of determination was 68% for the basal area model and 77–78% for the volume and biomass models. Despite the wide range of forest types model accuracy was comparable to similar studies. Model predictions were unbiased across the range of predicted values and crown cover percentages but positively biased for deciduous forest and negatively biased for coniferous forest. Species type specific (coniferous, deciduous, or mixed forest) models reduced root mean squared error by 3–12% and removed the bias. In application, model predictions will be improved by stratification into deciduous and coniferous forest using e.g. infrared orthophotos or satellite images. © 2012 Elsevier Inc. All rights reserved.

1. Introduction The commitment to the Kyoto Protocol has spurred a widespread conversion to renewable sources of energy as a means of reducing anthropogenic emissions of carbon dioxide. In Denmark, this has resulted in an increase in primary energy production in Denmark from forest biomass from 18 PJ in 1990 to 41 PJ in 2008 (Danish Energy Agency, 2009). The increase in the use of forest biomass for energy has created a concern that the resources may not be sufficient to meet the demand and a need for efficient location–allocation of conversion facilities and forest fuel resources. The dispersed nature of the forest fuel resource in Denmark has raised an interest in mapping of local forest resources in relation to the biomass supply problem. The Danish National Forest Inventory (NFI, Nord-Larsen et al., 2008) may be used for estimating regional availability of forest biomass, but the sampling design does not allow accurate estimation of the local potential for procurement of forest biomass for energy. Several studies have focused on the assessment of forest resources using airborne laser scanning (ALS). ALS used in forest inventory captures the three-dimensional forest canopy structure and makes use of the relationship between canopy structure and other forest properties. A number of studies have shown that mapping of forest volume and biomass using ALS may yield a satisfactory level of precision and

⁎ Corresponding author. Tel.: + 45 35331758. E-mail address: [email protected] (T. Nord-Larsen). 0034-4257/$ – see front matter © 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2011.12.022

accuracy at the forest stand level (e.g. Holmgren & Jonsson, 2004; Lefsky et al., 1999; Lim & Treitz, 2004; Lim et al., 2003; Næsset, 1997, 2004b; Patenaude et al., 2004). In a number of Nordic studies the reported RMSE of basal area and volume was 8.6–13.2% and 8.4–42.7% of the mean, respectively (Næsset, 2007; Næsset et al., 2004). The notion that sufficient accuracy may be obtained from estimating local forest resources using ALS has motivated applications in large scale forest inventory. In a first attempt to apply ALS in forest inventory, Næsset, (2002) used a two-stage procedure in a 10 km 2 study area and obtained a high level of precision. Since then ALS has been used operationally to estimate forest resources in areas ranging from 50 to 2000 km 2 (Næsset, 2007; Næsset et al., 2009). These studies have proven ALS to be a cost effective method for obtaining biophysical forest properties such as forest volume or biomass (Eid et al., 2004). However, complete scanning of larger regions may not be economically feasible using the hitherto used procedures due to the costs of acquisition and processing the large amounts of data associated with this technique. In recent studies, laser technology has been expanded to entire regions, using airborne laser scanning and/or laser profiling as sampling tools. Boudreau et al. (2008, 2009) combined several sources of information including small footprint airborne profiling laser data and large footprint spaceborne laser to estimate above ground dry biomass in Québec covering 1.3 M km 2. In this study, data from the profiling laser was used as auxiliary data for developing equations relating spaceborne laser pulse data to biomass and carbon pools.

T. Nord-Larsen, J. Schumacher / Remote Sensing of Environment 119 (2012) 148–157 Table 1 Summary of the laser scanner and flight data. System Flying altitude Pulse repetition frequency Scanning angle Average point density Footprint size Horizontal accuracy Vertical accuracy

Optech ALTM 3100 1600 m 70 kHz ± 24∘ 0.5 pulse/m2 50 cm 80 cm (1σ) 10 cm (1σ)

Gregoire et al. (2011) and Ståhl et al. (2011) compared the use of both a profiling laser and ALS as a strip sampling tool for inventorying timber volume and biomass in large areas. Rather than reducing the area covered by the laser scanner (i.e. by using profiling laser or strip sampling with a laser scanner), the costs of data acquisition and handling may be reduced by increasing flying altitude (Næsset, 2004a; Yu et al., 2004) and/or the scanning angle (Holmgren et al., 2003) hereby increasing the average point spacing (Thomas et al., 2006). Also, costs may be reduced by using data obtained in relation to other surveys, such as mapping terrain or other geographical features. In this study we hypothesize that ALS data obtained in a large regional survey for obtaining a digital terrain model (DTM) in combination with national forest inventory (NFI) data may be used for developing remote sensing tools for estimation of forest basal area, volume, above ground biomass, and total biomass. The overreaching objective of the study concerns the use of wall-to-wall ALS data for assessing biofuel resources in Denmark. More specifically, the objectives of the study are to combine wallto-wall ALS data with NFI data for 1) developing regression models to predict forest basal area, volume and biomass, 2) assessing the goodness of the parameterized models, and 3) evaluating model performance on an independent data. 2. Materials and methods 2.1. Laser scanning data The entire Danish land surface was scanned in 2006–2007 with the aim to improve existing DTM's (COWI, 2007a). The scanning was conducted in two surveys during leaf-off conditions in spring 2006 and fall 2006/spring 2007. First and last return pulses were recorded by the scanner. A summary of the laser scanner and flight data is provided in Table 1. The resulting point cloud was tested for geometrical accuracy using ground based data and a DTM was generated from the point cloud using TerraScan software. The generation of the DTM and testing of the point cloud data was carried out by COWI A/S (COWI, 2007b). Based on the DTM, the elevation above ground (Dz) was calculated for each point in the point cloud. The first and last return pulses were spatially assigned to the sample plots of the national forest inventory. For each individual plot, a

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large number of metrics were derived from the pulse height above ground distributions as potential variables for modeling above ground volume and biomass. The metrics were calculated on both the first (r = 1) and last return pulse data (r = 2), and both with (Dz ≥ 0 m; q = 1) and without ground hits (Dz > 1 m; q = 2). The metrics include: 1) Mean, maximum and minimum pulse height above ground (Dzmean, r, q, Dzmax, r, q, and Dzmin, r, q), 2) variance, standard deviation, and coefficient of variation (Dzvar, r, q, Dzstd, r, q, and Dzcv, r, q), 3) skewness and kurtosis (Dzskew, r, q and Dzkur, r, q), 4) distribution percentiles (Dzp, r, q; p = 10, 25, 50, 75, 90, 95, 99), 5) relative mean and median height (the mean and median pulse height above ground relative to maximum pulse height; Dzrelmean, r, q and Dzrelmed, r, q), and 6) canopy interception ratio (the number of pulses reflected from above ground (Dz > 1 m) relative to the total number of pulses; IRr). Additionally, the vertical space between Dzmax and the ground was divided into 10 strata where {Dzh|Dzmax/10 ⋅h≥Dzh >Dzmax/10 ⋅(h− 1)}, h=1,2,⋯ 10. For each stratum we calculated 7) the interception ratio (the number of pulses reflected from stratum h relative to the total number of pulses; IR(h), r) and 8) variance and distribution form parameters (Dzcv(h), r, q, Dzskew(h), r, q, and Dzkurt(h), r, q). Further, similar statistics were derived for the intensity of the reflections from the canopy, labeled IN. In this study we used the uncalibrated return pulse intensities as recorded by the scanning equipment. Such intensities have been reported to be noisy and varying with the range to the reflecting object (Höfle & Pfeifer, 2007; Kaasalainen et al., 2005). It is possible to correct the raw pulse intensities using range normalization (Korpela et al., 2010) but we lacked sufficient information to make such adjustments. However, the Danish terrain is quite flat and consequently the range variation and thus the possible corrections are likely to be relatively small (b10%). The resulting ALS meta data includes metrics from a total of 2265 national forest inventory plots selected for inventory during the period 2006–2007, corresponding to the time of the laser scanning survey. In a study using the same data for modeling canopy height from laser scanning data (Nord-Larsen & Riis-Nielsen, 2010), outliers were identified that resulted from crowns of neighboring trees reaching into and dominating the sample plots and logging that had happened between the time of the laser scanning and the time of ground data collection. A total of 87 outliers were identified and removed from the calibration data. Further, in 48 plots more than 10% of return pulses were erroneously recorded from below ground and these plots were removed from the calibration data. The resulting dataset contains data from 2130 plots inventoried in the field and their corresponding laser scanning data (Table 2).

2.2. Forest inventory data The Danish NFI is based on a 2 × 2 km grid placed over the Danish land surface. In each grid cell, a cluster of four circular plots for measuring forest factors (e.g. growing stock, biomass, or carbon stock) is

Table 2 Laser scanning data statistics for first and last return pulses from all plots used in model estimation (N = 2130). ‘Returns’ are the number of returns per plot. Variable

Returns Returns (>1 m) Average return pulse height Average return pulse height (> 1 m) Max return pulse height Canopy interception ratio Average return pulse intensity Average return pulse intensity (> 1 m) Max return pulse intensity

First return

Last return

Mean

Std. dev.

Range

Mean

Std. dev.

Range

452.1 248.6 6.6 9.9 15.6 56.3 18.7 11.8 42.0

161.1 165.4 5.7 5.8 8.0 31.2 7.9 7.2 12.7

27–1536 0–1281 0.0–30.1 1.0–31.7 0.0–42.1 0.0–100.0 2.8–48.4 1.4–40.2 14.0–260.0

460.6 125.0 2.8 8.3 13.3 27.0 206.9 156.6 421.9

145.3 140.3 3.9 5.5 8.3 27.1 72.2 66.7 130.6

96–1409 0–829 0.0–27.5 1.0–29.2 0.0–40.2 0.0–97.7 28.5–511.6 10.0–402.1 140.0–2600.0

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Table 3 Statistics of the Danish national forest inventory plots inventoried in 2006–2007. Includes only plots with corresponding laser scanning data. ‘Only one plot’ refers to NFI plots with only one sub-plot, i.e. sample plots not intersected by differing land uses or forest stands. ‘Only one species type’ refers to NFI plots with only broadleaves or only conifers. Variable

Canopy height (m) Crown cover (%) Dg (cm) Stem number (ha− 1) Basal area (m2ha− 1) Volume (m3ha− 1) Total biomass (tonnes ha− 1)

All plots (n = 2130) Mean

Std. dev.

17.6 67.9 17.9 1438.1 16.5 168.5 110.1

8.2 27.2 11.7 2351.2 13.2 169.3 110.1

Only one plot (n = 1267) Range

Mean

Std. dev.

0.5–46.5 0.0–100.0 0.7–119.9 0.0–27,803.4 0.0–91.5 0.0–1072.0 0.0–751.5

17.8 65.9 17.1 1667.2 17.7 182.7 118.7

8.6 28.1 11.5 2584.1 13.5 177.6 114.0

placed in the corners of a 200 × 200 m square (Nord-Larsen et al., 2008). The location of the sample plots was found in the field using a Trimble GPS Pathfinder Pro XRS receiver mounted with a Trimble Hurricane antenna, fitted into a backpack. This equipment is expected to yield sub-one meter precision even under dense canopies. Each circular plot has a radius of 15 m. When plots are intersected by different land use classes or different forest stands, the individual plot is divided into sub-plots. Each plot is divided into three concentric circles with radius 3.5, 10 and 15 m. A single caliper measurement of diameter is made at breast height for all trees in the 3.5 m circle, trees with diameter larger than 10 cm are measured in the 10 m circle and only trees larger than 40 cm are measured in the 15 m circle. Height measurements are obtained from a random sample of 2–6 trees per plot. A total of 2273 forested plots were inventoried in 2006–2007, corresponding to the time of the laser scanning survey (Table 3). A map showing inventoried plots with corresponding data from the laser scanning may be seen in Fig. 1.

Only one species type (n = 1308) Range

Mean

Std. dev.

1.5–46.5 0.0–100.0 0.7–86.0 0.0–27,803.4 0.0–74.4 0.0–1002.2 0.0–666.0

17.8 71.2 18.7 1475.8 18.0 188.9 123.0

8.5 23.7 12.5 2307.6 12.5 170.3 111.1

Range 1.5–42.7 0.0–100.0 0.7–119.9 14.1–23,386.0 0.0–74.4 0.1–1072.0 0.1–751.5

Based on the NFI data, stem number (N) and basal area per hectare (G) were calculated by scaling the tree measurements made within the 3.5, 10 and 15 m circles according to their share of the total 15 m circle plot area as Njk ¼

mjk X i¼1

1 Ac; jk

ð1Þ

1 g ; Ac; jk ijk

ð2Þ

and Gjk ¼

mjk X i¼1

where Ac, jk is the circular plot area of the cth circle (c = 3.5, 10.0, 15.0 m) corresponding to the diameter of the ith tree on the jth plot within the kth cluster, gijk is the individual tree basal area, and mjk is

Fig. 1. Map showing the position of inventoried national forest inventory plots 2006–2007. Larger dots and numbers refer to the 13 species trials used in model validation.

T. Nord-Larsen, J. Schumacher / Remote Sensing of Environment 119 (2012) 148–157

the total number of sampled trees within the plot. Quadratic mean diameter was subsequently estimated as Dg; jk ¼

4 Gjk : π N jk

ð3Þ

Based on the sample tree height measurements, generalized, species wise dh-regressions were estimated using the approach suggested by Sloboda et al. (1993): hijk

  d
jk ¼ 13 þ h
jk −13 ⋅exp a1 1 þ dijk

! þ a2

1 1 − d
jk dijk

!! ;

ð4Þ

where dijk and hijk are diameter (in mm) and height (in cm) of the ith tree within the jth plot and kth cluster, d
jk and h
jk are mean diameter and height, and a1 and a2 are parameters to be estimated. The height of trees not measured is subsequently estimated using Eq. (4), where species-specific parameters were estimated using data from all trees measured for height in the NFI during 2002–2010 (23,645 trees). Individual tree above ground volume of broadleaves and stem volumes of conifers (vijk) were estimated from d, (estimated) h, and Dg, using volume equations developed by Madsen, (1987) and Madsen and Heusérr, (1993). Tree biomass was subsequently estimated using species specific wood densities reported by Moltesen, (1988). Above-ground (bag, ijk) and total tree (btotal, ijk) biomass for individual broadleaf trees was estimated using expansion factors derived for beech (Skovsgaard & Nord-Larsen, 2011) whereas biomass for coniferous trees were estimated using expansion factors developed for Norway spruce (Skovsgaard et al., 2011). For both broadleaves and conifers, above ground biomass includes the branches (without foliage), stem and above-ground stump. Entire tree biomass further includes the below-ground stump and root system down to an approximate diameter of 2 mm. Above ground volume (Vjk), aboveground biomass (Bag, jk) and total biomass (Btotal, jk) were finally estimated by scaling the tree measurements made within the 3.5, 10.0, and 15.0 m circles according to their share of the total 15 m circle plot area as V jk ¼

mjk X i¼1

Bag;jk ¼

1 v ; Ac; jk ijk

mjk X i¼1

1 b ; Ac;jk ag;ijk

ð5Þ

ð6Þ

and Btotal; jk ¼

mjk X i¼1

1 b ; Ac; jk total;ijk

ð7Þ

where symbols are as defined above. 2.3. Permanent sample plot data Data from permanent sample plots was used for validation of the developed models. Measurements in a forest tree species trial established in 1965 were carried out in the fall of 2007, almost corresponding to the time of acquisition of the laser scanning data. The species trial consists of 13 different experimental sites covering the major growth regions in Denmark (Fig. 1) and 156 individual plots. Net plot sizes are about 0.15 ha. The tree species trial includes 12 different species at each site (totaling 15 different tree species) which include the 13 most commonly grown conifers (Norway spruce (Picea abies (L.) Karst.), Sitka spruce (Picea sitchensis (Bong.) Carr.), Serbian spruce (Picea omorika (Panv cić) Purk.), silver fir (Abies alba Mill.), grand fir (Abies grandis (Douglas ex D. Don) Lindley), noble fir

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(Abies procera Rehder), Douglas fir (Pseudotsuga menziesii (Mirb.) Franco), western red cedar (Thuja plicata Donn ex D. Don), Scots pine (Pinus sylvestris L.), French mountain pine (Pinus mugo Turra), lodgepole pine (Pinus contorta Douglas), cypress (Chamaecyparis lawsoniana (A. Murray) Parl.), and Japanese larch (Larix kaempferi (Lamb.) Carr.) and the two most commonly grown deciduous species (beech (Fagus sylvatica L.) and oak (Quercus robur L.)). In the fall of 2007, the species trial included 91 different plots and all the above mentioned species. Remaining plots were lost during stand establishment or due to catastrophic wind throws. In each plot all trees were uniquely identified and cross-calipered at breast height. Height was obtained for a subsample of 30 randomly selected trees from each plot. Calculations of stand variables were similar to those of the NFI data. To obtain an estimate of stand variables at the time of the laser scanning (spring 2007 for all plots), a linear interpolation was made between the state after thinning in the previous measurement (fall 2001) and the state before thinning in the fall 2007. 2.4. Model development In the first step of selecting predictor variables derived from the laser scanning data, a correlation matrix (Spearman's rank) of response variables (stand basal area, volume, or biomass) and potential predictor variables was calculated using data from NFI plots with only one sub-plot to exclude plots dominated by other land uses. Subsequently, a cluster analysis was conducted on the correlation matrix to identify groups of variables showing similar correlation structure with the response variable and among the predictor variables. The cluster analysis was based on least-squares minimization of the Euclidean distances to the cluster centers (k-means model) where the number of potential clusters were set at 5 (PROC FASTCLUS, SAS Institute, 2009). Based on the cluster analysis, the potential predictor variable showing the highest correlation with the specific response variable within each cluster was selected, while excluding variables having a similar correlation structure. This was done to avoid over-parametrization of the model. The overall procedure for selecting potential predictor variables was similar to the method in Nord-Larsen and Riis-Nielsen, (2010). In the next step of model development we assessed the performance of a large number of basic model forms in predicting stand basal area, volume, and biomass based on the previously selected laser metrics. The tested model forms included several forms of exponential and power functions previously used in similar studies. Using the procedure described above we found that the multiplicative αm model (Y = α0X1α1X2α2 … Xm , where m is the number of model parameters) was well suited to predict basal area, volume, above-ground biomass, and total biomass. Model parameters were estimated using nonlinear regression of the MODEL procedure in SAS Institute, (2009). As the variance of untransformed data was heteroscedastic, estimates are expected to be unbiased but inefficient. To improve efficiency of the parameter estimation we applied generalized methodof-moments estimation (GMM, Hansen, 1982) as the variance relationship was unknown. In the final model estimation we initially included all potential predictor variables selected from the cluster analysis, and selected the final predictor variables using backward elimination of nonsignificant parameters (P > 0.05). Model development was based on data from plots not divided into subplots (One plot only). This was done to capture generic properties of the relationship between variables derived from the laser scanning point cloud and forest biophysical properties. Such relationships are likely to be clouded when plots covering several forest types or even different land uses are included. The parameters of the final model formulations were estimated using data from both plots not divided into subplots and from all available plots to allow for assessment of the effect of including plots covering

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more than one forest type or different types of land use. Further, a preliminary study revealed that the relationship between laser scanning variables and forest properties differed between coniferous and deciduous forest. Consequently, we estimated models using all data as well as for individual strata including only coniferous, deciduous or mixed forests. The latter allows for improving model estimates when tree species composition is known from forest maps or other remote sensing efforts.

where εG, j is the random error of the jth plot and γ0 − γ4 are parameters to be estimated. The volume (V), above ground biomass (Bag), and total biomass (Btotal) models all included the mean height of the first return laser pulse distribution and the 95 percentile of above ground first return pulses (Dz95, 1, 2 ; j). The volume model included also the first pulse interception rate, whereas the two biomass models included the coefficient of variation of first return pulse intensities:

2.5. Model evaluation

1 2 V j ¼ ν 0 ⋅Dzmean;1;1;j ⋅Dz95;1;2;j ⋅IR1;j3 þ εV;j ;

ν

Model errors were first characterized in terms of magnitude and distribution by plotting residuals against predicted values of basal area, volume, above-ground biomass, and total biomass per hectare. Furthermore, residuals were plotted against observed values of other stand variables to expose any obvious trends. Spatial trends were evaluated by plots of residuals against natural-geographical regions of Denmark according to Jacobsen, (1976). In addition to the visual appraisal of the errors a number of summary statistics were calculated for the entire data set as well as for different strata of the model subject. The summary statistics include average error (AB), average absolute error (AAB), root mean squared error (RMSE), and coefficient of determination (R 2). Statistical tests of model assumptions on patterns and distribution of the residuals as well as model bias and stability, were carried out. Variance homogeneity was tested using a White-test and normality was tested using Andersson–Darling goodness-of-fit test. Model bias was tested using a simultaneous F-tests for unit slope and zero intercept of the linear regression of observed versus predicted data (Dent & Blackie, 1979). Predictive performance and stability of the parameter estimates were evaluated by leave-one-out cross validation in which individual NFI plots were left out of the estimation data one at a time and subsequently the estimated model was applied to the left-out plot. The models were further evaluated using permanent plot data from the species trial established in 1965. When constructing validation data, a square moving window with a size identical to the NFI sample plots (706 m 2) was repeatedly sampled among the laser scanning data 100 times within each plot and stand variables were estimated using the developed models. The average stand variables of the 100 estimates were compared with the measured values using similar methods as described above. The method implies that the 100 estimates are highly correlated as they are sampled within the same plot and the samples are partially overlapping. Hence the method yield unbiased mean values but biased estimates of variance. 3. Results Many of the potential predictor variables were highly correlated with the four response variables. For all response variables, the first return mean pulse height above ground (Dzmean, 1, 1 ; j) had the highest coefficient of correlation (Spearman rank-order) ranging from 0.85 (basal area) to 0.93 (volume, above-ground biomass, and total biomass). Other variables showing high levels of correlation with the predictor variables included the relative mean first pulse height (Dzrelmean, 1, 1 ; j), the first pulse interception rate (IR1 ; j), and the 50'th, 75'th, and 95'th percentiles of first return pulse heights (Dzp, 1, 1). The models for predicting basal area, volume, and biomass included only metrics derived from the first return pulse data. The final model for basal area (G) included the mean pulse height of all first return pulses (Dzmean, 1, 1 ; j), the relative mean height of the laser pulse distribution (Dzrelmean, 1, 1 ; j), the first pulse interception rate (IR1 ; j), and the coefficient of variation of first return pulse intensities (Incv, 1, 1 ; j): γ

γ

γ

γ

1 2 3 4 Gj ¼ γ0 ⋅Dzmean;1;1; j ⋅Dzrelmean;1;1; j ⋅IR1; j ⋅Incv;1;1; j þ ε G; j ;

ð8Þ

ν

α

ν

α

α

1 2 3 ⋅Dz95;1;2;j ⋅Incv;1;1;j þ εBag ;j ; Bag;j ¼ α 0 ⋅Dzmean;1;1;j

ð9Þ ð10Þ

and β

β

β

1 2 3 ⋅Dz95;1;2;j ⋅Incv;1;1;j þ εBtotal ;j : Btotal;j ¼ β0 ⋅Dzmean;1;1;j

ð11Þ

where εV, j, εBag, j, and εBtotal, j are the random errors of the jth plot and ν0 − ν3, α0 − α3, and β0 − β3 are parameters to be estimated. Parameter estimates are provided in Table 4. Using data from NFI plots with only one sub-plot, the coefficient of determination was 68% for the basal area model and 78% for the volume and biomass models, respectively (Table 5). Scatter plots of residuals across predicted values, species groups and observed crown cover revealed no obvious trends (Fig. 2). The distribution of residuals differed significantly from normality (P b 0.001) and homogeneity across predicted values (P b 0.001). Predictions were unbiased across all observations (P ≥ 0.05), but the basal area, volume, above ground biomass, and total biomass were overestimated for deciduous species and underestimated for conifers (P b 0.05). Residuals of the three models were generally unbiased for different growth regions except for the island of Funen, where basal area, volume and biomass were generally overestimated. We have no explanation for this behavior that was unrelated to species composition but may be related to forest structure as the forests on Funen are generally small and scattered. Fit statistics were generally little affected when using all plots (i.e. including NFI plots with more than one sub-plot). The leave-one-out cross validation lead to only a minor increase in RMSE (−0.8, 0.5, 0.6 and 0.6% for the basal area, volume, above ground biomass, and total biomass models, respectively.) The reason for the small decrease in RMSE of the cross validation for the basal area model may be due to failure to converge in 6 cases of the 1267 iterations of the procedure. The observed bias for different species types (broadleaves, conifers, and mixed forest) indicate that models could be improved by estimation of species type specific models. Such models could be employed when additional information on species is available e.g. from stand inventories or different types of remote sensing. We thus estimated the models in Eqs. (8), (9), (10), and (11) for the individual tree species types using the one-plot only data. Using the species specific estimates reduced overall RMSE of the basal area, volume, above ground biomass, and total biomass models by 12, 7, 4, and 3%, respectively and the previously observed bias was unobservable (Table 6). The models were validated using data from the species trials and corresponding laser scanning data. When applying the general models (Table 4), the coefficient of determination was 0.61, 0.75, 0.58, and 0.59 for the basal area, volume, above ground biomass and total biomass respectively, and the previously mentioned bias for broadleaves and conifers was very pronounced (not shown). When applying the species specific models (Table 6), the coefficient of determination was 0.77, 0.77, 0.66, and 0.69 for the basal area, volume, above ground biomass and total biomass respectively. Models for volume and biomass were largely unbiased, whereas the model overestimated basal area (Fig. 3). For some plots with a very large growing

T. Nord-Larsen, J. Schumacher / Remote Sensing of Environment 119 (2012) 148–157 Table 4 Parameter estimates of basal area, volume, and biomass models (Eqs. (8), (9), (10), and (11)) including their standard error and t-value. Full data

One plot only data

Parameter

Estimate

Std. error

t-value

Estimate

Std. error

t-value

Basal area γ0 γ1 γ2 γ3 γ4

4.16940 0.24622 0.37665 0.48451 − 0.03747

1.2918 0.0383 0.0879 0.0715 0.0259

3.23 6.43 4.28 6.77 − 1.44

2.54431 0.23311 0.50800 0.35363 − 0.04953

1.0087 0.0471 0.1098 0.0893 0.0320

2.52 4.95 4.63 3.96 − 1.55

Volume ν0 ν1 ν2 ν3

14.00878 0.70891 0.46195 0.25705

1.4527 0.1007 0.1137 0.1116

9.64 7.04 4.06 2.30

14.14401 0.79173 0.37868 0.16502

1.8541 0.1407 0.1586 0.1497

7.63 5.63 2.39 1.10

Above-ground α0 α1 α2 α3

biomass 7.18773 0.89634 0.21672 0.06462

0.8503 0.0312 0.0547 0.0259

8.45 28.72 3.96 2.50

7.88915 0.92030 0.17915 0.05071

1.1035 0.0469 0.0750 0.0330

7.15 19.60 2.39 1.54

Total biomass β0 β1 β2 β3

7.32482 0.88190 0.25125 0.08734

0.8757 0.0314 0.0549 0.0259

8.36 28.12 4.57 3.37

8.10945 0.91161 0.20274 0.07513

1.1400 0.0471 0.0752 0.0327

7.11 19.37 2.70 2.30

stock (Fig. 3), predicted values of volume and biomass were lower than the observed. 4. Discussion The models for predicting basal area, volume, and biomass yielded a satisfactory level of precision across a wide variety of tree species and stand conditions, explaining nearly 70% of the variation in basal area and nearly 80% of the variation in volume and biomass. This level of precision is comparable with similar studies in boreal and

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temperate regions. In series of studies in spruce and pine dominated forests in boreal areas of Norway, coefficients of determination ranged from 0.62 to 0.95 for models predicting basal area and from 0.46 to 0.97 for models predicting timber volume (Næsset, 1997, 2002, 2004a, 2004b, 2005). In general, higher coefficients of determination were obtained in young (and presumably more homogenous) forest than in mature forest and model fit was poorer in forests dominated by deciduous species. In a study in mountainous, temperate forests of Bavaria, the coefficient of determination for predicting basal area and volume was 0.43 and 0.52, respectively (Heurich & Thoma, 2008). Model predictions were improved when the study area was stratified into coniferous and deciduous forest. Again, coefficients of determination for the prediction of forest basal area and volume were higher in coniferous forest (R 2 = 0.78 and 0.86) than in deciduous forest (R 2 = 0.63 and 0.71). In a study in Douglas fir dominated forests in the western Cascades of Oregon, a very good correspondence was observed between field-measured basal area and volume and values estimated from ALS data (Means et al., 2000). Coefficients of determination were 0.94–0.95 for basal area and 0.95–0.97 for estimation of volume and precision was poorer in old-growth (200 to 500 years old) plots than in plots covered by young (20 to 80 years old) and mature (120 to 200 years old) trees. The high level of precision may be related to the very large plot size (2500 m 2) used in this study. When predicting forest biomass in temperate forests of eastern Texas, coefficient of determination was found to increase with plot sizes ranging from 0.01 (R 2 = 0.83) to 1 ha (R 2 = 0.94) (Zhao et al., 2009). In the above mentioned studies, field-measured plots were all inventoried extensively. The measurements conducted on the NFI plots used as ground truth in the present study were less extensive. As mentioned above, due to economic constraints only the largest trees (dbh > 40 cm) are measured within the full 15 m radius plots in the NFI. Smaller tree measurements are confined to the 3.5 m (dbh b 10 cm) and 10 m (dbh b 40 cm) circles, respectively. Estimates of basal area, volume and biomass are obtained by scaling the measurements from smaller trees to the full plot, assuming an even

Table 5 Fit statistics of the system of equations (Eqs. (8), (9), (10), and (11)) for both the full data and the ‘one plot only’ data. Fit statistic

Full data

Species

All

One plot only data Deciduous

Coniferous

Mixed

All

Deciduous

Coniferous

Mixed

Basal area AB AAB RMSE R2 RMSE (PRESS)

0.0000 5.2882 7.3947 0.6824 7.3503

− 1.7679 5.9224 8.0699 0.4847 8.0802

1.5981 5.1948 7.2326 0.7186 7.2474

0.2315 4.8149 6.9590 0.7527 6.8283

0.0000 5.4822 7.5805 0.6766 7.5177

− 2.2163 6.0225 8.2080 0.4594 8.2242

1.8428 5.4133 7.6750 0.7096 7.7087

0.2876 4.9916 6.8752 0.7674 6.6511

Volume AB AAB RMSE R2 RMSE (PRESS)

0.0000 51.3300 80.4392 0.7747 80.7008

− 10.4989 68.1899 101.8450 0.6799 102.2280

9.2336 41.0440 64.7690 0.8263 64.9000

1.5835 45.0937 70.8960 0.8137 71.1212

0.0000 52.8074 82.9469 0.7821 83.3589

− 15.7943 69.1529 103.9653 0.6812 104.5910

11.6355 43.1431 69.3827 0.8237 69.5970

3.7039 46.3465 72.2721 0.8286 72.6040

Above-ground biomass AB AAB RMSE R2 RMSE (PRESS)

0.0000 27.7478 43.6812 0.7721 43.8420

− 5.5272 36.0702 53.7535 0.7157 54.0063

3.1317 21.9231 36.3034 0.7825 36.3904

2.2399 25.2771 39.5336 0.8033 39.6465

0.0000 28.1192 44.4085 0.7824 44.6767

− 7.1203 36.0268 53.7343 0.7262 54.1442

3.6708 22.7787 39.0765 0.7768 39.2334

3.4103 25.7286 39.4408 0.8229 39.6436

Total biomass AB AAB RMSE R2 RMSE (PRESS)

0.0000 33.1476 52.5216 0.7729 52.7175

− 4.2786 44.2286 66.4189 0.7100 66.7309

1.9492 25.2492 40.8199 0.7970 40.9207

2.1202 29.9741 47.4462 0.8010 47.5811

0.0000 33.2203 52.4075 0.7884 52.7292

− 6.3301 43.6784 65.5664 0.7242 66.0637

2.8984 26.1436 43.7069 0.7936 43.8810

3.4355 30.0740 45.9825 0.8277 46.2219

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T. Nord-Larsen, J. Schumacher / Remote Sensing of Environment 119 (2012) 148–157

Fig. 2. Residuals of the basal area, volume and biomass models. Based on the one plot only data (1345 observations).

distribution across the plot. This stratification of measurements in the NFI introduces additional error to the dependent variables affecting the observed model precision negatively. We therefore expect that actual model precision may be even higher than estimated. Compared to similar studies, the variability of the study object was quite large. The data covered a wide ecological gradient from sandy outwash planes in western Jutland, to fertile tills in the eastern part of the country. The sample plots used in the analysis included a total of 56 different forest tree species, about 73% of the plots contained mixtures of different species and 39% of the plots had mixtures of broadleaves and conifers. The majority of forest stands included in this study had fully closed canopies (25% had a crown cover of more than 90%), but 20% had a crown cover of less than 50%.

Although the model yielded a satisfactory level of precision across the entire data, predictions were positively biased for broadleaves and negatively biased for conifers. This bias is possibly caused by differences in morphology of the different tree species, which was accentuated by the capture of laser scanning data during leaf-off conditions and is similar to the findings of other authors (Næsset, 2005; Næsset & Gobakken, 2008). Rigorous analysis did not reveal parameters suited for capturing the inter-species differences such as for individual trees in Brandtberg, (2007), Brandtberg et al., (2003), Holmgren and Persson, (2004), Holmgren et al., (2008), Korpela et al., (2010), Örka et al., (2009), Reitberger et al., (2008) and indicate a potential for stratifying measurements according to species type as also done by some authors (Heurich & Thoma, 2008; Næsset &

T. Nord-Larsen, J. Schumacher / Remote Sensing of Environment 119 (2012) 148–157 Table 6 Species specific parameter estimates of basal area, volume, and biomass models (Eqs. (8), (9), (10), and (11)) including their standard error. Models were estimated with the one-plot-only data. Fit statistics are provided for the full data set and for the individual species types.

Parameter

Broadleaves

Conifers

Estimate

Estimate

Std. error

Mixtures Std. error

Estimate

Basal area (AB = 0.0000, AAB = 4.7931, RMSE = 6.6995, R2 = 0.7474) γ0 1.22817 0.7027 1.64305 1.0451 2.40998 γ1 0.31337 0.0672 0.46101 0.0704 0.38049 γ2 0.29510 0.1546 0.67545 0.1486 0.48636 0.18779 0.1456 − 0.11357 0.1023 0.33665 γ3 γ4 0.22497 0.0437 − 0.23295 0.0753 − 0.08839 AB 0.0000 0.0000 0.0000 AAB 4.9356 4.7181 4.7265 RMSE 6.8185 6.6944 6.6841 R2 0.6269 0.7791 0.7801 Volume (AB = 0.0000, AAB = 48.7216, RMSE = 77.4627, R2 = 0.8099) ν0 10.82550 2.2564 19.68917 3.4980 15.40511 ν1 0.66846 0.1775 1.92446 0.1442 1.34476 ν2 0.53376 0.1959 − 0.71557 0.1637 − 0.12397 ν3 0.00756 0.2057 − 0.89276 0.1120 − 0.26717 AB 0.0000 0.0000 0.0000 AAB 65.0859 38.1463 43.2479 RMSE 98.6859 60.8475 69.1138 R2 0.7127 0.8644 0.8433

Std. error 1.5943 0.0798 0.1724 0.1723 0.0635

4.0804 0.2707 0.3013 0.2883

Above-ground biomass (AB = 0.0000, AAB = 27.2572, RMSE= 42.7447, R2 = 0.7984) α0 2.75662 0.7882 17.61783 5.3287 11.07974 3.3571 α1 0.80103 0.0658 1.10166 0.0846 1.10137 0.1002 α2 0.39316 0.1107 0.00597 0.1337 0.05088 0.1642 α3 0.19563 0.0470 − 0.12862 0.1088 − 0.03363 0.0682 AB 0.0000 0.0000 0.0000 AAB 34.6985 22.5133 24.6963 RMSE 51.5663 37.6862 38.1034 R2 0.7478 0.7924 0.8347 Total biomass (AB = 0.0000, AAB = 32.3332, RMSE = 50.7500, R2 = 0.8016) β0 3.52007 1.0183 20.23273 5.8492 11.80632 3.5527 β1 0.78434 0.0657 1.09759 0.0825 1.09657 0.1000 β2 0.39255 0.1114 0.03838 0.1295 0.05904 0.1646 β3 0.19566 0.0475 − 0.14571 0.1027 − 0.01087 0.0673 AB 0.0000 0.0000 0.0000 AAB 42.6714 25.5764 28.9591 RMSE 63.7448 41.9969 44.4936 R2 0.7393 0.8095 0.8387

Gobakken, 2008). Estimating equations for the two species types individually led to a reduction in RMSE of 3–17% for broadleaves and 4–13% for conifers, depending on the dependent variable. The model bias across tree species types (broadleaves or conifers) was also apparent when validating the models based on data from the species trials. Basal area, volume, above ground biomass and total biomass were generally underestimated at the conifer plots and overestimated for plots with broadleaves. When applying the species specific models, predictions were largely unbiased across all sites and species. The exception is an apparent underestimation of the four stand values for a small number of very dense stands of grand fir (experiments 1010, 1011 and 1012) and western red cedar (experiment 1006) grown on fertile sites in eastern Denmark. One possible explanation for this observation is that such dense stands are not often observed in the NFI and thus the models are extrapolated from the data. Another reason may be that the point cloud becomes saturated, i.e. that very few pulses are reflected from the ground and thus that the ground level is poorly determined. Across the ALS data extracted from the NFI plots the average proportion of ground hits were 18.4%. On 2% of the NFI plots, the proportion of ground hits were less than 5% and only on 0.5%, the proportion of ground hits were less than 1%. Hence, problems with saturation of the point cloud are possibly small.

155

Most authors (e.g. Heurich & Thoma, 2008; Lim & Treitz, 2004; Lim et al., 2003; Næsset, 1997; Næsset & Gobakken, 2008) have estimated model parameters using the linearized form of the multiplicative model (i.e., ln(Y) = ln(α0) + α1lnX1 + α2lnX2 + … + αmlnXm). It is well known that the log-linearized model introduces logarithmic bias when back-transformed and should be corrected for this bias when used for prediction (e.g. Sprugel, 1982). The standard factor for correcting for this bias (exp(SEE 2/2)) is unbiased under assumption of normality of model residuals. For comparison, we linearized the models presented in Eqs. (8)–(11) using logarithmic transformation i.e. using the same predictor variables as in the nonlinear models. Subsequently we estimated model parameters using multiple linear regression (REG procedure of SAS 9.2). Predictions in the original scale were made by back-transformation of model predictions, while correcting for logarithmic bias using the standard correction factor cited above. We observed excess variance heteroscedasticity and non-normality of the transformed model which could not easily be mended using a weighing procedure. Consequently, predictions of the linearized model were biased as much as 10% of the dependent variable in the original scale even after correction for logarithmic bias. Instead of linearizing the non-linear model we estimated model parameters using non-linear regression analysis and generalized method-of-moments estimation (GMM) to avoid problems with biased and inconsistent estimates. The model did not include possible spatial correlations. However, a subsequent analysis of empirical variograms revealed no residual spatial correlations. When selecting parameters for the linearized form of the multiplicative model most authors have applied various standard methods for parameter selection such as stepwise, backward or forward selection (e.g. Gobakken & Næsset, 2004; Lefsky et al., 1999; Means et al., 2000; Næsset, 2002, 2004a, b; Næsset et al., 2005). However, in this study potential predictor variables were highly correlated, and the resulting models often became over-parameterized. Further, the large number of observations in this study resulted in selection of a large number of significant parameters (>10), when applying the automated selection procedures. In comparison, the applied parameter selection method resulted in parsimonious models with moderate internal correlation between parameters and a larger or similar coefficient of determination. The study reveals that airborne laser scanning may be a suitable means for mapping forest biomass resources, even when data is obtained at a relatively low density using a large scanning angle across a wide range of forest types. The forest resources estimated in this study represent the overall theoretical potentials available within fundamental bio-physical limits, and do not take into account issues related to technical or economical constraints on the exploitation of the resource. Resource potentials may be categorized as theoretical, technical, economic or sustainable (Rettenmaier et al., 2010). The technically available potential is a fraction of theoretical potential limited by technological or structural conditions such as land accessibility, harvest and transportation technologies. The economic potential is a fraction of technical potential limited by economic constraints i.e. profitability of procuring the resource. Sustainable potential is a fraction of one of the above potentials, where various dimensions of sustainability are included e.g. nutrient depletion or leaching, green house gas emissions etc. Assessment of technically, economically or sustainably available potentials from the theoretical resources would require additional analyses using available information on terrain, infrastructure and socioeconomic parameters. Although laser scanning is suitable for characterizing the physical properties of forest crops, the method appeared less suitable for distinguishing different tree species. The different metrics derived from the laser point cloud, including both metrics based on the above ground height and intensity of the reflections, were tested for their ability to distinguish broadleaves from conifers. Although the coefficient of variation of first return pulse intensities (Incv, 1, 1 ; j) included in the biomass models (Eqs. 10 and 11) differed between the two species types (P b 0.001) inclusion of this or other variables did not

T. Nord-Larsen, J. Schumacher / Remote Sensing of Environment 119 (2012) 148–157

800 600 400 200

Predicted volume (m3ha−1)

60 50 40 30 20

1000

Volume

70

Basal Area

10

Predicted basal area (m2ha−1)

80

156

10

20

30

40

50

60

70

200

80

300

500

600

800

1000

700

300

500

700

Total biomass

100

Predicted total biomass (tonnes ha−1)

300

500

700

Above ground biomass

100

400

Volume (m3ha−1)

100

Predicted above ground biomass (tonnes ha−1)

Basal area (m2ha−1)

100

Above ground biomass (tonnes ha−1)

300

500

700

Total biomass (tonnes ha−1)

Fig. 3. Observed basal area, volume, above ground biomass and total biomass of the species trial versus the corresponding predicted values using laser scanning data and the species type specific models (Table 6). Conifers are represented by triangles and broadleaves by dots.

satisfactorily account for differences in tree species types. One reason may be the lack of range calibration of the return pulse intensities, which added a random error to the recorded intensity, depending on the plot distance to nadir. This random error affected the magnitude of absolute measures of intensity derived from the ALS data (e.g. mean, median, maximum or various percentiles of the return pulse intensity). Consequently, such variables may have lost predictive power due to the lack of range calibration. However, the relative measures of return pulse intensity (e.g. cv of the intensities included in Eqs. 10 and 11) are generally unaffected by the range calibration. This may in turn explain why parameter selection procedures selected a relative measure of return pulse intensity for the final model. Due to differences in phenology and in chlorophyllic activity, different forest tree species may be distinguished based on infrared photos obtained during leaf-on conditions (e.g. Stephens et al., 2008). Combining laser scanning data with infrared aerial photos would allow for stratification according to species types and allow for expedient and cost effective assessment of forest biomass with unprecedented accuracy (Erdody & Moskal, 2010). Such a system would increase efficiency in planning of local and regional initiatives regarding e.g. energy conversion facilities and monitoring carbon sequestration in forest biomass. Acknowledgments We wish to thank Michael Schultz Rasmussen and Johnny Koust Rasmussen from COWI A/S for providing laser scanning data and

technical support during the project. The project was financed by The Forest Product Development Fund (The Danish Forest and Nature Agency) and the SINKS project (The Ministry of Climate and Energy). The Danish NFI, which supplies the reference data in this study, is financed by The Danish Forest and Nature Agency, The Ministry of Environment.

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