Forestry Advance Access originally published online on December 14, 2006
Forestry 2007 80(1):73-81; doi:10.1093/forestry/cpl045
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Testing the usability of truncated angle count sample plots as ground truth in airborne laser scanning-based forest inventories
1 Faculty of Forestry, University of Joensuu, PO Box 111, FI-80101 Joensuu, Finland
2 Finnish Forest Research Institute, Joensuu Research Centre, PO Box 68, FI-80101 Joensuu, Finland
* Corresponding author. E-mail: matti.maltamo{at}forest.joensuu.fi
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Airborne laser scanner (ALS)-based forest inventory method usually adopt a laser canopy height distribution approach in which forest characteristics are predicted using measures such as percentiles of the distribution of laser canopy heights across a fixed area. The method requires a ground-truth sample of accurately measured field plots. One possibility for reducing the costs lies in the use of existing field plots for ground-truth purposes. The most obvious alternative in Finland would be to use truncated angle count sample plots of the National Forest Inventory or more locally data of checking of inventory by compartments. Due to the lack of suitable angle count ground-truth data and corresponding laser data, we tested this possibility using data on fixed-area sample plots, in which tree locations were simulated. The trees for a truncated angle count sample plot were then chosen and the resulting data together with the characteristics of an ALS-based canopy height distribution were used to construct regression models to predict stem volume, basal area, stem number, basal area median diameter and height. The accuracy of the stand attributes was found to be almost as good as in the case of models of fixed-area plots.
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Introduction |
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TopSummaryIntroductionMaterials and methodsResultsDiscussionConclusionsReferences |
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Applications of the airborne laser scanner (ALS)-based forest inventory method, especially in the Nordic countries, usually adopt the laser canopy height distribution approach (Næsset, 2002
, 2004a; Holmgren, 2004, Suvanto et al., 2005; Maltamo et al., 2006, see also Means et al., 2000; Lim et al., 2003). The first practical forest inventories using this approach in Norway were carried out in 2004 (Næsset, 2004b). Forest characteristics are predicted using quantiles (percentiles) of the distribution of laser canopy height averages over a fixed area (Næsset, 2004a, b), and the basic method includes low-resolution laser data (pulse density usually below 1 hit m–2) and a sample of accurately measured field plots. Regression models are then constructed to predict the stand variables of interest (volume, basal area, mean height and diameter) by reference to the laser scanner-based height characteristics. Various studies (see Næsset et al., 2004) have shown that this approach produces highly reliable estimates for stand variables, e.g. a root mean square error (RMSE) of 
10 per cent for stand volume.
According to Anttila (2005), the costs of acquiring low-resolution laser data in Finland are currently 1–5 
(1.21–5.6 USD) ha–1. Additional costs arise, however, from the necessary ground-truth measurements, which involve relatively large fixed-area (e.g. 200–400 m2) sample plots. Local field plots and models are used in each inventory area in Norway, usually of the order of 490 km2 in size (Næsset, 2004b) and numbering 50–150 per inventory (Næsset et al., 2004).
The possibilities for reducing the costs of laser scanning-based forest inventories lie in the discovering of alternatives that allow the use of constructed stand variable models in larger geographical areas or the use of existing field plots as sources of ground-truth data. Næsset (2004b) obtained even higher precision in terms of the estimated stand characteristics when using a separate test area located 80 km away from the modelling area. Suvanto et al. (2005) and Uuttera et al. (2006) have shown laser scanning-based models to achieve a satisfying level of transferability in Finland, i.e. the results are within the error tolerance of the Finnish compartment inventory system (Uuttera et al., 2002). Even models constructed in Norway (Næsset, 2002) were applicable to Finnish conditions, leading to a stand-level error of 24–26 per cent in the tree stock volume. The risk of obtaining biased results increases when applying models outside their original modelling area, however.
The possibilities for using existing field plots in Finland include permanent research and National Forest Inventory (NFI) sample plots, the stand-level compartment register and local sample plots of checking inventory of compartment register. The network of permanent research plots, (see Gustavson et al., 1988), is so sparse, however, that it cannot applied locally, and most of the research plot datasets are several years old. Similarly, the accuracy of the data in the stand-level compartment registers is not satisfactory for use in the construction of models (Haara and Korhonen 2004). In fact, the accuracy is in most cases worse than that of stand variable estimates based on ALS data (Suvanto et al., 2005). Furthermore, the compartment registers do not contain plot-level data, as all data have been aggregated to stand level. Therefore, the most promising alternatives are to use NFI data or sample plots of checking inventories.
In NFI's of Finland and Austria angle count (relascope) plots are applied (Bitterlich, 1984; Tomppo et al., 1998). This means that tree sampling is based on probability proportional to size sampling where tree basal area is used as a weight. The principles of angle count sampling can be found, e.g. from the publications by Bitterlich (1984) and Kangas (2006). In the Finnish NFI9, truncated angle count plots were measured a maximum radius of 12.52 m being in southern Finland and 12.45 m in northern Finland (Tomppo et al., 1998).
The checking of inventories by compartments has mainly been studied in Finland, Sweden and Russia (Jonsson and Lindgren, 1978; Laasasenahoand Päivinen, 1986; Kinnunen et al., 2007). The inventory has usually been carried out in Finland or Russia by means of sampling techniques, i.e. a sample of compartments is selected and a systematic plot network is designated for the compartments for measurements of angle count plots (Laasasenaho and Päivinen, 1986; Kinnunen et al., 2007; Haara and Korhonen, 2004). However, usually these checking inventory datasets only cover rather small local areas. Both of these inventory sample plot types, NFI and checking inventory, are also nowadays usually Global Positioning System (GPS) located.
The aim of the present investigation was to test the usability of truncated angle count plots as ground-truth data in a laser scanning-based forest inventory. Since no areas in Finland large enough to include an adequate number of angle count sample plots and corresponding reference plots with fixed area with same location have yet been submitted to laser scanning, this study relies on simulation.
For the simulation study, we applied data of Suvanto et al. (2005). They constructed regression models for the stand attributes stand volume, basal area, number of stems, basal area median diameter and median height by using the laser canopy height distribution approach (for the basic principle see e.g. Næsset, 2002). The gound truth data consisted of 472 circular sample plots. Suvanto et al. (2005) also validated their results in the same modelling data. In this study, an angle count plot is simulated inside each circular sample plot. Corresponding regression models are constructed for the stand attributes and the models are validated by using the values of original circular plots.
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Materials and methods |
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Test area
The Matalansalo test area (1200 ha) in eastern Finland is a typical Finnish southern boreal managed forest area. The area is dominated by coniferous tree species, i.e. Scots pine (the main tree species on 59 per cent of the plots) and Norway spruce (34 per cent), whereas deciduous trees, mainly birches (7 per cent), are usually the minority. Classified by stand development class, the area consists of young (27 per cent), middle-aged (42 per cent) and mature forests (31 per cent). The corresponding proportions of the site fertility classes are grass-herb sites (Oxalis type) 2 per cent, moist sites (Myrtillus type) 48 per cent, dry sites (Vaccinium type) 42 per cent and poor sites (Calluna type) 8 per cent.
Field measurements and calculation of plot characteristics
Both the remote sensing material and the field data were acquired in the summer of 2004. Altogether, 472 plots of radius 9 m were established in 67 randomly selected stands of average size 2.8 ha. The GPS was used to determine the position of the centre of each of the 472 plots. Positioning involved differential correction to a base station which enabled the accuracy of 1 m. Between five and nine plots were systematically placed in each stand (for the positioning principle, see Laasasenaho and Päivinen, 1986). The average distance between plots was 50 m. The diameter at breast height (d.b.h.), tree and storey class and species were recorded for all trees over 5 cm thick (d.b.h.). The tree species-specific height models of Veltheim (1987) were used to predict the heights of the trees. The height of one sample tree of each species and each storey class was measured on each plot. These height measurements were used to calibrate the height estimates of the models of Veltheim (1987). Finally, the volume models of Laasasenaho (1982) were used to calculate tree volumes. The plot characteristics of interest (Table 1) were then multiplied out at the hectare level. Corresponding stand-level characteristics are presented in Table 2.
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A truncated angle count sample on each plot was generated using a basal area factor of 2, which with a plot radius of 9 m implies that trees of diameter below 25.5 cm are selected from an angle count plot and larger trees from a fixed-area plot, i.e for trees of diameter over 25.5 cm, an angle count plot and fixed-area plot are equal.
As the locations of the trees were not recorded in the field, they were generated by assuming a random (Poisson) spatial pattern within the plot. Essentially, this means the generation of tree distances from the centre of the plot. On a plot with a random spatial pattern, the cumulative distribution function of the distance, i.e. the probability that of the distance R of an arbitrary tree from the centre of the plot being below a fixed value r, is calculated by dividing the area of a circle of radius r by the total area of the plot:
 | (1) |
Based on the probability integral transform (Casella and Berger, 2002, p. 247), the distance of a given tree from the centre of the plot was generated by means of a uniformly distributed random number between 0 and 1, denoted by u, in the inverse of the distribution function (1), so that 
The trees belonging to the sample were selected according to the generated distance and observed diameter of each.
The plot characteristics of interest in the angle count sample plots generated in this manner are presented in Table 1. Basal area was calculated as a sum of trees in a plot multiplied by the basal area factor 2. Correspondingly, basal area median diameter was the median of the sampled tree diameters and the height of the same tree was referred as basal area median tree height. Each tree chosen to angle count sample plot was modified to refer to the stem number per hectare by using the formula
 | (2) |
where, nhec is the number of stems per hectare, d = tree diameter (m) and q = basal area factor. Number of stems was calculated as a sum of modified stem numbers. Finally, tree volume was calculated correspondingly as in the case of circular plot but volumes were also multiplied by modified stem numbers. There were an average of 38.4 measured trees on the fixed-area plots and 12.4 trees on the simulated and truncated angle count plots.
Laser scanner data
Georeferenced laser scanner survey data were collected for an area of 1200 ha at Matalansalo on 4 August 2004 using an Optech ALTM 2033 scanner. Three differential global positioning system receivers were employed to record the carrying platform position: one on an aircraft and two on the ground (the first as the base station and the others for backup). The results provided a point cloud in which the x, y and z coordinates of the points were known. The test site was measured from an altitude of 1500 m above ground level using a field of view of 30 degrees. This gave a swath width of 800 m and a nominal sampling density of 0.7 measurements per square metre. The accuracy was 0.75 m for the x and y coordinates and 0.25 m for the z coordinate. Both first and last pulse data were recorded.
In order to generate the digital terrain model (DTM) from the laser scanner data, the points reflected from non-ground objects, i.e. from trees and buildings, must be classified as non-ground hits. The laser point clouds were therefore first classified using the TerraScan software (see www.terrasolid.fi) to separate the ground points from the others (method explained in Axelsson, 2000) and a raster DTM was then created from the classified ground points by calculating their mean values within each 1-m raster cell. Values for raster cells with no data were derived using Delaunay triangulation and the bilinear interpolation method.
Laser canopy heights were calculated as the differences between the z coordinates of laser hits and the estimated ground elevation values at the corresponding locations. Points for which the canopy height values were over 2 m were assumed to be vegetation hits (see Næsset, 2002). Various height metrics for the fixed plots of radius 9 m were calculated from the laser canopy height point data, including 5, 10, 20, ..., 90, 95 and 100 per cent canopy height percentiles, h5, ..., h100 (see Næsset, 2004) and the corresponding proportional canopy densities, p05, ..., p100. Finally, the standard deviation (SD), mean, coefficient of variation and proportion of vegetation hits were computed. All these characteristics were calculated for both the first and last pulse data and used as independent variables in the regression analysis.
Construction of models
Regression models were constructed for the plot-level variables stem volume, basal area, number of stems, basal area median diameter and basal area median height, values obtained for the angle count plots being used as dependent variables and laser canopy height characteristics as independent variables. First, variables for models were selected by using stepwise ordinary least square regression. Linear mixed modelling was then employed to estimate the stand characteristics because a hierarchical structure (forest stands, sample plots) existed in the study design (Searle, 1971). The stand characteristics were modelled as follows:
 | (3) |
where Yij denotes the stand characteristics chosen for plot j in stand i, X is a matrix of ALS-based explanatory variables, ß is the fixed-effects parameter vector, si is the random stand variance (si N(0, 
)) and eij is the random error term (eij N(0, 
)).
Calculation of the reliability characteristic
The reliability of the estimates obtained with the different models was tested in terms of the RMSE and bias of each of the stand characteristics. The absolute RMSE and bias were calculated as follows:
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 | (5) |
where n is the number of plots and Yi and 
are the observed (original fixed-area plot value) and predicted characteristics for plot i. Relative RMSEs were calculated by dividing the absolute RMSE by the observed value and expressing the result as a percentage. The results were also averaged to stand level by considering all the plots within one stand.
The reliability of constructed models was also compared with that of the models by Suvanto et al. (2005). Both models were constructed from the same material, the only difference being the simulation of angle count sample plots in this study. The variables used in the models of Suvanto et al. (2005) are presented in Table 3. In the case of models which were constructed from fixed-area sample plots, plot-level results were obtained from the study of Suvanto et al. (2005). Stand-level reliability figures were calculated in this study by using the models of Suvanto et al. (2005). Finally, relative biases of frequencies per diameter and height classes were calculated to compare per hectare level distribution of both data types.
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The model constructed for plot volume is
 | (6) |
where f or l denotes the laser pulse type (first or last pulse), h60 denotes the height at which 60 per cent of the height distribution has accumulated, veg is the proportion of vegetation hits, coeffva is the coefficient of variation in laser canopy heights and std is the SD of the laser canopy heights. The between-stand variance of the residual is 0.007 and the within-stand variance 0.088.
The model for the basal area is
 | (7) |
where hmean is the mean of the laser canopy heights. The between-stand variance of the residual is 0.018 and the within-stand variance 0.402.
The model for the number of stems is
 | (8) |
where h10 denotes the height at which 10 per cent of the height distribution has accumulated. The between-stand variance of the residual is 0.013 and the within-stand variance 0.253.
The model for the basal area median diameter is
 | (9) |
where h20, h40 and h80 denote heights at which the corresponding proportions of the height distribution have accumulated. The between-stand variance of the residual is 0.0165 and the within-stand variance 0.0981.
The model for the basal area median height is
 | (10) |
where h90 denotes the height at which 90 per cent of the height distribution has accumulated. The between-stand variance of the residual is 0.0199 and the within-stand variance 2.394.
The plot-level reliability figures are presented in Table 4, where it can be seen that the stand attribute estimates based on the truncated angle count plots are close to the fixed-area estimates obtained from the work of Suvanto et al. (2005) in terms of RMSE. However, the angle count estimates of stem number and basal area median height are biased and these attributes show the greatest differences in RMSE between the fixed-area and angle count plots.
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When the reliability figures are considered at the stand level, the differences between the plot types diminish further (Table 5), so that only the estimated stem number is seen to be biased. All in all, it can be said that the angle count estimates for the stand attribute seems to be relatively accurate.
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The relative biases of frequencies of tree diameters and heights showed no clear trends between sample plot types (Figure 1). In the case of the diameters, the obtained biases were smaller than 10 per cent in most of the classes and, correspondingly, below 5 per cent for the height classes.
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Discussion |
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TopSummaryIntroductionMaterials and methodsResultsDiscussionConclusionsReferences |
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The results of this assessment of the usability of truncated angle count plots as sources of ground truth for ALS-based forest inventories indicate that the accuracy achieved in estimating the stand attributes of interest was almost as good as in the case of fixed-area plots. The obtained diameter and height distributions of both sample plot types were also on average close to each other (Figure 1). However, this study presented only a special case concerning certain basal area factor and truncated sample plots. For angle count plots where no truncation is done, the results would be worse. Furthermore, in the case of angle count sample plots without maximum radius (truncation distance), the choice of the size of ALS plot would be highly problematic. Therefore, the results of this study are valid only for truncated angle count sample plots, such as current Finnish NFI data, where the maximum radius is also constant in each plot.
When the model forms of this study and the study by Suvanto et al. (2005) are compared, it can be seen that there are some differences. Only in the case of stand volume, the number of dependent variables is the same. There are more independent variables in the models concerning basal area median diameter and height in this study than in the Suvanto et al. (2005), whereas in the case of basal area and number of stems, the number of independent variables is smaller in this study. There are also differences in the independent variables but this is obvious since canopy height distribution approach usually includes numerous variables which are close to each other. In both model sets proportion of vegetation hits, mean height of laser hits and some upper height of the height distribution are usually applied.
Due to the lack of suitable angle count ground-truth data and corresponding ALS data, the tree locations in the present field data were simulated on the assumption of a random spatial pattern of trees within a plot. This may have affected the results. However, according to Tomppo (1986), 88 per cent of the forests in Finland have either random or regular spatial pattern. At least, the simulation meant that no observation errors occurred in the choice of trees on the angle count plot, although such plots are usually more sensitive to observation errors than fixed-area plots.
Due to the use of fixed-area plots as a starting point for the simulation, the resulting angle count plots are truncated to a maximum radius of 9 m. This may have improved the results since diameter distribution of trees which d.b.h. is larger than 25.5 cm is corresponding both in simulated angle count sample plots and original fixed-area sample plots. However, only 5.7 per cent of the trees measured were larger than the truncation point of 25.5 cm at breast height. The volume of these trees nevertheless accounts for 35.1 per cent of the volume of all the trees. Correspondingly, truncated angel count sample plots are measured in the Finnish NFI. However, since the real NFI plots are larger than the simulated data used here, slightly more unreliable results can be expected.
It is also clear that the sampling design of the present study is quite different from the NFI design, as all the plots were located inside an area of 1200 ha, whereas the NFI is usually based on systematic sampling over large areas. The number of plots examined here, 472, would be measured to cover a considerably larger geographical area in the NFI and would include more variation in forest structure, which would mean that the resulting models would also include more variation. In addition, when modelling stand attributes using NFI data, the hierarchical structure of the data must be taken into consideration. On the other hand, the study design of this study is correspondent to those of checking inventory of compartment register. In fact, the study material is based on checking inventory, but fixed-area sample plots were originally measured instead of angle count sample plots.
The most problematic stand attribute among those modelled was the number of stems, as was true of the fixed-area sample plots (Suvanto et al. 2005). This drawback may be emphasized still more in the case of angle count sample plots, as these are an inefficient means of measuring stem numbers (see also e.g. Siipilehto, 1999). The current compartment-based calculation system, however (see Haara and Korhonen, 2004), which employs basal area diameter distribution models together with tree-level height and volume models, does not require stem numbers.
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Conclusions |
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A rapid change is taking place in forestry practises in Finland, involving a move towards ALS-based forest inventories. This is due on the one hand to the possibility of improving the accuracy of the stand variables obtained, and on the other hand to the possibility of reducing the costs relative to the existing field inventory technique. The use of existing ground-truth data in combination with the ALS data would further improve the cost efficiency of forest inventories. The preliminary results reported here show that the accuracy of truncated angle count sample plots would also be almost as good as with fixed-area plots. This research into the use of angle count data in ALS-based forest inventories in Finland will continue and will include such topics as the georeferenced positioning accuracy of NFI plots, the role of small trees in angle count plots, the optimal size of inventory area, the estimation of species-specific stand attributes and the cost efficiency of angle count plots vs fixed-area plots.
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References |
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Received 14 November 2006.
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