TY - JOUR
AU - Tymińska-Czabańska,, Luiza
AB - Abstract Reliable information concerning stand volume is fundamental to making strategic decisions in sustainable forest management. A variety of remotely sensed data and different inventory methods have been used for the estimation of forest biometric parameters. Particularly, airborne laser scanning (ALS) point clouds are widely used for the estimation of stand volume and forest biomass using an area-based approach (ABA) framework. This method relies on the reference measurements of field plots with the necessary prerequisite of a precise co-registration between ground reference plots and the corresponding ALS samples. In this research, the allometric area-based approach (AABA) is proposed in the context of stand volume estimation of Scots pine (Pinus sylvestris L.) stands. The proposed method does not require detailed information about the coordinates of the field plots. We applied Polish National Forest Inventory data from 9400 circular field plots (400 m2) to develop a plot level stand volume allometric model using two independent variables: top height (TH) and relative spacing index (RSI). The model was developed using the multiple linear regression method with a log–log transformation of variables. The hypothesis was that, the field measurements of TH and RSI could be replaced with corresponding ALS-derived metrics. It was assumed that TH could be represented by the maximum height of the ALS point cloud, while RSI can be calculated based on the number of tree crowns delineated within the ALS-derived canopy height model. Performance of the developed AABA model was compared with the semi-empirical ABASE (with two predictors: TH and RSI) and empirical ABAE (several point cloud metrics as predictors). The models were validated at the plot level using 315 forest management inventory plots (400 m2) and at the stand level using the complete field measurements from 42 Scots pine dominated forest stands in the Milicz forest district (Poland). The AABA model showed a comparable accuracy to the traditional ABA models with relatively high accuracy at the plot (relative root mean square error (RMSE) = 22.8 per cent; R2 = 0.63) and stand levels (RMSE = 17.8 per cent, R2 = 0.65). The proposed novel approach reduces time- and cost-consuming field work required for the classic ABA method, without a significant reduction in the accuracy of stand volume estimations. The AABA is potentially applicable in the context of forest management inventory without the necessity for field measurements at local scale. The transportability of the approach to other species and more complex stands needs to be explored in future studies. Introduction Stand volume is one of the most important forest parameters in the context of forest management inventories. Reliable information concerning stand volume is fundamental to making strategic decisions in sustainable forest management because the estimates of the volume are key criteria when considering site- and species-specific decisions concerning silvicultural management guidelines, determining the allowable cut and when forecasting timber yield. Information about stand volume is also very important in the estimation of the terrestrial carbon sequestration (Eggleston et al., 2006; Jagodziński et al., 2019). Remote sensing technology has been extensively used for the spatial predictions of stand volume under various forest conditions. While a variety of remote sensing technologies have been tested in this context, airborne laser scanning (ALS) was frequently identified as the most robust data source for stand volume estimation (Rahlf et al., 2014; Yu et al., 2015). More recently, also image-derived point clouds (IPC) were recognized as very useful in the context of forest inventory activities (White et al., 2016). Two main approaches for forest biometric parameter estimations (including stand volume) are utilized when point cloud data (ALS or IPC) are available wall-to-wall: the area-based approach (ABA; Nilsson, 1996; Naesset, 1997; Means et al., 2000) and the individual tree detection approach (ITD; Gougeon, 1995; Borgefors et al., 1999; Hyyppä and Inkinen, 1999). In the ABA, the response variable, such as the stand volume or the above ground biomass, is calculated for a sample plot measured in the field. Then, the ALS or IPC point-clouds co-located with the sample plots are generalized into metrics that are subsequently used as predictor variables in regression models. The point cloud metrics typically describe the height distribution at the sample plot, such as the mean height, height percentiles or proportion of returns within a certain height layer. The trained regression models are subsequently used to predict forest attributes for individual grid cells (with their size typically matching the size of the field plots) within an area of interest and finally are aggregated to forest stands (Næsset, 2002; Vastaranta et al., 2013; White, Stepper et al., 2015a). Accurate co-location of field measurements and point cloud metrics is an important precondition for using the ABA since the positioning errors influence the prediction accuracy and bias (Frazer et al., 2011). It is also known that Global Positioning System (GPS) positional errors have a greater impact on the point cloud metrics and the accuracy of the volume models when extracted from small plots compared with large-sized plots (Gobakken and Næsset, 2009). The ITD approach usually relies on a raster-based canopy height model (CHM) interpolated from the ALS (or IPC) data. However, a combination of raster and point cloud data or solely point clouds can also be used, especially for single tree detection (Koch et al., 2014). The ITD approach starts with the detection of individual treetops followed by a delineation of tree crowns and an extraction of crown features. Finally, the CHM-derived individual tree metrics such as tree height and crown size are used as inputs to the allometric models to predict tree biomass or stem volume (Persson et al., 2002; Popescu, 2007). The values predicted for single trees might then be generalized into stand-level estimates of stand volume or biomass. A disadvantage of the ITD approach is that normally not all trees can be detected (Vauhkonen et al., 2012; Stereńczak, 2013; Lindberg and Holmgren, 2017); thus, errors in tree crown detection can result in estimates of stand parameters with considerable systematic errors. To address this challenge, the semi-ITD method with different variants was developed aiming to reduce the systematic errors often generated by the conventional ITD approach (Breidenbach and Astrup, 2014). In semi-ITD, the modelling and prediction of the volume are done not for a single tree but CHM-derived homogenous segments. In the simplest variant of semi-ITD, the volumes of several trees are aggregated (added) within a segment, whenever multiple trees are present. The aggregated volume is then regressed against predictor variables derived from the segments. There are also more advanced semi-ITD variants where the tree lists are imputed, however, compared with the ABA, systematic errors are still more likely to occur if semi-ITD or ITD approaches are applied (Breidenbach and Astrup, 2014; Rahlf et al., 2015). Hollaus et al. (2009) described three main approaches for modelling the relationship between forest attributes and point cloud data (ALS, IPC): physical, empirical and semi-empirical. While both the empirical and semi-empirical approaches are common in forestry applications, the physical modelling approach is rarely used (Hansen et al., 2017). Physical models generally use three-dimensional forest models to simulate the light detection and ranging (LiDAR) waveform (Sun and Ranson, 2000). In theory, once the interaction between the LiDAR signal and the biophysical forest attributes are well-understood and modelled, such physical models can be fed with LiDAR dataset and inverted to retrieve the forest attributes. For empirical and semi-empirical approaches, regression methods are required. In case of parametric methods, the most commonly used in this context is ordinary least squares regression, while from the non-parametric approaches, the k-nearest neighbours and random forest are among the most common approaches (White et al., 2017). In the empirical approach, many point cloud-derived or CHM-derived features are used as potential predictor variables. Thus, an objective procedure such as step-wise regression (Miścicki and Stereńczak, 2013; Phua et al., 2017), all possible combinations of the variables (Hawryło et al., 2017) or search algorithms (Holopainen et al., 2010; Packalén et al., 2012) is usually applied to find the optimal model. The selected predictor variables give the best possible fit to the estimated stand parameter. However, they do not necessarily provide physical insights into the retrieval process. Moreover, the empirical models are usually very accurate within the area they were developed but may predict poorly in new areas (Hollaus et al., 2009). In contrast, the semi-empirical models are based on a fewer carefully selected predictors that have physical reasoning with the intention to make them more stable when reusing them in new areas and with new input data (Hansen et al., 2017). In previous studies, ABA as well as ITD, based on empirical or semi-empirical methods, has been successfully used in the context of forest biophysical parameter estimations. Applications of each of these approaches require detailed information about field plot coordinates. However, in some cases, data from many field plots without detailed positional information are available. This might be the case in regions where traditional forest inventory methods are operationally used within a dense grid of field sample plots. In some countries, such as Poland, the National Forest Inventory (NFI) plots do not have precise information about plot coordinates. To the best of our knowledge, there is no method available to successfully predict the volume at the plot and stand levels using ALS point clouds without field plot measurements containing detailed positional information. In this study, we hypothesize that the two stand characteristics—top height (TH) and relative spacing index (RSI; a measure of stand density)—can be directly approximated using ALS-derived metrics and be used for stand volume estimations. In other words, we think that stand volume allometric models can be developed using NFI plots information only and then successfully applied to the prediction of volume at the plot and stand levels using wall-to-wall ABA and ALS-derived metrics. Thus, we propose an allometric area-based approach (AABA)—which we deem a cost-effective method for stand volume estimation based on ALS and NFI data. The four main objectives of this research are the following: (1) use NFI data to develop a plot-level volume allometric model for Scots pine (Pinus sylvestris L.) stands, which describes the stand volume as the function of TH and RSI; (2) evaluate if field-based measurements of TH and RSI can be replaced with corresponding ALS-derived metrics during stand volume estimations; (3) evaluate which trees should be used for the calculation of the RSI to develop an allometric model suitable to be connected to ALS data and (4) compare the accuracy of the proposed AABA method with the accuracy of the classic ABA. Figure 1 Open in new tabDownload slide Study area: Poland within Europe (a); study area within Poland (b); Polish National Forest Inventory (NFI) sample scheme (c) and Forest management inventory plots and test stands (d). Figure 1 Open in new tabDownload slide Study area: Poland within Europe (a); study area within Poland (b); Polish National Forest Inventory (NFI) sample scheme (c) and Forest management inventory plots and test stands (d). Materials and methods National Forest Inventory sample plot data From its first survey in 2005, the Polish NFI has been a continuous inventory featuring a systematic sample of permanent plots located at the nodes of a 4 km square grid. The NFI grid was created by densifying the pan-European 16 × 16 km forest monitoring network of the International Co-operative Programme on Assessment and Monitoring of Air Pollution Effects on Forests (Forests, 2016). A group of five plots is located at each node of the NFI grid (Figure 1c). The plots are re-measured using a 5-year inventory cycle; thus, in each year, approximately 20 per cent of the plots are measured. In the first two cycles of the NFI, the sample plots were circular with 7.98, 11.28 and 12.62 m radii depending on the forest stand age. In the third cycle (2015–2019) of the NFI, the radii for all plots were fixed to 11.28 (400 m2). In each plot, various tree and stand characteristics are recorded. Among others, the diameter at breast height (DBH) is measured and recorded for all trees with a DBH of at least 7 cm, and the heights of selected trees are measured. Allometric models are used to predict individual tree heights and volumes that are then aggregated to produce plot-level estimates. For this study, measurements from the third cycle of the NFI (2015–2019) were used. The development of the stand volume allometric model for Scots pine stands was based on 9400 plots (400 m2) dominated by Scots pine trees (species part/share from 24 to 100 per cent). The species share was calculated based on the volume of the single trees. No information about the plot coordinates was used in the model’s development. Forest management inventory plots and validation stands Forest management inventory plots and validation (test) stands from the Milicz Forest District (Polish National Forest Holding) located in western Poland (Figure 1) were used for creating classic ABA models and for validating the developed stand volume models. The forest stands in this area (8500 ha) are dominated by Scots pine (approximately 70 per cent of the forest district area). The stands in the 40–60 year age class cover approximately 30 per cent of the study area. The remaining age classes have similar shares of approximately 10 per cent each. The average stand volume of the pine stands is 300 m3 ha−1. Trees on 900 circular field sample plots with radii of 12.62 m (500 m2) were measured within the study area. The plots were distributed in a regular grid pattern (350 × 350 m). Plot centre locations were measured using a Global Navigation Satellite System in the Real-Time Kinematic mode (RTK GNSS) using Virtual Reference Stations technology. The horizontal precision of GNSS measurements was 0.044 m. On each sample plot, the diameters of all trees with DBH ≥ 7 cm were measured with an accuracy of 0.1 cm, while tree heights were measured with a Haglöf Vertex IV rangefinder (instrument accuracy of 0.1 m). For each tree, also the azimuth and distance to the plot centre were recorded. To make the two datasets—NFI and forest management inventory—comparable, only the trees within 11.28 m distance from the plot centre were selected that resulted in 900 circular field plots with an area of 400 m2. From all 900 available plots, only samples dominated by Scots pine were used for analysis, leading to a final number of 630 field plots. Summaries of the plot-level variability of mean DBH, mean height and volume from selected 630 plots are presented in Table 1. The species share was calculated based on the volume of the single trees and were within a range of 33–100 per cent. Half of the forest management inventory plots (315) were used for training the ABA models and the remaining 315 plots were used for validation of AABA and ABA models. The splitting to training and testing sets was done randomly with stratification. In the first step, all samples were grouped into five sections based on percentiles of observed stand volume, and then the random sampling into training/testing sets was performed within these subgroups. Table 1 Summary of forest management inventory plot characteristics (n = 630). Minimum First quartile Median Mean Third quartile Maximum Standard deviation Mean plot DBH (cm) 8.9 19.3 22.8 23.0 26.4 51.2 6.0 Mean plot height (m) 9.1 18.7 21.3 21.0 23.5 33.4 3.9 Plot volume (m3 ha−1) 26.7 268.5 348.4 357.2 436.2 921.6 134.8 Minimum First quartile Median Mean Third quartile Maximum Standard deviation Mean plot DBH (cm) 8.9 19.3 22.8 23.0 26.4 51.2 6.0 Mean plot height (m) 9.1 18.7 21.3 21.0 23.5 33.4 3.9 Plot volume (m3 ha−1) 26.7 268.5 348.4 357.2 436.2 921.6 134.8 Open in new tab Table 1 Summary of forest management inventory plot characteristics (n = 630). Minimum First quartile Median Mean Third quartile Maximum Standard deviation Mean plot DBH (cm) 8.9 19.3 22.8 23.0 26.4 51.2 6.0 Mean plot height (m) 9.1 18.7 21.3 21.0 23.5 33.4 3.9 Plot volume (m3 ha−1) 26.7 268.5 348.4 357.2 436.2 921.6 134.8 Minimum First quartile Median Mean Third quartile Maximum Standard deviation Mean plot DBH (cm) 8.9 19.3 22.8 23.0 26.4 51.2 6.0 Mean plot height (m) 9.1 18.7 21.3 21.0 23.5 33.4 3.9 Plot volume (m3 ha−1) 26.7 268.5 348.4 357.2 436.2 921.6 134.8 Open in new tab Additional to the test plots, 42 Scots pine dominated forest stands (minimum share of 70 per cent) with a mean area of 1.1 ha were used for validation of the models. In each stand, the diameters of all trees with a DBH ≥ 7 cm were measured. The heights of trees representing different species and forest stand layers were measured with rangefinders. The minimum number of measured heights for a dominant species was 20, which was distributed evenly across the DBH range. The DBH–height relationship (Bruchwald and Rymer-Dudzińska, 1981) was used to estimate the heights of all trees in the stand. The total volume of each stand was calculated as the sum of all individual trees’ volumes and scaled to an area of 1 ha. Field measurements at the plot and stand levels were conducted in summer 2015. The volume of every single tree was computed based on formulas commonly used in forest management in Poland (Bruchwald et al., 2000). Development of stand volume allometric model The general allometric model for estimating the stand volume of Scots pine stands was developed using the data from 9400 circular field plots based on two predictor variables. The idea was to identify variables that are related to the stand volume and simultaneously, can be directly obtained from the ALS point clouds or CHM. Based on the earlier study results, strong ALS-derived predictors of stand volume include the mean height of points and the percentage of all returns above the mean height of points. However, these variables do not have direct equivalents in the stand metrics that can be obtained from the standard field measurements. Here, we have selected two stand characteristics that we believe to have strong corresponding ALS-derived metrics: TH and the Hart and Becking RSI (Pardé and Bouchon, 1988). It was assumed that TH could be represented by the maximum height of the ALS point cloud, while RSI can be calculated based on a number of tree crowns delineated within the ALS-derived CHM. The second important assumption was that these two stand characteristics can explain a large part of the stand volume variability. TH is usually defined as the average height of either a fixed or relative number of the largest trees in a stand (Sharma et al., 2002; Ochal et al., 2017). In our case, TH was calculated as the mean height of the 100 largest trees per ha. Thus, when calculating the TH for the individual sample plots, the corresponding proportion of trees according to the plot area was used (i.e. the four highest trees for 0.04 ha). The RSI was calculated as the ratio, which was expressed as a percentage, between the average distance among trees and the TH, according to Equation (1) (Meredieu et al., 2003): $$\begin{equation} \mathrm{RSI}=\frac{\mathrm{AS}}{\mathrm{TH}}\times 100=\frac{10^4\times \sqrt{\frac{2}{N\times \sqrt{3}}}}{\mathrm{TH}} \end{equation}$$ (1) where TH is the top height of the stand (m), N is the number of trees per 1 ha and AS is the average spacing between trees (m). For the estimation of AS using N, trees are assumed to be positioned on a triangular grid. To make the RSI more compatible with ALS data, we assumed that the RSI should be calculated using only a certain fraction of the highest trees within a plot that dominates the ALS signal. Consequently, a series of RSI values were calculated for each plot using only the trees for which the ratio between tree height (h) and TH was higher than a certain threshold. To find the optimal value of the h/TH ratio, a regular sequence of thresholds from 0.0 to 0.8 with a 0.1 increment was tested. A threshold value of 0.0 means that all trees recorded on a plot were used for the RSI calculation, while a threshold value of 0.8 means that only trees with a height (h) higher than 80 per cent of the TH of a plot were used. The idea was to evaluate how the volume model’s accuracy changes depending on the applied h/TH ratio used in the RSI calculation. To make the allometric model more stable, we decided to remove outliers of predictor variables (TH and RSI) from the NFI data, before developing the model. We assumed that an outlier was an observation at an abnormal distance from other values in a random sample from a population. Outliers were detected using lower and upper quartiles (Q1–Q3), and interquartile range (IQ) was calculated as the difference between quartile Q3 and Q1. We defined extreme values in the tails of the distribution by the lower inner bound Q1 − 1.5 × IQ and the upper inner bound Q3 + 1.5 × IQ according to Tukey (1977), which picked 1.5 × IQ as the demarcation line for outliers. Reasonableness of this measure for bell-curve-shaped data means that usually, about 1 per cent of the data will ever be outliers. This measure is often used to find outliers in data (Antony and Singh, 2016). Outliers of TH and RSI were detected separately for each value of h/TH ratio. For model calibration, only those NFI plots were used where no outlier was identified at any variant of h/TH ratio. Finally, after removing outliers from input 9400 NFI plots, 8190 of them were used for calibration of the model. In the analysis of allometric relations often the residual heteroscedasticity occurs, with an increase in the residual variance of the dependent variable (in this case stand volume) with an increase in the values of the independent variable (Socha and Wezyk, 2007). Therefore, to obtain the homoscedasticity of the residuals, the volume model was developed after a logarithmic transformation of the allometric function (Equation (2)). Due to the logarithmic transformation, the relationships between dependent and independent variables (TH, RSI) were linearized, and homoscedasticity of the residuals was reached; therefore, multiple regression with an OLS estimation method may be used in the calibration of the allometric model (2): $$\begin{equation} \log (V)={\beta}_0+{\beta}_1\times \log \left(\mathrm{TH}\right)+{\beta}_2\times \log \left(\mathrm{RSI}\right) \end{equation}$$ (2) The exponential function was used to back-transform the estimated stand volume (V) log values to the original scale using Equation (3): $$\begin{equation} V={e}^{\beta_0}\times{\mathrm{TH}}^{\beta_1}\times{\mathrm{RSI}}^{\beta_2} \end{equation}$$ (3) The model precision was estimated using the following parameters: coefficient of determination R2, relative root mean square error (RMSE%) and Bias%. These metrics were used to select the best model, depending on the h/TH ratio applied for the RSI calculation. Since the aim was to obtain the best possible estimation of the allometric model parameters (⁠|${\beta}_0,{\beta}_1,{\beta}_2$|⁠) and not to optimize the prediction accuracy of the model, no cross-validation or splitting to the training and testing sets were applied. Equations (4)–(6) were used for calculating selected model parameters: $$\begin{equation} {\mathrm{R}}^2=\frac{\sum \limits_{i=1}^n{\left({\hat{y}}_i-\overline{y}\right)}^2}{\sum \limits_{i=1}^n{\left({y}_i-\overline{y}\right)}^2} \end{equation}$$ (4) $$\begin{equation} \mathrm{RMSE}\%=\sqrt{\frac{\sum \limits_{i=1}^n{\left({y}_i-{\hat{y}}_i\right)}^2}{n}}/\overline{y}\times 100 \end{equation}$$ (5) $$\begin{equation} \mathrm{Bias}\%=\frac{\sum \limits_{i=1}^n\left({y}_i-{\hat{y}}_i\right)}{n}/\overline{y}\times 100 \end{equation}$$ (6) where |${y}_i$| is the observed volume for the ith training plot, |$\hat{y}$| is the model estimation of volume for the ith training plot, |$\overline{y}$| is the mean volume of n training plots and n is the number of training plots. Calculating ALS-derived metrics corresponding to TH and RSI The ALS data were collected in August 2015 using a Riegl LMSQ680i laser scanning system with a 360 kHz pulse rate frequency. The mean flight altitude was 550 m, and the field of view of the scanning system was 60°. These system and flight parameters resulted in point clouds with an average density of 10 pulses m−2. Additionally, a digital terrain model (DTM) with a spatial resolution of 0.5 m generated in the TerraSolid software was provided by the data provider. Point clouds were normalized by subtracting the DTM elevation from the corresponding ALS points. Furthermore, a CHM with a spatial resolution of 0.5 m was generated using the PFSK method described in detail in Erfanifard et al. (2018), where a pit-free CHM is the final product of the processing. The CHM was then used for delineating tree crowns using the method described in detail in Miścicki and Stereńczak (2013) and Stereńczak et al. (2017). In this method, CHM is filtered with a varying kernel window size, which is dependent on the crown heights, before the watershed algorithm for a single tree delineation is applied. The ALS point clouds and CHMs were clipped to the borders of the 630 forest management inventory field plots (and 42 stands) and used for the calculation of ALS-derived metrics corresponding to TH and RSI (THALS and RSIALS). The maximum value of the ALS point cloud (Hmax) was used as the THALS. For the calculation of the RSIALS, the number of trees per 1 ha was obtained from ALS by calculating the number of tree crowns delineated from CHM (NALS). Consequently, the RSIALS was calculated using equation (1), assuming TH = THALS and N = NALS. For the 42 reference forest stands, the THALS and RSIALS were calculated within a 20 × 20 m raster grid, corresponding to the size of the field plots used for development of the allometric model (400 m2). Development of ABA models From 630 available forest management inventory plots, 315 of them were randomly selected as training plots for creating semi-empirical (ABASE) and empirical (ABAE) ABA models. Both models were created using a linear regression with the log–log transformation of variables. The ABASE model was created using the same predictors as used in AABA model—TH and RSI. For the development of ABAE, besides these two predictors, also several point cloud metrics were used (Table 2). Selection of the best predictor set for ABAE model was conducted with an approach similar to that used by Hawryło et al. (2017). In the first step, the collinearity of predictor variables was analysed. For two predictors with Pearson’s correlation coefficient > 0.9, the predictor with the higher mean correlation to other variables was dropped. After removing the highly correlated variables, all possible combinations of the predictors were evaluated. As the final ABAE model, the one with delta of second order Akaike Information Criterion lower than 2 and the lowest number of predictor variables was selected (Table 2) (Hawryło et al., 2017). Table 2 Point cloud metrics calculated based on normalized data for each field plot and used as predictor variables in the empirical ABA model. Description of LiDAR metric (unit) Mean value of point heights (m) Maximum value of point heights (m) Mode value of point heights (m) Standard deviation of point heights (m) Skewness of point heights Kurtosis of point heights Percentile values of point heights: 5th, 10th, 15th, … 95th (m) Interquartile distance of point heights: Elev.IQ = Elev.P75 − Elev.P25 (m) Canopy relief ratio = (Elev.mean − Elev.min)/(Elev.max − Elev.min), where Elev.min, Elev.mean, Elev.max are minimum, mean and maximum values of point heights, respectively Percentage of first returns above Elev.mean (%) Percentage of all returns above 2 m (%) Percentage of all returns above Elev.mean (%) Cumulative percentage of returns from nine height layers. The height measurements were divided into 10 equal intervals according to (Woods et al., 2008) (%) Description of LiDAR metric (unit) Mean value of point heights (m) Maximum value of point heights (m) Mode value of point heights (m) Standard deviation of point heights (m) Skewness of point heights Kurtosis of point heights Percentile values of point heights: 5th, 10th, 15th, … 95th (m) Interquartile distance of point heights: Elev.IQ = Elev.P75 − Elev.P25 (m) Canopy relief ratio = (Elev.mean − Elev.min)/(Elev.max − Elev.min), where Elev.min, Elev.mean, Elev.max are minimum, mean and maximum values of point heights, respectively Percentage of first returns above Elev.mean (%) Percentage of all returns above 2 m (%) Percentage of all returns above Elev.mean (%) Cumulative percentage of returns from nine height layers. The height measurements were divided into 10 equal intervals according to (Woods et al., 2008) (%) Open in new tab Table 2 Point cloud metrics calculated based on normalized data for each field plot and used as predictor variables in the empirical ABA model. Description of LiDAR metric (unit) Mean value of point heights (m) Maximum value of point heights (m) Mode value of point heights (m) Standard deviation of point heights (m) Skewness of point heights Kurtosis of point heights Percentile values of point heights: 5th, 10th, 15th, … 95th (m) Interquartile distance of point heights: Elev.IQ = Elev.P75 − Elev.P25 (m) Canopy relief ratio = (Elev.mean − Elev.min)/(Elev.max − Elev.min), where Elev.min, Elev.mean, Elev.max are minimum, mean and maximum values of point heights, respectively Percentage of first returns above Elev.mean (%) Percentage of all returns above 2 m (%) Percentage of all returns above Elev.mean (%) Cumulative percentage of returns from nine height layers. The height measurements were divided into 10 equal intervals according to (Woods et al., 2008) (%) Description of LiDAR metric (unit) Mean value of point heights (m) Maximum value of point heights (m) Mode value of point heights (m) Standard deviation of point heights (m) Skewness of point heights Kurtosis of point heights Percentile values of point heights: 5th, 10th, 15th, … 95th (m) Interquartile distance of point heights: Elev.IQ = Elev.P75 − Elev.P25 (m) Canopy relief ratio = (Elev.mean − Elev.min)/(Elev.max − Elev.min), where Elev.min, Elev.mean, Elev.max are minimum, mean and maximum values of point heights, respectively Percentage of first returns above Elev.mean (%) Percentage of all returns above 2 m (%) Percentage of all returns above Elev.mean (%) Cumulative percentage of returns from nine height layers. The height measurements were divided into 10 equal intervals according to (Woods et al., 2008) (%) Open in new tab Figure 2 Open in new tabDownload slide Flowchart of the performed analysis. Figure 2 Open in new tabDownload slide Flowchart of the performed analysis. Figure 3 Open in new tabDownload slide Distribution of the number of trees per hectare (N), TH, RSI and stand volume (V) within the 8190 training NFI plots. Figure 3 Open in new tabDownload slide Distribution of the number of trees per hectare (N), TH, RSI and stand volume (V) within the 8190 training NFI plots. Figure 4 Open in new tabDownload slide Scatterplots of stand volume (V) vs predictor variables-TH and relative pacing index (RSI)-before (a and b) and after (c and d) logarithmic transformation. Values from the 8190 NFI plots. Figure 4 Open in new tabDownload slide Scatterplots of stand volume (V) vs predictor variables-TH and relative pacing index (RSI)-before (a and b) and after (c and d) logarithmic transformation. Values from the 8190 NFI plots. Figure 5 Open in new tabDownload slide Residuals and relative errors of volume with relation to selected stand parameters: share of Scots Pine, TH, RSI and fitted volume. Values from 8190 NFI plots. Figure 5 Open in new tabDownload slide Residuals and relative errors of volume with relation to selected stand parameters: share of Scots Pine, TH, RSI and fitted volume. Values from 8190 NFI plots. Figure 6 Open in new tabDownload slide Scatterplots of the observed values of the selected stand parameters: number of trees per ha (N), RSI and TH vs their ALS-derived corresponding metrics (NALS, THASL, RSIALS; a, b and c). Values from 630 forest management inventory plots. Figure 6 Open in new tabDownload slide Scatterplots of the observed values of the selected stand parameters: number of trees per ha (N), RSI and TH vs their ALS-derived corresponding metrics (NALS, THASL, RSIALS; a, b and c). Values from 630 forest management inventory plots. Model validation The 315 forest management inventory plots (400 m2) and 42 forest stands (mean area of stands = 1.1 ha) were used for the validation of created models. To assess the model’s performance, the R2, RMSE % and Bias % were calculated. The predictions at stand level were performed within 20 × 20 m raster grid, and the volume of a stand was calculated as the mean of the grid cells falling within the stand borders. The model metrics were calculated separately for the plot and stand levels using equations (4)–(6), where |${y}_i$| is the observed volume for the ith test plot (stand), |$\hat{y}$| is the predicted volume for the ith test plot (stand), |$\overline{y}$| is the mean volume of n test plots (stands) and n is the number of test plots (stands). Besides predictions performed for validation plots and stands, predictive maps of stand volume were also created for the selected part of the study area in order to visually explore the spatial consistency of predictions obtained from three evaluated models. The flowchart in Figure 2 summarizes the described methodology. Results Allometric model created from NFI data The allometric model of stand volume was developed using linear regression and log–log transformation based on RSI and TH as independent variables. The distribution of N, TH, RSI and V calculated for the 8190 training sample plots (after removing the outliers from the input 9400 plots) are presented in Figure 3. The performed logarithmic transformation of variables resulted in a linear relationship between the dependent and independent variables (TH, RSI; Figure 4). Graphical diagnosis plotting residuals and relative errors (residual/fitted volume × 100 per cent) vs share of Scots pine, TH and RSI showed no systematic errors in the whole range of analysed variables (Figure 5a and b). When analysing the distribution of residuals (Figure 5a), we observed a decrease of model precision with increase of the TH. However, when considering the relative errors (Figure 5b), this tendency is not observed. Residuals and relative errors also showed no correlation with the fitted stand volume. Most plots showed residual values below 200 m3 ha−1 (Figure 5). The ALS-derived metrics corresponding to N, TH and RSI (NALS, THASL and RSIALS) calculated for 630 forest management inventory plots (training and test plots) showed different levels of agreement with the reference values (Figure 6; Table 3). The number of trees per ha (N) obtained from the CHM segmentation was significantly underestimated (bias = −34.4 per cent), whereas the bias for RSIALS was positive (12.9 per cent) and the absolute values were significantly smaller than that seen in N. The maximum height of the point cloud is an accurate metric of TH (R2 = 0.94; RMSE = 4.8 per cent) without a significant systematic error (bias = 0.4 per cent). The modelling and validation results showed that the quality of the volume model depends on the fraction of the highest trees used in the RSI calculation. An h/TH ratio of 0.6 was selected as the optimal value since it provided a model with low bias, lowest RMSE and highest R2 in the model fitting stage as well as in model validation stage at plot and stand levels (Figure 7). Examples of observed vs fitted values relationship with different h/TH ratios obtained at the model fitting stage are presented in Figure 8. Table 3 Accuracy of the ALS-derived metrics corresponding to the selected stand variables at plot level: number of trees per ha (N), RSI and TH. Variable (unit) R2 RMSE (%) Bias (%) NALS (trees/ha) 0.57 67.3 −34.4 RSIALS (%) 0.22 31.7 12.9 THALS (m) 0.94 4.8 0.4 Variable (unit) R2 RMSE (%) Bias (%) NALS (trees/ha) 0.57 67.3 −34.4 RSIALS (%) 0.22 31.7 12.9 THALS (m) 0.94 4.8 0.4 Values from 630 forest management inventory plots. Open in new tab Table 3 Accuracy of the ALS-derived metrics corresponding to the selected stand variables at plot level: number of trees per ha (N), RSI and TH. Variable (unit) R2 RMSE (%) Bias (%) NALS (trees/ha) 0.57 67.3 −34.4 RSIALS (%) 0.22 31.7 12.9 THALS (m) 0.94 4.8 0.4 Variable (unit) R2 RMSE (%) Bias (%) NALS (trees/ha) 0.57 67.3 −34.4 RSIALS (%) 0.22 31.7 12.9 THALS (m) 0.94 4.8 0.4 Values from 630 forest management inventory plots. Open in new tab Figure 7 Open in new tabDownload slide Model parameters (R2, RMSE and Bias) depending on the h/TH ratio used for calculation of the RSI. Model metrics calculated based on training NFI data (fitted allometric model) and validation data at the plot (315 plots) and stand level (42 stands). Figure 7 Open in new tabDownload slide Model parameters (R2, RMSE and Bias) depending on the h/TH ratio used for calculation of the RSI. Model metrics calculated based on training NFI data (fitted allometric model) and validation data at the plot (315 plots) and stand level (42 stands). Figure 8 Open in new tabDownload slide Observed vs fitted values of stand volume (V) from the 8190 NFI plots for selected h/TH ratios. Figure 8 Open in new tabDownload slide Observed vs fitted values of stand volume (V) from the 8190 NFI plots for selected h/TH ratios. The results of the logarithmic regression modelling enabled the creation of the allometric formula for calculating the stand volume of Scots pine stands using the TH and RSI (Equation (7)): $$\begin{equation} V=11.25\times{\mathrm{TH}}^{1.674}\times{\mathrm{RSI}}^{-0.674} \end{equation}$$ (7) where RSI is calculated from trees with h/TH ≥ 0.6. Comparison of AABA and ABA models The AABA model was developed based on two predictor variables (TH and RSI) using 8190 NFI plots from the whole territory of Poland without co-registered location with ALS point clouds. The ABA models were created using 315 local forest management inventory plots from the Milicz Forest District, co-located with ALS data. In ABASE, the same predictors as in AABA were used (THALS and RSIALS). For the ABAE model, the finally selected best model consisted of seven predictor variables: mean value of point heights, the maximum value of point heights (THALS), RSIALS, percentage of all returns above mean height of points, 30th percentile of point heights, 70th percentile of point heights and cumulative percentage of returns from sixth height layer (Woods et al., 2008). The crated AABA, ABASE and ABAE models were validated based on 315 forest management inventory plots and 42 measured forest stands (Table 4, Figure 9). The ABAE model provided the best accuracy at plot and stand level giving the highest R2 (0.79; 0.71), lowest RMSE (17.1; 16.0 per cent) and low bias (−1.8; −0.2 per cent). However, the proposed AABA model provided very similar performance, especially at stand level giving relatively high R2 (0.65), low RMSE (17.8 per cent) and bias comparable to the ABAE model (0.2 per cent). The lowest accuracy was found in case of ABASE model, both at plots and stand level (Table 4). Prediction maps of stand volume generated for the selected part of the study area demonstrated consistency within the spatial predictions obtained from the three examined methods (Figure 10). Figure 9 Open in new tabDownload slide Observed vs predicted volume values at the plot and stand level for the three evaluated methods: AABA, ABASE and ABAE. Model performance metrics (R2, RMSE and Bias) were calculated based on 315 forest management inventory test plots and 42 reference stands. Figure 9 Open in new tabDownload slide Observed vs predicted volume values at the plot and stand level for the three evaluated methods: AABA, ABASE and ABAE. Model performance metrics (R2, RMSE and Bias) were calculated based on 315 forest management inventory test plots and 42 reference stands. Figure 10 Open in new tabDownload slide CHM (0.5 m spatial resolution) and predictions of stand volume within 20 × 20 m raster grid generated for the selected part of the study area. Predictions obtained with the three examined methods: AABA, semi-empirical ABASE and empirical ABAE. Figure 10 Open in new tabDownload slide CHM (0.5 m spatial resolution) and predictions of stand volume within 20 × 20 m raster grid generated for the selected part of the study area. Predictions obtained with the three examined methods: AABA, semi-empirical ABASE and empirical ABAE. Discussion In this article, the new AABA was proposed for stand volume estimations. The selected independent variables used for developing the stand volume allometric model—TH and RSI—have been previously recognized as stand parameters, which strongly correlates with the stand volume (Barrio-Anta et al., 2006). Previous research showed that TH could be successfully derived from ALS data using the ABA method (Bolton et al., 2018; White, Arnett et al., 2015b) or, more directly, using an ALS-derived metric of maximum height from CHM (Socha et al., 2017). The calculation of the RSI requires the TH and the number of trees per hectare (N) as input variables (Equation (1)). Our results indicate that using the proportion of 60 per cent of the highest trees within a plot for calculating the RSI provides more accurate stand volume estimation as compared with the volume estimates using all trees from the plot. This finding is important in the context of applying the general allometric models with an ALS-derived RSI. The number of trees obtained from the ALS-derived CHM usually underestimates the true number of trees since smaller suppressed trees are often not visible in the CHM (Vauhkonen et al., 2012; Lindberg and Holmgren, 2017). Moreover, underestimation is especially common in young stands, where the 0.5 m resolution CHM applied here can have a negative influence on the ITD results (Stereńczak et al., 2008). Even though our results showed a significant underestimation of N, especially for young stands, they indicate that RSI can still be used as a valuable predictor variable for stand volume estimations without introducing bias into the predictions. This phenomenon is most probably caused by the fact, that the intermediate and suppressed trees, which are most likely be missed, are relatively small, especially in terms of volume, in comparison with dominant and codominant trees, whose volume makes up the main part of the stand volume. Therefore, the underestimation of the number of trees results in a relatively small worsening of the result of predicting the volume. The scale of the underestimation of the number of trees is most probably dependent on the stand structure. In stands with a left skewed height distribution and a large share of understorey, the underestimation of the number of trees is likely to be higher. In one-storeyed stands (like in our study) with the stand height structure close to the normal distribution, the problem of underestimation of N is less critical. In such a case, the application of the ALS-derived RSI variable, increases the accuracy of the stand volume models and does not cause systematic errors. Nevertheless, further development in tree detection algorithms are desired as they have the potential to further improve the stand volume predictions within the AABA and ABA frameworks. Improved methods of tree detection may result in increased accuracy of the proposed AABA method and potentially close the still existing small accuracy gap to the classic ABA method. Table 4 Performance of developed volume models at plot and stand level: AABA, semi-empirical ABASE and empirical ABAE. Method Plot-level Stand-level R2 RMSE (%) Bias (%) R2 RMSE (%) Bias (%) AABA 0.63 22.8 −2.2 0.65 17.8 0.2 ABASE 0.62 23.0 −3.6 0.57 20.4 −5.1 ABAE 0.79 17.1 −1.8 0.71 16.0 −0.2 Method Plot-level Stand-level R2 RMSE (%) Bias (%) R2 RMSE (%) Bias (%) AABA 0.63 22.8 −2.2 0.65 17.8 0.2 ABASE 0.62 23.0 −3.6 0.57 20.4 −5.1 ABAE 0.79 17.1 −1.8 0.71 16.0 −0.2 Open in new tab Table 4 Performance of developed volume models at plot and stand level: AABA, semi-empirical ABASE and empirical ABAE. Method Plot-level Stand-level R2 RMSE (%) Bias (%) R2 RMSE (%) Bias (%) AABA 0.63 22.8 −2.2 0.65 17.8 0.2 ABASE 0.62 23.0 −3.6 0.57 20.4 −5.1 ABAE 0.79 17.1 −1.8 0.71 16.0 −0.2 Method Plot-level Stand-level R2 RMSE (%) Bias (%) R2 RMSE (%) Bias (%) AABA 0.63 22.8 −2.2 0.65 17.8 0.2 ABASE 0.62 23.0 −3.6 0.57 20.4 −5.1 ABAE 0.79 17.1 −1.8 0.71 16.0 −0.2 Open in new tab The accuracy of the traditional ABA using ALS data and an empirical approach was previously investigated for the same forest area by Stereńczak et al. (2018), however, they explored all stands within the Milicz forest district, not only those dominated by Scots pine. They examined the effects of plot size and the number of training plots on the accuracy of stand volume estimation. The optimal models obtained in their study were characterized by an RMSE of approximately 20 per cent and an R2 of approximately 0.75. To make a stricter comparison in the presented study, we have developed the ABASE, and ABAE for Scots pine-dominated stands. Surprisingly, the ABASE model provided a lower accuracy than AABA. The possible explanation for that might be the fact that AABA was developed based on extensive training dataset (8190 NFI plots), while in case of ABA (empirical and semi-empirical) only 315 forest management inventory training plots were used. Thus, precise co-location of field plots with ALS data does not necessarily guarantee better model accuracy when using only the two selected predictors—TH and RSI. As expected, the ABAE model with several ALS-derived predictor variables delivered the highest model performance. The ABAE performed significantly better at the plot level; however, at the stand level, the RMSE was only slightly lower than in AABA (16.0 vs 17.8 per cent), while bias was comparable (−0.2 vs 0.2 per cent). Reducing the number of the required field sample plots has been an important research topic since many years because it has a considerable and direct impact on the final costs of the forest inventory (Gobakken and Næsset, 2008; Hummel et al., 2011; Stereńczak et al., 2018). Usually, the number of field plots should be kept at a minimum to reduce the total cost of inventory, while simultaneously providing the desired level of accuracy. The proposed AABA method relies only on the NFI and ALS data. Thus, there is no need for additional field measurements at the local level. Considering its cost-effectiveness and similar performance at the stand level, the AABA might be considered as an attractive alternative for traditional ABA in case of stand volume estimation of Scots pine-dominated stands. Our proposed AABA method has a common point with the method called LiDAR Individual Tree Imputed Diameter Algorithm (LITIDA) that was recently developed by Huang et al. (2019). In their study, the authors also proposed a methodology that can utilize the extensive and commonly available NFI databases in combination with LiDAR data without the need for dealing with the co-location of the two datasets. However, here the authors worked on the scale of single trees. Several predictor variables used by Huang et al. (2019) in their non-parametric imputation approach for the estimation of LiDAR-detected tree diameters might also be considered in the future improvements of AABA in context of stand volume estimation. For example, they used LiDAR-derived tree height and competition index, site index and a kind of local Landsat-based climate zone obtained from unsupervised image classification. Potentially, the site index might improve the quality of AABA stand volume model. However, this will limit the application of the method to the areas where the site index is known with good accuracy, which requires data on the age of the stands. In this context, it is worth noting that repeated ALS point clouds have found a valuable source of data for precise site index estimation (Socha et al., 2017). Thus, in the future development of AABA, when bi-temporal ALS data will be more commonly available, the site index might be considered as a useful predictor variable. Our previous experience (Hawryło and Wężyk, 2018) showed that in the case of Scots pine-dominated stands, the incorporation of Sentinel-2 satellite images into IPC-based stand volume predictive models does not significantly improve the model accuracy. Thus, in the presented AABA experiment, we decided to not include medium resolution satellite images (Landsat, Sentinel-2). Moreover, we intended to develop an allometric model that is applicable in the scale of the whole county, while obtaining a good quality medium-resolution satellite mosaic for such an extensive area is challenging. From our point of view, the medium resolution satellite images (Landsat, Sentinel-2) might be useful in the context of developing the AABA for multiple species. Then, a satellite-derived species map could define the zones leading the decision with species-specific allometric models to be applied. Here, we developed the allometric model for the stand volume estimation of Scots pine-dominated stands (Equation (8)) using only two predictor variables. Using more independent variables, and thus potentially improving prediction accuracy, could further develop the model. However, when accounting for the possible practical applications of the developed method, we decided to rely on predictors that are relatively easy to obtain from the ALS data without necessity to co-locate to ALS samples. We believe that our research will serve as a base for future studies in developing similar allometric models for other species, stand types and variables (forest biomass and volume increment). It would be valuable to undertake further research for developing allometric stand volume models for different dominant tree species, as was done previously at the single tree level for tree volume (Zianis et al., 2005). We also see real potential for the development of combined methods where the stand level estimates of volume obtained from AABA might be refined to the single tree level. This might be possible by combing the proposed AABA with individual tree-based methods which also do not require co-location of field measurements, like LITIDA (Huang et al., 2019) or the simple height-volume relationship approach proposed by Tinkham et al. (2016). A combination of methods might reduce the systematic error often observed for ITD approaches, but simultaneously provide information at the single tree level. Kangas et al. (2018) claimed that in the future, remote sensing data would be further utilized in NFIs as auxiliary information for defining the model’s design, estimation and inference. They argued that future inventory methods might be improved through the synergies of the NFI and forest management inventory systems. In the presented research, we demonstrated how the NFI data could be utilized in the context of a small-scale forest management inventory. Since the focus of our study was on Scots pine-dominated stands, there is some likelihood that dissimilar evaluations would have arisen if the focus had been on more complex (multi-layer) forest stands or stands dominated by broadleaf tree species. In deciduous forest stands, the issue of underestimation of the true number of trees based on CHM is particularly challenging (Koch et al., 2006). Furthermore, it is likely that in case of different forest species, the proposed h/TH ratio of 0.6 founded here as an optimal for RSI calculation may differ. We believe that the proposed approach is suitable to use for single layer stands dominated by coniferous tree species. However, further research is needed to explore its suitability for more complex stands where the trees from the lower layers of stand account for significant share of the stand volume. For more complex forest stands, the proposed AABA method may require additional predictor variables to achieve an accuracy comparable with the traditional ABA. Conclusions In this article, we proposed the AABA for estimating the stand volume of Scots pine stands. The proposed approach is novel and, when compared with the classic ABA method, it reduces time- and cost-consuming fieldwork without a significant reduction in accuracy of stand volume estimation. The prediction is made similarly to the ABA method; however, the model’s development does not require co-location of the training field plots with ALS samples, as the allometric model is developed on an independent data set. The proposed method is simple, and any set of field plots without a precise location could be used for model development. We showed that a national scale data set consisting of NFI plots is sufficient for the development of an allometric model useful for stand volume estimations in local conditions without systematic errors. These traits make the method particularly interesting for forested areas where inventory data with co-location to ALS samples are lacking. In future research, the proposed method must be investigated under a broader range of environmental conditions, species diversity and forest structures. Acknowledgements This work was carried out under project REMBIOFOR, “Remote sensing-based assessment of woody biomass and carbon storage in forests”, supported by The National Centre for Research and Development in Poland under BIOSTRATEG program, agreement no. BIOSTRATEG1/267755/4/NCBR/2015. We want to express our thanks to the Bureau for Forest Management and Geodesy (BULiGL) for collecting the field sample plot data used as the reference plot for the testing of the developed method. Conflict of interest statement None declared. Funding The National Centre for Research and Development in Poland under BIOSTRATEG program, agreement no. BIOSTRATEG1/ 267755/4/NCBR/2015. References Antony , D.A. and Singh , G. 2016 Model-based outlier detection system with statistical preprocessing . J. Mod. Appl. Stat. Methods 15 , 789 – 801 . Google Scholar Crossref Search ADS WorldCat Barrio-Anta , M. , Balboa-Murias , M.Á. , Castedo-Dorado , F. , Diéguez-Aranda , U. and Álvarez-González , J.G. 2006 An ecoregional model for estimating volume, biomass and carbon pools in maritime pine stands in Galicia (northwestern Spain) . For. Ecol. Manag. 223 , 24 – 34 . Google Scholar Crossref Search ADS WorldCat Bolton , D.K. , White , J.C. , Wulder , M.A. , Coops , N.C. , Hermosilla , T. and Yuan , X. 2018 Updating stand-level forest inventories using airborne laser scanning and Landsat time series data . Int. J. Appl. Earth Obs. Geoinf. 66 , 174 – 183 . Google Scholar Crossref Search ADS WorldCat Borgefors , G. , Brandtberg , T. and Walter , F. 1999 Forest parameter extraction from airborne sensors . Int. Arch. Photogramm. Remote Sens. 32 , 151 – 158 . WorldCat Breidenbach , J. and Astrup , R. 2014 The semi-individual tree crown approach. In Forestry Applications of Airborne Laser Scanning: Concepts and Case Studies . M. , Maltamo , E. , Næsset , J. , Vauhkonen (eds.). Springer , pp. 113 – 133 . Google Scholar Crossref Search ADS Google Preview WorldCat COPAC Bruchwald , A. , Rymer-Dudzińska , T. , Dudek , A. , Michalak , K. , Wróblewski , L. and Zasada , M. 2000 Wzory empiryczne do określania wysokości i pierśnicowej liczby kształtu grubizny drzewa . Sylwan 144 , 5 – 12 . WorldCat Bruchwald , A. and Rymer-Dudzińska , T. 1981 Zastosowanie funkcji Näslunda do budowy stałych krzywych wysokości dla świerka . Sylwan 125 , 21 – 29 . WorldCat Eggleston , H.S. , Buendia , L. , Miwa , K. , Ngara , T. and Tanabe , K. 2006 IPCC Guidelines for National Greenhouse Gas Inventories . Erfanifard , Y. , Stereńczak , K. , Kraszewski , B. and Kamińska , A. 2018 Development of a robust canopy height model derived from ALS point clouds for predicting individual crown attributes at the species level . Int. J. Remote Sens. 39 , 9206 – 9227 . Google Scholar Crossref Search ADS WorldCat Forests , I. 2016 Manual on Methods and Criteria for Harmonized Sampling, Assessment, Monitoring and Analysis of the Effects of Air Pollution on Forests . Frazer , G.W. , Magnussen , S. , Wulder , M.A. and Niemann , K.O. 2011 Simulated impact of sample plot size and co-registration error on the accuracy and uncertainty of LiDAR-derived estimates of forest stand biomass . Remote Sens. Environ. 115 , 636 – 649 . Google Scholar Crossref Search ADS WorldCat Gobakken , T. and Næsset , E. 2008 Assessing effects of laser point density, ground sampling intensity, and field sample plot size on biophysical stand properties derived from airborne laser scanner data . Can. J. For. Res. 38 , 1095 – 1109 . Google Scholar Crossref Search ADS WorldCat Gobakken , T. and Næsset , E. 2009 Assessing effects of positioning errors and sample plot size on biophysical stand properties derived from airborne laser scanner data . Can. J. For. Res. 39 , 1036 – 1052 . Google Scholar Crossref Search ADS WorldCat Gougeon , F.A. 1995 A crown-following approach to the automatic delineation of individual tree crowns in high spatial resolution aerial images . Can. J. Remote. Sens. 21 , 274 – 284 . Google Scholar Crossref Search ADS WorldCat Hansen , E.H. , Ene , L.T. , Mauya , E.W. , Patočka , Z. , Mikita , T. , Gobakken , T. , et al. 2017 Comparing empirical and semi-empirical approaches to forest biomass modelling in different biomes using airborne laser scanner data . Forests 8 , 1 – 17 . Google Scholar Crossref Search ADS WorldCat Hawryło , P. , Tompalski , P. and Wȩzyk , P. 2017 Area-based estimation of growing stock volume in scots pine stands using ALS and airborne image-based point clouds . Forestry 90 , 686 – 696 . Google Scholar Crossref Search ADS WorldCat Hawryło , P. and Wężyk , P. 2018 Predicting growing stock volume of scots pine stands using Sentinel-2 satellite imagery and airborne image-derived point clouds . Forests 9 , 274 . Google Scholar Crossref Search ADS WorldCat Hollaus , M. , Wagner , W. , Schadauer , K. , Maier , B. and Gabler , K. 2009 Growing stock estimation for alpine forests in Austria: a robust lidar-based approach . Can. J. For. Res. 39 , 1387 – 1400 . Google Scholar Crossref Search ADS WorldCat Holopainen , M. , Haapanen , R. , Karjalainen , M. , Vastaranta , M. , Hyyppä , J. , Yu , X. , et al. 2010 Comparing accuracy of airborne laser scanning and TerraSAR-X radar images in the estimation of plot-level forest variables . Remote Sens. 2 , 432 – 445 . Google Scholar Crossref Search ADS WorldCat Huang , S. , Ramirez , C. , Conway , S. , Evans , K. , Chu , C. , McElhaney , M. et al. 2019 LITIDA: a cost-effective non-parametric imputation approach to estimate LiDAR-detected tree diameters over a large heterogeneous area . Forestry 92 , 206 – 218 . Google Scholar Crossref Search ADS WorldCat Hummel , S. , Hudak , A.T. , Uebler , E.H. , Falkowski , M.J. and Megown , K.A. 2011 A comparison of accuracy and cost of LiDAR versus stand exam data for landscape management on the Malheur national forest . J. For. 267 – 273 . WorldCat Hyyppä , J. and Inkinen , M. 1999 Detecting and estimating attributes for single trees using laser scanner . Photogramm. J. Finl. 16 , 27 – 42 . WorldCat Jagodziński , A.M. , Dyderski , M.K. , Gęsikiewicz , K. and Horodecki , P. 2019 Effects of stand features on aboveground biomass and biomass conversion and expansion factors based on a Pinus sylvestris L. chronosequence in Western Poland . Eur. J. For. Res. 138 , 673 – 683 . Google Scholar Crossref Search ADS WorldCat Kangas , A. , Astrup , R. , Breidenbach , J. , Fridman , J. , Gobakken , T. , Korhonen , K.T. , et al. 2018 Remote sensing and forest inventories in Nordic countries—Roadmap for the future . Scand. J. For. Res. 7581 , 1 – 16 . WorldCat Koch , B. , Kattenborn , T. , Straub , C. and Vauhkonen , J. 2014 Segmentation of forest to tree objects. In Forestry Applications of Airborne Laser Scanning: Concepts and Case Studies . M. , Maltamo , E. , Næsset , J. , Vauhkonen (eds.). Springer , pp. 89 – 112 . Google Scholar Crossref Search ADS Google Preview WorldCat COPAC Koch , B. , Heyder , U. and Weinacker , H. 2006 Detection of individual tree crowns in airborne LiDAR data . Photogramm. Eng. Remote. Sens. 72 , 357 – 363 . Google Scholar Crossref Search ADS WorldCat Lindberg , E. and Holmgren , J. 2017 Individual tree crown methods for 3D data from remote sensing . Curr. For. Reports 3 , 19 – 31 . WorldCat Means , J.E. , Acker , S.A. , Fitt , B.J. , Renslow , M. , Emerson , L. and Abstract , C.J.H. 2000 Predicting forest stand characteristics with airborne scanning LiDAR . Photogramm. Eng. Remote. Sens. 66 , 1367 – 1371 . WorldCat Meredieu , C. , Perret , S. and Dreyfus , P. 2003 Modelling dominant height growth: effect of stand density. In Modelling Forest Systems. Workshop on the Interface Between Reality, Modelling and the Parameter Estimation Processes, Sesimbra, Portugal; 2–5 June 2002 . A. , Amaro , D. , Reed , P. , Soares (eds.). CABI , pp. 111 – 121 . Google Scholar Crossref Search ADS Google Preview WorldCat COPAC Miścicki , S. and Stereńczak , K. 2013 A two-phase inventory method for calculating standing volume and tree-density of forest stands in Central Poland based on airborne laser-scanning data . For. Res. Pap. 74 , 127 – 136 . WorldCat Naesset , E. 1997 Determination of mean tree height of forest stands using airborne laser scanner data . ISPRS J. Photogramm. Remote Sens. 52 , 49 – 56 . Google Scholar Crossref Search ADS WorldCat Næsset , E. 2002 Predicting forest stand characteristics with airborne scanning laser using a practical two-stage procedure and field data . Remote Sens. Environ. 80 , 88 – 99 . Google Scholar Crossref Search ADS WorldCat Nilsson , M. 1996 Estimation of tree heights and stand volume using an airborne LiDAR system . Remote Sens. Environ. 56 , 1 – 7 . Google Scholar Crossref Search ADS WorldCat Ochal , W. , Socha , J. and Pierzchalski , M. 2017 The effect of the calculation method, plot size, and stand density on the accuracy of top height estimation in Norway spruce stands . iForest 10 , 498 – 505 . Google Scholar Crossref Search ADS WorldCat Packalén , P. , Temesgen , H. and Maltamo , M. 2012 Variable selection strategies for nearest neighbor imputation methods used in remote sensing based forest inventory . Can. J. Remote. Sens. 38 , 557 – 569 . Google Scholar Crossref Search ADS WorldCat Pardé , J. and Bouchon , J. 1988 Dendrométrie . ENGREF. ENGREF , p. 328 . Google Preview WorldCat COPAC Persson , Å. , Holmgren , J. and Söderman , U. 2002 Detecting and measuring individual trees using an airborne laser scanner . Photogramm. Eng. Remote. Sens. 68 , 925 – 932 . WorldCat Phua , M.H. , Johari , S.A. , Wong , O.C. , Ioki , K. , Mahali , M. , Nilus , R. , et al. 2017 Synergistic use of Landsat 8 OLI image and airborne LiDAR data for above-ground biomass estimation in tropical lowland rainforests . For. Ecol. Manag. 406 , 163 – 171 . Google Scholar Crossref Search ADS WorldCat Popescu , S.C. 2007 Estimating biomass of individual pine trees using airborne LiDAR . Biomass Bioenergy 31 , 646 – 655 . Google Scholar Crossref Search ADS WorldCat Rahlf , J. , Breidenbach , J. , Solberg , S. , Næsset , E. and Astrup , R. 2014 Comparison of four types of 3D data for timber volume estimation . Remote Sens. Environ. 155 , 325 – 333 . Google Scholar Crossref Search ADS WorldCat Rahlf , J. , Breidenbach , J. , Solberg , S. and Astrup , R. 2015 Forest parameter prediction using an image-based point cloud: A comparison of semi-ITC with ABA . Forests 6 , 4059 – 4071 . Google Scholar Crossref Search ADS WorldCat Sharma , M. , Amateis , R.L. and Burkhart , H.E. 2002 Top height definition and its effect on site index determination in thinned and unthinned loblolly pine plantations . For. Ecol. Manag. 168 , 163 – 175 . Google Scholar Crossref Search ADS WorldCat Socha , J. , Pierzchalski , M. , Bałazy , R. and Ciesielski , M. 2017 Modelling top height growth and site index using repeated laser scanning data . For. Ecol. Manag. 406 , 307 – 317 . Google Scholar Crossref Search ADS WorldCat Socha , J. and Wezyk , P. 2007 Allometric equations for estimating the foliage biomass of scots pine . Eur. J. For. Res. 126 , 263 – 270 . Google Scholar Crossref Search ADS WorldCat Stereńczak , K. 2013 Factors influencing individual tree crowns detection based on airborne laser scanning data . For. Res. Pap. 74 , 323 – 333 . WorldCat Stereńczak , K. , Kraszewski , B. , Mielcarek , M. and Piasecka , Ż. 2017 Inventory of standing dead trees in the surroundings of communication routes – The contribution of remote sensing to potential risk assessments . For. Ecol. Manag. 402 , 76 – 91 . Google Scholar Crossref Search ADS WorldCat Stereńczak , K. , Lisańczuk , M. , Parkitna , K. , Mitelsztedt , K. , Mroczek , P. and Miścicki , S. 2018 The influence of number and size of sample plots on modelling growing stock volume based on airborne laser scanning . Drewno 61 , 5 – 22 . WorldCat Stereńczak , K. , Będkowski , K. and Weinacker , H. 2008 Accuracy of crown segmentation and estimation of selected trees and forest stand parameters in order to resolution of used DSM and NDSM models generated from dense small footprint LiDAR data . Int. Arch. Photogramm. Remote. Sens. Spat. Inf. Sci. XXXVII , 27 – 32 . WorldCat Sun , G. and Ranson , K.J. 2000 Modeling LiDAR returns from forest canopies . IEEE Trans. Geosci. Remote Sens. 38 , 2617 – 2626 . Google Scholar Crossref Search ADS WorldCat Tinkham , W.T. , Smith , A.M.S. , Affleck , D.L.R. , Saralecos , J.D. , Falkowski , M.J. , Hoffman , C.M. , et al. 2016 Development of height-volume relationships in second growth Abies grandis for use with aerial LiDAR . Can. J. Remote. Sens. 42 , 400 – 410 . Google Scholar Crossref Search ADS WorldCat Tukey , J.W. 1977 Exploratory Data Analysis . Addison-Wesley . Google Preview WorldCat COPAC Vastaranta , M. , Wulder , M.a. , White , J.C. , Pekkarinen , A. , Tuominen , S. , Ginzler , C. , et al. 2013 Airborne laser scanning and digital stereo imagery measures of forest structure: Comparative results and implications to forest mapping and inventory update . Can. J. Remote. Sens. 39 , 382 – 395 . Google Scholar Crossref Search ADS WorldCat Vauhkonen , J. , Ene , L. , Gupta , S. , Heinzel , J. , Holmgren , J. , Pitkänen , J. , et al. 2012 Comparative testing of single-tree detection algorithms under different types of forest . Forestry 85 , 27 – 40 . Google Scholar Crossref Search ADS WorldCat White , J. , Stepper , C. , Tompalski , P. , Coops , N. and Wulder , M. 2015a Comparing ALS and image-based point cloud metrics and modelled Forest inventory attributes in a complex coastal Forest environment . Forests 6 , 3704 – 3732 . Google Scholar Crossref Search ADS WorldCat White , J.C. , Tompalski , P. , Vastaranta , M. , Wulder , M.A. , and Saarinen , N. 2017 A model development and application guide for generating an enhanced forest inventory using airborne laser scanning data and an area-based approach . CWFC Information Report FI-X-018 , 38 White , J.C. , Arnett , J.T.T.R. , Wulder , M.A. , Tompalski , P. and Coops , N.C. 2015b Evaluating the impact of leaf-on and leaf-off airborne laser scanning data on the estimation of forest inventory attributes with the area-based approach . Can. J. For. Res. 45 , 1498 – 1513 . Google Scholar Crossref Search ADS WorldCat White , J.C. , Coops , N.C. , Wulder , M.A. , Vastaranta , M. , Hilker , T. and Tompalski , P. 2016 Remote sensing technologies for enhancing forest inventories: A review . Can. J. Remote. Sens. 42 , 619 – 641 . Google Scholar Crossref Search ADS WorldCat Woods , M. , Lim , K. and Treitz , P. 2008 Predicting forest stand variables from LiDAR data in the Great Lakes-St. Lawrence forest of Ontario . For. Chron. 84 , 827 – 839 . Google Scholar Crossref Search ADS WorldCat Yu , X. , Hyyppä , J. , Karjalainen , M. , Nurminen , K. , Karila , K. , Vastaranta , M. , et al. 2015 Comparison of laser and stereo optical, SAR and InSAR point clouds from air- and space-borne sources in the retrieval of forest inventory attributes . Remote Sens. 7 , 15933 – 15954 . Google Scholar Crossref Search ADS WorldCat Zianis , D. , Muukkonen , P. , Mäkipää , R. and Mencuccini , M. 2005 Biomass and stem volume equations for tree species in Europe . Silva Fenn. 4 , 1 – 63 . WorldCat © Institute of Chartered Foresters, 2019. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)
TI - An allometric area-based approach—a cost-effective method for stand volume estimation based on ALS and NFI data
JF - Forestry: An International Journal Of Forest Research
DO - 10.1093/forestry/cpz062
DA - 2020-05-14
UR - https://www.deepdyve.com/lp/oxford-university-press/an-allometric-area-based-approach-a-cost-effective-method-for-stand-iMHcZrECIx
SP - 1
VL - Advance Article
IS - 
DP - DeepDyve
ER -