Effects of terrain slope and aspect on the error of ALS-based predictions of forest attributes

Effects of terrain slope and aspect on the error of ALS-based predictions of forest attributes Abstract Wall-to-wall forest management inventories with the area-based method using airborne laser scanner (ALS) data are operational in many countries. With this method, empirical relationships are established between ALS metrics and ground reference observations of forest attributes, and wall-to-wall predictions can be made over large areas. However, the prediction errors may be influenced by terrain slope and aspect because the properties of the ALS point cloud are dependent on these factors. Two datasets covering wide ranges of terrain slope and aspect, collected in the western part of Norway, were analysed. The first dataset represented sample plots from an ordinary operational forest management inventory and the second dataset were collected as an experimental dataset where clusters of sample plots were distributed on slopes with different inclinations. Six forest attributes were predicted using non-linear regression and the prediction errors were analysed using univariate- and multivariate analysis of variance. The results showed that slope and aspect affected the prediction errors, but that the effects were small in magnitude. Thus, the current study concludes that terrain effects seem to be negligible in operational forest inventories. Introduction Area-based wall-to-wall forest management inventories using airborne laser scanner (ALS) data have been operational since 2002 in Norway (Næsset et al., 2004). Approximately 300 000 ha of forest is inventoried annually in Norway, and in 2016 close to 100 per cent of the area was inventoried by ALS-based methods (Pers. comm., Norwegian Agriculture Agency). In other Nordic countries, the proportion of ALS-based inventories is at about the same level. In Finland for example, ALS-based forest management inventories providing species-specific timber volume estimates are applied to almost 3 million ha of forest land annually (Maltamo and Packalen, 2014). The main advantage of the ALS-based inventories over the purely field-based sample plot inventories is that objective measurements of highly correlated metrics (the ALS data) are available over the entire area of interest (AOI). To utilize these measurements effectively for estimating timber volume (or other attributes of interest), empirical relationships have to be established between the ALS measurements and ground reference observations of timber volume on a number of field plots of a certain size, say 200–500 m2. In their raw form, the ALS measurements collected over the AOI constitute a continuous cloud of xyz-referenced echoes (points) from the laser pulses emitted from an airborne sensor. The z-values are relative to the Earth’s ellipsoid. Thus, the z-values have to first be converted to heights above the terrain before providing relevant information about forests. This is made possible by processing the ALS data by algorithms that aim to identify and classify those echoes that were reflected from the ground (Sithole and Vosselman, 2004). A digital terrain model (DTM) is then constructed from these ground echoes, and the height of all other echoes can be calculated relative to the DTM. The height distribution of the ALS echoes (heights above the terrain, Δz) for each field plot is represented by area-based, continuous metrics (e.g. height values at certain percentiles of the echo height distribution) and these metrics are used to model the ALS-to-timber volume relationship. The field plots are usually distributed systematically over the AOI so that they cover the full timber volume range to avoid extrapolation in the subsequent model prediction phase. Timber volume estimates for individual stands within the AOI are obtained by aggregating grid cell predictions. It is important that the prediction models are valid in the area of application in the sense that there should be no underlying property affecting the relationships that are not directly accounted for in the models or indirectly by means of stratification according to relevant forest attributes. Otherwise, the stand-wise estimators might be biased. Tree species, age class and site productivity are common stratification criteria for ALS timber volume models (Næsset, 2002, 2004a, 2007). However, terrain slope and aspect could also potentially be factors that affect the relationship between ALS metrics and forest attributes (Hodgson et al., 2003; Reutebuch et al., 2003; Næsset, 2004c; Hollaus et al., 2006; Su and Bork, 2006; Breidenbach et al., 2008). In operational implementation of the area-based approach, neither terrain slope nor aspect is usually accounted for in the empirical models or by stratification. There are several reasons why terrain slope could influence the relationship between ALS point clouds and observed timber volume. The properties of the ALS point cloud are primarily affected by the three-dimensional distribution of the tree crown biomass over an area. Trees are opportunistic and allocate their crowns towards gaps and open space to minimize the competition for light (e.g. Young and Hubbell, 1991; Purves et al., 2007), and thus to maximize photosynthesis (Berezovskaya et al., 1997). Light conditions are more favourable in the downslope direction compared with the upslope direction because downslope neighbouring trees shade a subject tree less than upslope neighbours do. It is, therefore, likely that trees will tend to have asymmetrical crowns relative to the stem position with more biomass in the downslope direction since the level of competition affects crown symmetry (e.g. Young and Hubbell, 1991). On flat terrain, asymmetrical crowns would probably not yield point clouds with different properties compared with symmetrical crowns. On a slope, however, trees with asymmetrical crowns and more biomass allocated in the downslope direction, will cause the mean height of echoes reflected from a particular tree to be shifted upwards compared with flat terrain since echo heights are relative to the ground elevation vertically below, and not relative to the elevation at the base of the stem (Vega et al., 2014). Breidenbach et al. (2008) documented this effect. Their data showed that the median of ALS echo height distributions from plots on steeper terrain were higher compared with those from plots situated on flat terrain. This effect will be even more pronounced if the trees also are leaning in the downslope direction (Gatziolis et al., 2010). Studies have also shown that terrain slope affects the quality of the DTM (Hodgson et al., 2003; Hollaus et al., 2006; Su and Bork, 2006). This could be a result of the slope itself, but could also be a consequence of differences in terrain surface between sloped and flat terrain, with for example higher frequency of boulders on slopes. The DTM quality directly affects the height distribution of the vegetation echoes since their heights are calculated relative to the DTM. Thus, if the quality of the DTM depends on slope, the ALS point clouds might have different properties on slopes compared with those on the flat terrain. In addition to terrain slope, the terrain aspect is also likely to affect the biomass allocation of a tree. Favourable light conditions for trees are directly dependent on the angle of the sun relative to the Earth’s surface. Trees growing in the boreal and temperate zones of the northern hemisphere will therefore generally tend to allocate more of their branch biomass towards the south where the sun angle is the greatest. For example, Rouvinen and Kuuluvainen (1997) examined the effect of local competition on crown architecture in a study site in Finland and found that Scots pine (Pinus sylvestris) trees were asymmetrical towards south and southwest. Thus, the point clouds from ALS are likely to be affected accordingly and might hence have different properties depending on aspect. In addition to these direct effects of slope and aspect that might alter point cloud metrics, slope and aspect might also have an effect on the accuracy of the co-registration of ALS and field data. Accurate geographical co-registration of ALS data and the field plots used for model calibration is essential for accurate predictions (Gobakken and Næsset, 2009). The positions of the field plots are typically obtained using global navigation satellite systems (GNSS) and the accuracy depends on many factors. Trees may cause multipath effects of the GNSS signals or they may even temporarily block the signals from reaching the antenna e.g. Tomaštík et al. (2016). Terrain features can have similar effects. With steeper slopes, fewer satellites are in view for the GNSS receiver on the ground because of the elevated upslope horizon. Furthermore, in Norway the Global Positioning System (GPS) satellites are all orbiting south of zenith, which means that fewer satellites will be available in north-facing slopes compared with south-facing slopes. However, south of 64.8°N the Russian Global Navigation Satellite System (GLONASS) satellites are in zenith view, so utilizing signals from both systems mitigates to some extent the effect of GPS satellites orbiting south of 55°N. Both slope and aspect can thus affect the positioning error of the field plots, which in turn affects the quality of the ALS-to-timber volume relationship. The objective of this study was hence to analyse the accumulated potential effect of terrain slope and aspect on the accuracy of forest attribute predictions obtained from an operational area-based forest inventory approach using ALS data. The influence of terrain slope and aspect were evaluated with respect to six important forest attributes, namely timber volume, dominant height, Lorey’s mean height, mean basal area diameter, stand basal area and number of stems. Material and methods The study took advantage of two separate datasets from the western part of Norway, collected in an area with great variation in terrain slope. The two datasets were used to create two model sets. The first model set (Modelset_C) was fitted to a dataset that comprised sample plots from a standard operational inventory, while the second model set (Modelset_V) was fitted to data from sample plots collected specifically for the study as validation data. The two model sets were both applied to the validation data and the influence of terrain slope and aspect were analysed. Figure 1 summarizes the work-flow of the study. Figure 1 View largeDownload slide Overview of the study using two different datasets (calibration and validation data) which are used to create two model sets (Modelset_C and Modelset_V). The two model sets are used to make predictions on the validation data and the prediction errors are further analysed with respect to terrain effects. Figure 1 View largeDownload slide Overview of the study using two different datasets (calibration and validation data) which are used to create two model sets (Modelset_C and Modelset_V). The two model sets are used to make predictions on the validation data and the prediction errors are further analysed with respect to terrain effects. In the validation dataset, an equal number of plots were measured in four 10.25° wide slope classes ranging between 2° and 43° of inclination. In the calibration dataset, the inclination ranged between 3° and 38° (Figure 2). Figure 2 View largeDownload slide Sample plots by dominant species distributed on slope and aspect for the calibration data and validation data. Figure 2 View largeDownload slide Sample plots by dominant species distributed on slope and aspect for the calibration data and validation data. Study area The study was conducted within three municipalities in western Norway, approximately 40 km south of the city of Bergen. The municipalities were Fusa, Tysnes and Kvinnherad (Figure 3). The forests in the area are naturally dominated by Scots pine (Pinus sylvestris) and deciduous species, mainly birch (Betula pubescens). However, during the 20th century, planting of non-native conifers, mainly Norway spruce (Picea abies) and Sitka spruce (Picea sitchensis) was common. Our study area comprised ~260 km2 of productive forests with volume proportions of ~ 66 per cent pine, 20 per cent deciduous and 13 per cent spruce. Figure 3 View largeDownload slide Study area in western Norway. Figure 3 View largeDownload slide Study area in western Norway. Field data collection Two separate field surveys were carried out within the study area. First, a dataset (calibration data) used to calibrate the relationship between field observations of forest attributes and ALS metrics was collected as part of an ordinary forest management inventory in the three municipalities. The calibration data comprised field reference values of 114 circular plots of 250 m2 in mature forests. The survey was conducted from 23 April to 10 August in 2012. The area was divided into two strata according to dominant tree species. Stratum A comprised stands dominated by either Norway spruce or Sitka spruce. Stratum B comprised stands dominated by Scots pine. There were 29 sample plots in Stratum A and 85 sample plots in stratum B. To enable an independent test of the accuracy of models calibrated with the calibration data, a second dataset (validation data) were collected within the same area during autumn of 2013. This dataset comprised 192 plots of 250 m2 laid out according to an experimental design with four uniform slope classes from 2° to 43° of inclination (mean 22°), two ALS sensor settings (Sensor 1 and Sensor 2) and two dominating tree species (Norway spruce and Scots pine). The plots where laid out in clusters of three (i.e. 64 clusters) with 20 m inter-distance between plot centres, and the clusters were established inside homogenous stands. Thirty-one clusters were allocated to stratum A and 33 to stratum B. Plot positioning The calibration data plots were positioned using real-time kinematic (RTK) GNSS with correction data with decimetre precision acquired from the Norwegian Mapping Authority (NMA) GNSS network. Base stations were always within a distance of ~25 km. To secure proper initialization, the GNSS receiver was running for minimum 10 min before recording started. An estimated horizontal root mean square error <0.5 m, a position dilution of precision <3.0 and a minimum of eight satellites with enabled correction data, were required before positioning started. In cases where these conditions could not be met, a self-operated base station was used rather than relying on the NMA service. Each plot was positioned twice using real-time correction and the positions were averaged to obtain the final position. In cases where the difference between the two positions was larger than 40 cm, a third position was recorded and the two positions with the smallest horizontal error estimate were averaged. The validation plots were positioned using GNSS with post-processing correction. Both the base station and the rover unit recorded GPS and GLONASS observation data. Base station observation data for post-processing were obtained from the three closest reference stations of the NMA GNSS network. The standard deviations reported from the post-processing at the respective plot centres indicated that some positions were inaccurately determined, as 48 positions had standard deviations >1 m. We, therefore, ranked plots according to the standard deviation value and were able to re-visit 35 plots for new measurements within the available resources. After this second positioning effort in the field, the average standard deviation was 45.5 cm. Only 13 of the 192 sample plots had standard deviations >1 m. Tree measurements and volume calculation – calibration data All trees with diamter at breast height (dbh) ≥4 cm were callipered (calliper trees) and tree species were registered. In addition, heights of an average of 10 trees (height sample trees) per plot were measured. These trees were sampled using a relascope, where every n’th relascope tree was selected (n = number of relascope trees on the plot/desired number of sample trees). An initial relascope count was carried out to calculate the ‘n’ for each field plot. Heights were measured using a Vertex hypsometer. Volume calculation was carried out using a ratio estimator to adjust the so-called base volume of each tree. Then single-tree volumes were summed and scaled to per hectare values. The details of this procedure are explained in the following. First, the base volume of each tree (both calliper trees and height sample trees) was calculated using the observed diameter and a height predicted using a base height model (Fitje and Vestjordet, 1977). Then, the ‘true’ volumes of the height sample trees were calculated using the observed diameters and observed heights. For each height sample tree, the ratio between the true volume and the base volume could then be calculated. Furthermore, plot- and species-wise mean ratios (mean-of-ratios) were calculated, and these mean ratios were then used to adjust all base volumes to ‘true’ volumes. However, if there were fewer than three height sample trees of a certain species on a plot, common stratum- and species-wise mean ratios were applied. The volume models applied were those reported in Vestjordet (1967) for Norway spruce, Brantseg (1967) for Scots pine, Braastad (1966) for deciduous species and Bauger (1995) for Sitka spruce. We also calculated dominant height (HO), Lorey’s mean height (HL), mean basal area diameter (DBA), stand basal area (BA) and number of stems (N). To calculate HO and HL, a single-tree height for each tree was estimated by setting height as unknown in the volume model with the estimated volume and observed diameter as fixed, and solving for the matching height numerically. Dominant height is defined as the mean height of the 100 largest trees per hectare with respect to dbh. In the current study where the plot size was 250 m2, we averaged the heights of the two largest trees per plot to obtain HO. Tree measurements and volume calculation – validation data As for the calibration data, the minimum dbh for calliper trees was 4 cm. Tree species was recorded in addition to diameter. The height sample trees, however, were selected as the n’th tree (n = number of trees on the plot/desired number of sample trees) regardless of size, as opposed to the calibration data for which the sampling was proportional to stem basal area. Thus, an initial stem count was carried out for each plot to determine the ‘n’. Three trees per plot (nine per cluster) were selected for the height measurement. Volume calculation was carried out in the same way as for the calibration data, with the exception that the calculation of the ratios to correct the base volumes of the calliper trees were calculated by cluster and species and using a ratio-of-means estimator as opposed to mean-of-ratios since the sample trees had equal inclusion probability. Common ratios calculated by tree species irrespective of cluster were applied when there were less than three sample trees of a certain species in a cluster. As for the calibration data, HO, HL, DBA, BA and N were also calculated (Table 1). Table 1 Summary of field data. Attribute  Mean  Standard deviation  Minimum  Maximum  Calibration plots (n = 114)   V (total) (m3 ha−1)  252.4  178.7  18.9  772.5   V (Norway spruce) (m3 ha−1)  96.6  194.6  0.0  769.0   V (Scots pine) (m3 ha−1)  119.4  103.0  0.0  488.4   V (deciduous) (m3 ha−1)  22.8  41.0  0.0  293.5   V (Sitka spruce) (m3 ha−1)  13.7  92.3  0.0  706.0   HO (m)  17.8  5.1  7.3  31.5   HL (m)  15.4  4.5  6.3  27.3   DBA (cm)  17.2  4.3  6.1  27.6   BA (m2 ha−1)  30.8  15.3  4.8  73.3   N (ha−1)  1447.4  802.6  280.0  4240.0  Validation plots (n = 192)   V (total) (m3 ha−1)  377.2  278.2  14.9  1318.6   V (Norway spruce) (m3 ha−1)  205.5  311.9  0.0  1305.2   V (Scots pine) (m3 ha−1)  80.9  94.2  0.0  400.5   V (deciduous) (m3 ha−1)  14.2  25.5  0.0  129.7   V (Sitka spruce) (m3 ha−1)  76.6  214.2  0.0  1143.9   HO (m)  20.2  5.9  7.9  37.9   HL (m)  17.6  5.0  6.2  35.5   DBA (cm)  22.0  5.5  6.7  40.7   BA (m2 ha−1)  40.2  20.6  3.9  104.2   N (ha−1)  1124.0  607.4  280.0  3600.0  Validation clusters (n = 64)   V (total) (m3 ha−1)  377.2  266.8  81.7  1150.8   V (Norway spruce) (m3 ha−1)  205.5  302.5  0.0  1150.8   V (Scots pine) (m3 ha−1)  80.9  88.1  0.0  354.4   V (deciduous) (m3 ha−1)  14.2  20.9  0.0  89.4   V (Sitka spruce) (m3 ha−1)  76.6  204.5  0.0  830.3   HO (m)  20.2  5.8  11.7  36.8   HL (m)  17.6  4.9  10.3  32.8   DBA (cm)  22.0  4.9  12.3  35.3   BA (m2 ha−1)  40.2  19.3  12.9  88.9   N (ha−1)  1124.0  566.2  373.3  3453.3  Attribute  Mean  Standard deviation  Minimum  Maximum  Calibration plots (n = 114)   V (total) (m3 ha−1)  252.4  178.7  18.9  772.5   V (Norway spruce) (m3 ha−1)  96.6  194.6  0.0  769.0   V (Scots pine) (m3 ha−1)  119.4  103.0  0.0  488.4   V (deciduous) (m3 ha−1)  22.8  41.0  0.0  293.5   V (Sitka spruce) (m3 ha−1)  13.7  92.3  0.0  706.0   HO (m)  17.8  5.1  7.3  31.5   HL (m)  15.4  4.5  6.3  27.3   DBA (cm)  17.2  4.3  6.1  27.6   BA (m2 ha−1)  30.8  15.3  4.8  73.3   N (ha−1)  1447.4  802.6  280.0  4240.0  Validation plots (n = 192)   V (total) (m3 ha−1)  377.2  278.2  14.9  1318.6   V (Norway spruce) (m3 ha−1)  205.5  311.9  0.0  1305.2   V (Scots pine) (m3 ha−1)  80.9  94.2  0.0  400.5   V (deciduous) (m3 ha−1)  14.2  25.5  0.0  129.7   V (Sitka spruce) (m3 ha−1)  76.6  214.2  0.0  1143.9   HO (m)  20.2  5.9  7.9  37.9   HL (m)  17.6  5.0  6.2  35.5   DBA (cm)  22.0  5.5  6.7  40.7   BA (m2 ha−1)  40.2  20.6  3.9  104.2   N (ha−1)  1124.0  607.4  280.0  3600.0  Validation clusters (n = 64)   V (total) (m3 ha−1)  377.2  266.8  81.7  1150.8   V (Norway spruce) (m3 ha−1)  205.5  302.5  0.0  1150.8   V (Scots pine) (m3 ha−1)  80.9  88.1  0.0  354.4   V (deciduous) (m3 ha−1)  14.2  20.9  0.0  89.4   V (Sitka spruce) (m3 ha−1)  76.6  204.5  0.0  830.3   HO (m)  20.2  5.8  11.7  36.8   HL (m)  17.6  4.9  10.3  32.8   DBA (cm)  22.0  4.9  12.3  35.3   BA (m2 ha−1)  40.2  19.3  12.9  88.9   N (ha−1)  1124.0  566.2  373.3  3453.3  ALS data ALS data were acquired using Optech ALTM Gemini instruments mounted on a PA31 Piper Navajo fixed-wing aircraft. The data acquisition was carried out from 5 June to 7 August 2010 with two slightly different setups because different resolutions of the DTM were requested by the NMA for different areas. The pulse densities over the plots comprised by the calibration and validation data were quite similar with 2.1 and 1.8 pulses m−2, respectively. The specifications of the two ALS acquisitions, hereafter referred to as Sensor 1 and 2, are given in Table 2. The initial processing of the ALS data was carried out by the contractor (Blom Geomatics, Norway) according to standard procedures. Echo heights were normalized using a triangular irregular network (TIN) created from ground echoes identified using the progressive TIN densification algorithm (Axelsson, 1999, 2000). Table 2 Acquisition settings for the two ALS sensors. Flight plans  Sensor 1  Sensor 2  Flight altitude (m above ground level)  1300  1600  Pulse repetition frequency (kHz)  100  70  Scan frequency (Hz)  58  41  Half scan angle (°)  12  19  Flight speed (ms−2)  80  80  Flight plans  Sensor 1  Sensor 2  Flight altitude (m above ground level)  1300  1600  Pulse repetition frequency (kHz)  100  70  Scan frequency (Hz)  58  41  Half scan angle (°)  12  19  Flight speed (ms−2)  80  80  ALS metrics for each field plot were calculated using the procedures described by Næsset (2004b). Thus, from the echo height distribution the 10th, 20th,…,90th and 100th height percentiles (denoted H10, H20,…, H90, H100), average height (Hmean) and the coefficient of variation (CV) were computed from first echoes (first of many and single echoes) and last of many echoes above a 2 m threshold. This standard threshold was used to avoid effects of shrubs and low vegetation and erroneously classified vegetation echoes, on the ALS metrics. Furthermore, density metrics for each plot were computed by first dividing the height range between the 2 m threshold and the 95th height percentile into 10 vertical bins of equal height. Then the number of echoes above each height bin were divided by the total number of echoes, and denoted D0, D1,…, D9. The numerator when calculating D0 was the number of echoes above the 2 m threshold, and for D1, D2,…, D9 it was the number of echoes above the 1st, 2nd,…, 9th height bin. Altogether, 44 different ALS metrics were used in the modelling of forest attributes. Modelling forest attributes from ALS To model the relationship between the forest attributes and the ALS metrics, we fitted models using non-linear regression with both dependent and independent variables at original scale. The models were of the form:   y=β0×x1β1×x2β2×⋯×x44β44×ε (1)where y is the response variable, x1, x2,…, x44 are the potential explanatory variables and β0, β1,…, β44 are parameters to be estimated and ε is the model error. Variable selection was carried out with a linearized form of the model using a best subset strategy according to the Bayesian information criterion. In the variable selection, the models were also penalized for collinearity using the variance inflation factor (VIF). Thus, if a model included variables with VIF-values >5, a model with fewer variables was iteratively selected (Ørka, et al., 2016). Separate models were fitted for V, HO, HL, DBA, BA and N. Furthermore, the accuracy of area-based forest inventories usually improves with relevant stratification (e.g. Næsset, 2014). Usually, stratification is based on species, site productivity and age class. We post-stratified the data (both calibration data and validation data) into spruce- and pine-dominated plots according to the field-measured species-specific stem volumes and fitted separate models for the two strata. Moreover, since different sensors are known to yield different relationships between ALS data and forest attributes (Næsset, 2009; Ørka et al., 2010), it was considered to include sensor as a stratification variable. However, in combination with species, this resulted in too few observations for some of the strata, so this option was rejected. Two sets of models were developed; one set (Modelset_C) based on the calibration data and an additional set (Modelset_V) based on the validation data. Both sets of models were applied to the validation data so that two sets of predictions were obtained. Because the calibration data did not cover the ranges of the validation data in terms of slope and aspect, Modelset_C reflects a situation of using models based on sample plots selected according to a sampling design that disregarded terrain properties. This is the current operational practice when using ALS for forest inventory in steep terrain. Predictions using models calibrated on Modelset_V reflect a situation with a balanced dataset regarding slope. Hence, it was expected that potential effects of slope would be less pronounced for these models since no extrapolation was carried out. It was also expected that the errors would be on a lower level because Modelset_V was tested on the same data as it was fitted. Validation plot predictions of V, HO, HL, DBA, BA and N were averaged by cluster to mimic a small stand. The accuracy of the models was assessed on cluster level by means of squared Pearson’s correlation coefficient (r2) between observed and predicted cluster level values. Mean prediction errors (MPE), root mean square prediction errors (RMSPE) and RMSPE relative to the observed value (RMSPE%) for each of the six response variables were calculated for Modelset_V and Modelset_C, both applied to the validation data. The corresponding standard deviations were also calculated, both in the original measurement units (SDPE) and relative to the observed value (SDPE%). The differences between the observed and predicted cluster level values were further analysed to assess the influence of terrain factors (see below). Experiment and analysis of terrain factors The analyses of terrain factors were divided into three different parts where we assessed the effects of slope and aspect (1) directly on the ALS metrics, (2) on the prediction errors (PE) and absolute prediction errors (|PE|) from applying Modelset_V on the validation data and (3) on PE and |PE| from applying Modelset_C on the validation data. In the analyses of effects on prediction errors (2, 3), errors relative to the observed value (PE%) of each respective forest attribute were analysed rather than PE, to control the effects related to the increasing potential for error as the size of the respective forest attribute increases. Furthermore, the |PE|-value of each forest attribute was also analysed relative to the observed value (|PE|%). In addition to slope and aspect, we assessed the effects of species and sensors because these factors previously have been shown to influence both ALS metrics (Ørka et al., 2009, 2010) and estimates of forest attributes using the area-based approach (Næsset, 2007, 2009). Prior to the analyses, a slope value for each field plot was derived from a 10 m × 10 m raster interpolated from the ALS-derived terrain model. The spatial resolution of the terrain model was found sufficient to locate the sample plots within the correct slope range in the field. Then, the plots were grouped into four uniform classes according to their inclination. Values of 2.00° (minimum), 12.25°, 22.50°, 32.75° and 43.00° (maximum) discriminated the groups. Furthermore, the plots were also grouped according to aspect in four classes; North (315°–45°), East (45°–135°), South (135°–225°) and West (225°–315°). These classes were used as factors in all analyses of the effects of slope and aspect on PE% and |PE|% of the six forest attributes. Thus, there were two terrain factors (slope and aspect) and two other factors (species and sensor). In all analyses mentioned above (1–3), both univariate- and multivariate analysis of variance tests were applied. These analyses were performed on the validation data only. With the multivariate tests, PE% and |PE|% for all six forest attributes were used as responses and analysed simultaneously. With the univariate tests, PE% and |PE|% for the different forest attributes were analysed one at a time to assess if they were differently affected. The analyses were conducted using functions for multivariate analysis of variance (MANOVA) and analysis of variance (ANOVA) in the R-package car (Fox and Weisberg, 2011). For MANOVA, the Type II Pillai-Bartlett trace was used as the test statistic, computed as recommended by Hand and Taylor (1987). In order to fulfil the required assumptions of multivariate normality, data were transformed if needed. For PE%, the differences in the log-transformed scale were analysed, while the |PE|% and the ALS metrics were kept in original scale. To test the assumption of multivariate normality, we used the Royston’s Multivariate Normality Test. In addition, to test if the factors significantly affected the PE% and |PE|% we also computed a measure of the magnitude of the effect similar to the variance explained (R2) in regression (Kline, 2004). Such measures are often referred to as effect sizes and are important to explain the impact of a phenomenon (Sullivan and Feinn, 2012). We computed and reported the effect sizes in terms of partial η2 for the MANOVA and ANOVA, which are similar to R2 and we refer to this as effect size (η2) in the text (Vacha-Haase and Thompson, 2004). Furthermore, for each analysis, we ranked the η2 of slope classes, aspect classes, sensors and species from most important to least important. As an additional analysis of the effects of slope and aspect, we fitted models where slope values and aspect classes were allowed to be selected in the variable selection phase. The models were tested if they provided different predictions than the models not including terrain variables using the t-test implemented in the R-package stats. Results Effects on ALS metrics Species was the factor that had the largest effect on the ALS metrics in the multivariate analysis in terms of effect magnitude. A subsequent univariate analysis confirmed that all metrics were influenced by species (P < 0.05; results not shown in table). Moreover, neither effects of aspect, slope, nor sensor were significant in the multivariate analysis (P > 0.05). However, the univariate analysis showed that aspect affected the upper and lower percentiles of the height distribution. Conversely, the ALS density metrics were not affected. However, the univariate analysis indicated that most density metrics from the first echoes were influenced by sensor. The differences in density metrics caused by sensor were found to be significant in the multivariate analysis when evaluating the echo categories separately (first echoes: P = 0.01; last echoes: P = 0.04). Additionally, it should be noted that in the univariate analysis, slope influenced H100 and H90 of both first and last echoes (P < 0.02). To sum up, species were the most influential factor for the ALS metrics. In addition, there seemed to be an effect of sensor on the first echo ALS metrics. There was an indication of a slight effect of aspect and slope on the upper canopy ALS metrics. Modelling forest attributes from ALS Selected models of Modelset_V had between one and three explanatory variables, including both density metrics and height metrics. The RMSPE% of the predicted forest attributes ranged from 6 per cent to 20 per cent for spruce and from 8 per cent to 34 per cent for pine (Table 3). Large Pearson’s correlation values and small RMSPE values indicated accurate predictions for HL, HO, and V (Table 3), while predicted values for BA, DBA and N were less accurate (Table 3). Allowing slope and aspect to be selected in the models resulted in inclusion of slope in the models for V, HO and BA for the spruce stratum, while aspect was selected for the N model in the pine stratum (results not shown in table). However, the predicted values of the models fitted using only ALS metrics did not differ significantly from those predicted using the models that included slope and aspect (t-test: P > 0.87). Thus, these models including slope and aspect were not used in the subsequent analyses. Table 3 Model performance and selected ALS metrics using Modelset_V for calibration. Values are reported separately for the spruce and pine stratum. Attribute  ALS metrics  r2  RMSPE  RMSPE%  MPE  SDPE  SDPE%  Spruce stratum   V (total) (m3 ha−1)  H30.L, D0.L, D6.L  0.73  117.70  19.89  −1.02  119.64  20.22   HO (m)  H40.L, D0.L, D6.L  0.88  1.46  5.82  0.01  1.49  5.92   HL (m)  H90.L, D0.L  0.89  1.36  6.34  0.00  1.38  6.44   DBA (cm)  Hmean.F, Hcv.F  0.76  2.27  9.82  −0.02  2.31  9.99   BA (m2 ha−1)  H20.L  0.42  10.39  18.39  −0.03  10.56  18.70   N (ha−1)  Hcv.F, H70.L  0.71  284.26  19.42  3.57  288.94  19.74  Pine stratum   V (total) (m3 ha−1)  Hcv.F, H70.L, D5.L  0.78  31.88  18.15  0.02  32.38  18.43   HO (m)  H50.L  0.63  1.28  8.21  0.00  1.30  8.34   HL (m)  H60.L  0.69  1.23  8.74  0.00  1.25  8.87   DBA (cm)  Hmax.F, D2.F, Hmean.L  0.61  3.02  14.35  0.01  3.06  14.57   BA (m2 ha−1)  D7.F, H30.L, D3.L  0.61  4.61  18.47  0.02  4.68  18.75   N (ha−1)  D0.F, H50.L  0.46  273.68  34.00  10.21  277.73  34.51  Attribute  ALS metrics  r2  RMSPE  RMSPE%  MPE  SDPE  SDPE%  Spruce stratum   V (total) (m3 ha−1)  H30.L, D0.L, D6.L  0.73  117.70  19.89  −1.02  119.64  20.22   HO (m)  H40.L, D0.L, D6.L  0.88  1.46  5.82  0.01  1.49  5.92   HL (m)  H90.L, D0.L  0.89  1.36  6.34  0.00  1.38  6.44   DBA (cm)  Hmean.F, Hcv.F  0.76  2.27  9.82  −0.02  2.31  9.99   BA (m2 ha−1)  H20.L  0.42  10.39  18.39  −0.03  10.56  18.70   N (ha−1)  Hcv.F, H70.L  0.71  284.26  19.42  3.57  288.94  19.74  Pine stratum   V (total) (m3 ha−1)  Hcv.F, H70.L, D5.L  0.78  31.88  18.15  0.02  32.38  18.43   HO (m)  H50.L  0.63  1.28  8.21  0.00  1.30  8.34   HL (m)  H60.L  0.69  1.23  8.74  0.00  1.25  8.87   DBA (cm)  Hmax.F, D2.F, Hmean.L  0.61  3.02  14.35  0.01  3.06  14.57   BA (m2 ha−1)  D7.F, H30.L, D3.L  0.61  4.61  18.47  0.02  4.68  18.75   N (ha−1)  D0.F, H50.L  0.46  273.68  34.00  10.21  277.73  34.51  Selected models of Modelset_C included between one and three variables. The RMSPE% ranged from 9 per cent to 69 per cent for the models in the spruce stratum and from 9 per cent to 62 per cent for the pine-stratum models (Table 4). There were systematic prediction errors for DBA (under-predicted) and N (over-predicted). For the other forest attributes, the results indicated only minor under-predictions. Adding slope and aspect to the pool of potential predictors resulted in the inclusion of aspect in the model (results not shown in table). Aspect was selected for N in the spruce stratum and for V, HL and BA in the pine stratum. However, predicted values did not differ between models including aspect and the models that did not include terrain variables (P > 0.77). Table 4 Model performance and selected ALS metrics using Modelset_V for calibration. Values are reported separately for the spruce and pine stratum. Attribute  ALS metrics  r2  RMSPE  RMSPE%  MPE  SDPE  SDPE%  Spruce stratum   V (total) (m3 ha−1)  H70.F, D6.L  0.70  129.60  21.90  36.70  126.35  21.35   HO (m)  H70.F  0.84  2.19  8.71  1.32  1.78  7.07   HL (m)  H70.F  0.87  1.93  9.01  1.24  1.50  7.01   DBA (cm)  D0.F, Hmax.L, D7.L  0.67  5.83  25.21  5.15  2.76  11.95   BA (m2 ha−1)  H20.F  0.40  11.74  20.79  4.98  10.81  19.14   N (ha−1)  Df.F, Hmax.L, H10.L  0.55  1013.73  69.26  −888.95  495.30  33.84  Pine stratum   V (total) (m3 ha−1)  D5.F, Hmean.L, D4.L  0.68  41.70  23.74  11.69  40.65  23.14   HO (m)  H80.F, Hcv.L, D0.L  0.61  1.44  9.24  0.03  1.46  9.38   HL (m)  H80.F, D1.F, D6.F  0.67  1.50  10.58  0.72  1.33  9.43   DBA (cm)  D0.F, H40.L  0.56  5.65  26.85  4.43  3.55  16.89   BA (m2 ha−1)  D5.F, H30.L, D4.L  0.60  4.94  19.78  1.20  4.86  19.48   N (ha−1)  D0.F, H60.L, D1.L  0.44  499.18  62.02  −394.97  309.98  38.51  Attribute  ALS metrics  r2  RMSPE  RMSPE%  MPE  SDPE  SDPE%  Spruce stratum   V (total) (m3 ha−1)  H70.F, D6.L  0.70  129.60  21.90  36.70  126.35  21.35   HO (m)  H70.F  0.84  2.19  8.71  1.32  1.78  7.07   HL (m)  H70.F  0.87  1.93  9.01  1.24  1.50  7.01   DBA (cm)  D0.F, Hmax.L, D7.L  0.67  5.83  25.21  5.15  2.76  11.95   BA (m2 ha−1)  H20.F  0.40  11.74  20.79  4.98  10.81  19.14   N (ha−1)  Df.F, Hmax.L, H10.L  0.55  1013.73  69.26  −888.95  495.30  33.84  Pine stratum   V (total) (m3 ha−1)  D5.F, Hmean.L, D4.L  0.68  41.70  23.74  11.69  40.65  23.14   HO (m)  H80.F, Hcv.L, D0.L  0.61  1.44  9.24  0.03  1.46  9.38   HL (m)  H80.F, D1.F, D6.F  0.67  1.50  10.58  0.72  1.33  9.43   DBA (cm)  D0.F, H40.L  0.56  5.65  26.85  4.43  3.55  16.89   BA (m2 ha−1)  D5.F, H30.L, D4.L  0.60  4.94  19.78  1.20  4.86  19.48   N (ha−1)  D0.F, H60.L, D1.L  0.44  499.18  62.02  −394.97  309.98  38.51  Effects on prediction errors from application of Modelset_V on validation data Sensor setting was the factor that had the largest effect on PE% in the multivariate analyses, and it was highly significant (P < 0.01). The univariate analysis showed that the sensor setting influenced mainly the PE% of V and BA (Table 5). Both were overpredicted with Sensor 1 and under-predicted with Sensor 2. The analysis also indicated that aspect was statistically significant (P < 0.05), influencing the PE%-values of V and N with large systematic errors in the North class, smaller in the East and West classes, and smallest in the South class (Figure 4). Slope was influential on the prediction errors of V according to the univariate analysis, where V was overpredicted for the two steepest slope classes. However, judged by the magnitude of the effects, the influence of both slope and aspect (0.16) was smaller than that of sensor (0.40). Species, however, did not significantly affect PE% for any of the forest attributes in neither the multivariate nor the univariate case (P > 0.89). Thus, sensor setting affected PE% the most, although effects of slope and aspect also seemed to be present, mainly influencing V. It should also be noted that there seemed to be an interaction between slope and aspect (Figure 4). Tree height errors in the North- and South class seemed to have a negative correlation with aspect, while for the East- and West class the correlation was positive. Table 5 Effect sizes (η2) of slope, aspect, sensor and species on PE% and |PE|% from application of Modelset_V on the validation data. Rank of effect based on effect sizes in parenthesis.   Multi-variate  Univariate  V  HO  HL  DBA  BA  N  PE%   Slope  0.16 (2)*  0.15 (3)*  0.05 (1)  0.05 (2)  0.03 (3)  0.06 (3)  0.06 (2)   Aspect  0.16 (3)*  0.15 (2)*  0.04 (2)  0.06 (1)  0.06 (1)  0.11 (2)  0.14 (1)*   Sensor  0.40 (1)*  0.18 (1)*  0.00 (4)  0.00 (4)  0.05 (2)  0.19 (1)*  0.06 (3)   Species  0.04 (4)  0.00 (4)  0.01 (3)  0.01 (3)  0.00 (4)  0.00 (4)  0.00 (4)  |PE|%   Slope  0.12 (2)  0.09 (2)  0.08 (1)  0.06 (3)  0.11 (1)  0.07 (1)  0.09 (1)   Aspect  0.11 (4)  0.10 (1)  0.06 (3)  0.02 (4)  0.01 (3)  0.03 (2)  0.05 (2)   Sensor  0.12 (3)  0.00 (4)  0.03 (4)  0.06 (2)  0.00 (4)  0.01 (3)  0.04 (4)   Species  0.22 (1)*  0.01 (3)  0.06 (2)  0.10 (1)*  0.10 (2)*  0.00 (4)  0.08 (2)*    Multi-variate  Univariate  V  HO  HL  DBA  BA  N  PE%   Slope  0.16 (2)*  0.15 (3)*  0.05 (1)  0.05 (2)  0.03 (3)  0.06 (3)  0.06 (2)   Aspect  0.16 (3)*  0.15 (2)*  0.04 (2)  0.06 (1)  0.06 (1)  0.11 (2)  0.14 (1)*   Sensor  0.40 (1)*  0.18 (1)*  0.00 (4)  0.00 (4)  0.05 (2)  0.19 (1)*  0.06 (3)   Species  0.04 (4)  0.00 (4)  0.01 (3)  0.01 (3)  0.00 (4)  0.00 (4)  0.00 (4)  |PE|%   Slope  0.12 (2)  0.09 (2)  0.08 (1)  0.06 (3)  0.11 (1)  0.07 (1)  0.09 (1)   Aspect  0.11 (4)  0.10 (1)  0.06 (3)  0.02 (4)  0.01 (3)  0.03 (2)  0.05 (2)   Sensor  0.12 (3)  0.00 (4)  0.03 (4)  0.06 (2)  0.00 (4)  0.01 (3)  0.04 (4)   Species  0.22 (1)*  0.01 (3)  0.06 (2)  0.10 (1)*  0.10 (2)*  0.00 (4)  0.08 (2)*  *Statistically significant (P < 0.05). Figure 4 View largeDownload slide Influence of terrain effects on PE% for different forest attributes using Modelset_V on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Figure 4 View largeDownload slide Influence of terrain effects on PE% for different forest attributes using Modelset_V on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. The | PE |%-values were influenced only by species (P < 0.01) according to the multivariate analysis, and the univariate analysis identified significant effects on HL, DBA and N. Generally, smaller |PE|%-values were observed for spruce than for pine. Thus, the effects of terrain factors seemed to be small on |PE|% for all the forest attributes, which is also evident from graphical plots of the errors against slope for the different aspect classes (Figure 5). Figure 5 View largeDownload slide Influence of slope and aspect on |PE|% for different forest attributes using Modelset_V on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Figure 5 View largeDownload slide Influence of slope and aspect on |PE|% for different forest attributes using Modelset_V on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Effects on prediction errors from application of Modelset_C on the validation data Sensor setting and species influenced PE% (Table 6). More specifically, the univariate tests indicated that sensor influenced the prediction errors of V and BA, while species influenced prediction errors of HO. The tests indicated over-predictions for Sensor 1 and under-predictions for Sensor 2. Furthermore, in the spruce stratum, the PE%-values for HO were smaller compared with the pine stratum. There were no effects of terrain factors on the PE%-values (Figure 6). The |PE|%-values were not significantly affected by any of the factors in either the multivariate or the univariate analysis (Table 6), and the trends (Figure 7) confirmed that the relationships were relatively weak. Table 6 Effect sizes (η2) of slope, aspect, sensor and species on PE% and | PE |% from application of Modelset_C on the validation data. Rank of effect based on effect sizes in parenthesis.   Multi-variate  Univariate  V  HO  HL  DBA  BA  N  PE %   Slope  0.10 (4)  0.06 (3)  0.02 (3)  0.02 (2)  0.03 (2)  0.06 (3)  0.07 (2)   Aspect  0.13 (3)  0.08 (2)  0.06 (2)  0.08 (1)  0.08 (1)  0.07 (2)  0.10 (1)   Sensor  0.28 (2)*  0.16 (1)*  0.02 (3)  0.02 (3)  0.02 (3)  0.19 (1)*  0.02 (3)   Species  0.65 (1)*  0.02 (4)  0.10 (1)*  0.01 (4)  0.01 (4)  0.00 (4)  0.00 (4)  |PE|%   Slope  0.11 (3)  0.01 (4)  0.12 (1)  0.08 (1)  0.10 (1)  0.02 (3)  0.11 (1)   Aspect  0.14 (2)  0.12 (1)  0.06 (2)  0.04 (2)  0.09 (2)  0.06 (1)  0.09 (2)   Sensor  0.20 (1)  0.03 (3)  0.00 (3)  0.01 (4)  0.06 (3)  0.06 (1)  0.01 (3)   Species  0.05 (4)  0.02 (3)  0.00 (4)  0.01 (3)  0.00 (4)  0.00 (4)  0.00 (4)    Multi-variate  Univariate  V  HO  HL  DBA  BA  N  PE %   Slope  0.10 (4)  0.06 (3)  0.02 (3)  0.02 (2)  0.03 (2)  0.06 (3)  0.07 (2)   Aspect  0.13 (3)  0.08 (2)  0.06 (2)  0.08 (1)  0.08 (1)  0.07 (2)  0.10 (1)   Sensor  0.28 (2)*  0.16 (1)*  0.02 (3)  0.02 (3)  0.02 (3)  0.19 (1)*  0.02 (3)   Species  0.65 (1)*  0.02 (4)  0.10 (1)*  0.01 (4)  0.01 (4)  0.00 (4)  0.00 (4)  |PE|%   Slope  0.11 (3)  0.01 (4)  0.12 (1)  0.08 (1)  0.10 (1)  0.02 (3)  0.11 (1)   Aspect  0.14 (2)  0.12 (1)  0.06 (2)  0.04 (2)  0.09 (2)  0.06 (1)  0.09 (2)   Sensor  0.20 (1)  0.03 (3)  0.00 (3)  0.01 (4)  0.06 (3)  0.06 (1)  0.01 (3)   Species  0.05 (4)  0.02 (3)  0.00 (4)  0.01 (3)  0.00 (4)  0.00 (4)  0.00 (4)  *Statistically significant (P < 0.05). Figure 6 View largeDownload slide Influence of terrain effects on PE% for different forest attributes using Modelset_C on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Figure 6 View largeDownload slide Influence of terrain effects on PE% for different forest attributes using Modelset_C on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Figure 7 View largeDownload slide Influence of terrain effects on |PE|% for different forest attributes using Modelset_C on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Figure 7 View largeDownload slide Influence of terrain effects on |PE|% for different forest attributes using Modelset_C on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Ranking effects on prediction errors The ranking of the effect sizes (η2) showed that slope and aspect were most frequently ranked as the most or second most influential factors (Figure 8). Figure 8 View largeDownload slide Count of univariate ranked effect sizes (η2) for the Modelset_C and Modelset_V used on the validation data. A rank of 1 refers to largest effect and a rank of 4 is the smallest effect. Figure 8 View largeDownload slide Count of univariate ranked effect sizes (η2) for the Modelset_C and Modelset_V used on the validation data. A rank of 1 refers to largest effect and a rank of 4 is the smallest effect. Discussion General remarks on terrain effects The current study focuses on the influence of terrain effects on prediction of forest attributes using the area-based method and ALS data. Until now, most research on terrain effects has focused on individual tree approaches (Vega et al., 2014; Khosravipour et al., 2015) or on a limited number of forest attributes (Breidenbach, et al., 2008). The terrain effects that were studied for a range of forest attributes herein were found to significantly influence the prediction errors. The volume (V) seemed to be most influenced, while Lorey’s mean height (HL) and dominant height (HO) were less influenced by terrain factors. Most area-based forest inventories rely on model-based approaches. Thus, the properties of the sample are important, as highlighted by the results of the current study. For example, a model fitted on the experimental clusters (Modelset_V) included slope as an explanatory variable, while for the forest inventory plots (Modelset_C), for which distribution on various terrain factors was not a sampling design consideration, only aspect was selected. Furthermore, the magnitudes of the effects clearly showed that the terrain properties affected both Modelset_V and Modelset_C. For both model sets, aspect and slope were more frequently ranked as the most or second most important effect, while sensor and species generally had lower ranks (Figure 8). However, even though the analyses showed that both slope and aspect influence both the modelling and the prediction errors, our results also show that the influence is relatively small in magnitude in area-based forest inventories. The terrain effect was only significant for the relative prediction error of two forest attributes in the Modelset_V. Influence of slope The multivariate analysis showed that PE% obtained with Modelset_V depended on slope. For V in particular, slope was the second largest multivariate effect after the effect of sensor. However, the terrain factors did not seem to affect |PE|%. On average, slope was the terrain factor with largest effect size, and it seemed to impact V more than other forest attributes. Breidenbach et al. (2008) found that slope had an effect on predictions of HL. In our study, the two height variables, HO and HL, were the two forest attributes least influenced by slope. In terms of the magnitude of the effects, the influence was 2–3 times larger for V than for HO and HL. Nevertheless, slope was ranked as the most and second most important effect for HO and HL, respectively. Næsset (2004a) found slope to be a significant explanatory variable for HO in mature forest on highly productive sites. However, he concluded that slope values of up to 35° did not have to be accounted for to estimate HO with reliable accuracies; even though it was pointed out that the effect could be larger in even steeper terrain because of the degrading quality of the terrain and canopy height models. Our study confirmed only a marginal effect of slope on the precision of common forest attributes derived with the area-based method, even if our data included forests growing on slopes up to 43° of inclination. When slope was added to the pool of potential explanatory variables of Modelset_V, it was selected for the models of V, HO, and stand basal area (BA) in the spruce stratum. In the pine stratum, however, slope was found to be non-significant. Thus, it seemed that spruce-dominated plots were more affected by slope than pine-dominated plots. However, these findings can hardly be generalized because the pine-dominated plots in the study had limited ranges of volume and height. Influence of aspect With regard to aspect, we found that the prediction errors were larger in the North class compared with the other aspect classes. The errors were smallest in the South class. Aspect was the most frequent top ranking variable with regard to effect size in Modelset_C and the second most frequent in Modelset_V (Figure 8). Breidenbach et al. (2008) did not find any influence of aspect on prediction of HL from ALS data. However, they found stem density and proportion of conifers to be influential on the prediction error. Crown allometry of trees depends on the angle of the sun. Depending on the distribution of the field reference plots in terms of slope aspect, prediction errors might not be uniformly distributed on slopes facing in different directions. A dataset dominated by north-facing plots, might yield smaller prediction errors for north-facing prediction units. In our case, where we found larger errors in the North class, there could be an effect of larger errors in the positioning. At the latitude of our study area, it is likely that positions are more accurately determined on south-facing slopes compared with north-facing slopes. Thus, the effect that we found might originate from better co-registration of field plots and ALS data towards the south. Our results indicated that aspect was more influential on the prediction errors for pine forests compared with those for spruce. Aspect was selected more frequently as an explanatory variable in the pine stratum compared with the spruce stratum. This might be due to the fact that pine is a more light-demanding species than spruce and that pine crowns are more prone to be asymmetrical towards south. A limitation in the current study is that the design of the experiment did not consider aspect, so the clusters in the validation data were not distributed with particular attention to aspect classes. However, we think this had only a minor influence on the results and hence decided to include aspect as a factor in the experiment since it added valuable information to understand the results. It can be argued that the negative impact of not having a perfectly balanced design was smaller than the added positive value of including aspect in the analysis. Other influencing factors From the interpretation of the graphical plots (Figures 4–7), an interaction between slope and aspect seems present for some forest attributes, e.g. HO and mean basal area diameter (DBA). However, here the number of observations did not allow for a detailed analysis of this potential influence. In future studies, this combined effect should be accounted for in the design because some of the graphical plots suggest that the relationship between slope and the prediction error depends on aspect. In the part of our analysis that most closely mimicked operational conditions, i.e. using Modelset_C on the validation data, effects of different sensors and species were found. The effects were in the order of 4–5 times larger than those related to slope and aspect (Table 6). However, both factors were frequently ranked below terrain properties based on effect sizes (η2) (Figure 8). The reason for this discrepancy between effect size and rank was mainly due to the fact that when the effects were statistically significant, the effects were also quite large in absolute terms, making the effects of sensor and species more influential than the terrain effects. The influence of sensor type and settings is also known to affect forest attributes predictions (Næsset, 2009; Ørka, et al., 2010) and it was clear from our results that these effects were larger than the terrain effects. Assuming that the point clouds from the two sensors were equally affected by slope and aspect, i.e. no confounding effects, the interpretation of the results in this study is straightforward. The potential risk, however, is that the differences between the two sensors in the interaction with terrain make the potential terrain effects less pronounced. Limitations of the study There was a time difference between the ALS data acquisition and the field inventories of minimum one and maximum three growing seasons. As long as the growth is similar across strata, this will not influence the result. However, since growth depends on site productivity, errors due to non-uniform increase in volume between plots might be present. The validation data were collected between two growing seasons. The calibration data, however, were collected during a growing season, which might influence Modelset_C. Nevertheless, having field data that do not entirely match the ALS data with respect to time is a common challenge in operational inventories since the growing season also is the best time for field data collection. All in all, we do not consider these temporal mismatches to affect the major trends that were found. The terrain effects were evaluated on the validation clusters by aggregating the predicted plot values. The analysis of variance was carried out on aggregated data so that the assumptions of independent observations were fulfilled. Still, Modelset_V was built on clustered sample plots, which means that the observations in Modelset_V were not spatially independent. However, since the clusters were equally designed, we assume that the influence of this was minor. Conclusion A major finding of this study is that slope and aspect affected the accuracy of forest attribute predictions using ALS data following the area-based approach. However, the effects were quite small and according to the present results, neglecting them in operational inventories can be justified. The effects of slope and aspect were largest on volume (V), stand basal area (BA) and number of stems (N). The influences on HO and HL were small. The effect of aspect was larger than that of slope in this particular study. Although the effects of terrain factors were found to be quite small in the current study, they are indeed present and methods to correct for these errors will likely improve the overall accuracy of the resulting stand-wise estimates in operational management inventories. Conflict of interest statement None declared. Funding This research has been supported by the Research Council of Norway as part of the project entitled ‘Sustainable Utilization of Forest Resources in Norway’ (grant #225329/E40). Acknowledgements We would like to thank Vestskog SA and Mjøsen skog SA for providing the forest inventory data (calibration data) and Gro Kamphaug, Mikkel Thilkjær Nielsen, Gunnar Kleve and Jan Ivar Rødland (Vestskog SA) for collecting the validation data. Dr. Fabian Ewald Fassnacht and two anonymous reviewers are acknowledged for constructive and helpful comments. References Axelsson, P. 1999 Processing of laser scanner data-algorithms and applications. ISPRS J. Photogramm. 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Google Scholar CrossRef Search ADS   Ørka, H.O., Gobakken, T. and Næsset, E. 2016 Predicting attributes of regeneration forests using airborne laser scanning. Can. J. Remote Sens.  42 ( 5), 541– 553. Google Scholar CrossRef Search ADS   © Institute of Chartered Foresters, 2018. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forestry: An International Journal Of Forest Research Oxford University Press

Effects of terrain slope and aspect on the error of ALS-based predictions of forest attributes

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Abstract

Abstract Wall-to-wall forest management inventories with the area-based method using airborne laser scanner (ALS) data are operational in many countries. With this method, empirical relationships are established between ALS metrics and ground reference observations of forest attributes, and wall-to-wall predictions can be made over large areas. However, the prediction errors may be influenced by terrain slope and aspect because the properties of the ALS point cloud are dependent on these factors. Two datasets covering wide ranges of terrain slope and aspect, collected in the western part of Norway, were analysed. The first dataset represented sample plots from an ordinary operational forest management inventory and the second dataset were collected as an experimental dataset where clusters of sample plots were distributed on slopes with different inclinations. Six forest attributes were predicted using non-linear regression and the prediction errors were analysed using univariate- and multivariate analysis of variance. The results showed that slope and aspect affected the prediction errors, but that the effects were small in magnitude. Thus, the current study concludes that terrain effects seem to be negligible in operational forest inventories. Introduction Area-based wall-to-wall forest management inventories using airborne laser scanner (ALS) data have been operational since 2002 in Norway (Næsset et al., 2004). Approximately 300 000 ha of forest is inventoried annually in Norway, and in 2016 close to 100 per cent of the area was inventoried by ALS-based methods (Pers. comm., Norwegian Agriculture Agency). In other Nordic countries, the proportion of ALS-based inventories is at about the same level. In Finland for example, ALS-based forest management inventories providing species-specific timber volume estimates are applied to almost 3 million ha of forest land annually (Maltamo and Packalen, 2014). The main advantage of the ALS-based inventories over the purely field-based sample plot inventories is that objective measurements of highly correlated metrics (the ALS data) are available over the entire area of interest (AOI). To utilize these measurements effectively for estimating timber volume (or other attributes of interest), empirical relationships have to be established between the ALS measurements and ground reference observations of timber volume on a number of field plots of a certain size, say 200–500 m2. In their raw form, the ALS measurements collected over the AOI constitute a continuous cloud of xyz-referenced echoes (points) from the laser pulses emitted from an airborne sensor. The z-values are relative to the Earth’s ellipsoid. Thus, the z-values have to first be converted to heights above the terrain before providing relevant information about forests. This is made possible by processing the ALS data by algorithms that aim to identify and classify those echoes that were reflected from the ground (Sithole and Vosselman, 2004). A digital terrain model (DTM) is then constructed from these ground echoes, and the height of all other echoes can be calculated relative to the DTM. The height distribution of the ALS echoes (heights above the terrain, Δz) for each field plot is represented by area-based, continuous metrics (e.g. height values at certain percentiles of the echo height distribution) and these metrics are used to model the ALS-to-timber volume relationship. The field plots are usually distributed systematically over the AOI so that they cover the full timber volume range to avoid extrapolation in the subsequent model prediction phase. Timber volume estimates for individual stands within the AOI are obtained by aggregating grid cell predictions. It is important that the prediction models are valid in the area of application in the sense that there should be no underlying property affecting the relationships that are not directly accounted for in the models or indirectly by means of stratification according to relevant forest attributes. Otherwise, the stand-wise estimators might be biased. Tree species, age class and site productivity are common stratification criteria for ALS timber volume models (Næsset, 2002, 2004a, 2007). However, terrain slope and aspect could also potentially be factors that affect the relationship between ALS metrics and forest attributes (Hodgson et al., 2003; Reutebuch et al., 2003; Næsset, 2004c; Hollaus et al., 2006; Su and Bork, 2006; Breidenbach et al., 2008). In operational implementation of the area-based approach, neither terrain slope nor aspect is usually accounted for in the empirical models or by stratification. There are several reasons why terrain slope could influence the relationship between ALS point clouds and observed timber volume. The properties of the ALS point cloud are primarily affected by the three-dimensional distribution of the tree crown biomass over an area. Trees are opportunistic and allocate their crowns towards gaps and open space to minimize the competition for light (e.g. Young and Hubbell, 1991; Purves et al., 2007), and thus to maximize photosynthesis (Berezovskaya et al., 1997). Light conditions are more favourable in the downslope direction compared with the upslope direction because downslope neighbouring trees shade a subject tree less than upslope neighbours do. It is, therefore, likely that trees will tend to have asymmetrical crowns relative to the stem position with more biomass in the downslope direction since the level of competition affects crown symmetry (e.g. Young and Hubbell, 1991). On flat terrain, asymmetrical crowns would probably not yield point clouds with different properties compared with symmetrical crowns. On a slope, however, trees with asymmetrical crowns and more biomass allocated in the downslope direction, will cause the mean height of echoes reflected from a particular tree to be shifted upwards compared with flat terrain since echo heights are relative to the ground elevation vertically below, and not relative to the elevation at the base of the stem (Vega et al., 2014). Breidenbach et al. (2008) documented this effect. Their data showed that the median of ALS echo height distributions from plots on steeper terrain were higher compared with those from plots situated on flat terrain. This effect will be even more pronounced if the trees also are leaning in the downslope direction (Gatziolis et al., 2010). Studies have also shown that terrain slope affects the quality of the DTM (Hodgson et al., 2003; Hollaus et al., 2006; Su and Bork, 2006). This could be a result of the slope itself, but could also be a consequence of differences in terrain surface between sloped and flat terrain, with for example higher frequency of boulders on slopes. The DTM quality directly affects the height distribution of the vegetation echoes since their heights are calculated relative to the DTM. Thus, if the quality of the DTM depends on slope, the ALS point clouds might have different properties on slopes compared with those on the flat terrain. In addition to terrain slope, the terrain aspect is also likely to affect the biomass allocation of a tree. Favourable light conditions for trees are directly dependent on the angle of the sun relative to the Earth’s surface. Trees growing in the boreal and temperate zones of the northern hemisphere will therefore generally tend to allocate more of their branch biomass towards the south where the sun angle is the greatest. For example, Rouvinen and Kuuluvainen (1997) examined the effect of local competition on crown architecture in a study site in Finland and found that Scots pine (Pinus sylvestris) trees were asymmetrical towards south and southwest. Thus, the point clouds from ALS are likely to be affected accordingly and might hence have different properties depending on aspect. In addition to these direct effects of slope and aspect that might alter point cloud metrics, slope and aspect might also have an effect on the accuracy of the co-registration of ALS and field data. Accurate geographical co-registration of ALS data and the field plots used for model calibration is essential for accurate predictions (Gobakken and Næsset, 2009). The positions of the field plots are typically obtained using global navigation satellite systems (GNSS) and the accuracy depends on many factors. Trees may cause multipath effects of the GNSS signals or they may even temporarily block the signals from reaching the antenna e.g. Tomaštík et al. (2016). Terrain features can have similar effects. With steeper slopes, fewer satellites are in view for the GNSS receiver on the ground because of the elevated upslope horizon. Furthermore, in Norway the Global Positioning System (GPS) satellites are all orbiting south of zenith, which means that fewer satellites will be available in north-facing slopes compared with south-facing slopes. However, south of 64.8°N the Russian Global Navigation Satellite System (GLONASS) satellites are in zenith view, so utilizing signals from both systems mitigates to some extent the effect of GPS satellites orbiting south of 55°N. Both slope and aspect can thus affect the positioning error of the field plots, which in turn affects the quality of the ALS-to-timber volume relationship. The objective of this study was hence to analyse the accumulated potential effect of terrain slope and aspect on the accuracy of forest attribute predictions obtained from an operational area-based forest inventory approach using ALS data. The influence of terrain slope and aspect were evaluated with respect to six important forest attributes, namely timber volume, dominant height, Lorey’s mean height, mean basal area diameter, stand basal area and number of stems. Material and methods The study took advantage of two separate datasets from the western part of Norway, collected in an area with great variation in terrain slope. The two datasets were used to create two model sets. The first model set (Modelset_C) was fitted to a dataset that comprised sample plots from a standard operational inventory, while the second model set (Modelset_V) was fitted to data from sample plots collected specifically for the study as validation data. The two model sets were both applied to the validation data and the influence of terrain slope and aspect were analysed. Figure 1 summarizes the work-flow of the study. Figure 1 View largeDownload slide Overview of the study using two different datasets (calibration and validation data) which are used to create two model sets (Modelset_C and Modelset_V). The two model sets are used to make predictions on the validation data and the prediction errors are further analysed with respect to terrain effects. Figure 1 View largeDownload slide Overview of the study using two different datasets (calibration and validation data) which are used to create two model sets (Modelset_C and Modelset_V). The two model sets are used to make predictions on the validation data and the prediction errors are further analysed with respect to terrain effects. In the validation dataset, an equal number of plots were measured in four 10.25° wide slope classes ranging between 2° and 43° of inclination. In the calibration dataset, the inclination ranged between 3° and 38° (Figure 2). Figure 2 View largeDownload slide Sample plots by dominant species distributed on slope and aspect for the calibration data and validation data. Figure 2 View largeDownload slide Sample plots by dominant species distributed on slope and aspect for the calibration data and validation data. Study area The study was conducted within three municipalities in western Norway, approximately 40 km south of the city of Bergen. The municipalities were Fusa, Tysnes and Kvinnherad (Figure 3). The forests in the area are naturally dominated by Scots pine (Pinus sylvestris) and deciduous species, mainly birch (Betula pubescens). However, during the 20th century, planting of non-native conifers, mainly Norway spruce (Picea abies) and Sitka spruce (Picea sitchensis) was common. Our study area comprised ~260 km2 of productive forests with volume proportions of ~ 66 per cent pine, 20 per cent deciduous and 13 per cent spruce. Figure 3 View largeDownload slide Study area in western Norway. Figure 3 View largeDownload slide Study area in western Norway. Field data collection Two separate field surveys were carried out within the study area. First, a dataset (calibration data) used to calibrate the relationship between field observations of forest attributes and ALS metrics was collected as part of an ordinary forest management inventory in the three municipalities. The calibration data comprised field reference values of 114 circular plots of 250 m2 in mature forests. The survey was conducted from 23 April to 10 August in 2012. The area was divided into two strata according to dominant tree species. Stratum A comprised stands dominated by either Norway spruce or Sitka spruce. Stratum B comprised stands dominated by Scots pine. There were 29 sample plots in Stratum A and 85 sample plots in stratum B. To enable an independent test of the accuracy of models calibrated with the calibration data, a second dataset (validation data) were collected within the same area during autumn of 2013. This dataset comprised 192 plots of 250 m2 laid out according to an experimental design with four uniform slope classes from 2° to 43° of inclination (mean 22°), two ALS sensor settings (Sensor 1 and Sensor 2) and two dominating tree species (Norway spruce and Scots pine). The plots where laid out in clusters of three (i.e. 64 clusters) with 20 m inter-distance between plot centres, and the clusters were established inside homogenous stands. Thirty-one clusters were allocated to stratum A and 33 to stratum B. Plot positioning The calibration data plots were positioned using real-time kinematic (RTK) GNSS with correction data with decimetre precision acquired from the Norwegian Mapping Authority (NMA) GNSS network. Base stations were always within a distance of ~25 km. To secure proper initialization, the GNSS receiver was running for minimum 10 min before recording started. An estimated horizontal root mean square error <0.5 m, a position dilution of precision <3.0 and a minimum of eight satellites with enabled correction data, were required before positioning started. In cases where these conditions could not be met, a self-operated base station was used rather than relying on the NMA service. Each plot was positioned twice using real-time correction and the positions were averaged to obtain the final position. In cases where the difference between the two positions was larger than 40 cm, a third position was recorded and the two positions with the smallest horizontal error estimate were averaged. The validation plots were positioned using GNSS with post-processing correction. Both the base station and the rover unit recorded GPS and GLONASS observation data. Base station observation data for post-processing were obtained from the three closest reference stations of the NMA GNSS network. The standard deviations reported from the post-processing at the respective plot centres indicated that some positions were inaccurately determined, as 48 positions had standard deviations >1 m. We, therefore, ranked plots according to the standard deviation value and were able to re-visit 35 plots for new measurements within the available resources. After this second positioning effort in the field, the average standard deviation was 45.5 cm. Only 13 of the 192 sample plots had standard deviations >1 m. Tree measurements and volume calculation – calibration data All trees with diamter at breast height (dbh) ≥4 cm were callipered (calliper trees) and tree species were registered. In addition, heights of an average of 10 trees (height sample trees) per plot were measured. These trees were sampled using a relascope, where every n’th relascope tree was selected (n = number of relascope trees on the plot/desired number of sample trees). An initial relascope count was carried out to calculate the ‘n’ for each field plot. Heights were measured using a Vertex hypsometer. Volume calculation was carried out using a ratio estimator to adjust the so-called base volume of each tree. Then single-tree volumes were summed and scaled to per hectare values. The details of this procedure are explained in the following. First, the base volume of each tree (both calliper trees and height sample trees) was calculated using the observed diameter and a height predicted using a base height model (Fitje and Vestjordet, 1977). Then, the ‘true’ volumes of the height sample trees were calculated using the observed diameters and observed heights. For each height sample tree, the ratio between the true volume and the base volume could then be calculated. Furthermore, plot- and species-wise mean ratios (mean-of-ratios) were calculated, and these mean ratios were then used to adjust all base volumes to ‘true’ volumes. However, if there were fewer than three height sample trees of a certain species on a plot, common stratum- and species-wise mean ratios were applied. The volume models applied were those reported in Vestjordet (1967) for Norway spruce, Brantseg (1967) for Scots pine, Braastad (1966) for deciduous species and Bauger (1995) for Sitka spruce. We also calculated dominant height (HO), Lorey’s mean height (HL), mean basal area diameter (DBA), stand basal area (BA) and number of stems (N). To calculate HO and HL, a single-tree height for each tree was estimated by setting height as unknown in the volume model with the estimated volume and observed diameter as fixed, and solving for the matching height numerically. Dominant height is defined as the mean height of the 100 largest trees per hectare with respect to dbh. In the current study where the plot size was 250 m2, we averaged the heights of the two largest trees per plot to obtain HO. Tree measurements and volume calculation – validation data As for the calibration data, the minimum dbh for calliper trees was 4 cm. Tree species was recorded in addition to diameter. The height sample trees, however, were selected as the n’th tree (n = number of trees on the plot/desired number of sample trees) regardless of size, as opposed to the calibration data for which the sampling was proportional to stem basal area. Thus, an initial stem count was carried out for each plot to determine the ‘n’. Three trees per plot (nine per cluster) were selected for the height measurement. Volume calculation was carried out in the same way as for the calibration data, with the exception that the calculation of the ratios to correct the base volumes of the calliper trees were calculated by cluster and species and using a ratio-of-means estimator as opposed to mean-of-ratios since the sample trees had equal inclusion probability. Common ratios calculated by tree species irrespective of cluster were applied when there were less than three sample trees of a certain species in a cluster. As for the calibration data, HO, HL, DBA, BA and N were also calculated (Table 1). Table 1 Summary of field data. Attribute  Mean  Standard deviation  Minimum  Maximum  Calibration plots (n = 114)   V (total) (m3 ha−1)  252.4  178.7  18.9  772.5   V (Norway spruce) (m3 ha−1)  96.6  194.6  0.0  769.0   V (Scots pine) (m3 ha−1)  119.4  103.0  0.0  488.4   V (deciduous) (m3 ha−1)  22.8  41.0  0.0  293.5   V (Sitka spruce) (m3 ha−1)  13.7  92.3  0.0  706.0   HO (m)  17.8  5.1  7.3  31.5   HL (m)  15.4  4.5  6.3  27.3   DBA (cm)  17.2  4.3  6.1  27.6   BA (m2 ha−1)  30.8  15.3  4.8  73.3   N (ha−1)  1447.4  802.6  280.0  4240.0  Validation plots (n = 192)   V (total) (m3 ha−1)  377.2  278.2  14.9  1318.6   V (Norway spruce) (m3 ha−1)  205.5  311.9  0.0  1305.2   V (Scots pine) (m3 ha−1)  80.9  94.2  0.0  400.5   V (deciduous) (m3 ha−1)  14.2  25.5  0.0  129.7   V (Sitka spruce) (m3 ha−1)  76.6  214.2  0.0  1143.9   HO (m)  20.2  5.9  7.9  37.9   HL (m)  17.6  5.0  6.2  35.5   DBA (cm)  22.0  5.5  6.7  40.7   BA (m2 ha−1)  40.2  20.6  3.9  104.2   N (ha−1)  1124.0  607.4  280.0  3600.0  Validation clusters (n = 64)   V (total) (m3 ha−1)  377.2  266.8  81.7  1150.8   V (Norway spruce) (m3 ha−1)  205.5  302.5  0.0  1150.8   V (Scots pine) (m3 ha−1)  80.9  88.1  0.0  354.4   V (deciduous) (m3 ha−1)  14.2  20.9  0.0  89.4   V (Sitka spruce) (m3 ha−1)  76.6  204.5  0.0  830.3   HO (m)  20.2  5.8  11.7  36.8   HL (m)  17.6  4.9  10.3  32.8   DBA (cm)  22.0  4.9  12.3  35.3   BA (m2 ha−1)  40.2  19.3  12.9  88.9   N (ha−1)  1124.0  566.2  373.3  3453.3  Attribute  Mean  Standard deviation  Minimum  Maximum  Calibration plots (n = 114)   V (total) (m3 ha−1)  252.4  178.7  18.9  772.5   V (Norway spruce) (m3 ha−1)  96.6  194.6  0.0  769.0   V (Scots pine) (m3 ha−1)  119.4  103.0  0.0  488.4   V (deciduous) (m3 ha−1)  22.8  41.0  0.0  293.5   V (Sitka spruce) (m3 ha−1)  13.7  92.3  0.0  706.0   HO (m)  17.8  5.1  7.3  31.5   HL (m)  15.4  4.5  6.3  27.3   DBA (cm)  17.2  4.3  6.1  27.6   BA (m2 ha−1)  30.8  15.3  4.8  73.3   N (ha−1)  1447.4  802.6  280.0  4240.0  Validation plots (n = 192)   V (total) (m3 ha−1)  377.2  278.2  14.9  1318.6   V (Norway spruce) (m3 ha−1)  205.5  311.9  0.0  1305.2   V (Scots pine) (m3 ha−1)  80.9  94.2  0.0  400.5   V (deciduous) (m3 ha−1)  14.2  25.5  0.0  129.7   V (Sitka spruce) (m3 ha−1)  76.6  214.2  0.0  1143.9   HO (m)  20.2  5.9  7.9  37.9   HL (m)  17.6  5.0  6.2  35.5   DBA (cm)  22.0  5.5  6.7  40.7   BA (m2 ha−1)  40.2  20.6  3.9  104.2   N (ha−1)  1124.0  607.4  280.0  3600.0  Validation clusters (n = 64)   V (total) (m3 ha−1)  377.2  266.8  81.7  1150.8   V (Norway spruce) (m3 ha−1)  205.5  302.5  0.0  1150.8   V (Scots pine) (m3 ha−1)  80.9  88.1  0.0  354.4   V (deciduous) (m3 ha−1)  14.2  20.9  0.0  89.4   V (Sitka spruce) (m3 ha−1)  76.6  204.5  0.0  830.3   HO (m)  20.2  5.8  11.7  36.8   HL (m)  17.6  4.9  10.3  32.8   DBA (cm)  22.0  4.9  12.3  35.3   BA (m2 ha−1)  40.2  19.3  12.9  88.9   N (ha−1)  1124.0  566.2  373.3  3453.3  ALS data ALS data were acquired using Optech ALTM Gemini instruments mounted on a PA31 Piper Navajo fixed-wing aircraft. The data acquisition was carried out from 5 June to 7 August 2010 with two slightly different setups because different resolutions of the DTM were requested by the NMA for different areas. The pulse densities over the plots comprised by the calibration and validation data were quite similar with 2.1 and 1.8 pulses m−2, respectively. The specifications of the two ALS acquisitions, hereafter referred to as Sensor 1 and 2, are given in Table 2. The initial processing of the ALS data was carried out by the contractor (Blom Geomatics, Norway) according to standard procedures. Echo heights were normalized using a triangular irregular network (TIN) created from ground echoes identified using the progressive TIN densification algorithm (Axelsson, 1999, 2000). Table 2 Acquisition settings for the two ALS sensors. Flight plans  Sensor 1  Sensor 2  Flight altitude (m above ground level)  1300  1600  Pulse repetition frequency (kHz)  100  70  Scan frequency (Hz)  58  41  Half scan angle (°)  12  19  Flight speed (ms−2)  80  80  Flight plans  Sensor 1  Sensor 2  Flight altitude (m above ground level)  1300  1600  Pulse repetition frequency (kHz)  100  70  Scan frequency (Hz)  58  41  Half scan angle (°)  12  19  Flight speed (ms−2)  80  80  ALS metrics for each field plot were calculated using the procedures described by Næsset (2004b). Thus, from the echo height distribution the 10th, 20th,…,90th and 100th height percentiles (denoted H10, H20,…, H90, H100), average height (Hmean) and the coefficient of variation (CV) were computed from first echoes (first of many and single echoes) and last of many echoes above a 2 m threshold. This standard threshold was used to avoid effects of shrubs and low vegetation and erroneously classified vegetation echoes, on the ALS metrics. Furthermore, density metrics for each plot were computed by first dividing the height range between the 2 m threshold and the 95th height percentile into 10 vertical bins of equal height. Then the number of echoes above each height bin were divided by the total number of echoes, and denoted D0, D1,…, D9. The numerator when calculating D0 was the number of echoes above the 2 m threshold, and for D1, D2,…, D9 it was the number of echoes above the 1st, 2nd,…, 9th height bin. Altogether, 44 different ALS metrics were used in the modelling of forest attributes. Modelling forest attributes from ALS To model the relationship between the forest attributes and the ALS metrics, we fitted models using non-linear regression with both dependent and independent variables at original scale. The models were of the form:   y=β0×x1β1×x2β2×⋯×x44β44×ε (1)where y is the response variable, x1, x2,…, x44 are the potential explanatory variables and β0, β1,…, β44 are parameters to be estimated and ε is the model error. Variable selection was carried out with a linearized form of the model using a best subset strategy according to the Bayesian information criterion. In the variable selection, the models were also penalized for collinearity using the variance inflation factor (VIF). Thus, if a model included variables with VIF-values >5, a model with fewer variables was iteratively selected (Ørka, et al., 2016). Separate models were fitted for V, HO, HL, DBA, BA and N. Furthermore, the accuracy of area-based forest inventories usually improves with relevant stratification (e.g. Næsset, 2014). Usually, stratification is based on species, site productivity and age class. We post-stratified the data (both calibration data and validation data) into spruce- and pine-dominated plots according to the field-measured species-specific stem volumes and fitted separate models for the two strata. Moreover, since different sensors are known to yield different relationships between ALS data and forest attributes (Næsset, 2009; Ørka et al., 2010), it was considered to include sensor as a stratification variable. However, in combination with species, this resulted in too few observations for some of the strata, so this option was rejected. Two sets of models were developed; one set (Modelset_C) based on the calibration data and an additional set (Modelset_V) based on the validation data. Both sets of models were applied to the validation data so that two sets of predictions were obtained. Because the calibration data did not cover the ranges of the validation data in terms of slope and aspect, Modelset_C reflects a situation of using models based on sample plots selected according to a sampling design that disregarded terrain properties. This is the current operational practice when using ALS for forest inventory in steep terrain. Predictions using models calibrated on Modelset_V reflect a situation with a balanced dataset regarding slope. Hence, it was expected that potential effects of slope would be less pronounced for these models since no extrapolation was carried out. It was also expected that the errors would be on a lower level because Modelset_V was tested on the same data as it was fitted. Validation plot predictions of V, HO, HL, DBA, BA and N were averaged by cluster to mimic a small stand. The accuracy of the models was assessed on cluster level by means of squared Pearson’s correlation coefficient (r2) between observed and predicted cluster level values. Mean prediction errors (MPE), root mean square prediction errors (RMSPE) and RMSPE relative to the observed value (RMSPE%) for each of the six response variables were calculated for Modelset_V and Modelset_C, both applied to the validation data. The corresponding standard deviations were also calculated, both in the original measurement units (SDPE) and relative to the observed value (SDPE%). The differences between the observed and predicted cluster level values were further analysed to assess the influence of terrain factors (see below). Experiment and analysis of terrain factors The analyses of terrain factors were divided into three different parts where we assessed the effects of slope and aspect (1) directly on the ALS metrics, (2) on the prediction errors (PE) and absolute prediction errors (|PE|) from applying Modelset_V on the validation data and (3) on PE and |PE| from applying Modelset_C on the validation data. In the analyses of effects on prediction errors (2, 3), errors relative to the observed value (PE%) of each respective forest attribute were analysed rather than PE, to control the effects related to the increasing potential for error as the size of the respective forest attribute increases. Furthermore, the |PE|-value of each forest attribute was also analysed relative to the observed value (|PE|%). In addition to slope and aspect, we assessed the effects of species and sensors because these factors previously have been shown to influence both ALS metrics (Ørka et al., 2009, 2010) and estimates of forest attributes using the area-based approach (Næsset, 2007, 2009). Prior to the analyses, a slope value for each field plot was derived from a 10 m × 10 m raster interpolated from the ALS-derived terrain model. The spatial resolution of the terrain model was found sufficient to locate the sample plots within the correct slope range in the field. Then, the plots were grouped into four uniform classes according to their inclination. Values of 2.00° (minimum), 12.25°, 22.50°, 32.75° and 43.00° (maximum) discriminated the groups. Furthermore, the plots were also grouped according to aspect in four classes; North (315°–45°), East (45°–135°), South (135°–225°) and West (225°–315°). These classes were used as factors in all analyses of the effects of slope and aspect on PE% and |PE|% of the six forest attributes. Thus, there were two terrain factors (slope and aspect) and two other factors (species and sensor). In all analyses mentioned above (1–3), both univariate- and multivariate analysis of variance tests were applied. These analyses were performed on the validation data only. With the multivariate tests, PE% and |PE|% for all six forest attributes were used as responses and analysed simultaneously. With the univariate tests, PE% and |PE|% for the different forest attributes were analysed one at a time to assess if they were differently affected. The analyses were conducted using functions for multivariate analysis of variance (MANOVA) and analysis of variance (ANOVA) in the R-package car (Fox and Weisberg, 2011). For MANOVA, the Type II Pillai-Bartlett trace was used as the test statistic, computed as recommended by Hand and Taylor (1987). In order to fulfil the required assumptions of multivariate normality, data were transformed if needed. For PE%, the differences in the log-transformed scale were analysed, while the |PE|% and the ALS metrics were kept in original scale. To test the assumption of multivariate normality, we used the Royston’s Multivariate Normality Test. In addition, to test if the factors significantly affected the PE% and |PE|% we also computed a measure of the magnitude of the effect similar to the variance explained (R2) in regression (Kline, 2004). Such measures are often referred to as effect sizes and are important to explain the impact of a phenomenon (Sullivan and Feinn, 2012). We computed and reported the effect sizes in terms of partial η2 for the MANOVA and ANOVA, which are similar to R2 and we refer to this as effect size (η2) in the text (Vacha-Haase and Thompson, 2004). Furthermore, for each analysis, we ranked the η2 of slope classes, aspect classes, sensors and species from most important to least important. As an additional analysis of the effects of slope and aspect, we fitted models where slope values and aspect classes were allowed to be selected in the variable selection phase. The models were tested if they provided different predictions than the models not including terrain variables using the t-test implemented in the R-package stats. Results Effects on ALS metrics Species was the factor that had the largest effect on the ALS metrics in the multivariate analysis in terms of effect magnitude. A subsequent univariate analysis confirmed that all metrics were influenced by species (P < 0.05; results not shown in table). Moreover, neither effects of aspect, slope, nor sensor were significant in the multivariate analysis (P > 0.05). However, the univariate analysis showed that aspect affected the upper and lower percentiles of the height distribution. Conversely, the ALS density metrics were not affected. However, the univariate analysis indicated that most density metrics from the first echoes were influenced by sensor. The differences in density metrics caused by sensor were found to be significant in the multivariate analysis when evaluating the echo categories separately (first echoes: P = 0.01; last echoes: P = 0.04). Additionally, it should be noted that in the univariate analysis, slope influenced H100 and H90 of both first and last echoes (P < 0.02). To sum up, species were the most influential factor for the ALS metrics. In addition, there seemed to be an effect of sensor on the first echo ALS metrics. There was an indication of a slight effect of aspect and slope on the upper canopy ALS metrics. Modelling forest attributes from ALS Selected models of Modelset_V had between one and three explanatory variables, including both density metrics and height metrics. The RMSPE% of the predicted forest attributes ranged from 6 per cent to 20 per cent for spruce and from 8 per cent to 34 per cent for pine (Table 3). Large Pearson’s correlation values and small RMSPE values indicated accurate predictions for HL, HO, and V (Table 3), while predicted values for BA, DBA and N were less accurate (Table 3). Allowing slope and aspect to be selected in the models resulted in inclusion of slope in the models for V, HO and BA for the spruce stratum, while aspect was selected for the N model in the pine stratum (results not shown in table). However, the predicted values of the models fitted using only ALS metrics did not differ significantly from those predicted using the models that included slope and aspect (t-test: P > 0.87). Thus, these models including slope and aspect were not used in the subsequent analyses. Table 3 Model performance and selected ALS metrics using Modelset_V for calibration. Values are reported separately for the spruce and pine stratum. Attribute  ALS metrics  r2  RMSPE  RMSPE%  MPE  SDPE  SDPE%  Spruce stratum   V (total) (m3 ha−1)  H30.L, D0.L, D6.L  0.73  117.70  19.89  −1.02  119.64  20.22   HO (m)  H40.L, D0.L, D6.L  0.88  1.46  5.82  0.01  1.49  5.92   HL (m)  H90.L, D0.L  0.89  1.36  6.34  0.00  1.38  6.44   DBA (cm)  Hmean.F, Hcv.F  0.76  2.27  9.82  −0.02  2.31  9.99   BA (m2 ha−1)  H20.L  0.42  10.39  18.39  −0.03  10.56  18.70   N (ha−1)  Hcv.F, H70.L  0.71  284.26  19.42  3.57  288.94  19.74  Pine stratum   V (total) (m3 ha−1)  Hcv.F, H70.L, D5.L  0.78  31.88  18.15  0.02  32.38  18.43   HO (m)  H50.L  0.63  1.28  8.21  0.00  1.30  8.34   HL (m)  H60.L  0.69  1.23  8.74  0.00  1.25  8.87   DBA (cm)  Hmax.F, D2.F, Hmean.L  0.61  3.02  14.35  0.01  3.06  14.57   BA (m2 ha−1)  D7.F, H30.L, D3.L  0.61  4.61  18.47  0.02  4.68  18.75   N (ha−1)  D0.F, H50.L  0.46  273.68  34.00  10.21  277.73  34.51  Attribute  ALS metrics  r2  RMSPE  RMSPE%  MPE  SDPE  SDPE%  Spruce stratum   V (total) (m3 ha−1)  H30.L, D0.L, D6.L  0.73  117.70  19.89  −1.02  119.64  20.22   HO (m)  H40.L, D0.L, D6.L  0.88  1.46  5.82  0.01  1.49  5.92   HL (m)  H90.L, D0.L  0.89  1.36  6.34  0.00  1.38  6.44   DBA (cm)  Hmean.F, Hcv.F  0.76  2.27  9.82  −0.02  2.31  9.99   BA (m2 ha−1)  H20.L  0.42  10.39  18.39  −0.03  10.56  18.70   N (ha−1)  Hcv.F, H70.L  0.71  284.26  19.42  3.57  288.94  19.74  Pine stratum   V (total) (m3 ha−1)  Hcv.F, H70.L, D5.L  0.78  31.88  18.15  0.02  32.38  18.43   HO (m)  H50.L  0.63  1.28  8.21  0.00  1.30  8.34   HL (m)  H60.L  0.69  1.23  8.74  0.00  1.25  8.87   DBA (cm)  Hmax.F, D2.F, Hmean.L  0.61  3.02  14.35  0.01  3.06  14.57   BA (m2 ha−1)  D7.F, H30.L, D3.L  0.61  4.61  18.47  0.02  4.68  18.75   N (ha−1)  D0.F, H50.L  0.46  273.68  34.00  10.21  277.73  34.51  Selected models of Modelset_C included between one and three variables. The RMSPE% ranged from 9 per cent to 69 per cent for the models in the spruce stratum and from 9 per cent to 62 per cent for the pine-stratum models (Table 4). There were systematic prediction errors for DBA (under-predicted) and N (over-predicted). For the other forest attributes, the results indicated only minor under-predictions. Adding slope and aspect to the pool of potential predictors resulted in the inclusion of aspect in the model (results not shown in table). Aspect was selected for N in the spruce stratum and for V, HL and BA in the pine stratum. However, predicted values did not differ between models including aspect and the models that did not include terrain variables (P > 0.77). Table 4 Model performance and selected ALS metrics using Modelset_V for calibration. Values are reported separately for the spruce and pine stratum. Attribute  ALS metrics  r2  RMSPE  RMSPE%  MPE  SDPE  SDPE%  Spruce stratum   V (total) (m3 ha−1)  H70.F, D6.L  0.70  129.60  21.90  36.70  126.35  21.35   HO (m)  H70.F  0.84  2.19  8.71  1.32  1.78  7.07   HL (m)  H70.F  0.87  1.93  9.01  1.24  1.50  7.01   DBA (cm)  D0.F, Hmax.L, D7.L  0.67  5.83  25.21  5.15  2.76  11.95   BA (m2 ha−1)  H20.F  0.40  11.74  20.79  4.98  10.81  19.14   N (ha−1)  Df.F, Hmax.L, H10.L  0.55  1013.73  69.26  −888.95  495.30  33.84  Pine stratum   V (total) (m3 ha−1)  D5.F, Hmean.L, D4.L  0.68  41.70  23.74  11.69  40.65  23.14   HO (m)  H80.F, Hcv.L, D0.L  0.61  1.44  9.24  0.03  1.46  9.38   HL (m)  H80.F, D1.F, D6.F  0.67  1.50  10.58  0.72  1.33  9.43   DBA (cm)  D0.F, H40.L  0.56  5.65  26.85  4.43  3.55  16.89   BA (m2 ha−1)  D5.F, H30.L, D4.L  0.60  4.94  19.78  1.20  4.86  19.48   N (ha−1)  D0.F, H60.L, D1.L  0.44  499.18  62.02  −394.97  309.98  38.51  Attribute  ALS metrics  r2  RMSPE  RMSPE%  MPE  SDPE  SDPE%  Spruce stratum   V (total) (m3 ha−1)  H70.F, D6.L  0.70  129.60  21.90  36.70  126.35  21.35   HO (m)  H70.F  0.84  2.19  8.71  1.32  1.78  7.07   HL (m)  H70.F  0.87  1.93  9.01  1.24  1.50  7.01   DBA (cm)  D0.F, Hmax.L, D7.L  0.67  5.83  25.21  5.15  2.76  11.95   BA (m2 ha−1)  H20.F  0.40  11.74  20.79  4.98  10.81  19.14   N (ha−1)  Df.F, Hmax.L, H10.L  0.55  1013.73  69.26  −888.95  495.30  33.84  Pine stratum   V (total) (m3 ha−1)  D5.F, Hmean.L, D4.L  0.68  41.70  23.74  11.69  40.65  23.14   HO (m)  H80.F, Hcv.L, D0.L  0.61  1.44  9.24  0.03  1.46  9.38   HL (m)  H80.F, D1.F, D6.F  0.67  1.50  10.58  0.72  1.33  9.43   DBA (cm)  D0.F, H40.L  0.56  5.65  26.85  4.43  3.55  16.89   BA (m2 ha−1)  D5.F, H30.L, D4.L  0.60  4.94  19.78  1.20  4.86  19.48   N (ha−1)  D0.F, H60.L, D1.L  0.44  499.18  62.02  −394.97  309.98  38.51  Effects on prediction errors from application of Modelset_V on validation data Sensor setting was the factor that had the largest effect on PE% in the multivariate analyses, and it was highly significant (P < 0.01). The univariate analysis showed that the sensor setting influenced mainly the PE% of V and BA (Table 5). Both were overpredicted with Sensor 1 and under-predicted with Sensor 2. The analysis also indicated that aspect was statistically significant (P < 0.05), influencing the PE%-values of V and N with large systematic errors in the North class, smaller in the East and West classes, and smallest in the South class (Figure 4). Slope was influential on the prediction errors of V according to the univariate analysis, where V was overpredicted for the two steepest slope classes. However, judged by the magnitude of the effects, the influence of both slope and aspect (0.16) was smaller than that of sensor (0.40). Species, however, did not significantly affect PE% for any of the forest attributes in neither the multivariate nor the univariate case (P > 0.89). Thus, sensor setting affected PE% the most, although effects of slope and aspect also seemed to be present, mainly influencing V. It should also be noted that there seemed to be an interaction between slope and aspect (Figure 4). Tree height errors in the North- and South class seemed to have a negative correlation with aspect, while for the East- and West class the correlation was positive. Table 5 Effect sizes (η2) of slope, aspect, sensor and species on PE% and |PE|% from application of Modelset_V on the validation data. Rank of effect based on effect sizes in parenthesis.   Multi-variate  Univariate  V  HO  HL  DBA  BA  N  PE%   Slope  0.16 (2)*  0.15 (3)*  0.05 (1)  0.05 (2)  0.03 (3)  0.06 (3)  0.06 (2)   Aspect  0.16 (3)*  0.15 (2)*  0.04 (2)  0.06 (1)  0.06 (1)  0.11 (2)  0.14 (1)*   Sensor  0.40 (1)*  0.18 (1)*  0.00 (4)  0.00 (4)  0.05 (2)  0.19 (1)*  0.06 (3)   Species  0.04 (4)  0.00 (4)  0.01 (3)  0.01 (3)  0.00 (4)  0.00 (4)  0.00 (4)  |PE|%   Slope  0.12 (2)  0.09 (2)  0.08 (1)  0.06 (3)  0.11 (1)  0.07 (1)  0.09 (1)   Aspect  0.11 (4)  0.10 (1)  0.06 (3)  0.02 (4)  0.01 (3)  0.03 (2)  0.05 (2)   Sensor  0.12 (3)  0.00 (4)  0.03 (4)  0.06 (2)  0.00 (4)  0.01 (3)  0.04 (4)   Species  0.22 (1)*  0.01 (3)  0.06 (2)  0.10 (1)*  0.10 (2)*  0.00 (4)  0.08 (2)*    Multi-variate  Univariate  V  HO  HL  DBA  BA  N  PE%   Slope  0.16 (2)*  0.15 (3)*  0.05 (1)  0.05 (2)  0.03 (3)  0.06 (3)  0.06 (2)   Aspect  0.16 (3)*  0.15 (2)*  0.04 (2)  0.06 (1)  0.06 (1)  0.11 (2)  0.14 (1)*   Sensor  0.40 (1)*  0.18 (1)*  0.00 (4)  0.00 (4)  0.05 (2)  0.19 (1)*  0.06 (3)   Species  0.04 (4)  0.00 (4)  0.01 (3)  0.01 (3)  0.00 (4)  0.00 (4)  0.00 (4)  |PE|%   Slope  0.12 (2)  0.09 (2)  0.08 (1)  0.06 (3)  0.11 (1)  0.07 (1)  0.09 (1)   Aspect  0.11 (4)  0.10 (1)  0.06 (3)  0.02 (4)  0.01 (3)  0.03 (2)  0.05 (2)   Sensor  0.12 (3)  0.00 (4)  0.03 (4)  0.06 (2)  0.00 (4)  0.01 (3)  0.04 (4)   Species  0.22 (1)*  0.01 (3)  0.06 (2)  0.10 (1)*  0.10 (2)*  0.00 (4)  0.08 (2)*  *Statistically significant (P < 0.05). Figure 4 View largeDownload slide Influence of terrain effects on PE% for different forest attributes using Modelset_V on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Figure 4 View largeDownload slide Influence of terrain effects on PE% for different forest attributes using Modelset_V on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. The | PE |%-values were influenced only by species (P < 0.01) according to the multivariate analysis, and the univariate analysis identified significant effects on HL, DBA and N. Generally, smaller |PE|%-values were observed for spruce than for pine. Thus, the effects of terrain factors seemed to be small on |PE|% for all the forest attributes, which is also evident from graphical plots of the errors against slope for the different aspect classes (Figure 5). Figure 5 View largeDownload slide Influence of slope and aspect on |PE|% for different forest attributes using Modelset_V on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Figure 5 View largeDownload slide Influence of slope and aspect on |PE|% for different forest attributes using Modelset_V on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Effects on prediction errors from application of Modelset_C on the validation data Sensor setting and species influenced PE% (Table 6). More specifically, the univariate tests indicated that sensor influenced the prediction errors of V and BA, while species influenced prediction errors of HO. The tests indicated over-predictions for Sensor 1 and under-predictions for Sensor 2. Furthermore, in the spruce stratum, the PE%-values for HO were smaller compared with the pine stratum. There were no effects of terrain factors on the PE%-values (Figure 6). The |PE|%-values were not significantly affected by any of the factors in either the multivariate or the univariate analysis (Table 6), and the trends (Figure 7) confirmed that the relationships were relatively weak. Table 6 Effect sizes (η2) of slope, aspect, sensor and species on PE% and | PE |% from application of Modelset_C on the validation data. Rank of effect based on effect sizes in parenthesis.   Multi-variate  Univariate  V  HO  HL  DBA  BA  N  PE %   Slope  0.10 (4)  0.06 (3)  0.02 (3)  0.02 (2)  0.03 (2)  0.06 (3)  0.07 (2)   Aspect  0.13 (3)  0.08 (2)  0.06 (2)  0.08 (1)  0.08 (1)  0.07 (2)  0.10 (1)   Sensor  0.28 (2)*  0.16 (1)*  0.02 (3)  0.02 (3)  0.02 (3)  0.19 (1)*  0.02 (3)   Species  0.65 (1)*  0.02 (4)  0.10 (1)*  0.01 (4)  0.01 (4)  0.00 (4)  0.00 (4)  |PE|%   Slope  0.11 (3)  0.01 (4)  0.12 (1)  0.08 (1)  0.10 (1)  0.02 (3)  0.11 (1)   Aspect  0.14 (2)  0.12 (1)  0.06 (2)  0.04 (2)  0.09 (2)  0.06 (1)  0.09 (2)   Sensor  0.20 (1)  0.03 (3)  0.00 (3)  0.01 (4)  0.06 (3)  0.06 (1)  0.01 (3)   Species  0.05 (4)  0.02 (3)  0.00 (4)  0.01 (3)  0.00 (4)  0.00 (4)  0.00 (4)    Multi-variate  Univariate  V  HO  HL  DBA  BA  N  PE %   Slope  0.10 (4)  0.06 (3)  0.02 (3)  0.02 (2)  0.03 (2)  0.06 (3)  0.07 (2)   Aspect  0.13 (3)  0.08 (2)  0.06 (2)  0.08 (1)  0.08 (1)  0.07 (2)  0.10 (1)   Sensor  0.28 (2)*  0.16 (1)*  0.02 (3)  0.02 (3)  0.02 (3)  0.19 (1)*  0.02 (3)   Species  0.65 (1)*  0.02 (4)  0.10 (1)*  0.01 (4)  0.01 (4)  0.00 (4)  0.00 (4)  |PE|%   Slope  0.11 (3)  0.01 (4)  0.12 (1)  0.08 (1)  0.10 (1)  0.02 (3)  0.11 (1)   Aspect  0.14 (2)  0.12 (1)  0.06 (2)  0.04 (2)  0.09 (2)  0.06 (1)  0.09 (2)   Sensor  0.20 (1)  0.03 (3)  0.00 (3)  0.01 (4)  0.06 (3)  0.06 (1)  0.01 (3)   Species  0.05 (4)  0.02 (3)  0.00 (4)  0.01 (3)  0.00 (4)  0.00 (4)  0.00 (4)  *Statistically significant (P < 0.05). Figure 6 View largeDownload slide Influence of terrain effects on PE% for different forest attributes using Modelset_C on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Figure 6 View largeDownload slide Influence of terrain effects on PE% for different forest attributes using Modelset_C on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Figure 7 View largeDownload slide Influence of terrain effects on |PE|% for different forest attributes using Modelset_C on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Figure 7 View largeDownload slide Influence of terrain effects on |PE|% for different forest attributes using Modelset_C on the validation data. The line represents a fitted linear regression line for the observations in each aspect class. Ranking effects on prediction errors The ranking of the effect sizes (η2) showed that slope and aspect were most frequently ranked as the most or second most influential factors (Figure 8). Figure 8 View largeDownload slide Count of univariate ranked effect sizes (η2) for the Modelset_C and Modelset_V used on the validation data. A rank of 1 refers to largest effect and a rank of 4 is the smallest effect. Figure 8 View largeDownload slide Count of univariate ranked effect sizes (η2) for the Modelset_C and Modelset_V used on the validation data. A rank of 1 refers to largest effect and a rank of 4 is the smallest effect. Discussion General remarks on terrain effects The current study focuses on the influence of terrain effects on prediction of forest attributes using the area-based method and ALS data. Until now, most research on terrain effects has focused on individual tree approaches (Vega et al., 2014; Khosravipour et al., 2015) or on a limited number of forest attributes (Breidenbach, et al., 2008). The terrain effects that were studied for a range of forest attributes herein were found to significantly influence the prediction errors. The volume (V) seemed to be most influenced, while Lorey’s mean height (HL) and dominant height (HO) were less influenced by terrain factors. Most area-based forest inventories rely on model-based approaches. Thus, the properties of the sample are important, as highlighted by the results of the current study. For example, a model fitted on the experimental clusters (Modelset_V) included slope as an explanatory variable, while for the forest inventory plots (Modelset_C), for which distribution on various terrain factors was not a sampling design consideration, only aspect was selected. Furthermore, the magnitudes of the effects clearly showed that the terrain properties affected both Modelset_V and Modelset_C. For both model sets, aspect and slope were more frequently ranked as the most or second most important effect, while sensor and species generally had lower ranks (Figure 8). However, even though the analyses showed that both slope and aspect influence both the modelling and the prediction errors, our results also show that the influence is relatively small in magnitude in area-based forest inventories. The terrain effect was only significant for the relative prediction error of two forest attributes in the Modelset_V. Influence of slope The multivariate analysis showed that PE% obtained with Modelset_V depended on slope. For V in particular, slope was the second largest multivariate effect after the effect of sensor. However, the terrain factors did not seem to affect |PE|%. On average, slope was the terrain factor with largest effect size, and it seemed to impact V more than other forest attributes. Breidenbach et al. (2008) found that slope had an effect on predictions of HL. In our study, the two height variables, HO and HL, were the two forest attributes least influenced by slope. In terms of the magnitude of the effects, the influence was 2–3 times larger for V than for HO and HL. Nevertheless, slope was ranked as the most and second most important effect for HO and HL, respectively. Næsset (2004a) found slope to be a significant explanatory variable for HO in mature forest on highly productive sites. However, he concluded that slope values of up to 35° did not have to be accounted for to estimate HO with reliable accuracies; even though it was pointed out that the effect could be larger in even steeper terrain because of the degrading quality of the terrain and canopy height models. Our study confirmed only a marginal effect of slope on the precision of common forest attributes derived with the area-based method, even if our data included forests growing on slopes up to 43° of inclination. When slope was added to the pool of potential explanatory variables of Modelset_V, it was selected for the models of V, HO, and stand basal area (BA) in the spruce stratum. In the pine stratum, however, slope was found to be non-significant. Thus, it seemed that spruce-dominated plots were more affected by slope than pine-dominated plots. However, these findings can hardly be generalized because the pine-dominated plots in the study had limited ranges of volume and height. Influence of aspect With regard to aspect, we found that the prediction errors were larger in the North class compared with the other aspect classes. The errors were smallest in the South class. Aspect was the most frequent top ranking variable with regard to effect size in Modelset_C and the second most frequent in Modelset_V (Figure 8). Breidenbach et al. (2008) did not find any influence of aspect on prediction of HL from ALS data. However, they found stem density and proportion of conifers to be influential on the prediction error. Crown allometry of trees depends on the angle of the sun. Depending on the distribution of the field reference plots in terms of slope aspect, prediction errors might not be uniformly distributed on slopes facing in different directions. A dataset dominated by north-facing plots, might yield smaller prediction errors for north-facing prediction units. In our case, where we found larger errors in the North class, there could be an effect of larger errors in the positioning. At the latitude of our study area, it is likely that positions are more accurately determined on south-facing slopes compared with north-facing slopes. Thus, the effect that we found might originate from better co-registration of field plots and ALS data towards the south. Our results indicated that aspect was more influential on the prediction errors for pine forests compared with those for spruce. Aspect was selected more frequently as an explanatory variable in the pine stratum compared with the spruce stratum. This might be due to the fact that pine is a more light-demanding species than spruce and that pine crowns are more prone to be asymmetrical towards south. A limitation in the current study is that the design of the experiment did not consider aspect, so the clusters in the validation data were not distributed with particular attention to aspect classes. However, we think this had only a minor influence on the results and hence decided to include aspect as a factor in the experiment since it added valuable information to understand the results. It can be argued that the negative impact of not having a perfectly balanced design was smaller than the added positive value of including aspect in the analysis. Other influencing factors From the interpretation of the graphical plots (Figures 4–7), an interaction between slope and aspect seems present for some forest attributes, e.g. HO and mean basal area diameter (DBA). However, here the number of observations did not allow for a detailed analysis of this potential influence. In future studies, this combined effect should be accounted for in the design because some of the graphical plots suggest that the relationship between slope and the prediction error depends on aspect. In the part of our analysis that most closely mimicked operational conditions, i.e. using Modelset_C on the validation data, effects of different sensors and species were found. The effects were in the order of 4–5 times larger than those related to slope and aspect (Table 6). However, both factors were frequently ranked below terrain properties based on effect sizes (η2) (Figure 8). The reason for this discrepancy between effect size and rank was mainly due to the fact that when the effects were statistically significant, the effects were also quite large in absolute terms, making the effects of sensor and species more influential than the terrain effects. The influence of sensor type and settings is also known to affect forest attributes predictions (Næsset, 2009; Ørka, et al., 2010) and it was clear from our results that these effects were larger than the terrain effects. Assuming that the point clouds from the two sensors were equally affected by slope and aspect, i.e. no confounding effects, the interpretation of the results in this study is straightforward. The potential risk, however, is that the differences between the two sensors in the interaction with terrain make the potential terrain effects less pronounced. Limitations of the study There was a time difference between the ALS data acquisition and the field inventories of minimum one and maximum three growing seasons. As long as the growth is similar across strata, this will not influence the result. However, since growth depends on site productivity, errors due to non-uniform increase in volume between plots might be present. The validation data were collected between two growing seasons. The calibration data, however, were collected during a growing season, which might influence Modelset_C. Nevertheless, having field data that do not entirely match the ALS data with respect to time is a common challenge in operational inventories since the growing season also is the best time for field data collection. All in all, we do not consider these temporal mismatches to affect the major trends that were found. The terrain effects were evaluated on the validation clusters by aggregating the predicted plot values. The analysis of variance was carried out on aggregated data so that the assumptions of independent observations were fulfilled. Still, Modelset_V was built on clustered sample plots, which means that the observations in Modelset_V were not spatially independent. However, since the clusters were equally designed, we assume that the influence of this was minor. Conclusion A major finding of this study is that slope and aspect affected the accuracy of forest attribute predictions using ALS data following the area-based approach. However, the effects were quite small and according to the present results, neglecting them in operational inventories can be justified. The effects of slope and aspect were largest on volume (V), stand basal area (BA) and number of stems (N). The influences on HO and HL were small. The effect of aspect was larger than that of slope in this particular study. 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Forestry: An International Journal Of Forest ResearchOxford University Press

Published: Apr 1, 2018

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