Introduction 

Tree height (H) survey is a fundamental measure in forest characterization; H is required to define a stand site index measuring the local fertility and give an estimate of standing trees volume. Especially tree stem volume has a key role in forest estimates being related to the amount of wooden commodity. Stem volume is ordinary calculated as ([22] - eqn. 1):

where DBH is the tree diameter at the breast height; f is the tree shape factor, i.e., the ratio between the real tree volume and the theoretical volume of a cylinder having the same height. According to eqn. 1 the error affecting tree height measure necessarily impacts the accuracy of the correspondent tree volume computation. Standard approach to measures tree height operates by hypsometer ([22], [26]), where angle and distance measures are coupled within simple trigonometric formulas. H is obtained by collimating the top and the basis of trees determining the correspondent angle and the horizontal distance separating observer and tree. This method suffers from different errors mainly related to the collimation process. Bragg ([6]) found that errors mainly depend on the wrong detection of tree tops and stem inclination. Another error is related to the operator’s hand motion during the collimation step that, in the most of cases, is operated with no fixed support. The uncertainty that this operational conditions can determine in angular measures is estimated to range between ± 0.5° and ± 2°, determining H errors between 1% to 10% ([1]). The introduction of RPAS (Remotely Piloted Aircraft System) have enriched the survey of vegetated surfaces ([5]). RPAS-based acquisitions can provide information about surfaces with a very high geometric resolution ([19], [15]). Remote survey of vegetation can be operated by PHODAR (PHOtogrammetric Detection and Ranging) or LiDAR (Light Detection and Ranging) techniques. Both of them have largely improved the possibility of accurately measuring morphometric and structural parameters of forest stand or individual trees ([25], [9], [17]), thus supporting forest inventories. Many studies and practical experiences demonstrated that tree counting and tree height measure can be achieved with high accuracy ([23], [24], [20], [10], [8]). In this context, these parameters are derived by tree crown segmentation from Canopy Height Models (CHMs - [11], [13], [27]), i.e., raster maps obtained by grid differencing between a Digital Surface Model (DSM) and Digital Terrain Model (DTM), possibly derived from point clouds. When trying to obtain tree measures from CHM, the Local Maxima approach, applied within the same segment (representing the entire tree crown), is often used to locate the top of the tree ([1], [18], [21]). When working with high geometric resolution CHMs, possibly obtained by PHODAR/LiDAR point clouds, the reference Ground Sampling Distance (GSD) sizes few centimeters. Such a value potentially allows to survey points representing single crown apexes that, according to the Local Maxima approach, can be labelled as the top when measuring tree height. Unfortunately, from a forestry point of view, apexes are not representatives of the actual tree height, since they do not represent the prevailing dendrometric height (PDH^CHM) but, conversely, the maximum height value (H^CHM_max - Fig. 1). Consequently, H^CHM_max could not be used to estimate tree volume or site indices, as a not negligible overestimation would occur. In this work, PDH is suggested to be newly defined as that height value corresponding to the most frequently one occurring within tree upper canopy.

Fig. 1 - A new definition of prevailing dendrometric height (PDH) is proposed, corresponding to the most frequent height value occurring within upper tree crown.

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  Materials and methods 

In this study, we propose a new definition of prevailing dendrometric height; consequently, a different approach, other than the Local Maxima one, has been considered to process CHM. A small and highly controllable CHM of 60 mixed broadleaf trees (Quercus robur L. 45%, Fraxinus excelsior L. 12%, Alnus glutinosa L. 7%, Ulmus campestris Mill. 8%, Robinia pseudoacacia L. 20%, Tilia spp. 8%) was processed. The study area is located in the “La Mandria” regional park (Piemonte, NW Italy). This study area was chosen for the presence of both ancient and young trees with different apexes length representing various ontological phases ([3]). A ground survey was conducted to obtain a reference dataset. For each of the 60 surveyed trees the correspondent crown ground projection was mapped by Field-map^© tools ([28]) and recorded as georeferenced vector layer P (Fig. 2). Tree height was measured by Vertex IV-360® ultrasound hypsometer (Haglof, Sweden) at 40 m distance having a nominal accuracy of ± 0.25° for angles and ± 0.2 m for distances. H^G_max was measured by collimating tree top (maximum visible height), while PDH^G was estimated with reference to the main development of the crown (i.e., pointing to the basis of the highest apexes). H^G_max and PDH^G values were, finally, recorded into the attributes table of P. The test CHM was generated by grid differencing between a DSM generated by regularization of a PHODAR-derived point cloud surveyed by RPAS. A DJI Phantom4 RPAS equipped with a 12.4 Megapixel RGB camera was used for data acquisition. Flight and sensor’s technical features are reported in Tab. 1. Obtained images (about 700) had a GSD of about 5 cm. Photogrammetric block bundle adjustment and point cloud generation were achieved by the software Photoscan® v. 1.2.4 (Agisoft LLC, St. Petersburg, Russia). Image block bundle adjustment was achieved using 9 ground control points (GCPs) surveyed in correspondence of target panels (markers) distributed over the area before the flight. GCPs survey was achieved by VRS-NRTK (Virtual Reference Station - Network Real Time Kinematic) GNSS mode using a Leica 1200^® receiver (3D positioning accuracy was ~ 3 cm). Leave-one-out procedure ([7]) was adopted to test bundle adjustment accuracy using the previous 9 GCPs without requiring additional survey and Mean Absolute Errors (MAE) were calculated. Point cloud was exported in .LAS format, filtered, classified as ground/not-ground, and regularized to generate the correspondent DSM (Digital Surface Model). Filtering, classifying and rasterizing processes were preformed using LAStools libraries ([12]). CHM was computed by grid differencing between the above-mentioned DSM and an available DTM (Digital Terrain Model) obtained from the Piemonte Region geoportal (ICE dataset - ⇒ http:/­/­www.­geoportale.­piemonte.­it/­geocatalogorp/­). DTM had a GSD = 5 m and a precision σ_z^DTM= 0.60 cm ([4]). DTM was oversampled by nearest neighbor method at 5 cm to make it consistent with the PHODAR derived DSM.

Fig. 2 - (a) Study area is located in “La Mandria” regional park (Piemonte - NW Italy); (b) RPAS-derived orthomosaic and surveyed tree crowns (reference frame is WGS84 UTM 32N); (c) Frequency distribution function of ground measured tree height (H^G_max ).

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  Results and discussions 

The following positioning errors (MAE) were obtained for GCPs after image block adjustment adopting leave-one-out procedure: 0.267 m (σ_x,y), 0.229 m (σ_z) and 0.352 m (σ_x,y,z). A high-density point cloud was generated (about 36 million points, 250 pts m^-2), filtered, classified and regularized to generate the correspondent DSM with a cell size of 0.1 m. After regularization DSM height accuracy was tested with reference to the GCPs to exclude a degradation of the native accuracy. Results proved that height accuracy of DSM was the about same (σ_z^DSM = 0.236 m) as the above mentioned one (σ_z = 0.229 m). CHM accuracy (σ_z^CHM) was finally estimated by the Variance Propagation Law (VPL - [2]) involving σ_z^DTM and σ_z^DSM; σ_z^CHM resulted to be equal to 0.64 m. Such accuracy is higher than that obtainable using hypsometer and adopted in ordinary forest inventory ([16]). An object-based approach aimed at mapping tree crowns from CHM was used, adopting the watershed segmentation algorithms (available in SAGA GIS v. 7.4 - ⇒ http:/­/­www.­saga-gis.­org/­). The following parameters were used: segmentation criterion was the local minima one; joining segment threshold (minimum difference between neighbored segments) was set to 0.8. For each segment, assumed as tree crown perimeter (hereafter called Detected Crown - DC), the correspondent CHM zonal statistics (average, standard deviation, minimum and maximum) were computed and the cumulative frequency distribution of H (H CFD) generated. H CFD was used as descriptor of the inter-crown variability and comparing tree CHM-based height with ground-based one. With reference to the above-mentioned H CFD (one for each of the segmented crowns) the percentile value (PV) correspondent to the local PDH^G was computed. Sixty different PVs were found depending on the assessed crown. PV mean value (μ_PV) was assumed as reference threshold, for broadleaves, to filter out apexes while measuring PDH^CHM from CHMs. The computed μ_PV value was 95%; consequently, PDH^CHM was found equal to the value within DC which corresponds to the 95 percentile of H CFD (Fig. 3). In Fig. 4the frequency distributions of H^CHM_max and PDH^CHM are compared, figuring out the effect on tree height measure given assuming PDH^CHM in place of H^CHM_max. The Kolmogorov-Smirnov test was run to test significance the similarity of the two distributions with a normal one. D-value was 0.075 (p = 0.871, Skewness: 0.046) and 0.069 (p = 0.957, Skewness: 0.020) for PDH^CHM and H^CHM_max, respectively, demonstrating that distributions did not significantly differ from a normal one. Since the two distributions were strictly correlated (r = 0.998, p < 0.001) a two-tailed paired t-test ([14]) was performed too, to determine if H^CHM_Max was significantly different from PDH^CHM. A t = -17.58 (p < 0.001) was found indicating a significant difference between mean values of the two compared distributions, i.e., tree height values computed as PDH^CHM are significantly different from those ordinarily computed in forestry (H^CHM_Max - [11], [1], [17]).

Fig. 3 - An example of oak crown in the study area. (a) CHM and apexes positions; (b) 3D view of CHM showing the role of outliers played by apexes within the crown; (c) H CFD of DC considered; dotted line represent the threshold value (95% PV) used to filter out apexes (red dots).

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Fig. 4 - H^CHM (left) and PDH^CHM (right) frequency distributions computed considering all surveyed trees in study area.

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Relative difference (ΔHs) between H^CHM_max and PDH^CHM was calculated for each tree and the correspondent cumulated frequency distribution generated. σ_z^CHM value was used as threshold to test if differences were significant or not (Fig. 5). The 57% of ΔHs resulted to be greater than σ_z^CHM further demonstrating that tree height computed according to PDH^CHM is significantly different from that computed with reference to H^CHM_max in more than a half of cases.

Fig. 5 - ΔHs cumulative distribution function and correspondent box-plot (min, Q1, median, Q3, max) computed with reference to all the trees in the study area. Red line shows CHM estimated accuracy (σ_z^CHM).

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  Conclusions 

PHODAR will represent a potential tool for more suitable and accurate forest inventories in the next future. Nevertheless, it introduces new ambiguities (i.e., potential errors) during forest parameters measurement (e.g., tree height, stem volume, etc.). With special concerns about tree height measures, we propose an approach based on the new concept of PDH. The value of tree height measure is an operative convention that, depending on the context, can be interpreted differently. In this study a new definition of tree height is proposed that is thought to be an alternative to the ordinary approach based of local maxima, with the aim of minimizing the effect of apexes within the crown, which can significantly affect the final accuracy of estimates. In particular, the prevailing dendrometric height within the crown (PDH) involves the use of a correcting factor based on the frequency distribution function of the CHM height values contained within the crown perimeter. We found that the 95^th percentile of this distribution can be assumed as PDH^CHM. Results showed that differences between PDH^CHM and H^CHM_Max (i.e., ordinary approach) were significant. Future developments are expected to be addressed to quantify the absolute accuracy of this method and the eventual improvements it can determine while estimating wood volume in forest stands with reference to different species.

  Acknowledgements 

We thank Dr. Martina Zucaro for the help in ground surveys, Dr. Claudio Rizzo for the RPAS flight, and La Mandria natural park technicians for the project support.

  References