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Silva Fennica 1926-1997
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Acta Forestalia Fennica
1953-1968
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Articles containing the keyword 'lidar'.

Category: Research article

article id 10179, category Research article
Lauri Korhonen, Jaakko Repola, Tomi Karjalainen, Petteri Packalen, Matti Maltamo. (2019). Transferability and calibration of airborne laser scanning based mixed-effects models to estimate the attributes of sawlog-sized Scots pines. Silva Fennica vol. 53 no. 3 article id 10179. https://doi.org/10.14214/sf.10179
Highlights: Attributes of individual sawlog-sized pines estimated by transferring ALS-based models between sites; Mixed effects models were more accurate than k-NN imputation tested earlier; Calibration with a small number of field measured trees improved the accuracy.

Airborne laser scanning (ALS) data is nowadays often available for forest inventory purposes, but adequate field data for constructing new forest attribute models for each area may be lacking. Thus there is a need to study the transferability of existing ALS-based models among different inventory areas. The objective of our study was to apply ALS-based mixed models to estimate the diameter, height and crown base height of individual sawlog sized Scots pines (Pinus sylvestris L.) at three different inventory sites in eastern Finland. Different ALS sensors and acquisition parameters were used at each site. Multivariate mixed-effects models were fitted at one site and the models were validated at two independent test sites. Validation was carried out by applying the fixed parts of the mixed models as such, and by calibrating them using 1–3 sample trees per plot. The results showed that the relative RMSEs of the predictions were 1.2–6.5 percent points larger at the test sites compared to the training site. Systematic errors of 2.4–6.2 percent points also emerged at the test sites. However, both the RMSEs and the systematic errors decreased with calibration. The results showed that mixed-effects models of individual tree attributes can be successfully transferred and calibrated to other ALS inventory areas in a level of accuracy that appears suitable for practical applications.

  • Korhonen, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID: http://orcid.org/0000-0002-9352-0114 E-mail: lauri.korhonen@uef.fi (email)
  • Repola, Natural Resources Institute of Finland (Luke), Natural resources, Eteläranta 55, FI-96300 Rovaniemi, Finland ORCID ID:E-mail: jaakko.repola@luke.fi
  • Karjalainen, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: tomikar@uef.fi
  • Packalen, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: petteri.packalen@uef.fi
  • Maltamo, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: matti.maltamo@uef.fi
article id 10075, category Research article
Matti Maltamo, Marius Hauglin, Erik Naesset, Terje Gobakken. (2019). Estimating stand level stem diameter distribution utilizing harvester data and airborne laser scanning. Silva Fennica vol. 53 no. 3 article id 10075. https://doi.org/10.14214/sf.10075
Highlights: Tree level-positioned harvester data were successfully used as plot-level training data for k-nearest neighbor stem diameter distribution modelling applying airborne laser scanning information as predictor variables; Stand-level validation showed that merchantable volume of total tree stock could be estimated with RMSE value of about 9%; The fit of the stem diameter distribution assessed by a variant of Reynold’s error index showed values smaller than 0.2; The most accurate results were obtained for the training plot sizes of 200 m2 and 400 m2.

Accurately positioned single-tree data obtained from a cut-to-length harvester were used as training harvester plot data for k-nearest neighbor (k-nn) stem diameter distribution modelling applying airborne laser scanning (ALS) information as predictor variables. Part of the same harvester data were also used for stand-level validation where the validation units were stands including all the harvester plots on a systematic grid located within each individual stand. In the validation all harvester plots within a stand and also the neighboring stands located closer than 200 m were excluded from the training data when predicting for plots of a particular stand. We further compared different training harvester plot sizes, namely 200 m2, 400 m2, 900 m2 and 1600 m2. Due to this setup the number of considered stands and the areas within the stands varied between the different harvester plot sizes. Our data were from final fellings in Akershus County in Norway and consisted of altogether 47 stands dominated by Norway spruce. We also had ALS data from the area. We concentrated on estimating characteristics of Norway spruce but due to the k-nn approach, species-wise estimates and stand totals as a sum over species were considered as well. The results showed that in the most accurate cases stand-level merchantable total volume could be estimated with RMSE values smaller than 9% of the mean. This value can be considered as highly accurate. Also the fit of the stem diameter distribution assessed by a variant of Reynold’s error index showed values smaller than 0.2 which are superior to those found in the previous studies. The differences between harvester plot sizes were generally small, showing most accurate results for the training harvester plot sizes 200 m2 and 400 m2.

  • Maltamo, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu ORCID ID:E-mail: matti.maltamo@uef.fi (email)
  • Hauglin, Norwegian Institute of Bioeconomy Research, Division of Forest and Forest Resources, P.O. Box 115, 1431 Ås, Norway ORCID ID:E-mail: marius.hauglin@nibio.no
  • Naesset, Norwegian University of Life Sciences, Faculty of Environmental Sciences and Natural Resource Management, P.O. Box 5003, 1432 Ås, Norway ORCID ID:E-mail: erik.naesset@nmbu.no
  • Gobakken, Norwegian University of Life Sciences, Faculty of Environmental Sciences and Natural Resource Management, P.O. Box 5003, 1432 Ås, Norway ORCID ID:E-mail: terje.gobakken@nmbu.no
article id 10006, category Research article
Matti Maltamo, Tomi Karjalainen, Jaakko Repola, Jari Vauhkonen. (2018). Incorporating tree- and stand-level information on crown base height into multivariate forest management inventories based on airborne laser scanning. Silva Fennica vol. 52 no. 3 article id 10006. https://doi.org/10.14214/sf.10006
Highlights: The most accurate tree-level alternative is to include crown base height (CBH) to nearest neighbour imputation; Also mixed-effects models can be applied to predict CBH using tree attributes and airborne laser scanning (ALS) metrics; CBH prediction can be included with an accuracy of 1–1.5 m to forest management inventory applications.

This study examines the alternatives to include crown base height (CBH) predictions in operational forest inventories based on airborne laser scanning (ALS) data. We studied 265 field sample plots in a strongly pine-dominated area in northeastern Finland. The CBH prediction alternatives used area-based metrics of sparse ALS data to produce this attribute by means of: 1) Tree-level imputation based on the k-nearest neighbor (k-nn) method and full field-measured tree lists including CBH observations as reference data; 2) Tree-level mixed-effects model (LME) prediction based on tree diameter (DBH) and height and ALS metrics as predictors of the models; 3) Plot-level prediction based on analyzing the computational geometry and topology of the ALS point clouds; and 4) Plot-level regression analysis using average CBH observations of the plots for model fitting. The results showed that all of the methods predicted CBH with an accuracy of 1–1.5 m. The plot-level regression model was the most accurate alternative, although alternatives producing tree-level information may be more interesting for inventories aiming at forest management planning. For this purpose, k-nn approach is promising and it only requires that field measurements of CBH is added to the tree lists used as reference data. Alternatively, the LME-approach produced good results especially in the case of dominant trees.

  • Maltamo, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: matti.maltamo@uef.fi (email)
  • Karjalainen, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: tomimkarjalainen@gmail.com
  • Repola, Natural Resources Institute of Finland (Luke), Natural resources, Eteläranta 55, FI-96300 Rovaniemi, Finland ORCID ID:E-mail: jaakko.repola@luke.fi
  • Vauhkonen, Natural Resources Institute of Finland (Luke), Bioeconomy and environment, Yliopistokatu 6, 80100 Joensuu, Finland ORCID ID:E-mail: jari.vauhkonen@luke.fi
article id 1567, category Research article
Eetu Kotivuori, Lauri Korhonen, Petteri Packalen. (2016). Nationwide airborne laser scanning based models for volume, biomass and dominant height in Finland. Silva Fennica vol. 50 no. 4 article id 1567. https://doi.org/10.14214/sf.1567
Highlights: Pooled data from nine inventory projects in Finland were used to create nationwide laser-based regression models for dominant height, volume and biomass; Volume and biomass models provided regionally different means than real means, but for dominant height the mean difference was small; The accuracy of general volume predictions was nevertheless comparable to relascope-based field inventory by compartments.

The aim of this study was to examine how well stem volume, above-ground biomass and dominant height can be predicted using nationwide airborne laser scanning (ALS) based regression models. The study material consisted of nine practical ALS inventory projects taken from different parts of Finland. We used field sample plots and airborne laser scanning data to create nationwide and regional models for each response variable. The final models had one or two ALS predictors, which were chosen based on the root mean square error (RMSE), and cross-validated. Finally, we tested how much predictions would improve if the nationwide models were calibrated with a small number of regional sample plots. Although forest structures differ among different parts of Finland, the nationwide volume and biomass models performed quite well (leave-inventory-area-out RMSE 22.3% to 33.8%, mean difference [MD] –13.8% to 18.7%) compared with regional models (leave-plot-out RMSE 20.2% to 26.8%). However, the nationwide dominant height model (RMSE 5.4% to 7.7%, MD –2.0% to 2.8%, with the exception of the Tornio region – RMSE 11.4%, MD –9.1%) performed nearly as well as the regional models (RMSE 5.2% to 6.7%). The results show that the nationwide volume and biomass models provided different means than real means at regional level, because forest structure and ALS device have a considerable effect on the predictions. Large MDs appeared especially in northern Finland. Local calibration decreased the MD and RMSE of volume and biomass models. However, the nationwide dominant height model did not benefit much from calibration.

  • Kotivuori, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: eetu.kotivuori@uef.fi (email)
  • Korhonen, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: lauri.korhonen@uef.fi
  • Packalen, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: petteri.packalen@uef.fi
article id 1414, category Research article
Rami Saad, Jörgen Wallerman, Johan Holmgren, Tomas Lämås. (2016). Local pivotal method sampling design combined with micro stands utilizing airborne laser scanning data in a long term forest management planning setting. Silva Fennica vol. 50 no. 2 article id 1414. https://doi.org/10.14214/sf.1414
Highlights: Most similar neighbor imputation was used to estimate forest variables using airborne laser scanning data as auxiliary data; For selecting field reference plots the local pivotal method (LPM) was compared to systematic sampling design; The LPM sampling design combined with a micro stand approach showed potential for improvement and has the potential to be a competitive method when considering cost efficiency.

A new sampling design, the local pivotal method (LPM), was combined with the micro stand approach and compared with the traditional systematic sampling design for estimation of forest stand variables. The LPM uses the distance between units in an auxiliary space – in this case airborne laser scanning (ALS) data – to obtain a well-spread sample. Two sets of reference plots were acquired by the two sampling designs and used for imputing data to evaluation plots. The first set of reference plots, acquired by LPM, made up four imputation alternatives (varying number of reference plots) and the second set of reference plots, acquired by systematic sampling design, made up two alternatives (varying plot radius). The forest variables in these alternatives were estimated using the nonparametric method of most similar neighbor imputation, with the ALS data used as auxiliary data. The relative root mean square error (RelRMSE), stem diameter distribution error index and suboptimal loss were calculated for each alternative, but the results showed that neither sampling design, i.e. LPM vs. systematic, offered clear advantages over the other. It is likely that the obtained results were a consequence of the small evaluation dataset used in the study (n = 30). Nevertheless, the LPM sampling design combined with the micro stand approach showed potential for improvement and might be a competitive method when considering the cost efficiency.

  • Saad, Swedish University of Agricultural Sciences (SLU), Department of Forest Resource Management, Skogsmarksgränd, SE-901 83 Umeå, Sweden ORCID ID:E-mail: rami.saad@slu.se (email)
  • Wallerman, Swedish University of Agricultural Sciences (SLU), Department of Forest Resource Management, Skogsmarksgränd, SE-901 83 Umeå, Sweden ORCID ID:E-mail: jorgen.wallerman@slu.se
  • Holmgren, Swedish University of Agricultural Sciences (SLU), Department of Forest Resource Management, Skogsmarksgränd, SE-901 83 Umeå, Sweden ORCID ID:E-mail: johan.holmgren@slu.se
  • Lämås, Swedish University of Agricultural Sciences (SLU), Department of Forest Resource Management, Skogsmarksgränd, SE-901 83 Umeå, Sweden ORCID ID:E-mail: tomas.lamas@slu.se
article id 1413, category Research article
Ilya Potapov, Marko Järvenpää, Markku Åkerblom, Pasi Raumonen, Mikko Kaasalainen. (2016). Data-based stochastic modeling of tree growth and structure formation. Silva Fennica vol. 50 no. 1 article id 1413. https://doi.org/10.14214/sf.1413
Highlights: We propose a stochastic version of the tree growth model LIGNUM for producing tree structures consistent with detailed terrestrial laser scanning data, and we provide the proof-of-concept by using model-based simulations and real laser scanning data; Trees produced with the data-based model resemble the trees of the dataset, and are statistically similar but not copies of each other; the number of such synthetic trees is not limited.

We introduce a general procedure to match a stochastic functional-structural tree model (here LIGNUM augmented with stochastic rules) with real tree structures depicted by quantitative structure models (QSMs) based on terrestrial laser scanning. The matching is done by iteratively finding the maximum correspondence between the measured tree structure and the stochastic choices of the algorithm. First, we analyze the match to synthetic data (generated by the model itself), where the target values of the parameters to be estimated are known in advance, and show that the algorithm converges properly. We then carry out the procedure on real data obtaining a realistic model. We thus conclude that the proposed stochastic structure model (SSM) approach is a viable solution for formulating realistic plant models based on data and accounting for the stochastic influences.

  • Potapov, Tampere University of Technology, Department of Mathematics, P.O. Box 553, FI-33101 Tampere, Finland ORCID ID:E-mail: ilya.potapov@tut.fi (email)
  • Järvenpää, Tampere University of Technology, Department of Mathematics, P.O. Box 553, FI-33101 Tampere, Finland ORCID ID:E-mail: marko.jarvenpaa@tut.fi
  • Åkerblom, Tampere University of Technology, Department of Mathematics, P.O. Box 553, FI-33101 Tampere, Finland ORCID ID:E-mail: markku.akerblom@tut.fi
  • Raumonen, Tampere University of Technology, Department of Mathematics, P.O. Box 553, FI-33101 Tampere, Finland ORCID ID:E-mail: pasi.raumonen@tut.fi
  • Kaasalainen, Tampere University of Technology, Department of Mathematics, P.O. Box 553, FI-33101 Tampere, Finland ORCID ID:E-mail: mikko.kaasalainen@tut.fi
article id 1071, category Research article
Ursula Kretschmer, Nadeschda Kirchner, Christopher Morhart, Heinrich Spiecker. (2013). A new approach to assessing tree stem quality characteristics using terrestrial laser scans. Silva Fennica vol. 47 no. 5 article id 1071. https://doi.org/10.14214/sf.1071
Highlights: Minimal deviations of the bark surface can be detected and visualized based on terrestrial laser scan data; Additionally the geometrical properties of bark scars and branched knots can be assessed; Two methods using two different approaches are presented: (1) a method using intensity data and (2) a method using bark surface models.
This paper presents an approach to assess and measure bark characteristics as indicators of wood quality using terrestrial laser scan data. In addition to the detection and measurement by use of the intensity information of the scan data a new approach was established. Bark surface models are calculated for each tree. They offer the representation of the bark as a height model. The reference is the tree stem approximated by a chain of cylinders. Minimal deviations of the bark surface can be detected and visualized and the geometrical properties of bark scars and branched knots can be assessed. Results of the measurement of 18 scars are presented using the two approaches: (1) a method using intensity data or (2) using bark surface models. The selection of the adequate approach depends on the stem characteristics. In a next step, methods for automatic measurement of bark scars will be developed.
  • Kretschmer, Chair of Forest Growth, Albert-Ludwigs-University Freiburg, Tennenbacher Str. 4, 79106 Freiburg, Germany ORCID ID:E-mail: ursula.kretschmer@iww.uni-freiburg.de (email)
  • Kirchner, VOLKE Consulting Engineers GmbH, Schätzweg 7-9, 80935 München, Germany ORCID ID:E-mail: nadeschda.kirchner@volke.muc.de
  • Morhart, Chair of Forest Growth, Albert-Ludwigs-University Freiburg, Tennenbacher Str. 4, 79106 Freiburg, Germany ORCID ID:E-mail: christopher.morhart@iww.uni-freiburg.de
  • Spiecker, Chair of Forest Growth, Albert-Ludwigs-University Freiburg, Tennenbacher Str. 4, 79106 Freiburg, Germany ORCID ID:E-mail: instww@uni-freiburg.de
article id 943, category Research article
Terje Gobakken, Lauri Korhonen, Erik Næsset. (2013). Laser-assisted selection of field plots for an area-based forest inventory. Silva Fennica vol. 47 no. 5 article id 943. https://doi.org/10.14214/sf.943
Highlights: Using laser data as auxiliary information in the selection of field plot locations helps to decrease costs in forest inventories based on airborne laser scanning; Two independent, differently selected sets of field plots were used for model fitting, and third for validation; Using partial instead of ordinary least squares had no major influence on the results; Forty well placed plots produced fairly reliable volume estimates.
Field measurements conducted on sample plots are a major cost component in airborne laser scanning (ALS) based forest inventories, as field data is needed to obtain reference variables for the statistical models. The ALS data also provides an excellent source of prior information that may be used in the design phase of the field survey to reduce the size of the field data set. In the current study, we acquired two independent modeling data sets: one with ALS-assisted and another with random plot selection. A third data set was used for validation. One canopy height and one canopy density variable were used as a basis for the ALS-assisted selection. Ordinary and partial least squares regressions for stem volume were fitted for four different strata using the two data sets separately. The results show that the ALS-assisted plot selection helped to decrease the root mean square error (RMSE) of the predicted volume. Although the differences in RMSE were relatively small, models based on random plot selection showed larger mean differences from the reference in the independent validation data. Furthermore, a sub-sampling experiment showed that 40 well placed plots should be enough for fairly reliable predictions.
  • Gobakken, Norwegian University of Life Sciences, Department of Ecology and Natural Resource Management, Ås, Norway ORCID ID:E-mail: terje.gobakken@umb.no
  • Korhonen, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: lauri.korhonen@uef.fi (email)
  • Næsset, Norwegian University of Life Sciences, Department of Ecology and Natural Resource Management, Ås, Norway ORCID ID:E-mail: erik.naesset@umb.no
article id 68, category Research article
Maria Villikka, Petteri Packalén, Matti Maltamo. (2012). The suitability of leaf-off airborne laser scanning data in an area-based forest inventory of coniferous and deciduous trees. Silva Fennica vol. 46 no. 1 article id 68. https://doi.org/10.14214/sf.68
This study examined the suitability of airborne laser scanner (ALS) data collected under leaf-off conditions in a forest inventory, in which deciduous and coniferous trees need to be separated. All analyses were carried out with leaf-on and leaf-off ALS data collected from the same study area. Additionally, aerial photographs were utilized in the Nearest Neighbor (NN) imputations. An area-based approach was used in this study. Regression estimates of plot volume were more accurate in the case of leaf-off than leaf-on data. In addition, regression models were more accurate in coniferous plots than in deciduous plots. The results of applying leaf-on models with leaf-off data, and vice versa, indicate that leaf-on and leaf-off data should not be combined since this causes serious bias. The total volume and volume by coniferous and deciduous trees was estimated by the NN imputation. In terms of total volume, leaf-off data provided more accurate estimates than leaf-on data. In addition, leaf-off data discriminated between coniferous and deciduous trees, even without the use of aerial photographs. Accurate results were also obtained when leaf-off ALS data were used to classify sample plots into deciduous and coniferous dominated plots. The results indicate that the area-based method and ALS data collected under leaf-off conditions are suitable for forest inventory in which deciduous and coniferous trees need to be distinguished.
  • Villikka, University of Easten Finland, Department of Forest Sciences, Joensuu, Finland ORCID ID:E-mail:
  • Packalén, University of Easten Finland, Department of Forest Sciences, Joensuu, Finland ORCID ID:E-mail: petteri.packalen@uef.fi (email)
  • Maltamo, University of Easten Finland, Department of Forest Sciences, Joensuu, Finland ORCID ID:E-mail:
article id 203, category Research article
Matti Maltamo, Jussi Peuhkurinen, Jukka Malinen, Jari Vauhkonen, Petteri Packalén, Timo Tokola. (2009). Predicting tree attributes and quality characteristics of Scots pine using airborne laser scanning data. Silva Fennica vol. 43 no. 3 article id 203. https://doi.org/10.14214/sf.203
The development of airborne laser scanning (ALS) during last ten years has provided new possibilities for accurate description of the living tree stock. The forest inventory applications of ALS data include both tree and area-based plot level approaches. The main goal of such applications has usually been to estimate accurate information on timber quantities. Prediction of timber quality has not been focused to the same extent. Thus, in this study we consider here the prediction of both basic tree attributes (tree diameter, height and volume) and characteristics describing tree quality more closely (crown height, height of the lowest dead branch and sawlog proportion of tree volume) by means of high resolution ALS data. The tree species considered is Scots pine (Pinus sylvestris), and the field data originate from 14 sample plots located in the Koli National Park in North Karelia, eastern Finland. The material comprises 133 trees, and size and quality variables of these trees were modeled using a large number of potential independent variables calculated from the ALS data. These variables included both individual tree recognition and area-based characteristics. Models for the dependent tree characteristics to be considered were then constructed using either the non-parametric k-MSN method or a parametric set of models constructed simultaneously by the Seemingly Unrelated Regression (SUR) approach. The results indicate that the k-MSN method can provide more accurate tree-level estimates than SUR models. The k-MSN estimates were in fact highly accurate in general, the RMSE being less than 10% except in the case of tree volume and height of the lowest dead branch.
  • Maltamo, University of Joensuu, Faculty of Forest Sciences, FI-80101 Joensuu, Finland ORCID ID:E-mail: matti.maltamo@joensuu.fi (email)
  • Peuhkurinen, University of Joensuu, Faculty of Forest Sciences, FI-80101 Joensuu, Finland ORCID ID:E-mail:
  • Malinen, Finnish Forest Research Institute, Joensuu Research Unit, FI-80101 Joensuu, Finland ORCID ID:E-mail:
  • Vauhkonen, University of Joensuu, Faculty of Forest Sciences, FI-80101 Joensuu, Finland ORCID ID:E-mail:
  • Packalén, University of Joensuu, Faculty of Forest Sciences, FI-80101 Joensuu, Finland ORCID ID:E-mail:
  • Tokola, University of Joensuu, Faculty of Forest Sciences, FI-80101 Joensuu, Finland ORCID ID:E-mail:

Category: Research note

article id 1125, category Research note
Anssi Krooks, Sanna Kaasalainen, Ville Kankare, Marianna Joensuu, Pasi Raumonen, Mikko Kaasalainen. (2014). Predicting tree structure from tree height using terrestrial laser scanning and quantitative structure models. Silva Fennica vol. 48 no. 2 article id 1125. https://doi.org/10.14214/sf.1125
Highlights: The analysis of tree structure suggests that trees of different height growing in similar conditions have similar branch size distributions; There is potential for using the tree height information in large-scale estimations of forest canopy structure.
We apply quantitative structure modelling to produce detailed information on branch-level metrics in trees. Particularly we are interested in the branch size distribution, by which we mean the total volume of branch parts distributed over the diameter classes of the parts. We investigate the possibility of predicting tree branch size distributions for trees in similar growing conditions. The quantitative structure model enables for the first time the comparisons of structure between a large number of trees. We found that the branch size distribution is similar for trees of different height in similar growing conditions. The results suggest that tree height could be used to estimate branch size distribution in areas with similar growing conditions and topography.
  • Krooks, Finnish Geodetic Institute, Geodeetinrinne 2, FI–02431 Masala, Finland ORCID ID:E-mail: Anssi.Krooks@fgi.fi
  • Kaasalainen, Finnish Geodetic Institute, Geodeetinrinne 2, FI–02431 Masala, Finland ORCID ID:E-mail: Sanna.Kaasalainen@fgi.fi (email)
  • Kankare, Department of Forest Sciences, University of Helsinki, P.O. Box 27, FI-00014 Helsinki, Finland ORCID ID:E-mail: ville.kankare@helsinki.fi
  • Joensuu, Department of Forest Sciences, University of Helsinki, P.O. Box 27, FI-00014 Helsinki, Finland ORCID ID:E-mail: marianna.joensuu@alumni.helsinki.fi
  • Raumonen, Tampere University of Technology, Department of Mathematics, P.O. Box 553, Tampere, FI-33101, Finland ORCID ID:E-mail: Pasi.Raumonen@tut.fi
  • Kaasalainen, Tampere University of Technology, Department of Mathematics, P.O. Box 553, Tampere, FI-33101, Finland ORCID ID:E-mail: Mikko.Kaasalainen@tut.fi

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