Multiscale Finite Element Formulations for 2D/1D Problems

Multiscale finite element methods for 2D/1D problems have been studied in this work to demonstrate their excellent ability to solve real-world problems. These methods are much more efficient than conventional 3D finite element methods and just as accurate. The 2D/1D multiscale finite element methods are based on a magnetic vector potential or a current vector potential. Known currents for excitation can be replaced by the Biot-Savart-field. Boundary conditions allow to integrate planes of symmetry. All presented approaches consider eddy currents, an insulation layer and preserve the edge effect. A segment of a fictitious electrical machine has been studied to demonstrate all above options, the accuracy and the low computational costs of the 2D/1D multiscale finite element methods.Comment: 7 pages, 18 figure

Forest structure and stem volume assessment based on airborne laser scanning Avaliação da estrutura florestal e do volume de madeira a partir de laser aerotransportado

This paper presents a methodology for the derivation of structural parameters and stem volume in forests based on Airborne Laser Scanning (ALS) data. We describe three different measures of horizontal and vertical canopy structure: (1) tree crown segmentation, (2) compactness of vegetation patches, and (3) vertical layering of vegetation patches and canopy cover. An empirical regression model for the derivation of stem volume from the ALS and forest inventory sample plot data is described and its results are validated with extensive reference data. Different study areas in Austria were used to illustrate the workflows. The presented study demonstrates the applicability of the proposed methods on study sites and ALS data of differing characteristics, as well as it points out the suitability of ALS as a tool for reliable wide area assessment of structural parameters and stem volume for forested areas.Resumo Esse artigo apresenta uma metodologia para derivação de parâmetros estruturais e de volume de madeira em florestas baseado em dados de Laser Scanner Aerotransportado (ALS). Nós descrevemos três diferentes medidas da estrutura horizontal e vertical da copa: (1) segmentação da copa da árvore, (2) compacidade das manchas de vegetação, (3) estratificação vertical das manchas de vegetação e cobertura do dossel. Um modelo empírico de regressão para derivar o volume de madeira fazendo uso de dados ALS e dados amostrais obtidos em inventário florestal é descrito e seus resultados são validados com extensivos dados de referência. Diferentes áreas na Áustria foram utilizadas para ilustrar o fluxo de trabalho. O estudo apresentado demonstra a aplicabilidade dos métodos propostos nas áreas de estudo e dos dados ALS de diferentes características, bem como aponta a adequação do ALS como ferramenta confiável para avaliação de parâmetros de estrutura e de volume de madeira de amplas áreas florestais

FOR-instance: a UAV laser scanning benchmark dataset for semantic and instance segmentation of individual trees

The FOR-instance dataset (available at https://doi.org/10.5281/zenodo.8287792) addresses the challenge of accurate individual tree segmentation from laser scanning data, crucial for understanding forest ecosystems and sustainable management. Despite the growing need for detailed tree data, automating segmentation and tracking scientific progress remains difficult. Existing methodologies often overfit small datasets and lack comparability, limiting their applicability. Amid the progress triggered by the emergence of deep learning methodologies, standardized benchmarking assumes paramount importance in these research domains. This data paper introduces a benchmarking dataset for dense airborne laser scanning data, aimed at advancing instance and semantic segmentation techniques and promoting progress in 3D forest scene segmentation. The FOR-instance dataset comprises five curated and ML-ready UAV-based laser scanning data collections from diverse global locations, representing various forest types. The laser scanning data were manually annotated into individual trees (instances) and different semantic classes (e.g. stem, woody branches, live branches, terrain, low vegetation). The dataset is divided into development and test subsets, enabling method advancement and evaluation, with specific guidelines for utilization. It supports instance and semantic segmentation, offering adaptability to deep learning frameworks and diverse segmentation strategies, while the inclusion of diameter at breast height data expands its utility to the measurement of a classic tree variable. In conclusion, the FOR-instance dataset contributes to filling a gap in the 3D forest research, enhancing the development and benchmarking of segmentation algorithms for dense airborne laser scanning data

Estimation of Aboveground Biomass in Alpine Forests: A Semi-Empirical Approach Considering Canopy Transparency Derived from Airborne LiDAR Data

In this study, a semi-empirical model that was originally developed for stem volume estimation is used for aboveground biomass (AGB) estimation of a spruce dominated alpine forest. The reference AGB of the available sample plots is calculated from forest inventory data by means of biomass expansion factors. Furthermore, the semi-empirical model is extended by three different canopy transparency parameters derived from airborne LiDAR data. These parameters have not been considered for stem volume estimation until now and are introduced in order to investigate the behavior of the model concerning AGB estimation. The developed additional input parameters are based on the assumption that transparency of vegetation can bemeasured by determining the penetration of the laser beams through the canopy. These parameters are calculated for every single point within the 3D point cloud in order to consider the varying properties of the vegetation in an appropriate way. Exploratory Data Analysis (EDA) is performed to evaluate the influence of the additional LiDAR derived canopy transparency parameters for AGB estimation. The study is carried out in a 560 km2 alpine area in Austria, where reference forest inventory data and LiDAR data are available. The investigations show that the introduction of the canopy transparency parameters does not change the results significantly according to R2 (R2 = 0.70 to R2 = 0.71) in comparison to the results derived from, the semi-empirical model, which was originally developed for stem volume estimation

Individual tree properties from ALS data as input to habitat analysis in boreal forest

This study shows examples of detailed analysis of forest canopy from ALS data with potential use as input to habitat analysis in forests. This includes delineation of individual tree crowns and analysis of the distribution of tree heights and the tree species composition

Influence of footprint size and geolocation error on the precision of forest biomass estimates from space-borne waveform LiDAR

Space-borne LiDAR systems can potentially assist large-area assessments of forest resources, in particular when a subset of the acquired LiDAR footprints is combined with field surveys of forest stand characteristics at footprint location. When combined, space-borne LiDAR geolocation error and the footprint size may however have considerable effects on the estimation accuracy of forest stand variables, such as aboveground biomass (AGB). The aim of this study was to draw recommendations for future space-borne LiDAR systems, which should deliver data for unbiased AGB assessments. The recommendations were drawn from AGB estimations based on space borne LiDAR waveforms simulated over a 1300 ha large study site in southern Sweden. Large-footprint, nadir looking satellite waveforms were simulated by stacking individual small-footprint, airborne LiDAR waveforms observed near a predefined sampling pattern. The stacked waveforms, represented by their metrics, were used as input for a two-phase systematic sampling in combination with model-assisted estimation or hybrid inference for estimating AGB and its variance. The second-phase sample included 264 inventory plots, whereas the first-phase sample included 1010 sample locations, where satellite waveforms were simulated. After simulating satellite waveforms with different footprint sizes and analyzing the AGB variance, the recommendation is to have a footprint size that is similar to the size of the field plots used for collecting reference data, i.e. 20 m diameter in our case. For the optimal footprint size, AGB was estimated with a precision of 2.9 Mg per hectare (2.9% of the average). The results also showed that variance estimates increased constantly with increasing geolocation error. For a geolocation error of 14 m, variance estimates increased by 17%, which justifies investing additional efforts in minimizing it

Aboveground forest biomass derived using multiple dates of WorldView-2 stereo-imagery : quantifying the improvement in estimation accuracy

The aim of this study was to investigate the capabilities of two date satellite-derived image-based point clouds (IPCs) to estimate forest aboveground biomass (AGB). The data sets used include panchromatic WorldView-2 stereo-imagery with 0.46 m spatial resolution representing 2014 and 2016 and a detailed digital elevation model derived from airborne laser scanning data. Altogether, 332 field sample plots with an area of 256 m(2) were used for model development and validation. Predictors describing forest height, density, and variation in height were extracted from the IPC 2014 and 2016 and used in k-nearest neighbour imputation models developed with sample plot data for predicting AGB. AGB predictions for 2014 (AGB(2014)) were projected to 2016 using growth models (AGB(Projected_2016)) and combined with the AGB estimates derived from the 2016 data (AGB(2016)). AGB prediction model developed with 2014 data was also applied to 2016 data (AGB(2016_pred2014)). Based on our results, the change in the 90(th) percentile of height derived from the WorldView-2 IPC was able to characterize forest height growth between 2014 and 2016 with an average growth of 0.9 m. Features describing canopy cover and variation in height derived from the IPC were not as consistent. The AGB(2016) had a bias of -7.5% (-10.6 Mg ha(-1)) and root mean square error (RMSE) of 26.0% (36.7 Mg ha(-1)) as the respective values for AGB(Projected_2016) were 7.0% (9.9 Mg ha(-1)) and 21.5% (30.8 Mg ha(-1)). AGB(2016_pred2014) had a bias of -19.6% (-27.7 Mg ha(-1)) and RMSE of 33.2% (46.9 Mg ha(-1)). By combining predictions of AGB(2016) and AGB(Projected_2016) at sample plot level as a weighted average, we were able to decrease the bias notably compared to estimates made on any single date. The lowest bias of -0.25% (-0.4 Mg ha(-1)) was obtained when equal weights of 0.5 were given to the AGB(Projected_2016) and AGB(2016) estimates. Respectively, RMSE of 20.9% (29.5 Mg ha(-1)) was obtained using equal weights. Thus, we conclude that combination of two date WorldView-2 stereo-imagery improved the reliability of AGB estimates on sample plots where forest growth was the only change between the two dates.Peer reviewe

A Benchmark of Lidar-Based Single Tree Detection Methods Using Heterogeneous Forest Data from the Alpine Space

In this study, eight airborne laser scanning (ALS)-based single tree detection methods are benchmarked and investigated. The methods were applied to a unique dataset originating from different regions of the Alpine Space covering different study areas, forest types, and structures. This is the first benchmark ever performed for different forests within the Alps. The evaluation of the detection results was carried out in a reproducible way by automatically matching them to precise in situ forest inventory data using a restricted nearest neighbor detection approach. Quantitative statistical parameters such as percentages of correctly matched trees and omission and commission errors are presented. The proposed automated matching procedure presented herein shows an overall accuracy of 97%. Method based analysis, investigations per forest type, and an overall benchmark performance are presented. The best matching rate was obtained for single-layered coniferous forests. Dominated trees were challenging for all methods. The overall performance shows a matching rate of 47%, which is comparable to results of other benchmarks performed in the past. The study provides new insight regarding the potential and limits of tree detection with ALS and underlines some key aspects regarding the choice of method when performing single tree detection for the various forest types encountered in alpine regions.The European Commissio