Forest resource mapping using 3D remote sensing: Combining national forest inventory data and digital aerial photogrammetry
Kartlegging av skogressurser med 3D fjernmåling: Kombinering av data fra landskogtakseringen og fotogrammetri med flybilder
Philosophiae Doctor (PhD) Thesis Johannes Rahlf Faculty of Environmental Science and Natural Resource Management Norwegian University of Life Sciences Ås 2017
Thesis number 2017:10 ISSN 1894-6402 ISBN 978-82-575-1419-8
PhD supervisors Professor Erik Næsset Department of Ecology and Natural Resource Management Norwegian University of Life Sciences Postboks 5003, 1432 Ås, Norway Dr. Svein Solberg, Research Professor National Forest Inventory Division for Forestry and Forest Resources Norwegian Institute of Bioeconomy Research Postboks 115, 1432 Ås, Norway Dr. Johannes Breidenbach, Research Professor National Forest Inventory Division for Forestry and Forest Resources Norwegian Institute of Bioeconomy Research Postboks 115, 1432 Ås, Norway Dr. Rasmus Astrup, Head of Research Division for Forestry and Forest Resources Norwegian Institute of Bioeconomy Research Postboks 115, 1432 Ås, Norway
Evaluation committee Professor Håkan Olsson Division of Forest Remote Sensing Department of Forest Resource Management Swedish University of Agricultural Sciences 90183 Umeå, Sweden Associate Professor L. Monika Moskal School of Environmental and Forest Sciences College of the Environment University of Washington Box 352100, Seattle, WA, 98115-2100, USA Professor Terje Gobakken Department of Ecology and Natural Resource Management Norwegian University of Life Sciences Postboks 5003, 1432 Ås, Norway
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Preface This dissertation was financed by, and conducted at the Norwegian Institute for Bioeconomy Research (prior to July 2015: the Norwegian Forest and Landscape Institute). First, I would like to thank my supervisors Johannes Breidenbach, Svein Solberg, Erik Næsset, and Rasmus Astrup for their support and guidance. Rasmus, your expertise, creativity and your contagious enthusiasm are a great inspiration. Erik, I could always count on your advice and your thorough manuscript reviews, even if you got them at the last minute. Svein, my first main supervisor, thank you for letting me peek into the world of SAR and for your always open door. I especially have to thank Johannes. Without you this thesis would not have been possible. Our nearly daily chats and discussions, work-related or not, guided me through my PhD. I am very grateful that you were not only a supervisor, but also became a friend. I would like to thank my colleagues at NIBIO for creating an open and friendly working environment. The lunch and coffee breaks, the short and long chats in the hallway, the fruitful discussions helped me through the ups and downs of the PhD. Thank you, Aksel, for being Norway’s best boss. And of course I would like to thank the field crew of the National Forest Inventory, who collected the data, which are the basis of this thesis. Thanks to my colleagues at INA, especially the SkogRover group, for all the interesting and useful discussions. I want to thank my parents, who have always supported me, even though I did not do my PhD in Italy. My thanks go to my brothers and their families, who always believed in me. My Fischer family helped out whenever there was need. Thank you! My friends in Norway and Germany motivated me and helped to distract me whenever I needed distraction. Thank you, friends and neighbours at Norderås. There is no better place to live. Finally, I would like to thank the two most important people in my life. Thank you, Caro, for always being there for me. Thank you bearing my moods and for all your support and understanding, especially during the last weeks. Frida, your smiles, laughs, and hugs are the best things in my life. You always remind me what really is important, and I would like to thank you for that.
Ås, December 2016 Johannes Rahlf
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Contents Preface
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List of papers
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Abstract
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1 Introduction
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2 Objectives
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3 Usage of 3D remote sensing in forest inventory applications
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3.1
3D remote sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2
Merging remote sensing and forest inventory data . . . . . . . . . . . . . 10
3.3
Forest resource maps and their use in forest inventories . . . . . . . . . . 11
4 Material and methods
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4.1
Study areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2
Forest inventory data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.3
Remote sensing data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.4
Computations of metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.5
Statistical analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.6
Additional variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.7
Operationalizing large area forest mapping . . . . . . . . . . . . . . . . . 20
5 Results and Discussion
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5.1
Comparing DAP and other 3D remote sensing methods (Paper I) . . . . 23
5.2
Semi-ITC with DAP (Paper II) . . . . . . . . . . . . . . . . . . . . . . . 24
5.3
Large-area application (Paper III) . . . . . . . . . . . . . . . . . . . . . . 25
5.4
Operationalizing the use of DAP in an NFI context (Paper IV) . . . . . . 26
6 Conclusions and Perspectives
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6.1
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.2
Future perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
References
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List of papers Paper I Rahlf, J., Breidenbach, J., Solberg, S., Næsset, E. & Astrup, R. (2014). Comparison of Four Types of 3D Data for Timber Volume Estimation. Remote Sensing of Environment, 155, 325–33.
Paper II Rahlf, J., Breidenbach, J., Solberg, S. & Astrup, R. (2015). Forest Parameter Prediction Using an Image-Based Point Cloud: A Comparison of Semi-ITC with ABA. Forests, 6(11), 4059–71.
Paper III Rahlf, J., Breidenbach, J., Solberg, S., Næsset, E. & Astrup, R. (2017). Digital Aerial Photogrammetry and NFI Data for a Large-area Forest Inventory. Forestry, in review.
Paper IV Astrup, R., Rahlf, J., Bjørkelo, K., Debella-Gilo, M., Gjertsen, A.K. & Breidenbach, J. (2017). Forest information at multiple scales: Development, evaluation and application of the Norwegian Forest Resources Map. Manuscript.
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Abstract National forest inventories (NFI) provide information at national and regional scales. At smaller scales, however, often too few sample plots are available for accurate estimates. The increasing availability of large area 3D remote sensing data gives the opportunity to create wall-to-wall forest maps based on reference data from NFIs. Digital aerial photogrammetry (DAP) allows the creation of detailed 3D information from overlapping digital aerial images over large areas at low costs. The objective of this thesis was to assess the use of DAP in combination with NFI data. In the first study, DAP was compared to other 3D remote sensing techniques, namely airborne laser scanning (ALS), satellite interferometric synthetic aperture radar (InSAR), and satellite radargrammetry based on the accuracies of timber volume models. All models had good model fits. It could be shown that at stand level predictions with ALS were slightly more accurate than predictions based on DAP, which were more accurate than predictions using satellite SAR data. The second study analyzed the use of DAP in a semi individual tree crown (semi-ITC) approach for modeling various forest parameters. At plot level, timber volume predictions of the semi-ITC approach had accuracies and systematic errors similar to the area based approach (ABA). Multivariate kNN models were slightly more accurate with the semi-ITC approach than with the ABA, but had larger systematic errors. In the third study a timber volume model was fit for a large study area and the influence of large-area factors on the accuracy of timber volume predictions was investigated. The obtained accuracy of the predictions was lower than reported for earlier studies conducted on smaller study areas. The solar incidence angle relative to the terrain had a significant influence on the model. Finally, the use of DAP for an operational forest resource map was analyzed. Various forest parameters were mapped for a large area using 3D and spectral information from DAP combined with NFI data. Forest parameter models were less accurate than reported for earlier studies on small areas, but stand volume estimates were in line with existing forest management inventories. Model-assisted estimates at regional and municipality level were more precise than estimates based on NFI sample plots alone. The update of a forest mask produced a highly accurate classification of forest and non-forest. A tree species classification showed low accuracies, which, however did not differ greatly from accuracies reported in earlier studies. In conclusion, the combination of DAP with NFI data allows cost-efficient mapping of forest parameters over large areas with high detail. Such maps showed to improve the estimates of the Norwegian NFI at various scales. Stand-level estimates of large mapping applications might be sufficiently accurate to be used in forest management planning or in the design of forest management inventories.
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1
Introduction
Forest inventories provide information on forests on various scales. The range of variables reported by forest inventories varies, but typically includes the forested area, tree species, timber volume, and age. In sampling based forest inventories, measurements are taken only on parts of the area of interest (AOI). From this sample the forest parameters of the whole population (i.e. the AOI) can be estimated. In addition, remote sensing is often used in the design phase (e.g. in stratification) and in the estimation phase as auxiliary data. In many developed countries, two different forest inventory systems provide statistics on different spatial scales. National forest inventories (NFI) provide information on forest resources on national and regional level. Such statistics are the basis for forest policies and national forest programs, but also serve a variety of other uses such as international reporting and the monitoring of ecosystem services (Tomppo et al. 2010). As in many developed countries, the Norwegian NFI consists of a network of permanent sample plots. The Norwegian NFI traditionally provides estimates of forest resources for the whole of Norway and for counties (Tomter et al. 2010). However, on smaller scales the number of NFI plots is usually too small to assure accurate estimates. Therefore, estimates for municipalities, estates, or single stands cannot be derived from NFI data alone. At local scales, forest information is typically provided by forest management inventories (FMI). FMIs aim to provide information on individual forest stands which allow strategic and tactical planning of forest properties. Until the 1970s a common practice to obtain stand information in FMIs in Norway were stand-wise field inventories. those required field visits to every stand, where stand parameters were measured or visually assessed. Nowadays, most FMIs combine field surveys with remote sensing, particularly airborne laser scanning (ALS), which allows estimation of stand parameters (Næsset 2014). Remote sensing data are linked to the sample plot measurements by statistical modeling. These linking models are then used to predict forest parameters for the AOI, creating wall-to-wall covering forest maps. Forest maps give an overview of the forest resources and can therefore be used to support tactical planning of forest operations. The main purpose of prediction maps, however, is serve as basis for estimation of stand level means and totals. In recent years, increasingly more three-dimensional (3D) remote sensing data have become available over large areas, which have proven highly suitable for forestry applications. These data give now the opportunity to create forest maps by combining NFI sample plots with remote sensing. Due to the large spatial extent, sufficient numbers of NFI sample plots intersect with the remote sensing data. This allows fitting of linking 1
models and thus the construction of forest resource maps. Depending on the auxiliary remote sensing data, such maps may have great spatial detail and high accuracy and may be used to estimate forest parameters in small areas, such as municipalities, estates or even forest stands. ALS is a popular source of 3D data for forestry applications and has been thoroughly studied for over two decades. Its advantage over most other remote sensing technologies is the ability to provide information on the terrain below the tree canopy and to characterize structure of the canopy (Vauhkonen et al. 2014). In several countries, such as Norway, Sweden, and Finland, ALS is an operational method in FMIs (Næsset 2014). With increasingly more area covered by ALS and country-wide acquisitions, often with the purpose of acquiring detailed terrain information, ALS has also become a source of data for large-area forest resource mapping (e.g. Nord-Larsen & Schumacher 2012, Nilsson et al. 2016). A genuine source of large-area information is satellite imagery. An advancing technique for acquiring 3D data from satellites is synthetic aperture radar (SAR), which uses microwaves to illuminate the surface. Among the processing methods to derive 3D information from satellite SAR are interferometric SAR (InSAR) and radargrammetry, which have been used to model key forest parameters such as height and biomass (Solberg et al. 2013, Askne & Santoro 2015, Soja et al. 2015b,a, Solberg, Riegler & Nonin 2015). With upcoming satellite missions, an increase in the use of space-borne InSAR for forestry applications can be expected. Another promising technique of acquiring 3D data is digital aerial photogrammetry (DAP). While photogrammetry has been used in forest mensuration for over a century (Müller 1931), only with its full digitalization and the recent developments in hardware and processing algorithms is it now possible to automatically obtain 3D information from aerial photographs over large areas with point densities and accuracies similar to ALS (Leberl et al. 2010). An early study processing DAP data similar to ALS data was conducted by Næsset (2002), who showed the possibilities of using DAP in forest parameter mapping. Even though DAP is not able to depict the structure of forest canopies as well as ALS, Bohlin et al. (2012) and Nurminen et al. (2013) compared forest parameter models using DAP and ALS, and obtained similar accuracies on standlevel. A large advantage of DAP is that 3D data can be obtained from aerial images acquired with the aim of orthophoto generation, which makes DAP a promising tool for large-area forestry applications. An example of a large-area application is the creation of country-wide 3D data in Switzerland (Ginzler & Hobi 2015) which were then used to map forest area by Waser et al. (2015). However, contrary to ALS, which has been thoroughly investigated, studies on the use of DAP as a source for auxiliary data in forest inventories are yet few, but rapidly increasing. 2
In countries where survey programs are in place, which aim to collect aerial images for orthophoto generation at regular intervals, DAP allows inexpensive generation of 3D data over large areas. Together with its high spatial resolution DAP is therefore an ideal data source for large-area forest mapping using NFI sample plots as reference data for forest parameter modeling. However, since both data are acquired for different purposes, and DAP is still a relatively new data source in forestry applications, little is known about possibilities and accuracies when combining the DAP and NFI data for forest resource mapping over large areas.
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Objectives
This thesis addresses the synergistic integration of NFIs and forest resource mapping using 3D remote sensing. The main objective of the thesis was to assess the use of DAP combined with NFI data for mapping of forest resources. In particular, I wanted to (1) bring DAP into perspective with other 3D remote sensing techniques based on model accuracies for forest attribute prediction. A second aim (2) was to investigate the performance of DAP and NFI data in a semi-individual tree crown (semi-ITC) approach. Moreover, I aimed to (3) assess how the application on a large area influences the accuracy of forest attribute predictions with DAP, and how environment conditions such as terrain position and geographical location, and the conditions of the image acquisition affect the accuracy. Finally, (4) the development and validation of an operational, largearea forest resource map based on DAP should be described. The four scientific papers included in this thesis address these four objectives sequentially. The specific objectives of the individual papers are: Paper I The aim of our study was [. . . ] to compare four different 3D remote sensing data sets in the same study area. In particular, we wanted to quantify the accuracy of ALS, AP, InSAR, and radargrammetry for timber volume estimation. Additionally, we analyzed the influence of topography on the accuracy of the four methods. (Rahlf et al. 2014) Paper II The objective of this study was to apply semi-ITC on a very high resolution (15.6 points m-2 ) image-based point cloud to predict timber volume, stem density, basal area (G), and quadratic mean diameter (QMD). The performance of the semi-ITC approach will be compared with the ABA. (Rahlf et al. 2015)
Paper III The aim of our paper was to develop and assess an area-based timber volume prediction model for a large study area (24,473 km2 ) in Mid-Norway covering heterogeneous terrain and forest conditions using data derived from DAP
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combined with NFI data. DAP was based on imagery from different acquisition dates with changing conditions and was processed separately for the eastern and the western parts of the study area with different image matching settings. An additional aim was to clarify the effects of various factors describing terrain and acquisition conditions on the accuracy. (Rahlf et al. 2017) Paper IV The objective of this paper is threefold; to describe the development of the Norwegian forest resources map (SR16), to evaluate the generated forest information at local scales through comparison of the result to commercial FMIs, and finally to illustrate the gain in precision when using SR16 in addition to NFI sample plots for making estimates at the municipality and regional level. (Astrup et al. 2017)
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Usage of 3D remote sensing in forest inventory applications
3.1 3.1.1
3D remote sensing Measurement of vegetation heights
3D remote sensing provides information about distances of objects from the sensor. To derive 3D information, three general principals are used: measuring the time difference between a transmitted and received energy pulse, interferometry, or triangulation (Beraldin et al. 2010). While the former two are exclusively principals of active sensors, the latter can be applied to data from both active and passive sensors. In earth observation, 3D remote sensing aims to obtain the shape of the earth’s surface. In general two different surfaces can be distinguished: the surface with the highest elevation including objects and vegetation, and the terrain surface. The difference between these two surfaces represents the heights of the objects and vegetation. While not fully consistent in literature, digital representation of these surfaces are commonly referred to as digital elevation models (DEM), with digital surface models (DSM) describing the height of the surface including objects and vegetation, and digital terrain models (DTM) describing the height of the terrain (Li et al. 2004). A canopy height model (CHM) represents the heights of the objects and vegetation above the surface. This terminology is most commonly used for elevation data in raster and triangulated irregular network (TIN) format. Moreover, 3D information can be stored in point clouds, which allow irregular distances between the single height measurements. This format is useful for the storage of 3D data received from sensors with irregular measurement patterns, such as laser scanners (Beraldin et al. 2010). An important requirement for the extraction of vegetation heights from 3D remote sensing data is the availability of an accurate DTM. A remote sensing system, which can be used to produce highly detailed, accurate DTMs also under vegetation canopies is ALS. Despite its rather high costs, DTMs derived by ALS become increasingly available because of their high value for terrain and land cover analyses. For forestry applications the heights of the vegetation are the most important product of 3D remote sensing. Remotely sensed canopy heights are determined either by tree height, or by tree height and stand density in combination, which are highly correlated to many important forest parameters such as timber volume and biomass. Using allometric relationships, forest parameters can be derived directly from 3D remote sensing data by using remotely sensed canopy heights (e.g. Straub et al. 2009) or properties of delineated tree crowns (e.g. Villikka et al. 2007). However, standard approaches combine field 7
measurements with 3D remote sensing data, which allows fitting of empirical models to the forest parameters of interest.
3.1.2
Digital aerial photogrammetry
Stereo photogrammetry of aerial images is the oldest method to derive 3D information using airborne sensors. Already in the 19th century, photographs have been used in measuring buildings, terrestrial and balloon surveys. However, it took the development of stereoscopic measurement together with analogue stereo plotters, as well as aviation in the early 20th century to make stereo photogrammetry an effective tool in topographic mapping. Further improvements, which eventually lead to digital photogrammetry, were the introduction of computers into the process in the second half of the century, and the use of digital cameras which allow now complete automation (Kraus 2007, p.3ff). The principle of stereo photogrammetry is similar to human stereo vision. Instead of eyes, cameras are used to triangulate lines of sight to derive the relative position of an object. Images need to be taken from two or more positions and the interior and exterior orientation of the cameras has to be known or calculated. The object for which coordinates are to be derived must be located on all overlapping images. By constructing lines between the perspective centers of the cameras and the object, the coordinates of the object can be calculated from the images by triangulation (Kraus 2007, p.32ff). While in the past stereo measurements have been taken manually using analogue or digital stereo plotters, modern methods use automatic methods, i.e. image matching, for finding corresponding points between the images and allow stereo measurements of high density over many overlapping images. Image matching is now implemented in a range of photogrammetric processing software and available algorithms for image matching are plentiful, with each algorithm having specific strengths and weaknesses (Haala 2014). Even though forest canopies can be problematic for image matching algorithms because of occlusions, varying illumination, and shadows with little texture (Gruen 2012), high-quality DSMs of forests can be generated (Baltsavias et al. 2008). The first use of stereo photogrammetry in forestry was the estimation of parameters of standing trees from terrestrial photographs in the beginning of the 20th century (Müller 1931). The derivation of forest properties from aerial photographs with stereophotogrammetry has been investigated from the 1920s, with e.g. Hugershoff (1933) presenting a method using stand profiles and yield tables to estimate timber volume. Until the end of the century, aerial photographs became increasingly important in forest management inventories. In Norway, by the 1990s, the estimation of volume from aerial images using stereo plotters was a common method in stand-based inventories (Næsset 2014). After the introduction of fully digital aerial photogrammetry, Næsset (2002) pre8
sented a new method for forest parameter mapping from aerial images by applying the ABA to point clouds produced by DAP. While ALS has become popular in forestry due to high prediction accuracies of forest parameters and its ability to penetrate vegetation canopy, recent studies have shown that key forest parameters at stand level can be derived from DAP point clouds with comparable accuracy (Bohlin et al. 2012, Nurminen et al. 2013), given the availability of an accurate DTM. The use of DAP in forest inventories and forest monitoring has been investigated especially in the Nordic countries (Järnstedt et al. 2012, Breidenbach & Astrup 2012, Vastaranta et al. 2013, Gobakken et al. 2015), Canada (White et al. 2013, Pitt et al. 2014, White et al. 2015, St-Onge et al. 2015) and central Europe (Straub et al. 2013, Stepper et al. 2014b,a, Waser et al. 2015).
3.1.3
Airborne laser scanning
Laser scanning (or LiDAR, light detection and ranging) is an active 3D remote sensing technique, which measures the distance between the sensor and the reflections of emitted laser beams. The sensor records the time between emission of a light pulse and reception of its reflection to calculate the distance. Time can be measured either directly (timeof-flight measurement) or indirectly by modulating the phase of the emitted light, with amplitude and frequency modulation as the most common methods. Phase modulation allows the continuous emission of light resulting in higher measurement rate than with time-of-flight measurements. While phase modulation is also more accurate than timeof-flight measurement, it has a much shorter range of usually less than 100 m, which makes it unusable for airborne and spaceborne applications (Beraldin et al. 2010). Most commercial time-of-flight laser scanners for airborne applications capture discrete returns (or echoes), which represent peaks of the received energy. Such discrete-return ALS data sets are represented as point clouds with each return having a coordinate in 3D space and often additional data such as the intensity of the return and the scanning angle. Todays time-of-flight laser scanners record several returns per emitted pulse (Beraldin et al. 2010), and such multiple returns can occur when the light is reflected from more than one object in its path, which happens especially within vegetation. Full waveform laser scanners, on the other hand, report profiles of all the received energy for each pulse (Mallet & Bretar 2009). Since ALS is able to penetrate vegetation canopies, it can provide information on terrain below vegetation unlike any other remote sensing technique. ALS is therefore an important tool for topographic mapping, which is one of its primary applications. To obtain terrain heights from ALS data, many algorithms have been developed to identify ground returns (Meng et al. 2010), from which DTMs can be created.
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Over the last two decades ALS has become a popular method for forest analyses. While first studies using airborne profiling lasers were already conducted in the 1970s (e.g. Solodukhin et al. 1977), technical obstacles in positioning of the laser measurements had to be overcome. Only with the integration of inertial navigation systems and satellite positioning systems in the early 1990s was it possible to locate ALS returns with accuracies that made the development of operational scanners for topographic measurements possible (Næsset et al. 2004). First studies on the estimation of mean stand height and volume were conducted in Sweden (Nilsson 1996) and in Norway (Næsset 1997a,b). Building on the results of these initial studies, research on the use of 3D data in forest inventories focused mainly on ALS. Today ALS is used in operational inventories in the Nordic (McRoberts et al. 2010, Næsset 2014, Maltamo & Packalen 2014) and other countries (Næsset 2014).
3.1.4
SAR
Synthetic aperture radar is another remote sensing technique that allows the acquisition of 3D data. Among the processing methods to derive 3D information from satellite SAR are interferometric SAR (InSAR) and radargrammetry, which have been used to model key forest parameters such as height and biomass (Solberg et al. 2013, Solberg, Riegler & Nonin 2015). ith new satellite missions having 3D capabilities for forestry being planned or under consideration, including SAOCOM-CS, Tandem-L and BIOMASS (Le Toan et al. 2011), an increase in the use of space-borne InSAR for forestry applications can be expected. While airborne SAR systems have been used in forestry applications (Neeff et al. 2005, Perko et al. 2011), satellite SAR sensors receive increasingl attention due to their independence of sunlight and insensitivity to most weather conditions (Moreira et al. 2013). Main methods for the extraction of 3D information from satellite SAR are interferometry and radargrammetry, which have been both used in forest parameter estimation (Solberg et al. 2013, Askne & Santoro 2015, Soja et al. 2015b,a, Solberg, Riegler & Nonin 2015). Especially for forest carbon stock analyses in the tropics satellite SAR is a promising 3D remote sensing technique (Solberg, Gizachew, Næsset, Gobakken, Bollandsås, Mauya, Olsson, Malimbwi & Zahabu 2015, Næsset et al. 2015).
3.2
Merging remote sensing and forest inventory data
The method of merging field and 3D remote sensing is dependent on the spatial resolution of the data. Remote sensing data with spatial resolution similar to the sample plot size can be linked to the field measurements by e.g. assigning the value of the pixel closest to the sample plot center or averaging the values of cells intersecting with the sample plot. For fine resolution 3D data with many observations per sample plot, like 10
ALS or DAP data, two types of approaches have been used: the area based approach (ABA) and individual tree crown (ITC) approaches. For the ABA, all remotely sensed heights intersecting with each sample plot are extracted and height distribution metrics are calculated from all heights within each sample plot. Such metrics usually include basic distribution metrics such as minimum, mean, maximum, and variance of the heights, as well as height percentiles. To analyze and describe canopy density the proportion of points above or between certain heights are used. These metrics are then used as independent variables in statistical models fitted to the measured forest parameters. The application of an area-based model requires the gridding of the area into cells, for which all metrics used in the model fitting are computed. Subsequently, the fitted models are used to predict the forest parameters of interest for each grid cell creating a wall-to-wall map. The grid cells should be of similar size as the forest inventory sample plots, because the relationship between the measured properties and certain metrics is dependent on the size of the grid cells unless specific measures are taken (Magnussen et al. 2016). While most studies use rectangular grid cells, which allow an easy handling of the data, areas have also been segmented into hexagons, which resemble the shape of circular sample plots more closely (e.g. Breidenbach, Nothdurft & Kändler 2010, Stepper et al. 2014b). ITC approaches on the other hand aim on estimating properties of individual trees or tree crowns. Such approaches require field data with individually recorded, spatially registered tree measurements and need delineation of tree crowns from the remote sensing data using segmentation algorithms (e.g. Eysn et al. 2015, Vauhkonen et al. 2012, Solberg et al. 2006, Strîmbu & Strîmbu 2015). The methodology is similar to the ABA, but uses the delineated tree crown segments instead of sample plots and grid cells for calculation of metrics for modeling and prediction. Because segmentation errors result in errors of omission and commission of trees, ITC approaches are often biased when aggregated on larger spatial units, such as forest stands. Approaches that have been used to reduce the bias include the semi-individual tree crown approach (semi-ITC) (Breidenbach, Næsset, Lien, Gobakken & Solberg 2010), the combination of the ABA and the ITC approach (Maltamo et al. 2004), and the application of plot level corrections (Yu et al. 2010, Vastaranta et al. 2011). While ITC approaches might be intuitive since trees are a natural unit in forests and feature a higher spatial resolution than ABA, they do not necessarily produce estimates with higher accuracies (Breidenbach & Astrup 2014).
3.3
Forest resource maps and their use in forest inventories
Field surveys give highly accurate information on the measured trees but are expensive and therefore usually only acquired for a sample of the inventory area, from which the 11
properties of interest are estimated for the whole population. Remote sensing on the other hand measures properties of forests which are often less related to the parameters of interest, but is usually less expensive given the large area covered. Statistical models linking remote sensing data with properties measured at the sample plots allow the prediction of the properties of interest also in areas where only remote sensing data are available. The product of such predictions is a map of the forest properties of interest, covering the area wall-to-wall. Forest maps give an overview of the forest resources of an area and can therefore be used to support tactical planning of forest operations. Their main purpose, however, is the support of forest inventories, where forest maps are used as basis for estimates at stand level (McRoberts et al. 2014, Breidenbach et al. 2016, Magnussen & Breidenbach 2017). In the design phase of an forest inventory, available forest maps can be used to optimize the number and locations of field plots (Næsset 2014, McRoberts et al. 2014). However, remote sensing data covering the inventory area and a model relating the data to the response variable have to be available prior to the field campaign. Maltamo et al. (2011) showed that using a stratified sampling design the number of sample plots can be reduced without decreasing the accuracy of the linking model. Stratification, and the adjustment of sample size and plot size are methods to optimize field sampling according to the remote sensing data. After the field campaign post-stratification can be used to increase the precision of the estimate (McRoberts et al. 2012). The already measured sample plots are assigned to strata, which should be more homogeneous than the population as a whole. This approach is useful for forest inventories with a fixed design using equal probability sampling, as is often the case for NFIs. The model to create the map which serves as basis for the stratification can be fitted after the field campaign using the sample plot measurements as reference data. By weighting the within-strata measurements according to the strata sizes, estimates for the entire population, the whole area, can be derived, which should ideally be better than the unstratified estimated means and variances. Forest resource maps from remote sensing can also be used to improve field based estimates or to derive estimates for areas where no or too few sample plots are available. In general, two types of estimators have been used in forest inventories with auxiliary data from remote sensing: design-based and model-based estimators (McRoberts et al. 2014). Design-based estimators rely on probability samples for estimation and inference. Model-assisted estimators (Särndal et al. 1992) use models to improve the precision of estimates. One such design-based model-assisted estimator is the “survey regression” estimator (Rao 2003, p.136). It uses predictions to estimate the mean parameter of interest with a bias correction based on probability sampling, while the variance is estimated 12
from the residuals. Model-based estimators (e.g. Ståhl et al. 2016) rely more strongly on models than modelassisted estimators and are therefore suitable in areas where design-based estimation is not possible because no or too few sample plots are present. Additionally, because field measurements are only used to fit models using auxiliary data, probability sampling is not necessary. The resulting maps can be used to to estimate forest parameters in small areas, such as municipalities, estates, or even forest stands (Breidenbach et al. 2016, Magnussen & Breidenbach 2017). However, since no bias correction based on field data is included, model-based estimators require more careful modeling than model-assisted estimators (McRoberts et al. 2014).
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4 4.1
Material and methods Study areas
The study areas were located in south and central Norway (Figure 1). The boreal forests were dominated by Norway spruce (Picea abies (L.) Karst.) or pine (Pinus sylvestris L.). In varying amounts, birch (Betula spp.) and other broadleaved species were mixed in. For Paper I and II two study areas in southern Norway were selected: Lardal in Vestfold County and Odal in Hedmark County, which covered parts of the municipalities NordOdal, Sør-Odal, and Kongsvinger. The study areas for Paper III and IV were located in Trøndelag, central Norway. Trøndelag-Vest and Nord-Trøndelag were used in Paper III, Sør-Trøndelag in Paper IV. The biggest differences can be found between the two southern areas and the northern areas. The two southern areas were smaller than the Trøndelag study areas (TrøndelagVest and Nord-Trøndelag 24,473 km2 , total 49,880 km2 ) and featured mainly commercially managed forests besides mire and agricultural land. Additionally, though hilly, the southern areas did not show significant differences in terrain and altitude, while the study site in Trøndelag covered various terrain forms and altitudes between 0 and 1400 m above sea level.
4.2
Forest inventory data
An important part of the thesis was the use of NFI data. In Paper II, III, and IV data of the Norwegian NFI were used The sampling design and the field measurements of the Norwegian NFI are described in detail by Tomter et al. (2010) and in the NFI field manual (Landsskogtakseringen 2008). The sample plots of the Norwegian NFI are located in a 3 km × 3 km grid, except for mountain forests where the grid is 3 km × 9 km. The sample plots are remeasured every five years. Accurate positions of the sample plot centers were measured using differential GPS and GLONASS. In the NFI, a fixed sample plot radius of 8.92 m (250 m2 ) is used. On the plot a large range of variables is recorded, including tree, stand, and terrain properties as well as forest health and biodiversity indicators. Position relative to the plot center and diameter at breast height (dbh) are measured for every tree with dbh ≥ 5 cm. Using a Vertex hypsometer tree heights of all trees are measured on plots with ten or less trees, while on plots with more trees a sub-sample of approximately ten trees is selected using an adjustable basal area factor. The height of the remaining trees is estimated by 14
66°N
Nord−Trøndelag
64°N
Trøndelag−Vest
62°N
Sør−Trøndelag
60°N
Odal
56°N
58°N
Lardal
0°
5°E
10°E
15°E
20°E
25°E
Figure 1: Overview over the study areas used in this thesis. applying models calibrated with observations from the measured trees. Timber volume is derived using species-specific allometric models for spruce, pine, and birch (Vestjordet 1967, Braastad 1966, Brantseg 1967). For Paper I a standwise-clustered forest inventory was used, which was originally conducted for an earlier study (Breidenbach et al. 2016). Besides the differences in the sampling grid, the sample plots where measured according to the Norwegian NFI protocol (Tomter et al. 2010). Sample plot centers were selected by stratification. Forest stands were divided into two strata using a stand map of a privious FMI: Stands with an estimated volume > 150 m3 ha-1 and stands with a volume < 150 m3 ha-1 . 20 stands with sizes of 1–3 ha were randomly selected from each stratum. Only stands with a √ compactness of A/P > 0.2 were selected, with A as the area and P is the perimeter of the stand. The locations of the sample plot centers were set by creating a 20 m × 20 m grid within each stand and random selection of 7 nodes of the grid.
15
Table 1: Summary statistics of the ground measured timber volume for Paper I in Lardal (n=170). Min
Mean
Max
Std.dev
Spruce
0
153.40
596
129.50
Pine
0
13.37
267
35.80
Deciduous
0
19.68
199
33.93
Total
0
186.45
596
130.70
Table 2: Summary statistics of the ground measured timber volume for Paper II in Nord-Odal (n=40). Min
Mean
Max
Std.dev
Spruce
0.00
127.00
454.00
138.30
Pine
0.00
44.35
369.80
78.75
Deciduous 0.00
27.53
195.52
43.18
2.76 198.88
459.16
141.97
Total
Table 3: Summary statistics of the ground measured timber volume for Paper III in Nord-Trøndelag and Trøndelag-Vest (n=483). Min Mean
Max
Std.dev
Spruce
0
49.89
539.24
85.85
Pine
0
9.81
222.04
23.68
Deciduous
0
16.08
290.00
30.06
Total
0
75.78
577.08
92.90
16
4.3 4.3.1
Remote sensing data ALS data and DTM generation
ALS data were used for two different purposes in this thesis. In all studies, DTMs were created from ALS ground returns to extract vegetation heights from the 3D data, and, in Paper I, a timber volume model was fitted based on ALS data. The ALS data in this thesis were collected on behalf of public authorities for various purposes, such as terrain modeling and forest management inventories. For the study sites in Odal and Trøndelag (Paper II–IV) multiple ALS acquisitions from different years were merged. In Lardal (Paper I) a ALS point cloud from a single acquisition covered the whole study area. DTMs were generated from ALS ground returns, which were classified by the data vendor. DTM raster cell values were populated by averaging the ground returns’ heights within each cell. Missing cell values were interpolated from the neighbouring cells. DTM resolution was 1 m × 1 m for Paper I and 0.5 m × 0.5 m for Paper I–IV.
4.3.2
DAP data
The aerial images used in this thesis were acquired with the purpose of orthophoto generation. Acquisitions were part of a national survey program which aims on generating orthophotos at regular time intervals. Vendors, cameras and aircrafts were varying between the aquisitions. Point clouds from DAP in Paper I, II, and IV were based on a single acquisition. In Paper III–IV DAP data from separate acquisitions were used. Image overlap in Odal, Lardal, Nord-Trøndelag and Trønelag-Vest was 60% along-strip and 20% between-strip, in Sør-Trøndelag 80% and 20%, respectively. Characteristics of the image acquisitions are listed in Table 4. Image matching for the extraction of 3D information from the aerial images was conducted by external vendors. Point clouds were created using Trible Inpho’s Match-T software with the parameter settings “DSM_Mountainious” in Odal, “DSM_Mountainious” in Trøndelag Vest and Sør-Trøndelag and “DSM_Extreme” in Nord-Trøndelag. In Lardal the aerial images were processed to a DSM using BAE Socet Set software.
17
Table 4: Image acquisition characteristics. Number of images in Lardal was not available (NA). GSD, ground sampling distance. Site
Camera
Lardal
Vexcel UltraCam X
20
2007
NA
Odal
Vexcel UltraCam Eagle
10
2010
1024
Troøndelag-Vest
Vexcel UltraCam Eagle
25
2013
2402
Nord-Trøndelag (East)
Vexcel UltraCam Xp
35
2010
1548
Sør-Trøndelag
Vexcel UltraCam Xp
25
2014–2015
14057
4.3.3
GSD
Year No. of images
SAR data
Spaceborne SAR data was used to model timber volume in Paper I. Two sets of 3D data were obtained using different techiques, InSAR and radargrammetry. Three InSAR DSMs were created from three co-registered TanDEM-X StripMap pairs in single look complex format. The DSMs were combined using coherence as weight, since coherence is related to noise and accuracy. The radargrammetry data were processed using 3 TerraSAR-X StripMap image pairs taken in ascending and descending pass. From each of the image pairs a DSM was created using a SAR stereo-matching algorithm, which was developed by the commercial vendor providing the data. A single DSM was obtained by averaging. Errors and data gaps were removed by automated and manual editing of the DSM. Both DSMs had a grid cell size of 10 m × 10 m.
4.4
Computations of metrics
In all papers the ABA was applied as it is described in Section 3.2. From the ALS and DAP data following height metrics were derived: minimum, maximum, mean, coefficient of variation (in Paper I), standard deviation of the height (in Paper II and III), and a set of height percentiles. In Paper I and II, canopy density metrics were derived as proportions of points within vertical bins, which were created by dividing the distance between the minimum and maximum point height into ten equal parts (Næsset 2004). In Paper III the percentage of points above the mean height and above 2 m were used as density metrics. In addition to metrics based on point heights following color metrics were computed in Paper II and IV: minimum, maximum, mean, standard deviation and percentiles of each color band values stored in the point cloud, as well as the ratios of the mean band values divided by the sum of all mean band values.
18
Paper II includes a comparison of ABA with a semi-ITC approach (see Section 3.2). Tree crown objects were segmented using a watershed algorithm on a DAP CHM. For each segment the above described height and color metrics were computed. Geometric properties of the segments were also used as explanatory variables in the modeling.
4.5
Statistical analyses
Various types of statistical models, parametric and non-parametric, were used as linking models. Linear mixed effects models were used in Paper I to account for the hierarchical structure of the field inventory data. In Paper II, kNN models with k = 1 were fitted to multiple response variables (timber volume, basal area, quadratic mean diameter, stemdensity) and to a single response variable (timber volume). Additionally, a non-linear logistic regression model (McRoberts et al. 2012) was used. In Paper III simple linear regression models were fitted. Forest parameters were modeled using generalized and simple linear regression models. Due to the large amount of available variables, explanatory variables were selected using stepwise forward algorithms. In Paper I and III the quadratic terms of the variables were added to the pool of selectable variables to account for exponential trends in the data. The root mean square error (RMSE), relative RMSE and the coefficient of determination (R2 ) were used as goodness of fit measures.
4.6
Additional variables
In two papers the influence of additional factors on the forest parameter models was investigated. In Paper I slope and aspect were calculated based on the ALS DTM. To avoid averaging of terrain variables the DTM was resampled in such way, that each forest inventory sample plots was covered by one raster cell. In Paper III a more comprehensive analysis was conducted using terrain variables, geographic position, camera position of the closest aerial image, and solar position. Terrain variables were altitude, slope, aspect, and topographic position index. Additionally, slope, aspect, and topographic position index were calculated for the surrounding 100 m × 100 m. Geographic position was represented by latitude and longitude. To measure the influence of the camera position we calculated the relative viewing angle onto the plot, considering aspect and slope of the terrain (Figure 2). Solar elevation and azimuth described the sun position at the moment of the image acquisition. The solar incidence angle relative to the terrain incorporated sun position and terrain slope and aspect. The angular difference between the sun light direction and the viewing direction was used to measure the influence of visible shadows in the canopy. 19
al
n tio re c di y ra n
rm
no
su
viewin g dire ction
in rra te
VSdiff
relVA relSOLINC
Figure 2: Visualization of the variables relative viewing angle of the camera (relVA), relative sun incidence angle (relSOLINC), and angular difference between the sun light direction and the viewing direction (VSdiff).
4.7
Operationalizing large area forest mapping
The development and and evaluation of an operational, large-area forest resource map were described in Paper IV. For the modeling of forest parameters timber volume, biomass, and Lorey’s height some of the methods used in Paper I to III were applied to a large DAP dataset covering Nord-Trøndelag, Trøndelag-Vest and Sør-Trøndelag. Additionally, tree species were modeled using a multinomial logistic model. NFI plots with a dominant species, i.e. where one species group had a proportion of more than 75% of the volume, were used as training data. Beside DAP height metrics also color metrics, elevation and terrain wetness index (TWI), as well as variables from a highly detailed land resource map were used as explanatory variables. Subsequently, the developed models were used to create a wall-to-wall covering forest map. The application of the models followed the description in Section 3.2. For the validation of the forest map four existing commercial FMI projects from 2015 and 2016 with a total of 27,740 stands were selected. For each stand, timber volume predictions were extracted and totaled, and compared to the the ALS predictions of the FMI.
20
Furthermore, an existing forest mask was updated using object based image classification on height and color metrics derived from the DAP point clouds. The forest mask could be validated using NFI sample plots, because they were not used in the creation of the mask. The main challenges in creating such a large forest resource map were the handling of large data volumes as well as the combination of the various data sources. However, parallel, tile-wise processing of the point clouds and the use of spatial databases minimized the processing time and difficulties.
21
22
5 5.1
Results and Discussion Comparing DAP and other 3D remote sensing methods (Paper I)
We ranked four 3D remote sensing techniques based on the RMSEs of timber volume linking models. At plot level, the ALS model showed the highest accuracy, followed by DAP, InSAR and Radargrammetry (Table 5). The difference between the data sets is visualized in Figure 3. The aggregation of the predictions on stand-level reduced the RMSE of all data sets. DAP however was influenced by an outlier, which remained unexplainable. Stand level RMSEs of the models omitting the outlier were 12% for ALS, 13% for DAP, 19% for InSAR, and 25% for radargrammetry, reducing the difference between the ALS and DAP model RMSE to 1% of the mean observed timber volume.
20
Cross Section Sample Plot ●
● ●
● ●
15 10 5
height [m]
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●
●●
●● ● ●● ● ●● ● ● ● ●● ● ● ● ●● ●● ● ● ● ●● ● ●● ●● ●●● ●● ●
●
●
● ● ●
0
●
0
ALS AP InSAR Radargrammetry ●●
●
● ● ● ●● ● ● ● ● ● ● ●● ● ●● ● ●● ●● ● ● ●● ● ● ● ●● ●●● ● ●● ●●●●● ● ● ● ●● ● ● ● ● ● ● ●●● ●●● ● ●●● ● ● ●●● ● ● ●● ●● ● ● ● ● ● ●● ●● ● ●●● ● ● ● ●● ●●●● ●●● ● ● ●● ● ● ● ● ●●●●
● ● ●
● ● ●
●
● ● ● ● ● ● ●● ● ● ●● ● ●● ● ●●●●●●● ●●● ●● ● ● ● ●● ● ● ● ●● ●● ● ● ●● ●● ● ● ● ● ● ●● ● ●● ●●● ● ● ●● ● ● ● ●●● ● ●● ● ● ●● ●●● ● ●● ●● ● ● ● ●● ● ● ●●● ● ●●● ● ● ●● ● ●● ●● ●●●● ● ●● ● ● ●●● ● ●● ● ●● ● ●● ● ● ●● ● ● ●● ● ● ● ●●● ● ● ● ●●●● ●● ●● ●●● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ●● ● ●● ●● ● ●●●● ●● ● ●● ● ●● ● ● ● ● ● ● ●● ●● ● ●● ● ● ● ●● ● ● ●
5
10
15
20
cross section length [m]
Figure 3: Cross section through a sample plot with vegetation height measurements of the four data sets. All models at stand level had good model fits, which shows the strong relationship between remotely sensed vegetation heights and forest parameters. The differences between the different remote sensing techniques are not surprising and have been reported earlier, however for the first time these techniques were compared on the same study site, making the differences independent of study design and varying site conditions. A similar study, which was conducted later on a study site in southern Finland, ranked 23
the techniques in the same order (Yu et al. 2015). Table 5: LOSOCV RMSEs of the timber volume prediction. RMSE (%) is calculated as the percentage of the mean observed timber volume. Remote sensing data set
Plot-level RMSE (%)
Stand-level RMSE (%)
ALS
19.4
12.4
DAP
31.4
18.1
InSAR
41.0
18.1
Radargrammetry
44.4
23.3
The differences between the DAP and ALS models on stand level is in accordance to the findings by Bohlin et al. (2012) and Nurminen et al. (2013). Timber volume estimates based on DAP have comparable accuracy to estimates based on ALS. Models based on the space-borne SAR data showed lower accuracy, which might mainly be caused by their lower spatial resolution.
5.2
Semi-ITC with DAP (Paper II)
We compared a semi-ITC approach to an area based approach for timber volume mapping. When aggregated on plot level, timber volume predictions using semi-ITC had RMSEs and systematic errors similar to the ABA model. Multivariate kNN models were slightly more accurate with semi-ITC than with ABA, but had larger systematic errors (Table 6). At segment level the multivariate kNN model of the semi-ITC approach had RMSEs of 175% of the mean observed timber volume, 149% of the mean observed stem density, 160% of the mean observed basal area, and 156% of the mean observed quadratic mean diameter. Despite these rather low accuracies, a comparison to null-models with only the mean observed values as intercept showed that semi-ITC is beneficial for the prediction of certain parameters at segment level. The segment level results also show that the combination of DAP and NFI data is suitable for tree level analyses. They indicated that both the position of the measured trees is sufficiently accurate in the NFI data, and that the canopy representation from DAP makes segmentation of trees crown possible.
24
Table 6: RMSEs and systematic errors of the model predictions in percent of the mean observed values. V, timber volume. D, stem-density. G, basal area. QMD, quadratic mean diameter. Model
Approach
V
D
RMSE
sys.err
RMSE
G sys.err RMSE
QMD sys.err
RMSE sys.err
multivariate kNN
semi-ITC
30
15
46
11
25
12
26
6
multivariate kNN
ABA
30
-3
51
-2
26
-3
35
-1
univariate kNN
semi-ITC
25
5
univariate kNN
ABA
22
2
logistic regression ABA
23
0
5.3
Large-area application (Paper III)
The application of DAP for large-area forest resource mapping was investigated by modeling timber volume based on reference data from NFI sample plots. The model had a RMSE of 55% of the mean observed timber volume and a R2 of 0.80. However, the removal of a single outlier would improve the model fit, resulting in a RMSE of 45% and a R2 of 0.87. The outlier could not be detected by analyzing the explanatory variables, and its removal could therefore not be justified. The obtained accuracy was lower than reported for earlier studies conducted on smaller study areas (e.g. Rahlf et al. 2014, Puliti et al. 2016). Two factors might be responsible for the lower relative accuracy: The heterogeneity of the study area and the low mean timber volume in the region. Since the relative RMSE is calculated in percent of the mean observed timber volume, a lower mean value causes higher relative RMSEs. The R2 is similar or better than reported by earlier studies. We then tested the influence of various terrain and image acquisition variables on the residuals of the timber volume model by including them in the model. The only variable which improved the model accuracy by more than one percentage point was the sun inclination relative to the terrain, which describes terrain normalized illumination at the moment of image acquisition.
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5.4
Operationalizing the use of DAP in an NFI context (Paper IV)
The use of DAP data in a large-area operational application mapping forest resources was analyzed. The forest parameters timber volume, biomass were modeled using generalized linear models, Lorey’s height using simple linear regression. The biomass and volume models had RMSEs around 50% of the mean observed values and explained about 70% of the variance. The relatively high RMSEs can be explained by low volume and biomass levels, as discussed in Paper III. Models for Lorey’s height had RMSEs of around 20% and explained 70% of the variation. Tree species were classified using multinomial logistic models. For the assessment of the classification accuracy predictions were compared to NFI classifications. Leave-one-out cross validation was applied to all sample plots used in the model fitting. The accuracy was 67% with a kappa of 0.47. This low accuracy shows the challenges of tree species classification using remote sensing data. The values, however, are not much lower than reported by studies dedicated to tree species classification (e.g. Puliti et al. 2016, Korpela et al. 2014). The updated forest mask was validated using NFI sample plots. The classification showed a high accuracy of 0.89 and a kappa of 0.77 in the confer-dominated, productive lowlands, and an accuracy of 0.95 and a Kappa of 0.63 in the birch-dominated, lowproductive mountain areas. Misclassifications were compared with a second land use classification in the NFI data, which showed that the majority of the plots that was misclassified as forest was other wooded land. The remaining misclassified plots where composed of other land use categories with some tree cover such as grasslands.
26
6
Conclusions and Perspectives
6.1
Conclusions
In this thesis the use of 3D information from DAP in combination with NFI data for forest resource mapping was analyzed. In Paper I–III different aspects of resource mapping based on DAP were investigated: the accuracy of forest parameter models based on DAP compared to other 3D remote sensing techniques, the mapping approach, and the application on a large area. Across the three papers different statistical models for forest parameter prediction were tested, it was analyzed if the use of additional variables describing terrain, image acquisition conditions, and illumination improved model accuracies. Additionally, the suitability of the Norwegian NFI data for forest parameter modeling were investigated. The conclusions which can be drawn from Paper I–III are: • Forest parameter predictions using DAP data are less accurate than predictions using ALS data, but more accurate than predictions based on satellite SAR data. • A semi-ITC approach increases resolution and allows prediction at plot level with similar accuracy as with an ABA. However, the complex and time consuming processing makes semi-ITC currently less attractive. • Forest parameter models based on DAP are stable over varying terrain, illumination, and acquisition conditions, which are properties of large area applications. Model fits could not be substantially improved by introducing additional variables. Only the sun incidence angle relative to the terrain slightly increased the accuracy of a timber volume model. • The choice of the statistical modeling approach seems not to have a substantial influence on the accuracy when predicting forest parameters using DAP. Good model fits were obtained using both parametric and non-parametric models. • The Norwegian NFI provides data which is well suited for model calibration. Tree positions are accurate enough to use NFI data in single tree analyses. In Paper IV these findings were used in the development of an operational forest resource map. The mapped parameters were evaluated using data from commercial FMIs. The final conclusions of this thesis are based to a great extent on the findings of Paper IV. • While not as accurate as models based on ALS, models based on 3D information from DAP show strong relationships and good predictive ability. It has been shown, that 3D information from DAP can be used to map various forest parameters, as well as forest area itself. 27
• Combining DAP and NFI data allows the estimation of forest parameters at small scales and improves estimates at larger scales. Stand level estimates of large mapping applications might be sufficiently accurate to be used in forest management planning or in the design of forest management inventories.
6.2
Future perspectives
Forest canopies present difficult surfaces for image matching. Especially solitary trees and open forests show high error rates. Improvement of matching algorithms in these areas might therefore help to decrease errors in forest parameter models. Additionally, the influence of interpolation and smoothing of height measurements, which are inherent to commonly used photogrammetric software packages, has to be analysed. Both 3D data obtained from aerial images and the spectral information of the images have been used in forest analyses. However, combining these two different data might increase prediction potentials of aerial photogrammetry. The influence of the method of assignment of colors to the point cloud has to be investigated together with the possibility to use colors of two or more aerial images to create multiangle spectral information. Another source of spectral information could be satellite imagery which can provide radiometrically coherent color information over large areas. Fusing satellite imagery with 3D information from DAP might improve model accuracies, especially if the parameter of interest is less related to vegetation height, such as tree species. Single tree segmentation from DAP data has been investigated by only few studies. While many algorithms used with ALS data can be adopted to delineate trees in DAP data, an algorithm specifically designed for DAP data might be necessary to fully utilize the potential of DAP. Spectral information from the aerial images might again be useful for this application. The variability in airborne spectral data might, however, cause problems for large area applications. Especially in operational applications, where, beside photogrammetric data, a range of different data sources are available in different spatial extents, data assimilation could be used to combine all data in a consistent way. Data assimilation would also allow the integration of aerial imagery from repeated acquisitions.
28
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PAPER I
Remote Sensing of Environment 155 (2014) 325–333
Contents lists available at ScienceDirect
Remote Sensing of Environment journal homepage: www.elsevier.com/locate/rse
Comparison of four types of 3D data for timber volume estimation Johannes Rahlf a,⁎, Johannes Breidenbach a, Svein Solberg a, Erik Næsset b, Rasmus Astrup a a b
Norwegian Forest and Landscape Institute, National Forest Inventory, P.O. Box 115, NO-1431 Ås, Norway Norwegian University of Life Sciences, Department of Ecology and Natural Resource Management, P.O. Box 5003, NO-1432 Ås, Norway
a r t i c l e
i n f o
Article history: Received 10 February 2014 Received in revised form 27 August 2014 Accepted 30 August 2014 Available online 27 September 2014 Keywords: Forest inventory Timber volume Airborne laser scanning Digital aerial photographs Digital photogrammetry TanDEM-X TerraSAR-X Radargrammetry Mixed effects models
a b s t r a c t The study compares the accuracy of timber volume prediction based on four different three-dimensional remote sensing data sets in one study area in southern Norway: airborne laser scanning (ALS), stereo aerial photogrammetry (AP), satellite interferometric synthetic aperture radar (InSAR) based on the TanDEM-X mission, and satellite radargrammetry based on the TerraSAR-X mission. We fitted linear mixed effects models with vegetation height and density metrics obtained from the remote sensing data sets as explanatory variables. The crossvalidated root mean squared error (RMSE) relative to the observed mean was used as the measure of goodness-of-fit. ALS provided the most accurate prediction at plot level with RMSE = 19%, followed by AP (31%), InSAR (42%), and radargrammetry (44%). At stand level the methods' performances were equally ordered, with RMSE values of 12–23%. Including the variables terrain slope and aspect in the models improved the accuracy of AP, InSAR, and radargrammetry slightly. © 2014 Elsevier Inc. All rights reserved.
1. Introduction Remote sensing data are often used for forest parameter prediction or to provide wall-to-wall information (mapping). In this way remote sensing can provide useful information for forest inventories. Common fields of application are stratification and small area estimation where remote sensing data serve as auxiliary variables to improve the precision of estimates. Particularly three-dimensional (3D) remote sensing data contain useful information for forest inventories. Canopy height measurements obtained by remote sensing show a strong correlation with the product of height and density of vegetation, which is proportional to important forest characteristics such as biomass and timber volume (Treuhaft & Siqueira, 2000). Especially airborne laser scanning (ALS) has been in the focus of research for the last two decades and is used today in operational forest inventories (e.g., Maltamo & Packalen, 2014; McRoberts, Tomppo, & Næsset, 2010; Næsset, 2014; Næsset et al., 2004). Besides measuring the surface elevation, a sufficient portion of the ALS beams penetrates the canopy and provides measurements taken from the forest floor. Such echoes can be used to create a digital terrain model (DTM), which is needed to calculate the measurements' height above ground. Due to large mapping campaigns in recent years, the coverage with ⁎ Corresponding author. E-mail address:
[email protected] (J. Rahlf).
http://dx.doi.org/10.1016/j.rse.2014.08.036 0034-4257/© 2014 Elsevier Inc. All rights reserved.
accurate DTMs has increased in many countries. These accurate DTMs are used to derive the height above ground of forest canopies from other 3D remote sensing data. Stereo aerial photogrammetry (AP) is a technique to derive 3D information from overlapping aerial photographs taken from different positions. While AP has been used in forestry for several decades (e.g., Hugershoff, 1933), recent developments in image matching and computing power have led to its renaissance in forest inventory research. Photogrammetry with a fully digital, automated work flow is also known as 3D vision (Leberl et al., 2010). Early studies applying 3D vision showed the suitability of AP data for forest parameter prediction (Næsset, 2002a; Schardt, Hruby, Hirschmugl, Wack, & Franke, 2004). Järnstedt et al. (2012) found that AP has a great potential for estimating and updating forest information, when comparing AP and ALS for their ability to estimate different forest parameters in Finland. In southern Germany, Straub, Stepper, Seitz, and Waser (2013) estimated plot-level attributes from AP data in mixed species forest and identified improvements by stratified estimation. Bohlin, Wallerman, and Fransson (2012) and Nurminen, Karjalainen, Yu, Hyyppä, and Honkavaara (2013) achieved similar accuracies with AP as with ALS-based methods for test sites in Sweden and Finland, respectively. AP data as well as fused AP and ALS data have been used for small area estimation by Breidenbach and Astrup (2012) and Steinmann, Mandallaz, Ginzler, and Lanz (2013). Synthetic aperture radar (SAR) is another prominent remote sensing technique that can provide 3D data. Four methods to generate 3D data from SAR exist (Toutin & Gray, 2000): interferometry (InSAR),
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radargrammetry, clinometry, and polarimetry. Whereas airborne systems often have a higher spatial resolution, satellite systems can cover larger areas. Forest parameters have been successfully predicted and estimated with both airborne SAR systems (Neeff, Dutra, dos Santos, da Costa Freitas, & Araujo, 2005; Perko, Raggam, Deutscher, Gutjahr, & Schardt, 2011) and spaceborne SAR systems (Næsset et al., 2011; Solberg, Astrup, Gobakken, Næsset, & Weydahl, 2010). The satellite SAR mission TanDEM-X (Krieger et al., 2007) acquires single-pass SAR image pairs, which allow DSM generation based on interferometry. The TerraSAR-X mission (Buckreuss, Balzer, Muhlbauer, Werninghaus, & Pitz, 2003) acquires repeat-pass pairs for digital surface model (DSM) generation using radargrammetry. Data from the TanDEM-X and TerraSAR-X missions have produced promising results for estimating volume and biomass (Solberg, Astrup, Breidenbach, Nilsen, & Weydahl, 2013, Solberg, Riegler, & Nonin, 2015). Solberg et al. (2013) found a linear relationship between InSAR height and both biomass and timber volume that allows change estimation without the availability of a DTM. The accuracy of 3D remote sensing is affected by topography. Earlier studies have found that terrain can influence elevation measurements from ALS (Estornell, Ruiz, Velázquez-Martí, & Hermosilla, 2011; Hodgson & Bresnahan, 2004). Honkavaara, Markelin, Rosnell, and Nurminen (2012) observed larger AP height errors in shaded areas and on forest canopy surfaces with low solar angle. Such errors occur more often on slopes facing away from the sun. As a principally sidelooking system, SAR is especially influenced by slope and aspect (Breidenbach, Koch, et al., 2008; Toutin, 2002). Most studies that have explored 3D remote sensing for forest parameter prediction have analyzed data from one acquisition system. However, in survey planning it is crucial to know about the differences between potential prediction accuracies of remote sensing data. Only with comparable numbers is it possible to find costefficient combinations of auxiliary data under the given forest conditions. Previous studies that have compared three or more remote sensing data sets are few in number (e.g. Hyyppä et al., 2000). Moreover, a comparison between different studies is complicated because study design, forest structure, and other factors influence the results. The aim of our study was therefore to compare four different 3D remote sensing data sets that have the potential of being used in forest inventories in the same study area. In particular, we wanted to quantify the accuracy of ALS, AP, InSAR, and radargrammetry for timber volume estimation. Additionally, we analyzed the influence of topography on the accuracy of the four methods. 2. Material 2.1. Study area and field data The study area was in Lardal, a municipality in Vestfold County, located in southern Norway on the west side of the Oslofjord (central coordinates: 59.4° North, 9.9° East). The forested area is dominated by Norway spruce (Picea abies (L.) Karst.) but also includes stands dominated by Scots pine (Pinus sylvestris L.) and broad-leaved tree species (mainly Betula spp.; scattered Sorbus aucuparia, Populus tremula, and Alnus incana). The terrain is hilly with altitudes ranging from 50 to 650 m a.s.l. (Fig. 1). Field data were collected in 2011. From a forest stand map we divided stands into two strata: Stands with a volume N150 m3 ha− 1 and stands with a volume b 150 m3 ha−1. From each of these strata, 20 stands were randomly selected, each of which was 1–3 ha in size. To make the identification of the stands during fieldwork easier only compact stands were considered in the selection. The compactness criterion was pffiffiffi A=PN0:2 ð1Þ
where A is the area and P is the perimeter of the stand. Within each of the selected stands we constructed a 20 m × 20 m grid from which we randomly selected 7 nodes. At these nodes we set the center points of the inventory plots. Only the inventory plots covered by all remote sensing data sets were considered. This resulted in a total of 170 plots located in 25 stands. The spatial distribution of the stands within the study area is shown in Fig. 1b. The plots were located on slopes of 1–30° with a mean of 9° evenly distributed on all aspects. All field measurements were taken in accordance with the Norwegian National Forest Inventory protocol (Tomter, Hylen, & Nilsen, 2010). The circular sample plots had an area of 250 m2. Diameter at breast height (DBH) and species were recorded for all trees with a DBH N 5 cm. Tree height was measured for a sample of 10 trees per plot. The heights of the remaining trees were estimated using diameter–height models for each plot (Landsskogtakseringen, 2008). Tree stem volumes including bark were estimated using standard models for spruce, pine, and birch (Braastad, 1966; Brantseg, 1967; Vestjordet, 1967). Plot-level stem volume (m3 ha−1) was obtained by aggregating the single-stem volume estimates. Stand-level stem volume was calculated as the mean volume of the sample plots within the stands. Table 1 lists descriptive statistics for the response variable timber volume. The model-related uncertainties of the volume estimates for the individual plots were assumed to be negligible compared to the between-plot variability and were thus ignored. To ensure an accurate plot location, the center coordinate of all sample plots was measured using a survey-grade differential global positioning system receiver. Related studies have been conducted in the study area. Korhonen, Kaartinen, Kukko, Solberg, and Astrup (2010) and Breidenbach and Astrup (2014) used the same ALS data, Breidenbach and Astrup (2012) the same AP data, Solberg et al. (2015) the same radargrammetry data, Solberg et al. (2013) a subset of the present InSAR data, and Solberg et al. (2013, 2015) field data from the same forest inventory with a focus on spruce-dominated stands.
2.2. ALS ALS data were acquired in May 2009 by Blom Geomatics AS, Norway, for the Norwegian Mapping Authority, using two different Optech ALTM Gemini laser scanners mounted on a fixed-wing aircraft. The average flying height was 690 m above ground at an average speed of 80 m s−1. The footprint diameter was 13 cm. The resulting data had an average density of approximately 10 pulses per m2. The vendor delivered a point cloud containing first, intermediate, and last echoes that were classified as either ground or non-ground echoes. From the classified ground echoes we created a DTM with a grid cell size of 1 m × 1 m by averaging the height values within each cell using FUSION software (McGaughey, 2013). The DTM was used in all following processing tasks that required ground information, except for the AP data processing.
2.3. AP Aerial images were acquired in summer 2007 by TerraTec AS, Norway, with a Vexcel UltracamX digital camera. The images had a pan-sharpened ground sampling distance of 20 cm. The within-strip overlap was 60% and the side overlap was 20%. Blom Geomatics AS, Norway, created a DSM with 20 cm × 20 cm grid cell size from the images using SocetSet version 5.5.0 software (BAE Systems) with the NGATE image matching algorithm. A canopy height model (CHM) was created by subtracting a DTM with 1 m × 1 m grid cell size obtained from ALS data derived by the data provider. The CHM was delivered as a raster layer with a grid cell size of 0.2 m × 0.2 m and a vertical resolution of 0.1 m. All negative values in the raster were set to 0. The data have been described in detail by Breidenbach and Astrup (2012).
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a
327
b Fig. 1. Overview of the study area (a); terrain and locations of the stands (b).
2.4. InSAR Three co-registered TanDEM-X StripMap pairs in single look complex format from summer 2011 were used to create the InSAR DSM. Properties of the acquisitions are listed in Table 2. The look direction was always to the right, so that the ascending acquisitions were obtained from a western position relative to the study area and the descending acquisitions from an eastern position. The SARscape 5.0 module of ENVI 5.0 software was used to process the SAR images into DSMs. Using the ALS DTM, differential interferograms were created for every image pair, representing the phase differences caused by vegetation height. After removing random errors with a Boxcar adaptive filter, offset and ramp errors were removed using 30 ground control points. Phase unwrapping was carried out with a ‘region growing’ method (Reigber & Moreira, 1997). Finally, we converted the unwrapped phases into geocoded DSMs. A CHM was created by subtracting the ALS DTM. Local coherence γ was calculated within 3 pixel × 3 pixel windows. Since coherence is related to noise and accuracy, it was used as weighting factor in averaging the three CHMs: CHM mean ¼ ðγ 1 CHM 1 þ γ 2 CHM2 þ γ3 CHM3 Þ=ðγ 1 þ γ 2 þ γ 3 Þ
ð2Þ
Table 1 Summary of field data for the 170 field plots (m3 ha−1). Variable
Total volume Spruce volume Pine volume Broad-leaved species volume
Plot level
where CHMmean is the height of the combined CHMs; CHM1, CHM2, and CHM3 are the CHM heights derived from the three TanDEM-X data sets; and γ1, γ2, and γ3 are the corresponding coherence values. The InSARCHM had a grid cell size of 10 m × 10 m. 2.5. Radargrammetry Six TerraSAR-X StripMap images were acquired over the study area in May 2011. Four of the images were taken in an ascending pass and two in a descending pass (Table 3). The look direction of the sensor was always toward right, so that the images were taken from a western and eastern point of view during ascending and descending passes, respectively. The images were grouped into three stereo pairs with intersection angles of 16°, 15°, and 21°, respectively. We used 3 pairs of images for both InSAR and radargrammetry, in order to make the performance of the two technologies comparable. Each of the TerraSAR-X stereo pairs was processed into a radargrammetry DSM using a SAR stereo-matching algorithm developed by the vendor, EADS Astrium (Solberg et al., 2015). The three DSMs were merged to a single DSM by averaging. This step reduced random errors and errors from shadowing, foreshortening, and layover. Small voids (up to 8 pixels) were filled by mean value interpolation using the 8 neighboring pixels. Table 2 Characteristics of the TanDEM-X acquisitions for InSAR.
Stand level
Mean
Std.dev
Maximum
Mean
Std.dev
Maximum
186.45 153.40 13.37 19.68
130.70 129.50 35.80 33.93
596.00 596.00 267.00 199.00
185.18 151.78 13.83 19.58
105.64 101.87 24.70 19.21
364.71 338.71 80.00 67.86
Acquisition date
Passa
23 July 2011 05 Sept 2011 01 Sept 2011
Asc Asc Desc
a
Incidence angle
Normal baseline
Height of ambiguity
(°)
(m)
(m)
36 36 43
251 238 59
23 24 122
Asc = ascending pass, Desc = descending pass.
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Table 3 Characteristics of the TerraSAR-X acquisitions for radargrammetry. Pair
Acquisition date
Passa
Incidence angle (°)
1 1 2 2 3 3
07 May 2011 06 May 2011 18 May 2011 17 May 2011 14 May 2011 13 May 2011
Asc Asc Asc Asc Desc Desc
35 52 37 53 44 21
a
Asc = ascending pass, Desc = descending pass
Single pixels with a height difference of ±20 m compared to the surrounding pixels were automatically detected and removed. Approximately 100 linear artifacts that occurred at the scene edges were manually corrected. The DSM had a grid cell size of 10 m × 10 m and a vertical resolution of 1 m. A CHM was created by subtracting the ALS DTM. 3. Methods 3.1. Computation of explanatory variables 3.1.1. ALS and AP To acquire height above ground (m) for the ALS data we subtracted the corresponding terrain height of the ALS DTM from the heights of the ALS echoes. The AP data were already delivered as heights above ground (m) by the vendor, who used an ALS-derived DTM (Breidenbach & Astrup, 2012). From these data we derived metrics describing the height distribution of each sample plot. The selection of metrics followed Næsset (2004), with the exception that also echoes with height b 2 m were considered in the calculation. No other height limit was applied to select echoes for the calculation of metrics. 9 different metrics were calculated: height percentiles for 10%, 50%, and 90% (denoted p10, p50, p90, respectively); maximum, mean, and coefficient of variation (hmax, hmean, hCV); and canopy density metrics, which were created by dividing the height between minimum and maximum height by 10 and calculating the proportion of echoes above the vertical parts #1, #5, and #9 (d1, d5, d9). From the ALS data, the above-described metrics were computed separately from three echo categories: all echoes, first and single echoes, and last echoes. This resulted in a total of 27 metrics for ALS and 9 metrics for AP. For ALS we used the notation p10 a, p50 a, p90 a, hmax a, hmean a, hCV a, d1 a, d50 a, d9 a; p10 f, p50 f, p90 f, hmax f, hmean f, hCV f, d1 f, d5 f, d9 f; p10 l, p50 l, p90 l, hmax l, hmean l, hCV l, d1 l, d5 l, d9 l, where a = metrics derived from all echoes, f = metrics derived from first and single echoes, and l = metrics derived from last echoes. 3.1.2. InSAR and radargrammetry From the InSAR and radargrammetric CHMs, mean heights (m) were calculated for use as explanatory variables in the models. For each plot, intersecting pixels of the CHM were weighted by their intersection area: hmean ¼ ðh1 a1 þ h2 a2 þ … þ hi ai Þ=ða1 þ a2 þ … þ ai Þ
ð3Þ
where hi is the height of the ith pixel covering a sample plot and ai is the intersection area of that pixel. A maximum of i = 9 pixels could cover a sample plot.
For ALS and AP data we identified relevant fixed effects using a stepwise forward variable selection algorithm minimizing the Bayesian information criterion (BIC). In addition to the derived metrics, their quadratic terms were added to the pool of candidate explanatory variables to allow potential nonlinearities in the data. Subsequently, the importance of the selected variables was analyzed in a backward elimination based on the cross-validated root mean squared error at plot level (RMSEplot, see (Eq. 5)). If the removal of a variable improved the RMSE, the variable was omitted from the final model. The resulting models were formulated as yij ¼ β0 þ bi þ β1 xij1 þ β2 xij2 þ … þ βk xijk þ ε ij 2 2 2δ ε ij ∼N 0; σ ε υij i ¼ 1; …; m j ¼ 1; …; ni bi ∼N 0; σ b
ð4Þ
where yij is the observed volume of the jth sample plot in the ith stand, xij1, …, xijk are the k fixed effects, β0, …, βk are the fixed parameters, ni is the number of sample plots within stand i, and m is the number of forest stands. We assumed that the stand-level random effects bi were independent of the plot-level residuals εij. The variance in the random effect is denoted σ2b . σ2ε υ2δ ij is the variance function to model the heteroscedasticity in the residual errors with δ as the variance parameter and the metric hmean a or hmean, respectively, as the variance covariate υ. Similarly, linear mixed effects models were fitted for the InSAR and radargrammetry data sets. The explanatory variable in the models was the hmean of the InSAR and radargrammetric CHM. It was analyzed if the addition of the quadratic term h2mean reduced the cross-validated plot-level RMSE. The models for the SAR data were in accordance with Eq. (4). For all statistical computations we used the R software for statistical computing (R Core Team, 2013), expanded with the package nlme (Pinheiro, Bates, DebRoy, Sarkar, & R Core Team, 2013) for mixed effects modeling. Following Breidenbach, Koch, et al. (2008), who observed spatial dependencies between sample plot residuals, we investigated within-stand spatial autocorrelation by visual analysis of variograms of the model residuals implemented in the nlme package. We calculated the RMSE at plot level by leave-one-stand-out crossvalidation (LOSOCV):
RMSEplot
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u ni m X 2 X u 1 ¼ tXm yij −e yij n i¼1 i i¼1 j¼1
ð5Þ
where e yij is the predicted timber volume, using the fixed effects of the model Eq. (4), at plot j when omitting all plots in stand i for the model fit. To compare the accuracy of the remote sensing methods at stand level, we aggregated the plot-level observations and LOSOCV predictions within each stand. Aggregation of field plots has the advantage that stand-level field observations are available rather than estimates. The disadvantage is that the stands only consist of the area covered by 5–7 sample plots and are therefore rather small. Eq. (6) was used to compute the RMSE of the mean volume estimates at stand level.
RMSEstand
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 1ffi u u X ni m X 2 u1 @1 ¼t y −e yij A m i¼1 ni j¼1 ij
ð6Þ
3.2. Modeling Linear mixed effects models were fitted to each of the four remote sensing data sets. Plot-level timber volume was the response variable and the metrics derived from the remote sensing data served as candidate explanatory variables. To account for the hierarchical field sample design we introduced a random intercept at stand level. Heteroscedasticity was handled by introducing a variance function based on a mean-height metric (ALS: hmean a; AP, InSAR, radargrammetry: hmean).
Subsequently, the relative RMSE of plot and stand level in percent was calculated as: RMSE½% ¼
RMSE 100 y
where y is the arithmetic mean timber volume of all plots.
ð7Þ
J. Rahlf et al. / Remote Sensing of Environment 155 (2014) 325–333
3.3. Terrain influence To test the terrain influence on the prediction accuracy we calculated slope and aspect of the terrain at every sample plot, based on the ALS DTM. For each sample plot, we cut the DTM to a 60 m × 60 m area around the plot center and resampled it to a grid cell size of 20 m × 20 m, so that every sample plot was covered by a single DTM raster cell centered on the plot. In this way we obtained a single value for slope and aspect using an algorithm by Horn (1981) for each sample plot. For a visual assessment the LOSOCV model residuals were plotted against slope and aspect. The same was done with relative yij =yij to eliminate the effect of the magnitude of the residuals yij −e response variable. To analyze interaction between slope and aspect we also plotted the residuals of stands on slopes of more than 10° against aspect. Subsequently, a statistical analysis was performed. Aspect was converted into a categorical variable where 0–45° and 315–360° was north, 45–135° was east, 135–225° was south, and 225–315° was west. We included the terrain properties slope and aspect of the sample plots in the previously selected models of each data set. The first model contained the variable slope (slope model). The second model contained slope and a slope–aspect interaction term (slope–aspect model). It was considered meaningless to fit a model containing the variable aspect as single term, since an aspect-dependent intercept on near-horizontal slopes does not make sense. Likelihood-ratio tests were used to compare the original model and the two models incorporating terrain properties. For likelihood ratio testing, all three models were fitted using maximum likelihood estimation. A final analysis of the terrain influence was performed by calculating the relative LOSOCV RMSE of the slope–aspect model and comparing it with the plot-level RMSE of the original model. 4. Results 4.1. Prediction models For ALS, four explanatory variables were selected using the stepwise forward selection algorithm based on the BIC. The selected variables were the height metric hmean f, the quadratic terms h2mean a and p290 a, and the density metric d29 f. The metric h2mean a was removed in the backward elimination. For AP, the stepwise forward selection algorithm identified the height metrics hmean and p250, and the density metric d21 as influential variables. However, a lower RMSE was achieved when p250 was removed during backward selection. The InSAR and the radargrammetry models were fitted with the mean CHM height hmean as the only predictor variable. The quadratic term h2mean did not decrease the RMSE in either model and was therefore not included. Details of the models are listed in Table 4. Fig. 2 shows observed timber volume plotted against the corresponding predictions from the remote sensing models. The smallest deviation from the 1:1 line is visible in the ALS model scatterplot, followed by the AP model scatterplot with larger residuals in the stands with the highest observed volume. The variability in the residuals of InSAR and radargrammetry was generally higher than for the other remote sensing methods. The heteroscedasticity was considered using variance models. There was no indication of spatial autocorrelation of the residuals within the stands when considering the random effect on stand level. The LOSOCV RMSEs of the models are presented in Table 5. The aggregation resulted in the underestimation of the stand with the highest timber volume. While five plots within that stand were underestimated with all remote sensing data sets, the underestimation was most severe with the AP data. Additionally, the remaining two plots were close to the 1:1 line in AP, as opposed to the InSAR and radargrammetry predictions where they reduced the underestimation. In AP the
329
Table 4 Variables and parameter estimates of the linear mixed models. Remote sensing data set
Variablea
Estimateb
Standard deviation
Intercept hmean f p290 a d29 f δ σb
−2.82ns 26.20*** 0.33*** −9042.60** 0.91
3.68 1.42 0.05 2684.09
Intercept hmean d21 δ σb
23.27** 24.73*** −47.93*** 0.39
Intercept hmean δ σb
1.42ns 27.04*** 0.35
Intercept hmean δ σb
12.25ns 23.16*** 0.26
ALS
11.15
AP 8.11 1.21 14.10 18.26
InSAR 10.67 1.60 17.78
Radargrammetry
a b
14.52 1.80 29.21
δ is the variance parameter in the variance function σ2ε υ2δ ij . With level-of-significance of t-tests (*** p b 0.001, ** p b 0.01, * p b 0.05; ns p N 0.05).
absolute residual of the stand was three times bigger than the standard deviation of all residuals. No error was found in the field or remote sensing data. When omitting the stand, the RMSEs on stand level were 12% for ALS, 13% for AP, 19% for InSAR, and 25% for radargrammetry. To show the potential of the different data sets for practical application and to visualize the timber volume prediction accuracy we created wall-to-wall prediction maps for a subset of the test area using each of the data sets. Fig. 3 shows the prediction maps based on the fitted models. While in the InSAR map the open areas are recognizable, only the high volume area is apparent at the central eastern border of the radargrammetry map.
4.2. Terrain influence The analysis of terrain influence did not give consistent results for all data sets. The visual assessment of aspect and slope revealed no obvious trends or patterns in the residuals. However, the statistical analysis revealed the influence of slope and aspect. The results of the likelihood ratio tests are given in Table 6. Agreeing on the common level of significance of 0.05, the p-values showed that the inclusion of slope and the interaction term of slope and aspect provided a significantly better model fit for AP and InSAR. Slope alone was not significant when included in any of the four original models. Additionally, the slope decreased the RMSE of the AP, InSAR, and radargrammetry models, while no change was observed for ALS (Table 7). Taken together, there was an influence of terrain on timber volume prediction with AP, InSAR and radargrammetry even though the RMSEs decreased by less than 1 percentage point. The results of the analysis suggested that the only predictions not influenced by topography were the ALS predictions. Table 8 shows the change in predicted timber volume when slope is increased by 1° and all other parameters remain the same. The slope– aspect models of the SAR data sets show a strong negative impact of eastern slopes and a positive impact of western and southern slopes. The slope–aspect model of AP behaves differently. It shows a positive slope impact on southern and eastern slopes and a negative impact on western and northern slopes.
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Fig. 2. Observed versus predicted (LOSOCV) timber volume for all fitted models; crosses = sample plots; circles = stand means.
5. Discussion In our study we quantified the accuracy of timber volume estimation based on ALS, AP, InSAR, and radargrammetry. At plot level the RMSEs suggested the following accuracy ranking, starting with the highest accuracy: ALS, AP, InSAR, radargrammetry. At stand level the RMSE of AP was slightly higher than the RMSE of InSAR. This was caused by one outlying stand in the AP predictions. Taking the scatterplots and the influence of the largely underpredicted stand into account, the accuracy ranking at plot level is also valid at stand level. Earlier studies compared only one or two different 3D remote sensing data sets for the same study area. We tried to relate our results to some of those studies to verify the achieved accuracies in order to generalize our results. Comparisons of RMSEs between studies are problematic, since different study designs, forest structure, and study site properties lead to different results. An important factor that must be considered is the sample plot size, since standard errors decrease with increasing plot size (Mascaro, Detto, Asner, & Muller-Landau, 2011; Table 5 LOSOCV RMSEs of the timber volume prediction. Remote sensing data set
Plot-level RMSE 3
(m ha ALS AP InSAR Radargrammetry
36.20 58.59 77.56 82.82
−1
)
Stand-level RMSE (%)
(m3ha−1)
(%)
19.42 31.43 41.60 44.42
23.05 33.79 33.74 43.38
12.36 18.12 18.10 23.27
Næsset, 2002b). The decrease becomes visible when comparing the plot-level RMSEs to the stand-level RMSEs. The RMSE of our ALS model was similar to the findings of Breidenbach and Astrup (2014) and in the ranges Næsset et al. (2004) reported for stem volume estimation models in the Nordic Countries, which were 15–25% at plot level and 9–43% at stand level. Järnstedt et al. (2012) obtained an RMSE of 31% for timber volume estimation with ALS data and 40% with AP data for 300 m2 plots. In the same area and with similar field data Vastaranta et al. (2013) achieved a plotlevel RMSE of 18% and 25% with ALS and AP, respectively. They explain the difference compared to the findings by Järnstedt et al. (2012) as being due to a higher sample plot number, higher field measurement means, and a different estimation technique. Straub et al. (2013) obtained an RMSE at plot level of 34% and 41% with ALS (first and last echoes) and AP respectively, for 500 m2 plots. Taken together, the abovementioned studies identified that models based on ALS data produce more accurate predictions than models based on AP. By contrast, Nurminen et al. (2013) and Bohlin et al. (2012) reported similar accuracies for estimations based on ALS and AP. Nurminen et al. (2013) achieved an RMSE of 21% with ALS and 23% with AP for plots of various sizes with a mean of 390 m2. On stand level Bohlin et al. (2012) obtained an RMSE of 13% for volume predictions with AP and compared it to an earlier ALS study in the same area that had obtained an RMSE of 11% (Holmgren, 2004). Our findings correspond to those from both of the aforementioned studies. Although the AP data were delivered as a raster representing a smoothed surface, we treated ALS and AP data in the same way. The use of a raw point cloud of matched points might improve the accuracy of the AP predictions.
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Fig. 3. Timber volume prediction maps (m3 ha−1) derived from the four remote sensing data sets (a–d), and orthophoto (e) for a subset of the test area; the coordinate system is UTM zone 32 N.
Solberg et al. (2013) combined two TanDEM-X InSAR DSMs to estimate timber volume in spruce-dominated stands for a slightly larger study area than ours, which also included the present data. They reported a relative RMSE of 44% for 250 m2 plots and 20% for stands. Comparable to our study, Næsset et al. (2011) evaluated the performance of ALS and Shuttle Radar Topography Mission (SRTM) InSAR for aboveground biomass area estimates. They achieved standard errors of 1.6
and 3.2 Mg ha− 1 using ALS and InSAR respectively, which supports our finding that the InSAR RMSE is approximately twice as high as the ALS RMSE. To date, few studies have compared radargrammetry with other remote sensing systems for forest parameter estimation. Solberg et al. (2015) used TerraSAR-X radargrammetry data to estimate timber volume in spruce-dominated stands in the same study area. In common with our results, they achieved a relative plot-level RMSE of 42% and a
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Table 6 Results of likelihood ratio tests comparing the initially selected models with models incorporating slope and the interaction term of slope and aspect of the sample plots. Remote sensing data set
Compared model
Degrees of freedom
Likelihood ratio
p-value
ALS
Slope model Slope–aspect model Slope model Slope–aspect model Slope model Slope–aspect model Slope model Slope–aspect model
8 11 7 10 6 9 6 9
0.07 6.30 1.23 11.92 0.00 17.95 0.03 7.13
0.793 0.178 0.267 0.018 0.969 0.001 0.867 0.129
AP InSAR Radargrammetry
stand-level RMSE of 18%. One reason for the larger prediction errors with both SAR systems compared to ALS and AP may be their larger grid cell size. In contrast to Breidenbach, Kublin, et al. (2008), who fitted mixed effects models to predict timber volume from ALS, no influential spatial autocorrelation in the residuals within stands was found in our study. Thus, the stands' homogeneity is such that the random effect covers the natural spatial autocorrelation. This is particularly important for SAR data because distances between sample plot boundaries are sometimes smaller than the grid cell size of the SAR CHMs. The absence of spatial autocorrelation simplifies the estimation of stand-level variance estimates (McRoberts, Næsset, & Gobakken, 2013). The analysis of the terrain influence showed that the inclusion of slope and aspect in prediction models can improve the accuracy of timber volume predictions. The RMSEs of the AP, InSAR, and radargrammetry models decreased by less than 1 percentage point, which may be marginal for practical applications. The results indicate that of all compared methods, InSAR predictions are affected most by topography. Correspondingly, Breidenbach, Koch, et al. (2008) found that aspect had a strong effect on mean tree height estimates based on InSAR data. While they used only one scene, we combined ascending and descending acquisitions to generate a DSM, which presumably moderated the effects of slope and aspect. Future studies using InSAR data on rugged terrain should pay attention to these effects. The similar behavior of the SAR slope–aspect models on eastern, southern, and western slopes might be caused by the SAR-specific geometry resulting in layover, foreshortening, and shadowing. Since AP is derived from a passive sensor, the impact of slope and aspect is likely caused by solar elevation during image acquisition. The results of our study are relevant to inform data selection decisions in forest survey planning when using remote sensing data for forest parameter prediction. Næsset et al. (2011) indicated how the field costs of a forest inventory might change when using different remote sensing data. They estimated that in order to achieve the same precision in an overall biomass estimate for their study area the number of field plots could be reduced by approximately 80% when using ALS data to support the estimation compared to a pure field survey with no use of remote sensing data. Similarly, there was a 25% reduction in the required field plot numbers when using InSAR data from SRTM. Our analysis was solely based on the 3D information contained in the data sets. We did not consider other information that could have improved timber volume predictions, such as intensity values in ALS Table 7 Relative LOSOCV RMSEs of slope–aspect models compared to initial models. Remote sensing data set ALS AP InSAR Radargrammetry
ΔRMSE
Initial model
Slope–aspect model
RMSE (%)
RMSE (%)
(percentage points)
19.42 31.43 41.60 44.42
19.43 30.76 40.62 43.87
−0.01 0.67 0.98 0.55
Table 8 Change of predicted timber volume when slope is increased by 1° and all other parameters remain the same. Remote sensing data set AP InSAR Radargrammetry
Timber volume change (m3 ha−1) North
East
South
West
−0.489 1.962 −0.284
0.582 −2.816 −2.204
1.636 0.773 1.754
−1.890 2.428 1.181
data (Ørka et al., 2009) or coherence in SAR data (Balzter, 2001; Schlund, von Poncet, Hoekman, Kuntz, & Schmullius, 2014). A known potential lies in the color information of AP data, which presumably can be used for tree species specific estimations of forest attributes. Additionally, special properties of remote sensing systems might outweigh higher prediction accuracy. An example is the capacity of SAR systems to acquire images under cloudy conditions. 6. Conclusions Common types of 3D remote sensing data were compared on a single test site using the same reference data and methods. Therefore we were able to rank the data sets based on their prediction accuracy. While ALS provided the most accurate predictions, we observed higher errors with the other airborne system, AP. At plot level, the InSAR RMSE was approximately twice as high as the ALS RMSE. Radargrammetry showed a slightly lower accuracy than InSAR. Aggregation at stand level decreased the RMSE by 36–56%. Additionally, we conclude that terrain has a significant but marginal influence on the prediction accuracy of AP, InSAR, and radargrammetry. Acknowledgments The authors are grateful to the anonymous reviewers whose comments greatly helped to improve the clarity and precision of the paper. We acknowledge Deutsches Zentrum für Luft und Raumfahrt (DLR) for the provision of TanDEM-X science data free of charge. References Balzter, H. (2001). Forest mapping and monitoring with interferometric synthetic aperture radar (InSAR). Progress in Physical Geography, 25(2), 159–177. Bohlin, J., Wallerman, J., & Fransson, J. (2012). Forest variable estimation using photogrammetric matching of digital aerial images in combination with a high-resolution DEM. Scandinavian Journal of Forest Research, 27(7), 692–699. Braastad, H. (1966). Volume tables for birch. Norwegian with English summary. Meddr. Norske SkogforsVes., Oslo. (pp. 265–365). Brantseg, A. (1967). Volume functions and tables for Scots pine. South Norway. Norwegian with English summary. Meddr. Norske SkogforsVes. (pp. 695–739). Breidenbach, J., & Astrup, R. (2012). Small area estimation of forest attributes in the Norwegian National Forest Inventory. European Journal of Forest Research, 1–13. Breidenbach, J., & Astrup, R. (2014). The semi-individual tree crown approach. Forestry applications of airborne laser scanning (pp. 113–133). Springer. Breidenbach, J., Koch, B., Kändler, G., & Kleusberg, A. (2008). Quantifying the influence of slope, aspect, crown shape and stem density on the estimation of tree height at plot level using lidar and InSAR data. International Journal of Remote Sensing, 29(5), 1511–1536. Breidenbach, J., Kublin, E., McGaughey, R., Andersen, H. -E., & Reutebuch, S. (2008). Mixed-effects models for estimating stand volume by means of small footprint airborne laser scanner data. Photogrammetric Journal of Finland, 21(1), 4–15. Buckreuss, S., Balzer, W., Muhlbauer, P., Werninghaus, R., & Pitz, W. (2003). The TerraSARX satellite project. Geoscience and remote sensing symposium, 2003. IGARSS'03. Proceedings. 2003 IEEE International, Vol. 5. (pp. 3096–3098). IEEE. Estornell, J., Ruiz, L. A., Velázquez-Martí, B., & Hermosilla, T. (2011). Analysis of the factors affecting LiDAR DTM accuracy in a steep shrub area. International Journal of Digital Earth, 4(6), 521–538. Hodgson, M. E., & Bresnahan, P. (2004). Accuracy of airborne lidar-derived elevation: Empirical assessment and error budget. Photogrammetric Engineering and Remote Sensing, 70(3), 331–340. Holmgren, J. (2004). Prediction of tree height, basal area and stem volume in forest stands using airborne laser scanning. Scandinavian Journal of Forest Research, 19(6), 543–553. Honkavaara, E., Markelin, L., Rosnell, T., & Nurminen, K. (2012). Influence of solar elevation in radiometric and geometric performance of multispectral photogrammetry. ISPRS Journal of Photogrammetry and Remote Sensing, 67, 13–26.
J. Rahlf et al. / Remote Sensing of Environment 155 (2014) 325–333 Horn, B. K. (1981). Hill shading and the reflectance map. Proceedings of the IEEE, 69(1), 14–47. Hugershoff, R. (1933). Die photogrammetrische Vorratsermittlung. Tharandter Forstliches Jahrb, 84, 159–166. Hyyppä, J., Hyyppä, H., Inkinen, M., Engdahl, M., Linko, S., & Zhu, Y. (2000). Accuracy comparison of various remote sensing data sources in the retrieval of forest stand attributes. Forest Ecology and Management, 128(1), 109–120. Järnstedt, J., Pekkarinen, A., Tuominen, S., Ginzler, C., Holopainen, M., & Viitala, R. (2012). Forest variable estimation using a high-resolution digital surface model. ISPRS Journal of Photogrammetry and Remote Sensing, 74, 78–84. Korhonen, L., Kaartinen, H., Kukko, A., Solberg, S., & Astrup, R. (2010). Estimating vertical canopy cover with terrestrial and airborne laser scanning. 10th International Conference on LiDAR Applications for Assessing Forest Ecosystems (Silvilaser 2010). Krieger, G., Moreira, A., Fiedler, H., Hajnsek, I., Werner, M., Younis, M., et al. (2007). TanDEM-X: A satellite formation for high-resolution SAR interferometry. IEEE Transactions on Geoscience and Remote Sensing, 45(11), 3317–3341. Landsskogtakseringen (2008). Landsskogtakseringens feltinstruks 2008. Håndbok fra Skog og landskap 05/08. Norway: Skog og landskap, Ås. Leberl, F., Irschara, A., Pock, T., Meixner, P., Gruber, M., Scholz, S., et al. (2010). Point Clouds: Lidar versus 3D Vision. Photogrammetric Engineering & Remote Sensing, 76(10), 1123–1134. Maltamo, M., & Packalen, P. (2014). Species-specific management inventory in Finland. Forestry Applications of Airborne Laser Scanning (pp. 241–252). Springer. Mascaro, J., Detto, M., Asner, G. P., & Muller-Landau, H. C. (2011). Evaluating uncertainty in mapping forest carbon with airborne LiDAR. Remote Sensing of Environment, 115(12), 3770–3774. McGaughey, R. (2013). FUSION/LDV: Software for LIDAR Data Analysis and Visualization. Tech. rep., USDA, Pacific North-West Research Center, Seattle, USA. McRoberts, R. E., Næsset, E., & Gobakken, T. (2013). Inference for lidar-assisted estimation of forest growing stock volume. Remote Sensing of Environment, 128, 268–275. McRoberts, R. E., Tomppo, E. O., & Næsset, E. (2010). Advances and emerging issues in national forest inventories. Scandinavian Journal of Forest Research, 25(4), 368–381. Næsset, E. (2002a). Determination of mean tree height of forest stands by digital photogrammetry. Scandinavian Journal of Forest Research, 17(5), 446–459. Næsset, E. (2002b). Predicting forest stand characteristics with airborne scanning laser using a practical two-stage procedure and field data. Remote Sensing of Environment, 80(1), 88–99. Næsset, E. (2004). Effects of different flying altitudes on biophysical stand properties estimated from canopy height and density measured with a small-footprint airborne scanning laser. Remote Sensing of Environment, 91(2), 243–255. Næsset, E. (2014). Area-based inventory in Norway—from innovation to an operational reality. Forestry Applications of Airborne Laser Scanning (pp. 215–240). Springer. Næsset, E., Gobakken, T., Holmgren, J., Hyyppä, H., Hyyppä, J., Maltamo, M., et al. (2004). Laser scanning of forest resources: The Nordic experience. Scandinavian Journal of Forest Research, 19(6), 482–499. Næsset, E., Gobakken, T., Solberg, S., Gregoire, T., Nelson, R., Stå̊hl, G., et al. (2011). Modelassisted regional forest biomass estimation using LiDAR and InSAR as auxiliary data: A case study from a boreal forest area. Remote Sensing of Environment, 115(12), 3599–3614. Neeff, T., Dutra, L., dos Santos, J., da Costa Freitas, C., & Araujo, L. (2005). Tropical forest measurement by interferometric height modeling and P-band radar backscatter. Forest Science, 51(6), 585.
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Nurminen, K., Karjalainen, M., Yu, X., Hyyppä, J., & Honkavaara, E. (2013). Performance of dense digital surface models based on image matching in the estimation of plot-level forest variables. ISPRS Journal of Photogrammetry and Remote Sensing, 83, 104–115. Ørka, H., Næsset, E., & Bollandsås, O. (2009). Classifying species of individual trees by intensity and structure features derived from airborne laser scanner data. Remote Sensing of Environment, 113(6), 1163–1174. Perko, R., Raggam, H., Deutscher, J., Gutjahr, K., & Schardt, M. (2011). Forest assessment using high resolution SAR data in X-band. Remote Sensing, 3(4), 792–815. Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D., & R Core Team (2013). nlme: Linear and nonlinear mixed effects models. R package version 3.1-111. R Core Team (2013). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing (URL http://www.R-project.org). Reigber, A., & Moreira, J. (1997). Phase unwrapping by fusion of local and global methods. Geoscience and Remote Sensing, 1997. IGARSS'97. Remote Sensing—A Scientific Vision for Sustainable Development., 1997 IEEE International, Vol. 2. (pp. 869–871). IEEE. Schardt, M., Hruby, W., Hirschmugl, M., Wack, R., & Franke, M. (2004). Comparison of aerial photographs and laser scanning data as methods for obtaining 3D forest stand parameters. Proc. of the ISPRS working group VII/2 — laser-scanners for forest and landscape assessment (pp. 272–276). Schlund, M., von Poncet, F., Hoekman, D. H., Kuntz, S., & Schmullius, C. (2014). Importance of bistatic SAR features from TanDEM-X for forest mapping and monitoring. Remote Sensing of Environment, 151, 16–26. Solberg, S., Astrup, R., Breidenbach, J., Nilsen, B., & Weydahl, D. (2013). Monitoring spruce volume and biomass with InSAR data from TanDEM-X. Remote Sensing of Environment, 139, 60–67. Solberg, S., Astrup, R., Gobakken, T., Næsset, E., & Weydahl, D. J. (2010). Estimating spruce and pine biomass with interferometric X-band SAR. Remote Sensing of Environment, 114(10), 2353–2360. Solberg, S., Riegler, G., & Nonin, P. (2015). Estimating forest biomass from TerraSAR-X stripmap radargrammetry. IEEE Transactions on Geoscience and Remote Sensing, 53(1), 154–161. Steinmann, K., Mandallaz, D., Ginzler, C., & Lanz, A. (2013). Small area estimations of proportion of forest and timber volume combining Lidar data and stereo aerial images with terrestrial data. Scandinavian Journal of Forest Research, 28(4), 373–385. Straub, C., Stepper, C., Seitz, R., & Waser, L. T. (2013). Potential of UltraCamX stereo images for estimating timber volume and basal area at the plot level in mixed European forests. Canadian Journal of Forest Research, 43(8), 731–741. Tomter, S., Hylen, G., & Nilsen, J. -E. (2010). National forest inventories: Pathways for common reporting. Springer Verlag, Ch. Norways national forest inventory. Toutin, T. (2002). Impact of terrain slope and aspect on radargrammetric DEM accuracy. ISPRS Journal of Photogrammetry and Remote Sensing, 57(3), 228–240. Toutin, T., & Gray, L. (2000). State-of-the-art of elevation extraction from satellite SAR data. ISPRS Journal of Photogrammetry and Remote Sensing, 55(1), 13–33. Treuhaft, R., & Siqueira, P. (2000). Vertical structure of vegetated land surfaces from interferometric and polarimetric radar. Radio Science, 35(1), 141–177. Vastaranta, M., Wulder, M.A., White, J. C., Pekkarinen, A., Tuominen, S., Ginzler, C., et al. (2013). Airborne laser scanning and digital stereo imagery measures of forest structure: Comparative results and implications to forest mapping and inventory update. Canadian Journal of Remote Sensing, 39(05), 1–14. Vestjordet, E. (1967). Functions and tables for volume of standing trees. Norway spruce. Norwegian with English summary. Meddr. Norske SkogforsVes. (pp. 543–574).
PAPER II
Forests 2015, 6, 4059-4071; doi:10.3390/f6114059
OPEN ACCESS
forests ISSN 1999-4907 www.mdpi.com/journal/forests Article
Forest Parameter Prediction Using an Image-Based Point Cloud: A Comparison of Semi-ITC with ABA Johannes Rahlf *, Johannes Breidenbach, Svein Solberg and Rasmus Astrup National Forest Inventory, Norwegian Institute of Bioeconomy Research, P.O. Box 115, NO-1431 Ås, Norway; E-Mails:
[email protected] (J.B.);
[email protected] (S.S.);
[email protected] (R.A.) * Author to whom correspondence should be addressed; E-Mail:
[email protected]; Tel.: +47-9749-0945. Academic Editor: Joanne C. White Received: 26 June 2015 / Accepted: 28 October 2015 / Published: 10 November 2015
Abstract: Image-based point clouds obtained using aerial photogrammetry share many characteristics with point clouds obtained by airborne laser scanning (ALS). Two approaches have been used to predict forest parameters from ALS: the area-based approach (ABA) and the individual tree crown (ITC) approach. In this article, we apply the semi-ITC approach, a variety of the ITC approach, on an image-based point cloud to predict forest parameters and compare the performance to the ABA. Norwegian National Forest Inventory sample plots on a site in southeastern Norway were used as the reference data. Tree crown objects were delineated using a watershed segmentation algorithm, and explanatory variables were calculated for each tree crown segment. A multivariate kNN model for timber volume, stem density, basal area and quadratic mean diameter with the semi-ITC approach produced RMSEs of 30%, 46%, 25%, 26%, respectively. The corresponding measures for the ABA were 30%, 51%, 26%, 35%, respectively. Univariate kNN models resulted in timber volume RMSEs of 25% for the semi-ITC approach and 22% for the ABA. A non-linear logistic regression model with the ABA produced an RMSE of 23%. Both approaches predicted timber volume with comparable precision and accuracy at the plot level. The multivariate kNN model was slightly more precise with the semi-ITC approach, while biases were larger. Keywords: forest inventory; remote sensing; image matching; photogrammetry; kNN; tree segmentation; ALS; semi-global matching; timber volume
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1. Introduction High resolution, three-dimensional (3D) point clouds from remote sensing are valuable for forest inventories, because vegetation height is correlated to key forest parameters. In combination with field inventories, such height information can be used to create resource maps or to estimate forest variables for small areas [1,2]. Currently, the most prominent method of acquiring point clouds is airborne laser scanning (ALS). Remote sensing data, which increasingly attracts attention in forest inventory research, are image-based point clouds from digital aerial photogrammetry [3–6]. Advances in image quality, algorithms and computing power allow the creation of height information over large areas with high spatial resolution from images of aerial photographic surveys. Image-based point clouds and canopy height models (CHM) provide less structural information of the canopy than ALS, but can be equally accurate for predicting timber volume [7–9]. Two approaches have been used to estimate forest parameters from ALS. The area-based approach (ABA) uses ALS height distribution metrics of the entire plot as input to a statistical model for forest parameters, such as timber volume [10]. Individual tree crown (ITC) approaches, on the other hand, produce predictions for tree crown objects. Tree crowns are delineated from the remote sensing data by using segmentation algorithms, e.g., [11–13]. One approach, that corrects for biases due to segmentation errors, is the semi-individual tree crown (semi-ITC) approach [14]. The difference of semi-ITC from other ITC approaches is that crown segments can contain none, one or several trees. While often not resulting in higher accuracies than using the ABA [15], ITC approaches can be attractive for forest owners because of their higher spatial resolution. Most studies using image-based point clouds for forest parameter prediction apply the ABA. Only one study applied the semi-ITC approach on an image-based CHM [16], but focused on tree height estimation and used a coarse resolution of 4 m × 4 m. The objective of this study was to apply the semi-ITC approach on a very high resolution (15.6 points·m−2 ) image-based point cloud to predict timber volume, stem density, basal area (G) and the quadratic mean diameter (QMD). The performance of the semi-ITC approach was compared to the ABA. 2. Material and Methods 2.1. Study Area The study area is located in Hedmark county in southeastern Norway. It covers parts of the municipalities Nord-Odal, Sør-Odal and Kongsvinger. The boreal forest is dominated by Norway spruce (Picea abies (L.) Karst.) and includes Scots pine (Pinus sylvestris L.), birch (Betula spp.) and small portions of other tree species, such as aspen (Populus tremula L.) and rowan (Sorbus aucuparia L.). The terrain is hilly with altitudes ranging from 130 to 535 m a.s.l (Figure 1).
4061 56°N 58°N 60°N 62°N 64°N 66°N
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Figure 1. Overview of the study area with a standard Norwegian DTM in the background.
2.2. Field Data The field data used in this study are sample plots of the Norwegian National Forest Inventory (NFI). The plots were located on a 3 km × 3 km grid. Within the sample plot radius of 8.92 m (250 m2 ), the recorded variables include species, tree positions, diameter at breast height (dbh) of all trees with dbh >5 cm and tree height measured with a Vertex hypsometer. On sample plots with 10 or less trees, the heights of all trees are measured. On plots with more than 10 trees, a sub-sample is selected using a relascope. The relascope factor for the selection is calculated on site for each sample plot to achieve a sub-sample size of approximately 10 trees. The height of trees without height measurement is estimated with dbh height models derived from trees having height measurements [17]. Timber volume for each tree is estimated with species-specific allometric models [18–20]. A total of 44 NFI sample plots were located within the study area. Four plots were discarded due to harvesting between the image acquisition and the field inventory. The NFI plots were measured between 2008 and 2012. An accurate positioning of the plots was achieved using differential GPS. Descriptive statistics of the forest inventory data can be found in Table 1. Table 1. Descriptive statistics of the 40 National Forest Inventory (NFI) plots. Variable
Min
Mean
Max
SD
Total volume (m3 ·ha−1 ) Spruce volume (m3 ·ha−1 ) Pine volume (m3 ·ha−1 ) Deciduous species volume (m3 ·ha−1 ) Basal area (m2 ·ha−1 ) Quadratic mean diameter (cm) Stem density (ha−1 )
3 0 0 0 1 7 40
199 121 45 33 23 16 1332
459 445 382 198 49 39 4520
142 135 81 48 14 6 909
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2.3. Image-Based Point Cloud A Vexcel Ultracam Eagle camera was used to acquire the images on 11 May 2010. The image ground sampling distance (resolution) was 10 cm. A total of 1024 images covered the study area. The stereo matching of the aerial images was conducted by an external vendor, Blom AS, Norway. The software used for matching was Match-T Version 5.5.2. with the “mountainous” matching strategy. Corresponding heights of a digital terrain model (DTM) obtained from airborne laser scanning were subtracted from the point cloud z-coordinate to extract the vegetation heights. The point density was 15.6 points·m−2 . The points were assigned RGB color values from the corresponding pixel of the aerial image with the closest center point. 2.4. ALS Data We generated a digital terrain model (DTM) from ALS data acquired in 2009 and 2010. The mean pulse density was 1.2 m−2 , and each echo was classified as ground and non-ground by the vendor. The DTM had a cell size of 0.5 m × 0.5 m, and the terrain elevation was derived as the mean height of the ground echoes within each cell. The elevation of cells containing no echoes was interpolated by inverse distance weighting the closest data cells in each of the eight directions of the raster (orthogonal and diagonal) [21]. 2.5. Semi-ITC Approach For the tree crown segmentation, we created a canopy height model (CHM) with a pixel size of 0.5 m × 0.5 m using the highest point within each cell. No-data cells caused by missing points in the point cloud were interpolated by inverse distance weighting the closest data cells in each of the eight directions of the raster (orthogonal and diagonal). We used a watershed algorithm [22] to segment crown outlines based on the CHMs. A threshold of 2 m was applied to separate ground and low vegetation from areas covered by trees. These areas were segmented in two different ways. Above 2 m, we set the height tolerance of the algorithm to 10 cm. The height tolerance is the minimum height between the highest point of a segment and all of its border pixels. If a segment has a minimum height smaller than the tolerance, the segment is merged with the highest neighboring segment. In this way, small maxima, which occur often in the CHM, are ignored. Below 2 m, the tolerance was set to 5 cm to reduce the size of the segments. All segments smaller than 2 m2 were discarded, and each of their pixels was assigned to the closest neighboring segment. In earlier studies applying the semi-ITC approach to ALS, e.g., [15], the segmentation resulted in segments covering only the parts of the plot where tree crowns were detected. Treeless areas were therefore ignored in the statistical modeling. In this study, the sample plot area was completely covered by segments. Such coverage was desired to avoid omission errors, since single tree crowns were occasionally invisible in the point cloud. Based on the field inventory data, timber volume, G and the quadratic diameter of all trees within each segment were summed. The parameters of segments without trees were set to 0. For the statistical modeling, the segments were classified in reference and target segments. Reference segments were all
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segments lying completely within the sample plots and were used as training data to fit the statistical models. Target segments were segments partly intersecting with the sample plot, for which the response variables were only predicted with the fitted models. For each segment, height-distribution metrics were calculated from the image-based point cloud using FUSION [21]. The height metrics were minimum (Hmin ), mean (Hmean ), maximum (Hmax ) and the standard deviation (Hsd ) of the point heights, as well as the 1%, 5%, 10%, 20%, 25%, 30%, 40%, 50%, 60%, 70%, 75%, 80%, 90%, 95% and 99% height percentiles (HP 01 ,...,HP 99 ). Density metrics were derived by dividing the vertical distance between the lowest and the highest point within each segment into ten equal sections and calculating the proportion of the number of points within each section to the total number of points in the segment (D1 ,...,D10 ) [23]. Color metrics, i.e., radiometric distribution metrics, which describe the distribution of the numeric color values, were derived similarly to the height metrics for each color band (Rmin , Rmean , Rmax , Rsd , RP 01 ,...,RP 99 , Gmin , Gmean , Gmax , Gsd , GP 01 ,...,GP 99 , Bmin , Bmean , Bmax , Bsd , BP 01 ,...,BP 99 ). Ratios (Rratio , Gratio , Bratio ) were calculated for each color by dividing the mean color value (e.g., Gmean ) by the sum of all mean color values. Additionally, geometric properties of the segments were derived, i.e., area (GeoA ), perimeter (GeoP ) √ and compactness (GeoC = GeoA / GeoP ). 2.6. Area-Based Approach As explanatory variables for the ABA, we derived the same height, density and color metrics as for the semi-ITC approach. The metrics were calculated from point heights and colors of the entire area of each plot. Geometry metrics were not calculated, because area and shape do not differ between sample plots. 2.7. Statistical Modeling To compare the approaches thoroughly, we fitted kNN-models for both the semi-ITC approach and the ABA: a kNN-model with multiple response variables (multivariate kNN) and a kNN model with a single response variable (univariate kNN). Additionally, we fitted a non-linear logistic regression model for the ABA, because parametric models are commonly used for the ABA. The response variables for the kNN-model with multiple response variables were timber volume, G, QMD and stem density. For the kNN model with the single response variable, we used timber volume as the response variable. The kNN-models are based on using Euclidean distance as the distance metric and k = 1. We selected explanatory variables with the help of a forward stepwise algorithm. We fitted a non-linear logistic regression model to the response variable timber volume for the ABA. A logistic model was preferred over a linear model, because curvilinearity was found in the data. Additionally, the model incorporates two asymptotes, which restrict possible predictions to a range between zero and an adjustable maximum value and, thus, prevent extreme predictions [24]. The model is given by: yi =
α 1 + exp β0 +
J X j=1
! + εj βj xji
(1)
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where yi is the prediction for the i-th plot, xij is the value of the j-th explanatory variable of the i-th plot, β0 and βj are the parameters to be estimated, α is the maximum asymptote and εi is the residual error. The best value for asymptote α was determined by an optimization algorithm set to minimize the RMSE of the cross-validated predictions. Mean elevation was used as the explanatory variable in the optimization. Cross-validation was applied to all models to avoid overfitting. For the semi-ITC approach, the model was fitted for each plot without using the reference segments of the plot. Subsequently, the response variables were predicted for all target and reference segments within the plot. For the ABA, a leave-one-out cross-validation at the plot level was applied. For the semi-ITC approach, plot-level predictions were derived by aggregating the segment predictions: segment predictions were multiplied by the proportion of the segment area shared with the sample plot to correct overprediction caused by segments overlapping the sample plot boundary. This correction, however, introduces an error, because it assumes homogeneity within the segments. The segment predictions of timber volume, G and stem density were then totaled at the plot level. For the QMD, the quadratic diameter was first aggregated like the other parameters and then divided by the predicted number of stems. The QMD at the plot level was the square root of this number. We used the root mean square error (RMSE) on the plot level as the goodness-of-fit criterion. The RMSE was used as a basis for the comparison and the stepwise variable selection. RMSE on the plot and segment level was calculated as: r Pn RM SE =
i=1 (yi
− yˆi )2
(2) n where n is the sample size, yi is the observed forest parameter of the i-th population unit (plots or segments) and yˆi is the predicted forest parameter of the i-th population unit. The RMSE in percent was calculated as: RM SE × 100 y¯ where y¯ is the mean observed forest parameter on the plot or segment level. To assess the systematic error of the models, we calculated the bias as: Pn yi − yˆi BIAS = i=1 n RM SE (%) =
(3)
(4)
3. Results 3.1. Comparison of the Two Approaches Timber volume models show a reasonably good fit with both the semi-ITC approach and the ABA. The semi-ITC univariate kNN model produced a slightly higher RMSE than the ABA univariate kNN model (Table 2). The ABA univariate kNN model was marginally better than the logistic regression model. The best volume model of each approach, which was for both approaches the univariate kNN model, is shown in Figure 2. Both univariate kNN models performed similarly. No strong indication for
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the heteroscedasticity of the residuals was given. A curvilinear relationship between the residuals and the observed timber volumes was not visible. None of the models produced outliers. Table 2. RMSEs of the model predictions. G, basal area. QMD, quadratic mean diameter. Volume
Approach
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%
cm
%
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46 51
6 6
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4 6
26 35
logistic regression
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45
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Figure 2. Observed versus predicted timber volume at the plot level using (a) the semi-ITC approach and (b) the ABA. The biases of the semi-ITC models were all positive and, in absolute terms, larger than the biases of the ABA (Table 3). The smallest difference in accuracy was found between the univariate kNN models. All ABA multivariate kNN models showed a negative bias. The logistic regression model had the smallest bias. The multivariate kNN model predictions of both approaches differ more. The semi-ITC approach performed better than or equally as good as the ABA for all forest parameters. The biggest differences can be found in the QMD and stem density predictions.
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Table 3. Biases of the model predictions. G, basal area. QMD, quadratic mean diameter. Model
Volume
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Stem density
G
QMD
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%
ha−1
%
m2 ·ha−1
%
cm
%
146 −23
11 −2
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29 −6
15 −3
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1
0
3.2. Semi-ITC Approach The segmentation of the CHM produced 1240 segments, which intersected with the sample plots. A total of 440 segments lay completely within the sample plots and were used as reference segments. Table 4 shows the statistics describing the number of segments intersecting with the plots, the area of the segments and the aggregated tree list within each segment. Large area segments were caused by flat ground, where local maxima were below the height tolerance of the watershed algorithm. Table 4. Statistics of segments and assigned field data. Variable
Min
Mean
Max
SD
Segments per plot Segment area (m2 ) Number of trees Timber volume (m3 ) G (m2 ) QMD (cm)
9.00 2.00 0.00 0.00 0.00 0.00
31.00 14.81 1.07 1.60 0.02 6.91
55.00 331.56 14.00 32.48 0.31 43.90
9.00 20.22 1.62 3.12 0.03 8.60
Based on the result of the stepwise algorithm, we selected HP 01 , HP 10 , HP 90 , D2 , D9 , Gmin , GeoP for the semi-ITC multivariate kNN model. For the semi-ITC univariate kNN model, Hmin , Hsd , HP 99 , D2 , D7 , Rmin , GP 01 , GeoP were selected. The RMSEs at the segment level of the multivariate kNN prediction were: 175% for timber volume, 149% for stem density, 160% for G and 156% for QMD. The segment level timber volume predictions of the univariate kNN model had an RMSE of 178%. For comparison, we define a null-model as a model containing only an intercept at the observed mean of the variable of interest (ˆ y = y¯). The null model is created with the field data within the segments alone, and its precision serves as a threshold to assess the benefit of the statistical modeling. The RMSEs of the null models at the segment level were: 194% for timber volume, 151% for stem density, 173% for G and 124% for QMD. Except for QMD, all kNN parameter predictions at the segment level were better than the null model predictions.
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3.3. ABA For the ABA multivariate kNN model, the variables HP 05 , HP 10 , HP 25 , HP 30 , HP 60 , GP 01 were selected, for the ABA univariate kNN model the variables Hmean , Hmax , Hsd , HP 40 , HP 60 , BP 01 , BP 25 , B30 and for the logistic regression model the variables H30 , H90 , GP 80 . The optimal upper asymptote was at 598 m3 ·ha−1 . 4. Discussion Both the semi-ITC approach and the ABA showed a similar level of precision and accuracy at the plot level when predicting timber volume. Multivariate predictions of timber volume, stem density and G were equally or slightly more precise with the semi-ITC approach than with the ABA. QMD predictions with the semi-ITC multivariate kNN model had a higher precision. The accuracy of the timber volume predictions is in accordance to earlier studies comparing the two approaches based on ALS data, which showed no or only slight accuracy improvements when using the semi-ITC approach over the ABA [14,15]. Although RMSE values are difficult to compare among studies covering different areas, the timber volume prediction accuracy at the plot level is within the range reported by earlier studies applying the ABA on image-based point clouds [7,25,26]. G predictions were more precise than previously reported with image-based point clouds [5,6]. Biases, however, were larger using the semi-ITC approach. The biases of the multivariate kNN models were positive when using the semi-ITC approach, thus indicating underestimation of the observed parameters. In contrast, biases of the multivariate kNN models were negative when using the ABA. Similarly, a larger positive bias with the semi-ITC approach was reported by an earlier study comparing ITC approaches and the ABA based on ALS for biomass prediction [15]. The semi-ITC predictions of timber volume, G and stem density at the segment level had an equal or slightly higher precision than the null model. Using the image-based point cloud can therefore be a beneficial prediction of certain forest parameters at the tree crown level. However, since the errors are still high, this benefit has to be carefully weighed against the costs of applying the semi-ITC approach. The aggregation to the plot level seems to balance out large parts of the errors similarly to aggregating ABA predictions to the stand level [7]. Comparing the variables, which were selected by the stepwise algorithm, shows an important difference of the two approaches. The variable size of the crown segments has to be considered when modeling forest parameters with the semi-ITC approach. Interestingly, the geometry metric segment perimeter (GeoP ) was selected in both semi-ITC models rather than the area (GeoA ). Many crown segmentation algorithms have been developed for ALS, e.g., [27,28]; however, no study has yet investigated tree crown delineation with image-based point cloud data. Since no optimized segmentation algorithm for image-based 3D data exists, we chose to use a simple watershed algorithm [29], which we adjusted to the present data. Using color as an additional input could be one possibility to improve the tree crown segmentation. Mismatches between field and remote sensing data can have a negative influence on forest parameter models. Discarding segments with mismatching data by selecting reference segments for modeling based on the correlation between field-measured tree heights and remote sensing height [14] does not
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necessarily improve the accuracy [15]. Similarly, also in our study, a pre-analysis showed that this method did not increase the accuracy and was therefore not used. The study shows that the Norwegian NFI can provide suitable data for model calibration for the semi-ITC approach. Especially, timber volume was reasonably well distributed through its range. However, a forest inventory, designed specifically for model calibration, would ensure that plots were located more evenly throughout the ranges of the response variables. Furthermore, due to the low sample plot density, only a few sample plots were available in the study area. The small number of plots has to be taken into account to avoid overfitting. The semi-ITC approach is less sensitive, since the sample plots are divided into more, smaller segments, which are the reference for the statistical model. Due to the small number of sample plots, an independent validation dataset was not available. The study relies therefore on cross-validation. We ignored measurement errors and errors introduced by allometric models. All NFI data were considered to be ground truth. Especially for small-scale predictions, as in this study, however, these errors could increase the variances of the predictions and introduce a bias [30]. Even though the model fits were reasonably good, we see possibilities for improvement in the image-based point cloud. The data were delivered as a smooth point cloud with mostly regular horizontal spacing. The point cloud depicts the general appearance of the forest, i.e., height and area, as well as large tree crowns. Some trees, however, especially in open areas, were not visible in the data. Reasons for such omissions might lie in the general problems of image matching of forests [31] and in the software internal algorithm to filter out erroneously-matched points. Additional information on the matching quality of each point or using an improved filtering algorithm, or even the raw point cloud might lead to better prediction accuracy. Additionally, color information seems to be related to timber volume, since it improved the timber volume model of the ABA. Radiometric correction might contribute to a higher prediction accuracy, as it does for tree species classification [32]. We conclude that the semi-ITC approach based on the image-based point cloud produced timber volume predictions with precision and accuracy comparable to the ABA. Multivariate parameter prediction was equally or more precise with the semi-ITC-approach than with the ABA, but produced larger biases. Improved segmentation algorithms, adapted stereophotogrammetric processing and better color information might improve the semi-ITC approach with image-based point clouds in the future. Acknowledgments The authors would like to thank advisor/forestry Roar Kjær, County governor of Hedmark, for supporting the acquisition of image matching data used in this study. The authors are grateful to the anonymous reviewers whose comments and suggestions significantly improved both clarity and precision of the paper.
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Author Contributions Johannes Rahlf performed the experiments and wrote the paper. Johannes Breidenbach and Svein Solberg contributed to the data analysis and reviewed the paper. Rasmus Astrup supervised the experiments and reviewed the paper. Conflicts of Interest The authors declare no conflict of interest. References 1. Magnussen, S. Arguments for a model-dependent inference? Forestry 2015, 88, 317–325. 2. Breidenbach, J.; Astrup, R. Small area estimation of forest attributes in the Norwegian National Forest Inventory. Eur. J. For. Res. 2012, 131, 1255–1267. 3. White, J.C.; Wulder, M.A.; Vastaranta, M.; Coops, N.C.; Pitt, D.; Woods, M. The utility of image-based point clouds for forest inventory: A comparison with airborne laser scanning. Forests 2013, 4, 518–536. 4. Stepper, C.; Straub, C.; Pretzsch, H. Using semi-global matching point clouds to estimate growing stock at the plot and stand levels: Application for a broadleaf-dominated forest in central Europe. Can. J. For. Res. 2014, 45, 111–123. 5. Straub, C.; Stepper, C.; Seitz, R.; Waser, L.T. Potential of UltraCamX stereo images for estimating timber volume and basal area at the plot level in mixed European forests. Can. J. For. Res. 2013, 43, 731–741. 6. Järnstedt, J.; Pekkarinen, A.; Tuominen, S.; Ginzler, C.; Holopainen, M.; Viitala, R. Forest variable estimation using a high-resolution digital surface model. ISPRS J. Photogramm. Remote Sens. 2012, 74, 78–84. 7. Rahlf, J.; Breidenbach, J.; Solberg, S.; Næsset, E.; Astrup, R. Comparison of four types of 3D data for timber volume estimation. Remote Sens. Environ. 2014, 155, 325–333. 8. Pitt, D.G.; Woods, M.; Penner, M. A comparison of point clouds derived from stereo imagery and airborne laser scanning for the area-based estimation of forest inventory attributes in Boreal Ontario. Can. J. Remote Sens. 2014, 40, 214–232. 9. Bohlin, J.; Wallerman, J.; Fransson, J. Forest variable estimation using photogrammetric matching of digital aerial images in combination with a high-resolution DEM. Scand. J. For. Res. 2012, 27, 692–699. 10. Næsset, E. Estimating Timber Volume of Forest Stands Using Airborne Laser Scanner Data. Remote Sens. Environ. 1997, 61, 246–253. 11. Eysn, L.; Hollaus, M.; Lindberg, E.; Berger, F.; Monnet, J.M.; Dalponte, M.; Kobal, M.; Pellegrini, M.; Lingua, E.; Mongus, D.; et al. A Benchmark of Lidar-Based Single Tree Detection Methods Using Heterogeneous Forest Data from the Alpine Space. Forests 2015, 6, 1721–1747. 12. Vauhkonen, J.; Ene, L.; Gupta, S.; Heinzel, J.; Holmgren, J.; Pitkänen, J.; Solberg, S.; Wang, Y.; Weinacker, H.; Hauglin, K.M.; et al. Comparative testing of single-tree detection algorithms under different types of forest. Forestry 2012, 85, 27–40.
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13. Solberg, S.; Næsset, E.; Bollandsås, O. Single tree segmentation using airborne laser scanner data in a structurally heterogeneous spruce forest. Photogramm. Eng. Remote Sens. 2006, 72, 1369–1378. 14. Breidenbach, J.; Næsset, E.; Lien, V.; Gobakken, T.; Solberg, S. Prediction of species specific forest inventory attributes using a nonparametric semi-individual tree crown approach based on fused airborne laser scanning and multispectral data. Remote Sens. Environ. 2010, 114, 911–924. 15. Breidenbach, J.; Astrup, R. The Semi-Individual Tree Crown Approach. In Forestry Applications of Airborne Laser Scanning; Springer: Berlin, Germany, 2014; pp. 113–133. 16. Wallerman, J.; Bohlin, J.; Fransson, J.E. Forest height estimation using semi-individual tree detection in multi-spectral 3D aerial DMC data. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Munich, Germany, 22–27 July 2012; pp. 6372–6375. 17. Landsskogtakseringen. Landsskogtakseringens Feltinstruks 2008, Håndbok Fra Skog og Landskap 05/08; Skog og Landskap: Ås, Norway, 2008. 18. Braastad, H. Volume tables for birch. Meddr. Norske SkogforsVes. 1966, 21, 265–365. 19. Vestjordet, E. Functions and tables for volume of standing trees. Norway spruce. Meddr. Norske SkogforsVes. 1967, 22, 543–574. 20. Brantseg, A. Volume functions and tables for Scots pine. South Norway. Meddr. Norske SkogforsVes. 1967, 22, 695–739. 21. McGaughey, R.J. FUSION/LDV: Software for LIDAR Data Analysis and Visualization; Technical Report; U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station: Seattle, WA, USA, 2014. 22. Pau, G.; Fuchs, F.; Sklyar, O.; Boutros, M; Huber, W. EBImage—An R package for image processing with applications to cellular phenotypes. Bioinformatics 2010, 26, 979–981. 23. Næsset, E. Effects of different flying altitudes on biophysical stand properties estimated from canopy height and density measured with a small-footprint airborne scanning laser. Remote Sens. Environ. 2004, 91, 243–255. 24. McRoberts, R.E.; Gobakken, T.; Næsset, E. Post-stratified estimation of forest area and growing stock volume using lidar-based stratifications. Remote Sens. Environ. 2012, 125, 157–166. 25. Vastaranta, M.; Wulder, M.A.; White, J.C.; Pekkarinen, A.; Tuominen, S.; Ginzler, C.; Kankare, V.; Holopainen, M.; Hyyppä, J.; Hyyppä, H. Airborne laser scanning and digital stereo imagery measures of forest structure: Comparative results and implications to forest mapping and inventory update. Can. J. Remote Sens. 2013, 39, 1–14. 26. Nurminen, K.; Karjalainen, M.; Yu, X.; Hyyppä, J.; Honkavaara, E. Performance of dense digital surface models based on image matching in the estimation of plot-level forest variables. ISPRS J. Photogramm. Remote Sens. 2013, 83, 104–115. 27. Kaartinen, H.; Hyyppä, J.; Yu, X.; Vastaranta, M.; Hyyppä, H.; Kukko, A.; Holopainen, M.; Heipke, C.; Hirschmugl, M.; Morsdorf, F.; et al. An international comparison of individual tree detection and extraction using airborne laser scanning. Remote Sens. 2012, 4, 950–974. 28. Jakubowski, M.K.; Li, W.; Guo, Q.; Kelly, M. Delineating Individual Trees from Lidar Data: A Comparison of Vector-and Raster-based Segmentation Approaches. Remote Sens. 2013, 5, 4163–4186.
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29. Breidenbach, J.; Næsset, E.; Gobakken, T. Improving k-nearest neighbor predictions in forest inventories by combining high and low density airborne laser scanning data. Remote Sens. Environ. 2012, 117, 358–365. 30. Berger, A.; Gschwantner, T.; McRoberts, R.E.; Schadauer, K. Effects of measurement errors on individual tree stem volume estimates for the Austrian National Forest Inventory. For. Sci. 2014, 60, 14–24. 31. Baltsavias, E.; Gruen, A.; Eisenbeiss, H.; Zhang, L.; Waser, L.T. High-quality image matching and automated generation of 3D tree models. Int. J. Remote Sens. 2008, 29, 1243–1259. 32. Korpela, I.; Heikkinen, V.; Honkavaara, E.; Rohrbach, F.; Tokola, T. Variation and directional anisotropy of reflectance at the crown scale—Implications for tree species classification in digital aerial images. Remote Sens. Environ. 2011, 115, 2062–2074. c 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article
distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).
PAPER III
Forestry
An International Journal of Forest Research
Forestry 9999; 00, 1–21, doi:10.1093/forestry/xxxxx
1
Digital aerial photogrammetry and NFI data for a
2
large-area forest inventory
3
Johannes Rahlf1,∗ , Johannes Breidenbach1 , Erik Næsset2 , Svein Solberg1 , Rasmus
4
Astrup1 1
5
P.O.Box 115, NO-1431 ˚ As, Norway
6 7 8
9
National Forest Inventory, Norwegian Institute of Bioeconomy Research,
2
Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, P.O.Box 5003, NO-1432 ˚ As, Norway ∗ Corresponding
author. E-mail:
[email protected]
10
21/12/2016
11
The use of digital aerial photogrammetry (DAP) for forest inventory purposes has
12
been increasingly investigated in recent years. Forest attributes have been predicted
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with comparable accuracy as with airborne laser scanning (ALS) in small study
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areas with homogeneous conditions. Accuracies for large scale applications with
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heterogeneous terrain and forest vegetation, however, have not yet been reported.
16
In this study we analyzed the accuracy of timber volume prediction models based
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on DAP and national forest inventory (NFI) data on a large area in central Norway.
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Aerial images were acquired in 2010 and 2013 and processed separately to point
19
clouds. Vegetation heights were extracted by subtracting terrain elevation derived
20
from airborne laser scanning. Timber volume estimates from 489 NFI sample plots
21
measured between 2010 and 2014 were used to fit linear timber volume models
22
with height metrics derived from the DAP data as explanatory variables. Cross
23
validation was used to calculate R2 and RMSE (root mean squared error) of the
24
model. Variables describing the heterogeneous environmental and image acquisition
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conditions were calculated and their influence on the model accuracy was tested.
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The results showed that timber volume prediction using DAP works well even across
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a large area. The model fit was good with a R2 of 0.80 and a RMSE of 41.43 m3 ha−1
28
(55% of the mean measured timber volume). Only little of the variation could be
29
attributed to heterogeneous conditions, leading to an improvement of the RMSE by
30
1.02 m3 ha−1 (2%). The relative low cost and a stability across large areas make
31
DAP an attractive source of auxiliary information for large scale forest inventories.
Institute of Chartered Foresters, 2012. All rights reserved. For Permissions, please e-mail:
[email protected] 1
Forestry
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Introduction
33
Background
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Digital aerial photogrammetry (DAP) allows the creation of wall-to-wall, three
35
dimensional (3D) information from digital aerial images. 3D data, i.e. point clouds or
36
digital elevation models (DEM), are extracted from overlapping images by means of
37
image matching. For forest inventories DAP has become a source of auxiliary infor-
38
mation, with comparable properties and similar accuracy as airborne laser scanning
39
(ALS) (White et al., 2016). While ALS has been in the focus of research for decades
40
and is already established as an data source in operational forest inventories (Næs-
41
set, 2014), advances in sensors and computing have made it only recently possible
42
to produce 3D data with similar high spatial resolution from aerial images.
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Contrary to ALS, DAP gives no information about vegetation and terrain below
44
the canopy. For the extraction of vegetation heights, DAP is therefore dependent
45
on an existing digital terrain model (DTM). Its advantage over ALS, however, is
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its lower cost. 3D point clouds for forest inventory applications can be produced
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for large areas from aerial imagery, also as a by-product of acquisitions aiming at
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orthophoto generation (Ginzler and Hobi, 2015). In countries which have established
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national aerial survey programs with regular acquisition intervals DAP is a promising
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data source for continuous forest monitoring (Stepper et al., 2014; Breidenbach and
51
Astrup, 2012).
52
The most common approach for 3D remote sensing in forest inventories is the
53
area-based approach (ABA), which was, in fact, first adopted to 3D data from DAP
54
(Næsset, 2002a) and later to ALS (Næsset, 2002b), where it is now widely used.
55
The ABA is based on numerical metrics, which describe the vertical distribution
56
of remote sensing vegetation height measurements within an area, such as a forest
2
Digital aerial photogrammetry and NFI data for a large-area forest inventory
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inventory sample plot. Combining these metrics with field measurements from the
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same area allows the creation of prediction models which can be applied to new
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areas containing remote sensing data only.
60
Recent studies have reported only small differences between DAP and ALS in
61
predictive models for various forest attributes, e.g. timber volume, canopy heights,
62
and basal area (Gobakken et al., 2015; Pitt et al., 2014; Nurminen et al., 2013;
63
Straub et al., 2013).
64
Large area application
65
Most studies which use 3D remote sensing from DAP focus on small study areas,
66
which feature homogeneous conditions. While such small areas might be desirable
67
for research by enabling narrow and focused studies, they lack larger areas’ variety
68
of forest types and terrain forms. Additionally, acquisition conditions like illumi-
69
nation, weather or season are often more heterogeneous on large areas since it is
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time consuming and can be logistically challenging to cover large areas. Varying
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forest types do not only increase the variation in the forest inventory data but can
72
also influence the quality of the DAP height measurement because certain spectral
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and geometrical properties of the tree canopy can cause difficulties for the image
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matching algorithm (Baltsavias et al., 2008). Additionally, relationships between
75
DAP height measurements and biophysical parameters may vary with forest prop-
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erties, as it has been reported for different degrees of canopy closure (White et al.,
77
2015). Further difficulties for image matching can be encountered in steep terrain
78
with occlusion and lower illumination of parts of the canopy, where texture might
79
be reduced (Baltsavias et al., 2008). Between-image heterogeneity can be caused by
80
different acquisition conditions. Solar elevation influences illumination within the
81
canopy, which affects the accuracy of DAP (Honkavaara et al., 2012). Additionally,
Forestry
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the influence of terrain and solar elevation on the aerial image is relative to the
83
position of the aerial camera. By being based on aerial images, DAP is influenced
84
by weather conditions, i.e. occlusion by clouds, cloud shadows and haze, which can
85
change the radiometric response and therefore image texture (Cohen et al., 1996).
86
To analyze the influence of heterogeneous site and acquisition conditions, White
87
et al. (2015) investigated differences between ALS and DAP within various slope
88
and canopy cover strata, as well as different image acquisition dates in a in a coastal
89
forest in western Canada. An ABA was used to estimate canopy height, basal area,
90
and gross volume at plot-level. Subsequently, they compared metrics and model
91
accuracies between ALS and DAP and strata defined by slope, canopy cover, and
92
acquisition date. Significant differences between metrics were reported for all strata.
93
DAP and ALS gross volume model accuracies differed by 3.63% in RMSE. No trends
94
were found associated to strata or acquisition date.
95
A large-area application of DAP, however, has been described so far only for
96
Switzerland. Ginzler and Hobi (2015) used image matching to create a digital surface
97
model (DSM) covering the whole of Switzerland. A canopy height model (CHM) was
98
calculated by subtracting an ALS DTM from the DSM. Subsequently, they compared
99
CHM heights to single tree height measurements of the national forest inventory
100
(NFI) and obtained a Pearson’s correlation coefficient of 0.83. Waser et al. (2015)
101
used the same CHM for countrywide forest mapping i accordance with the Swiss
102
NFI forest definition. While both studies showed the usefulness of DAP for large
103
area forest mapping, little is known about how large-area conditions influence the
104
accuracy of area-based forest parameter prediction models using DAP.
4
Digital aerial photogrammetry and NFI data for a large-area forest inventory
105
Objectives
106
The aim of our paper was to develop and assess an area-based timber volume
107
prediction model for a large study area (24,473 km2 ) in Mid-Norway covering hetero-
108
geneous terrain and forest conditions using data derived from DAP combined with
109
NFI data. DAP was based on imagery from different acquisition dates with chang-
110
ing conditions and was processed separately for the eastern and the western parts
111
of the study area with different image matching settings. An additional aim was to
112
clarify the effects of various factors describing terrain and acquisition conditions on
113
the accuracy.
114
Materials and methods
115
Study area
116
The study area was located in Mid-Norway covering the northern part of Nord-
117
Trøndelag county, as well as parts of Sør-Trøndelag and Nordland counties (Figure
118
1). The area was 24,473 km2 in size and it extended from 9.31° to 14.23° East and
119
from 63.72° to 65.14° North. The study area included a wide range of terrain forms,
120
from coastal areas in the east to mountains at the Swedish border in the west. The
121
mountains reach elevations of 1400 m above sea level. The lowlands and valleys are
122
covered by boreal forests. Main tree species are Norway spruce (Picea abies (L.)
123
Karst.) and birch (Betula spp.). Scots pine (Pinus sylvestris L.) is less frequent, and
124
while some other broad-leaved species are present they are rare.
125
NFI data
126
The study contained 483 permanent field sample plots of the Norwegian NFI, which
127
are located on a 3 km × 3 km grid. Among the variables recorded within the 8.92 m
128
sample plot radius are tree species and diameter at breast height (dbh) for all trees
64 ° N
65 ° N
Forestry
0
50 km 10 ° E
Figure 1
Study area DAP project boundary NFI sample plot
100
12 ° E
14 ° E
Map of the study area.
129
with dbh ≥ 5 cm (Landsskogtakseringen, 2008). Tree heights are measured for a
130
maximum of 10 trees per plot. If the plot covered more than 10 trees, a sub-sample
131
of 10 trees is selected by relascope (proportional to size) implemented in the field
132
computer. The remaining tree heights are estimated by applying models calibrated
133
with observations from the measured trees. Subsequently, species-specific allometric
134
models for spruce, pine, and birch are used to estimate timber volume for each tree
135
(Vestjordet, 1967; Braastad, 1966; Brantseg, 1967). Finally, timber volume is totalled
136
at plot level and scaled to per hectare values. Differential GPS and GLONASS is
137
used to obtain accurate positions of the sample plot centers.
138
Each plot had field measurements once during the 5-year period between 2010
139
and 2014. This created a time difference against the DAP acquisition of up to 4
140
years and a corresponding mismatch between the forest inventory and the DAP
141
vegetation height measurements, in particular in the case of harvesting and natural
142
mortality. The inventory plots were therefore examined thoroughly by comparing 6
Digital aerial photogrammetry and NFI data for a large-area forest inventory
Table
1 Summary statistics of the ground measured timber volume (m3 ha−1 ) of the 483 sample plots
Measured timber volume Spruce Pine Deciduous Total
Min
Mean
Max
Std.dev.
0 0 0 0
50 10 16 76
539 222 290 577
86 24 30 93
143
the DAP height measurements and field measured tree heights, and inspecting the
144
aerial images. From an initial number of 491 plots, which were completely covered by
145
all remote sensing data, we discarded eight plots clearly having missing trees. Tree
146
growth, on the other hand, caused a less severe mismatch. Measured tree heights and
147
diameters were therefore not adjusted by adding or subtracting growth. Statistics of
148
the forest inventory data of the remaining 483 sample plots are shown in Table 1.
149
Remote sensing data
150
Point clouds calculated from DAP data were provided by an external vendor (Blom
151
Geomatics AS, Norway), and were based on aerial images acquired as part of a
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national program for orthophoto production at regular intervals (Table 2). The image
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overlap was 60% along-track and 20% across-track. The western and eastern part
154
of the study area had separate image acquisitions and photogrammetric processing
155
workflows. Point clouds were created using Trimble’s Match-T DSM software. The
156
eastern part was processed using version 5.4.1 of the software and parameter settings
157
”DSM Extreme”. The western part was processed using version 5.7.2 and parameter
158
settings ”DSM Mountainous”. Both point clouds represented smooth surfaces with
159
the points evenly distributed in a horizontal grid with point densities of 8.5 m−2
160
and 3.7 m−2 in the eastern and the western parts, respectively. Table
East West
2 Summary of the aerial image acquisitions.
Area (km2 )
Camera
No. of images
Date
GSD (cm)
17148 8454
Vexcel UltraCam Xp Vexcel UltraCam Eagle
2402 1548
17.–18.08.2010, 09.09.2010 23.–24.07.2013
35 25
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To extract vegetation heights from the DAP point clouds, we calculated DTMs
162
from existing ALS acquisitions in the study area. These ALS data were acquired
163
between 2006 and 2015 for various uses including forest resource mapping. We gen-
164
erated a DTM with a cell size of 0.5 m × 0.5 m as the mean elevation of the
165
ground-classified ALS returns using FUSION version 3.42 (McGaughey, 2014).
166
For all sample plots we extracted DAP and ALS data which intersected with
167
the plot. Numerical metrics were calculated describing the distribution of the DAP
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point heights above ground: minimum height (hmin ), maximum height (hmax ), mean
169
height (hmean ), standard deviation of the height (hSD ) and heights of the 5%, 25%,
170
50%, 75%, 95% height percentiles (hP 05 , hP 25 ,hP 50 , hP 75 , hP 95 ). From the point
171
heights the density metrics percentage of points above the mean height (dmean ) and
172
above 2 m (d2 ) were calculated.
173
The point clouds of the eastern and western parts were similar, based on a com-
174
parison in an overlapping area. However, in order to address possible differences of
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the two DAP projects, we added a 0-1 dummy variable (DAP project) for the point
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cloud, from which the DAP data was extracted, and the interaction between this
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dummy variable and the height metrics.
178
Additional variables
179
To analyze the influence of the heterogeneous data a range of variables was com-
180
puted, which describe the conditions of the environment and the image acquisition.
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From the ALS DTM we calculated altitude (ALT), slope (SLP), aspect (ASP), and
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topographic position index (TPI) for each sample plot. Single values were extracted
183
for each sample plot by resampling the ALS DTM to smaller tiles with 20 m × 20 m
184
cell size around each plot. The TPI describes the position within the terrain and
185
is calculated by subtracting the mean elevation of the 8 surrounding cells from the 8
Digital aerial photogrammetry and NFI data for a large-area forest inventory
186
cell elevation. As a measure of flatness independent of slope, the absolute value
187
of the TPI was also included as a variable (TPIabs). Larger scale landscape pat-
188
terns were covered by aspect, slope, TPI, and absolute TPI (ASP100, SLP100,
189
TPI100, TPIabs100), which were calculated from a country-wide available DTM
190
with 10 m × 10 m cell size which was resampled to 100 m × 100 m cell size around
191
each sample plot. The country-wide available DTM assured complete data coverage,
192
also for sample plots close to areas where no ALS DTM was available. ASP and
193
ASP100 were used as categorical variables encoded as North-East (NE), East (E),
194
South-East (SE), South (S), South-West (SW), West (W), North-West (NW), and
195
North (N).
196
197
The longitude (LONG) and latitude (LAT) of the sample plots were used as variables describing geographical position.
198
To capture conditions of the image acquisition, the image with the closest image
199
center was assigned to each sample plot. From the position of the camera, which was
200
derived by aerotriangulation and delivered with the image metadata by the vendor,
201
we calculated the relative viewing angle onto the sample plot taking slope and aspect
202
of the terrain into account (relVA), i.e. the angle between the normal vector of the
203
terrain surface and the viewing direction of the camera onto the sample plot.
204
Illumination conditions were represented by variables derived from the date and
205
time of the image acquisitions. The position of the sun was estimated for every
206
sample plot at the moment of image acquisition as solar elevation (SOLELEV) and
207
azimuth (SOLAZI) angles using an algorithm by Michalsky (1988). SOLAZI was
208
used as categorical variable with classes according to ASP and ASP100. Subse-
209
quently, the solar incidence angle relative to the terrain (relSOLINC) was computed
210
by including the plots’ slope and aspect. Similar to relVA relSOLINC is the angle
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Table 3 Statistics of the numerical variables describing the environment and the conditions of the image acquisition.
Variable ALT SLP TPI TPIabs SLP100 TPI100 LONG LAT relVA SOLELEV relSOLINC VSdiff Tdiff
Unit
Minimum
Mean
Maximum
Std.dev.
m degrees m m degrees m degrees E degrees N degrees degrees degrees degrees years
3.40 0.13 -7.03 0.01 0.12 -23.87 9.77 63.75 0.05 24.25 14.39 8.08 -3.13
251.20 12.39 0.03 0.93 9.22 0.04 12.02 64.37 15.46 34.89 55.98 55.63 0.99
708.97 47.02 5.34 7.03 35.86 33.60 14.11 64.99 86.94 44.97 97.08 94.80 4.11
170.74 8.41 1.37 1.00 6.45 6.84 1.18 0.32 14.33 5.18 12.30 12.44 1.90
Table 4 Categorical variables describing the environment and the conditions of the image acquisition. The number of plots falling in each class is provided in parentheses.
Variable
classes
ASP
NE(60), E(42), SE(67), S(66), SW(57), W(50), NW(82), N(59)
ASP100
NE(60), E(46), SE(58), S(64), SW(53), W(65), NW(72), N(65)
SOLAZI
NE(0), E(0), SE(221), S(121), SW(113), W(28), NW(0), N(0)
211
between the normal vector of the terrain surface and the sun light direction. The
212
angular difference between the sun light direction and the viewing direction (VSdiff)
213
of the plane was computed to address the influence of shadows considering both sun
214
and airplane positions.
215
The time difference in years (with a temporal resolution in days) between the
216
forest inventory and the image acquisition (Tdiff) was calculated by subtracting the
217
time of the image acquisition from the time of measuring the field data, resulting in
218
negative numbers for plots that were measured in field prior to image acquisition.
219
As Tdiff measures time between the inventory and the image acquisitions it can be
220
seen as a simple proxy for growth. Table 3 and 4 give an overview and statistics of
221
the variables describing the conditions of the image acquisition. 10
Digital aerial photogrammetry and NFI data for a large-area forest inventory
222
Modeling timber volume
223
Linear regression models were fitted to the observed timber volume at plot level. As
224
goodness-of-fit measure we used the root mean squared error (RMSE): v u n u1 X (yi − yˆi )2 , RM SE = t n i=1
225
226
where n is the number of sample plots, yi is the observed timber volume at sample
227
plot i, and yˆi is the predicted timber volume at sample plot i. The relative RMSE
228
in percent was calculated as:
RM SE[%] =
RM SE , y¯
229
230
where y¯ is the mean observed timber volume of all sample plots. For all predictions
231
we used leave-one-out cross validation. Additionally, the cross-validated coefficient
232
of determination (R2 ) was Pn (yi − yˆi ) R = 1 − Pni=1 . ¯i ) i=1 (yi − y 2
233
Explanatory variables were selected using a stepwise forward algorithm reducing
234
the relative RMSE. To avoid overfitting, we set the minimum threshold for the reduc-
235
tion to 1%. Hence, variables reducing the RMSE by less than 1% were not considered
236
in the model. Subsequently, model coefficients were tested for their deviation from 0
237
using t-statistics (H0 : βj = 0, with j = 1, ..., p and p the number of explanatory vari-
238
ables). The categorical variables were dummy coded without a benchmark category,
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239
because we wanted every category to be selectable by the stepwise algorithm. Before
240
the final model was selected the data set was analyzed for the presence of influential
241
outliers using Cook’s distance measure. All statistical analyses were performed in R
242
version 3.1.2 (R Core Team, 2016).
243
Two models were fitted: The basic model only included variables from the DAP
244
point clouds. The extended model was fitted using the selected variables of the
245
basic model and additional variables describing the environment and the acquisition
246
conditions. This two-step approach allows the quantification of the influence of the
247
additional variables.
248
For the basic model we allowed only the vegetation height metrics extracted from
249
the DAP point clouds to be selected: height metrics, DAP project, and their inter-
250
actions. By manual inspection of scatter plots of model predictions we identified an
251
exponential trend in the data. We therefore added the squares of these variables
252
to the selectable variables. To account for the visible heteroscedasticity, we applied
253
a heteroscedasticity-consistent covariance matrix estimator as suggested by White
254
(1980).
255
The first step in fitting the extended model was to assess the correlation between
256
the additional variables and the residuals of the basic model to avoid false repre-
257
sentation of apparently non-linear relationships by the linear regression. Again, the
258
stepwise algorithm was used, which was set to reduce the RMSE with a minimum
259
threshold at 1%. Due to the large amount of variables available, a complete assess-
260
ment of interaction effects was not possible. However, we included the interactions
261
between the terrain parameters SLP and ASP, and SLP100 and ASP100.
12
Digital aerial photogrammetry and NFI data for a large-area forest inventory
262
Results
263
The obtained models show a strong relationship between the DAP height metrics and
264
the observed timber volume on the large study area. Including additional variables
265
improved the accuracy only marginally (Table 7).
266
For the basic model predicting timber volume, which used DAP point cloud vari-
267
ables, the stepwise algorithm selected hmean , d2 2 , and the interaction between DAP
268
project and hSD as predictor variables. hP 25 reduced the RMSE further, but less
269
than 1%. The RMSE was 50%. However, one plot was identified as an influential
270
outlier having a Cook’s distance measure of 1.59, which is the 82th percentile of the
271
corresponding F distribution, F (p, n − p) = F (4, 480). A percentile value of more
272
than 50 percent implies a major influence on the model fit (Kutner et al., 2005).
273
The sample plot had a measured volume of 306 m3 ha−1 and was overpredicted by
274
301 m3 ha−1 . The sample plot was located on a steep slope facing North-East, and
275
the aerial images showed that the plot was lying completely in the shadow. Only
276
two tree tops were visible. We excluded the influential outlier from the model fitting
277
and repeated the variable selection. Consequently, the vegetation height variables
278
included in the basic model (selected without the influential outlier) were hP 75 2 ,
279
hP 05 2 and hP 95 (Table 5). The dummy variable DAP project reduced the RMSE by
280
only 0.2% and was therefore not included in the model. The outlying sample plot
281
was later used in the model accuracy assessment by including its residual in the
282
RMSE calculation.
283
The residual error of the extended model including additional variables was
284
marginally lower than the basic model with only DAP variables indicating that only
285
little additional variance could be explained by these variables. For the extended
286
model the stepwise algorithm selected one additional predictor, relSOLINC, which
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Table
5 Selected variables and parameter estimates of the linear models. p-value is the result of t-statistics.
Model basic model
extended model
Variable
estimate
Std.error
p-value
Intercept hP 75 2 hP 05 2 hP 95
-1.40 0.75 0.78 4.80
2.38 0.12 0.17 0.83
0.55 0 0 0
Intercept hP 75 2 hP 05 2 hP 95 relSOLINC
36.99 0.75 0.81 4.86 -0.70
7.76 0.12 0.17 0.83 0.14
0 0 0 0 0
Table 6 Influence of the environment and acquisition variables. ∆ RMSE is the change of RMSE when including the variable in the vegetation height model and p-value is the result of t-statistics. Coef gives the direction of the parameter estimate.
Variable
∆ RMSE [%]
p-value
Coef
-1.3 -0.5 -0.5 -0.4 -0.4 -0.3 -0.2 -0.2 -0.2 -0.1 -0.1 -0.1 -0.1 -0.1
< 0.001 0.001 < 0.001 0.001 < 0.001 0.010 0.002 0.016 0.026 0.027 0.006 0.052 0.034 0.064
+ + + + + + + -
relSOLINC relVA Tdiff SOLAZI (W) SLP100 ×ASP100 (N) SLP ×ASP (N) SLP ×ASP (NE) SOLELEV SOLAZI (SE) LONG SLP ×ASP (SW) TPI SLP100 ×ASP100 (SW) SLP
287
improved the RMSE by 1.34% compared to the basic model based on vegetation
288
heights. Further steps of the stepwise algorithm added Tdiff, the dummy variable
289
for SOLAZI for South-East, and relVA. However, each of these subsequent steps
290
decreased the relative RMSE by less than 1%. The variables with the largest RMSE
291
reduction in the first step of the stepwise algorithm are presented in Table 6.
292
When including the outlying plot in the calculation of the goodness-of-fit measures
293
of the extended model, the RMSE increased by 7.65 m3 ha−1 (9.83%) and the R2
294
decreased by 0.06. Figure 2 shows observed timber volume plotted against predicted
295
timber volume of the extended model. While heteroscedasticity is visible, the plots 14
Digital aerial photogrammetry and NFI data for a large-area forest inventory
7 Cross-validated RMSE and R² of the selected models without and with the residuals of the outlying plot. All models were fitted without the outlier.
Table
Without outlier model
RMSE [%]
33.77 32.76
45.00 43.50
RMSE
RMSE [%]
R2
0.87 0.87
41.43 40.41
55.00 53.33
0.80 0.81
R
400 300 200 0
100
Observed timber volume (m3ha−1)
500
600
basic model extended model
RMSE
With outlier 2
0
200
400
600
800
Predicted timber volume (m3ha−1)
Figure 2
Observed versus predicted timber volume using the extended model.
296
spread evenly around the 1:1 line. The sample plot with the highest volume was
297
underpredicted. The outlier can easily be identified in the scatter plot as clearly
298
separated from the rest of the sample plots having the highest predicted timber
299
volume.
300
Discussion
301
The results of the study show the possibilities of combining DAP and NFI data
302
for large area forest inventories. The good model fit is an indicator of the strong
303
relationship between DAP height metrics and biophysical forest attributes even over
304
changing terrain and image acquisition conditions. Together with the relative low
Forestry
305
cost, this stability across large areas make DAP an attractive remote sensing method
306
for large scale forest inventories.
307
Earlier studies on small study areas using DAP for timber volume estimation
308
achieved plot level model accuracies of 20—37% (Puliti et al., 2016; Gobakken et al.,
309
2015; White et al., 2015; Rahlf et al., 2014; Vastaranta et al., 2013). In a mixed forest
310
in southern Germany, Straub et al. (2013) reported a timber volume model accuracy
311
of 41% based on DAP. However, comparisons between different studies have to be
312
taken with caution because many factors, e.g. peculiarities of the study area, data
313
quality, and the statistical method can influence model accuracies. The relative
314
RMSE of the timber volume predictions in this study is higher than the accuracies
315
given by other studies. Beside the effects of the heterogeneous study area, the main
316
reason is that the RMSE is calculated using the mean timber volume, which was
317
considerably lower than in other studies, e.g. White et al. (2015) reported mean
318
timber volumes more than ten times larger than in this study. The R2 , however,
319
is similar or better than model fits obtained in earlier studies on small study areas
320
(Puliti et al., 2016; Gobakken et al., 2015; Straub et al., 2013). The good model fit is
321
in line with the findings by Ginzler and Hobi (2015) who reported a good correlation
322
(r = 0.83) of DAP CHM heights and terrestrially measured canopy heights in a
323
nationwide study in Switzerland.
324
We derived variables to quantify the heterogeneous terrain, geographical position,
325
and illumination conditions and investigated their influence on the timber volume
326
model accuracy. Variables were computed and added to the model to quantify their
327
effect on the model residuals. While many variables improved the model accuracy,
328
the improvement was generally negligible with only the relative sun elevation to the
329
terrain, relSOLINC, decreasing the RMSE more than 1%. A major improvement by
16
Digital aerial photogrammetry and NFI data for a large-area forest inventory
330
including these variables could, however, not be expected as DAP vegetation height
331
metrics alone already explained 80% of the variation. Beside errors introduced by the
332
heterogeneity of the study area, the remaining variation includes also measurement
333
errors of the remote sensing and the field inventory, and other noise.
334
relSOLINC describes the height of the sun relative to the terrain at the moment of
335
image acquisition, which is influencing the distribution of light within the canopy. A
336
high incidence angle causes more shadows in canopy gaps, which could lead to prob-
337
lems for the image matching algorithm due to little or missing texture (Honkavaara
338
et al., 2012; Baltsavias et al., 2008). We observed that the point heights in such
339
canopy gaps appear interpolated and do not reflect the true height of the terrain or
340
lower vegetation. Such higher point heights lead to higher timber volume predictions,
341
which explains the negative coefficient of relSOLINC. These findings correspond to
342
St-Onge et al. (2008) who found lower correlations between ALS and DAP CHMs
343
where shadow was present. Looking at the general influence of sun position, White
344
et al. (2015) found no difference in model performance associated with average solar
345
elevation. They used, however, only the date as a measure of sun elevation. In addi-
346
tion, relSOLINC might also be an indicator for the general light availability at the
347
plot, with northwards facing plots having always a higher sun incidence angle and
348
thus less light than southwards facing plots. Light availability may have an influence
349
on the vegetation. However, a general effect of north-facing slopes was not visible.
350
The DAP project had a significant but marginal influence on the model accu-
351
racy. This suggests that the different matching strategies produced only a small
352
variation in the point clouds, especially when compared to variations caused by the
353
heterogeneous terrain and image acquisition conditions.
Forestry
354
Surprisingly, also the time difference between the field measurements and the
355
image acquisition, Tdiff, which has the potential to correct the differences in mea-
356
sured and predicted timber volume caused by growth, showed only a little effect
357
on the accuracy, even though the time differences were substantial. Reasons for the
358
minor effect of Tdiff might be the relative low growth rate of 0.81 m3 ha−1 yr−1 in
359
the region (Tomter and Dalen, 2014).
360
We analyzed the influence of factors covering terrain, geography, viewing and illu-
361
mination conditions. However, also other factors can influence the accuracy of image
362
matching, e.g. weather and vegetation (Gruen, 2012). The benefit of stratification
363
based on forest type and tree species has been shown by Gobakken et al. (2015) and
364
Straub et al. (2013). Gobakken et al. (2012) used satellite imagery to classify forest
365
types for stratification for a large area forest inventory based on ALS strip sampling.
366
For the extraction of vegetation heights from DAP data, an accurate DTM is
367
needed. We had an ALS DTM available for large parts of our study area. However,
368
the ALS data were collected mainly in the valleys where the productive forests of
369
the area can be found and they covered only small parts of the mountainous regions
370
with sparse vegetation. For forest management purposes, underrepresentation of
371
non-productive forests might, however, not be problematic.
372
In our study we did not compare DAP with ALS data because the available ALS
373
data were too inhomogeneous, e.g. multiple flight campaigns over a time span of 10
374
years. However, earlier studies have shown that ALS and DAP produce comparable
375
model accuracies (Gobakken et al., 2015; Pitt et al., 2014; Rahlf et al., 2014; Bohlin
376
et al., 2012).
377
The mismatch between the point cloud heights and the measured trees at the
378
sample plot which was identified as an influential outlier was apparently caused by
18
Digital aerial photogrammetry and NFI data for a large-area forest inventory
379
shadows. The large height of the DAP points seemed to be the result of interpolation
380
between the visible tree tops, while the actual canopy was much lower, but not
381
visible on the aerial images. The outlying sample plot, however, was included in the
382
accuracy assessment of the model because we could not justify its removal in that
383
part of the analysis. Over large and heterogeneous forest areas such errors should
384
be expected. If however, areas where image matching fails to depict canopy heights
385
could be identified, these areas and therefore also the outliers could be removed
386
from the dataset. Criteria for a classification of such areas, e.g. brightness thresholds,
387
could not be determined from our reference data. An approach to prevent such errors
388
caused by interpolation and smoothing could also be the use of raw matched point
389
clouds.
390
The use of the spectral information of the aerial images could potentially improve
391
timber volume estimation estimation as it was used by Puliti et al. (2016) to derive
392
species specific timber volume.
393
Conclusion
394
We showed that digital aerial photogrammetry combined with NFI sample plots
395
are valuable data to predict forest attributes for large areas. The obtained models
396
had a good model fit and an accuracy comparable to accuracies reported for small
397
study areas. Heterogeneous conditions of the environment and image acquisition
398
influence the stability of DAP heights only marginally. A small improvement could
399
be achieved by taking the height of the sun relative to the terrain at the moment of
400
image acquisition into account.
Forestry
401
Funding
402
This research was funded by the Norwegian Institute of Bioeconomy Research
403
(NIBIO).
404 405
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PAPER IV
Forest information at multiple scales: Development, evaluation and application of the Norwegian Forest Resources Map
Authors Rasmus Astrup*, Johannes Rahlf, Knut Bjørkelo, Misganu Debella Gilo, Arnt-Kristian Gjertsen, Johannes Breidenbach.
Address Norwegian Institute for Bioeconomy Research Postboks 115, 1431 Ås
*Corresponding Author Rasmus Astrup
[email protected]
1
Abstract This paper describes the development and utility of the freely available Norwegian forest resources map (SR16). SR16 is developed using photogrammetric point cloud data with ground plots from the Norwegian National Forest Inventory (NFI). First, the forest mask was updated with object-based image analysis methods. Evaluation against the NFI forest definitions showed Cohen’s kappa of 0.77 and accuracy of 0.89 in the lowlands and an accuracy of 0.95 with a kappa of 0.63 in the mountains. Within the updated forest mask, a 16×16 m raster map was developed with tree height, volume, biomass, and tree species as attributes (SR16 raster). All attributes were predicted with generalized linear models and explained about 70% of the observed variation. SR16 raster was segmented into stand-like polygons that are homogenous in respect to tree species, volume, site index, and tree height (SR16 vector). A comparison of the SR16 raster with volume estimates for 27.740 stands in commercial Forest Management Inventories (FMIs) illustrated that the majority were within 25 m3 of the FMI values while 95% were within 50 m3. When SR16 was utilized in a combination with the NFI plots and a model-assisted estimator, the precision of the model-assisted estimates were considerably higher than direct estimates. In conclusion, SR16 is useful for improved estimates from the Norwegian NFI at various scales. The mapped products are of a quality that they may be useful as base information in the development of FMIs.
2
Introduction Through a variety of sampling schemes, National Forest Inventories (NFI) provide forest statistics at national and regional scales (Tomppo et al. 2010). At more local scales, such as municipalities, the NFI sample size usually becomes too small to provide forest statistics with an acceptable associated precision (e.g. Breidenbach and Astrup 2012). The role of remote sensing in NFIs is manifold: In the design-phase to optimize the sampling scheme by stratification, before field work for the visual recognition of plot conditions, in the estimation phase to improve the precision of estimates, as well as base information in the production of wall to wall maps of forest resources (McRoberts and Tomppo 2007). Throughout the boreal forest, optical satellite imagery in combination with ground-based inventory plots have been used to generate wall-to-wall forest maps (e.g. Sweden: Reese et al. 2003; Finland: Tomppo et al. 2008; Norway: Gjertsen 2007; Canada: Beaudoin et al. 2014). These maps have been useful for a variety of purposes such as generation of regional statistics and landscape-level analysis of forest attributes such as road networks or wildlife habitat (e.g. Tomppo et al. 2008; Bjørneraas et al. 2011) but has generally been associated with higher uncertainty than normally desired for Forest Management Inventories (FMI). In Fennoscandia especially and increasingly throughout the world, FMIs are established by combining purposefully acquired forest inventory plots and airborne scanning lidar (light detection and ranging) data (Næsset et al.2004) or as a recent alternative with point clouds from digital air- or space-borne photogrammetry replacing the lidar data (e.g. Puliti et al 2016; Bohlin et al. 2012; Immitzer et al. 2015). Generally, 3D data obtained by lidar, photogrammetry, and interferometric synthetic aperture radar (InSAR) show a much stronger correlation with key forest inventory attributes such as height, volume, or biomass (Rahlf et al. 2014; Yu
3
et al.2015) than observed for purely optical remote sensing. Covariates derived from lidar are typically found to be slightly better predictors of forest structural attributes than those derived from photogrammetric point clouds which again are slightly better than those derived from InSAR or radargrammetry data. However, all three data types can be used to predict forest structural attributes with associated error rates that make them attractive for use in FMIs (Rahlf et al. 2014; Yu et al. 2015).
In recent years, the availability of 3D data for the mapping of forest structural attributes at large scales have increased dramatically through national laser scanning campaigns that have been carried out in many European countries (e.g. Nilsson et al. 2016; Monnet et al. 2016; Nord-Larsen and Schumacher 2012). Increased processing power combined with improved photogrammetric software have made it possible to obtain national photogrammetric points clouds as a low-cost byproduct of existing national aerial ortho photo campaigns (e.g. Ginzler and Hobi 2015, Breidenbach and Astrup 2012), and new satellite missions have improved the access to InSAR data (e.g., Solberg et al. 2013). The availability of large-scale 3D data and the advancement of methods (e.g., Magnussen & Breidenbach 2017, Breidenbach et al. 2016) gives a previously non-existing possibility for using NFI sample plots as ground data for development of both forest maps (e.g. Nilsson et al. 2016; Monnet et al. 2016; Immitzer et al. 2015) and local forest statistics that simultaneously satisfies information requirements at multiple scales (e.g. Breidenbach and Astrup 2012). This includes national and regional forest statistics typically satisfied by NFIs as well as local information for stand- and estate-level inventories typically satisfied by FMIs. In other words, the increased availability of largescale 3D data can be viewed as the bridge for linking the worlds of NFIs with that of
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FMIs which so far to a large extend have been separate processes carried out at different spatial scales by different actors within the forest sector.
The motivation behind this study is the development of a Norwegian framework that links NFI data with national datasets of 3D remote sensing in order to bridge the divide between NFI statistics and the need for local forest information in municipal forest statistics, and FMIs. In Norway both 3D remote sensing data and precisely geo-located NFI plots are available. One fifth of the country is covered with airborne photography every year, which makes it possible to obtain low-cost photogrammetric point clouds as a byproduct. Simultaneously, a national laser scanning campaign is on-going that will be finalized in 2019. The Norwegian NFI operates with more than 12.600 forested permanent sample plots located in a systematic grid that are re-measured in a five-year interpenetrating panel design.
The objective of this paper is threefold; to describe the development of the Norwegian forest resources map (SR16), to evaluate the generated forest information at local scales through comparison of the result to commercial FMIs, and finally to illustrate the gain in precision when using SR16 in addition to NFI sample plots for making estimates at the municipality and regional level.
Methods Overall framework The intended overall output from the study are threefold: (1) a raster based forest map with a 16 by 16 meter resolution including tree height, volume, biomass, and tree species as attributes (SR16 raster), (2) a vector map with stand-like polygons that
5
includes site index in addition to all the parameters form the raster map (SR16 vector), and (3) municipal level forest statistics based on the NFI plots and SR16 raster. The 16 meter resolution was chosen to resemble the size of the Norwegian NFI plots which are 250m2 circular plots. The overall framework for the study is outlined in Figure 1.
Figure 1. Overall data and workflow. The main products are blue; updated forest mask, SR16 raster, SR vector, and model assisted NFI estimates. Green boxes illustrate the developed models, while the first part of the figure illustrates the data processing.
Study area and data The study area used in this manuscript is located in central Norway (Figure 2) and consists of three photo projects named Nord-Trøndelag, Trøndelag-Vest and SørTrøndelag. The Nord-Trøndelag area is 17.248 km2 and the images were acquired during three days in August and September of 2010. The Trøndelag-Vest area is 8.454 km2 and the images were acquired on July 24th 2013. The Sør-Trøndelag area is 25.745 km2 and images were acquired on July 1st 2014 and 12th of July 2015. There is some small
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overlap between the photo projects and the total area of the study area without overlaps is 49.880 km2.
Figure 2. Outline of the study area. The study area consists of three photo projects named Nord-Trøndelag, Trøndelag-Vest, and Sør-Trøndelag.
The aerial images were acquired with an overlap of 60% along strips and 20% between strips in Nord-Trøndelag and Trøndelag-Vest, and 80% and 20%, respectively, in SørTrøndelag. In order to obtain a photogrammetric point cloud, Blom Geomatics AS, Norway, processed the images using Trimble's Match-T DSM software. The images in Nord-Trøndelag were matched with version 5.4.1 of the software and the parameter settings ''DSM_Extreme'', which resulted in a point cloud with a point density of 8.5 m⁻². In Trøndelag-Vest version 5.7.2 of the software was used and the parameter settings ''DSM_Mountainous'', resulting in point density of 3.7 m⁻². In Sør-Trøndelag version
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7.0.2 was used with the ''DSM_Mountainous'' parameter settings resulting in a point cloud with a point density of 3.8 m⁻².
The photogrammetric point cloud was normalized by subtracting a digital terrain model (DTM) and obtaining a corresponding point cloud representing the canopy. We utilized two types of DTMs. Where available, ALS data were used to compute the DTM. The data vendors of the various scanning projects delivered the ALS data classified in ground and non-ground returns. From the ground returns a DTM was created by averaging the return heights within 1 × 1 m cells. For areas without ALS projects we applied the national DTM (DTED10; Kartverket 2016) which covers the whole country and has a spatial resolution of 10 m. The DTED10 was created from various sources, such as contour lines from topographic maps. Depending on the input data, the accuracy of the elevation varies with a reported standard deviation between 2 m and 6 m. As an explanatory variable in models, the Topographic Wetness Index (TWI) was calculated with the DTED10 as input for the multiflow algorithm (Toma et al. 2002) in the GRASS GIS software. High TWI values correspond to areas receiving water from the surrounding terrain.
The National Land Resource Map (AR5) (Ahlstrøm et.al. 2014) in scale 1:5000 was used extensively in the various models that were used in SR16 raster. AR5 includes land information on soil conditions, vegetation, site productivity, and tree species groups. AR5 is based on extensive field inventories and aerial image interpretation and uses a detailed, standardized classification system. AR5 is the best available national Norwegian forest mask but has not been systematically updated since it was developed in the 1960s.
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The study area contains 2.967 Norwegian NFI plots (Tomter et al. 2010) whereof 2.379 plots were located in a 3 by 3 km grid in conifer-dominated lowlands while 588 where located in the 3 by 9 km grid in the birch-dominated mountain forests. Out of the 2.967 NFI 1.522 plots were located in forest. The NFI plots were used as reference data for all models of volume, biomass, tree species, tree height, site index. Based on the individual tree measurements standing volume without bark (Vestjordet 1967, Braastad 1966, Brantseg 1967) and above-ground biomass (Marklund 1988) were estimated for all plots for all trees with a diameter bigger than 5 cm in dbh. Prior to this project, the NFI plots were only utilized in direct estimation of regional or national forest statistics.
Updating the AR5 forest mask The AR5 forest mask was updated with object-based image analysis (OBIA) methods (Blaschke 2010, Hay & Castilla 2006). OBIA has well documented advantages over pixelbased classification (Blaschke 2010, Hay & Castilla 2006, Whiteside et al. 2011) and involves segmentation of images into homogeneous objects which are made of spatially contiguous pixels with minimum dissimilarity at a given scale (Blaschke 2010). The objects can then be characterized based on a given set of attributes, and classes can be assigned to the objects using appropriate algorithms. Trimble eCognition™ was used for the update of the forest mask.
The first step of the analysis was to prepare the utilized datasets. The normalized photogrammetric point cloud data was converted to a raster dataset with 2 m spatial resolution and a mean canopy height and the Normalized Difference Vegetation Index (NDVI) (NDVI = [NIR – R]/[NIR + R]) were calculated. For areas with ALS DTM the
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normalized photogrammetric point cloud was used directly. For areas covered by DTED10 an improved normalized point cloud was computed following the approach of Debella-Gilo (2016). In brief, most of the areas without ALS DTM are located in the mountains with relatively sparse vegetation which allows for some photogrammetric points to reach the ground and can be utilized to improve the canopy height representation compared to using DTED10 (Debella-Gilo 2016). The 2 m raster dataset with the three color bands, NDVI and point-cloud height metrics were used as basis for segmentation using the multi-resolution segmentation algorithm.
Following the segmentation, a two-step classification procedure was carried out. First, the objects were classified using the decision tree classification method (Friedl & Brodley, 1997). The aim was to follow the definitions of the AR5 forest and other land cover types as faithfully as possible. The metrics as NDVI, CHM, and 90% percentile of the normalized point cloud were used in the decision tree. The decision tree separates green objects from non-green objects, above ground objects from ground objects to finally classify the segmented objects in to forests and other land cover types (Figure 3).
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Figure 3. Outline of the decision tree for forest classification as implemented in eCognition. The image scene as the root node (blue), the intermediate subclasses as branch nodes (red) and the land cover classes including forest as the terminal nodes (green). The branches are separated based on the CHM, NDVI, and other spectral metrics.
The outlined classification method cannot detect temporarily unstocked forests such as clear-cuts and newly planted areas. Hence, a second procedure to detect temporarily unstocked stands was developed as a rule-based method. To include clear-cuts and young forests, a rule set based on AR5 variables was developed. Areas classified as biotic open areas (Figure 3) were included as forest if the area was registered as productive
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forest in AR5. Abiotic open areas were assumed to be clear cuts and included in the forest area if they fulfilled the following two criteria: productive forest in the AR5 map and no indication of permanent land use change in terms of roads or building construction. An update from forest to non-forest without the presence of infrastructure was only accepted if the area is classified as non-productive in AR5 and if the area is larger than 0.5 hectare. Non-forest areas in the AR5 can be classified as forest if they fulfill all the requirements of forest including the minimum area of 0.5 hectare. These mainly include regenerated forests in open areas, planted or regenerated forest on mire, and forest in areas not mapped in the AR5. Both forested mire and grazing areas with dense trees are classified as forest.
Evaluation of the forest mask The updated AR5 forest mask was developed independently of the NFI plots; the NFI plots can hence be used to evaluate the performance of the forest mask. Each NFI plot is classified to a land use category including forest, other wooded lands and non-forest categories. For the evaluation of the forest mask, we used the classification of the forest used for the Norwegian LULUCF reporting (Norwegian Environment Agency 2015) which is consistent with the international forest definitions and is defined in terms of canopy cover (>10%), potential tree height (>5m) and minimum area (0.1 ha). To evaluate the updated AR5 forest mask performance, it was overlaid with the NFI plots and the forest classifications were compared. More specifically, separate confusion matrices were produced for the lowland coniferous dominated forests (3 by 3 km grid) and the mountainous birch-dominated forests (3 by 9 km grid). Subsequently, misclassifications were further investigated.
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Tree species, volume, biomass and height For each photo project, the available forested NFI plots were used for fitting independent models for tree species, volume without bark, aboveground biomass (AGB), and Lorey’s height. Before fitting models, response variables and covariates were visually inspected in order to remove some extreme outliers that would have influenced the model parameter estimates. There were typically 2-5 such outliers per photo project. Most of those outliers resulted from harvests due to temporal mismatches of the field and the remote sensing data.
The tree species models classify into three groups; Spruce, Scots pine (Pinus sylvestris), and deciduous. The classification of the NFI plots was done according to the species group with the highest proportion of volume. The spruce group is mainly composed of Norway spruce (Picea abies) but also contained minor amount of other spruce species such as Sitka spruce (Picea sitchensis). The deciduous group is dominated by birch species (Betula pubescens and Betula pendula) but contains small portions of aspen (Populus tremula) and rowan (Sorbus aucuparia).
A multinomial logistic model (Venables & Ripley 2002) was fit to all NFI plots where one species group had a proportion of more than 75% of the volume. The following DAPderived covariates were used: 90th percentile of the vegetation height, NDVI, mean and 75th percentile of the red band, 75th percentile of the near infrared band, and mean of the green band. In addition, the following covariates obtained from other sources were used: Elevation and terrain wetness index (TWI); deciduous and coniferous classification and site productivity class was taken from AR5 maps as categorical
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variables. No difference between DTM origin (DTED10 or ALS DTM) was made for the tree species models.
For prediction of volume and biomass, several parametric and non-parametric models have been tested (see Rahlf et al. 2017, Rahlf et al. 2015). As transparency and robustness had high priority, we selected independent, parametric regression models to link the variables of interest to predictor variables. The NFI sample plots in an area were visited within an interval of five years. In order to avoid the influence of random misbalances in the differences between the field visit date and the image acquisition date, volume and biomass were adjusted to the image acquisition date by multiplying the difference between the field visit date and the acquisition date with the volume and biomass growth per year on the plot within the past five years.
Generalized linear models (GLS) (Pinheiro et al. 2016) were independently fit for each photo project and within a photo project fit independently for areas with a DTED10 and with ALS DTM. This resulted in a total of 6 independent GLS models per forest attribute for the study area. GLS models were preferred over weighted linear models, because they allowed a more flexible variance model. Mean vegetation height and its square were chosen as the only explanatory variables. The model had the general form:
̂
where y is the response, β is the vector of parameters to be estimated, t is transpose, x is the vector of covariates including a “one” as the first element to accommodate an
14
intercept, e is a residual, σ is the residual variance, ̂ is the expected value, and δ is a variance parameter.
For application of the models in wall-to-wall prediction, an R function was written that constrained the models from producing negative or unrealistically high values. The difference between the fitted model and the function used for prediction, together with the sample plot observations for above ground biomass in Sør-Trøndelag are illustrated in Figure 4A. The adjusted prediction intervals can be interpreted as a heuristic that indicates the uncertainty of the predictions. Approximately 95% of the observations are within the adjusted prediction intervals.
For predicting Lorey’s height a simple linear regression was fit using the 99th percentile (P99) of the normalized photogrammetric point cloud as predictor. The smallest Lorey’s height detectable in the NFI data is 4 m at a vegetation height P99 of 1 m. In order to avoid unrealistic height predictions, the model interpolates linearly between a Lorey’s height of 4 m at 1 m P99 and a Lorey’s height of 0 m at 0 m P99. Because the height of solitary trees in areas with discontinuous crown cover was often considerable underestimated in the point could, completely heuristic prediction intervals were constructed as 1.65 and 0.65 times the expected value for the upper and lower bound, respectively.
Evaluation of volume predictions against FMIs In order to evaluate the volume predictions, a comparison to recent commercial lidarbased FMIs were carried out. Four FMI projects completed in 2015 and 2016 within the Trøndelag-Vest project area were selected. A total of 27.740 stands were included in the
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four projects. The volume predictions from SR16 raster were intersected with the stand boundaries to estimate synthetic mean and total volumes for each stand.
Site index A detailed description of the site index modelling approach can be found in Mola-Yudego et al. (2017). The modelling approach utilizes Boosted Regression Trees and follows the general modelling outlined for short-rotation plantation yield for Fennoscandia detailed by Mola-Yudego et al. (2015). The models predict site index (Tveite & Braastad 1981) for spruce, pine, and birch for each grid cell in SR16 raster. The models were fit to the NFI plots and use AR5 map parameters, climatic data, TWI, and location information as predictors. Only marginal improvements were observed when including metrics from the photogrammetric point clouds. Point cloud metrics were therefore not included in the final model.
Segmentation In order to create SR16 vector (Figure 4) we carried out a segmentation of SR16 raster within the newly produced forest mask. The segmentation was carried out in Trimble eCognitionTM software. The segmentation was carried out for the resulting polygons to resemble the appearance of typical stand boundaries in Norwegian FMIs. The target for the segmentation was set as: minimum, average, and maximum segment sizes of 0.3 ha, 1 ha and 5 ha respectively and internally homogeneous with respect to canopy height, site index, and tree species composition. Input datasets to the segmentation process were rasters representing the canopy height model, site index, tree species, the original channels (except blue) from the aerial images, plus NDVI. All data were resampled to a 2 m spatial resolution which was judged as appropriate in terms computational cost and
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at the same time preserves the textural characteristic distinguishing forest stands of different tree size and density.
(A)
(B)
(C)
(D)
Figure 4. Illustration of SR16 vector and the SR16 raster layers. (A) SR16 vector polygons; (B) SR16 raster dominant species; (C) SR16 raster volume; (D) SR16 raster spruce site index.
The main steps of the implemented segmentation rule set were: 1) region growing into small and homogeneous image objects, 2) image object fusion into larger objects more
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closely representing stands, and 3) generalization of borders and removal of small segments. In the first step we used the multiresolution segmentation algorithm to produce relatively small segments, i.e. smaller than a stand. After a heuristic trial-anderror process including visual inspection of the results, the scale parameter was set to 175, compactness and shape parameters to 0.7 and image layer weights to 5, 1.5, and 1 for CHM, site index, and NDVI, respectively. After the first step, there were many unwanted borders splitting areas belonging to the same stand. In the second step, image objects were therefore merged, using the image object fusion algorithm, with adjacent objects based on a set of spectral and geometric thresholds: difference in canopy height, difference in site index, difference in NDVI, area of resulting fused object, and absolute and relative border lengths. A separate set of threshold values were defined for objects with mean CHM < 1 m (classified as clear-cut) and > 1 m (classified as forest). A final image object fusion with more relaxed thresholds merged adjacent objects with the same tree species classification. The third step consisted of removing remaining small objects below a size threshold and smoothing of borders to remove long, thin slivers using the morphology algorithm with a circular binary mask of 11 pixels width and the opening operation, which work like “sanding” the objects.
The datasets over the project area were divided into overlapping tiles each covering 27.2 km x 20.4 km (13,600 x 10,200 cells). The analysis jobs were sent to the eCognition Server, which is based on a grid architecture for large image analysis jobs. In our setup, a typical tile took about 80 minutes to finish. Results were exported as shape files, and the overlapping shape files were later merged in ArcInfo into a seamless dataset. Once all polygons were merged mean predicted volume, biomass, height and dominant tree species were assigned to the polygon based on an overlay with SR16 raster.
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Using SR16 raster for improving estimates for municipalities and other regional units The design-based, model-assisted (MA) survey regression estimator (Rao 2003, p. 136) was used to estimate means and their variances by combining NFI sample plots and the SR16 raster maps. The NFI is stratified into lowland and mountain areas with a higher sampling density in the lowland area (3x3 km) than in the mountain area (3x9km). Because the stratification is largely based on a two-phase procedure, no map of the strata is available. Sample plots were therefore weighted according to their stratum instead of stratifying the estimator (Gobakken et al. 2015). Because mountain forest usually contains low standing volumes, this results in conservative variance estimates in the sense of too wide confidence intervals (Breidenbach, 2016). Estimates were made for municipalities with at least 10 NFI plots in forest and for each complete photo project. MA estimates are compared to the standard (stratified) simple random sampling (SRS) estimates for comparison. This way, the relative efficiency was calculated as the ratio of the standard SRS variance and the MA variance. The relative efficiency can be interpreted as a multiplier for the number of sample plots that would be needed for SRS to obtain the same precision as with MA.
Results The updated forest mask Generally the forest mask performed well when evaluated against the NFI plots (Table 1, Figure 5). For the low-land coniferous-dominated forests (3 by 3 km grid) Cohen’s kappa of the forest mask was 0.77 and the obtained accuracy was 0.89 while in the mountains (3 by 9 km grid) the accuracy was 0.95 with a kappa of 0.63 (Table 1).
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Table 1. Confusion matrix of the forest mask compared to NFI plots . Confusion matrix for low-land conifer-dominated forests (3 by 3 km grid)
MASK-Forest MASK-NonForest
NFI Forest
NFI Non-forest
1341
123
138
777
Confusion matrix for mountainous birch-dominated forests (3 by 9 km grid) NFI Forest
NFI Non-forest
MASK-Forest
26
10
MASK-Non-forest
17
535
Generally, the misclassifications were distributed quite evenly across the study area (Figure 5). The majority of the plots that were misclassified as forest in the forest mask (76 of 127 plots) were classified as other wooded land in the NFI while the remaining plots where other land use categories with some tree cover, such as grasslands. The majority of the plots that were misclassified as non-forest in the forest mask (105 of 155 plots) were classified as unproductive forest while the remaining 50 plots generally were in low-productive forests.
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Figure 5. Illustration of the geographic distribution of the forest/non-forest misclassification.
Tree species The accuracy of the tree species models was similar in all photo projects and is illustrated here for Sør-Trøndelag. Of the 884 sample plots within forest that were used for fitting the biomass and volume models, 785 were dominated by a tree species and were used to fit the species prediction model. Cohen’s kappa for the LOOCV confusion matrix (Table 2) was 0.59. Including predictions for sample plots that were not dominated by one of the species groups (and thus not part of the model) into the confusion matrix, reduced the kappa value to 0.50. The latter is the accuracy of the actual map prediction as it is a priori unknown whether a SR16 raster cell is dominated by a species or covers a mixed forest. As can be seen for the confusion matrices, the
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misclassification rates between the coniferous species is rather even, while the misclassification rate between coniferous and deciduous trees results in a relatively larger prediction of coniferous dominated areas.
Table 2. Confusion matrices for tree species classification. Model data based on LOOCV Observed Spruce Predicted
Spruce
Pine
Deciduous trees
173
42
31
Pine
43
271
35
Deciduous trees
32
23
135
Combination of model data (LOOCV) and data not dominated by a species group Observed
Predicted
Spruce
Pine
Deciduous trees
Spruce
233
72
61
Pine
70
300
49
Deciduous trees
49
36
160
Volume and biomass For volume and biomass, the model performance was very similar across all three photo projects, across DTMs and here we only illustrate the models for aboveground biomass and Lorey’s height in Sør-Trøndelag using DTED10 (Figure 6). For all models of volume
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and biomass the RMSEs were around 50% and the models explained approximately 70% of the observed variance. The high RMSEs for volume and biomass are, as noted by Rahlf et al. (2017), caused by the general low levels of volume and biomass for very large areas within the study area. For the models for Lorey’s height, the RMSE were around 20% while the explained variances were around 70%. In spruce-dominated stands, the biomass models show a tendency for underestimation whereas the model slightly overestimated in deciduous dominated stands (Figure 6D). No tendency was visible for pine-dominated stands. The Sør-Trøndelag biomass model explained 71% of the total variance. Within the three species groups, it explained 69%, 70%, 62%, of the variance for spruce, pine, and birch, respectively. For productive forests, additional information on the development class (HKL) is available in the NFI. The five development classes in the Norwegian NFI are: (1) regeneration; (2) young forest, (3) intermediate forest, (4), mature forest, and (5) old forest. Each development class is further separated into sufficiently stocked (1) or insufficient stocked (2). The biomass model has a tendency for overestimation in development class 1 and 2 (Figure 6C). This overestimation in young forests is likely caused by remaining trees mature trees that influence the height model more than they contribute to the biomass per ha values. The same is true for forest with insufficient stocking which is indicated by a 2 as the second digit of the development class numbering in Figure 6C.
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(A)
(B)
(C)
(D)
Figure 6.: Illustration of the model for above ground biomass (AGB) and Lorey’s height in Sør-Trøndelag. (A) AGB vs. mean AP height with lines that represent upper and lower limits of prediction intervals and the expected values, (B) Lorey’s height vs. 99th percentile of AP height. Lines represent upper and lower limits of heuristic prediction intervals and expected values (C) Distribution of residuals across harvest classes, and
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(D) residuals according to dominant species on the NFI plot where 1 represents spruce, 2 is pine dominated and 3 is birch dominated plots.
Evaluation against FMIs The results of the evaluation of the volume prediction from SR16 against the commercial FMIs for the 27,740 stands in Trøndelag-Vest are illustrated in Figure 7. The volume/ha in SR16 is slightly higher than in the FMIs in forest with low standing volume but slightly lower in forests with higher volumes (Figure 7A). A small overestimation from SR16 should be expected given that the minimum tree diameter in SR16 is 5 cm while it is 10 cm in the FMIs. This effect should be larger in stands with smaller volume given the larger proportion of small trees. For the total stand-level volume, the average SR16 predictions are slightly higher for the low-volume forest but on average very similar to the FMI values for the higher-volume forests. If we consider the magnitude of the differences between the SR16 and FMI predictions, it becomes apparent that the majority of stand-level volume estimates are within plus minus 25 m3 of the forest management inventories. More than 95% of the differences in total standing volume between SR16 and the FMIs are within plus minus 50 m3. However, it should also be noted that there are stands where SR16 and the FMIs provided very diverging estimates.
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(A)
(B)
Figure 7. Comparison of SR16 stand-level synthetic volume estimates with commercial FMIs. The FMI includes trees with a dbh greater than 10 cm while SR16 includes trees with a dbh greater than 5 cm. The shape shows the distribution of the differences between SR16 and FMI values and the horizontal lines the median value of the differences.
Using SR16 raster for improving estimates for municipalities and other regional units While examples for Sør-Trøndelag and biomass are presented here, the full list of estimates can be accessed freely at http://shiny.nibio.no/apps/lsk/ under the
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municipality tab. Even though the applied regression models were fairly simple, the precision of the MA estimates was considerably higher than standard direct SRS estimates. This is reflected in the relative efficiency, which was 3.4 for the whole photo project. This result can be interpreted in the sense that 3.4 times as many field samples would be needed in order to achieve the same precision with an SRS estimator as with the MA estimator. A total of 844 NFI sample plots were within Sør-Trøndelag which resulted in an SRS estimate of 61.6 t/ha with a standard error of 2.0 t/ha, compared to an estimate of 61.3 t/ha with a standard error of 1.1 t/ha using the MA estimator.
For municipalities, the relative efficiency ranged between 0.8 and 7.5 and was on average 3.6. One municipality had a relative efficiency which was below one, which means that in this case, the standard SRS estimator is more precise (Table 2).
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Table 2. Comparison of standard simple random sampling estimates and model-assisted estimates for municipalities with the smallest, the medium and the largest relative efficiencies Municipality n*
SRS**
SE***
MA****
SE MA
ID
estimate SRS
estimate (t/ha)
(t/ha)
(t/ha)
(t/ha)
rel. eff*****.
1612
29
45.1
6.9
45.4
7.7
0.8
1718
32
37.3
7.6
55.6
6.0
1.6
1617
23
41.5
6.2
44.5
3.3
3.5
1613
29
59.7
13.2
63.1
5.2
6.5
1653
45
80.0
11.5
77.7
4.2
7.5
*n = number of sample plots, **SRS = simple random sampling, ***SE = standard error, ****MA = model assisted, *****rel. eff. = relative efficiency
Discussion In this study we have presented the development of the Norwegian forest resources map (SR16) and associated products (SR16 raster, SR16 vector, and model-assisted estimates). At the same time, SR16 has been compared to results from commercial lidarbased FMIs in order to facilitate the evaluation of the possibility for use of SR16 in an FMI context. In recent years, a series of studies have illustrated the possibility of using large-scale 3D remote sensing in combination with NFI plots for national or regional mapping of single or a limited number of forest attributes such as forest area (e.g. Waser 2015) or volume and height maps (e.g. Nilsson et al. 2016; Immitzer et al. 2015). Fewer,
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if any, studies have looked at the overarching challenge of how to create a forest information system that utilizes 3D data in combination with NFI plots in order to provide products that are both relevant for NFIs in terms of statistics and easily accessible maps that potentially can bridge the world of NFIs and that of FMIs. The presented works represents one attempt at creating such a forest information system and the results have been made freely available on the web.
The following sections briefly discuss the quality of each of the individual components of SR16. The updated SR16 forest mask expanded the forest area considerably, had relatively high accuracy, and is a clear improvement of the existing Norwegian forest mask. The existing Norwegian AR5 forest mask (Ahlstrøm et al. 2014) is approximately 40 years old and since then, there has been a considerable expansion of the forest area in the mountains due to lower grazing pressure and a warmer climate (e.g. Bryn and Hemsig 2012). Further, significant forest areas have been established on drained mires. Two typical areas where the forest area has expanded is illustrated in Figure 8 where (A) and (B) represents the typical forest expansion in the mountains while (C) and (D) represent an established spruce plantation on a drained mire. There are misclassifications in the updated forest mask but for the most part they follow expected patterns. The majority of the plots that were misclassified as forest in the updated SR16 forest mask was classified as other wooded land in the NFI. The remaining misclassified plots were composed of other land use categories with some tree cover such as grasslands. Even in the field, the separation of other wooded lands from low-productive forest is challenging and misclassification should be expected in the areas with transition from forest to an open landscape such as observed along mires or in the mountain forest. The majority of the plots that were misclassified as non-forest in the
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updated SR16 forest mask was classified as unproductive forest in the NFI indicating that it mainly was the open low-productive forest that were misclassified and not dense productive forests. As previously shown by Waser (2015) our results illustrate that large-scale development or updates of existing forest masks is possible based on photogrammetric point clouds.
The tree species classification was found to be challenging with relatively low accuracies. Automated tree species classification have often been found to be difficult with both 3D and regular optical data resulting in accuracies in the same range as presented here (Puliti et al. 2016, Korpela et al. 2014). On the other hand, studies with better data, foremost multispectral data, have shown considerably higher accuracies for individual trees (Ørka et al. 2009, Dalponte et al.2014). It is clear that one component of SR16 that could be improved is the tree species classification but this would likely have to be done by introducing an additional data source such as multispectral time series data from SENTINEL 2. It should be noted that also in the commercial FMIs the tree species classification is one of the most uncertain parameters even when done with manual photo interpretation.
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(A)
(C)
(B)
(D)
Figure 8. Illustration of the updated forest mask. The original AR5 forest mask is shaded while the updated SR16 forest mask is marked in blue. (A) Original AR5 forest mask in a mountainous location; (B) The updated SR16 forest mask with a natural expansion of the mountain forest; (C) Original AR5 forest mask in a lowland location with mires; (D) The updated SR16 forest mask with an expansion of the forested area due to forest establishment on a mire.
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As expected from the literature on estimation of forest height, volume and biomass with photogrammetric point clouds (Bohlin et.al. 2012, Breidenbach and Astrup 2012, Nurminen et al. 2013, Vastaranta et al. 2013, Rahlf et al. 2014, White et al. 2015) the developed models showed strong relationships and good predictive ability. The developed models for volume, height and biomass generally explained around 70% of the variation in the data and can as such be considered relatively strong relationships given the simple chosen model structure. The reported observed %RMSE values for volume and biomass were high compared to what is often reported in the literature but as noted by Rahlf et al. (2017) this is mainly due to the forest structure with large areas of very low standing volume where a low absolute error will correspond to a high relative RMSE. When the residuals of the biomass and volume models were investigated with respect to dominant tree species (Figure 6D), underprediction was observed for spruce-dominated stands while overprediction was observed for birch-dominated stands. These systematic errors can be reduced by including the known tree species into the model. However, for wall-to-wall mapping only the predicted trees species or the AR5 tree species groups are available and these variables only made a marginal improvement to the systematic errors. Hence, improvement of the model by inclusion of dominant tree species would only be possible if the areas were classified to tree species by some other means.
The main potential for improving the height, volume, and biomass estimates in SR16 is likely by utilizing data from the current (2016 - 2019) national lidar scanning campaign. The lidar data itself would likely show slightly better predictive ability than the photogrammetric data (e.g. Rahlf et al. 2014; Yu et al. 2015; Gobakken 2015) but the
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expected main improvement would be in a consistent and improved DTM. There is no doubt that the current national DTM (DTED10) is responsible for a significant part of the errors in the all models including height, volume, and biomass, but also in the updating of the forest mask.
The comparison to the standing volume in the commercial FMIs illustrated that on average the SR16 stand-level predictions correspond well with the FMI values for stands with high volume. However, there is a tendency for some underestimation of the stands with the highest volumes which likely is caused by the underprediction observed for spruce-dominated stands in the model residuals (Figure 6D). For stands with low volume, SR16 overestimated volume compared to the FMis. To a large extend, this is assumed to be caused by differences in the minimum dbh thresholds in SR16 (>5 cm) compared to the FMIs (>10cm). The majority of the residuals for total stand volume were within 25 m3 of the FMI values and 95% were within 50 m3 of the FMI values. It should be noted that the divergences between SR16 and the FMIs are caused by errors in both products. In the best case, FMIs can be expected to have stand-level errors of approximately 10% and hence contribute considerably to the observed divergence in the comparison. However, there is no doubt that the FMIs that are lidar-based, use species and development class specific volume models have lower errors than SR16 where all processing is automated and the models are simple but robust and applicable across large areas without any manual interpretation..
The presented municipal statistics illustrate that the development of SR16 in combination with the appropriate model assisted estimators (Rao 2003; Gobakken et al. 2015) provide an improved ability to provide NFI-based statistics at multiple scales.
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Given the size of most Norwegian municipalities, direct estimation of NFI statistics from the sample plots is generally not feasible due to a very low number of sample plots per unit (Breidenbach and Astrup 2012). However, providing forest statistics for municipalities is important as a large portion of the public governance structure is located in the municipalities.
SR16 is presented with SR16 raster and SR16 vector freely available on the web (http://kilden.nibio.no) and the municipally level estimates are also available on line (http://shiny.nibio.no/apps/lsk/, municipality tab). SR16 is unquestionable a useful product seen from an NFI perspective. SR16 will also without doubt be useful in various large-scale analyses of the forest resources in the same way as the current Landsat based maps have been throughout Fennoscandia (see Tomppo et al. 2008). The open question is if SR16 or similar large scale maps based on 3D remote sensing and NFI plots can create a bridge between NFIs and FMIs. SR16 contains the same basic information as included in today’s FMIs but is associated with slightly larger errors. At the same time, SR16 is less costly than today’s FMIs. An optimal data acquisition method minimizes the acquisition costs and the losses caused by decisions based on inaccurate data, which are dependent on the use of the information (Kangas 2010). As obvious from the presented data, there are many areas in Norway with low productive and low volume stands – these stands are often very extensively managed and many are not even included in forest management inventories. For these types of stands, SR16 vector may be a sufficient source of information to forest managers. For intensively managed areas of higher productivity the errors in SR16 may be too large for direct use in an FMI but in this case SR16 may possibly be used as a foundation for developing improved FMI. This could for example be by improving the predictions by including known tree species and
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development class in areas of special interest and replace the SR16 estimates with predictions of the forest structure attributes with more complex models than currently include in SR16.
In conclusion, the presented Norwegian forest resource map is a significant improvement of the forest mask and useful as a means to improve estimates for the Norwegian NFI at various scales. The mapped products and the municipal estimates are freely available on the web. The mapped products are of a quality that they under some circumstances can be used directly by forest managers or as base information for development of FMIs.
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Acknowledgements Funding for this study was provided by the Norwegian Institute for Bioeconomy Research. The authors are thankful for the support of Jostein Frydelund, Hildegunn Norheim and Ingvild Nystuen in the development and production of SR16.
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