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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In this study, a semi-empirical model that was originally developed for stem volume estimation is used for aboveground biomass (AGB) estimation of a spruce dominated alpine forest. The reference AGB of the available sample plots is calculated from forest inventory data by means of biomass expansion factors. Furthermore, the semi-empirical model is extended by three different canopy transparency parameters derived from airborne LiDAR data. These parameters have not been considered for stem volume estimation until now and are introduced in order to investigate the behavior of the model concerning AGB estimation. The developed additional input parameters are based on the assumption that transparency of vegetation can bemeasured by determining the penetration of the laser beams through the canopy. These parameters are calculated for every single point within the 3D point cloud in order to consider the varying properties of the vegetation in an appropriate way. Exploratory Data Analysis (EDA) is performed to evaluate the influence of the additional LiDAR derived canopy transparency parameters for AGB estimation. The study is carried out in a 560 km^{2} alpine area in Austria, where reference forest inventory data and LiDAR data are available. The investigations show that the introduction of the canopy transparency parameters does not change the results significantly according to R^{2} (R^{2} = 0.70 to R^{2} = 0.71) in comparison to the results derived from, the semi-empirical model, which was originally developed for stem volume estimation.

In times of higher market prices of fossil fuels and due to the increasing environmental and economic threats of climate change, there will be a rising demand for renewable energy production, such as solar or bio energy. The latter is the focus of the presented paper. Accurate estimation of Aboveground Biomass (AGB), also referred to as dry total tree biomass, in forested areas is essential for developing sustainable low carbon climate friendly strategies. This includes the reduction of costs for the provision of energy resources, the mobilization of wood in local forests and the optimization of timber harvesting chains in order to minimize the environmental impact. AGB is defined as the total amount of aboveground oven dry mass of a tree, which is expressed in tons per unit area [

In contrast to time consuming and expensive field methods remote sensing such as spaceborne optical remote sensing or synthetic aperture radar (SAR) is capable for mapping area-wide forest inventory (FI) data in a cost effective, fast and accurate way and has been used widely to retrieve AGB [

In recent years Airborne Laser Scanning (ALS), also referred to as Light Detection and Ranging (LiDAR), has been established as a standard technology for high precision three dimensional topographic data acquisition. The three dimensional information is obtained by using an ALS system, which consists of three main components: (i) a Global Positioning System, which is used to record the aircraft position, (ii) an Inertial Measurement Unit (IMU) that measures the angular attitude of the aircraft (roll, pitch and heading), and (iii) a laser scanner unit transmitting short and collimated pulses towards the Earth surface and recording both the travel time of the laser beam and the energy (intensity), which is scattered by the target surface [^{2}) and are mostly based on regression models focusing on a relationship between LiDAR derived individual tree parameters (e.g., tree height, crown dimensions) and field based estimates of AGB. Area-wide AGB estimation on regional level can also be performed with low point density LiDAR data and is mainly based on the extrapolation of FI reference data measured at stand or plot level. Therefore, the vertical distribution of the laser echoes is analyzed at stand or plot level in order to derive various statistical quantities that are used as input parameters for empirical models estimating area-based forest inventory parameters (e.g., mean tree height, basal area, stem volume) and AGB, respectively. Both approaches are mainly based on the geometrical information of the point cloud. The usage of the intensity information of the LiDAR data as a complimentary data source offers promising opportunities for, e.g., tree species classification [^{2} alpine forest. The model was evaluated by comparing it to the multiplicative empirical model of Naesset [^{2} = 0.76 – 0.86). Furthermore, the model was successfully applied for the entire Federal State of Vorarlberg, Austria with an area of 2,601 km [

In this paper the semi-empirical model of Hollaus ^{2} alpine area. Furthermore, the model is extended by different canopy transparency parameters (CTPs) derived from LiDAR data in order to consider the varying properties of vegetation within the study area. These parameters are based on the assumption that transparency of vegetation can be measured by determining their penetration of the laser light through the canopy. The effect of the integrated CTPs is evaluated by comparison with the results of the model not explicitly considering the transparency of vegetation. An Exploratory Data Analysis (EDA) is performed to investigate the behavior of the different extended models for AGB estimation.

The investigated alpine spruce dominated forest land is located in the southern part of the Federal State of Vorarlberg (Austria) in the so-called ^{2}. The elevations within the area range from 800 m above sea level in the valleys to 3,312 m at the Piz Buin Mountain in the Silvretta Mountain range. The landscape is characterized by coniferous and mixed forests, alpine meadows, alpine wasteland and agricultural land. The average timberline is at about 1,950 m whereas two thirds of the forests are located below 1,000 m. The main tree species in the area are Norway spruce (

The forest administration Stand Montafon Forstfonds manages about 65 km^{2} of forests in the

In this study AGB per unit area is used as ground reference quantity. It is estimated from stem volume by means of tree specific expansion factors as described in Weiss ^{−1}], _{i} is the aboveground biomass of a single tree in kilograms and n is the number of measured trees per sample plot unit.

The LiDAR data were acquired during several flight campaigns in the framework of a commercial Vorarlberg-wide terrain mapping project using Optech Airborne Laser Terrain Mapper systems (ALTM 1225, ALTM 2050) and a Leica ALS-50 scanner. All campaigns recorded first and last echoes and took place under snow-free conditions in the years 2002 to 2004. The LiDAR data were acquired at an average flying height of 1,100m above ground (^{2} and 2.7 points/m^{2}. Further information about the used LiDAR sensors are listed in

The georeferenced 3D point clouds as well as the Digital Terrain Model (DTM) and the Digital Surface Model (DSM) were provided by the Land Survey Administration Feldkirch, Austria. The DTM, which has a spatial resolution of 1 m was generated by using last echoes and applying the hierarchic robust filter technique as described e.g., in Kraus and Pfeifer [

The semi-empirical model is based on the assumption that AGB, given in tons per hectare (t ha^{−1}) can be expressed as a linear function of the canopy volumes (_{can}(m^{3} ha^{−1})). The canopy volume is defined as the entire volume between the terrain surface and the topmost tree surface. The calculation of _{can} is based on the heights (_{can} is determined by using a fixed circular reference area (^{2})) around the center of the forest inventory sample plots. The height above terrain surface of each first echo point is used to classify the points into _{i} (i=1,2...,m), whereas the size of _{i}_{fe,i} (between 0 and 1, whereas the sum of _{fe,i} is 1) of first echo points, whose heights fall within the canopy height class _{can,i} is calculated as:
_{mean,i} is the mean canopy height of all first echoes within the corresponding canopy height class. To guarantee that both, the reference AGB (t ha^{−1}) and the estimated AGB are given per unit area, _{can,i} has to be divided by _{i}^{4} was added to take the different area units of AGB (t ha^{−1}) and _{can,i} (m^{3}m^{−2}) into account.

According to former studies [_{can,1} ranges between 2 m and 12 m, _{can,2} ranges between 12 m and 22 m, _{can,3} ranges between 22 m and 32 m and _{can,4} contains all first echoes having a height greater than 32 m.

In this study three different CTPs are defined and investigated with respect to their influence on AGB estimation of the semi-empirical model. They describe the transparency of the canopy surface towards the first laser echoes and are introduced in order to describe the varying properties of the vegetation within the study area in more detail. The CTPs underlie the assumption that all laser pulses enter the canopy parallel to the stems of the trees. Due to lack of LiDAR data representing identical canopy structures scanned with various scan angles, the influence of flying altitude and scan angle on the penetration of the laser pulses into the canopy and their impact on the resulting 3D point cloud have not been assessed in this study as performed in e.g., Morsdorf

The CTPs are integrated in the semi-empirical model of Hollaus _{can,i} in areas that are transparent towards the laser beam because it is assumed that such areas contribute less to AGB than areas that are not penetrated by the laser shots. Due to overlapping flight strips, changing airplane attitude and topographic conditions, the distance between points as well as the point density vary between the sample plots. These circumstances are considered in each of the following parameters. Hence, the developed CTPs should guarantee that the estimated AGB of identical sample plots having different point densities is comparable to each other.

As illustrated in _{2d}) within a static search radius _{2d} (e.g., 1.0 m, measured in 2D) that were reflected from below the current search point. The term static search radius means that the same search distance is applied on every single point of each sample plot. The detected points must have a minimum vertical distance of, e.g., 0.3 m to guarantee that points that were reflected from the canopy surface, but differ slightly in elevation due to the sloped canopy surface, are not selected as points that penetrated the canopy surface. However, the varying average first echo point densities (_{fe}) between the different circular sample plots are not considered yet and a normalization of _{2d} with the _{fe} of the corresponding circular sample plot is required. _{fe} is determined by dividing the number of first echoes within the corresponding sample plot (_{fe}) by its area (_{static}).
_{2d} is the number of points (including the search point) found in a search distance of _{2d}, whereas the height of the vertical search cylinder is equal to the height of the search point minus the defined minimum vertical distance.

This CTP is based on a dynamic 2D search radius (_{dynamic}) in order to find all first echoes that were reflected from below the current search point. The selected points must also have a minimum vertical distance of e.g., 0.3 m from the current search point to overcome the problems mentioned above. Dynamic search radius means that _{2d} is adjusted to the _{fe} of the corresponding sample plot. Hence, it varies between the sample plots but takes the varying _{fe} between the sample plots into account. _{2d} is defined as:

_{dynamic} is calculated using the following equation:

The Echo Ratio (ER), which is a measure for local transparency and canopy surface roughness has been used in various studies to separate solid objects characterized by planarity such as building roofs from non-planar objects like vegetation [_{ER} is derived for each first echo and is defined as:

As illustrated in _{3d} is defined as the number of first echoes (including the search point) found in a dynamic search distance measured in 3D. _{2d} is the number of first echo points found in the same distance measured in 2D, whereas the vertical expansion of the search cylinder is infinite. The dynamic search distance is calculated according to

Each of the LiDAR based CTPs (Section 3.2) is integrated in the semi-empirical AGB model (Section 3.1). This leads to four different semi-empirical models (including the model without a CTP), which are analyzed according to their predictive accuracy. The canopy transparency is calculated for every single first echo point. The integration of _{fe,i} is the number of all first echoes and _{fe,k} is the height of each first echo point within the corresponding height class _{fe} is the total number of all first echoes within _{k} is the canopy transparency parameter of the corresponding first echo point and is set to one if _{can,i} is calculated without any CTP and hence equal to the model as described by Hollaus

The estimation of the optimal sample plot area is performed as described in former studies [

The 90% coniferous trees threshold resulted in a selection of 450 out of 488 successfully co-registered sample plots. These sample plots are taken as input for the determination of the optimum circular sample plot size. As shown in ^{2} and the lowest SD of the prediction errors and thus in the highest accuracy of the calibrated model.

In a next step, those sample plots, which contain only trees that are located within a sample plot radius of 12.0 m are selected. 196 out of 450 coniferous sample plots fulfill this condition and are taken for the calibration of the semi-empirical models.

The models are calibrated using the 196 selected sample plots (Section 4.1). The first echo point cloud serves as input for calculating the canopy volumes.

Calibrating the model without using a CTP results in a R^{2} of 0.70 and a SD of the prediction errors of 87.6 t ha^{−1} (35.8%). Extending the model by the CTP based on a static radius of 1.0 m degrades the R^{2} to 0.64, while the SD of the prediction errors increases to 101.9 t ha^{−1} (41.7%). Normalizing the number of points found below the current canopy point by the sample plot point density _{fe} is required (_{fe} is not considered, R^{2} decreases to 0.55, while the SD of the prediction errors increases to 113.7 t ha^{−1} (46.5%). Introducing the CTP based on the ER as a measure for transparency of vegetation towards the laser beams results in a R^{2} of 0.70 and in a SD of the prediction errors of 88.8 t ha^{−1} (36.3%). Extending the model by the CTP based on a dynamic search radius a R^{2} of 0.71 and a SD of the prediction errors of 87.4 t ha^{−1} (35.8%) is achieved. The accuracy statistics, the

According to R^{2} _{dynamic} results in a minor improvement compared to the model not using any canopy transparency factor. The CTP based on a dynamic search radius leads to a slight increase of R^{2} to 0.71. The accuracy of the model using the CTP based on the ER is similar to the accuracy of the model not using any CTP. The R^{2} values in the presented approach differ from the study of Hollaus ^{2} values up to 0.86 for stem volume estimation. These deviations can be explained by the different target variables of the models (AGB versus stem volume estimation) and the transformation of stem volume to AGB, which is accompanied with uncertainties (Section 2.2), respectively. The _{3} has the highest fraction for calculating AGB and varies between 29.75 × 10^{−4} and 59.50 × 10^{−4} (

The CTPs are introduced in order to reduce _{can,i} in areas that are transparent towards the laser beam. It is assumed that such areas contribute less to AGB than areas that are not penetrated by the laser shots. As shown above, the integration of the CTPs has not led to a significant improvement concerning R^{2}. This can be explained by the usage of first echoes for the calculation of _{can,i}. First echoes being reflected from below the canopy surface are characterized by lower heights than laser points being reflected from, e.g., the tree crowns and hence, contribute less to the calculation of _{can,i}. Therefore, the integration of CTPs that are also based on first echo point clouds may not change the behavior of the semi-empirical model concerning R^{2} significantly. However, the reflection of first echoes from below the canopy surface is also dependent on the settings of the LiDAR sensors acquiring the three dimensional point cloud of the area of investigation such as beam divergence and range between sensor and object (

Within the EDA all 196 selected sample plots are analyzed according to their under- and overestimation of AGB by the different models. Additionally, the 10 sample plots leading to the highest under- and overestimation, respectively, by the original model are selected for further analysis. This procedure is based on the assumption that the original model leads to outliers concerning AGB estimation due to the heterogeneity of the properties of the vegetation within the study area. Analyzing these sample plots separately offers the possibility to check if the integration of CTPs is useful to consider the varying properties of the vegetation of the outlying sample plots in a proper way. The box-whisker plots in ^{−1} to 242.50 t ha^{−1}. The model based on a dynamic search radius results in values ranging from −281.50 t ha^{−1} to 202.00 t ha^{−1}. The median value changes from −2.78 t ha^{−1} to −7.30 t ha^{−1} meaning that a higher amount of sample plots is underestimated by using the model based on a dynamic search radius (103 sample plots ^{2} value in Section 4.2. In

Single outliers of each model can be detected by analyzing the frequency distribution of the residuals in ^{2} nor by a different frequency distribution of the residuals.

In this study LiDAR data is used for area-wide AGB estimation of a spruce dominated alpine forest. In the presented approach a semi-empirical model, which was originally developed for stem volume estimation is used and investigated concerning its reliability for AGB estimation. Local forest inventory data are used for the calculation of reference AGB per sample plot by means biomass expansion factors. Furthermore, the semi-empirical model is extended by different CTPs derived from airborne LiDAR data that have not been considered yet and are introduced in order to investigate the behavior of the different models concerning AGB estimation. The introduction of these parameters is based on the assumption that the varying properties of vegetation within the study area can be described in a better way and consequently leads to better result concerning R^{2}. The determination of the optimum sample plot size is performed as described in Hollaus [

The results of the presented approach show that the semi-empirical stem volume model can also be used for AGB estimation of a spruce dominated alpine forest. The extension of the model by different CTPs does not change R^{2} significantly. The varying point densities of the sample plots, which are a consequence of overlapping flight strips and the topographic conditions in the Montafon region are considered in each of the presented CTPs, either by adjusting the search radius or by normalizing the number of selected points by the local point density. In future studies the different models will be applied on areas, which are characterized by both a wider range of tree species and a higher point density than it was the case in the presented study. Furthermore, those areas that are strongly over- and underestimated by the original model will be investigated according to their vegetation characteristics in order to use models based on a CTP in such areas. Additionally, the impact of the different LiDAR parameters discussed in Section 4.2 on the resulting 3D point cloud and the semi-empirical model, respectively, have not been considered in this study but will be in the focus of future research.

The authors would like to thank the Landesvermessungsamt Feldkirch, Austria for granting the use of the LiDAR data, and the Stand Montafon Forstfonds for supplying the forest inventory data. This study was partly done within the project LASER-WOOD (822030) which is funded by the Klima- und Energiefonds in the framework of the program NEUE ENERGIEN 2020.

The study area is situated in the western part of the Austrian Alps in the Montafon region. The image on the left shows the dates and the flight paths of the ALS campaigns. The blue circles on the right image represent the location of the forest inventory plots collected by the local forest administration Stand Montafon Forstfonds.

Illustration of the canopy transparency parameters (CTPs), which are applied to every first echo laser point. In

Scatter plots showing the aboveground biomass derived from the local forest inventory versus the aboveground biomass estimated from 3D LiDAR first echo point cloud data. Different canopy transparency parameters (b–d) are introduced and investigated concerning AGB estimation.

The box-whisker plots show the under- and overestimation of the different semi-empirical models. The reference AGB is subtracted from the AGB estimated from LiDAR data. The impact of LiDAR derived canopy transparency is investigated on sample plots that are highly under- and overestimated by the original model.

The histograms show the frequency distribution of residuals (estimated minus reference AGB) of all 196 sample plots for all investigated models.

Summary of characteristics of applied LiDAR sensors.

Beam Divergence [mrad] | 0.3 | 0.3 | 0.33 |

Fields of View [°] | 0–40 | 0–40 | up to 75 |

Wavelength [nm] | 1,064 | 1,067 | 1,064 |

Pulse Repetition[kHz] | <25 | <50 | <83 |

Multiple Targets | up to 2 | up to 2 | up to 4 |

Determination of the optimum circular sample plot size by analyzing various radii according to their R^{2} and standard deviation of the residuals.

^{2} |
0.60 | 0.64 | 0.66 | 0.64 | 0.61 |

^{3} ha^{−1}] |
120.2 | 111.4 | 109.0 | 111.2 | 115.7 |

Accuracy statistics of the fitted AGB models. R^{2}, SD of the prediction errors and the estimated

Parameters | without CTP | static CTP | EchoRatio CTP | dynamic CTP |
---|---|---|---|---|

^{2} |
0.70 | 0.64 | 0.70 | 0.71 |

^{−1}] |
87.6 (35.8%) | 101.9 (41.7%) | 88.8 (36.3%) | 87.4 (35.8%) |

7.71 × 10^{−4} / 0.15 |
12.50 × 10^{−4} / 0.21 |
9.14 × 10^{−4} / 0.365 |
16.21 × 10^{−4} / 0.05 | |

19.91 × 10^{−4} / 1.41 × 10^{−12} |
37.74 × 10^{−4} / 7.27 × 10^{−11} |
46.16 × 10^{−4} / 3.34 × 10^{−15} |
39.02 × 10^{−4} / <2 × 10^{−16} | |

29.75 × 10^{−4} / <2 × 10^{−16} |
54.60 × 10^{−4} / <2 × 10^{−16} |
59.50 × 10^{−4} / <2 × 10^{−16} |
50.72 × 10^{−4} / <2 × 10^{−16} | |

15.87 × 10^{−4} / 2.15 × 10^{−5} |
20.23 × 10^{−4} / 0.026 |
38.12 × 10^{−4} / 1.27 × 10^{−6} |
24.78 × 10^{−4} / 2.74 × 10^{−4} |