Extracting LiDAR indices to characterise multilayered forest structure using mixture distribution functions
Research Highlights
► Mixture models produce canopy profile indices of understorey and overstorey vegetation. ► Theoretical distribution functions are used to characterise LiDAR for forest hydrology research. ► Mixture models can be used to predict eucalyptus basal area and stand volume.
Introduction
Light Detection and Ranging (LiDAR) data are facilitating extraordinary advances in improving our understanding of the Earth's biomass by directly measuring the three-dimensional biophysical properties of the vegetation profile. The resulting representation of vertical structure of vegetation and topographic features over the terrain provides insight into the functional characteristics and processes of the land surface. Most LiDAR systems have a multi-echo capability and may capture between two and five returns for every laser pulse by penetrating beyond the first reflective surfaces of the canopy. The ability of discrete return sensors to capture a few echoes per pulse is particularly useful for forest industry applications, which require broad-area information on stand characteristics for timber inventory evaluation and forest growth modelling. For this particular purpose, mean tree height, basal area, and stand volume have been the most important forest mensuration parameters of interest (Naesset et al., 2004).
As well as characterising dominant forest stand attributes, LiDAR data may be used to categorise single-storey and multi-storey forest types, which has proven useful for mapping understorey fire behaviour (Zimble et al., 2003). Quantiles of height distribution in LiDAR forest data can be used to predict the vertical structure of forests (Magnussen and Boudewyn, 1998, Maltamo et al., 2005, Naesset, 1997a, Naesset, 1997b, Naesset et al., 2004). Also, Canopy Height Models (CHM), such as mean canopy height, when derived from LiDAR data, are very accurate at characterising stand attributes because they are directly measured rather than indirectly calculated.
However, LiDAR indices based on discrete statistics such as percentiles and CHM may be improved further by classifying the LiDAR data into vegetation layers to determine vegetation specific statistics. In particular, in vertically heterogeneous multilayered forests it is necessary to stratify the vegetation to address the problem of inter-stand variation in the ratio of LiDAR hits represented in the dominant canopy and the hits in the understorey.
A range of methods has been used to stratify the vegetation profile and develop layer-specific indices. Zimble et al. (2003) used height variance in LiDAR data to determine differences between single-storey and multi-storey forest types, but the method did not stratify each layer. Riano et al. (2003) on the other hand discriminated overstorey and understorey vegetation hits using a cluster analysis technique based on a minimum Euclidean distance method. The crown base of the overstorey was then defined as the 1st percentile of the overstorey layer.
A canopy volume method using volumetric pixels (voxels) was adapted by Holmgren and Persson (2004) to separate the vegetation profile into overstorey and understorey layers. With the horizontal extent of each voxel being the sample plot size, and each voxel element being 0.5 m tall, they were able to assign a value of 0 or 1 to each element according to the relative frequency of z values occurring within the corresponding voxel. By assigning zero to each element that contained less than 1% of the total returns in a given voxel, the authors were able to define the base of the crown as the highest voxel element with a value of zero in a given column.
Barilotti et al. (2008) use polynomial regression functions applied to frequency histograms of vegetation profile data to identify base of the crown of dominant trees, by interpreting the local frequency minimum of the linear regression function as the vegetation layer threshold. Maltamo et al. (2005) determined the existence and number of understorey trees by examining the cumulative distributions of the canopy height density, computed as the proportion of hits above different height quantiles. The authors applied a histogram threshold method, developed by Lloyd (1982), to the cumulative distributions to cluster similar data vectors into groups as a means to define a threshold of the dominant tree layer and understorey trees. Although the procedure determined whether the height distribution of hits is multimodal, the accuracy of the results was largely dependent on the density of the dominant tree layer.
Donoghue et al. (2007) used near-infrared intensity of LiDAR hits to differentiate forest species common to different forest layers, as some species reflect light more intensely than others. Distinguishing vegetation layers based on intensity of hits is complicated because intensity values are dependent on variation in laser path length, orientation of the target relative to sensor, laser beam divergence which alters the footprint size, and the attenuation of the signal by the atmosphere. As a result, this approach needs calibration of the intensity values with configurations of the LiDAR system.
A promising method for separating LiDAR hits of different vegetation layers involves fitting of probability distribution models to the density profile of LiDAR data. To date, only unimodal distributions of the Weibull distribution function have been applied to derive LiDAR indices (Coops et al., 2007, Dean et al., 2009, Maltamo et al., 2004).
Coops et al. (2007) recognised that distribution functions provide a mechanism to summarise complex canopy attributes into a short list of parameters that can be empirically analysed against stand characteristics. They found Weibull parameter β, which varies the spread of the distribution, was significantly correlated (P < 0.05) to mean tree diameter at breast height (DBH), DBH, and stem density (r2 = 0.92, r2 = 0.77, r2 = 0.65). The authors empirically identified a relationship between crown depth and Weibull parameter α, which provides for the scaling and positioning of the distribution.
Dean et al. (2009) estimated height to the base of crown and the height to the median of canopy using truncated Weibull functions. The height to the canopy median was defined as height at the median of the distribution, whereas the height to the base of the live crown was defined as the height where the upper tail asymptotes to zero. Ground-based estimates and LiDAR-based indices of crown median and crown base differed by 0.3 m and 0.6 m respectively. Maltamo et al. (2004) found parameters from the Weibull distribution function may be used to identify suppressed trees in multilayered spruce forests. By applying Weibull distribution functions to estimated tree height distributions obtained from LiDAR data, the authors used Weibull parameters to predict heights of small suppressed trees not identified in the point cloud data. The use of the method reduced RMSE values from 25% to 16% for stand volume estimates, and 75% to 49.2% for the number of stems.
Mixture models are often used in forest management to quantify merchantable timber by characterising the irregular diameter frequency distributions of mixed-species or uneven-aged forest stands (Liu et al., 2002, Zhang et al., 2001, Zhang and Liu, 2006). The present study distinguishes itself from this typical use of mixture models in forest inventory analysis by applying mixture models to LiDAR height distributions in order to estimate plot level stand characteristics. This study generalises the unimodal distribution approach applied by Coops (2007), Dean (2009), and Maltamo (2004) by using mixture models with a range of theoretical distribution functions to develop LiDAR indices that are useful for a broad range of forest management purposes, including forest hydrological research. Forest structure regulates evapotranspiration rates through its influence on the wind profile, which partially determines the vapour pressure deficit at the transpiring leaf surface (Monteith, 1965). For this reason, LiDAR indices relating to crown height, density, depth, and closure of both understorey and overstorey layers, are of interest for quantifying forest aerodynamic properties that influence evapotranspiration rates. Canopy profile attributes such as crown density, depth, and closure are also strongly related to Leaf Area Index (LAI), which is an important predictor of evapotranspiration (Vertessy et al., 2001). LiDAR indices that can predict forest productivity are important for forest hydrological research as forest growth rates may be used to predict forest water use (Raison et al., 2001).
In order to produce hydrologically related canopy profile indices, the two main objectives of this paper are:
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to develop a methodology the uses mixture models with a wide range of theoretical distribution functions as a means to provide a generalised approach for characterising the structure of specific layers of multilayered forests from LiDAR data, and
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to empirically evaluate the LiDAR derived canopy profile indices of understorey and overstorey vegetation for their capacity to predict vegetation specific plot level basal area and stand volumes in multilayered forests.
Section snippets
Study site and field measurement description
The forested catchments used for this study were long-term research sites established in Melbourne's water catchment to investigate the impacts of land cover disturbance on the water resource. The 1939 bushfire in Victoria, Australia burnt much of Melbourne's water catchments and the regeneration process resulted in changes to the rainfall–runoff relationship as the dense regrowth forest consumed more water than the pre-disturbance mature forest (Kuczera, 1987). Permanent growth plots were
Identifying the best fitting mixture models
The first step in identifying the most suitable bimodal distribution function for each plot required the following iterative procedure. We used the normal distribution function in the first component (understorey) of the mixture model whilst testing all available distribution functions in the second component (overstorey). The five best performing second component distribution functions are listed in the first column of Table 4. In the second step, these five distributions were used in the
Discussion
A generalised methodology has been presented for representing the vertical forest structure of a broad range of forest types. We have demonstrated that canopy attributes captured by LiDAR data may be summarise into a short list of parameters for empirical analyses against field measured stand characteristics using mixture modelling methods. To evaluate the robustness of the methodology, mixture models of each sample plot were visually assessed to determine how well each component represented
Conclusion
Mixture models provide an elegant and robust method for stratifying the vegetation profile into distinct vegetation layers whilst preserving vegetation specific characteristics of the canopy profile. Unlike most previously proposed LiDAR indices in literature that categorise the vertical profile of forest structure into a finite assemblage of statistics (Hall et al., 2005, Lefsky et al., 1999, Lefsky et al., 2005, Zimble et al., 2003), mixture models can capture a more complete representation
Acknowledgements
The authors would like to thank the following funding bodies that provided assistance: Melbourne Water under the Wildfire and Water Security project, the Cooperative Research Centre for Forestry project 4.1, and the Victorian Department of Sustainability and Environment. We would like to thank three anonymous reviewers for their valuable suggestions that have improved the final manuscript. We would also like to thank Jack Snodgress for his assistance with field work.
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2018, ISPRS Journal of Photogrammetry and Remote SensingCitation Excerpt :At each vertical increment the physical quantity described by the profile is the plant area volume density (PAVD) as described by Lovell et al. (2003). Fitted distribution functions are often used to provide a structural profile that is less sensitive to rapid changes in vegetation density (Coops et al., 2007; Jaskierniak et al., 2011; Armston et al., 2013). A number of probability distribution functions have been used including Gaussian, Weibull, Loess, Friedman super smoother, spline, among others (Maltamo et al., 2004; Coops et al., 2007; Dean et al., 2009; Jaskierniak et al., 2011; Muss et al., 2011; Leiterer et al., 2015; Wilkes et al., 2015).