Elsevier

Remote Sensing of Environment

Volume 115, Issue 2, 15 February 2011, Pages 573-585
Remote Sensing of Environment

Extracting LiDAR indices to characterise multilayered forest structure using mixture distribution functions

https://doi.org/10.1016/j.rse.2010.10.003Get rights and content

Abstract

Discrete Light Detection and Ranging (LiDAR) data is used to stratify a multilayered eucalyptus forest and characterise the structure of the vertical profile. We present a methodology that may prove useful for a very broad range of forest management applications, particularly for timber inventory evaluation and forest growth modelling. In this study, we use LiDAR data to stratify a multilayered eucalyptus forest and characterise the structure of specific vegetation layers for forest hydrology research, as vegetation dynamics influence a catchment's streamflow yield. A forest stand's crown height, density, depth, and closure, influence aerodynamic properties of the forest structure and the amount of transpiring leaf area, which in turn determine evapotranspiration rates. We present a methodology that produces canopy profile indices of understorey and overstorey vegetation using mixture models with a wide range of theoretical distribution functions. Mixture models provide a mechanism to summarise complex canopy attributes into a short list of parameters that can be empirically analysed against stand characteristics.

Few studies have explored theoretical distribution functions to represent the vertical profile of vegetation structure in LiDAR data. All prior studies have focused on a Weibull distribution function, which is unimodal. In a complex native forest ecosystem, the form of the distribution of LiDAR points may be highly variable between forest types and age classes. We compared 44 probability distributions within a two component mixture model to determine the most suitable bimodal distributions for representing LiDAR density estimates of Mountain Ash forests in south-eastern Australia. An elimination procedure identified eleven candidate distributions for representing the eucalyptus component of the mixture model.

We demonstrate the methodology on a sample of plots to predict overstorey stand volumes and basal area, and understorey basal area of 18-, 37-, and 70-year old Mountain Ash forest with variable density classes. The 70-year old forest has been subjected to a range of treatments including: thinning of the eucalyptus layer with two distinct retention rates, removal of the understorey, and clear felling of patches that have 37 year old regenerating forest. We demonstrate that the methodology has clear potential, as observed versus predicted values of eucalyptus basal area and stand volume were highly correlated, with bootstrap based r2 ranging from 0.61 to 0.89 and 0.67 to 0.88 respectively. Non-eucalyptus basal area r2 ranged from 0.5 to 0.91.

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:

  • 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

  • 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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