A voxel-based lidar method for estimating crown base height for deciduous and pine trees

Abstract

The overall goal of this study was to develop methods for assessing crown base height for individual trees using airborne lidar data in forest settings typical for the southeastern United States. More specific objectives are to: (1) develop new lidar-derived features as multiband height bins and processing techniques for characterizing the vertical structure of individual tree crowns; (2) investigate several techniques for filtering and analyzing vertical profiles of individual trees to derive crown base height, such as Fourier and wavelet filtering, polynomial fit, and percentile analysis; (3) assess the accuracy of estimating crown base height for individual trees, and (4) investigate which type of lidar data, point frequency or intensity, provides the most accurate estimate of crown base height. A lidar software application, TreeVaW, was used to locate individual trees and to obtain per tree measurements of height and crown width. Tree locations were used with lidar height bins to derive the vertical structure of tree crowns and measurements of crown base height. Lidar-derived crown base heights of individual trees were compared to field observations for 117 trees, including 94 pines and 23 deciduous trees. Linear regression models were able to explain up to 80% of the variability associated with crown base height for individual trees. Fourier filtering used for smoothing the vertical crown profile consistently provided the best results when estimating crown base height.

Introduction

Reliable forest canopy structure metrics and individual tree crown characteristics, such as crown base height, tree height, crown dimensions, and crown bulk density, are required by forest resources and fire managers to support their management plans. Prediction of crown base height is important in several forestry problems. Crown ratio, which is the ratio of crown length to total tree height, is related to tree vigor and thus to the timing and potential response to thinning (Smith, 1986). Crown dimensions are strongly correlated with stem diameters and, therefore, to forest volume and biomass (Avery & Burkhart, 1994, p. 265). Crown metrics can be used to derive crown volume and crown surface area, which are measures of the photosynthetic potential (Sprinz & Burkhart, 1987). Crown dimensions are also useful for fire behavior analysis (Andersen et al., 2005), being used to calculate crown bulk density or total canopy fuel weight which are data layers for input into fire behavior models such as FARSITE (Finney, 1998). However, in the past, tree crowns have usually not been measured in the field due to difficulties in defining and measuring their changing dimensions and shapes (Sprinz & Burkhart, 1987). Tree crowns have also been measured on aerial photographs and aerial volume tables were derived to substitute the usual ground measurements of stem diameter (Avery & Burkhart, 1994, p. 267). Lately, advances in remote sensing have produced other tools that afford the estimation of crown dimensions, such high resolution aerial and satellite imagery and lidar.

The use of remote sensing for mapping the spatial distribution of canopy characteristics has the potential to allow an accurate and efficient estimation of tree dimensions and canopy properties from local to regional scales. In particular, lidar remote sensing has the capability to acquire direct three-dimensional measurements of the forest canopy that are useful for estimating a variety of forest inventory parameters, including tree height, volume, and biomass, and also for deriving useful information for input into fire simulation models, such as FARSITE (Finney, 1998), e.g., (Mutlu et al., in press).

Previous lidar studies, whether using waveform or discrete return lidar data, attempted to derive measurements, such as tree height and crown dimensions, at stand level (Hall et al., 2005, Næsset and Bjerknes, 2001), plot level (Holmgren et al., 2003, Hyyppä et al., 2001, Lim and Treitz, 2004, Popescu et al., 2004), or individual tree level (Chen et al., 2006, Coops et al., 2004, Holmgren and Persson, 2004, Persson et al., 2002, Popescu, in press, Roberts et al., 2005, Yu et al., 2004), and then use allometric relationships or statistical analysis to estimate other characteristics, such as biomass, volume, crown bulk density, and canopy fuel parameters. Forest canopy structure was estimated using data from scanning lasers that provided lidar data with full waveform digitization (Harding et al., 1994, Harding et al., 2001, Lefsky et al., 1997, Means et al., 1999). Small-footprint, discrete-returns systems were used to estimate canopy characteristics, with many studies focusing on tree height (Magnussen and Boudewyn, 1998, Magnussen et al., 1999, Maltamo et al., 2004, McCombs et al., 2003, Næsset, 1997, Næsset and Økland, 2002, Popescu and Wynne, 2004, Popescu et al., 2002).

Few lidar studies focused on assessing canopy structure and characteristics, such as fuel weight, canopy and crown base height, and crown bulk density (Andersen et al., 2005, Holmgren and Persson, 2004, Pyysalo and Hyyppä, 2002, Riano et al., 2004). Among these studies, there seems to be a unanimous acceptance that lidar overestimates crown base height for individual trees or plot-level canopy base height, which is an intuitive finding given the fact that airborne lidar portrays crowns from above and lower branches have a reduced probability of being intercepted by laser pulses which might be blocked by higher branches. Holmgren and Persson (2004) calculated crown base height as the distance from ground to the lowest laser data height interval containing more than 1% of the total number of non-ground laser points within a crown area. Andersen et al. (2005) estimated plot-level canopy base height using linear regression with several percentile-based metrics of the lidar heights distribution and a canopy density metric calculated as the percentage of first returns within the canopy. Lovell et al., 2003, used both airborne and ground-based lidar to measure canopy structure in Australian forests.

Most of the studies dealing with crown base height estimation analyze the vertical profile of laser hits within a single crown or at plot level. Holmgren and Persson (2004) use a binary series of 0.5 m height layers to estimate crown base height. Each layer with less than 1% of the total number of vegetation hits was set to zero and the others to one. Reutebuch et al. (2005) proposed various types of lidar-derived products useful for multiple resource inventories. One of the products, namely canopy cover maps, consists of images that provide a direct measurement of cover by height aboveground. Mutlu et al. (in press) and Griffin et al. (in review) used this concept by creating height bins of laser hits frequency at various height intervals above ground for mapping surface fuels, leaf area index (LAI), and percent canopy cover. The number of laser hits above an area, in various height bins, indicates the canopy cover in each of the height bins.

With discrete lidar points collected over the forest canopy, laser hits at various height intervals or within height bins above ground elevation contain information about the reflective surfaces that exist in the vertical canopy space, i.e., in a “slice” of canopy space above ground. The lidar height bins are essentially conventional, multiband, two-dimensional representations of lidar-derived voxels, or volumetric pixels, as they contain the frequency of laser returns within a three-dimensional space. Other studies have used a binary approach to characterizing the vertical space of forest canopies with voxels, by considering occupied or unoccupied voxels, i.e., voxels with or without laser hits within their volumetric space (e.g., Chasmer et al., 2004, Parker, 1995, Weishampel et al., 1997). A concept similar to the height bins was used by Næsset (2004) to derive independent variables for regression models of total tree height. In his study of 2004, Naesset divided the range between the lowest laser canopy height and the maximum canopy height into 10 fractions of equal length and computed canopy densities for each fraction.

Although morphological computer vision algorithms have been used to automatically identify tree crown structures visible on lidar-derived three-dimensional canopy height models (CHM) and to measure tree height and crown diameter, results are usually reported at plot level, as in Popescu and Wynne, 2004, or stand level, e.g., Hall et al., 2005. The main reason is the difficulty of validating results for individual trees, when an objective correspondence needs to be established between field- and lidar-measured individual trees, e.g., Yu et al., 2004. This difficulty arises due to uncertainties with individual tree mapping on the ground, e.g., GPS locations, closed canopy conditions, vertical tree position in the canopy, etc. The current study attempts to estimate individual tree crown parameters and reports results at individual tree levels.

The overall goal of this study was to develop new representations of lidar data for assessing the crown base height for individual trees using airborne lidar data in forest settings typical for the southeastern United States. More specific objectives were to:

• develop new lidar-derived features such as multiband height bins and processing techniques for characterizing the vertical structure of individual tree crowns;

• investigate several techniques for filtering and analyzing vertical profiles of individual trees for deriving crown base height, such as Fourier filtering and wavelet shrinkage, polynomial fit, and percentile analysis;

• assess the accuracy of estimating crown base height for individual trees; and

• investigate which type of lidar data, point frequency or intensity, provides the most accurate estimate of crown base height.