Csiro Marine And Atmospheric Research Paper No 02215


There are many techniques for measuring leaf area index (LAI) and forest canopy foliage profiles but their accuracy is questionable. This paper briefly reviews current methods of estimating forest LAI and presents a novel, ground-based laser system, Echidna® that can make a wide range of measurements of forest structure, including LAI. Here, use of the system to provide field data and derived gap probabilities in the form of a ‘hemispherical photograph with range’ is demonstrated. The results show consistency and reproducibility and do not depend on special conditions for the natural light field.


Leaf area index (LAI), or mean one-sided surface area (called ‘foliage area’ in this paper) of leaves per unit area of ground, is an integrated quantity that is widely used in the description and modelling of forests. The volume density function of foliage area is called the foliage area volume density (FAVD). Leaf area index and FAVD can be used to describe light interception as well as forest respiration, transpiration and photosynthesis in various layers of a forest. Moreover, relationships between LAI and biomass (which depend on growth form and structure of the forest in question) have been used to infer biomass from remotely sensed data. Two related factors that often limit the successful use of LAI and FAVD are that they are difficult to measure directly and it is difficult to provide objective reference measurements against which to validate indirect estimates of either parameter such as those provided by remote sensing.

Leaf area index, FAVD and other forest parameters are usually estimated in field plots and are extrapolated to larger blocks, which are generally stratified into homogeneous areas. There are currently no alternatives to costly and time-consuming field measurements to benchmark remotely sensed data. The high variability in crown distribution and the variable leaf clumping within canopies add to the difficulty of inferring LAI from ground measurements, as they do for interpreting remote measurements. Basal area and its variance are easier to establish in the field than to establish LAI, which explains the common practice of estimating LAI from basal area in accordance with allometric relationships.

In recent years, LAI and foliage profiles have been estimated from the air by both lidars (Blair et al. 1994, 1999, Lefsky et al. 1999a, 1999b) and radars (Imhoff et al. 2000). The platform and data scale result in large-scale averaging and allow wide area coverage. However, most current systems need reference ground calibration and have a limited ability to sense forest structure. In this paper, a brief review of methods for measuring LAI and FAVD is followed by an introduction to ground-based lidar, which sounds the canopy from below. An example is provided showing the potential of the method to calibrate data from remote sensing systems.

Ground-based estimation of LAI and foliage profile

Two widely used approaches to estimate LAI in forests are allometry from basal area and the estimation of canopy cover and gaps. The latter may be measured either visually or by light transmission sensed by film and digital multi-view angle sensors. Reviews of both approaches have been provided by Bréda (2003) and Jonckheere et al. (2004).

Allometry-based estimates of LAI

Leaf area index is easily described mathematically. If tree crowns are described as a volume envelope filled with leaves with a particular volume density (foliage area per unit crown volume, or FAVD), then the leaf area of a single tree (aL,i) and the corresponding LAI within an area A could be written (with ‘E’ denoting the mathematical expectation):


where VC,i is the volume of the crown of tree ‘i’, i ∈ A means the sum is taken over trees with stems in the area sample A, is the mean (expected) foliage area of leaf for a single tree in a stand, λ is the stem density of the stand and {#:i ∈ A} is taken as a Poisson variable with density λA.

This simple expression is the basis for allometric approaches to LAI estimation (e.g., Law et al. 2001) in which total foliage area measured by destructive harvest of sample trees is related to an easily measured quantity such as stem diameter at breast height (DBH), which allows extrapolation to stand LAI from stand basal area. The model includes field techniques in which leaf ‘modules’ are counted in sample trees and total leaf foliage area per module is estimated from cut samples (e.g., Andrew et al. 1979) and can be applied using methods ranging from hemispherical photography to the laser system described in this paper.

Forests are structurally complex and spatially variable. Therefore, all methods used to estimate LAI are subject to large error variation that can be kept within acceptable limits only by extensive and costly sampling. In Australia, the need for rapid surveys of natural forests has led to the use of canopy descriptions, the counting of ‘modules’ (clumps of foliage in trees equivalent to shoots in conifers) and some module sampling (Walker and Hopkins 1990, Andrew et al. 1979). Rapid surveys have also been conducted with calibrated visual keys (Cherry et al. 2002) which can be carried out at the crown level (Jupp and Lovell 2005).

Cover- and gap-based estimates of LAI

Hemispherical photographs (formerly film but now digital) and light transmission methods provide rapid, low-cost, nondestructive methods for estimating LAI and for obtaining canopy structural information. All such methods infer a gap probability (Pgap) distribution for the canopy from estimates based on the percentage of gap to sky or sun, possibly as a function of view angle from a ground-based instrument. Estimation of LAI from Pgap has a long history. These were the first techniques that attempted to overcome structural effects to estimate LAI (cf. Warren Wilson 1959, 1960, 1963, 1965) as reviewed by Bréda (2003) and Jonckheere et al. (2004).

For many years, from the early work of Warren Wilson (1959, 1960) through hemispherical photograph analysis (Anderson 1971, Bonhomme and Chartier 1972) until the present-day use of digital-camera-based image acquisition, the (Pgap) data have mostly been analysed on the basis of a random (and convex) leaf canopy model that is applicable to many crops and some grasslands but not directly to forests. In this model, the gaps in a photograph taken from the ground pointing upward are measured and averaged over azimuths of near constant zenith angle (θ) and are interpreted as estimates of (Pgap) against the models:


In these equations, L is LAI and G(θ) is an expression called the Ross G-function (Ross 1981) that expresses the mean area projection of plant elements in the direction θ. As shown by Lang (1991), the projected area need not be only of leaves, but generally the components need to be convex, which for thin leaves implies that they are flat and for needles implies that they are straight. There are several methods for analysing these equations for ‘effective’ LAI as described in the listed reviews by Bréda (2003) and Jonckheere et al. (2004). The first line of Eq. (2) provides an integral equation and does not need all zeniths to be sampled, whereas the second line (Miller 1964, 1967, Anderssen et al. 1985) requires that all zeniths be sampled.

Foliage profiles and clumping

The original work by Warren Wilson (1959, 1960, 1963) and others in crops and grasslands was aimed at determining vertical foliage profiles (Ross 1981). Methods with the same objective have been developed for use in forests, but they often fail to provide information on angular structure. An example is the method of MacArthur and Horn (1969) that is based on vertical range to first hit with a camera rangefinder. In other cases, hemispherical photographs have been used at various heights in the canopy (e.g., Bonhomme 1976, Rich 1990) to obtain profile information. Recently, laser-based instruments have been developed to replace the camera system used by MacArthur and Horn (Parker et al. 2004, http://www.serc.si.edu/labs/forest_ecology/portlaser.jsp).

When foliage profile data are available, the ‘range to hit’ distribution has been related to Pgap using an extension of the simple random equations (Eq. (2)) as:


In these equations, f(z) is the FAVD profile or the horizontally averaged FAVD as a function of height and z0 is the height at which measurements are taken (usually above the ground). In the last equation, Phit(θ,z) is the probability of a ‘hit’ at height z and zenith angle θ which, if the expressions are re-derived for the view from above the canopy, provide the profile of sunlit elements in the canopy with θ as the sun zenith angle.

Although these expressions seem to provide a means to derive profile information such as sunlit areas from transmittance or photographic data and have been used in simple canopies, clumping and tree shape result in significant bias and variance that must be taken into account (Nilson 1971, 1999, Chen and Cihlar 1995a, 1995b, Kucharick et al. 1999, Walter et al. 2003, Nilson and Kuusk 2004, Leblanc et al. 2005). The clumping of foliage into crowns and possibly into modules or shoots within crown envelopes means that there is more ‘gap’ than expected if leaves were randomly distributed in space, and much greater spatial variance. Another factor to be considered in making such ground-based measurements is the presence of trunks and stems (Nilson 1971, Nilson and Kuusk 2004).

Approaches to dealing with effects of clumping have generally been through the development of a measurable canopy ‘clumping’ function Ω(θ) that modifies the first line of Eq. (3) as:


In this and in the previous equations, it is assumed that the clumping function and the Ross G-function are independent of position in the canopy. The best current approach to deal with this is based on the work of Chen and his coworkers (Chen et al. 1991). The basic methods can be described in several ways, but all need to classify gaps according to the level of clumping to which they belong. For example, if foliage is assumed to be clumped into crown envelopes, there is a need to identify gaps between crowns from those that are within crowns. However, methods developed so far do not allow precise measurement of LAI, clumping and foliage angles from hemispherical photography.

In the pursuit of more accurate and generally applicable methods, both ground-based and airborne laser distance measurements of forest canopies have been investigated (Blair et al. 1994, 1999, Lefsky et al. 1999a, 1999b). These methods can provide useful estimates of apparent foliage profiles and other information over wide areas. Airborne instruments have the advantage of a remote platform, but are limited in view angle.

Measuring LAI and foliage profile with Echidna®

Echidna® is a laser waveform-recording, multi-view, angle-scanning lidar system. It is designed to capture data from at least the full upper hemisphere in a single acquisition and cover the field of view with no gaps in laser illumination. A prototype Echidna® or Echidna® Validation Instrument (EVI) has been constructed and initial experiments have been performed (Jupp et al. 2005).

The scanning pattern of the EVI is controlled by a rotating mirror that directs the beam through the vertical plane, and by rotation of the sensor head to provide azimuthal coverage. The sensor head contains the laser, detector and optics, the scan head and embedded logic control for implementing commands and for monitoring system status. The optical system is coaxial, which provides an efficient optical system, compact assembly and essentially no minimum detectable range. The optical design of the instrument means that some of the outgoing laser pulse is present in the recorded signal, which allows precise temporal alignment of the individual waveforms.

The EVI uses a diode pumped solid state 1064 nm Nd:YAG laser operating at a fixed pulse repetition frequency of 2 kHz. The optical system within the sensor head modifies the beam to a diameter of 29 mm with a manually variable divergence of between 2 and 15 mrad. Empirical tests of temporal pulse shape have determined that the pulse width has a stable value of 14.9 ns at full-width-half-maximum which corresponds to an effective width in ‘range’ of about 2.4 m. Despite the width of the pulse the peak is sharp and well defined, allowing accurate determination of range to targets producing a single clear return.

In contrast to the most terrestrial lidar systems that record a single range for each laser shot, the EVI records the light reflected from objects along the laser path which can be calibrated to power units. The waveform is recorded with a maximum sampling rate of 2 GS s−1, which equates to one sample every 7.5 cm of range from the instrument. In addition to the core waveform data, ancillary information is recorded continually throughout a scan.

The data recorded have three geometric dimensions; zenith angle (0 ≤ θ ≤ 180°), azimuth angle (0 ≤ φ ≤ 360°) and range (r) to target. However, the instrument generates the scan coordinates in a different system. The angle coverage of a single mirror rotation is measured by using the scan encoder as about +137° to −130° (where + and – indicate which side of the zenith the scan is at) while the instrument rotary table rotates through 180° as measured by a rotary encoder, providing more than full hemispherical coverage. The coordinates are reformatted in the preprocessing. The rotation rate is normally selected to provide contiguous shots at the horizontal and overlapping data closer to zenith. The precise positional information that is recorded allows the data to be reprojected into a number of different formats.

For example, a hemispherical reprojection converts the data into a form similar to a hemispherical photograph (but with an additional dimension of range). The most efficient file structure for extracting data uses what we have called an ‘Andrieu projection’ (since it was used by Andrieu et al. (1994) for hemispherical photographs), as shown in Figure 1. In this projection, the x direction is azimuth and the y direction is zenith with zero zenith (the central point of a hemispherical photograph) at the top. This simple geometry is often used for cartographic and GIS data where it is known as the Geometric or ‘Plate Carrée’ projection (see Steers 1962). The intensity and colour in Figure 1 were generated by combining the mean waveform (mean return power over all ranges), the mean weighted by range and the mean weighted by the square of range into a colour composite. This provides clear distinctions of both range and target type.

Figure 1.

Colour composite of the mean waveform (mean return power over all ranges), the mean weighted by range and the mean weighted by the square of range using an ‘Andrieu’ reprojection of the Echidna® data. The x dimension is azimuth while the y dimension is zenith with 0° at the top and about 130° at the bottom.

Figure 1.

Colour composite of the mean waveform (mean return power over all ranges), the mean weighted by range and the mean weighted by the square of range using an ‘Andrieu’ reprojection of the Echidna® data. The x dimension is azimuth while the y dimension is zenith with 0° at the top and about 130° at the bottom.

Transformation of original data to the selected projection involves reduction of data redundancy in the instrument scan pattern and the regularisation of pointing variations and other factors. A number of structural analysis algorithms assess the data by the conventional dimensions of horizontal and vertical distance. In this case, the data may be further reprojected into a cylindrical projection allowing analysis of slices in the horizontal or vertical plane (Jupp et al. 2005).

Situations generating characteristic waveforms from within a forest environment may be generalised into two broad categories, ‘hard’ target and ‘soft’ target responses. ‘Hard’ target responses are a waveform resulting from the beam hitting a single impervious object such as a tree trunk. The reflection is a pulse similar in shape to the outgoing pulse, and a waveform similar to that shown in Figure 2A. A ‘soft’ target response is obtained when the beam intersects dispersed and fragmented targets that are smaller than the beam cross-section. This is typical of the reflection from tree crowns in which the small leaf size or small cross sectional area in the line of the beam means that the beam intersects a number of objects distributed over a range of distances. The response is composed of returns from multiple ranges, resulting in waveforms such as those shown in Figure 2A and B, and as expressed in the colour variations in Figure 1. As the beam size increases or shots are averaged, the waveform from soft targets merges into a smooth, range-distributed shape containing information on amount and spatial distribution of the scattering objects. In this case, the data become similar to those obtained with large footprint airborne lidars (Blair et al. 1994, 1999). Differences in energy and spread of waveform peaks and other characteristics allow woody components such as trunks and branches to be distinguished from foliage (as suggested by Figure 1) and allow separate analysis of foliage amount and structure.

Figure 2.

Typical waveforms associated with the interception of the laser beam by a hard target such as a trunk (A) or multiple smaller targets (B and C). Intensity units are uncalibrated.

Figure 2.

Typical waveforms associated with the interception of the laser beam by a hard target such as a trunk (A) or multiple smaller targets (B and C). Intensity units are uncalibrated.

Basic lidar equations

In a lidar system, the returned signal intensity from a solid object perpendicular to the beam at range R from the instrument as a function of time, t

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