Measurements of branch area and adjusting leaf area index indirect measurements

https://doi.org/10.1016/S0168-1923(98)00064-1Get rights and content

Abstract

Estimates of leaf area index obtained with indirect measurement techniques, which are replacing more arduous destructive sampling methods, are frequently questioned due to light interception by woody elements and a non-random distribution of foliage elements. Usually, branches are assumed to be positioned randomly with respect to leaves or shoots in the canopy. However, in this study of boreal forest architecture, branches are shown to be preferentially shaded by other non-woody elements (e.g. shoots or leaves) in both coniferous and deciduous species of the boreal region. A new instrument called a Multiband Vegetation Imager (MVI) is used to capture two-band (Visible, 400–620 nm and Near-Infrared, 720–950 nm) image pairs of contrasting Canadian boreal forest canopies during the BOReal Ecosystem-Atmosphere Study (BOREAS). The spatial relationship of branches and photosynthetically active foliage is studied to estimate the fraction of the effective branch hemi-surface area index (Be) that is masked by leaves and shoots. We suggest an approach that corrects indirect LAI measurements using the LAI-2000 or a similar instrument by correcting for the following biases: (1) the effective canopy branch hemi-surface area that is not masked by leaves or shoots in the canopy, (2) the amount of stem hemi-surface area beneath crowns, (3) leaf (or shoot) (Ωe(θ)) and branch (Ωb(θ)) non-random spatial distributions in the canopy, and (4) the fraction of maximum LAI resulting from defoliation in the canopy. In boreal aspen, MVI image analysis shows that 95% of the effective branch hemi-surface area is masked by other foliage in the canopy. In jack pine and black spruce forests, 80–90% of the effective branch hemi-surface area is masked by other foliage in the canopy. These estimates suggest the fraction of indirect LAI that consists of branches intercepting light is less than 10%. Therefore, branches generally do not intercept a significant amount of beam radiation in boreal forests, and do not significantly bias indirect LAI measurements. However, stems, which comprise 30–50% of the total woody area in this study, may not be preferentially shaded by leafy foliage. Therefore, stem contribution to indirect LAI estimates measured with the LAI-2000 or a similar instrument cannot be overlooked. MVI estimates of the total branch hemi-surface area index agree to within 10–40% of direct measurements made in similar species; however, the error between indirect and direct measurements may be due largely to difficulties associated with obtaining adequate sampling so that the error may fall within the noise level of measurements.

Introduction

The penetration of direct beam radiation through a forest canopy is influenced by all of the contained foliage elements; this includes leaves, stems and branches, needles, and flowers. The position and angle distribution of these elements along with their spatial relationship are significant to the understanding of the extinction and utilization of solar radiation once it enters a forest canopy (Chen and Black, 1991; Norman and Jarvis, 1974; Smith et al., 1993; Welles, 1990). Recently, much emphasis has been placed on interpreting the results of indirect methods that estimate one of the key quantities significant to canopy photosynthesis; namely, the leaf area index (LAI) of a canopy. These indirect measurement techniques are becoming increasingly more important. The LAI of a vegetative canopy can be estimated indirectly by using one of several optical instruments (e.g. LAI-2000, DEMON, Ceptometer or hemispherical photography; Welles, 1990; Welles and Cohen, 1996) that measure the canopy gap fraction as a function of zenith angle. One problem with gap fraction approaches is that all elements of the canopy including woody components (branches and stems), contribute to intercepting beam radiation, and are therefore included in the estimate of LAI. Environmental studies often require a measure of the actual LAI of a canopy, and not a composite value of both leaf and woody area because the actual LAI defines the total leaf surface area that contributes to photosynthesis and ultimately dominates the exchange of heat, water, and carbon in a forest. A second problem arises because all instruments used to measure LAI indirectly assume that leaves and branches are randomly positioned throughout the canopy volume.

The probability P(θ) of a direct beam penetrating through a plant canopy at a zenith angle of θ, assuming azimuthal symmetry, can be described byP(θ)=exp[−K(θ)Le(θ)/cos(θ)]where K(θ) is the fraction of foliage projected into direction θ, and Le(θ) is the indirect measure of LAI (Welles, 1990). The Le(θ) term, which includes all canopy foliage elements, has been referred to as the effective LAI because it is not a measure of the actual LAI in many forest canopies (Chen et al., 1997a). The value of Le(θ) is a composite quantity composed of the actual canopy leaf area index and a canopy non-randomness factor (Le(θ)]). Values of Le(θ) cannot simply be substituted for values of the actual LAI because canopy non-randomness (e.g. clumping of foliage) and woody area may bias canopy gap fraction measurements (Chen et al., 1997b). Thus, correct treatment of the branch and stem area and knowledge about the spatial arrangement of foliage elements in forest canopies is essential to estimating an accurate LAI value based on indirect measurements. Errors from such assumptions of randomness can be large, exceeding 100% in some conifers (Fassnacht et al., 1994). Depending on the forest species and fraction of full cover LAI, tree stems and branches may or may not significantly contribute to the interception of light in forest canopies. Some debate has taken place on whether the contribution of branches and stems to values of Le(θ) measured with optical instrumentation should be subtracted from the indirect measurement for the purpose of correction (Deblonde et al., 1994; Chen et al., 1997a). If the entire canopy branch and stem area were subtracted from the final LAI estimate (after correcting for canopy non-randomness), this would amount to assuming that branches and stems would not be preferentially shaded by leaves or shoots but would be randomly positioned with regard to photosynthetically active foliage. In this case, the shading of woody canopy elements due to leaves or shoots is a function of the randomness of the leaf position only; meaning that some predictable percentage of woody material is always masked by other foliage. However, if leaves or shoots preferentially mask branches in the canopy, branch location has a distinct correlation with leaf or shoot location in the crown so that branches may contribute much less to obscuring sky than their branch area index might at first suggest. In most natural forests, stems can be assumed to be randomly positioned with respect to other crowns in the canopy. Since stems do not have a specific spatial relationship to other foliage, their contribution to Le(θ) values could be significant. In this study, we will show that the tree stem hemi-surface area represents the majority of the woody area that biases measurements of Le(θ).

The area basis for the definition of the canopy woody elements and leafy foliage can be confused because of numerous ways of describing the actual surface area of these elements that intercept light in the canopy. For our study, the total LAI, derived from direct measurement methods (Lt) or from adjustments made to values of indirect measurements (L), is defined as one-half of the total foliage surface area per unit ground surface area (Chen and Black, 1992; Lang, 1991) and we refer to this as hemi-surface area index. This definition allows for the spherical (foliage angular distribution) projection coefficient of 0.5 to remain valid for cylindrical shapes that can be used to represent branches and stems in the canopy provided these woody elements are randomly orientated. Thus, the total woody area (W) is defined as one-half the total surface area of all woody components, or hemi-surface area index (Fassnacht et al., 1994).

Gap fraction measurements that are used to estimate LAI can be applied to quantify the woody surface area if non-woody foliage elements are absent. The effective woody area index (We), analogous to Le(θ) but for woody components, can therefore be determined in the same manner that the indirect LAI is computed, by inverting the gap fraction using Eq. (1), provided good spatially representative measurements are obtained. Thus, instruments such as the LAI-2000, DEMON, or hemispherical photography measure the quantity We of branches and stems in leafless canopies; We is a combined quantity of stem hemi-surface area located beneath crowns (S) and the effective branch hemi-surface area index (Be), where Be is the product of the actual branch hemi-surface area (B) and a non-randomness factor for branch location in canopy space (Ωb(θ)). Thus, some knowledge about the arrangement of branches (e.g. random or clumped) and the diameter, length, and density of tree stems is needed to estimate W (B + S) using gap-fraction measurements. Values of W can also be obtained through destructive sampling procedures; however, these methods are extremely laborious and rely on statistical relations between woody dimensions and tree diameter at breast height (DBH) to achieve even minimal sampling. In conifers, values of W have typically been measured using direct, destructive sampling techniques (Whittaker and Woodwell, 1969; Norman and Jarvis, 1974; Hutchinson et al., 1986; Deblonde et al., 1994). While these methods provide reasonable estimates of the total branch and stem biomass, which are important to allometric relationships and studies of forest net primary production (NPP), a key canopy structural relationship important to characterizing direct beam penetration in forests is not attainable with these direct measurements; namely, whether woody material intercepts a substantial amount of incoming photosynthetically active radiation (PAR). Therefore, an instrument such as the MVI, which can provide measurements of foliage non-randomness and distinguish leaves from branches, provides a unique opportunity to quantify the role of branches in indirect estimates of canopy architecture of forests. This extensive study on branch structure in Canadian boreal forests will illustrate how branch and stem area should be treated for the purpose of adjusting indirect measurements of LAI that are obtained in environmental studies using either the MVI, LAI-2000, Ceptometer or similar instrument. We will extend our solution and results using a simple model to include measurements that might be made in forest canopies that are partially defoliated.

Over the last few decades, measurements of the woody structure and area in forests have emphasized both direct and indirect methods (e.g. Whittaker and Woodwell, 1969; Norman and Jarvis, 1974; Hutchinson et al., 1986; Deblonde et al., 1994; Chen et al., 1997a). Within the past few years, some forest studies have tried to characterize the spatial relationship between woody canopy elements and other leafy foliage and the importance of this relationship to indirect canopy architectural measurements (Chason et al., 1991; Chen and Black, 1991; Deblonde et al., 1994; Chen et al., 1997a). Chason et al. (1991)suggests that woody material may actually be uniformly distributed, and that a positive binomial model (Ross, 1981) may be used with indirect measurements of direct and diffuse light transmission to more accurately describe the hemi-surface area of woody material, instead of the Poisson and negative binomial theoretical approaches. Chen and Black (1991)suggest that branch geometry is of equal importance as other foliage elements in determining the canopy light interception; a canopy extinction coefficient (K(θ)) is dependent not only on leaf geometry, but also branch architecture. The work of Deblonde et al. (1994)in jack and red pine forests showed that woody components may have significantly contributed to LAI-2000 values of Le(θ). Direct measurements of the woody-to-leaf area ratios (one-half total stem surface area to total (direct) LAI) in the Deblonde et al. (1994)study were 8–12% for red pine, resulting in a W=0.5–0.6 (total LAI∼3–6), and 10–33% for jack pine, giving a value of W ranging from 0.2–0.7 (total LAI∼1.5–2.2). However, conclusions about how woody components should be subtracted from Le(θ) to obtain LAI are not made as the authors suggest that more experiments and studies are needed. However, they suggest that the woody contribution to radiation interception for mature stands might be minimal because in their plots where the stem-to-leaf area ratios were <10%, indirect LAI measurements (made with LAI-2000) underestimated the direct values; however, in stands where the stem-to-leaf area ratios were between 19–33%, an overestimate of the direct LAI was made (Deblonde et al., 1994).

Until most recently, no single method has addressed how to account for woody area and canopy non-randomness together to adjust indirect LAI measurements. However, a more complete and complex form of Eq. (1)has been used by Chen et al. (1997a)to correct for woody area and canopy non-randomness, and more accurately define radiation penetration in forest canopies. Chen et al. (1997a)show that the probability of a direct beam penetrating through a forest at zenith angle θ can be approximated byP(θ)=exp−K(θ)Ωe(θ)Lγe(1−α)cos(θ)where L is the LAI; Ωe(θ) is a canopy non-randomness index for the arrangement of both leaves and branches obtained from analyzing the canopy gap–size distribution (Chen and Cihlar, 1995); γe is a correction factor for within-shoot clumping in conifers; and α is defined as the woody-to-total foliage hemi-surface area ratio in the canopy, which can be obtained from direct measurement techniques. Numerically, α can be represented by the following equation:α=WW+Lwhere W is the total woody hemi-surface area index of branches and stems, and L is equal to an estimate of the total LAI. The α factor in Eq. (2)allows for non-leafy material in the canopy (branches, stems, moss, etc.) to be removed from the Le(θ) measurement because these do not contribute to the true value of the LAI. Instruments such as the LAI-2000, DEMON, Ceptometer or MVI measure the quantity Le(θ)] (Le(θ)) in Eq. (2)as a product; thus some knowledge about canopy clumping is essential if L is to be derived (L=Le(θ)/[Ωe(θ)]). The MVI (Kucharik et al., 1997) or TRAC (Chen and Cihlar, 1995) can be used to approximate Ωe(θ) by analyzing the canopy gap–size distribution. The reader should note that values of Ωe(θ) have been shown to be strongly dependent on zenith angle; thus there are several possible values of Ωe(θ) that could be used in Eq. (2)(Kucharik et al., 1997). This theory will be discussed and used later. Measurements of Ωe(θ) in conifers are complicated because as many as four levels of clumping may be present; namely, grouping occurs at the shoot, branch, whorl, and tree crown level (Norman and Jarvis, 1974; Chen et al., 1997a). The TRAC is unable to account for within-shoot clumping because penumbral effects in the canopy (Miller and Norman, 1971) cause small gaps (less than a few millimeters in some cases) between needles to disappear in shadows within the sunfleck gap–size distribution projected onto the ground. The MVI also experiences similar resolution problems because the size of a needle and gaps between needles in conifers are smaller than an image pixel in most cases; thus small gaps between needles are also difficult to measure. Typically, an MVI image pixel represents about 5 mm at the top of a 10 m tree, whereas a conifer needle may be as small as 1 mm wide. Therefore, the amount of needle area within a shoot is not accurately measured as part of the gap–size distribution by either the MVI or TRAC, and values of Ωe(θ) must be corrected for this bias. Chen et al. (1997a)correct Ωe(θ) by using an equation given byΩ(θ)=Ωe(θ)γewhere γe is defined as the needle-to-shoot hemi-surface area ratio, which approximates the amount of clumping that occurs within a typical shoot, and has been measured in many other studies for a variety of species (Gower and Norman, 1991; Deblonde et al., 1994; Fassnacht et al., 1994; Chen et al., 1997a). The Ωe(θ) that is measured with the TRAC or MVI includes clumping at scales larger than the average element size; in deciduous forests this is a leaf, and in conifers, shoots are the primary foliage elements. If shoots are randomly distributed in a canopy, then Ωe(θ)=1. In deciduous forest species such as aspen, γe=1; thus a correction to Ωe(θ) is not necessary. Chen et al. (1997a)show that the true LAI of a canopy can be estimated by using an equation of the formL=(1−α)Le(θ)γeΩe(θ)

This approach assumes that branches and stems are randomly located with respect to leafy foliage, and are thus not preferentially shaded by leaves or shoots in the canopy. By combining Eq. (3)with Eq. (5), the total LAI is shown to be calculated by L=[Le(θ)/Ωe(θ)]−W. This equation shows that the entire canopy woody hemi-surface area is subtracted from the adjusted indirect LAI to obtain L. This type of approach may be true for the woody hemi-surface area of randomly dispersed tree stems (S), but needs to be tested for branches in full cover canopies. Clearly, branches support leaves and may be preferentially shaded by these leaves. Accounting for stem and branch area separately is quite important because branches typically comprise at least 50% of the total woody hemi-surface area in forest canopies. A study performed with MVI data in aspen (Populus tremuloides), black spruce (Picea mariana), and jack pine (Pinus banksiana) during the BOReal Ecosystem-Atmosphere Study (BOREAS) suggests that branches and leaves, or shoots, are located in close proximity to one another; thus , may not be accurate for some full cover forest species. Furthermore, branches may be more nearly randomly distributed than leaves. Eq. (5)also needs clarification as to which value of Ωe(θ) should be chosen because of its dependence on zenith angle (Kucharik et al., 1997). Therefore, we propose two independent techniques to correct indirect measurements of LAI made with the LAI-2000 or MVI for the influence of living and dead branches, stem area, and branch, leaf, shoot and needle clumping. Two separate corrections are discussed because the MVI typically only measures branch contributions to Le(θ), while the LAI-2000 has a larger field-of-view, and therefore measures some quantity of the stem hemi-surface area as part of the Le(θ) value in addition to branch hemi-surface area.

Section snippets

Measuring woody hemi-surface area with the MVI

The MVI is a new instrument that uses a filter exchange mechanism mounted on a 16-bit charge-coupled device (CCD) camera to capture digitized, two-band (visible (VIS) 400–620 nm, near infrared (NIR) 720–950 nm) image pairs (each image is 512×1024 pixels) of plant canopies from the ground looking upward in about 50 ms (Kucharik et al., 1997). The system is operated by a laptop computer which is also used to store each 2 megabyte image pair, and is completely portable as it uses a 33 Amp-hour 12

Correcting MVI measurements of Le(0) for non-randomness and branches

The MVI allows for several key canopy architectural quantities to be estimated from MVI image pairs; namely, Le(0), Be, Ωe(0), and Ωb(0) in deciduous canopies, and fraction of Be not shaded by leaves or shoots in any coniferous or deciduous forest. To make terminology in the following sections concerning branch architecture as clear and simple as possible for the purpose of adjusting values of Le(θ) for light intercepting woody material, we must define several quantities. The fraction of Be

Adjusting LAI-2000 measurements for non-randomness, stems, and branches

Indirect measurements of LAI are frequently made in forests using an instrument called the LAI-2000 plant canopy analyzer (PCA) (see review by Welles, 1990). Since the LAI-2000 measures the canopy gap fraction at zenith angles from 0–70° and over a wide range of azimuthal directions, this instrument includes a majority of the tree stem surface area as part of the indirect LAI (Le(θ)) measurement; more specifically, that portion of tree stems located below crowns, and are not preferentially

Comparison of two approaches for correcting indirect LAI measurements

The approach of Chen et al. (1997a), which uses Eq. (5), determines an adjusted value of L from indirect measurements of LAI. This method requires knowledge of the total woody area and total foliage area in the canopy obtained by destructive sampling techniques. Since Lmax and W will be known, Eq. (3)is used to derive a value for α, and this value is then used in Eq. (5), which corrects for branch and stem contributions to Le(θ) and canopy non-randomness (L=Le(θ)/Ωe(θ)−W). The value for L in

Conclusions

A new method is suggested that corrects indirect LAI measurements for non-random distributions of leaves or shoots and branches using the MVI or LAI-2000, and for the fraction of the effective branch area index (Bb(θ)]) (based on one-half the total surface area) that intercepts light in MVI images. Alternatively, theory is suggested that corrects for the fraction of branches and stems that intercept light with respect to indirect measurements of LAI obtained with the LAI-2000. Recently, much

Symbols

aTypical length of exposed branch hemi-surface area in canopy with respect to unit leaf hemi-surface area; Eq. (10)
BHemi-surface area index of branches; one-half the total surface area of branches per unit ground surface area; , , ,
BeEffective branch hemi-surface area index; product of B and Ωb(θ), derived from gap fraction measurements; one-half the total surface area of branches per unit ground surface area; , ,
BeEffective branch hemi-surface area index measured by the MVI from below the

Acknowledgements

This research was supported by NASA grant #NAG5-2601 through the Science Division of the Office of Mission to Planet Earth and a NSF grant #DEB-9221668 to S.T. Gower and J.M. Norman. The authors gratefully acknowledge the use of the image clustering algorithm BIRCH, developed by T. Zhang, R. Ramakrishnan, and M. Livny at the University of Wisconsin-Madison; and to Martha Anderson for additional consultation on image processing algorithms at the University of Wisconsin-Madison. CJK wishes to

References (27)

  • G. Deblonde et al.

    Measuring leaf area index with the LI-COR LAI-2000 in pine stands

    Ecology

    (1994)
  • S.T. Gower et al.

    Rapid estimation of leaf area index in conifer and broad-leaf plantations

    Ecology

    (1991)
  • Gower, S.T., Vogel, J., Norman, J.M., Kucharik, C.J., Steele, S.J., Stow, T.K, 1997. Carbon distribution and...
  • Cited by (178)

    • Moving beyond the incorrect but useful paradigm: reevaluating big-leaf and multilayer plant canopies to model biosphere-atmosphere fluxes – a review

      2021, Agricultural and Forest Meteorology
      Citation Excerpt :

      Big-leaf models can accommodate separate streams of transpiration and canopy evaporation (Deardorff, 1978), but the models assume that leaves and stems are intermingled in the canopy while multilayer models can accommodate separate vertical distributions of leaf and stem area in which, for example, the upper canopy is mostly leaves while the lower canopy is mostly stem. Observations of forest canopies do indeed show that that branches and stems are shaded by foliage (Kucharik et al., 1998). Whether big-leaf or multilayer, plant canopy models must parameterize turbulent fluxes between vegetation and the atmosphere.

    View all citing articles on Scopus
    View full text