Canopy clumping index (CI): A review of methods, characteristics, and applications
Introduction
The spatial distribution of leaves or needles within a vegetation canopy is critical in determining the canopy radiation transfer (Baldocchi and Harley, 1995; Carrer et al., 2013; Kucharik et al., 1999; Naudts et al., 2015; Nouvellon et al., 2000), photosynthesis (Law et al., 2001; Rambal et al., 2003), and hydrological processes (Chen et al., 2016; Lunka and Patil, 2016). Leaf spatial distribution can be quantified using a canopy clumping index (CI) defined as a ratio of the effective leaf area index (LAIe) to the leaf area index (LAI) (Chen, 2018; Fernandes et al., 2014; Nilson, 1971).where Ω is the canopy CI. LAI quantifies the amount of live green leaf material present in the canopy per unit ground surface and is an essential climate variable identified by the Global Climate Observing System (GCOS) (2016). LAIe is the LAI value that would produce the same indirect gap measurement as that observed, assuming a simple random foliage distribution (Chen et al., 2005). When the foliage spatial distribution is random, Ω=1. If foliage elements are regularly distributed, Ω >1. When elements are clumped, Ω <1. In the following texts, CI and Ω are used interchangeably, in slightly more descriptive and arithmetic meanings, respectively.
Accounting for the clumping effect is essential for the correct estimation of LAI using the indirect optical approach.
Failure to account for CI would lead to an LAI error of up to 70% (Chen and Cihlar, 1995a; Stenberg, 1996; Woodgate et al., 2015). In land surface modeling, LAI is closely related to canopy photosynthesis, leaf respiration, and litterfall, whereas LAIe governs the light absorption and precipitation interception (Davi et al., 2008). In theory, Ω varies from zero to infinity in the extreme cases when all foliage elements are stacked on top of each other or laid side by side. Remote sensing studies have shown that the global CI values generally vary between 0.3 (very clumped canopies) and 1.0 (randomly distributed foliage elements) (Jiao et al., 2018; Wei et al., 2019).
In many earlier studies, a foliage dispersion parameter was frequently calculated from the contact number using the relative variance approach (Baldocchi and Harley, 1995; Myneni et al., 1989l; Nilson, 1971; Warren Wilson, 1965). The dispersion parameter was then used to calculate the canopy gap fraction with a negative binomial model. A major difference between the foliage dispersion parameter and the current CI is that the former quantifies the ratio of canopy gap fractions under real and random conditions, whereas the latter quantifies the ratio of LAIe and LAI (Eq. (1)). The definition of CI is also different from the aggregation metrics in landscape ecology and spatial statistics. In landscape ecology, the aggregation index and the clumpiness index are calculated as a measure of spatial aggregation for ecological adjacencies and class patches (John et al., 2009; McGarigal, 2015; Rasmussen et al., 2011). Although conceptually similar, the aggregation index and the clumpiness index provide quantitative metrics to quantify the spatial aggregation level of a landscape unit, whereas the CI, defined for the non-randomness of individual leaves or needles, is used to better quantify the transmittance and interception of light and precipitation. Similarly, spatial statistics provide tools to analyze the non-randomness patterns of spatial points (Perry et al., 2006; Szmyt, 2014). However, the spatial pattern metrics derived from statistical methods are not necessarily equal to the CI definition in Eq. (1) and cannot be applied in land surface models (LSMs) for radiation and hydrological modeling within the canopy.
This paper provides a comprehensive review of the canopy CI. Sections 2 and 3 present the CI field and remote sensing methods, respectively. Section 4 discusses the general characteristics of canopy CI. Sections 5 describes the application of CI in LAI estimation, canopy reflectance and land surface models. Section 6 concludes the paper.
Section snippets
Field methods
In field measurements, CI is obtained through direct or indirect methods (Table 1). Direct methods estimate CI by separately estimating LAIe and LAI (Eq. (1)). Indirect methods estimate the distribution of gap fractions or use an allometric relationship with other canopy biophysical variables, e.g., diameter at breast height (DBH) for tree canopies. Both direct and indirect methods are physically consistent with the CI definition (Eq. (1)). Other proxy aggregation parameters have also been
Passive optical methods
CI can be estimated from passive optical remote sensing data through an empirical relationship with vegetation indices or bidirectional reflectance shape indicators, e.g., the commonly used normalized difference hotspot and darkspot (NDHD) index (Chen et al., 2005; Leblanc et al., 2005b).where a and b are coefficients that vary with θ, and NDHD is defined aswhere ρh and ρd are the reflectance values at the hotspot and darkspot in the principal plane, respectively (
Characteristics of CI
It has been known since the 1970s that the CI shows scale, directional, and temporal variations (Nilson, 1971; O'Toole et al., 1979). This section synthesizes the CI variations in these dimensions.
LAI estimation
Because of the coupling relationship between CI, LAIe, and LAI, the most significant application of CI is for the transformation between LAIe and LAI (Eq. (2)). When the measured CI is not available, empirical values from similar vegetation types or from remote sensing products can be used. Pinty et al. (2006) suggested a second-order polynomial relationship between LAI and LAIe, indirectly accounting for the clumping effect. The vertical CI profile derived from the waveform LiDAR can even be
Conclusion
This paper provides a comprehensive review of the field measurement and remote sensing methods to determine the canopy CI and its general characteristics and applications in the LAI estimation, canopy reflectance and land surface models. Indirect optical methods are commonly used to determine the CI in field measurements. The two standard methods, the gap-fraction based (the LX method) and the gap-size based (the CC method) methods, are based on the general rationale to calculate the spatial
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This study was supported by the National Key Research and Development Program of China (2016YFA0600201). The author is thankful for personal communications with Prof. Jing M. Chen of the University of Toronto during the preparation of the manuscript. Prof. Dennis Baldocchi and another anonymous reviewer graciously provided constructive reviews of this work and are gratefully acknowledged. Mr. Yinghui Zhang helped prepare Fig. 1.
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