A meta-analysis of the canopy light extinction coefficient in terrestrial ecosystems

Abstract

The canopy light extinction coefficient (K) is a key factor in affecting ecosystem carbon, water, and energy processes. However, K is assumed as a constant in most biogeochemical models owing to lack of in-site measurements at diverse terrestrial ecosystems. In this study, by compiling data of K measured at 88 terrestrial ecosystems, we investigated the spatiotemporal variations of this index across main ecosystem types, including grassland, cropland, shrubland, broadleaf forest, and needleleaf forest. Our results indicated that the average K of all biome types during whole growing season was 0.56. However, this value in the peak growing season was 0.49, indicating a certain degree of seasonal variation. In addition, large variations in K exist within and among the plant functional types. Cropland had the highest value of K (0.62), followed by broadleaf forest (0.59), shrubland (0.56), grassland (0.50), and needleleaf forest (0.45). No significant spatial correlation was found between K and the major environmental factors, i.e., mean annual precipitation, mean annual temperature , and leaf area index (LAI). Intra-annually, significant negative correlations between K and seasonal changes in LAI were found in the natural ecosystems. In cropland, however, the temporal relationship was site-specific. The ecosystem type specific values of K and its temporal relationship with LAI observed in this study may contribute to improved modeling of global biogeochemical cycles.

Keywords

canopy light extinction coefficient / ecological modeling / biogeochemical model / forest / grassland / cropland / leaf area index

Introduction

The canopy light extinction coefficient (K) is a parameter that describes the efficiency of light interception for the canopy of a terrestrial ecosystem. A low K indicates that much radiation can reach the bottom of the canopy. Conversely, a high K indicates that only a little radiation can penetrate into the understory of the canopy. Theoretically, K is determined by leaf inclined angle (α) and solar zenith angle (θ) ( Monsi and Saeki, 1953; Campbell, 1986), i.e.,

(1) \{\begin{array}{l}K=\cos \alpha \cos \theta ,\alpha +\theta \le \mathrm{\pi }/2\hfill \\ K={\displaystyle \frac{2}{\mathrm{\pi }}}\left[\cos \alpha \cos \theta {\sin }^{-1}\left(\tan \theta \tan \alpha \right)+{\left({\mathrm{1+cos}}^2\alpha -{\cos }^2\theta \right)}^{1/2}\right],\alpha +\theta >\mathrm{\pi }/2\hfill \end{array}.

K is usually calculated with the Beer Lambert Law ( Monsi and Sakei, 1953):

(2) K=-\ln \left(I_i/I_o\right)\cos \theta /\left(\mathrm{L}\mathrm{A}\mathrm{I}\mathrm{\Omega }\right),

where I_i is solar radiation under the canopy, I_o is solar radiation above the canopy, θ is solar zenith angle, LAI is leaf area index, and Ω is clumping index. In many cases, the Beer Lambert law is simply expressed as ( Runyon et al., 1994; Liu et al., 1997; Sampson and Allen, 1998):

(3) K=-\ln \left(I_i/I_o\right)/\mathrm{L}\mathrm{A}\mathrm{I}.

In this case, both solar zenith angle and clumping index are implicitly included in K, which implies that K may vary both temporally and spatially more than expected. However, owing to the lack of in-site measurements at diverse terrestrial ecosystems, K (expressed in the form of Eq. (3)) is assumed as a constant in many biogeochemical models and remote sensing models of evapotranspiration and gross primary productivity (GPP). For example, it is fixed as 0.5 in the CEVSA (Carbon Exchange in the Vegetation-Soil-Atmosphere) model ( Cao and Woodward, 1998; Gao et al., 2013), LPJ (The Lund-Potsdam-Jena Dynamic Global Vegetation Model) ( Sitch et al., 2003), and 3-Pg (Physiological Principles in Predicting Growth) model ( Esprey et al., 2004), and as 0.65 in some crop growth models, such as CERES-Maize ( Jones and Kiniry, 1986). In addition, a constant value of K is given in terms of estimating regional or global evapotranspiration and GPP, e.g., the MODIS GPP and evapotranspiration algorithm ( Zhao and Running, 2010; Mu et al., 2011), VPM (Vegetation Photosynthesis Model) ( Xiao et al., 2004), etc. Some models used plant functional type-specific values of K. For example, Thornton and Rosenbloom ( 2005) used 0.6 and 0.5 for the grass and evergreen needleleaf forest, respectively, in the Biome-BGC (BioGeochemical Cycles) model. Wang et al. ( 2011) used 0.58 and 0.50 for broadleaf forest and the other plant functional types in the GLOPEM-CEVSA (Global Production Efficiency Model with the Carbon Exchange in the Vegetation-Soil-Atmosphere) model. Kiniry et al. ( 1992) used different values among species for cropland in the ALMANAC (Agricultural Land Management Alternatives with Numerical Assessment Criteria) model, e.g., 0.90 for cocklebur, 0.65 for maize and wheat, and 0.45 for soybean.

K is a key factor determining ecological processes which may have significant impact on predicting ecosystem carbon and water processes in the biogeochemical models. For example, with the Biome-BGC model, White et al. ( 2000) found that increasing K from the mean minus 20% to the mean plus 20% would cause a 54% decrease of net primary production (NPP) at broadleaf forest areas in the USA. Domingo et al. ( 1999) illustrated that the evapotranspiration of shrubs increased by 4.8% on the average (by 12.2% maximally) in Spain from April to May in 1997 when K was reduced by 15% ( Brenner and Incoll, 1997). Therefore, an accurate determination of K is important for modeling ecological processes.

Nevertheless, the fixed values of K in the models are mostly based on quite limited in-site measurements, and little is known about the representativeness of these values. Many studies documented significant variations in K within and across ecosystems ( Kubota et al., 1994; Wheeler et al., 1995; White et al., 2000; Wang et al., 2001; Rouphael and Colla, 2005; Binkley et al., 2013). Therefore, in order to minimize the uncertainty of model prediction, it is imperative to make a comprehensive investigation of K across global terrestrial ecosystems.

In this study, we conducted a meta-analysis of the canopy light extinction coefficient by compiling data from 88 terrestrial plant communities selected from 59 published journal articles. Our objectives were (i) to establish a look-up table of the canopy light extinction coefficient for main plant functional types in global terrestrial ecosystems; and (ii) to explore the spatial and temporal variations in K in terms of climatic and biotic factors. In our study, both the mean K in the whole growing season in a year (K_mean) and the K in the peak growing season in the year (K_pg) were compiled to qualify the magnitude of seasonal variations in this parameter. We defined the peak growing season as the period when LAI reached its maximum in a year.

Materials and methods

Journal articles on K in terrestrial plant ecosystems published before April 2012 were compiled. In order to make K among various ecosystems comparable, K selected for this study followed a certain criteria: 1) K was calculated by the simplified Beer-Lambert law (Eq. (3)), which is used by most biogeochemical models. All of the variables in the equation were measured directly, and LAI was one half the total interception leaf area per unit ground surface area ( Chen and Black, 1992; Jonckheere et al., 2004; Liu et al., 2013). The LAI was considered as 2 times and 1.28 times the projected leaf area for spruce needles and conifer needles, respectively ( Chen and Black, 1992; Chen and Cihlar, 1996). 2) Only the data measured at noon were used in order to eliminate the influence of solar zenith angle ( Flénet et al., 1996). 3) K of different plant communities measured at the same site, or the same plant community at different sites were considered as independent observations. Finally, data from 88 ecosystems from 59 published articles were extracted and analyzed for this study (details is available in Table A1).

In addition to K, LAI, mean annual temperature (MAT), and mean annual precipitation (MAP) were extracted from the journal articles where possible. In cases when MAP and MAT were not available, we used the data from the global climate database (WorldClim–Global Climate Data at http://www.worldclim.org/) according to the latitude and longitude provided. Due to the limited data for each plant functional type (PFT) based on IGBP (International Geosphere-Biosphere Programme) classification, we aggregated the ecosystems into five PFTs: grassland (grassland & savanna), shrubland (open shrubland & closed shrubland), cropland, broadleaf forest (evergreen & deciduous & mixed forest), and needleleaf forest (evergreen & deciduous).

Results and discussion

Variations in the canopy light extinction coefficient across plant functional types

The average (±sd) K in an entire growing season, K_mean, for all of the PFTs was 0.56±0.16 (Table 1), which was in between the two most frequently used values by most models ( Jones and Kiniry, 1986; Cao and Woodward, 1998; Sitch et al., 2003; Esprey et al., 2004; Xiao et al., 2004) (i.e., 0.5 and 0.65). However, there were certain variations in K_mean across PFTs. It was highest for cropland (0.62±0.17), followed by broadleaf forest (0.59±0.12), shrubland (0.56±0.13), grassland (0.50±0.15), and needleleaf forest (0.45±0.11) (Table 1). When compared with the values used in PFT-specific fixed models, we found K_mean of broadleaf forest was close to that set by the GlOPEM-CEVSA model (0.58, Wang et al., 2011), and that of cropland was close to the 0.65 used in crop growth models ( Jones and Kiniry, 1986). The K_mean for grassland (0.50) was the same as the commonly used value, i.e., 0.5 (e.g., CEVESA, VPM, LPJ, etc.), but smaller than that set in Biome-BGC (i.e., 0.6, Thornton and Rosenbloom, 2005). Notably, the calculated K_mean for needleleaf forest (0.45) is smaller than the constants set in most models.

The average canopy light extinction coefficient of all the PFTs in the peak growing season, i.e., K_pg, was 0.49 (±0.22), which was 12.5% lower than K_mean (p<0.05). This indicates that there were seasonal variations in K to a certain degree in these ecosystems. Among PFTs, there were also certain variations in K_pg. The cropland had the largest value (0.65), followed by grassland (0.40), needleleaf forest (0.39), and shrubland (0.38). The largest difference between K_pg and K_mean occurred in shrubland (32.14%, p=0.08), followed by grassland (20.00%, p<0.05), and needleleaf forest (13.33%, p<0.05). However, no difference was found between these two values in cropland (p=1.00).

The variations in K across PFTs are mostly related to the changes in canopy structure, such as leaf angle distribution and spatial arrangement ( Monsi and Saeki, 1953; Chen et al., 2005; Awal et al., 2006; Wang et al., 2007). From Eq. (3), we can see that K contains the effects of clumping. Therefore, K in this study reflects the influence of leaf angle distribution and clumping. K is expected to be small when the leaves are vertical and clumped, which would allow more solar radiation to penetrate through the canopy than otherwise ( Monsi and Saeki, 1953; Chen et al., 2005; Tesfaye et al., 2006). Our meta-analysis results are consistent with this expectation. For example, values for K in the cropland and broadleaf forest were high, but the values for K of the needleleaf forest were low. In general, the clumping effects of plant leaves in cropland are lower ( Chen et al., 2005), which is the likely reason causing the largest K in cropland. Similarly, the overall distribution of leaf-inclination angles in broadleaf forest tends to be horizontal ( Hutchison et al., 1986), leading to a relatively high K. Values for K in needleleaf forest were smallest, which may be due to the clumped arrangement of needle leaves ( Chapin et al., 2002; Chen et al., 2005). Our results also indicated that values for K in grassland and shrubland were quite variable. This may be due to the fact that these two PFTs are widely distributed in diverse environments, in which the leaf size and arrangement would be quite variable. Further classification of K for shrubland and grassland according to the climate might be necessary once sufficient data are available.

Spatiotemporal relationships between the canopy light extinction coefficient and environmental factors

Spatially, no significant correlation between K_mean (or K_pg) and the two major climatic factors (i.e., MAP and MAT) was found within and across PFTs (Fig. 1). Further, no significant correlation was found between K and LAI across space for both within and across PFTs (Fig. 2). In contrast, the significant difference between K in the peak growing season, K_pg, and the average of the entire growing season, K_mean, suggests that seasonal variations in K exist for most ecosystems. Our further investigation illustrated that K was negatively correlated with LAI for the natural ecosystems: grassland, shrubland, and needleleaf forest (Fig. 3, p<0.01, no seasonal data available for broadleaf forest). The R² of the relationship differed among PFTs, with the maximum at needleleaf forest (0.30), followed by grassland (0.19), and shrubland (0.13). For the cropland, however, the relationship between K and LAI varied with the crop species planted. For example, no significant relationship was found in the crops of cauliflower (Brassica oleracea L. botrytis) and mustard (Brassica juncea L.) (Fig. 4(a)). Positive relationships were found in other crop species, e.g., squash (Cucurbita pepo L.), tobacco (Nicotiana tabacum L.), peanut (Araehis hypogaea L.), and chickpea (Cicer arietinum L.) (Fig. 4(b)). However, negative relationships were found in triticale (×Triticosecale), and wheat (Triticumaestivum L.) (Fig. 4(c)).

The negative correlation between K and LAI for the natural PFTs may be the fact that the increase of LAI in the growing season is usually associated with the change in canopy architecture, such as foliage density, stem length, and clumping intensity ( Brown and Parker, 1994; Kubota et al., 1994). For species in grasslands, the angle of inclination of leaves would become steeper with increasing LAI ( Kubota et al., 1994), which allows for more light to penetrate into the sward and thus decreases K. For shrubland and needleleaf forest, light interception per unit of leaf area decreased as LAI increased due to the increasing clumpiness as gaps develop between trees ( Assmann, 1970; Kellomaki et al., 1985). For broadleaf forest, Brown and Parker ( 1994), who adopted the method of spatial sequence instead of time successional sequence to study the temporal changes of K in broadleaf forests, suggested that K decreased as LAI increased (p<0.05, R²=0.69). Thus, we speculated that values for K in broadleaf forest are negatively correlated with LAI. Just as in shrubland and needleleaf forest, the reason is the increasing clumpiness as gaps develop between trees ( Brown and Parker, 1994).

The relationship between K and seasonal LAI in cropland varied among ecosystems, which was different from the natural PFTs (i.e., grassland, shrubland, and needleleaf forest). Two reasons may cause such variability. First, it may be due to the contrast in leaf angular distribution among different crop species. For the crop species with planophile leaves (e.g., zucchini and tobacco), light interception per leaf area increased as LAI increased due to the decreased clumped effects as the distance between the plants decreased ( Chen et al., 2005). In this case, increasing LAI will lead to an increase of K. By contrast, for the crop species with plagiophile leaves (e.g., wheat and triticale), the inclination angle of leaves would become steeper with increasing LAI ( Kubota et al., 1994), which allows more light to penetrate into the canopy and thus decreases K. Second, many crop species experience continual management practices, such as thinning, irrigation, maturing, etc., which may substantially change the canopy structure and K-LAI relationship.

Theoretically, seasonal changes of the solar zenith angle may also cause the differences between K in the peak growing season and the growing season average. However, our investigation indicated that this factor is negligible. First, if this effect has significant impact, the difference (i.e., K_mean–K_pg) would be higher at high latitude ecosystems and lower at the low latitude ecosystems. However, the result indicated no significant relationship between the difference and latitude (p>0.05, data not shown). Second, the effect of solar zenith angle (θ) on K (i.e., 1–cosθ) in growing season would be 1%–12% in low latitudes (30°S–30°N), and 1%–26% in middle latitudes (30°S–60°S, 30°N–60°N). In our meta-analysis, most of the ecosystems were distributed in middle latitudes, implying that solar zenith angle is not an important factor causing the differences in K in different stages of a growing season.

Conclusions

This meta-analysis investigated the spatial and temporal variations in the canopy light extinction coefficient, K, in main terrestrial ecosystems. Our results showed that the average K of main PFTs in the whole growing season was 0.56. However, this value in the peak growing season was 0.49, indicating obvious seasonal variations in K. Large variations in K exist within and among PFTs. Cropland had the highest value of K (0.62), followed by broadleaf forest (0.59), shrubland (0.56), grassland (0.50), and needleleaf forest (0.45). No significant spatial correlation was found between K and the major environmental factors, i.e., MAP, MAT, and LAI. However, significant negative correlations between K and seasonal changes in LAI were found in the natural ecosystems. The PFT specific values of K and its temporal relationship with LAI observed in this study may contribute to improved modeling of global carbon and water processes.

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