Implications of shoot structure on the rate of photosynthesis at different levels in a coniferous canopy using a model incorporating grouping and penumbra

1. The connection between high leaf area index (LAI) and photosynthetic production with two attributes of coniferous canopy structure: small leaf size and grouping of needles on shoots, was analysed using a simulation model.
2. The small size of conifer needles gives rise to penumbras, which even out the distribution of direct sunlight on the leaf area and thereby act to increase the rate of canopy photosynthesis per unit of LAI.
3. Grouping, by producing a non-uniform distribution of leaf area, causes a decrease in total canopy light interception at any given LAI, but improves the photosynthetic light capture by shoots in the lower canopy.
4. Application of the model on a case study showed that: (a) grouping had a negative effect on the rate of photosynthesis in the upper canopy, but deeper down in the canopy the situation was reversed; (b) in the lower canopy, photosynthetic rates were up to 10 times higher as a result from the combined effect of grouping and penumbra; (c) grouping did not improve the rate of canopy photosynthesis per unit of LAI, however, it can have a positive effect on the total photosynthetic production by allowing a higher productive LAI to be maintained; (d) penumbra, on the other hand, increased the rate of canopy photosynthesis by as much as 40% for moderate values of the LAI.     

Carbon gain in a multispecies canopy: the role of specific leaf area and photosynthetic nitrogen-use efficiency in the tragedy of the commons

Models have been formulated for monospecific stands in which canopy photosynthesis is determined by the vertical distribution of leaf area, nitrogen and light. In such stands, resident plants can maximize canopy photosynthesis by distributing their nitrogen parallel to the light gradient, with high contents per unit leaf area at the top of the vegetation and low contents at the bottom. Using principles from game theory, we expanded these models by introducing a second species into the vegetation, with the same vertical distribution of biomass and nitrogen as the resident plants but with the ability to adjust its specific leaf area (SLA, leaf area:leaf mass). The rule of the game is that invaders replace the resident plants if they have a higher plant carbon gain than those of the resident plants. We showed that such invaders induce major changes in the vegetation. By increasing their SLA, invading plants could increase their light interception as well as their photosynthetic nitrogen-use efficiency (PNUE, the rate of photosynthesis per unit organic nitrogen). By comparison with stands in which canopy photosynthesis is maximized, those invaded by species of high SLA have the following characteristics: (1) the leaf area index is higher; (2) the vertical distribution of nitrogen is skewed less; (3) as a result of the supra-optimal leaf area index and the more uniform distribution of nitrogen, total canopy photosynthesis is lower. Thus, in dense canopies we face a classical tragedy of the commons: plants that have a strategy to maximize canopy carbon gain cannot compete with those that maximize their own carbon gain. However, because of this strategy, individual as well as total canopy carbon gain are eventually lower. We showed that it is an evolutionarily stable strategy to increase SLA up to the point where the PNUE of each leaf is maximized.     

Photosynthetic acclimation to elevated CO2 in a sunflower canopy

Sunflower canopies were grown in mesocosom gas exchange chambers at ambient and elevated CO2 concentrations (360 and 700 ppm) and leaf photosynthetic capacities measured at several depths within each canopy. Elevated [CO2] had little effect on whole-canopy photosynthetic capacity and total leaf area, but had marked effects on the distribution of photosynthetic capacity and leaf area within the canopy. Elevated [CO2] did not significantly reduce the photosynthetic capacities per unit leaf area of young leaves at the top of the canopy, but it did reduce the photosynthetic capacities of older leaves by as much as 40%. This effect was not dependent on the canopy light environment since elevated [CO2] also reduced the photosynthetic capacities of older leaves exposed to full sun on the south edge of the canopy. In addition to the effects on leaf photosynthetic capacity, elevated [CO2] shifted the distribution of leaf area within the canopy so that more leaf area was concentrated near the top of the canopy. This change resulted in as much as a 50% reduction in photon flux density in the upper portions of the elevated [CO2] canopy relative to the ambient [CO2] canopy, even though there was no significant difference in the total canopy leaf area. This reduction in PFD appeared to account for leaf carbohydrate contents that were actually lower for many of the shaded leaves in the elevated as opposed to the ambient [CO2] canopy. Photosynthetic capacities were not significantly correlated with any of the individual leaf carbohydrate contents. However, there was a strong negative correlation between photosynthetic capacity and the ratio of hexose sugars to sucrose, consistent with the hypothesis that sucrose cycling is a component of the biochemical signalling pathway controlling photosynthetic acclimation to elevated [CO2].     

阔叶红松林6种阔叶树单个叶片叶面积和叶干质量的垂直变异及模型构建

快捷、准确地测定植物叶片尺度上的叶面积(LA)和叶干质量(LDM)对于探讨植物性状对气候变化的响应机制至关重要,但适于测定区域尺度上不同阔叶植物单个叶片LA和LDM的经验模型尚未提出.本研究以中国东北4个分布区阔叶红松林内的白桦、紫椴、山杨、枫桦、水曲柳和裂叶榆6种阔叶树种为研究对象,分别测定其不同冠层高度(上层、中层和下层)叶片的叶长、叶宽、叶厚、LA及LDM.以叶长与叶宽之比(叶长宽比)的中位数为标准将6种阔叶树分为两组,检验每组树种不同冠层高度对构建预测LA和LDM的经验模型是否存在显著影响;构建适于预测区域尺度上不同冠层单个叶片LA和LDM的经验模型,验证其预测精度;并进一步评估构建的经验模型预测其他区域相同阔叶树种LA和LDM的适用性.结果表明: 整体上6种阔叶树单个叶片的LA随冠层高度的降低呈显著增大趋势,而部分树种的LDM呈下降趋势;冠层高度对构建预测LA和LDM的经验模型具有显著影响;构建的经验模型预测两组阔叶树种不同冠层单个叶片LA和LDM的平均精度分别为95%和83%,且基于这些模型预测其他区域相应树种LA和LDM的平均精度分别为94%和80%,表明本研究构建的经验模型在我国东北区域具有普遍适用性.     

Monoterpene emission from coniferous trees in response to elevated CO2 concentration and climate warming

It was hypothesized that high CO₂ availability would increase monoterpene emission to the atmosphere. This hypothesis was based on resource allocation theory which predicts increased production of plant secondary compounds when carbon is in excess of that required for growth. Monoterpene emission rates were measured from needles of (a) Ponderosa pine grown at different CO₂ concentrations and soil nitrogen levels, and (b) Douglas fir grown at different CO₂ concentrations. Ponderosa pine grown at 700 μmol mol^–1 CO₂ exhibited increased photosynthetic rates and needle starch to nitrogen (N) ratios when compared to trees grown at 350 μmol mol^–1 CO₂. Nitrogen availability had no consistent effect on photosynthesis. Douglas fir grown at 550 μmol mol^–1 CO₂ exhibited increased photosynthetic rates as compared to growth at 350 μmol mol^–1 CO₂ in old, but not young needles, and there was no influence on the starch/N ratio. In neither species was there a significant effect of elevated growth CO₂ on needle monoterpene concentration or emission rate. The influence of climate warming and leaf area index (LAI) on monoterpene emission were also investigated. Douglas fir grown at elevated CO₂ plus a 4 °C increase in growth temperature exhibited no change in needle monoterpene concentration, despite a predicted 50% increase in emission rate. At elevated CO₂ concentration the LAI increased in Ponderosa pine, but not Douglas fir. The combination of increased LAI and climate warming are predicted to cause an 80% increase in monoterpene emissions from Ponderosa pine forests and a 50% increase in emissions from Douglas fir forests. This study demonstrates that although growth at elevated CO₂ may not affect the rate of monoterpene emission per unit biomass, the effect of elevated CO₂ on LAI, and the effect of climate warming on monoterpene biosynthesis and volatilization, could increase canopy monoterpene emission rate.     

Development of the Monsi-Saeki theory on canopy structure and function

BACKGROUND AND AIMS: Monsi and Saeki (1953) published the first mathematical model of canopy photosynthesis that was based on the light attenuation within a canopy and a light response of leaf photosynthesis. This paper reviews the evolution and development of their theory. SCOPE: Monsi and Saeki showed that under full light conditions, canopy photosynthesis is maximized at a high leaf area index (LAI, total leaf area per unit ground area) with vertically inclined leaves, while under low light conditions, it is at a low LAI with horizontal leaves. They suggested that actual plants develop a stand structure to maximize canopy photosynthesis. Combination of the Monsi-Saeki model with the cost-benefit hypothesis in resource use led to a new canopy photosynthesis model, where leaf nitrogen distribution and associated photosynthetic capacity were taken into account. The gradient of leaf nitrogen in a canopy was shown to be a direct response to the gradient of light. This response enables plants to use light and nitrogen efficiently, two resources whose supply is limited in the natural environment. CONCLUSION: The canopy photosynthesis model stimulated studies to scale-up from chloroplast biochemistry to canopy carbon gain and to analyse the resource-use strategy of species and individuals growing at different light and nitrogen availabilities. Canopy photosynthesis models are useful to analyse the size structure of populations in plant communities and to predict the structure and function of future terrestrial ecosystems.     

双季稻光合生产模型的建立与应用

综合已有作物模型(包括冠层结构、冠层光分布和冠层光合作用与干物质生产模型)的优点,构建了双季稻光合生产模型.利用独立的田间试验资料,对冠层内的光分布和干物质积累量进行了初步检验;利用模型定量分析了直接辐射在上挺下挺、上挺下披和上披下披3种典型株型水稻冠层内水平面上和叶面上的分布、冠层日光合量及其随叶面积指数的变化特征.结果表明: 模拟值与观测值之间具有较好的一致性,预测双季稻冠层内光分布的根均方差、相对根均方差和相关系数分别为12.01 J·m^-2·s^-1、8.2%和0.9929;预测双季稻干物质积累量的根均方差、相对根均方差和相关系数分别为0.83 t·hm^-2、14.6%和0.9772,表明模型预测性较好;上挺下披株型水稻的冠层日光合量最高,取决于较大的叶面受光量、叶片光合效能和叶面积指数.     

Impact of nitrogen allocation on growth and photosynthesis of Miscanthus (Miscanthus × giganteus)

Nitrogen (N) addition typically increases overall plant growth, but the nature of this response depends upon patterns of plant nitrogen allocation that vary throughout the growing season and depend upon canopy position. In this study seasonal variations in leaf traits were investigated across a canopy profile in Miscanthus (Miscanthus × giganteus) under two N treatments (0 and 224 kg ha^?1) to determine whether the growth response of Miscanthus to N fertilization was related to the response of photosynthetic capacity and nitrogen allocation. Miscanthus yielded 24.1 Mg ha^?1 in fertilized plots, a 40% increase compared to control plots. Photosynthetic properties, such as net photosynthesis (A), maximum rate of rubisco carboxylation (V_cmax), stomatal conductance (g_s) and PSII efficiency (F_v'/F_m'), all decreased significantly from the top of the canopy to the bottom, but were not affected by N fertilization. N fertilization increased specific leaf area (SLA) and leaf area index (LAI). Leaf N concentration in different canopy layers was increased by N fertilization and the distribution of N concentration within canopy followed irradiance gradients. These results show that the positive effect of N fertilization on the yield of Miscanthus was unrelated to changes in photosynthetic rates but was achieved mainly by increased canopy leaf area. Vertical measurements through the canopy demonstrated that Miscanthus adapted to the light environment by adjusting leaf morphological and biochemical properties independent of nitrogen treatments. GPP estimated using big leaf and multilayer models varied considerably, suggesting a multilayer model in which V_cmax changes both through time and canopy layer could be adopted into agricultural models to more accurately predict biomass production in biomass crop ecosystems.     

基于PROSAIL辐射传输模型的毛竹林分冠层反射率模拟研究

冠层光谱反射率直接关系到毛竹（Phyllostachys pubescens Mazel）林冠层参数的反演,对毛竹林地土壤肥力间接估测具有重要意义。以PROSPECT5、PROSAIL模型为基础,从叶片尺度和冠层尺度分析模型参数对叶片和冠层反射率的影响,构建毛竹冠层叶面积指数（LAI）-冠层反射率查找表并通过代价函数选取最优冠层反射率,从而实现毛竹林分冠层反射率的准确模拟。结果表明,在叶片尺度,PROSPECT模型参数敏感性从高到低依次为叶肉结构参数（N） > 叶绿素含量（C_ab） > 等效水厚度（EWT） > 干物质含量（C_m） > 类胡萝卜素含量（C_ar）;在冠层尺度,PROSAIL模型参数敏感性从高到低依次为LAI > C_ab > EWT > C_m > N > C_ar > ALA（平均叶倾角）;叶片尺度反射率整体大于冠层尺度反射率;在400~900 nm波长范围内,PROSAIL模型模拟的冠层光谱反射率与实测光谱反射率拟合效果较好,相对误差为6.71%。     

RATP: a model for simulating the spatial distribution of radiation absorption, transpiration and photosynthesis within canopies: application to an isolated tree crown

The model RATP (radiation absorption, transpiration and photosynthesis) is presented. The model was designed to simulate the spatial distribution of radiation and leaf-gas exchanges within vegetation canopies as a function of canopy structure, canopy microclimate within the canopy and physical and physiological leaf properties. The model uses a three-dimensional (3D) representation of the canopy (i.e. an array of 3D cells, each characterized by a leaf area density). Radiation transfer is computed by a turbid medium analogy, transpiration by the leaf energy budget approach, and photosynthesis by the Farquhar model, each applied for sunlit and shaded leaves at the individual 3D cell-scale. The model typically operates at a 20–30 min time step. The RATP model was applied to an isolated, 20-year-old walnut tree grown in the field. The spatial distribution of wind speed, stomatal response to environmental variables, and light acclimation of leaf photosynthetic properties were taken into account. Model outputs were compared with data acquired in the field. The model was shown to simulate satisfactorily the intracrown distribution of radiation regime, transpiration and photosynthetic rates, at shoot or branch scales.     

Whole-canopy carbon gain as a result of selection on individual performance of ten genotypes of a clonal plant

Game theoretical models predict that plant competition for light leads to reduced productivity of vegetation stands through selection for traits that maximize carbon gains of individuals. Using empirical results from a 5-year competition experiment with 10 genotypes of the clonal plant Potentilla reptans, we tested this prediction by analyzing the effects of the existing leaf area values on the carbon gain of the different genotypes and the consequent whole canopy carbon gain. We focused on specific leaf area (SLA) due to its role in the trade-off between light capture area and photosynthetic capacity per unit area. By combining a canopy model based on measured leaf area and light profiles with a game theoretical approach, we analyzed how changes in the SLA affected genotypic and whole-stand carbon gain. This showed that all genotypes contributed to reduced stand productivity. The dominant genotype maximized its share of total carbon gain, resulting in lower than maximal absolute gain. Other genotypes did not maximize their share. Hypothetical mutants of the dominant genotype were not able to achieve a higher carbon gain. Conversely, in other genotypes, some mutations did result in increased carbon gain. Hence, genotypic differences in the ability to maximize performance may determine genotype frequency. It shows how genotypic selection may result in lower carbon gains of the whole vegetation, and of the individual genotypes it consists of, through similar mechanisms as those that lead to the tragedy of the commons.     

Within-tree spatial variation in the leaf monoterpenes of Sequoia sempervirens

Location within a tree was analyzed as a source of variation in Sequoia sempervirens leaf monoterpenes. No differences were found for quantitative composition or total yield/dry wt among lower, middle and upper canopy positions. The awlshaped, spirally arranged leaves of vigorous upper shoots showed small quantitative compositional differences, but not differences in total yield. The intermediate leaf form of young sprouts had the most different monoterpene quantitative composition and about three times the total yield of the above two leaf forms. Analysis of a clonal ring of 17 adult trees resulted in coefficients of variation similar to those for samples collected from different canopy levels of the same shoot. Results revealed the sources and magnitudes of experimental error in comparative studies of this species' leaf monoterpenes, and did not support the concept that somatic mutation provides an important source of variation in a large, long-lived organism such as coast redwood.     

Characteristics of canopy evapotranspiration from a small heterogeneous grassland using thermal imaging

We used thermal imaging in conjunction with the eddy covariance technique to characterize canopy evapotranspiration (ET) from a small heterogeneous grassland. We compared ET estimated by a simple soil–vegetation–atmosphere transfer (SVAT) at field scale (a few 100 m²) with that estimated by the eddy covariance method. These two independent estimates of ET showed a good correlation when the flux source area was the same. However, whereas the eddy covariance method yielded integrated results over a large, variable landscape area, the SVAT model primarily yielded values reflecting just the grassland area. We estimated mapped transpiration (Tr) at a point scale (1 m²) and showed that Tr increased linearly with increasing leaf area index (LAI). Although stomatal conductance of C₃ plants was appreciably larger than that of C₄ plants at the leaf scale, this difference was not reflected in Tr at the canopy scale. Tr may be more sensitive to aerodynamic conditions (wind speed and radiation) or environmental heterogeneity (soil–water) than stomatal conductance. The SVAT model clarified variations in the spatial distribution of Tr over a heterogeneous grassland.     

落叶阔叶林冠层光合有效辐射分量的遥感模拟与分析

冠层绿色叶片(光合组分)的光合有效辐射分量(绿色FPAR)真实地反映了植被与外界进行物质和能量交换的能力,获取冠层光合组分吸收的太阳光合有效辐射,对生态系统生产力的遥感估算精度的提高具有重要的意义。研究以落叶阔叶林为例,基于SAIL模型模拟森林冠层光合组分和非光合组分吸收的光合有效辐射,研究冠层FPAR变化规律以及与植被指数的相关关系。结果表明,冠层结构的改变会影响冠层对PAR的吸收能力,冠层绿色FPAR的大小与植被面积指数及光合组分面积比相关;在高覆盖度植被区,冠层绿色FPAR占冠层总FPAR的80%以上,非光合组分的贡献较小,但在低植被覆盖区,当光合组分和非光合组分面积相同时,绿色FPAR不及冠层总FPAR的50%;相比于NDVI,北方落叶阔叶林冠层EVI与绿色FPAR存在更为显著的线性相关关系(R~20.99)。     

Exploring the spatial distribution of light interception and photosynthesis of canopies by means of a functional-structural plant model

Background and Aims

At present most process-based models and the majority of three-dimensional models include simplifications of plant architecture that can compromise the accuracy of light interception simulations and, accordingly, canopy photosynthesis. The aim of this paper is to analyse canopy heterogeneity of an explicitly described tomato canopy in relation to temporal dynamics of horizontal and vertical light distribution and photosynthesis under direct- and diffuse-light conditions.

Methods

Detailed measurements of canopy architecture, light interception and leaf photosynthesis were carried out on a tomato crop. These data were used for the development and calibration of a functional–structural tomato model. The model consisted of an architectural static virtual plant coupled with a nested radiosity model for light calculations and a leaf photosynthesis module. Different scenarios of horizontal and vertical distribution of light interception, incident light and photosynthesis were investigated under diffuse and direct light conditions.

Key Results

Simulated light interception showed a good correspondence to the measured values. Explicitly described leaf angles resulted in higher light interception in the middle of the plant canopy compared with fixed and ellipsoidal leaf-angle distribution models, although the total light interception remained the same. The fraction of light intercepted at a north–south orientation of rows differed from east–west orientation by 10 % on winter and 23 % on summer days. The horizontal distribution of photosynthesis differed significantly between the top, middle and lower canopy layer. Taking into account the vertical variation of leaf photosynthetic parameters in the canopy, led to approx. 8 % increase on simulated canopy photosynthesis.

Conclusions

Leaf angles of heterogeneous canopies should be explicitly described as they have a big impact both on light distribution and photosynthesis. Especially, the vertical variation of photosynthesis in canopy is such that the experimental approach of photosynthesis measurements for model parameterization should be revised.     

The phenology of leaf quality and its within‐canopy variation is essential for accurate modeling of photosynthesis in tropical evergreen forests

Leaf quantity (i.e., canopy leaf area index, LAI), quality (i.e., per‐area photosynthetic capacity), and longevity all influence the photosynthetic seasonality of tropical evergreen forests. However, these components of tropical leaf phenology are poorly represented in most terrestrial biosphere models (TBMs). Here, we explored alternative options for the representation of leaf phenology effects in TBMs that employ the Farquahar, von Caemmerer & Berry (FvCB) representation of CO₂ assimilation. We developed a two‐fraction leaf (sun and shade), two‐layer canopy (upper and lower) photosynthesis model to evaluate different modeling approaches and assessed three components of phenological variations (i.e., leaf quantity, quality, and within‐canopy variation in leaf longevity). Our model was driven by the prescribed seasonality of leaf quantity and quality derived from ground‐based measurements within an Amazonian evergreen forest. Modeled photosynthetic seasonality was not sensitive to leaf quantity, but was highly sensitive to leaf quality and its vertical distribution within the canopy, with markedly more sensitivity to upper canopy leaf quality. This is because light absorption in tropical canopies is near maximal for the entire year, implying that seasonal changes in LAI have little impact on total canopy light absorption; and because leaf quality has a greater effect on photosynthesis of sunlit leaves than light limited, shade leaves and sunlit foliage are more abundant in the upper canopy. Our two‐fraction leaf, two‐layer canopy model, which accounted for all three phenological components, was able to simulate photosynthetic seasonality, explaining ~90% of the average seasonal variation in eddy covariance‐derived CO₂ assimilation. This work identifies a parsimonious approach for representing tropical evergreen forest photosynthetic seasonality in TBMs that utilize the FvCB model of CO₂ assimilation and highlights the importance of incorporating more realistic phenological mechanisms in models that seek to improve the projection of future carbon dynamics in tropical evergreen forests.     

Foliage randomness and light interception in 3-D digitized trees: an analysis from multiscale discretization of the canopy

Light models for vegetation canopies based on the turbid medium analogy are usually limited by the basic assumption of random foliage dispersion in the canopy space. The objective of this paper was to assess the effect of three possible sources of non-randomness in tree canopies on light interception properties. For this purpose, four three-dimensional (3-D) digitized trees and four theoretical canopies – one random and three built from fractal rules – were used to compute canopy structure parameters and light interception, namely the sky-vault averaged STAR (Silhouette to Total Area Ratio). STAR values were computed from (1) images of the 3-D plants, and (2) from a 3-D turbid medium model using space discretization at different scales. For all trees, departure from randomness was mainly due to the spatial variations in leaf area density within the canopy volume. Indeed STAR estimations, based on turbid medium assumption, using the finest space discretization were very close to STAR values computed from the plant images. At this finest scale, foliage dispersion was slightly clumped, except one theoretical fractal canopy, which showed a marked regular dispersion. Taking into account a non-infinitely small leaf size, whose effect is theoretically to shorten self-shading, had a minor effect on STAR computations. STAR values computed from the 3-D turbid medium were very sensitive to plant lacunarity, a parameter introduced in the context of fractal studies to characterize the distribution of gaps in porous media at different scales. This study shows that 3-D turbid medium models based on space discretization are able to give correct estimation of light interception by 3-D isolated trees, provided that the 3-D grid is properly defined, that is, discretization maximizes plant lacunarity.     

Nitrogen use efficiency in instantaneous and daily photosynthesis of leaves in the canopy of a Solidago altissima stand

Photosynthetic capacity was measured on detached leaves sampled in a canopy of Solidago altissima L. Non-rectangular hyperbola fitted the light response curve of photosynthesis and significant correlations were observed between leaf nitrogen per unit area and four parameters which characterize the light-response curve. Using regressions of the parameters on leaf nitrogen, a model of leaf photosynthesis was constructed which gave the relationships between leaf nitrogen, photon flux density (PFD) and photosynthesis. Curvilinear relations were obtained between leaf nitrogen and photosynthetic rate on both an instantaneous and a daily basis. Nitrogen use efficiency (NUE, photosynthesis per unit leaf nitrogen) was calculated against leaf nitrogen under varying PFDs. The optimum nitrogen content per unit leaf area that maximizes NUE shifted to higher values with increasing PFD. Field measurements of PFD showed high positive correlations between the distribution of leaf nitrogen in the canopy and relative PFD. The predicted optimum leaf nitrogen content for each level in the canopy, to achieve maximized NUE during a clear day, was close to the actual nitrogen distribution as found through sampling.     

Simple scaling of photosynthesis from leaves to canopies without the errors of big-leaf models

In big-leaf models of canopy photosynthesis, the Rubisco activity per unit ground area is taken as the sum of activities per unit leaf area within the canopy, and electron transport capacity is similarly summed. Such models overestimate rates of photosynthesis and require empirical curvature factors in the response to irradiance. We show that, with any distribution of leaf nitrogen within the canopy (including optimal), the required curvature factors are not constant but vary with canopy leaf area index and leaf nitrogen content. We further show that the underlying reason is the difference between the time-averaged and instantaneous distributions of absorbed irradiance, caused by penetration of sunflecks and the range of leaf angles in canopies. These errors are avoided in models that treat the canopy in terms of a number of layers – the multi-layer models. We present an alternative to the multi-layer model: by separately integrating the sunlit and shaded leaf fractions of the canopy, a single layered sun/shade model is obtained, which is as accurate and simpler. The model is a scaled version of a leaf model as distinct from an integrative approach.