Plant competition for light analyzed with a multispecies canopy model

Summary Competition for light among species in a mixed canopy can be assessed quantitatively by a simulation model which evaluates the importance of different morphological and photosynthetic characteristics of each species. A model was developed that simulates how the foliage of all species attenuate radiation in the canopy and how much radiation is received by foliage of each species. The model can account for different kinds of foliage (leaf blades, stems, etc.) for each species. The photosynthesis and transpiration for sunlit and shaded foliage of each species is also computed for different layers in the canopy. The model is an extension of previously described single-species canopy photosynthesis simulation models. Model predictions of the fraction of foliage sunlit and interception of light by sunlit and shaded foliage for monoculture and mixed canopies of wheat (Triticum aestivum) and wild oat (Avena fatua) in the field compared very well with measured values. The model was used to calculate light interception and canopy photosynthesis for both species of wheat/wild oat mixtures grown under normal solar and enhanced ultraviolet-B (290–320 nm) radiation (UV-B) in a glasshouse experiment with no root competition. In these experiments, measurements showed that the mixtures receiving enhanced UV-B radiation had a greater proportion of the total foliage area composed of wheat compared to mixtures in the control treatments. The difference in species foliage area and its position in the canopy resulted in a calculated increase in the portion of total canopy radiation interception and photosynthesis by wheat. This, in turn, is consistent with greater canopy biomass of wheat reported in canopies irradiated with supplemental UV-B.     

Angle distribution of foliage in individual Chamaecyparis obtusa canopies and effect of angle on diffuse light penetration

 The vertical distribution of foliage angle and area of three Chamaecyparis obtusa trees was determined by the triangle method, which calculates foliage geometry using measured coordinates of the leaf ”corners”, in a 43-year-old plantation in central Japan. Vertical distribution patterns of leaf area were different depending on tree size, but the boundary heights, which divide the canopy into sunlit and shaded parts, were similar in the three sample trees. The value of the average foliage angle [I(Z)] at a given depth (Z) from the tip of the stem decreased continually from the upper to lower layers within the canopy. The vertical patterns of changes in I(Z) were different among the three trees, but could be expressed by the following allometric equation as a function of depth.

Three-dimensional Structure of an Old-growth <Emphasis Type="Italic">Pseudotsuga-Tsuga</Emphasis> Canopy and Its Implications for Radiation Balance,Microclimate, and Gas Exchange

We describe the three-dimensional structure of an old-growth Douglas-fir/western hemlock forest in the central Cascades of southern Washington, USA. We concentrate on the vertical distribution of foliage, crowns, external surface area, wood biomass, and several components of canopy volume. In addition, we estimate the spatial variation of some aspects of structure, including the topography of the outer surface, and of microclimate, including the within-canopy transmittance of photosynthetically active radiation (PAR). The crowns of large stems, especially of Douglas-fir, dominate the structure and many aspects of spatial variation. The mean vertical profile of canopy surfaces, estimated by five methods, generally showed a single maximum in the lower to middle third of the canopy, although the height of that maximum varied by method. The stand leaf area index was around 9 m² m^–2, but also varied according to method (from 6.3 to 12.3). Because of the deep narrow crowns and numerous gaps, the outer canopy surface is extremely complex, with a surface area more than 12 times that of the ground below. The large volume included below the outer canopy surface is very porous, with spaces of several qualitatively distinct environments. Our measurements are consistent with emerging concepts about the structure of old-growth forests, where a high degree of complexity is generated by diverse structural features. These structural characteristics have implications for various ecosystem functions. The height and large volume of the stand indicate a large storage component for microclimatic variables. The high biomass influences the dynamics of those variables, retarding rates of change. The complexity of the canopy outer surface influences radiation balance, particularly in reducing short-wave reflectance. The bottom-heaviness of the foliage profile indicates much radiation absorption and gas exchange activity in the lower canopy. The high porosity contributes to flat gradients of most microclimate variables. Most stand respiration occurs within the canopy and is distributed over a broad vertical range.     

Developing and validating novel hyperspectral indices for leaf area index estimation: Effect of canopy vertical heterogeneity

Leaf area index (LAI) is one of the key biophysical parameters for understanding land surface photosynthesis, transpiration, and energy balance processes. Estimation of LAI from remote sensing data has been a premier method for a large scale in recent years. Recent studies have revealed that the within-canopy vertical variations in LAI and biochemical properties greatly affect canopy reflectance and significantly complicate the retrieval of LAI inversely from reflectance based vegetation indices, which has yet been explicitly addressed. In this study, we have used both simulated datasets (dataset I with constant vertical profiles of LAI and biochemical properties, dataset II with varied vertical profile of LAI but constant vertical biochemical properties, and dataset III with both varied vertical profiles) generated from the multiple-layer canopy radiative transfer model (MRTM) and a ground-measured dataset to identify robust spectral indices that are insensitive to such within canopy vertical variations for LAI prediction. The results clearly indicated that published indices such as normalized difference vegetation index (NDVI) had obvious discrepancies when applied to canopies with different vertical variations, while the new indices identified in this study performed much better. The best index for estimating canopy LAI under various conditions was D(920,1080), with overall RMSEs of 0.62–0.96 m²/m² and biases of 0.42–0.55 m²/m² for all three simulated datasets and an RMSE of 1.22 m²/m² with the field-measured dataset, although it was not the most conservative one among all new indices identified. This index responded mostly to the quantity of LAI but was insensitive to within-canopy variations, allowing it to aid the retrieval LAI from remote sensing data without prior information of within-canopy vertical variations of LAI and biochemical properties.     

An analytical model for bidirectional reflectance factor of multicomponent vegetation canopies

Based on radiative transfer theory in vegetation and geometric-optical principles, an analytical physi-cal mode] for calculating multiangular, multispectral reflectance over a non-random, multiple component vegetation canopy is developed. This model is derived by taking advantages of the previous leaf canopy and multicomponent canopy BRF models. It quantitatively accounts for both the impact of foliage elements' orientation on the canopy hotspot through an innovative algorithm to estimate the hotspot function for any arbitrarily oriented foliage element and contributions of all foliage elements to the reflectance by multiple scattering. Thus, it is characterized by more com-pletely considering the integrative influence of spatial variations in optical and structural properties of all foliage ele-ments on canopy reflectance than any previous analytical BRF models. Simulation results from this model demonstrate that canopy hotspot becomes strongest when the mean inclination angle of foliage elements is ar     

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.     

The influence of temperature on within-canopy acclimation and variation in leaf photosynthesis: spatial acclimation to microclimate gradients among climatically divergent Acer rubrum L. genotypes

Leaf gas exchange and temperature response were measured to assess temperature acclimation within a tree canopy in climatically contrasting genotypes of Acer rubrum L. Over the course of two 50 d continuous periods, growth temperature was controlled within tree crowns and the steady-state rate of leaf gas exchange was measured. Data were then modelled to calculate the influence of genotype variation and vertical distribution of physiological activity on carbon uptake. The maximal rate of Rubisco carboxylation (V(cmax)), the maximum rate of electron transport (J(max)), leaf dark respiration rate (R(d)), maximum photosynthesis (A(max)), and the CO(2) compensation point (Gamma) increased with temperature during both (i) a constant long-term (50 d) daytime temperature or (ii) ambient daytime temperature with short-term temperature control (25-38 degrees C). In addition, within-crown variation in the temperature response of photosynthesis and R(d) was influenced by acclimation to local microclimate temperature gradients. Results indicated that carbon uptake estimates could be overestimated by 22-25% if the vertical distribution of temperature gradients is disregarded. Temperature is a major factor driving photosynthetic acclimation and within-crown gas exchange variation. Thus, this study established the importance of including spatial acclimation to temperature- and provenance-, ecotype-, and/or genotype-specific parameter sets into carbon uptake models.     

Modeling the vertical foliage distribution of an individual <Emphasis Type="Italic">Castanopsis cuspidata</Emphasis> (Thunb.) Schottky,a dominant broad-leaved tree in Japanese warm-temperate forest

The vertical foliage distribution of Castanopsis cuspidata (Thunb.) Schottky was examined in trees of various sizes to clarify its variation in relation to tree size and the light environment in a stand. As indices of these parameters, we analyzed crown social position (CSP: percent of stand height) and specific leaf area (SLA). The vertical foliage distribution of trees was expressed by a Weibull function. The variation in the vertical foliage distribution of C. cuspidata could be categorized into three types using crown social position and light environment. In the first type, leaves were concentrated to the top 20% of the tree; such trees are canopy trees that can receive full sunlight. The second type had a large relative crown depth and an asymmetric distribution with the maximum foliage located near the top of the tree; such trees are suppressed trees whose crowns do not receive sufficient light. The third type had a large relative crown depth and a symmetric distribution; such trees occur in high light environments, although their crowns are in the understory layer. The differences in the vertical foliage distribution are related to the strategies used to capture light. Multiple regression analysis showed that CSP and SLA at the top layer of the tree explained successive changes in the vertical foliage distribution. These results will contribute to scaling-up the vertical foliage distribution to the community level in pure stands of C. cuspidata using an individual-based model.     

六盘山辽东栎、少脉椴天然次生林夏季蒸散研究

2004年8～9月份,利用热扩散技术,结合微型蒸渗仪和水文学方法,研究了辽东栎、少脉椴次生林蒸散组成及其与林分结构的关系.结果表明,辽东栎和少脉椴树干的液流密度在"相对静止期"内比较稳定和微弱,其值在0.05μl·cm^-2·min^-1以下;在"活跃期"内树干液流密度上升较快,并呈单峰、双峰或多峰曲线,其值在0.25μl·cm^-2·min^-1以下;两树种单株蒸腾量有明显的种间差异,前者晴天和阴雨天单株蒸腾量分别为5.31和2.48 L·d^-1,为后者的2.3倍和3.75倍.林下灰_栒子和黄刺玫蒸腾速率日均值接近,分别为0.331和0.321 g·g^-1·h^-1.次生林日均蒸散量1.4 mm·d^-1,其中蒸腾量0.72 mm·d^-1、土壤蒸发量0.19 mm·d^-1、林冠截留量0.4 mm·d^-1,各占总量的49.6%、13.3%和37.1%.乔、灌木树种组成对次生林蒸腾量影响的表现不同,前者表现为个体蒸腾量的种间差异,而后者取决于单位林地面积上各树种的叶量.乔木层、灌木层和草本层(含土壤层)日均蒸散量分别为0.96、0.30和0.19 mm·d^-1,各占总量的65.8%、20.9%和13.3%,说明乔木层对林分日蒸散量大小起主要作用,灌木层次之,草本和土壤蒸发量的贡献最小.     

Effects of elevated atmospheric carbon dioxide on gas exchange and growth of white clover

Effects of rising atmospheric CO₂ concentrations on gas exchange, growth and productivity were investigated on an important grassland species, Trifolium repens L. cv. Blanca. Pure stands of this species were cultivated over an entire growing season in small acrylic greenhouses with an artificial atmosphere of ±367 or ±620 ppm CO₂, respectively. Effects on growth and development were examined in a functional growth analysis, while consequences for gas exchange were determined by photosynthesis and transpiration measurements on canopy level. The stands were regularly clipped for production assessment. Canopies grown at high CO₂ levels showed an average increase in productivity of almost 75%. Growth analysis indicated development of a larger foliage area as the major cause, particularly in the first days of regrowth after cutting. The growth advantage that began in this stage was maintained or bettered during the following weeks. The difference between gas exchange measurements expressed per unit leaf area and per unit ground area suggested that changes in net photosynthesis and respiration did not contribute to the increase in total yield. Transpiration declined under high CO₂ if expressed on a leaf area basis but total canopy transpiration was at least as large as in ambient CO₂ due to the larger leaf area. Water-use efficiency calculations on the summer data indicated a 35% improvement with a doubling of CO₂ concentration.     

Sensitivity of volatile monoterpene emission to changes in canopy structure: a model-based exercise with a process-based emission model

This paper investigates the dependence of monoterpene emissions at the canopy scale on total leaf area and leaf distribution. Simulations were carried out for a range of hypothetical but realistic forest canopies of the evergreen Quercus ilex (holm oak). Two emission models were applied that either did (SIM-BIM2) or did not (G93) account for cumulative responses to temperature and light. Both were embedded into a canopy model that considered spatial and temporal variations of foliage properties. This canopy model was coupled to a canopy climate model (CANOAK) to determine the micrometeorological conditions at the leaf scale. Structural properties considerably impacted monoterpene emission. The sensitivities to changes in total leaf area and to leaf area distribution were found to be of similar magnitude. The two different models performed similarly on a whole-year basis but showed clear differences during certain episodes. The analysis showed that structural indices have to be carefully evaluated for proper scaling of emission from leaves to canopy. Further research is encouraged on seasonal dynamics of emission potentials.     

Using Light-Use and Production Efficiency Models to Predict Photosynthesis and Net Carbon Exchange During Forest Canopy Disturbance

Vegetation growth models are used with remotely sensed and meteorological data to monitor terrestrial carbon dynamics at a range of spatial and temporal scales. Many of these models are based on a light-use efficiency equation and two-component model of whole-plant growth and maintenance respiration that have been parameterized for distinct vegetation types and biomes. This study was designed to assess the robustness of these parameters for predicting interannual plant growth and carbon exchange, and more specifically to address inconsistencies that may arise during forest disturbances and the loss of canopy foliage. A model based on the MODIS MOD17 algorithm was parameterized for a mature upland hardwood forest by inverting CO₂ flux tower observations during years when the canopy was not disturbed. This model was used to make predictions during a year when the canopy was 37% defoliated by forest tent caterpillars. Predictions improved after algorithms were modified to scale for the effects of diffuse radiation and loss of leaf area. Photosynthesis and respiration model parameters were found to be robust at daily and annual time scales regardless of canopy disturbance, and differences between modeled net ecosystem production and tower net ecosystem exchange were only approximately 2 g C m⁻² d⁻¹ and less than 23 g C m⁻² y⁻¹. Canopy disturbance events such as insect defoliations are common in temperate forests of North America, and failure to account for cyclical outbreaks of forest tent caterpillars in this stand could add an uncertainty of approximately 4–13% in long-term predictions of carbon sequestration.     

Assessing transpiration in the tussock grass Stipa tenacissima L.: the crucial role of the interplay between morphology and physiology

Plant transpiration has a key role on both plant performance and ecosystem functioning in arid zones, but realistic estimates at appropriate spatial-temporal scales are scarce. Leaf and tiller morphology and crown architecture were studied together with leaf physiology and whole plant water balance in four individual plants of Stipa tenacissima of different sizes to determine the relative influence of processes taking place at different spatial and temporal scales on whole plant transpiration. Transpiration was estimated in potted plants by leaf-level gas exchange techniques (infrared gas analyzer and porometer), by sap flow measurements, and by integrating leaf physiology and crown architecture with the 3-D computer model Yplant. Daily transpiration of each individual plant was monitored using a gravimetric method, which rendered the reference values. Leaves on each individual plant significantly varied in their physiological status. Young and green parts of the leaves showed five times higher chlorophyll concentration and greater photosynthetic capacity than the senescent parts of the foliage. Instantaneous leaf-level transpiration measurements should not be used to estimate plant transpiration, owing to the fact that extrapolations overestimated individual transpiration by more than 100%. Considering leaf age effects and scaling the estimates according to the relative amount of each foliage category reduced this difference to 46% though it was still significantly higher than gravimetric measurements. Sap flow calculations also overestimated tussock transpiration. However, 3-D reconstruction of plants with Yplant and transpiration estimates, considering both the physiological status and the daily pattern of radiation experienced by each individual leaf section within the crown, matched the gravimetric measurements (differences were only 4.4%). The complex interplay of leaf physiology and crown structure must be taken into account in scaling up plant transpiration from instantaneous, leaf-level measurements, and our study indicates that transpiration of complex crowns is easily overestimated.     

Stomatal control of transpiration from a developing sugarcane canopy

Abstract. Stomatal conductance of single leaves and transpiration from an entire sugarcane (Saccharum spp. hybrid) canopy were measured simultaneously using independent techniques. Stomatal and environmental controls of transpiration were assessed at three stages of canopy development, corresponding to leaf area indices (L) of 2.2, 3.6 and 5.6. Leaf and canopy boundary layers impeded transport of transpired water vapour away from the canopy, causing humidity around the leaves to find its own value through local equilibration rather than a value determined by the humidity of the bulk air mass above the canopy. This tended to uncouple transpiration from direct stomatal control, so that transpiration predicted from measurement of stomatal conductance and leaf-to-air vapour pressure differences was increasingly overestimated as the reference point for ambient vapour pressure measurement was moved farther from the leaf and into the bulk air. The partitioning of control between net radiation and stomata was expressed as a dimensionless decoupling coefficent ranging from zero to 1.0. When the stomatal aperture was near its maximum this coefficient was approximately 0.9, indicating that small reductions in stomatal aperture would have had little effect on canopy transpiration. Maximum rates of transpiration were, however, limited by large adjustments in maximum stomatal conductance during canopy development. The product of maximum stomatal conductance and L. a potential total canopy conductance in the absence of boundary layer effects, remained constant as L increased. Similarly, maximum canopy conductance, derived from independent micrometeorological measurements, also remained constant over this period. Calculations indicated that combined leaf and canopy boundary layer conductance decreased with increasing L such that the ratio of boundary layer conductance to maximum stomatal conductance remained nearly constant at approximately 0.5. These observations indicated that stomata adjusted to maintain both transpiration and the degree of stomatal control of transpiration constant as canopy development proceeded.     

Assessing transpiration in the tussock grass Stipa tenacissima L.: the crucial role of the interplay between morphology and physiology

Plant transpiration has a key role on both plant performance and ecosystem functioning in arid zones, but realistic estimates at appropriate spatial-temporal scales are scarce. Leaf and tiller morphology and crown architecture were studied together with leaf physiology and whole plant water balance in four individual plants of Stipa tenacissima of different sizes to determine the relative influence of processes taking place at different spatial and temporal scales on whole plant transpiration. Transpiration was estimated in potted plants by leaf-level gas exchange techniques (infrared gas analyzer and porometer), by sap flow measurements, and by integrating leaf physiology and crown architecture with the 3-D computer model Yplant. Daily transpiration of each individual plant was monitored using a gravimetric method, which rendered the reference values. Leaves on each individual plant significantly varied in their physiological status. Young and green parts of the leaves showed five times higher chlorophyll concentration and greater photosynthetic capacity than the senescent parts of the foliage. Instantaneous leaf-level transpiration measurements should not be used to estimate plant transpiration, owing to the fact that extrapolations overestimated individual transpiration by more than 100%. Considering leaf age effects and scaling the estimates according to the relative amount of each foliage category reduced this difference to 46% though it was still significantly higher than gravimetric measurements. Sap flow calculations also overestimated tussock transpiration. However, 3-D reconstruction of plants with Yplant and transpiration estimates, considering both the physiological status and the daily pattern of radiation experienced by each individual leaf section within the crown, matched the gravimetric measurements (differences were only 4.4%). The complex interplay of leaf physiology and crown structure must be taken into account in scaling up plant transpiration from instantaneous, leaf-level measurements, and our study indicates that transpiration of complex crowns is easily overestimated.     

Transpiration decline curves and stomatal characteristics of faba bean genotypes

Nine F1 crosses of faba bean (Vicia faba L.) and their parental genotypes were evaluated for transpiration decline curves (TDC) and stomatal characteristics. The most common type of TDC had one inflexion. One parent and three crosses were characterized by TDC of two inflexions, while one cross had TDC without inflexion. The genotypes which exhibited TDC with 2inflexions showed later time to stomatal closure (SC). Also stomatal and cuticular transpiration rates differ significantly among studied genotypes. A model for selecting genotypes with effective water retaining features was suggested. This model includes relative water content (RWC) at SC, stomatal density, guard cell length, stomatal pore width at both sides of the leaf, stomatal pore length at lower side and leaflet dry mass This revised version was published online in July 2006 with corrections to the Cover Date.     

Complexity of leaf miner–parasitoid food webs declines with canopy height in Patagonian beech forests

1. Consumer–resource species interactions form complex, dynamic networks, which may exhibit structural heterogeneity at various scales. This study set out to address whether host–parasitoid food web size and topology vary across forest canopy strata, and to what extent foliar resources and species abundances account for vertical patterns in network structure. 2. The vertical stratification of leaf miner–parasitoid food webs was examined in two monotypic beech (Nothofagus pumilio) forests in northern Patagonia, Argentina. Quantitative food webs were constructed for separate canopy layers by sampling foliage from three tree‐height classes at 0.5–1, 2–3 and 5–6 m above ground. 3. Leaf miner abundance per unit leaf mass and foliar damage (%) did not differ across strata, although foliage quality and quantity increased from the understorey to the upper canopy. Parasitism rates and food web complexity decreased with canopy height, as reflected by reduced linkage richness, linkage density, mean interaction strength, and host vulnerability. 4. Null model analyses revealed that food web metrics, especially in the upper canopy, were often lower than expected when compared with randomly structured networks. Overall, these patterns held for two forests differing in vertical structure and in dominant miner morphotype and parasitoid species. 5. These results suggest that vertical declines in network complexity may be driven by the parasitoids' limited functional response to host abundance and dispersal from pupation sites in the forest floor. A broader constraint on food web structure seemed to be imposed by host–parasitoid trait matching, a reflection of large‐scale assembly processes.     

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.     

Inferring changes in foliar mass and area from foliage cover: A mechanistic model

Measuring foliar area or mass directly is destructive, and precludes long‐term, repeated observations of individual trees as they suffer or recover from foliar damage. Instead, foliage cover indices are often used as a proxy for foliar mass. Patterns of fluctuations in foliage cover indices can be used to infer qualitative changes in canopy health. However, foliage cover is not necessarily linearly related to foliar area or mass, and this may confound the detection of significant foliar damage, and comparisons of herbivore browse impacts between individual trees, tree species or sites. I derived a mechanistic model to quantify the relationship between foliar area or mass and foliage cover measured as the proportion of sky occluded by leaves. This one parameter model is close to linear for single‐tiered trees, but increasingly non‐linear for multi‐tiered trees. I compared the non‐linear model to a linear model using foliage cover data from an artificial defoliation experiment on two single‐tiered, sub‐canopy species and from simulated photographic images of single‐ and multi‐tiered canopies. The non‐linear model had lower errors than the linear model, and errors did not increase with foliage density (leaf area per unit area), variation (of leaf sizes within and between canopies) or leaf geometry. The non‐linear model can be easily parameterized from relatively low‐cost observations of foliage cover, independently of empirical measurements of foliar area or mass, and is applicable to a wide range of tree species. It should therefore help managers quantify how changes in foliage cover due to natural fluctuations or foliar damage affect foliar area and mass, and can be used to quantify parameters for models of browse impacts in mixed forest.