Mathematical models of the photosynthetic response of tree stands to rising CO2 concentrations and temperatures

Two published models of canopy photosynthesis, MAESTRO and BIOMASS, are simulated to examine the response of tree stands to increasing ambient concentrations of carbon dioxide (C_a) and temperatures. The models employ the same equations to described leaf gas exchange, but differ considerably in the level of detail employed to represent canopy structure and radiation environment. Daily rates of canopy photosynthesis simulated by the two models agree to within 10% across a range of CO₂ concentrations and temperatures. A doubling of C_a leads to modest increases of simulated daily canopy photosynthesis at low temperatures (10% increase at 10°C), but larger increases at higher temperatures (60% increase at 30°C). The temperature and CO₂ dependencies of canopy photosynthesis are interpreted in terms of simulated contributions by quantum-saturated and non-saturated foliage. Simulations are presented for periods ranging from a diurnal cycle to several years. Annual canopy photosynthesis simulated by BIOMASS for trees experiencing no water stress is linearly related to simulated annual absorbed photosynthetically active radiation, with light utilization coefficients for carbon of ?= 1.66 and 2.07g MJ^?1 derived for C_a of 350 and 700 μmol mol^?1, respectively.     

Estimation of the primary productivity of Spartina alterniflora using a canopy model

A comprehensive canopy productivity model was built to study the productivity of a primary salt marsh grass, Spartina alterniflora. in Georgia, USA The canopy model was unique in employing plant demographic data to reconstruct canopy profiles and dynamics, which showed many growth processes that are otherwise difficult to discern in the field By linking canopy dynamics and leaf photosynthesis, the net total primary productivity of S alterniflora m a Georgia salt marsh was estimated to be 1421, 749, and 1441 g C m^-2 yr^-1 for the tall, short, and N-fertilized short populations respectively These estimates are reasonable in terms of the physiological capacity of S alterniflora and well below the range of 3000–4200 g C m^-2 yr^-1 as reported by some recent harvest studies Our detailed analysis suggested the net total productivity of S alterniflora might be greatly overestimated in the past This is mainly because of 1) failure to consider the translocation of photosynthate between aboveground and belowground parts, and 2) possible overestimates of belowground production We estimated the net belowground production to be 872, 397, and 762 g C m^-2 yr^-1 for the tall, short, and N-fertilized populations respectively After receiving nitrogen fertilizer, the net leaf carbon fixation in the short population increased from 1489 to 2487 g C m^-2 yr^-1, and our simulation showed the contribution of elevated leaf N to this increase was small, 21%, compared with that of increased leaf area, 79% Both tall and short populations allocated ca 48-49% of their annual gross leaf carbon fixation to belowground structures Nitrogen enrichment caused more allocation to aboveground parts in the short population, mainly for increasing leaf area The canopy model assumed that there was no leaf photosynthesis under tidal submergence, but if this assumption was relaxed, then leaf carbon fixation might increase 7–13% for different S alterniflora populations Although this research focused only on a salt marsh species, our general approaches, especially the coupling of leaf physiology with the reconstructed canopies, should be applicable to the study of production processes of many other plant populations     

The vertical distribution of nitrogen and photosynthetic activity at different plant densities in Carex acutiformis

Shoots of the monocotyledonous perennial Carex acutiformis were grown in open (28 shoots m⁻²) and dense stands (280 shoots m⁻²). For fully grown stands the distribution of relative PPFD and leaf nitrogen per unit leaf area over canopy depth was determined. Light response of photosynthesis was measured on leaf segments sampled at various heights in the stands. Relations between parameters of these curves and leaf nitrogen were investigated. Simulations showed that in the open stand daily canopy photosynthesis was not affected by nitrogen redistribution in the canopy. For the dense stand however, a uniform nitrogen distribution would lead to only 73% of the maximum net carbon gain by the stand under optimal nitrogen distribution. The actual canopy photosynthesis was only 7% less than this theoretical maximum; the actual nitrogen distribution of the dense stand clearly tended to the optimal distribution. The vertical pattern of the nitrogen distribution was to a large extent determined by the minimum leaf nitrogen content. The relatively high minimum leaf nitrogen content found for Carex leaves may perhaps be necessary to maintain the physiological function of the basal parts of the leaves.     

Plant competition for light analyzed with a multispecies canopy model

Summary A multispecies canopy photosynthesis simulation model was used to examine the importance of canopy structure in influencing light interception and carbon gain in mixed and pure stands of wheat (Triticum aestivum L.) and wild oat (Avena fatua L.), a common weedy competitor of wheat. In the mixtures, the fraction of the simulated canopy photosynthesis contributed by wheat was found to decline during the growing season and this decline was closely related to reductions in the amount of leaf area in upper canopy layers. For both species in mixture and in monoculture, simulated photosynthesis was greatest in the middle or upper-middle canopy layers and sensitivity analyses revealed that canopy photosynthesis was most sensitive to changes in leaf area and leaf inclination in these layers. Changes in LAI and leaf inclination affected canopy carbon gain differently for mixtures and monocultures, but the responses were not the same for the two species. Results from simulations where the structural characteristics of the two species were substituted indicated that species differences in leaf inclination, sheath area and the fraction of leaf area alive were of minor consequence compared with the differences in total leaf area in influencing relative canopy carbon gain in mixtures. Competition for light in these species mixtures appears to be influenced most by differences in the positioning of leaf area in upper canopy layers which determines, to a great extent, the amount of light intercepted.     

Carbon balance in a monospecific stand of an annual herb <Emphasis Type="Italic">Chenopodium album</Emphasis> at an elevated CO<Subscript>2</Subscript> concentration

Elevated CO₂ enhances carbon uptake of a plant stand, but the magnitude of the increase varies among growth stages. We studied the relative contribution of structural and physiological factors to the CO₂ effect on the carbon balance during stand development. Stands of an annual herb Chenopodium album were established in open-top chambers at ambient and elevated CO₂ concentrations (370 and 700 μmol mol⁻¹). Plant biomass growth, canopy structural traits (leaf area, leaf nitrogen distribution, and light gradient in the canopy), and physiological characteristics (leaf photosynthesis and respiration of organs) were studied through the growing season. CO₂ exchange of the stand was estimated with a canopy photosynthesis model. Rates of light-saturated photosynthesis and dark respiration of leaves as related with nitrogen content per unit leaf area and time-dependent reduction in specific respiration rates of stems and roots were incorporated into the model. Daily canopy carbon balance, calculated as an integration of leaf photosynthesis minus stem and root respiration, well explained biomass growth determined by harvests (r ² = 0.98). The increase of canopy photosynthesis with elevated CO₂ was 80% at an early stage and decreased to 55% at flowering. Sensitivity analyses suggested that an alteration in leaf photosynthetic traits enhanced canopy photosynthesis by 40–60% throughout the experiment period, whereas altered canopy structure contributed to the increase at the early stage only. Thus, both physiological and structural factors are involved in the increase of carbon balance and growth rate of C. album stands at elevated CO₂. However, their contributions were not constant, but changed with stand development.     

Estimating photosynthetic rate and annual carbon gain in conifers from specific leaf weight and leaf biomass

Summary Canopy photosynthesis is difficult to measure directly or to predict with complex models demanding knowledge of seasonal variation in environmental and physiological properties of the canopy. Trees in particular offer a challenge with their large, aerodynamically rough and seasonally-changing canopy properties. In this paper we assess the possibility of using specific leaf weight to predict seasonal and annual net photosynthetic rate in deciduous (Larix sp.) and evergreen (Picea abies) conifers.Annual photosynthetic rate and specific leaf weight of different positions of the crown in both species were highly correlated (r ²=0.930). Annual carbon uptake by different segments in a mature P. abies crown was closely related to leaf biomass. The relationship was improved by adjusting the leaf biomass of each segment in regard to its specific leaf weight relative to the maximum found in the canopy. The adjustment accounted for associated differences in photosynthetic activity. This combined structural index (leaf biomassxrelative specific leaf weight) could, when calibrated, predict the total annual carbon uptake by different parts of the crown. If direct measurements of photosynthesis are not available, the combined structural index may still serve as a comparative estimator of annual carbon uptake.     

Fluxes of carbon dioxide and water vapor above paddy fields

Atmospheric fluxes of carbon dioxide and water vapor were measured by the eddy correlation technique over a paddy field in 1989. The carbon dioxide was transported downward during daylight hours due to photosynthesis of the paddy crop. The downward flux of carbon dioxide increased with increasing net radiation. Maximum values of downward flux varied with the growing stage of the paddy crop: ca. 0.3 mg m^–2 s^–1 at early vegetative growth stage and ca. 1.3 mg m^–2 s^–1 at ear formation stage. The daytime totals of downward flux of carbon dioxide also showed seasonal variation reflecting the photosynthetic activity of the paddy crop: ca. 6 g m^–2 at early vegetative growth stage in June and 40 g m^–2 at ear formation stage in September. The seasonal variation of daily totals of carbon dioxide flux shows that carbon dioxide of about 28 t ha^–1 is fixed by the paddy crop from transplanting to harvesting. Taking into account the water use efficiency, the paddy crop requires water in amounts at least 100 times that of carbon dioxide fixed by photosynthesis. It is noted that the correlation coefficients between carbon dioxide, water vapor and vertical wind velocity have constant values under near neutral and free convective regimes.     

Rice responses to drought under carbon dioxide enrichment. 2. Photosynthesis and evapotranspiration

Future climate change is projected to include a strong likelihood of continued increases in atmospheric carbon dioxide concentration ([CO₂]) and possible shifts in precipitation patterns. Due mainly to uncertainties in the timing and amounts of monsoonal rainfall, drought is common in rainfed rice production systems. The objectives of this study were to quantify the effects and possible interactions of [CO₂] and drought stress on rice (Oryza sativa, L.) photosynthesis, evapotranspiration and water-use efficiency. Rice (cv. IR-72) was grown to maturity in eight naturally sunlit, plant growth chambers in atmospheric carbon dioxide concentrations [CO₂] of 350 and 700 μmol CO₂ mol^–1 air. In both [CO₂], water management treatments included continuously flooded controls, flood water removed and drought stress imposed at panicle initiation, anthesis, and both panicle initiation and anthesis. Potential acclimation of rice photosynthesis to long-term [CO₂] growth treatments of 350 and 700 μmol mol^–1 was tested by comparing canopy photosynthesis rates across short-term [CO₂] ranging from 160 to 1000 μmol mol^–1. These tests showed essentially no acclimation response with photosynthetic rate being a function of current short-term [CO₂] rather than long-term [CO₂] growth treatment. In both long-term [CO₂] treatments, photosynthetic rate saturated with respect to [CO₂] near 510 μmol mol^–1. Carbon dioxide enrichment significantly increased both canopy net photosynthetic rate (21–27%) and water-use efficiency while reducing evapotranspiration by about 10%. This water saving under [CO₂] enrichment allowed photosynthesis to continue for about one to two days longer during drought in the enriched compared with the ambient [CO₂] control treatments.     

THE CHLOROPHYLL-CARBON DIOXIDE RATIO DURING PHOTOSYNTHESIS

Using a rapid spectrographic method of carbon dioxide measurement previously described by McAlister (1937) further studies on the time course of photosynthesis in the higher plant, wheat, variety Marquis, are herein reported. Of major importance in this work is the discovery of a pick-up of carbon dioxide in darkness immediately following a high rate of photosynthesis (see Figs. 3 and 4). This pick-up is believed to be due to the action of a carbon dioxide-combining intermediate; i.e., the "acceptor molecule" for carbon dioxide in photosynthesis. The conditions under which this phenomenon has so far been observed indicate that the intermediate is formed in relatively large quantities during the actual process of photosynthesis and not before. That the intermediate is chlorophyllous in nature is suggested by a simple stoichiometry of the order of unity that is found to exist between the number of carbon dioxide molecules taken up and the total number of chlorophyll molecules present in the plant. This is in opposition to the idea of a large photosynthetic unit of some 2000 chlorophyll molecules operating together in the reduction of 1 carbon dioxide molecule. Further studies of the induction phase under various conditions of previous dark rest and of carbon dioxide and light limitation are herein described. Employing the simple hypothesis that the number of carbon dioxide molecules not reduced during the induction period (induction loss) gives a measure of the number of elementary photosynthetic cycles unoperative or compensated for during induction together with the experimental fact that this induction loss is of the order of the total number of chlorophyll molecules present, these latter studies also indicate, in a less direct manner, that chlorophyll participates in photosynthesis as an individual molecule and not as part of a very large multimolecular chlorophyll unit. The fast dark reaction lasting about 1 minute (Fig. 7) required to reproduce both (a) the phenomena of induction in carbon dioxide assimilation and (b) the recovery of fluorescence of chlorophyll in leaves in darkness as observed by Franck and Wood (1936), demonstrates a close relationship between the fluorescence of chlorophyll and induction in photosynthesis. The rate of respiration (carbon dioxide production) of the higher plant, wheat, was measured under intense illumination and in the absence of carbon dioxide (to suppress assimilation). This value was found to be identical with the dark respirational rate measured before and after the light period, indicating very positively the absence of any direct effect of light on respiration.     

THE INFLUENCE OF WATER STRESS ON STEM AND LEAF PHOTOSYNTHESIS IN GLYCINE MAX AND SPARTEUM JUNCEUM (LEGUMINOSAE)

Stem and leaf photosynthesis were measured in Glycine max var. essex (soybean) and Sparteum junceum (Spanish broom). The significance of stem photosynthesis to whole plant growth was evaluated by blocking stem photosynthesis with black straw sections. The growth of S. junceum was reduced by 18% when black straws were used in comparison to clear straws. The whole plant growth of G. max was not influenced by blocking the stem carbon contribution. Mean midday leaf photosynthesis was 12 μmol CO₂ m^–2 s^–1 and 17 μmol CO₂ m^–2 s^–1 for G. max and 5. junceum, respectively. Mean midday stem photosynthesis of S. junceum was 6.5 μmol CO₂ m^–2 s^–1; however, positive net photosynthesis did not occur in G. max stems. Water stress caused a proportionally greater decrease in leaf photosynthesis compared to that of stems during diurnal cycles of photosynthesis in S. junceum. As a result the contribution to canopy carbon gain by stem photosynthesis increased from 38% to 48% of the total plant carbon gain under reduced water availability.     

A model of canopy photosynthesis incorporating protein distribution through the canopy and its acclimation to light, temperature and CO2

Background and Aims

The distribution of photosynthetic enzymes, or nitrogen, through the canopy affects canopy photosynthesis, as well as plant quality and nitrogen demand. Most canopy photosynthesis models assume an exponential distribution of nitrogen, or protein, through the canopy, although this is rarely consistent with experimental observation. Previous optimization schemes to derive the nitrogen distribution through the canopy generally focus on the distribution of a fixed amount of total nitrogen, which fails to account for the variation in both the actual quantity of nitrogen in response to environmental conditions and the interaction of photosynthesis and respiration at similar levels of complexity.

Model

A model of canopy photosynthesis is presented for C₃ and C₄ canopies that considers a balanced approach between photosynthesis and respiration as well as plant carbon partitioning. Protein distribution is related to irradiance in the canopy by a flexible equation for which the exponential distribution is a special case. The model is designed to be simple to parameterize for crop, pasture and ecosystem studies. The amount and distribution of protein that maximizes canopy net photosynthesis is calculated.

Key Results

The optimum protein distribution is not exponential, but is quite linear near the top of the canopy, which is consistent with experimental observations. The overall concentration within the canopy is dependent on environmental conditions, including the distribution of direct and diffuse components of irradiance.

Conclusions

The widely used exponential distribution of nitrogen or protein through the canopy is generally inappropriate. The model derives the optimum distribution with characteristics that are consistent with observation, so overcoming limitations of using the exponential distribution. Although canopies may not always operate at an optimum, optimization analysis provides valuable insight into plant acclimation to environmental conditions. Protein distribution has implications for the prediction of carbon assimilation, plant quality and nitrogen demand.     

Biogenic fluxes of carbon dioxide in the old-growth spruce forest in the middle taiga: Results of eddy covariance measurements

Fluxes of carbon dioxide in the old-growth bilberry spruce forest in the European Taiga are measured by the eddy covariance technique. A carbon dioxide sink to the ecosystem was observed from April until September; the maximum net-exchange rate of carbon dioxide was recorded in July. During the cold period of the year from October to March, the biogenic flux of CO₂ was directed from the forest canopy to the atmosphere. According to measurements at u* > 0.2, the total annual NEE was 219 g C m^–2; the annual values of the ecosystem respiration R _eco and the gross photosynthesis P _gross were 483 and 966 g C m^–2, respectively. The conclusion is that the old-growth bilberry spruce forest in the middle taiga subzone was the sink of carbon from the atmosphere during the year of observation.     

Vegetation clumping modulates global photosynthesis through adjusting canopy light environment

The spatial dispersion of photoelements within a vegetation canopy, quantified by the clumping index (CI), directly regulates the within-canopy light environment and photosynthesis rate, but is not commonly implemented in terrestrial biosphere models to estimate the ecosystem carbon cycle. A few global CI products have been developed recently with remote sensing measurements, making it possible to examine the global impacts of CI. This study deployed CI in the radiative transfer scheme of the Community Land Model version 5 (CLM5) and used the revised CLM5 to quantitatively evaluate the extent to which CI can affect canopy absorbed radiation and gross primary production (GPP), and for the first time, considering the uncertainty and seasonal variation of CI with multiple remote sensing products. Compared to the results without considering the CI impact, the revised CLM5 estimated that sunlit canopy absorbed up to 9%–15% and 23%–34% less direct and diffuse radiation, respectively, while shaded canopy absorbed 3%–18% more diffuse radiation across different biome types. The CI impacts on canopy light conditions included changes in canopy light absorption, and sunlit–shaded leaf area fraction related to nitrogen distribution and thus the maximum rate of Rubisco carboxylase activity (V_cmax), which together decreased photosynthesis in sunlit canopy by 5.9–7.2 PgC year⁻¹ while enhanced photosynthesis by 6.9–8.2 PgC year⁻¹ in shaded canopy. With higher light use efficiency of shaded leaves, shaded canopy increased photosynthesis compensated and exceeded the lost photosynthesis in sunlit canopy, resulting in 1.0 ± 0.12 PgC year⁻¹ net increase in GPP. The uncertainty of GPP due to the different input CI datasets was much larger than that caused by CI seasonal variations, and was up to 50% of the magnitude of GPP interannual variations in the tropical regions. This study highlights the necessity of considering the impacts of CI and its uncertainty in terrestrial biosphere models.     

Interaction of ozone pollution and light effects on photosynthesis in a forest canopy experiment

Ozone pollution may reduce net carbon gain in forests, yet data from mature trees are rare and the effects of irradiance on the response of photosynthesis to ozone remain untested. We used an open-air system to expose 10 branches within the upper canopy of an 18-m-tall stand of sugar maple (Acer saccharum Marsh.) to twice-ambient concentrations of ozone (95nmol mol^?1, 0900 to 1700, 1 h mean) relative to 10 paired, untreated controls (45nmol mol^?1) over 3 months. The branch pairs were selected along a gradient from relatively high irradiance (PPFD 14.5 mol m^?2 d^?1) to deep shade (0.7mol m^?2 d^?1). Ozone reduced light-saturated rates of net photosynthesis (A_sat) and increased dark respiration by as much as 56 and 40%, respectively. Compared to sun leaves, shade leaves exhibited greater proportional reductions in A_sat and had lower chlorophyll concentrations, quantum efficiencies, and leaf absorptances when treated with ozone relative to controls. With increasing ozone dose over time, A_sat became uncoupled from stomatal conductance as ratios of internal to external concentrations of carbon dioxide increased, reducing water-use efficiency. Ozone reduced net photosynthesis and impaired stomatal function, with these effects depending on the irradiance environment of the canopy leaves. Increased ozone sensitivity of shade leaves compared to sun leaves has consequences for net carbon gain in canopies.     

Negative relationship between photosynthesis and late-stage canopy development and senescence over Tibetan Plateau

Canopy greening, which is associated with significant canopy structure changes, is the most notable signal of ecosystem changes in response to anthropogenic climate change. However, our knowledge of the changing pattern of canopy development and senescence, and its endogenous and climatic drivers is still limited. Here, we used the Normalized Difference Vegetation Index (NDVI) to quantify the changes in the speed of canopy development and senescence over the Tibetan Plateau (TP) during 2000–2018, and used a solar-induced chlorophyll fluorescence dataset as a proxy for photosynthesis, in combination with climate datasets to decipher the endogenous and climatic drivers of the interannual variation in canopy changes. We found that the canopy development during the early green-up stage (April–May) is accelerating at a rate of 0.45–0.8 × 10⁻³ month⁻¹ year⁻¹. However, this accelerating canopy development was largely offset by a decelerating canopy development during June and July (−0.61 to −0.51 × 10⁻³ month⁻¹ year⁻¹), leading to the peak NDVI over the TP increasing at a rate of only one fifth of that in northern temperate regions, and less than one tenth of that in the Arctic and boreal regions. During the green-down period, we observed a significant accelerating canopy senescence during October. Photosynthesis was found to be the dominant driver for canopy changes over the TP. Increasing photosynthesis stimulates canopy development during the early green-up stage. However, slower canopy development and accelerated senescence was found with larger photosynthesis in late growth stages. This negative relationship between photosynthesis and canopy development is probably linked to the source–sink balance of plants and shifts in the allocation regime. These results suggest a sink limitation for plant growth over the TP. The impact of canopy greening on the carbon cycle may be more complicated than the source-oriented paradigm used in current ecosystem models.     

What is the most prominent factor limiting photosynthesis in different layers of a greenhouse cucumber canopy?

Background and Aims

Maximizing photosynthesis at the canopy level is important for enhancing crop yield, and this requires insights into the limiting factors of photosynthesis. Using greenhouse cucumber (Cucumis sativus) as an example, this study provides a novel approach to quantify different components of photosynthetic limitations at the leaf level and to upscale these limitations to different canopy layers and the whole plant.

Methods

A static virtual three-dimensional canopy structure was constructed using digitized plant data in GroIMP. Light interception of the leaves was simulated by a ray-tracer and used to compute leaf photosynthesis. Different components of photosynthetic limitations, namely stomatal (S_L), mesophyll (M_L), biochemical (B_L) and light (L_L) limitations, were calculated by a quantitative limitation analysis of photosynthesis under different light regimes.

Key Results

In the virtual cucumber canopy, B_L and L_L were the most prominent factors limiting whole-plant photosynthesis. Diffusional limitations (S_L + M_L) contributed <15 % to total limitation. Photosynthesis in the lower canopy was more limited by the biochemical capacity, and the upper canopy was more sensitive to light than other canopy parts. Although leaves in the upper canopy received more light, their photosynthesis was more light restricted than in the leaves of the lower canopy, especially when the light condition above the canopy was poor. An increase in whole-plant photosynthesis under diffuse light did not result from an improvement of light use efficiency but from an increase in light interception. Diffuse light increased the photosynthesis of leaves that were directly shaded by other leaves in the canopy by up to 55 %.

Conclusions

Based on the results, maintaining biochemical capacity of the middle–lower canopy and increasing the leaf area of the upper canopy would be promising strategies to improve canopy photosynthesis in a high-wire cucumber cropping system. Further analyses using the approach described in this study can be expected to provide insights into the influences of horticultural practices on canopy photosynthesis and the design of optimal crop canopies.     

Modelling canopy CO2 fluxes: are ‘big‐leaf’ simplifications justified?

• 1 The ‘big‐leaf’ approach to calculating the carbon balance of plant canopies is evaluated for inclusion in the ETEMA model framework. This approach assumes that canopy carbon fluxes have the same relative responses to the environment as any single leaf, and that the scaling from leaf to canopy is therefore linear.
• 2 A series of model simulations was performed with two models of leaf photosynthesis, three distributions of canopy nitrogen, and two levels of canopy radiation detail. Leaf‐ and canopy‐level responses to light and nitrogen, both as instantaneous rates and daily integrals, are presented.
• 3 Observed leaf nitrogen contents of unshaded leaves are over 40% lower than the big‐leaf approach requires. Scaling from these leaves to the canopy using the big‐leaf approach may underestimate canopy photosynthesis by ~20%. A leaf photosynthesis model that treats within‐leaf light extinction displays characteristics that contradict the big‐leaf theory. Observed distributions of canopy nitrogen are closer to those required to optimize this model than the homogeneous model used in the big‐leaf approach.
• 4 It is theoretically consistent to use the big‐leaf approach with the homogeneous photosynthesis model to estimate canopy carbon fluxes if canopy nitrogen and leaf area are known and if the distribution of nitrogen is assumed optimal. However, real nitrogen profiles are not optimal for this photosynthesis model, and caution is necessary in using the big‐leaf approach to scale satellite estimates of leaf physiology to canopies. Accurate prediction of canopy carbon fluxes requires canopy nitrogen, leaf area, declining nitrogen with canopy depth, the heterogeneous model of leaf photosynthesis and the separation of sunlit and shaded leaves. The exact nitrogen profile is not critical, but realistic distributions can be predicted using a simple model of canopy nitrogen allocation.