SEARCH

SEARCH BY CITATION

Keywords:

  • Coniferous canopy structure;
  • LAI;
  • light interception;
  • photosynthetic production

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model and calculation method
  5. Simulation conditions
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

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.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model and calculation method
  5. Simulation conditions
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

The leaf area index (LAI) is the main determinant of the amount of photosynthetically active radiation (PAR) that is intercepted by the canopy. However, the fraction of intercepted PAR reaches values close to one at moderate values of LAI, after which an investment in additional leaf area no longer appreciably increases energy capture. Consequently, it has been suggested that the advantage of maintaining a large leaf area must be associated with an efficient utilization (rather than a maximization) of the absorbed PAR (Sprugel 1989; Leverenz & Hinckley 1990; Stenberg 1996).

At a fixed amount of absorbed PAR by the canopy, the rate of photosynthesis would be highest if all leaves operated at the ‘linear’ part of the photosynthetic radiation response curve, e.g. at irradiances below saturation but above the light compensation point. This ideal condition is approached by homogenization of light gradients within leaves (morphological acclimation) and by acclimation of the photosynthetic apparatus to the local light environment (Terashima & Hikosaka 1995; Sprugel, Brooks & Hinckley 1996). In addition, the irradiance on leaves in the canopy is greatly influenced by the leaf orientation, and by the size and spatial arrangement of leaves.

The irradiance on the surface of a leaf in full sunlight is modified by the angle between leaf and sun. A general but somewhat heuristic conclusion from this fact is that, displaying sun leaves at a steep angle to the horizontal is an effective means to reduce the irradiance of direct sunlight on the leaves and, thereby, to minimize saturation losses. The conclusion is obviously true assuming near-zenith sun position. However, saturating irradiances can occur at any sun elevation if the leaf surface is at right angles with the solar beam. Thus, a steep leaf angle would not eliminate saturation throughout the day (when the sun is low) but would reduce saturation losses more the larger is the fraction of direct PAR received from near-zenith sun angles. In canopies of small LAI, on the other hand, a steep leaf angle could result in a significant loss in intercepted PAR by the canopy. These considerations elucidate why a near-vertical leaf inclination would be favourable for canopy photosynthesis at southern latitudes and high LAIs, whereas at northern latitudes and in canopies of small LAI this would not be the case (e.g. Duncan et al. 1967; Oker-Blom & Kellomäki 1982; Wang & Jarvis 1990; Wang, McMurtrie & Landsberg 1992).

Less well studied are the effects of leaf size and non-random leaf arrangement on canopy photosynthesis. The arrangement of needles around shoots results in a highly clumped (grouped) distribution of leaf area in coniferous stands (Norman & Jarvis 1975; Whitehead, Grace & Godfrey 1990). The effect of a grouped leaf area distribution on canopy photosynthesis is not straightforward. Because grouping decreases total canopy PAR interception at fixed LAI, it would potentially decrease canopy photosynthesis. On the other hand, grouping results in more penetration of radiation to the lower canopy and thereby improves the photosynthetic light capture of leaves deeper down in the canopy (Stenberg 1996).

A leaf (or part of the leaf) receiving less than full sunlight, owing to a partial shading of the solar disc by other leaves, is said to lie in a penumbra. The occurrence of penumbra does not affect the total light interception by a canopy of fixed LAI, but causes a redistribution of the direct sunlight hitting the leaves. Penumbras act to increase the rate of canopy photosynthesis per unit of LAI, because they level off peak values of direct solar irradiance on the leaf area, and reduce the fraction of fully shaded leaf area. The frequency of penumbra in the canopy is inversely related to the ratio of characteristic leaf width to canopy depth (Denholm 1981). Consequently, the effect of penumbra is likely to be important especially in coniferous stands, owing to the small size of conifer needles combined with deep crowns (Stenberg 1995). The significance of penumbra has long been recognized (Horn 1971; Miller & Norman 1971; Anderson & Miller 1974). However, because of the complexity involved in estimating penumbral irradiances (e.g. Denholm 1981), models of canopy photosynthesis generally do not account for this phenomenon (Wang et al. 1992).

In this paper, a model is presented by which the effects of grouping and penumbra on canopy photosynthesis can be quantified. The model is applied on a case study. First, the effect of grouping is evaluated by comparing rates of photosynthesis in a canopy with randomly (Poisson) distributed leaves and shoots, respectively. Second, the effect of penumbra is incorporated using the method by Stenberg (1995), where shading from a short distance (within a shoot) is treated as non-penumbral and that from a longer distance (between shoots) is treated as diffuse shading.

Model and calculation method

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model and calculation method
  5. Simulation conditions
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

STATISTICAL MODEL OF RADIATION PENETRATION

The Poisson model was used to describe the spatial distribution of foliage in the canopy. The penetration of direct PAR to the level L in the canopy can be expressed in terms of the probability of a gap in the sun's direction ωs=(γs, φs) (where γ is elevation angle and φ is azimuth):

inline image

where L denotes the downward cumulative leaf area index, H is the ratio of projected to total surface area of the leaves (needles) and β (≤1) is a grouping factor.

Equation 1 represents a generalized version of the Poisson model (e.g. Nilson 1971), originally formulated without the grouping factor (β). In that case (β=1), the model represents a canopy where individual leaves are Poisson distributed. Notice that the leaf area index (L) here is defined on a total surface area basis instead of the one-sided area basis, commonly used for planar (flat) leaves. This means that the extinction coefficient (H) must also be expressed on a total surface area basis. Accordingly, the parameter H used in equation 1 is defined as the sum of the projected area of individual leaves (needles), when projected on a surface perpendicular to the sun, divided by their total surface area. Lang (1991) refers to this ratio as ‘mean projection of unit surface area’. It differs from the traditionally used extinction coefficient, the so-called ‘mean projection of unit flat area’ (G) (Nilson 1971), in that one-sided leaf area is used as denominator in G. For flat leaves, the total surface area is twice the one-sided leaf area and we have G=2H.

Clumping of needles in shoots was considered by assuming shoots (instead of individual leaves) to be Poisson distributed. The parameter β (<1) in equation 1 then quantifies the reduction in shoot silhouette area caused by mutual shading of needles. More specifically, β is interpreted as the mean ratio of shoot silhouette area to the projection area of all needles, assumed to have their natural orientation, but spread out so that they do not shade each other. The quantity βH is equal to the mean ratio of shoot silhouette area to total needle area (STAR) (Stenberg 1996).

The gap probability (po) represents the penetrated fraction of PAR to a given level (L) in the canopy. Consequently, the mean irradiance of direct solar radiation on the horizontal plane at L is given by:

inline image

where Ish denotes the irradiance of the direct solar beam on a horizontal plane above the canopy. The (momentary) interception of direct radiation by the canopy above L is Qs(L)=IshIsh (L).

Gap probabilies in different directions of the sky can similarly be used to describe the attenuation of diffuse sky radiation. Let Idh be the above-canopy irradiance of diffuse PAR on the horizontal plane:

inline image

where id(ω) is the sky radiance (PAR) in the direction ω of the upper hemisphere Ω, and dω=cosγ dγ dφ. The mean diffuse irradiance on the horizontal plane at the level L is then:

inline image

and the interception of diffuse PAR by the canopy above L is Qd(L)=IdhIdh(L). The total momentary interception of PAR by the canopy above level L is obtained as the sum of intercepted direct and diffuse PAR, i.e. as Q(L)=Qs(L)+Qd(L).

ESTIMATING THE MEAN RATE OF PHOTOSYNTHESIS

The momentary mean rate of photosynthesis at the level L in the canopy can formally be expressed as:

inline image

where Pleaf denotes the photosynthetic response curve of a leaf surface element and fL is the density function of irradiance on the leaf surface area at depth L (in the canopy layer between L and L+ΔL).

The rate of canopy photosynthesis (per unit of ground area) (Pcanopy) is obtained as:

inline image

where LAI is the canopy leaf area index.

It is straightforward to derive mean irradiance on the leaf area based on a model of radiation penetration. The irradiance on a leaf surface element can be expressed as I=Isl+Idl, where Isl denotes the direct solar beam component and Idl the diffuse component. The mean direct and diffuse irradiances on leaves situated at the depth L in the canopy are obtained by differentiating Qs(L) and Qd(L) with respect to L, yielding (see equations 2 and 4):

¯Isl=Qs(L)=Isβ(ωs)H(ωs)exp[–β(ωs)H(ωs)L/sinγs] eqn 7

where Is=Ish/sinγs is the irradiance of the direct solar beam on a plane normal to the sun and

inline image

However, because the photosynthetic radiation response (Pleaf in equation 5) is known to be a concave function (a function of diminishing returns, ΔP/ΔI), the rate of photosynthesis computed using the mean irradiance yields an overestimate. For diffuse radiation, use of the mean irradiance (¯Idl) is usually considered to be acceptable because the diffuse component (Idl), being formed as a sum of many nearly independent variables (radiation incident from different directions of the sky), has a small variance (Gutschick 1984; Oker-Blom 1986). The direct component of radiation, in contrast, reaches high values of irradiance and has a large variance. Calculation of photosynthesis therefore involves methods for estimating the statistical behaviour of the direct component (Isl).

METHODS TO ESTIMATE THE DIRECT IRRADIANCE ON THE LEAVES

Method 1. Division into sunlit and shaded leaf area

In the most commonly used approach, the leaf area is divided into a shaded and sunlit fraction, one receiving only diffuse radiation and the other receiving both direct and diffuse radiation (Norman 1980). The diffuse irradiance is assumed to be constant (=¯Idl) on all leaves at a given level L. The problem thus is reduced to determining the sunlit fraction (ps) of leaf area at given level L and the distribution of direct irradiance on the sunlit area.

When penumbral effects are ignored, the direct irradiance at a sunlit point on the leaf surface is Isl=Iscos(ωs,ωn), where ωn is the direction of the leaf normal (at that point) and cos(ωs,ωn) denotes the cosine of the angle between the leaf normal and the sun. The mean (expected) value of cos(ωs,ωn) is equal to 2H(ωs) (note that 2H=G for flat leaves). The mean direct irradiance on the leaves situated at the depth L, consequently, is ¯Isl=2psIsH(ωs) and substitution into equation 7 gives:

inline image

Notice that in a canopy with Poisson-distributed individual leaves (β=1), equation 9 yields ps=(1/2)po, i.e. the sunlit fraction of leaf area equals one half of the mean canopy gap fraction. (One half because the leaf area is expressed as total surface area.) In the case of grouping (β<1), the sunlit fraction of leaf area (ps) is smaller than (1/2)po, because needles on a shoot shade each other.

Variation in the direct irradiance on the sunlit leaf area results from variation in the factor cos(ωs,ωn), which is determined by the leaf angle distribution. In the simulations, the leaves (needles) were assumed to be spherically orientated, implying that H=0·25 (G=0·5) and the direct irradiance on the sunlit leaf area, Isl=Iscos(ωs,ωn), is uniformly distributed over [0, Is] (e.g. Gutschick 1991). The density function (fL) in that case can be expressed as:

inline image

fL(I)=δ[I–¯Idl] with probability 1–ps

where δ(x)=1 when x=0, and δ(x)=0 otherwise. For the spherical leaf orientation, the sunlit fraction of leaf area at L is ps=0·5βexp(–0·25βL/sinγs) (equation 9 with H=0·25).

Method 2. Incorporating penumbra

The effect of penumbra was incorporated by separating shading from a short distance (within-shoot shading) and that from a longer distance (between-shoot shading), as suggested by Stenberg (1995). We picture the shoots as envelopes (e.g. shoot cylinders) and define the shoot transmission coefficient c (<1) and the fraction of gap area in the projected shoot envelope area. It was assumed that penumbras are not created within a shoot, i.e. a needle on the same shoot would either obscure the entire solar disc or no part of it. In contrast, shading from another shoot (a shoot envelope intersecting the direction of view) was assumed to reduce the fraction of visible sun, and the consequent direct solar irradiance by the factor c.

Thus, the sunlit fraction of leaf area of a shoot not shaded by any other shoot, is equal to β/2, where β is the reduction caused by shading from other needles on the same shoot and the factor 1/2 corrresponds to the fraction of leaf area not facing the sun. (Again, note that it is because leaf area is defined on a total surface area basis.) The direct irradiance on a leaf is Isl=Iccos(ωs,ωn)ck with probability fkβ/2, where fk denotes the probability of k (= 0, 1, 2, ...) shading shoots and Isl=0 with probability 1–β/2. The diffuse irradiance (Idl) was modelled as in Method 1, i.e. it was represented by its mean value (equation 8). If leaves (needles) are spherically orientated, the direct irradiance Isl=Iscos(ωs,ωn)ck is uniformly distributed over [0, Isck], and the density function (fL) is obtained as:

inline image

fL(I)=δ[I–¯Idl] with probability 1–β/2.

When shoots are Poisson distributed, the probability(fk) that there are k=0, 1, 2, ... shoot envelopes in the way of the solar beam is given by:

inline image

where μ denotes the sine of the solar elevation angle (γ).

The conditional probability of a gap through k shoot envelopes is ck and the canopy gap fraction is obtained as:

inline image

inline image

Simulation conditions

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model and calculation method
  5. Simulation conditions
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

ABOVE-CANOPY RADIATION

Simulations were made assuming clear-sky conditions. The daily pattern of incoming (above canopy) irradiance Ih=Ish+Idh was modelled by Ish=Soτmsinγs and Idh=0·5(0·91SssinγsIsh) (Campbell 1981), where So=2700μmolm–2s–1 (≈600Wm–2) was used to represent the PAR-equivalent of the solar constant (Weiss & Norman 1985), m is the air mass (approximated as m=1/sinγs) and τm is the transmittance of the atmosphere to direct radiation. The value of τ=0·7 was used to represent clear-sky conditions (Gates 1980) and the angular distribution of diffuse sky radiation was assumed to be isotropic, implying that id(ω)=Idh/π in all directions of the sky.

The simulated pattern of incoming direct, diffuse and total irradiance as a function of the solar elevation angle is shown in Fig. 1. With increasing total irradiance, the proportion of diffuse radiation decreases and the proportion of direct radiation increases. When the sun is in zenith, the proportions are 13 and 87%, respectively.

image

Figure 1. . Simulated pattern of above canopy irradiance (PAR) as a function of the solar elevation angle assuming clear sky conditions.

Download figure to PowerPoint

PHOTOSYNTHETIC RADIATION RESPONSE

A Blackman curve with the initial slope of 0·05 (moles of CO2 per moles of photons) and saturating at 250μmolm–2s–1 was used as the photosynthetic response function of a leaf surface area element (Pleaf in equation 5). Thus, the rate of photosynthesis Pleaf(I) was assumed to increase linearly with the irradiance on the leaf surface (I=Isl+Idl) when I≤250μmolm–2s–1 and to remain at its maximum value of 0·05×250μmol (CO2)m–2s–1=12·5μmol (CO2)m–2s–1, whenever I>250μmolm–2s–1.

The Blackman curve represents an extreme in the family of response curves described by the non-rectangular hyperbola (Prioul & Chartier 1977), which involves a ‘convexity parameter’ ranging from 0 (the Michaelis–Menten curve) to 1 (the Blackman curve). Fitting the non-rectangular hyperbola to empirical measurements of shoot or leaf photosynthesis normally yields values of the convexity parameter <<1 (Leverenz 1988). However, when the variation in irradiance on the needle surface area is diminished, e.g. using a light-integrating sphere, values are close to one (Leverenz 1995). The parameter values used here correspond to those estimated for Scots pine (Pinus sylvestris L.) by Smolander et al. (1987).

LEAF AND SHOOT PARAMETERS

In all simulations, leaves (needles) were assumed to be spherically orientated, implying that H=0·25, irrespective of the solar elevation angle. The value of β=0·6 was used to quantify the grouping of needles on shoots. This value means that, on average, the projected area of a shoot (the shoot silhouette area) is reduced by 40% from mutual shading of needles, in agreement with measured values for Scots pine and Norway spruce (Picea abies L.) (Stenberg et al. 1994; Stenberg, Linder & Smolander 1995). The shoot transmission coefficient was given the tentative value c=0·4.

No variation in the structural parameters (H, β and c) was applied, although they may vary with solar angle and change with depth in the canopy. For example, in Picea abies and Abies amabilis, shoot structure has been shown to change in response to canopy shading so that within-shoot shading decreases (larger β), implying an improved efficiency of light capture by shade shoots (Stenberg et al. 1995; Sprugel et al. 1996). Because such morphological acclimation or changes in the photosynthetic response (biochemical acclimation) were not incorporated, the ‘actual’ decrease in rates of photosynthesis with depth in the canopy might be less sharp than in our simulations. However, this should not affect the relative differences in local rates of photosynthesis caused by grouping and penumbra and thus not the interpretation of the results.

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model and calculation method
  5. Simulation conditions
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

EFFECT OF GROUPING ON PAR INTERCEPTION

Grouping causes a decrease in the relative amount of intercepted PAR by the canopy, but the loss in intercepted PAR becomes minor at high values of LAI (Fig. 2). The interception of PAR is proportional to the length of the path of the solar beam through the canopy. Thus, the relative interception is maximal when the sun is still low (solar elevation≈20°), but when the share of direct radiation is already comparatively high (see Fig. 1).

image

Figure 2. . The effect of grouping on the relative interception of PAR by the canopy for LAI=4 and LAI=16. The value β=0·6 refers to the grouped stand (filled diamonds) and β=1 (crossed squares) refers to the non-grouped stand.

Download figure to PowerPoint

At a fixed LAI, the total area of sunlit leaves is smaller in a grouped canopy, but grouping redistributes the fraction of sunlit leaf area in different canopy layers (Fig. 3). The sunlit fraction ps=(1/2)βpo (equation 9) is proportional to the canopy gap fraction (po) multiplied by the shoot shading factor (β), which is <1 when grouping is considered and =1 otherwise (no grouping). Initially (at small L), ps is smaller in the grouped canopy because of the factor β<1. However, because po decreases more slowly when β<1 (see equation 1), ps eventually becomes larger in the grouped canopy. The higher is the sun, and the smaller is the value of β, the larger is the value of L at which this occurs.

image

Figure 3. . The effect of grouping on the fraction of sunlit leaf area (ps) at different levels (L) in the canopy. The solar elevation angle was here assumed to be 60°.

Download figure to PowerPoint

EFFECT OF GROUPING AND PENUMBRA ON LOCAL RATES OF PHOTOSYNTHESIS

Rates of photosynthesis, expressed as a function of the above canopy irradiance, were calculated for three different cases: (1) assuming no grouping and no penumbra (Method 1, with β=1); (2) considering grouping but not penumbra (Method 1, with β=0·6); (3) considering both grouping and penumbra (Method 2, with β=0·6). The calculations were made assuming clear-sky conditions and the increase in above canopy irradiance was accompanied by an increasing solar elevation angle (Fig. 1).

The effect of grouping (Method 1, with β=1 and β=0·6, respectively) on the mean rate of photosynthesis at different depths (L=2, 4, 8 and 16) in the canopy is shown in Fig. 4. In the upper canopy (L=2), grouping caused a decrease in the rate of photosynthesis, but deeper down (L≥4), the situation was reversed.

image

Figure 4. . Effect of grouping. Comparison of local rates of photosynthesis at different depths (L) in the canopy, calculated by Method 1 (no penumbra) with grouping (β=0·6; filled diamonds) and without grouping (β=1; crossed squares).

Download figure to PowerPoint

The effect of penumbra (Method 2, with β=0·6 and c=0·4) increases deeper down in the canopy, where penumbral irradiances occur more frequently (Fig. 5). At L=2, the increase in the rate of photosynthesis from penumbra was modest (≈15%), but in the lower canopy (L=16), rates were more than doubled by penumbra (Fig. 5).

image

Figure 5. . Effect of penumbra. Comparison of local rates of photosynthesis at different depths (L) in the grouped canopy (β=0·6), calculated without penumbra (filled diamonds) and with penumbra (open triangles).

Download figure to PowerPoint

The combined effect of grouping and penumbra became positive for L>2, and increased at higher values of L (Fig. 6). At L=16, the rate of photosynthesis was up to five times higher in the grouped canopy than rates calculated without grouping, and up to 10 times higher when the additional effect of penumbra was considered.

image

Figure 6. . The relative effect of grouping without penumbra (filled diamonds) and grouping with penumbra (open triangles) on the rate of photosynthesis at different depths (L) in the canopy. The value 1·0 corresponds to the rate calculated without grouping and penumbra (Method 1, with β=1).

Download figure to PowerPoint

IMPLICATIONS FOR TOTAL CANOPY PHOTOSYNTHESIS

In canopies of small LAI, grouping causes a significant loss in intercepted PAR (see Fig. 2) and a subsequent decrease in the rate of total canopy photosynthesis (Fig. 7, LAI=2). Grouping becomes favourable for photosynthesis deeper down in the canopy. However, because this happens along with the decrease in the rate of photosynthesis (Fig. 5), the increase in total canopy photosynthesis with LAI is slow. Grouping (without penumbra) continued to cause a decrease in the rate of canopy photosynthesis up to the value of LAI=16, where the rate was the same with or without grouping (Fig. 7). However, when the additional effect of penumbra was considered, the rate of total canopy photosynthesis was up to 20% higher for LAI=8 and up to 40% higher for LAI=16, as compared with rates obtained without grouping and penumbra (Fig. 7).

image

Figure 7. . The rate of total canopy photosynthesis for different values of LAI, calculated without grouping and penumbra (crossed squares), with grouping (filled diamonds), and with grouping and penumbra (open triangles).

Download figure to PowerPoint

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model and calculation method
  5. Simulation conditions
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

Grouping of foliage decreases the absorbed PAR by the canopy at fixed LAI but results in a more even distribution of absorbed PAR between different canopy layers. This implies that the rate of photosynthesis in the upper canopy (or in a canopy of small LAI) will be lower as a result from grouping, but in the lower canopy the situation is reversed (Fig. 4). In the model applied here, shoots were assumed to be uniformly (Poisson) distributed and only the grouping of needles on shoots was considered. In addition, scattering of PAR was not accounted for, i.e. it was implicitly assumed that needles are all-absorbing in the PAR-region. Grouping may occur at other levels as well, e.g. shoots may be grouped together within branches and tree crowns (e.g. Smith, Chen & Black 1993). This could be incorporated in the model by reducing the grouping factor (β) (equation 1). Similarly, the enhancement of diffuse PAR from scattering could to some extent be accounted for by multiplying β by a parameter (<1). A smaller value of β than applied here would cause a downward shift in the value of L, where the effect grouping becomes favourable for the local rate of photosynthesis (see Fig. 4).

For high values of LAI, grouping no longer decreases the rate of canopy photosynthesis, because the small loss in absorbed PAR (Fig. 2) is compensated for by a more even distribution of PAR (Fig. 7, LAI=16). However, grouping does not change the distribution of direct irradiance on the leaves, it only causes a vertical redistribution of the sunlit leaf area (Fig. 3). The variation in irradiance on the sunlit and shaded leaf area, which is the factor most reducing the mean rate of photosynthesis per unit of absorbed PAR, is not affected by grouping. Consequently, grouping cannot significantly improve the rate of total canopy photosynthesis per unit of LAI.

On the other hand, it may not be relevant to compare rates of canopy photosynthesis, with and without grouping, assuming the same LAI. Because grouping increases the rate of photosynthesis deeper down in the canopy (Figs 4 and 6), the level (L) at which gross photosynthesis balances respiration costs would be higher in a grouped stand. Consequently, the advantage of grouping is related to the fact that it enables a higher productive LAI to be maintained.

Leaf angles and leaf size are the only attributes of canopy structure, which affect the irradiance of direct PAR on the leaf area, and thus can contribute to reducing the energy loss caused by leaves operating above saturation. The leaf orientation is entered as an input parameter (G or H) in most canopy radiation models and its effect on canopy photosynthesis has been extensively studied. These models, however, are based on the assumption of parallel solar beam geometry, in which case leaf size is of no significance. The actual finite size of the sun implies that penumbras occur whenever leaves obscure only part of the solar disc. Because this happens more frequently the smaller the ratio of leaf width to shading distance, the penumbra effect is likely to be important in coniferous stands.

There are no analytical (exact) models, which could be applied to calculate penumbral irradiances in conifers. The model used here is a simplification, based on the results from an earlier study (Stenberg 1995), which showed that the penumbral effect in within-shoot shading is small, whereas shading from another shoot is better characterized as diffuse shading. In the model, the frequency of penumbra depends on the shoot transmission coefficient (c). The probability of a penumbra is smaller the less ‘transparent’ are the shoots, i.e. when needles are densely packed in the shoots (small c). A large variation in the shoot transmission is likely to exist between different conifer species and, in lack of empirical data, an intermediate value of c=0·4 was used in the simulations. It should be recognized also, that the probability of a penumbra becomes smaller the more shoots are grouped together. Thus, the effects of grouping and penumbra are to some extent mutually exclusive. Had grouping of shoots been incorporated in the simulations, the effect of penumbra would have been smaller. On the other hand, the penetration of PAR to the lower canopy would have increased.

Penumbra, in contrast to grouping, does not affect the vertical gradient in mean irradiance but diminishes the variation in direct sunlight on the leaf area. Consequently, whenever the incoming direct solar irradiance is above saturation, the mean rate of photosynthesis is higher with penumbra. This is true at all levels in the canopy; however, the effect of penumbra increases with depth in the canopy. The increase in the mean rate of photosynthesis caused by penumbral irradiances depends on the shape of the photosynthetic response function of a leaf surface area element. The sharply bending Blackman curve would tend to overestimate rather than underestimate this increase. However, use of the Blackman curve seemed justified based on empirical data (e.g. Leverenz 1995; Smolander et al. 1987).

Simulated rates of photosynthesis at L=16 were more than doubled by penumbra (Fig. 5) and up to 10 times higher as a result of the combined effect of grouping and penumbra (Fig. 6). The increasing effect of penumbra on the rate of total canopy photosynthesis was significant already at small values of LAI and for higher values of LAI (LAI=16), it was up to 40% (Fig. 7).

Results show the implications of two typically coniferous attributes, the small size of needles (creating penumbra) and the grouping of needles on shoots, on local and total rates of canopy photosynthesis during a clear day. The effect of penumbra is present only during clear skies, and becomes more important the higher is the proportion of direct PAR. On a seasonal basis, the combined effect of grouping and penumbra would depend on the proportions of sunny and overcast days and would vary with geographical latitude.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model and calculation method
  5. Simulation conditions
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

I thank Douglas Sprugel and two anonymous reviewers for their constructive comments on the manuscript.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model and calculation method
  5. Simulation conditions
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References
  • 1
    Anderson, M.C. & Miller, E.E. (1974) Forest cover as a solar camera: penumbral effects in plant canopies. Journal of Applied Ecology 12, 691697.
  • 2
    Campbell, G.S. (1981) Fundamentals of radiation and temperature relations. Physiological Plant Ecology. I. Responses to the Physical Environment (eds O. L. Lange, P. S. Nobel, C. B. Osmond & H. Ziegler), pp. 11–40. Springer-Verlag, Berlin-Heidelberg.
  • 3
    Denholm, J.V. (1981) The influence of penumbra on canopy photosynthesis. I. Theoretical considerations. Agricultural Meteorology 12, 145166.
  • 4
    Duncan, W.G., Loomis, R.S., Williams, W.A., Hanau, R. (1967) A model for simulating photosythesis in plant communities. Hilgardia 12, 181205.
  • 5
    Gates, D.M. (1980) Biophysical Ecology. Springer-Verlag, New York.
  • 6
    Gutschick, V.P. (1984) Statistical penetration of diffuse light into vegetative canopies: effect on photosynthetic rate and utility for canopy measurement. Agricultural Meteorology 12, 327341.
  • 7
    Gutschick, V.P. (1991) Joining leaf photosynthesis models and canopy photon-transport models. Photon-Vegetation Interactions: Applications in Optical Remote Sensing and Plant Ecology (eds R. B. Myneni & J. Ross), pp. 501–535. Springer-Verlag, Berlin-Heidelberg.
  • 8
    Horn, H.S. (1971) The Adaptive Geometry of Trees. Princeton University Press, Princeton, NJ.
  • 9
    Lang, A.R.G. (1991) Application of some of Cauchy's theorems to estimation of surface areas of leaves, needles and branches of plants, and light transmittance. Agricultural and Forest Meteorology 12, 191212.
  • 10
    Leverenz, J.W. (1988) The effects of illumination sequence, CO2 concentration, temperature and acclimation on the convexity of the photosynthetic light response curve. Physiologia Plantarum 12, 332341.
  • 11
    Leverenz, J.W. (1995) Shade shoot structure of conifers and the photosynthetic response to light at two CO2 partial pressures. Functional Ecology 12, 413421.
  • 12
    Leverenz, J.W. & Hinckley, T.M. (1990) Shoot structure, leaf area index and productivity of evergreen conifer stands. Tree Physiology 12, 135149.
  • 13
    Miller, E.E. & Norman, J.M. (1971) A sunfleck theory for plant canopies. I. Lengths of sunlit segments along a transect. Agronomy Journal 12, 735738.
  • 14
    Nilson, T. (1971) A theoretical analysis of the frequency of gaps in plant stands. Agricultural Meteorology 12, 2538.
  • 15
    Norman, J.M. (1980) Interfacing leaf and canopy light interception models. Predicting Photosynthesis for Ecosystem Models (eds J. D. Hesketh & J. W. Jones), vol. 2, pp. 49–67. CRC Press, Boca Raton, FL.
  • 16
    Norman, J.M. & Jarvis, P.G. (1975) Photosynthesis in Sitka Spruce (Picea stitchensis (Bong.) Carr.). V. Radiation penetration theory and a test case. Journal of Applied Ecology 12, 839877.
  • 17
    Oker-Blom, P. (1986) Photosynthetic radiation regime and canopy structure in modeled forest stands. Acta Forestalia Fennica 12, 144.
  • 18
    Oker-Blom, P. & Kellomäki, S. (1982) Effect of angular distribution of foliage on light absorption and photosynthesis in the plant canopy: theoretical computations. Agricultural Meteorology 12, 105116.
  • 19
    Prioul, J.L. & Chartier, P. (1977) Partitioning of transfer and carboxylation components of intracellular resistance to photosynthetic CO2 fixation: a critical analysis of the methods used. Annals of Botany 12, 789800.
  • 20
    Smith, N.J., Chen, J.M., Black, T.A. (1993) Effects of clumping on estimates of stand leaf area index using the LI-COR LAI-2000. Canadian Journal of Forest Research 12, 19401943.
  • 21
    Smolander, H., Oker-Blom, P., Ross, J., Kellomäki, S., Lahti, T. (1987) Photosynthesis of a Scots pine shoot: test of a shoot photosynthesis model in a direct radiation field. Agricultural and Forest Meteorology 12, 6780.
  • 22
    Sprugel, D.G. (1989) The relationship of evergreeness, crown architecture, and leaf size. The American Naturalist 12, 465479.
  • 23
    Sprugel, D.G., Brooks, J.R., Hinckley, T.M. (1996) Effect of light on shoot and needle morphology in Abies amabilis. Tree Physiology 12, 9198.
  • 24
    Stenberg, P. (1995) Penumbra in within-shoot and between-shoot shading in conifers and its significance for photosynthesis. Ecological Modelling 12, 215231.
  • 25
    Stenberg, P. (1996) Simulations of the effect of shoot structure and orientation on vertical gradients in intercepted light by conifers. Tree Physiology 12, 99108.
  • 26
    Stenberg, P., Linder, S., Smolander, H., Flower-Ellis, J. (1994) Performance of the LAI-2000 plant canopy analyzer in estimating leaf area index of some Scots pine stands. Tree Physiology 12, 981995.
  • 27
    Stenberg, P., Linder, S., Smolander, H. (1995) Variation in the ratio of shoot silhouette area to needle area in fertilized and non-fertilized trees of Norway spruce. Tree Physiology 12, 705712.
  • 28
    Terashima, I. & Hikosaka, K. (1995) Comparative ecophysiology of leaf and canopy photosynthesis. Plant, Cell and Environment 12, 11111128.
  • 29
    Wang, Y.P. & Jarvis, P.G. (1990) Description and validation of an array model—MAESTRO. Agricultural and Forest Meteorology 12, 257280.
  • 30
    Wang, Y.P., McMurtrie, R.E., Landsberg, J.J. (1992) Modelling canopy photosynthetic productivity. Crop Photosynthesis: Spatial and Temporal Determinants (eds J. R. Baker & H. Thomas), pp. 43–67. Elsevier Science Publishers BV, Amsterdam.
  • 31
    Weiss, A. & Norman, J.M. (1985) Partitioning solar radiation into direct and diffuse, visible and near-infrared components. Agricultural and Forest Meteorology 12, 205213.
  • 32
    Whitehead, D., Grace, J.C., Godfrey, M.J.S. (1990) Architectural distribution of foliage in individual Pinus radiata D. Don crowns and the effects of clumping on radiation interception. Tree Physiology 12, 135155.