Structural acclimation and radiation regime of silver fir (Abies alba Mill.) shoots along a light gradient


Correspondence: Alessandro Cescatti. Fax: + 39 0461 948190; e-mail:


Shoot architecture has been investigated using the ratio of mean shoot silhouette area to total needle area ( inline image) as a structural index of needle clumping in shoot space, and as the effective extinction coefficient of needle area. Although inline image can be used effectively for the prediction of canopy gap fraction, it does not provide information about the within-shoot radiative regime. For this purpose, the estimation of three architectural properties of the shoots is required: needle area density, angular distribution and spatial aggregation. To estimate these features, we developed a method based on the inversion of a Markov three-dimensional interception model. This approach is based on the turbid medium approximation for needle area in the shoot volume, and assumes an ellipsoidal angular distribution of the normals to the needle area. Observed shoot dimensions and silhouette areas for different vertical and azimuth angles (AS) are used as model inputs. The shape coefficient of the ellipsoidal distribution (c) and the Markov clumping index (λ0) are estimated by a least square procedure, in order to minimize the differences between model prediction and measurements of AS. This methodology was applied to silver fir (Abies alba Mill.) shoots collected in a mixed fir–beech–spruce forest in the Italian Alps. The model worked effectively over the entire range of shoot morphologies: c ranged from 1 to 8 and λ0 from 0·3 to 1 moving from the top to the base of the canopy. Finally, the shoot model was applied to reconstruct the within-shoot light regime, and the potential of this technique in upscaling photosynthesis to the canopy level is discussed.


The aggregation of narrow needles in clumped shoots is a common architectural strategy in several genera of conifers such as Abies, Picea, Pinus, Pseudotsuga and Larix. Needle clumping in shoots has a profound impact on ecosystem processes, as it affects the radiative regime, the photosynthesis and the aerodynamics of coniferous canopies (Norman & Jarvis 1974; Leverenz & Jarvis 1980; Carter & Smith 1985; Stenberg 1996a).

The relationships between shoot morphology and microclimate have been investigated extensively by several authors, both from an experimental (Smith & Carter 1988; Leverenz & Hinckley 1990) and theoretical point of view (Oker-Blom & Kellomäki 1983; Cescatti 1998). The plasticity of conifers in developing variable architectures according to the light microclimate suggests that shoot structure is relevant to the overall acclimation process of these canopies (Niinemets & Kull 1995a).

Several empirical coefficients have been proposed to account for the effect of needle clumping in shoots on the interception efficiency of the leaf area and on the canopy gap fraction (Oker-Blom & Smolander 1988; Chen 1996). These clumping indices, based on the ratio of the shoot silhouette area over different view angles to the needle area, can be readily integrated into light interception models based on the turbid medium analogy (Stenberg 1996a). The ratio of the spherical mean shoot silhouette to total needle area ( inline image) has also been proposed as a correction factor in the indirect estimation of leaf area index (LAI) based on the inversion of gap fraction data (Stenberg 1996b). Furthermore, the angular description of the shoot to needle area ratio, together with a detailed reconstruction of the light microclimate based on hemispherical photographs, have been used to estimate the light intercepted by single shoots over the whole growing season (Stenberg et al. 1998).

Nilson & Ross (1997) presented a first approach to the application of the turbid medium analogy at the shoot scale, assuming a random needle distribution in cylindrically idealized shoots. On the basis of these assumptions, the mean number of contacts was estimated as the ratio of the observed needle silhouette area to the projected area of the cylindrical shoot.

In order to overcome the limitations of silhouette analysis, several attempts have been made to describe the shoot radiative field with geometrical models based on a deterministic description of needle shape and position (Oker-Blom 1985; Wang & Jarvis 1993). In contrast, detailed experimental descriptions of the light microclimate have been obtained with the application of innovative multipoint light sensors to Scots pine shoots (Palmroth et al. 1999).

The scientific relevance of describing the shoot radiative field is mainly linked to the typical non-linearity of the physiological responses to light intensity. In fact, a detailed reconstruction of the shoot radiative regime is required to estimate the needle photosynthetic capacity from shoot level measurements in direct light, or to upscale needle responses to shoot and canopy levels (Smolander et al. 1987; Wang & Jarvis 1993).

In this study, a new methodology to investigate the architectural features and radiative regime of conifer shoots is presented. In comparison with the current available methodologies, this indirect approach has the following advantages:

  • 1it is based on a consistent procedure to retrieve architectural parameters from standard measurements such as shoot dimensions and silhouette areas;
  • 2it allows the analytical description of the light distribution on the leaf area, and therefore is appropriate for upscaling photosynthetic responses from needle to shoot level;
  • 3it can be embedded in canopy radiative transfer models based on the turbid medium analogy in order to predict light distribution at the canopy scale.


Study site

Silver fir shoots (Abies alba Mill.) were collected at an intensive study site, where water and carbon fluxes are continuously monitored by eddy covariance, within the framework of the European network CarboEuroflux (Aubinet et al. 2000) (Lavarone, Italian Alps; 45·96° N, 11·28° E; 1300 m asl, mean annual temperature 6·2 °C, total precipitation 1370 mm).

The area is characterized by an uneven-aged mixed forest dominated by Abies alba (70%), Fagus sylvatica (15%) and Picea abies (15%), with an average of 1300 stems ha−1 (diameter at breast height > 7·5 cm) and a LAI of 9·6, expressed as half the total surface area according to Chen & Black (1992). The canopy has a dominant layer reaching to 30 m and crown lower limits at about 12 m. In the understorey, suppressed beeches and firs form a discontinuous second layer from 0 to 4 m.

The site is equipped with a 36 m tall tower for micrometeorological measurements [photosynthetically active radiation (PAR), global and net radiation, wind, humidity and temperature] and for the estimation of the momentum, energy and mass fluxes (water and carbon dioxide) by means of the eddy covariance technique, according to the Euroflux methodology (Aubinet et al. 2000).

Shoot sampling and light microclimate

Shoot sampling was conducted during the summers of 1998–2001; a total of 60 fully developed current-year shoots were collected at different heights from 10 dominant and 13 suppressed trees in the area surrounding the tower. The sampling strategy in the different canopy layers aimed to represent the variability in shoot morphology in both dominant and suppressed trees (Fig. 1). Sunlit shoots belonging to dominant trees were collected from the tower, whereas shaded shoots were sampled both from dominant and suppressed trees in a larger area surrounding the tower (3000 m2). Due to the spatial heterogeneity of the canopy, the light microclimate in the understorey was relatively variable (Fig. 1).

Figure 1.

Vertical profiles of leaf area density (ρC), relative frequency of sampled shoots, and mean daily quantum flux density (1 May to 31 July). Photon fluxes were computed from hemispherical pictures and radiation measurements above the canopy.

Global radiation and PAR above the canopy were measured with the sensors 200-SZ and 190-SZ (LiCor Inc., Lincoln, NE, USA) installed at the top of the micrometeorological tower. The direct and diffuse components were estimated according to the methodology proposed by Weiss & Norman (1985). The mean daily quantum flux density above the sampled shoots (Qint) was computed from the radiation measurements above the canopy for the period 1 May to 31 July, taking hemispherical pictures at the sample location to evaluate the shading effect of the canopy on the direct and diffuse radiative fluxes.

Hemispherical pictures (lens: Sigma 8 mm, Sigma Corp., Tokyo, Japan; cameras: Nikon FM2 and D1, Nikon Corp., Tokyo, Japan) were taken at 35 sampling spots from where one to four shoots were collected (Fig. 2). Images were analysed with the software Gap Light Analyzer versus 2·0 (Frazer, Canham & Lertzman 1999) in order to compute the canopy gap fraction at 10-degree zenith and azimuth resolution.

Figure 2.

Hemispherical photographs and shoot silhouettes of six representative shoots collected at different heights in the canopy. Shoot architecture is described by the needle area to dry weight ratio (SM), the spherical mean shoot silhouette to needle area ratio ( inline image, Eqn 2), the Markov index of spatial clumping (λ0), and the coefficient of the ellipsoidal angular distribution of the normals to the needle area (c).

Needle and shoot morphology

The morphology of needle cross-sections was investigated in order to estimate the total needle area from the projected area. Images of five sections per sampled shoot were obtained with a Nikon D1 digital camera mounted on a Leitz Laborlux S microscope (Leitz, Wetzlar, Germany) at 20×. The perimeter and the major axis of the needle section were determined by image analysis (ImageTools 2·0, UTHSCSA by C. D. Wilcox, S. B. Dove, W. D. McDavid and D. B. Greer) and used to compute the half of the total to projected needle area ratio (AHTL/APL).

After removing the needles from the shoot, needle (APL) and twig (AA) projected areas were digitally recorded by an optical scanner at 300 dpi resolution. Needle dry weight (M) was determined for all the shoots after oven drying at 65 °C for 48 h. The specific leaf area (SM) was calculated as the ratio between the total needle area and the needle dry weight (M).

Shoot morphology was described by the shoot silhouette area (AS) in 26 different view directions, and by three shoot axes: height, width and length. Measurements of silhouette areas include the visible part of the shoot axis. To minimize the parallax error in the estimate of AS, shoot pictures were taken with a Nikkor 500 mm lens (Nikon Corp.). Using this configuration the distance between shoots and camera was approximately 5 m. Pictures were taken at the following angles of shoot inclination (φ): 90°, 60°, 30°, 0°, −30°, −60°; and shoot rotation (ϕ): 0°, 30°, 60°, 90°, −45° (Stenberg et al. 1998). The inclination angle (φ) is defined as the angle of the shoot axis to the plane of projection, being positive when the shoot tip is pointing towards the viewer; the rotation angle (ϕ) is defined as the angle of the shoot rotation around its main axis (Stenberg et al. 1999. The φ= 90° view direction was recorded once (ϕ = 0°), because at this inclination the effect of the rotation angle on AS is negligible.

The spherically averaged shoot silhouette area ( inline image) was computed as:


The integration over rotation angles was performed by averaging the silhouette measurements for each inclination angle φ to obtain inline image (φ). The integration over inclination angles was then obtained by interpolating inline image (φ) with a quadratic spline. The estimate of inline image was used to calculate the spherically averaged silhouette to total needle area ratio inline image:


The maximal shoot length, height and width were measured from the digital images of the shoots relative to the angles (0°,0°) and (0°,90°).

Shoot interception model

The relationships between shoot architecture (spatial and angular distribution of the needle area), interception efficiency ( inline image) and shoot radiative regime were investigated with the application of a three-dimensional interception model. For this purpose shoots were represented as an aggregation of shading elements in a confined volume. On the basis of this assumption, the probability of photon interception in the shoot space can be computed with the classic theory of light penetration in aggregated media based on Markov processes (Nilson 1971).

The needle surface area and the cylinder with elliptical cross-section delimiting the shoot volume were measured on the single samples, whereas the angular distribution of the normals to the leaf area and the level of clumping in the needle spatial distribution were indirectly estimated by inverting the light interception model.

The model predicts the probability of photon interception, F(φ,ϕ), in the shoot volume as a function of the extinction coefficient (G function, Ross 1981), of the Markov coefficient for spatial aggregation (λ0, Nilson 1971), of the needle area density in the shoot volume (ρS), and of the beam path-length in the shoot volume for specific rotation (ϕ) and inclination (φ) angle, LB(φ,ϕ):


The Markov coefficient is a measure of the needle spatial aggregation within the shoot and decreases from a maximum value of 1 (random distribution) at increasing clumping. The G(c,ϕ) function is obtained by the ellipsoidal leaf angle distribution (Campbell 1986; Campbell & Norman 1989):


The parameter c is the ratio of the spheroid horizontal to vertical semi-axis (c > 1 for an oblate spheroid, and c < 1 for a prolate spheroid), and B depends on c as:


In the model we impose that λ0 does not depend on the view direction and that G is independent on the inclination angle of the shoot, assuming that the leaf azimuth angle distribution is uniform (Campbell & Norman 1989).

The shoot silhouette area at each specific angle AS′(φ,ϕ) was predicted as the probability of photon interception F(φ,ϕ) times the projected area of the cylinder with elliptical cross-section representing the shoot ASC(φ,ϕ), accounting for the shading effect of the cylindrical shoot axis with projected area AA(φ,ϕ):


In the application of the light interception model to the shoot data, two parameters are unknown: the angular distribution of leaf normals (c), and the Markov coefficient of spatial aggregation (λ0). These parameters were estimated for each shoot by iteratively minimizing the square error (E) between the observed shoot silhouette areas AS(φ,ϕ), and the model prediction AS′(φ,ϕ), at the different rotation and inclination angles:


Shoot radiative regime

Morphological plasticity in plants is largely dependent on light-driven physiological processes such as photosynthesis and photomorphogenesis. In order to investigate the physiological implication of the morphological shoot acclimation, the interplay between architecture and radiative field was investigated using the shoot interception model.

For the prediction of light distribution on the needle area, the angular distribution of sunlit and shaded leaf fractions is assumed to be equal, and penumbra generated within the shoot is ignored, considering the short beam path-lengths in the shoot volume (Stenberg 1995; Nilson & Ross 1997).

Given a collimated light beam incident on the shoot from a specific view direction, the fraction of one-sided sunlit area (δS), was computed as the ratio of the silhouette area to half of the total needle area, projected onto an orthogonal plane:


The direct radiation on the sunlit fraction is obtained by correcting the flux of incident direct beams on a perpendicular plane with the cosine of the angle between the leaf normal and the sun direction. The correction is performed for different inclination and rotation needle angular classes according to the ellipsoidal distribution (Eqn 4).

The diffuse radiation is assumed to be uniform within the shoot, considering that the even distribution of diffuse fluxes is likely to produce minor effects on the variability of the needle light microclimate. Therefore, the mean level of diffuse radiation, expressed on half of the total needle area basis, is computed as the incoming diffuse radiation time twice inline image.

The parameterized shoot interception model was further applied to calculate the mean daily quantum flux density per unit needle area and mass (QSh mol m−2 d−1, QSh/M, mol g−1 d−1). The absolute quantum flux densities on the needle surface depend on the above-canopy quantum flux density, on the canopy shading, and on the shoot architecture. The estimates of canopy gap fraction I(ω), determined from the hemispherical photographs, were used to quantify the canopy shading. The angular distribution of the daily average amount of PAR incident on a flat surface above the canopy Q(ω) was computed for the period from 1 May to 31 July with an angular resolution of 10°, using the estimates of direct and diffuse fluxes, considering the path of the sun and assuming a uniform distribution of diffuse radiation. The quantum flux density on a horizontal surface above the shoot from the specific solid angle ω is equal to I(ω) Q(ω). Integrating this quantity over the sky hemisphere, the mean daily quantum flux density per unit one-sided needle area (QSh, mol m−2 d−1) was estimated as:


where γ is the solar zenith angle, φ and ϕ are the shoot inclination and rotation angles for the view direction ω (Stenberg et al. 1998). In this simulation shoots were assumed to lie horizontally. The shoot efficiency in light absorption ϑ, was computed as the ratio of QSh to the radiation intercepted by a spherical surface at the same location in the canopy:



Light distribution

The mean daily quantum flux density above the canopy in the period 1 May to 31 July was 46·1 mol m−2 d−1. Along the vertical profile of the meteorological tower the mean daily quantum flux density on a flat surface (Qint) at the shoot location decreases sharply from 35 to 5 mol m−2 d−1 in the upper layers of the canopy (28–18 m), where most of the leaf area is located (Fig. 1). In the shaded canopy layers (18–10 m) the extinction rate is lower, and the light availability gradually decreases down to the crown insertion height (9 m). The trunk space (9–0 m) is characterized by a constant irradiance, wheres in the understorey light availability varies in the range 2–14 mol m−2 d−1 depending on the occurrence of canopy gaps or dense regeneration patches. The hemispherical pictures in Fig. 2 clearly show the changes in the angular distribution of the gap fraction along the vertical profile of the canopy. In the lower layers canopy gaps occur mainly at the steepest vertical angles, generating an anisotropic radiative field.

Needle and shoot morphology in the light gradient

Silver fir shows high plasticity in the acclimation of both needle and shoot morphology to light availability. At the leaf level light acclimation occurs both in the shape of the needle cross-section and in the leaf area to dry weight ratio. In particular, the ratio of half the total to projected needle area (AHTL/APL) in dominant trees linearly increases with light availability, because of the circular section of sunlit needles (Fig. 3a; r2 = 0·72, P < 0·00). On the contrary, suppressed trees do not show any acclimation of this morphological trait to light availability (r2 = 0·06, P < 0·43).

Figure 3.

Needle and shoot morphological indices in the gradient of light availability (mean daily quantum flux density in the period 1 May to 31 July): (a) half of the total to projected needle area AHTL/APL; (b) maximum value of the shoot silhouette to total needle area ratio SS(0°,0°); (c) needle area to dry weight ratio SM; (d) spherical mean shoot silhouette to needle area ratio inline image (Eqn 2); (e) spherical mean shoot silhouette per unit needle dry weight inline imageM−1 (Eqn 1); (f) ratio of the silhouette area AS(0°,0°)/AS(0°,90°). Solid and open circles refer to dominant and suppressed trees, respectively. The coefficients b[0] and b[1] are the intercept and the slope of the regression lines.

The needle area to dry weight ratio (SM), decreases from 110 to 60 cm2 g−1 at increasing light availability (Fig. 3c; r2 = 0·49, P < 0·00). This trend, common to dominant and suppressed trees, is due to the progressive thickening of needles and was similarly observed in Abies amabilis (Sprugel, Brooks & Hinckley 1996) and in Picea abies (Niinemets & Kull 1995b; Stenberg et al. 1999).

Light acclimation in shoot morphology is evident both on the maximum and mean silhouette to needle area ratio. These two shoot parameters have been extensively used in ecophysiological studies on conifers as indices of the plant efficiency in light interception and as the extinction coefficient in radiative transfer models (Leverenz & Hinckley 1990; Stenberg 1996a). Suppressed trees show larger values of both these parameters in comparison with shaded shoots of dominant trees, but without significant trend at varying light availability.

In dominant trees, the maximum value of silhouette to needle area ratio SS(0°,0°) decreases from 0·3 to 0·1 at increasing light availability (Fig. 3b; r2 = 0·72, P < 0·00), as observed by Sprugel et al. (1996) for Abies amabilis. Similarly, the spherical mean shoot silhouette to needle area ratio ( inline image) decreases from 0·17 to 0·07 (Fig. 3d; r2 = 0·60, P < 0·00). Stenberg et al. (1998) found similar values of inline image in shaded shoots of Abies amabilis, but interestingly inline imagevalues in sunlit shoots were higher (0·11) than those observed for Abies alba (0·07), probably because the longer needles of Abies amabilis reduce the shoot self-shading.

Shoot acclimation occurs by increasing both the silhouette area per unit of leaf area ( inline image, Fig. 3b & d) and the silhouette area per unit of leaf mass (Fig. 3e) at decreasing light availability. It is noteworthy that the variation in inline image is twofold, whereas changes in inline imageM−1 for dominant trees is fourfold, as a joint effect of needle morphology (increasing SM in shade) and spatial needle arrangement within the shoot volume (lower clumping in shade) (r2 = 0·75, P < 0·00).

As a result of the angular distribution of needle normals, shaded shoots are significantly more anisotropic in comparison with sunlit shoots. This effect is evident in the AS(0°,0°) to AS(0°,90°) ratio, which shows a sharp increase at decreasing irradiance (Fig. 3f; r2 = 0·48, P < 0·00).

Parameters of the shoot model

The inversion of the interception model supports the analysis of the architectural features, which jointly determine the shoot radiative field. The three architectural parameters affecting the interception efficiency of the shoot are: needle area density, angular distribution and needle clumping. The needle area density (ρS) shows a positive trend at increasing irradiance, although uncertainty in the definition of the shoot volume induces a high variability in the values (Fig. 4b; r2 = 0·48, P < 0·00). The Markov index of spatial clumping (λ0) of dominant trees is significantly larger at low irradiance, as a consequence of the decreasing level of needle aggregation in the shade (λ0 = 1 for random distribution, λ0 < 1 at increasing clumping; Fig. 4a; r2 = 0·56, P < 0·00). Suppressed trees show uniform values of λ0 independent of the irradiance level and are characterized by the lowest level of aggregation (λ0 close to unity).

Figure 4.

Trends of the architectural parameters, retrieved from the inversion of the shoot interception model, in the gradient of light availability. (a) Markov index of spatial clumping (λ0); (b) needle area density in the shoot volume (ρS); (c) parameter of the ellipsoidal angular distribution of the normals to the needle surfaces (c); (d) fraction of variance in the silhouette areas of the single samples explained by the shoot interception model (r2). Symbols and legends as in Fig. 3.

Similarly, the angular distribution of the normals to the needle area, represented by the ratio of the ellipse semi-axes, varies from 1 to 2 at irradiances higher than 22 mol m−2 d−1, the angular distribution of the leaf area in the shoots of the upper canopy layers being spherical. At lower irradiances the ellipsoidal coefficient increases linearly from 2 to 4, because of the tendency of shade shoots to become flatter. As observed for the other shoot features (Fig. 3b & d), suppressed trees show larger values of the ellipsoidal coefficient (4–6) and a weaker sensitivity to irradiance (Fig. 4c; r2 = 0·53, P < 0·00).

Overall, the predictive capacity of the shoot model is very high (r2 = 0·95 on average), with few cases of asymmetrical shoots where r2 is below 0·8 (Fig. 4d). A similar approach in comparing observed shoot silhouette areas with the prediction of a geometrical model was reported by Smolander et al. (1987), Wang & Jarvis (1993) and Smolander, Stenberg & Linder (1994).

The shoot architectural features, generally represented with empirical indices such as inline image and AS(0°,0°)/AS(0°,90°), can be described in physically robust terms with the clumping index λ0 and the parameter c of the surface angular distribution. In particular, inline image is an estimate of the shoot self-shading and is therefore strictly correlated to the clumping index λ0 (Fig. 5b; r2 = 0·95, P < 0·00). From a conceptual point of view, the spatial clumping in the distribution of the needles surfaces, which is measured by the Markov index, affects the degree of self shading, which ultimately determines the STAR index. The differences in the angular distribution of the leaf normals, described by the ellipsoidal parameter c, generate shoots with different level of anisotropy, represented by the ratio AS(0°,0°)/AS(0°,90°). The two morphological parameters are therefore well correlated (Fig. 5d; r2 = 0·87, P < 0·00).

Figure 5.

Relationships between architectural parameters in the shoots of dominant (solid circle) and suppressed (open circle) trees. Dependence of the Markov index of spatial clumping (λ0) (a) on the parameter of the ellipsoidal angular distribution of the normals to the needle area (c) and (b) on the spherical mean shoot silhouette to needle area ratio ( inline image, Eqn 2). Ratio of the silhouette areas AS(0°,0°)/AS(0°,90°) in relation to (c)inline image and (d) c.

The relationship between architectural features of the shoot suggests that the structural acclimation results from a highly co-ordinated morphological development. In particular, the angular distribution of the leaf normal (c) and the degree of clumping (λ0) are positively correlated (Fig. 5a; r2 = 0·45). As a consequence, the surface areas of the shoots at canopy top have a spherical angular distribution and a clumped spatial pattern, acting, from a radiative point of view, as a leaf cluster with large self-shading. On the contrary, shoots in the understorey have a plagiotropic distribution and a very low level of clumping, behaving from the radiative point of view as single leaves.

Shoot radiative regime

The joint effect of the needle and shoot morphological acclimation produces a linear decrease of the efficiency index (ϑ) at increasing light availability (Fig. 6a; r2 = 0·63, P < 0·00). In particular, the shoot efficiency decreases by increasing the shoot self-shading and therefore the clumping index (Fig. 6b; r2 = 0·92, P < 0·00).

Figure 6.

Dependence of the shoot efficiency (Eqn 10, ϑ = ratio of the mean daily quantum flux density per unit one-sided needle area (QSh) to the flux on a spherical surface) (a) on the available radiation and (b) on the Markov clumping coefficien (λ0). Mean daily quantum flux density on a flat surface (Qint) in relation to (c) the mean daily quantum flux density per unit one-sided of leaf area and (d) mean daily quantum flux density per unit of leaf mass. Symbols as in Fig. 3.

Dominant and suppressed trees show different trends in the dependence of the daily average amount of intercepted quanta per unit one-sided needle area (QSh) from the irradiance on a flat surface (cosine corrected). For simple geometrical reasons, typical flat shoots of suppressed trees show a linear dependence of QSh on light availability, which is due to the limited self-shading (Fig. 6c; r2 = 0·95, P < 0·00). On the contrary, the variable shoot architecture of dominant trees generates a non-linear relationship, which was interpolated with a non-rectangular hyperbola (Fig. 6c; r2 = 0·90, P < 0·00). As a result, the acclimation in shoot morphology generates a constant maximum value of QSh (4 mol m−2 d−1) in a wide range of irradiance (12–35 mol m−2 d−1), reducing the risk of saturation and photo-inhibition. A similar non-linear trend appears when considering the value of QSh per unit leaf mass (Fig. 6d; r2 = 0·76, P < 0·00), supporting the hypothesis that optimal biomass allocation occurs when the intercepted light is proportional to the photosynthetic capacity (Farquhar 1989).

The distribution of direct radiation on the leaf area was simulated with the shoot interception model for the six shoots reported in Fig. 2, assuming the shoot silhouette AS(0°,0°) orthogonal to the solar beam. The pie charts in Fig. 7 represent the percentage of sunlit/shaded leaf area on a half of the total basis, and the histograms show the frequency distribution of leaf area in classes of direct irradiance relative to the irradiance on a flat surface. Similar trends in the distribution of the irradiance for unidirectional radiation were obtained by Oker-Blom (1985) using a shoot geometical model for Scots pine.

Figure 7.

Average, standard deviation and frequency distribution of the leaf area in classes of direct irradiance relative to a flat surface for the six shoots presented in Fig. 2. Solar beams are assumed to be orthogonal to the main shoot axis (projection 0,0). Pie charts represent the fraction of shaded (black) and sunlit (white) leaf area.

It is noteworthy that the shoots at the canopy top have a lower sunlit fraction (0·4) due to the high level of clumping and to the spherical angular distribution of the normals to the needle area (Fig. 7a & b). As a consequence, this type of shoot architecture produces a uniform distribution of direct radiation on the sunlit area, independent of the direction of the incoming direct radiation. This strategy should reduce the light-saturated leaf area and therefore could generate a shoot photosynthetic response to light which is more linear than the needle response, resulting in a higher photosynthetic efficiency in full sun condition.

On the contrary, shade-acclimated shoots have larger values of interception efficiency for light incoming from steep vertical angles [larger SS(0°,0°)] (Fig. 7d–f). This behaviour is due to the flat surface angle distribution and to the limited self-shading. As a result, these shoots show a larger sunlit fraction (0·6), most of which is in the highest irradiance class. The interception efficiency and light distribution in these shoots are similar to those of flat leaves. Therefore, the shoot photosynthetic response to light is similar to the single-needle response, with high quantum use efficiency and low saturation point. This strategy should work effectively at low irradiance in the understorey, where most of the radiation penetrates at steep vertical angles.


Functional interpretation of shoot acclimation to light

Species of the genus Abies, similarly to species of the genus Picea, Pseudotsuga and Sequoia, when growing in favourable environmental conditions, develop dense canopies with LAI values larger than 5 (Leverenz & Hinckley 1990). The average canopy transmittance, assuming an LAI value of 5, random leaf distribution and spherical leaf orientation, is approximately 0·02. At this value of transmittance light availability is close to the compensation point for photosynthesis. To overcome this limitation, coniferous canopies can maintain an LAI that is twice as high by developing a clustered structure with a low extinction capacity in the upper part of the canopy, thereby increasing light availability in the underlying layers (Stenberg 1996a; Cescatti 1998). The architectural features supporting this general strategy occur at three hierarchical scales: needle, shoot and crown (Norman & Jarvis 1974).

At the needle level the amount of leaf area per unit of mass (SM) decreases at a higher irradiance (Fig. 3c) as a joint effect of the variability in the needle cross-section (Fig. 3a) and of the density of leaf tissues (Niinemets & Kull 1995b). The variability in SM produces an uneven distribution of carbon and nitrogen per unit leaf area, following the requirements for higher photosynthetic capacity in sunlit layers and for lower respirative costs in shaded layers.

At the shoot level acclimation to light occurs by concurrent variation in the spatial aggregation and angular distribution of the leaf area (Fig. 4a & c). Clustered needles produce strong self-shading within the shoot (Fig. 7), which may be larger than the between-tree shading (Oker-Blom & Kellomäki 1983). Considering that the shading effect is inversely proportional to the square of the distances between objects, it is clear why the self-shading within shoots is larger than that between shoots or between crowns (Oker-Blom 1986). Thanks to the plasticity in shoot architecture, a single tree can adjust light distribution on the leaf surface by varying shoot clumping, independently from the shading of neighbouring trees (Fig. 7). Clustering directly increases the shaded fraction at high irradiance, reducing the extinction coefficient of the leaf area and the risk of saturation and photo-inhibition. In parallel, the angular distribution of the surfaces adapts the shoot interception efficiency to the specific light micro-environment of the specific shoot. At the top of the canopy, where radiation is incoming from the entire hemisphere, shoots are characterized by a spherical leaf angle distribution and therefore are equally efficient in intercepting light incoming from different angles. On the contrary, in shaded canopy layers, radiation penetrates mainly from the steepest vertical angles and shoots adapt by developing a flat angular distribution (Fig. 4c). As a result of these co-ordinated acclimation strategies, the distribution of the irradiance on the needle surface varies with the specific light condition (Fig. 7).

The comprehensive result of the acclimation to light should lead to a linear, or close to linear relation between intercepted light and invested biomass (Fig. 3e; Sprugel et al. 1996), which is theoretically defined as an ‘optimal architectural strategy’ (Farquhar 1989; ‘resource use is optimized when the distribution of photosynthetic capacity and nitrogen is proportional to the distribution of intercepted light’).

A complete understanding of the functional significance of plant acclimation will require an integrated analysis of the morphological and physiological properties at needle, shoot and crown levels in a complete soil-vegetation–atmosphere transfer model (Baldocchi & Harley 1995).

From the shoot extinction coefficient to the shoot radiative regime

The quantitative description of shoot morphology was originally developed to account for the effect of needle aggregation on the leaf interception capacity. The first attempt in this direction was proposed by Norman & Jarvis (1974) who computed the ratio of the shoot silhouette to the needle area, in order to describe the shoot as the basic shading element of a Sitka spruce canopy.

The use of this ratio as an extinction coefficient was adopted and further extended by several authors both in predictive models and in the inversion of gap fraction data, although the effect of the shoot angular orientation was not considered (Carter & Smith 1985; Leverenz & Hinckley 1990; Gower & Norman 1991). In the last decade, the spherical orientation of the shoots assumed by Oker-Blom & Smolander (1988), has lead to the definition of inline image as the spherical average of the shoot silhouette area to needle area ratio, and to the application of this morphological index in the correction of indirect estimates of the leaf area index, assuming a random distribution of shoots in the canopy space (Stenberg 1996b).

A major limitation in the application of inline image in light interception models is the strong dependence of this parameter on light availability as reported for different coniferous species (Stenberg et al. 1998; Stenberg et al. 1999; Fig. 3b, d & f). Both SS(0°,0°) and inline image show a two- to three-fold decrease at increasing irradiance, as a result of the increasing needle clumping within the shoot. This acclimation strategy generates a feedback between light availability and shoot structure, because shoot morphology is determined by light availability and at the same time affects the radiative field in the underlying canopy layers.

The application of inline image as a clumping index is formally correct in the prediction of the canopy gap fraction, but cannot be used to reconstruct the distribution of the irradiance on the leaf area, and therefore, for upscaling photosynthetic predictions from needles to whole trees (Wang & Jarvis 1993). The novel methodology reported in this work is an attempt to improve the description of shoot morphology in the estimation of canopy gap fraction and in the prediction of the irradiance distribution on the leaf area. By assimilating the shoot to a turbid medium, whose properties can be indirectly estimated from measurements of silhouette areas, its radiative regime can be described in detail, supporting the upscaling of photosynthetic responses from the single needle to the shoot.

The original aspect of the proposed methodology is the description of the turbid medium with two architectural parameters: the angular distribution of the leaf normals c and the Markov clumping coefficient λ0. Both parameters show a clear dependence on light availability in dominant trees (Fig. 4a & c) as a result of a co-ordinated acclimation strategy for needle clustering and angular distribution. Interestingly, λ0 and c are highly correlated with the empirical parameters inline image and AS(0°,0°)/AS(0°,90°), respectively (Fig. 5b & d), and could therefore be estimated from simple silhouette measurements already available for different species and study sites.

The turbid medium analogy versus the geometrical approach

The radiative regime and photosynthetic response of conifer shoots has usually been described with deterministic three-dimensional shoot models (Oker-Blom 1985; Wang & Jarvis 1993). This class of models, although very accurate for the description of the radiative regime given a specific architecture, presents some major drawbacks which have limited their application.

In particular, the relative advantages and limitations in using a turbid medium approximation as opposed to geometrical shoot models concern four different aspects: assumptions, parameterization, accuracy and upscaling.

The model based on the turbid medium assumes a simplified shoot architecture, with a constant leaf area density in the shoot volume, clumping coefficient independent from the vertical angle and azimuthal isotropy in the distribution of the leaf normal. These assumptions may affect the description of the irradiance distribution on the leaf area. On the other hand, geometric models generally assume equal cylindrical needles, randomly attached to the shoot axis, with a constant angle between the needle and the shoot axes (Smolander et al. 1987; Wang & Jarvis 1993). Because these architectural features are likely to acclimate to light availability (Figs 3a & 4c for the variability in needle cross-section and leaf angle distribution, respectively), simple geometrical models cannot be easily applied to the analysis of the adaptation of shoot architecture to light availability.

As for parameterization, geometrical shoot models are based on the detailed description of needle shape and orientation. This level of detail in the architectural description cannot be performed routinely, limiting the applicability of this class of models. For this reason, geometrical models seem likely to be restricted to theoretical studies on the effect of architectural strategies on the radiative regime, rather than to the experimental characterization of shoot morphology and physiology. On the contrary, the turbid medium model can be parameterized simply using the indirect technique presented and few direct measurements such as needle area, shoot dimensions and silhouettes. These data have been already collected extensively in several studies in order to estimate morphological indices such as inline image. Concerning accuracy, the geometrical shoot model can provide a very detailed description of the shoot radiative regime based on ray tracing techniques, when the actual architecture of the shoot is accurately represented in the model. The turbid medium model presented has demonstrated a high predictive capacity in terms of silhouette areas for the different shoots (Fig. 4d), whereas the accuracy in the prediction of the irradiance distribution on the leaf area cannot be tested, except by comparison with the output of a geometrical model. One of the most important reasons for developing a shoot model is for the upscaling of photosynthetic responses from the needle to the shoot and finally to the canopy level. Geometrical models based on a three-dimensional description of needle shape and position cannot be implemented in a canopy model because of their intrinsic complexity (high number of objects and parameters). On the contrary, the shoot model based on the turbid medium analogy can be embedded in canopy multilayer models, based on the turbid medium analogy and the same fundamental equation of canopy transmittance (Markov interception model).

Needles versus shoots as the basic unit of coniferous canopies

Shoots have been extensively proposed as the basic unit of coniferous canopies instead of single needles (Norman & Jarvis 1974; Gower & Norman 1991; Oker-Blom, Lappi & Smolander 1991; Nilson & Ross 1997). This assumption can be correctly applied in the estimation of the canopy gap fraction or light interception capacity once the shoot extinction coefficient inline image is known. Following this approach, the mean irradiance on the one-sided leaf area can be estimated as 2 inline image, but no information about the variability of the within-shoot irradiance can be retrieved. Considering that the architectural complexity of conifer shoots generates a highly variable light distribution, and that the photosynthetic response to light is typically non-linear, the use of the mean irradiance in photosynthesis models produces an over-estimation of the photosynthetic rate (Leverenz & Jarvis 1980; Smolander et al. 1987). In addition, as correctly pointed out by Wang & Jarvis (1993), shoot self-shading can induce co-limitation of photosynthesis within the same shoot exposed to direct radiation, generating apparent quantum use efficiency that cannot be interpreted and predicted as a single leaf response. This phenomena is particularly relevant when shoot level gas exchange measurements are analysed and upscaled with a biochemical model to predict canopy level photosynthesis (Baldocchi & Harley 1995).

Because of the strong dependence of the photosynthetic response on the shoot radiative field, shoots cannot be considered as basic units in plant physiology and the prediction of canopy scale photosynthesis should be derived from the upscaling of needle responses (Carter & Smith 1985; Smolander et al. 1987; Wang & Jarvis 1993).


This paper benefited from helpful discussion with Ylo Niinements. Thanks are also due to Heidi Hauffe for the linguistic revision. The constructive comments of two anonymous referees significantly improved the first version of the manuscript. Study supported by the CaRiTRo Foundation (Trento) and by the Province of Trento, Italy (ref. 14616 and 1060).

Received 11 February 2002; received in revised form 26 August 2002; accepted for publication 27 August 2002


List of symbols used

AA(φ,ϕ)Projected area of the shoot axis (cm2)
APLProjected needle area (cm2)
AHTLHalf of the total needle area (cm2)
AS(φ,ϕ)Measured shoot silhouette area (cm2)
AS′(φ,ϕ)Predicted shoot silhouette area (Eqn 6, cm2)
ASC(φ,ϕ)Silhouette of the cylinder delimiting the shoot (cm2)
inline imageSpherically averaged shoot silhouette area (Eqn 1, cm2)
cParameter of the ellipsoidal angular distribution of the normals to the needle surface (Eqns 4 & 5)
F(φ,ϕ)Probability of photon interception (Eqn 3)
G(c,ϕ)Extinction coefficient (Eqn 4)
I(γ)Canopy gap fraction at the zenith angle γ above the sampled shoots
LB(φ,ϕ)Beam path-length in the shoot volume (cm)
MTotal needle mass per shoot (g)
SMTotal needle area per unit needle dry weight (cm2 g−1)
PARPhotosynthetically active radiation (µmol m−2 s−1)
Q(γ)Daily integrated above-canopy quantum flux density on a horizontal plane from zenith angle γ (mol m−2 d−1)
QintMean daily quantum flux density on a flat surface above the shoot for the period 1 May to 31 July (mol m−2 d−1)
QShMean daily quantum flux density intercepted per unit one-sided needle area (Eqn 9, mol m−2 d−1)
SS(φ,ϕ)Shoot silhouette to total needle area ratio
inline imageSpherically averaged SS(φ,ϕ) (Eqn 2)
δS(φ,ϕ)Fraction of one-sided sunlit area (Eqn 8)
φShoot inclination angle
φShoot inclination angle for the view direction ω
γSolar zenith angle
ωSolid angle
ϑShoot efficiency in light interception relative to a spherical surface
ϕShoot rotation angle around its axis
ϕShoot rotation angle for the view direction ω
λ0Markov coefficient of spatial aggregation
ρSNeedle area density within the shoot volume (m2 m−3)
ρCNeedle area density in the canopy layer (m2 m−3)