Radiative transfer modeling of direct and diffuse sunlight in a Siberian pine forest

[1] We have expanded the Monte Carlo, ray-tracing model FLIGHT in order to simulate photosynthesis within three-dimensional, heterogeneous tree canopies. In contrast to the simple radiative transfer schemes adopted in many land-surface models (e.g., the Big Leaf approximation), our simulation calculates explicitly the leaf irradiance at different heights within the canopy and thus produces an accurate scale-up in photosynthesis from leaf to canopy level. We also account for both diffuse and direct sunlight. For a Siberian stand of Scots pine Pinus sylvestris, FLIGHT predicts observed carbon assimilation, across the full range of sky radiance, with an r.m.s. error of 12%. Our main findings for this sparse canopy, using both measurements and model, are as follows: (1) Observationally, we detect a light-use efficiency (LUE) increase of only 10% for the canopy when the proportion of diffuse sky radiance is 75% rather than 25%. The corresponding enhancement predicted by our simulations is 10–20%. With such small increases in LUE, our site will not assimilate more carbon on overcast days compared to seasonally equivalent sunny days; (2) the scale-up in photosynthesis from top-leaf to canopy is less than unity. The Big Leaf approximation, based on Beer’s law and light-acclimated leaf nitrogen, overpredicts this scale-up by 60% for low sky radiance ( 500 mmolPAR m 2 s ); (3) when leaf nitrogen is distributed so as to maximize canopy photosynthesis, the increase in the canopy carbon assimilation, compared with a uniform nitrogen distribution, is small (’4%). Maximum assimilation occurs when the vertical gradient of leaf nitrogen is slightly shallower than that of the light profile.


Introduction
[2] Downwelling, shortwave (l = 0.4-2 mm; hereafter SW) radiation is one of the principle driving variables in land-surface schemes coupled to climate and dynamic vegetation models.It has a major influence on surface temperature (thus microbial and plant respiration), energy budget (including exchanges of sensible and latent heat), and carbon uptake and release.Indeed, in the context of the carbon cycle, it might be argued that our representation of radiative transfer (RT) must predict photosynthesis to an accuracy of better than 10% if we are to monitor terrestrial vegetation and its response to changing atmospheric carbon (anthropogenically introduced carbon is currently estimated at 0.1 global net primary production (NPP); see also Knorr and Heimann [2001]; Adams and Piovesan [2002] for a discussion).
[3] Simple RT schemes are not computationally expensive.On these grounds the light representation implemented in land-surface schemes such as MOSES [Cox et al., 2000;Cox et al., 1998] and SiB2 [Denning et al., 2003] bases itself on the Big Leaf approximation for the calculation of canopy photosynthesis.Here, sunlight is treated as a direct beam decreasing exponentially with depth through the canopy according to Beer's Law.Canopy assimilation is assumed to be a scalar multiplication of the leaf photosynthetic rate.As we show in this paper, leaves situated at the same depth in the canopy are subject to a widely varying range of Photosynthetically Active Radiation (PAR).This, combined with the highly nonlinear leaf response to light, necessitates a more rigorous calculation of leaf irradiance for foliage possessing different orientations and locations within the canopy.The new generation of multilevel and sunlit-shaded models accounts, to some extent, for this dispersion in irradiance by estimating the fraction of both light-limited and lightsaturated foliage before scaling up from leaf to canopy level [Medlyn et al., 2003;de Pury and Farquhar, 1997].
A second problem with the Big Leaf paradigm is that active leaf nitrogen is assumed to decline with depth through the canopy in the same way as light extinction.Field measurements for a wide range of canopies indicate that the vertical falloff is much shallower [Lewis et al., 2000;Meir et al., 2002].
[4] Many land surface schemes fail to represent sufficiently well the directionality of incoming sky radiation, in particular its diffuse component (e.g., the LPG model) [Sitch et al., 2003].Diffuse sunlight is likely to be important when aerosol loading or cloud cover is high.Compared to direct sunlight, diffuse PAR is expected to expose a greater fraction of the foliage to moderate irradiances rather than leaving parts of the canopy in intense sunlight or deep shade [Farquhar and Roderick, 2003].An increase of 50-100% in light-use efficiency (LUE) has been claimed for some tree canopies when cloud cover is high [Hollinger et al., 1994;Gu et al., 2002;Niyogi et al., 2004].Thus the purported 5 -10% ''dimming'' of SW radiation at the land surface during the last 40 years, attributed to increased aerosol loading and thickening cloud cover [Stanhill and Cohen, 2001;Liepert, 2002], may be offset, in terms of photosynthesis, by a more efficient carbon uptake under diffuse sky radiation.In contrast to clouds, aerosols are expected to increase diffuse sunlight with relatively little reduction in total sky radiance [Roderick et al., 2001].Gu et al. [2003] claim a 20% increase in the NPP of an American broadleaf forest following the aerosol outgassing associated with the Pinatubo volcanic eruption.However, tree ring widths for the last 600 years indicate a lowering of global or hemispherical NPP, due to subdued surface temperatures, in the wake of violent volcanic eruptions [Briffa et al., 1998].Finally, one might conjecture that the rather symmetric distribution and orientation of leaves relative to the solar azimuth [Falster and Westoby, 2003], particularly for deciduous trees located in the midlatitudes, demonstrates the influence of diffuse sky radiance on plant light acclimation.Diffuse light is largely isotropic and thus best captured by an azimuthally symmetric foliage.
[5] This paper has three main aims: (1) to determine the extent to which canopy carbon assimilation is more efficient under diffuse sky radiance, (2) to calculate rigorously the scale-up of carbon assimilation from leaf to canopy level and compare our results with simple RT schemes such as the Big Leaf approximation, and (3) to determine the vertical distribution of leaf nitrogen which maximizes assimilation within the canopy.To realize our objectives we have taken the novel and crucial step of incorporating a colimited leaf photosynthesis model into a three-dimensional, numerical, ray-tracing simulation.The enhanced RT model allows predictions of carbon assimilation when the canopy is subject to both direct and diffuse sunlight.It has been hypothesized that diffuse radiation, acting in concert with a heterogenous canopy architecture, increases substantially the LUE of the system compared to pure direct sunlight [Gu et al., 2002].We test this hypothesis, using our three-dimensional simulations, for a Siberian pine forest where carbon exchange has been measured extensively.This paper is structured as follows.The next two sections describe the expansion of the RT scheme to calculate photosynthesis in 3-D canopies.In section 2 we describe the measurements of carbon flux and diffuse light obtained at the test site.In section 3 we compare our simulations against the observations.In section 4 we discuss the three main themes outlined above: diffuse light, scale-up, and optimal assimilation.Our conclusions are summarized in section 5.

Radiative Transfer Modeling
[6] The Forest LIGHT Interaction Model (FLIGHT) is a Monte Carlo numerical simulation of optical and nearinfrared photons propagating through either a onedimensional (1-D) homogeneous or 3-D heterogeneous leaf canopy [North, 1996].For 3-D simulations, tree crowns are represented by geometric primitives (ellipses and cones) with a range of prescribed dimensions (e.g., radius and height).In all cases, foliage is represented by volume-averaged parameters such as leaf area index (LAI), leaf-angle distribution (LAD), and scattering phase function.FLIGHT operates in two modes: ''forward'' and ''reverse.''In forward mode, photons are traced as they enter the top of the canopy, scatter off the ground and/or canopy foliage, and then are either absorbed or escape to the sky.By monitoring where light is absorbed and where it emerges from the forest it is possible to ascertain such quantities as the fraction of absorbed PAR and the bidirectional reflectance function of the surface.
[7] The reverse mode is more recent, although it has been used to estimate the LUE in 1-D canopies [Barton and North, 2001].It estimates irradiances on leaf surfaces using Monte Carlo sampling, and we have expanded this technique here in order to treat 3-D canopies.A technical description and validation of the reverse mode is presented elsewhere (P.North et al., Sampling of leaf irradiances using the three-dimensional forest light interaction model FLIGHT, manuscript in preparation, 2005), although we summarize the salient points here.Random locations within the canopy are chosen as representative of leaf positions.Likewise, leaf orientations are statistically selected according to the LAD.Irradiances on the leaf surface are estimated as the sum of two components: First, a ''direct'' beam emanating from the solar disk and, second, a ''diffuse'' beam composed of (1) light reflected from surrounding foliage, (2) light scattered from the ground, and (3) diffuse radiation emanating from the sky.At the beginning of the simulation, the sky radiation field is prescribed fractions of direct and diffuse sunlight.For any given leaf, the degree of illumination by direct and diffuse light follows from reverse ray tracing.For the direct component the ray path is followed backward through the canopy toward the solar position.The optical depth to the top of the canopy determines the probability of illumination by the Sun and thence the magnitude of direct light normal to the leaf surface.For the diffuse component a number of random directions is selected and each ray path is followed back to its next point of interaction (the ground, the sky, or another leaf) in order to determine the irradiance arising from that particular direction.This is carried out recursively until the ray paths are traced back to the sky.Monte Carlo reverse tracing has been applied successfully to a range of canopy representations in the past and is fairly well established [Dawson et al., 1999;Goel and Thompson, 2000;Disney et al., 2000].The canopy angular reflectance, as well as the profile of light absorption through the canopy, are consistent across reverse and forward modes.The forward mode predicts values of albedo and reflectance which agree closely with both measurements obtained in the field [North, 1996] and the predictions from other RT models [Pinty et al., 2004].
[8] FLIGHT possesses two main advantages over simpler RT schemes based on, for example, Beer's Law or the Big Leaf approximation.First, we estimate much more rigorously the irradiance on any given leaf according to its position in the canopy and its particular orientation.Second, by subsequently determining the photosynthetic rate for any given leaf (see below), we can accurately scale up from leaf level to canopy-wide photosynthesis.Figure 1 depicts the leaf irradiances derived from the reverse mode in FLIGHT and compares them with the mean light attenuation predicted by Beer's law.At any height within the canopy the leaf irradiances are well dispersed with respect to the mean (mainly due to sunlit foliage).It is precisely this dispersion, in conjunction with the highly nonlinear response of leaves to incident PAR, that necessitates a rigorous determination of leaf irradiance at different positions within the canopy in order to integrate successfully from leaf to canopy level photosynthesis.

Leaf Photosynthesis Model
[9] FLIGHT provides an estimate of PAR at the leaf surface for different positions within the canopy.In order to determine leaf photosynthetic rate from incident PAR we have implemented a colimitation model for C 3 leaf photosynthesis.This is the Farquhar et al. [1980] model as extended by Collatz et al. [1991].The C 3 colimitation model, once calibrated against observed physiological parameters, has been shown to be a robust predictor of canopy photosynthesis for North American deciduous woodland [Harley and Baldocchi, 1995].We refer to Appendix A for the precise formulae governing the model and summarize here the main functional dependencies only.Leaf photosynthetic rate A l (mmol m À2 s À1 ) is determined as the smoothed minimum of three limiting quantities: the photosynthetic rate due to incident PAR normal to the leaf, J PAR ; the photosynthetic capacity due to the concentration and chemical activity of Ribulose-1,5-bisphosphate carboxylase/oxygenase, i.e., Rubisco, J r ; and the photosynthetic rate limited by the ability of the plant to export the products of photosynthesis out of the leaf, J e .These quantities depend on physiological leaf properties and environmental conditions in the following way: where the CO 2 concentration inside the leaf, C i (mol mol À1 ) depends on the ambient CO 2 concentration (mol mol À1 ), leaf temperature T l (K), and the stomatal conductance (see where O a (mol mol À1 ) is the ambient oxygen concentration and V cmax is a physiological constant related to the concentration of Rubisco in the leaves (see below).During this study, 90% of the variation exhibited in J r was due to changes in T l .
[10] Finally, we note that J e = f(V cmax , T l ) but, for the simulations carried out in this work, the export limit was seldom reached.In general, the system passes from a lightlinear to a Rubisco-limited regime as I PAR increases.We employ a quadratic function, with colimitation parameters close to 0.9, to facilitate a smooth transition from one limiting rate to another.From A l we subtract a leaf respiration (<0.5 mmol m À2 s À1 ) which depends on V cmax and T l (see Appendix A).
[11] The stomatal conductance imposes a further constraint on the rate of photosynthesis and is inferred from the measured canopy transpiration.For carbon flow we can write where A c (mmol m À2 s À1 ) is the net photosynthetic rate for the canopy, C a (mol mol À1 ) is the ambient CO 2 concentration and g c (mmol m À2 s À1 ) constitutes the total canopy conductance to CO 2 (stomata, boundary layer, and aerodynamic flow).Similarly, for water flow we can write where E (mmol m À2 s À1 ) is the canopy transpiration rate, P (Pa) is ambient air pressure, D (Pa) is the water vapor deficit and g v (mmol m À2 s À1 ) is the total canopy conductance to water vapor.For the two relations (3) and ( 4) we have made the (necessary) simplification that at any given moment, all leaves within the canopy possess the same internal CO 2 concentration and the same temperature.The latter is approximated by the measured air temperature (T).For open forest with stomata closing down, total canopy conductance is likely to be dominated by the stomatal term.Thus g v = 1.6g c and relations (3) and ( 4) combine to yield [e.g., Campbell and Norman, 1998] Note that when aerodynamic or boundary-layer resistance dominates g v = 1.4g c [Sellers et al., 1996].
[12] The canopy rate of photosynthesis can now be solved by iteration.Our FLIGHT model provides estimates of irradiance at the leaf level (I PAR ) for an observed downwelling sky radiance I 0 expressed as top-of-canopy PAR measured in the horizontal plane (mmol m À2 s À1 ).This, combined with measured air temperature and air pressure, allows us to estimate A l via equations ( 1) and (2).Through repeated sampling and integration in the FLIGHT simulation, we obtain A c .Canopy photosynthesis must, in turn, be consistent with the observed canopy transpiration rate and the observed water vapor deficit.Thus inferred A c is substituted into equation ( 5) to isolate C i , itself a prerequisite for the calculation of A l .Equations ( 1), (2), and ( 5) are solved iteratively until C i and A c converge.
[13] In summary, the leaf photosynthesis model is driven primarily by sky radiance and air temperature.Stomatal conductance is inferred from measured values of canopy transpiration and air vapor deficit.Two physiological constants, a and V cmax , determine the leaf response to temperature and light.They are prescribed values from field campaigns or data in the literature.Soil moisture is only accounted for indirectly in our simulations.Low water potential will reduce measured transpiration inducing stomatal closure in equation ( 5).

Observational Data 2.3.1. Carbon Fluxes
[14] Our simulations of canopy photosynthesis were tested against measurements of carbon flux recorded during June, July, and August of 1999 and 2000 (hereafter JJA period) for a 200 year-old Siberian stand of monotypic Scots Pine.Wirth et al. [1999] designate the site 200ld and we refer to it simply as ''Zotino'' hereafter.Lloyd et al. [2002] have already presented hourly estimates of net CO 2 assimilation for Zotino during 1999 and 2000.Here we analyze these data, for the first time, in the context of diffuse light and interpret the canopy response by means of RT modeling.Zotino is an open stand of 470 trees/ha with only 60% of the ground directly below tree crowns [Wirth et al., 1999].Needles harvested from the site and analyzed with a LICOR light cuvette indicate an LAI as low as 1.3 m 2 m À2 for the site [Wirth et al., 1999].Los et al. [2000] estimate LAI = 3.5 m 2 m À2 for the 80 km square containing Zotino using reflectances detected by the AVHRR satellite.Although the latter measurement encompasses an area ten times larger than the pine stand itself, we have obtained MODIS data which indicate that the reflectances of the 0.5 km square containing Zotino are typical of the 80 km square as a whole.Given its importance in our simulations, we have adopted minimum and maximum values for the LAI characterizing the Zotino site (1.3 m 2 m À2 and 3.5, respectively).Table 1 summarizes the main geographical features of the pine stand.
[15] Zotino forms part of the EUROSIBERIAN CARBOFLUX network.A flux tower provides estimates of CO 2 and energy exchange between the stand and the abovecanopy airspace with a ''footprint'' of 1 km 2 .The same installation records micrometeorology (above-canopy temperature, pressure, humidity, and the downwelling radiances of SW, PAR, and thermal radiation).We follow Lloyd et al. [2002] in estimating canopy photosynthetic rate, A c as follows: where C top (mmol m À2 s À1 ) and C bot (mmol m À2 s À1 ) are the carbon fluxes at the top and bottom eddy-covariance device, respectively, and DC store (mmol m À2 s À1 ) is the rate of change in CO 2 concentration in the canopy airspace between the two devices (DC store is provided by gas profile measurements).The trunk respiration R st is estimated at 0.3 and 0.4 mmol m À2 s À1 for 1999 and 2000, respectively [Shibistova et al., 2002].We follow previous authors in designating skyward carbon flow as positive, although, when quantifying photosynthesis and respiration, we discuss them in terms of their magnitude.

Diffuse Light
[16] The fraction of diffuse downwelling shortwave radiation (fDIF) has been measured at a bog 1.5 km from the Zotino flux tower for nearly all the JJA period in 1999 and only half the JJA period in 2000.When fDIF was not available we inferred its value by comparing the observed shortwave radiation, SW obs , with its anticipated clear-sky value, SW cl .The latter can be calculated from the solar position and simple empirical relationships given by, for example, Campbell and Norman [1998] for clear-sky opacity.We have defined a ''cloud factor,'' 1-SW obs /SW cl , indicating the level of direct sunlight obscured by clouds.Figure 2 reveals a positive correlation between fDIF and the cloud factor except when the latter exceeds 0.6 and the diffuse fraction begins to saturate.A very similar relationship has been found for sites globally by Roderick et al. [2001].For the purposes of this study, we divide Zotino carbon fluxes into measurements collected under direct (fDIF < 0.5) and diffuse (fDIF !0.5) sky radiance.Where fDIF has not been measured, we use a cloud factor threshold of 0.3 to separate diffuse and direct samples.With the cloud factor ! 0.3, fDIF !0.5 for 92% of the points in Figure 2 and, similarly, 91% of the points with cloud factor <0.3 possess fDIF < 0.5.Comparing SW obs with maximum Figure 2. The observed fraction of diffuse downwelling shortwave radiation, fDIF, against the inferred cloud cover at Zotino during the growing seasons of 1998, 1999, and 2000 (May -September, inclusive).The quantity fDIF was measured close to the forest stand and has been integrated over hourly intervals.The cloud factor constitutes the fractional deficit in downwelling shortwave radiation.SW obs and SW cl denote the observed and anticipated clear-sky shortwave radiation, respectively.Note that the cloud factor can become negative when clouds are present to reflect light to the ground but the solar disk remains unobscured.[1999].The satellite-derived LAI is inferred from the Normalized Difference Vegetation Index [Los et al., 2000].
values recorded over 15 day composites indicates that the cloud factor, as we have defined it, works rather well in estimating obscuration of the Sun (uncertainty 10%).
[17] We shall test the hypothesis that canopies assimilate more carbon under diffuse light compared to direct sunlight.To do this, we must compare photosynthetic rate under similar conditions of temperature, canopy humidity and, above all, under equal sky radiance (I 0 ).Since increased fDIF is usually accompanied by lower levels of direct shortwave radiation (Figure 2), to enable a comparison at a given value of I 0 , the Sun will generally be higher in the sky for high fDIF measurements compared to the low fDIF category.One notable consequence of this was that our low fDIF (clear sky) sample initially contained a preponderance of measurements from early June and late August (when solar elevations are lower).Since highest photosynthetic rates are attained in late July and remain constant for August [Lloyd et al., 2002], we felt it necessary to remove any bias towards measurements collected early in the JJA period.Thus for each fDIF category we have randomly sampled the data to ensure an even distribution of measurements throughout the JJA period.Note that we have limited the current analysis to the midsummer months since photosyn-thesis appears to be physiologically impaired for dates close to the spring thaw and the first autumn frosts [Lloyd et al., 2002].Furthermore, measurements of carbon exchange were only used if the solar elevation angle was greater than 18°and the air temperature lay between 281 and 293 K. Eliminating high temperature measurements mitigates the influence of stomatal closure on canopy photosynthetic response.

Configuring the Simulation for Zotino
[18] Our simulations are driven by observed values of air temperature and sky radiance with measured transpiration and water vapor deficit constraining stomatal closure.Diffuse sky radiance is assumed to be perfectly isotropic and the solar zenith angle of the direct sky component follows from the date and time of day.Table 2 shows the mean values of the environmental driving variables for 1999.Hourly carbon and meteorological measurements have been separated according to the sky radiation field (fDIF < 0.5 and fDIF !0.5) and then averaged into I 0 bins.An RT simulation is run for each I 0 bin using the corresponding mean values of temperature, I 0 , q s , vapor deficit, and transpiration rate.Table 2 indicates that the mean fDIF is close to 0.25 and 0.75 for the diffuse and direct sky radiance categories, respectively, as we have defined them above (fDIF < 0.5 and fDIF !0.5).Thus initially our simulations are conducted pairwise with fDIF = 0.25 and fDIF = 0.75 (hereafter, simply referred to as ''direct'' and ''diffuse'' simulations, respectively).
[19] Our leaf photosynthesis model requires us to set two physiological constants: the quantum efficiency, a, and the capacity due to Rubisco, V cmax .The latter scales with the active [Stitt and Schulze, 1994] concentration of leaf nitrogen.In the absence of values in the literature for Scots Pine we have calibrated a and V cmax from measurements of leaf gas exchange conducted for top leaves of Canadian Jack Pine Pinus banksiana obtained independently during the Boreal Ecosystem-Atmosphere Study (BOREAS) [Gamon et al., 2004].A least-squares fit for V cmax yielded 56 ± 2 mmol m À2 s À1 (Figure 3).Similarly, a was derived as 0.030 ± 0.005 mol mol À1 , i.e., toward the lower end of values cited for tree species (0.025 -0.075) [Dang et al., 1998;Lewis et al., 2000;Singsaas et al., 2001].We allow for the slightly higher leaf nitrogen measured at Zotino (3.20 gNm À2 ) [Wirth et al., 2002] compared to the Canadian site (2.75 gNm À2 assuming cylindrical pine needles) [Dang et al., 1997] and thus set V cmax to 65 mmol m À2 s À1 at the top of the canopy in the simulation.
[20] FLIGHT calculates photosynthesis at the leaf level before scaling up to canopy level.This allows us to ascribe a depth-dependent value for V cmax .Thus where H (m) is the height of the canopy and h (m) the depth below the canopy ceiling.We define k rub as the exponential parameter for Rubisco analogous to the dimensionless extinction coefficient for PAR, k ext .The latter is defined thus:  Hourly measurements have been separated according to direct (left side) and diffuse sunlight (right side).For increasing sky radiance (hI 0 i) we list the mean values of solar zenith angle (q s ), evaporation rate (E), Vapor Pressure Deficit (VPD), and top-of-canopy temperature (T).The data have been averaged over I 0 bins spanning 100 mmol m À2 s À1 for I 0 < 800 and spanning 200 mmol m À2 s À1 for I 0 > 800.The quantity n denotes the number of hourly measurements in each I 0 bin.Note that the same I 0 is not always available for direct and diffuse light (e.g., at solar noon the maximum I 0 under diffuse conditions is '1100 mmol m À2 s À1 , whereas the irradiance attains nearly 1500 under direct sunlight conditions).
where I h (mmol m À2 s À1 ) is PAR in the horizontal plane at depth h.Neither k ext nor k rub has been measured for Zotino but the RT simulations we conduct below imply k ext ' 0.75 for a site of this latitude.The Big Leaf approximation assumes k rub = k ext which purportedly maximizes the value of canopy photosynthesis for a given total of leaf nitrogen [e.g., Schulze et al., 1994] and simplifies its calculation in the land-surface scheme.Field measurements, however, indicate that light acclimation is incomplete with Rubisco declining as k rub ' k ext /3 for a range of tree canopies [Lewis et al., 2000;Meir et al., 2002].Initially, we assume k rub = 0.75/3 = 0.25 but we undertake to run a ''light-acclimated scenario'' where k rub = 0.75.Note that for both k rub = 0.25 and k rub = 0.75, V cmax (h = 0) = 65 mmol m À2 s À1 , as determined above for top leaves.
[21] FLIGHT allows us to configure either 1-D uniform canopies or 3-D heterogeneous forest stands.In this study the latter have been created using ellipsoid crowns with major and minor axes of 5 m and 2.5 m, respectively.In accordance with in situ measurements (Table 1), trunks have been assigned heights between 8 m and 12 m and the fraction of open ground, not lying vertically below trees, is 0.4.For all simulations, scattering from leaf elements is assumed to be bi-Lambertian.We adopt respective reflection and transmission coefficients of 0.07 and 0.06 in the PAR waveband, consistent with measurements of pine needles obtained in the field [Williams, 1991].The ground albedo has been set to 0.15 and reflection from the ground is assumed to be isotropic.A spherical LAD has been employed [Falster and Westoby, 2003].

Results
[22] Figure 4 illustrates the observed canopy photosynthetic response at Zotino for the JJA period of 1999 and 2000.The response flattens for relatively low sky radiance ('800 mmol m À2 s À1 ) which may be attributable to the rather low LAI of the site or closure of the stomata during the late morning.The pine stand is nevertheless fairly well adapted to the maximum I 0 at this latitude with only 30% of daylight hours during the JJA period lying above the aforementioned saturation threshold.Carbon assimilation appears to be slightly enhanced under diffuse light conditions but at a level which is barely statistically significant.For example, for I 0 > 300 mmol m À2 s À1 , A c is higher under diffuse sky radiance by 0.53 ± 0.28 mmol m À2 s À1 and 0.71 ± 0.33 for 1999 and 2000, respectively.This corresponds to relative increases of just 7% and 9%.
[23] Figure 5 depicts the FLIGHT simulations for 1999 using minimum and maximum values of LAI.The figure also demonstrates the light-acclimated case where k rub = k ext $ 0.75.For maximum LAI (3.5 m 2 m À2 ), the model is fairly close to the observed response although it fails to saturate at high I 0 in the same way as the measurements.A more saturated response is produced by both the LAI = 1.3 m 2 m À2 case and the light-acclimated scenario but, here, the predicted canopy assimilation is $50% too low.A gentle vertical fall-off in Rubisco (k rub < k ext ) is a prerequisite to fitting the model to the observations.However, the low LAI scenario is still possible if the quantum efficiency is increased from 0.03 to 0.045 and the leaf nitrogen is increased by 23% so that V cmax is 80 mmol m À2 s À1 at the canopy top.The increase in quantum efficiency seems reasonable given that our calibration for this parameter was originally based on Jack Pine rather than Scots Pine.A value of 0.045 is much closer to field measurements recorded by other authors for needleleaves [Lewis et al., 2000].The 23% increase in V cmax implies a leaf nitrogen that is close to the upper limit recorded by Wirth et al. [2002] at the site (3.20 ± 0.55 gNm À2 ).The LAI = 3.5 m 2 m À2 and Figure 3. BOREAS measurements of leaf photosynthetic rate, A l , against internal CO 2 concentration for light-saturated (>1500 mmol m À2 s À1 ) Jack Pine needles maintained at 20°C at the top of the canopy and at high ambient humidity.The solid line represents our C 3 leaf model calibrated with V cmax = 56 mmol m À2 s À1 .LAI = 1.3 (nitrogen-adjusted) simulations predict the observed response to within an error of 12% (r.m.s.).
[24] For all model predictions (including 1-D simulations not shown here), carbon assimilation appears to be 10-20% higher under diffuse sky radiance (fDIF = 0.75) compared to direct sunlight (fDIF = 0.25).About half of this increase can be attributed purely to diffuse light, the remainder arising from systematic differences in solar zenith angle and stomatal closure under the two light regimes (Table 2).While the forest absorbs an almost identical fraction of PAR under diffuse and direct sky radiance, diffuse photons are absorbed preferentially near the canopy top where Rubisco concentration, and therefore light-saturated photosynthetic rates, are highest.To test the idea that diffuse sky radiance exposes a greater fraction of the canopy foliage to sunlight [Gu et al., 2002], we have repeated our simulations using a uniform Rubisco distribution (i.e., k rub = 0) and a sky radiation field of either pure diffuse (fDIF = 1) or pure direct (fDIF = 0) light.Furthermore, we have configured LAI-equivalent, uniform 1-D canopies to compare with the 3-D model and thus elucidate the interplay of canopy architecture with isotropic sky radiance.For our LAI = 3.5 m 2 m À2 simulations, between 0.25 and 0.5 of the foliage contributes nothing to the canopy photosynthetic rate (A l 0) when exposed to pure direct sunlight.Under a purely diffuse sky this inactive fraction reduces to 0.25 (comparison made for I 0 = 500 mmol m À2 s À1 and I 0 = 1000 with q s = 57°).Notably, the median leaf-irradiance is smaller in the diffuse regime, increasing the average LUE of leaves exposed to sunlight.Somewhat surprisingly, the fractions of foliage exposed to PAR are the same for both the 3-D and 1-D architectures (for both the direct and diffuse regimes).
[25] In Figure 6 we illustrate the equivalent Big Leaf response (hypothetical flat leaf of area 1 m 2 situated at the top of the canopy) for the simulations in Figure 5.Note that for LAI = 1.3 m 2 m À2 model we have adjusted V cmax and the quantum efficiency, as described above.In Figure 7 we have tested the importance of the vertical Rubisco distribution in maximizing the canopy assimilation rate.We have simulated canopy photosynthesis for k rub varying between 0 to 2, while conserving the total amount of Rubisco (active leaf nitrogen) present in the canopy.Figure 7 illustrates the case for our LAI = 3.5 m 2 m À2 model but the behavior for LAI = 1.3 (adjusted V cmax ) is qualitatively similar.The figure also shows the assimilation rate for a 1-D uniform closed canopy possessing the same LAI as Zotino.

Discussion
[26] The discussion of our results focuses on the three main themes of the paper, diffuse light, scale-up of photosynthesis, and optimal canopy assimilation.

Diffuse Light
[27] The observed ( 10%) and predicted (10 -20%) enhancement in LUE for Zotino under diffuse sky irradiance is much lower than the 50-100% increase found by other authors for both broadleaf and needleleaf canopies [Hollinger et al., 1994;Gu et al., 2002;Niyogi et al., 2004].Moreover, an increase in the diffuse fraction, fDIF, from 0.25 to 0.75 is associated with a SW dimming of factor 2 (Figure 2).For the observed Zotino response in 1999 this corresponds to a reduction in canopy assimilation of $25-50% (comparison made at I 0 = 500 mmol m À2 s À1 and 1000 when fDIF = 0.25).After varying the configurations of our simulations (LAI, q s , cover fraction), we conclude that in general, the LUE enhancement due to diffuse light is greatest for isolated trees of moderate/high LAI (!3 m 2 m À2 ) exposed to an overhead Sun (LUE increase of factor $2).Only under these circumstances is the total carbon assimilated likely to be greater under overcast skies compared to seasonally equivalent cloud-free days.
[28] We emphasize that the carbon flux measurements, against which we compare the simulations, are themselves subject to a large degree of scatter (s.d.$2 mmol m À2 s À1 ) although adopting a mean response over a limited part of the season reduces this uncertainty.It might be argued that the footprint of the lower eddy covariance device is much smaller than the corresponding instrument situated above the canopy and that this may distort our results.To test this idea, we have substituted the bottom flux in equation ( 6) by a temperature-dependent respiration model created from nighttime fluxes with moderate wind speed (>3 ms À1 ; see, for example, Medlyn et al. [2003]).The observed canopy response remained unchanged within the errors.This is in contrast to the storage term in equation ( 6), which we found highly influential in determining the canopy response.Much of the carbon dioxide respired during the night is reabsorbed during the early and midmorning period with imperceptible downflow at the top eddy-covariance device.By deliberately neglecting the storage term in equation ( 6), we became aware of two important consequences for those FLUXNET sites where no storage is measured.Early morning reabsorption tends to linearize the canopy response (i.e., subdued response for low I 0 ) if storage is neglected.Second, the response is more severely reduced for the direct regime (by up to 30%) because here, we select lower Sun elevation angles in order to able to compare with the equivalent diffuse sky radiance.The FLUXNET sites used in the diffuse/direct light comparison of Niyogi et al. [2004] Figure 6.The big leaf response to photosynthetically active radiation incident in the horizontal plane (I 0 ).Responses are shown for the LAI = 3.5 m 2 m À2 scenario (V cmax = 65 mmol m À2 s À1 ) and the nitrogen-adjusted LAI = 1.3 scenario (V cmax = 80).The plot shows the observed canopy assimilation for 1999, removing the error bars for clarity.do not appear to record storage but the authors do avoid flux measurements obtained before 10 am.During our analysis it became clear that limiting the temperature range over which measurements were compared reduced the impact of stomatal closure, particularly for the direct sunlight regime where air vapor deficits tend to be high.Moreover, as alluded to in section 2.3.2,any seasonal bias in the sampling of diffuse and direct measurements is likely to lead to spurious differences in the recorded responses.While previous authors have accepted the importance of seasonal effects, it is not clear to us if, and how, systematic offsets in temperature and canopy humidity have been eliminated or accounted for in the past.
[29] We emphasize that the inferences from our simulations are more or less insensitive to the particular optical properties that we have adopted for the leaves and the ground.Changes of ±0.05 in leaf reflectance, leaf transmission, and ground albedo generally modify the predicted canopy assimilation rate by 3 -5% and thus our conclusions remain unchanged.Perhaps due to the high latitude of Zotino, adopting a planar or erectophile LAD alters our predictions by very little ( 3%).The radiance from an overcast sky can deviate somewhat from perfect isotropy.When implementing the empirical relation given by Steven and Unsworth [1980], for example, our predicted canopy assimilation changes by 1%.The assumption that leaf temperature is both uniform and close to that of the above-canopy airspace is a serious limitation in our model.Small needleleaves appear to remain within 2 -3 K of air temperature whatever the stomatal resistance [Campbell and Norman, 1998] and we estimate the impact on canopy assimilation to be less than 8%.The comparative study of diffuse and direct light would not be affected since the mean temperature is approximately the same for both groups of measurements (Table 2).We have also assumed (necessarily) that all leaves in the canopy maintain the same internal CO 2 concentration at any given time (section 2.2).There is some evidence that leaves act to regulate their internal CO 2 concentration so as to maintain a steady value [Campbell and Norman, 1998].

Scale-Up
[30] Figure 6 demonstrates the main problems associated with the Big Leaf approximation.Note that this formulation assumes Beer's law and a light-acclimated vertical distribution of Rubisco.Under such circumstances the scale-up in photosynthetic rate from a hypothetical, flat top-leaf of area 1 m 2 , A tl , to the total canopy assimilation rate, A c , is given as follows [e.g., Schulze et al., 1994]: For light extinction appropriate to the Zotino stand (k ext $ 0.75) the Big Leaf approximation predicts a scale-up factor, A c /A tl , of 0.83 and 1.23 for LAI of 1.3 m 2 m À2 and 3.5, respectively.Such scaling of the top leaf overpredicts the canopy photosynthetic rate by 18% (r.m.s.) and 30%, respectively, compared to observations.This should be compared with the FLIGHT prediction (section 3) where the corresponding error is 12%.The overestimation of the Big Leaf is particularly severe at low I 0 ( 500 mmol m À2 s À1 ) where canopy assimilation is at least 50% too high compared to observation.In spite of this, the true canopy response does flatten (somewhat like a Big Leaf) but at higher sky radiance (I 0 !800 mmol m À2 s À1 ).This may be attributable to light saturation of a canopy possessing a sparse foliage.In the future, it will be of interest to see ).In all cases, the fraction of diffuse sky radiance is 0.5 and the sun has a position of q s = 57°.Sky radiance (I 0 ) is either 500 mmol m À2 s À1 (solid circles) or 1000 (solid squares).
whether such behavior is exhibited by canopies of higher LAI or whether the observed canopy response is so linear that it cannot possibly be reproduced by the Big Leaf approximation.The inability of the Big Leaf model to predict canopy assimilation correctly for the whole range of sky radiances has been recognized by previous authors [Friend, 2001;Medlyn et al., 2003].Since the Big Leaf approximation assumes a 1-D canopy, it is not too surprising that it does not perform convincingly for an open canopy such as Zotino.

Optimal Canopy Assimilation
[31] Figure 7 reveals two interesting aspects of carbon assimilation in the Zotino canopy and how it is affected by the vertical distribution of Rubisco (leaf nitrogen): (1) The assimilation rate changes slowly for relatively large changes in k rub such that the value maximizing A c is poorly defined.For the 3-D configuration, for example, the maximum assimilation rate is only 6% higher compared to a zero redistribution in leaf nitrogen (k rub = 0).(Strictly speaking, this applies only to the LAI = 3.5 m 2 m À2 scenario.The same simulation run with the nitrogen-adjusted LAI = 1.3 m 2 m À2 model produces a corresponding gain of just 2%.) (2) Maximum assimilation does not occur when k rub = k ext ($0.8) as assumed in the Big Leaf approximation.For optimal assimilation in the 3-D canopy a slightly shallower vertical falloff is required (k rub $ 0.5), whereas a steeper Rubisco distribution (k rub $ 1.1) maximizes photosynthesis within the uniform 1-D stand.
[32] The smooth change in canopy assimilation rate can be attributed, in part, to the colimitation factors of the C 3 photosynthesis model which ensure a smooth transition from one limiting rate to another (e.g., the transition from a light-limited to a Rubisco-limited regime).These factors are present in the model to reflect observed leaf behavior.The large dispersion in leaf irradiance, which is expected to occur for foliage of different geometrical orientations (Figure 1), also limits the advantage that any one distribution of Rubisco may confer to the canopy assimilation rate (leaves in full sunlight will nearly always be Rubiscolimited whatever the vertical distribution in leaf nitrogen).The shallow Rubisco gradient required for the 3-D canopy can be explained by the shape of the trees.Optimal configuration requires a compromise between lightattenuation (k ext ) and the amount of foliage available to absorb PAR.The latter is maximum at the midheight of the canopy.The 1-D canopy removes all considerations of tree shape and here the optimal Rubisco distribution is much steeper.Thus in the 1-D scenario k rub > k ext and this steep, optimal Rubisco distribution is explained by a vertical falloff in leaf irradiance which is actually somewhat steeper for a spherical LAD compared to flat leaves (k ext in equation ( 8) refers to the horizontal plane).This difference can be attributable to the component of diffuse light which has a distribution of photon angles which changes significantly between the top and bottom of the canopy.In particular, sky photons impinging obliquely with respect to the horizontal plane at the top of the canopy are absorbed preferentially by foliage situated near the canopy ceiling.The result is that when diffuse light constitutes an important fraction of sky radiance the exponential falloff in leaf irradiance is slightly steeper than that indicated by light attenuation in the horizontal plane.This point underlines the likelihood that vertical profiles of light extinction are, in any case, unlikely to be purely exponential in the field [e.g., Parker et al., 2002].Similarly, leaf nitrogen may also deviate from an exponential vertical decline [Warren and Adams, 2001;Meir et al., 2002].Such considerations compound the difficulty of quantifying light acclimation within ''real'' tree canopies.

Conclusions
[33] Our main conclusions can be summarized as follows: [34] 1.We have enhanced the numerical, ray-tracing simulation FLIGHT to calculate photosynthesis in 3-D heterogeneous tree canopies.The primary variables of the model are leaf area index, air temperature, and photosynthetically active radiation incident at the top of the canopy.Measurements of canopy transpiration and air humidity regulate stomatal conductance.For the minimum and maximum LAI recorded for the site (1.3 m 2 m À2 and 3.5 respectively), the expanded model reproduces well the canopy assimilation measured for a Siberian pine forest (Zotino) where carbon flow has been monitored extensively with multiple eddy-covariance devices.The r.m.s.difference between model and observation is 12% across the full range of sky radiance.The minimum LAI scenario requires adjustments to the two physiological parameters controlling leaf photosynthesis in the simulation (quantum efficiency and top-leaf nitrogen).However, these modifications appear reasonable within the uncertainties of leaf properties for the site.
[35] 2. For the same sky radiance, the observed canopyassimilation at Zotino is only modestly enhanced, if at all ( 10%), under diffuse sky radiance compared to direct sunlight.Similarly, our simulations predict an enhancement of only 10-20% in canopy LUE when the proportion of diffuse sky radiation is 75% compared to 25%.Thus in contrast to the findings of previous authors, monitoring both broadleaf and needleleaf canopies [Hollinger et al., 1994;Gu et al., 2002;Niyogi et al., 2004], we believe the Zotino pine stand does not assimilate more carbon on overcast days compared to seasonally equivalent sunny days.The enhancement in LUE under diffuse sky radiance arises from (1) absorption of photons closer to the canopy top where Rubisco capacity is higher and (2) an increase in the fraction of foliage exposed to moderate light levels.
[36] 3. The scale-up from leaf model to observed canopy photosynthesis, in mmol m À2 s À1 , is less than unity.The former assumes a (hypothetical) flat leaf of 1 m 2 situated at the canopy top.The Big Leaf approximation, based on Beer's law for light attenuation and a light-acclimated Rubisco distribution, implies scale-up factors of 1.24.It overestimates the observed canopy response by 24% on average, i.e., twice the r.m.s.error of the FLIGHT simulation.The overprediction is particularly severe (!50%) at low sky radiance ( 500 mmol m À2 s À1 ).
[37] 4. Our RT model allows us to prescribe the vertical fall-off in Rubisco concentration through the canopy.To reproduce the canopy-assimilation observed at Zotino, we require a Rubisco gradient which is shallower than the gradient of the corresponding light profile.According to our simulations, the canopy assimilation-rate varies only slightly for relatively large changes in the vertical distribution of Rubisco (assuming conservation of total active leaf nitrogen).This is due to the colimitation factors of our C 3 leaf model which reflect the observed smooth transition from one limiting rate to another for individual leaves (e.g., light-limited to Rubisco-limited regime).Furthermore, the high dispersion in leaf irradiance at any depth within the canopy, which can be expected for foliage possessing a range of geometrical orientations, reduces the benefit that any particular configuration in leaf nitrogen might confer to the stand.Our 3-D simulations of Zotino imply that assimilation is only 2 -6% higher when Rubisco is distributed so as to maximize canopy photosynthesis compared to a vertically uniform distribution in leaf nitrogen.Furthermore, even when leaf nitrogen is configured optimally, the implied Rubisco gradient is shallower than that of the light gradient due to the concentration of foliage at the midheight of the canopy.

Appendix A
[38] Our photosynthesis model follows the Collatz formulation for C 3 type vegetation [Collatz et al., 1991].The leaf photosynthetic rate A l (mmol m À2 s À1 ) is the smoothed minimum of three limits: photosynthetic rate due to incident light J PAR ; photosynthetic capacity due to the concentration and chemical activity of Ribulose-1,5-bisphosphate carboxylase/oxygenase (i.e., Rubisco) J r ; and the photosynthetic rate based on the ability of the leaf to export the products of photosynthesis J e .Thus where the quantum efficiency a is a dimensionless, physiological parameter describing the quasi-linear response of leaf photosynthesis to low light levels.I PAR (mmol m À2 s À1 ) is the leaf irradiance.C i (mol mol À1 ) and C 0 (mol mol À1 ) are the CO 2 concentration internal to the leaf and the photorespiratory compensatory point, respectively.The latter depends on the ambient oxygen concentration O a (mol mol À1 ) and the leaf temperature T l (K).Thus The Rubisco-limited rate of leaf photosynthesis is given by where K c (mol mol À1 ) and K o (mol mol À1 ) are the Michaelis constants determining the competing rates of carboxylation and oxygenation.Although denoted as ''constants'' both of these parameters depend on leaf temperature.V m (mmol m À2 s À1 ) describes the chemical activity of Rubisco and is expressed thus: where q 10 is a dimensionless coefficient for leaf respiration which we set to 2.0.T lo (K) and T hi (K) are instrumental in limiting the temperature bandwidth over which photosynthesis is possible and we set these parameters to 268 K and 304 K, respectively, for the purposes of this study.The conclusions of this work remain independent of T lo and T hi .
Although J r can change by '10% for reasonable adjustments in these parameters, the impact on canopy photosynthetic rate is much less ($1%).V cmax (mmol m À2 s À1 ) is a physiological parameter of the plant which determines the Rubisco-limited rate of photosynthesis under optimal conditions of leaf temperature and the saturation of carboxylation sites within the leaf by CO 2 .It is proportional to the active nitrogen content of the leaf expressed as mol N per m 2 of leaf surface.Finally, the export-limited rate of leaf photosynthesis is determined by Leaf respiration is set to 0.015 Â V m [Collatz et al., 1991].
[39] Acknowledgments.We thank the BOREAS team for making available in a public archive their leaf measurements of Jack Pine.Similarly, we thank CARBOFLUX colleagues at MPIfB, Jena for archival data on diffuse light.Our sincere thanks to Jon Lloyd who made the carbon fluxes for Zotino available to us.

Figure 4 .
Figure 4.The canopy photosynthetic rate, A c , measured for the Scots Pine stand at Zotino during the June/July/ August period of 1999 (top) and 2000 (bottom).I 0 is the photosynthetically active radiation incident in the horizontal plane at the top of the canopy.Solid and open circles denote the estimated canopy assimilation rate under diffuse light conditions (fDIF !0.5) and under direct sunlight (fDIF < 0.5), respectively.The error bars represent the error in the mean ( ffiffiffiffiffiffiffiffiffiffiffiffi s:d:=n p ).

Figure 5 .
Figure 5. FLIGHT simulations of canopy photosynthetic rate at Zotino, A c , with low and high fractions of diffuse light (fDIF).The plot shows the same measurements as those plotted in Figure 4 for 1999, removing the error bars for clarity.The broken lines correspond to model predictions: (1) minimum foliage density (LAI = 1.3 m 2 m À2 ), (2) maximum foliage density (LAI = 3.5), and (3) a ''lightacclimated'' scenario with k rub = k ext (and LAI = 3.5).

Figure 7 .
Figure7.The predicted photosynthetic rate for the Zotino pine canopy, A c , with the Rubisco exponential parameter k rub ranging from 0 to 2. The total amount of leaf nitrogen within the canopy is conserved.Simulations are shown for an open 3-D stand with cover fraction 60% (solid lines) and a uniform, closed 1-D canopy (dashed lines) of the same LAI (3.5 m 2 m À2 ).In all cases, the fraction of diffuse sky radiance is 0.5 and the sun has a position of q s = 57°.Sky radiance (I 0 ) is either 500 mmol m À2 s À1 (solid circles) or 1000 (solid squares).
Sunlight incident at the top of the canopy is direct only (2000 mmol m À2 s À1 in the horizontal plane) and emanates from an overhead Sun.The dotted and solid lines trace the mean leaf irradiance according to Beer's Law and the FLIGHT simulation, respectively.The latter is slightly higher due to the treatment of scattered radiation as well as direct sunlight.below).I PAR (mmol m À2 s À1 ) is the PAR irradiance normal to the leaf surface.The quantum efficiency a (mol mol À1 ) is a physiological constant determining LUE in the light-linear (low I PAR ) regime.Under normal circumstances, and certainly during this study, the largest variation in J PAR arise due to variations in I PAR .

Table 1 .
Geographical and Structural Features of the Scots Pine Stand at Zotino a a Compiled from Lloyd et al. [2002]; Wirth et al.

Table 2 .
Mean Environmental Variables for the Zotino Canopy During the JJA Period of 1999 a n hI 0