Joining Leaf Photosynthesis Models and Canopy Photon-Transport Models

  • V. P. Gutschick


The photosynthetic rate of a leaf or a canopy is determined largely by radiation, particularly photosynthetically active radiation, PAR, comprising the 400 to 700 nm band. In order to estimate canopy photosynthesis, Pcan, one must predict PAR irradiances on all the inclined leaf surfaces and one must have a model for responses of individual leaves to irradiance. For the moment, we may ignore the phenomena of temperature dependence of photosynthesis (in which total radiative energy balance plays a key role) and of transient responses in photosynthesis. We then turn our attention to predicting PAR irradiance on individual leaves, FL, from radiative-transfer models that typically estimate radiant flux densities (or angularly resolved radiances) at given spatial locations or only as lateral averages over sunflecks and shaded areas. The problem has traditionally been difficult (Anderson and Denmead 1969) but it is far from intractable. With modern computing facilities even at the level of a personal computer, the resolution is straightforward, with some subtleties. Details can be tedious but they are largely resolved once and for all.


Photosynthetic Rate Leaf Area Index Solar Zenith Angle Leaf Angle Canopy Photosynthesis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



logarithmic slope of temperature dependence of maximal photosynthetic rate [Eqs. (37), (41)] (K-1)


coefficient of maintenance respiration [g glucose (g dry matter)-1 d-1]


conversion factor from moles of CO2 to g glucose in photosynthesis


logarithmic slope of temperature dependence of maximal photosynthetic rate [Eq. (37)] (K-1)


coefficient of convective-conductive heat transfer (Wm-2 K-1)


complex dry matter

Ca CO2

concentration in ambient air (mol m-3)

Ci CO2

concentration in leaf interior air space (mol m-3)


concentration in air at leaf surface (mol m-3)


coefficient of variation of plant height (Sect. 3) (-)


radiance of diffuse skylight (mol m-2 s-1 sr-1)


radiant flux density of diffuse skylight (mol m-2 s-1)


same, at top of canopy


dry matter per unit leaf area (kg m-2)


water-vapor concentration at leaf surface (mol m-3)


water-vapor concentration at saturation (mol m -3)


canopy transpiration rate (mol m-2 s-1)


average transpiration rate per unit leaf area at a given canopy depth (molm-2s-1)


soil evaporation rate (mol m-1 s-1)


average radiant flux density from direct solar beam (molm-2 s-1)


irradiance on leaf (mol m-2 s-1)


stomatal conductance per unit leaf area (ms-1)


average fractional projection of leaf area along a direction (-)

average canopy height (m)


canopy height at location of cell j (m)

H(L), H’(L)

penetration function for diffuse skylight, and its derivative with respect to cumulative leaf area index (-)


heat of vaporization of water (Jmol-1)


vertical attenuation coefficient of radiant flux density in canopy (-)


cumulative leaf area index (-, or m2m2 leafm-2 ground)


characteristic depth in L over which solar tracking ability of leaves declines (-)


total leaf area index (-, or m2 leafm-2 ground)


leaf area index


dry biomass per unit ground area (kg m-2) or total plant mass (kg)


mass of complex dry matter (kg)


mass of raw photosynthate (kg)


near infrared


moles of CO2 gas released in respiration


probability of irradiance on a leaf having value JL(-)


probability of a ray penetrating to a given canopy depth (-)


probability of leaf area being irradiated by direct beam (sunfleck) (-)


canopy photosynthetic rate (mol m-2 s-1)


leaf photosynthetic rate (mol m-2 s-1)


average value of PL,a at a given depth (mol m-2 s-1)


light-saturated rate of photosynthesis per unit leaf area (molm-2 s-1)


photosynthetically active radiation


quantum yields of photosynthesis for uniform leaf angle distribution(U) or for horizontal leaves (H) [mol CO2 mol photons)-1]


rate of sensible heat loss by conduction and convection, per unit leaf area (Wm-2 s-1)


rate of latent heat loss by transpiration (Wm-2)


initial quantum yield of photosynthesis at low irradiances [mol CO2 (mol photons)-1]


rate of leaf energy gain from absorption of shortwave radiation (Wm-2)


rate of leaf energy gain (loss) from absorption (emission) of thermal infrared radiation (Wm-2)


resistance of leaf boundary layer to CO2 transport (s m-1)


stomatal resistance to CO2 transport (s m-1)


rate of CO2 loss from maintenance processes (mol m-2 s-1 or mol d-1)


rate of CO2 loss from biosynthetic processes (mol m-1 s-1 or mold-1)


ribulose 1,5 bisphosphate carboxylase/oxygenase


total optical path length (m)


direct-beam radiant flux density (mol m-2 s-1)


direct-beam radiant flux density, perpendicular to its direction of propagation (mol m-2 s-1)


temperature (°C or K)


optimal temperature for photosynthesis (°C or K)


temperature of ambient air (°C or K)


leaf temperature (°C or K)


thermal infrared radiation


weighting of diaheliotropic response [Eq. (3)] (-)


water-use efficiency


lateral position in canopy (m)


lateral dimension of hypothetical cells in canopy that differ in height (m)


depth in canopy (m)


conversion efficiency from photosynthate to complex dry matter [-, or kg dry matter (kg glucose)-1]


Dirac delta function


thermal infrared emissivity (—)


random variate (-)


zenith angle (degrees or radians)


leaf zenith angle


solar zenith angle

µd, µo

cosine of zenith angle for diffuse skylight component or for direct beam (-)


dry matter per unit leaf area (kg m-2)


optimal distribution of ρDMA to maximize canopy photosynthesis


Stefan-Boltzmann constant (W m-2 K-4)


azimuthal angle for diffuse skylight component, leaf normal, or direct solar beam (degrees or radians)

Ω̱d, Ω̱L, Ω̱o

zenith-azimuth angle pair for diffuse skylight component, leaf normal, or direct solar beam


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© Springer-Verlag Berlin Heidelberg 1991

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  • V. P. Gutschick

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