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Joining Leaf Photosynthesis Models and Canopy Photon-Transport Models

  • V. P. Gutschick
Chapter

Abstract

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.

Keywords

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.

Symbols

a

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

amaint

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

A

conversion factor from moles of CO2 to g glucose in photosynthesis

b

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

Bcc

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

CDM

complex dry matter

Ca CO2

concentration in ambient air (mol m-3)

Ci CO2

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

CL CO2

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

Cv

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

d0

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

D

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

D0

same, at top of canopy

DMA

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

eL

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

esat

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

Ecan

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

ĒL,a

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

Esoil

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

F0

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

FL

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

gs

stomatal conductance per unit leaf area (ms-1)

G

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

average canopy height (m)

hj

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 (-)

AHvap

heat of vaporization of water (Jmol-1)

k

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

L

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

Lh

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

Ltot

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

LAI

leaf area index

M

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

MCDM

mass of complex dry matter (kg)

MPSate

mass of raw photosynthate (kg)

NIR

near infrared

nCO2

moles of CO2 gas released in respiration

p(JL)

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

ppen

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

psf

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

Pcan

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

PL,a

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

L,a

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

PmaxL,a

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

PAR

photosynthetically active radiation

QU, QH

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

cc

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

E

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

Qnet

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

Q+sw

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

Q±TIR

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

ra

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

rs

stomatal resistance to CO2 transport (s m-1)

Rmaint

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

Rsyn

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

Rubisco

ribulose 1,5 bisphosphate carboxylase/oxygenase

stotal

total optical path length (m)

So

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

Soo

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

T

temperature (°C or K)

Topt

optimal temperature for photosynthesis (°C or K)

Ta

temperature of ambient air (°C or K)

Tleaf

leaf temperature (°C or K)

TIR

thermal infrared radiation

w

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

WUE

water-use efficiency

x

lateral position in canopy (m)

Δx

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

z

depth in canopy (m)

β

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

δ

Dirac delta function

ε

thermal infrared emissivity (—)

ζ

random variate (-)

θ

zenith angle (degrees or radians)

θL

leaf zenith angle

θo

solar zenith angle

µd, µo

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

ρDMA

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

ρodpDMA

optimal distribution of ρDMA to maximize canopy photosynthesis

σ

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

φdLo

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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