Incorporating diffuse photosynthetically active radiation in a single-leaf model of canopy photosynthesis for a 56-year-old Douglas-fir forest

A simple top-down model of canopy photosynthesis (P) was developed and tested in this study. The model (referred to as the Q_e-MM model) is P = αQ _e P _max/(αQ _e + P _max), α and P _max are quantum-use efficiency and potential P, respectively. Q _e is given by Q _{d 0} + kQ _{b 0}, where Q _{d 0} and Q _{b 0} are the diffuse and direct photosynthetically active radiation (PAR) incident on the canopy, respectively. Q _e can be considered to be the effective incident PAR contributing to P and k is a measure of the contribution of Q _{b 0} to Q _e. When k = 1, the Q_e-MM model becomes the regular Michaelis-Menten type model of P (referred to as the MM model). A major objective of this study was to determine how well the Q_e-MM model could estimate P of a 56-year-old coastal Douglas-fir stand. To this end, we parameterized the Q_e-MM model using five and half years of eddy-covariance measurements of CO₂ flux above the Douglas-fir stand. The Q_e-MM model, with the incorporation of a function of air temperature, accounted for 74% of the variance in over 34,000 half-hourly P measurements. P estimated using the Q_e-MM model had no systematic errors with respect to Q _{d 0}. Although the Q_e-MM model has only one more parameter than the MM model, it accounted for 30% more variance in P than the latter when total incident PAR exceeded 900 μmol m⁻² s⁻¹. On average, k was found to be 0.22. We show that this small value of k reflects the significant effect of the scattering of the solar beam and the fraction of light-limited sunlit leaves. We also show that the success of the Q_e-MM model was due to the fact that a large fraction of the sunlit leaves were light-limited as a result of their orientation to the solar beam.

Funding for this study was provided by a Forest Renewal British Columbia (FRBC) grant from the British Columbia Science Council, a Natural Sciences and Engineering Research Council (NSERC) research operating grant, a NSERC strategic projects grant, and through funding for the Fluxnet-Canada Research Network (NSERC, BIOCAP, Canadian Foundation for Climate and Atmospheric Sciences). T.C. received support through an NSERC Postgraduate Scholarship and a University Graduate Fellowship (UGF) from the University of British Columbia. We sincerely thank Profs. John Norman (University of Wisconsin), Jan Goudriaan (Wageningen University) and Michael Unsworth (Oregon State University) for their extremely insightful comments on an earlier draft of this manuscript. Their comments greatly improved the quality of this paper.

Authors and Affiliations

1. Faculty of Land and Food Systems, University of British Columbia, Vancouver, BC, Canada

   Tiebo Cai, Andrew Black, Rachhpal S. Jassal, Kai Morgenstern & Zoran Nesic

Corresponding author

Correspondence to Tiebo Cai.

Appendix: list of symbols and acronyms

γ :

angle of incidence between the solar beam and a normal to the leaf surface

\(\overline {\cos \gamma _1 } \) :

average of all the cosγ values for all the light-limited sunlit leaves

γ _Threshold :

maximum angle of incidence below which sunlit leaves become light-saturated

\(\overline {\cos \gamma _{Threshold} } \) :

average of all the cos γ _Threshold values at different canopy depth ℓ

\(\overline {\Delta \cos \gamma _{Threshold} } \) :

difference between \(\overline {\cos \gamma } \) for the light-saturated sunlit leaves and \(\overline {\cos \gamma _{Threshold} } \)

f _shd(ℓ):

fraction of the shaded leaves at canopy depth ℓ

f _{sun_LightLimited}(ℓ):

fraction of the light-limited sunlit leaves at canopy depth ℓ

f _{sun_LightSaturated}(ℓ):

fraction of the light-saturated sunlit leaves at canopy depth ℓ

α :

quantum-use efficiency, μmol (CO₂) μmol⁻¹ (quanta)

α ₀ :

quantum-use efficiency as used in the LUE model, μmol μmol⁻¹

α _d, α _b :

quantum-use efficiency for diffuse PAR (α _d) and direct PAR (α _b), respectively as used in the m-MM model, μmol (CO₂) μmol⁻¹ (quanta)

α _M :

quantum-use efficiency for total PAR as used in the MM model

β :

solar elevation angle

σ :

leaf scattering coefficient for PAR including reflected and transmitted PAR

σ′:

canopy scattering coefficient

ϕ :

a curvature parameter for the photosynthetic light response curve

A _j :

rate of photosynthesis limited by RuBP regeneration, μmol m⁻² s⁻¹

A _v :

rate of photosynthesis limited by Rubisco, μmol m⁻² s⁻¹

D :

vapour pressure deficit, kPa

F _C :

half-hourly CO₂ flux, μmol m⁻² s⁻¹

F _S :

rate of change in CO₂ storage (the “storage flux”) in the air column beneath the eddy-covariance sensors, μmol m⁻² s⁻¹

k :

a fraction of Q _{d 0} added to Q _{b 0} to give Q _e, i.e., Q _e = Q _{d 0} + kQ _{b 0}

k ₀ :

a fraction used to modify α

k ₁ :

fraction of the sunlit leaves that are light limited

K _b :

extinction coefficient for direct PAR assuming total absorption of PAR

\(K_b^\prime \) :

extinction coefficient for direct PAR for green leaves, \(K_b \prime = K_b \sqrt {1 - \sigma } \)

K _n :

vertical nitrogen extinction coefficient as used in the sun/shade model

LAI and L :

leaf area index, m² (leaf area) m⁻² (ground area)

L _sun :

total LAI for sunlit leaves

L _{sun_LightLimited} :

total LAI for light-limited sunlit leaves

L _{sun_LightSaturated} :

total LAI for light-saturated sunlit leaves

ℓ :

cumulative LAI from canopy top. ℓ was used as a variable in scaling photosynthesis from leaf-level to canopy-level

NEE:

net ecosystem exchange, μmol m⁻² s⁻¹

NEP:

net ecosystem production, μmol m⁻² s⁻¹

P :

rate of canopy photosynthesis (same as gross ecosystem photosynthesis), μmol m⁻² s⁻¹

PAR:

photosynthetically active radiation, μmol m⁻² s⁻¹

P _max :

potential photosynthesis rate (the asymptote) as used in the MM and Q_e-MM models, μmol m⁻² s⁻¹

P _maxd, P _maxb :

P _max for diffuse PAR (P _maxd) and direct PAR (P _maxb), respectively as used in the m-MM model, μmol m⁻² s⁻¹

P _sun :

total photosynthesis of all the sunlit leaves, μmol m⁻² s⁻¹

P _{sun_LightLimited} :

total photosynthesis of all the light-limited sunlit leaves, μmol m⁻² s⁻¹

P _{sun_LightSaturated} :

total photosynthesis of all the light-saturated sunlit leaves, μmol m⁻² s⁻¹

Q _b(γ):

un-scattered direct PAR absorbed by a sunlit leaf at the angle of incidence of γ, μmol m⁻² s⁻¹

Q _{b 0} :

incident direct PAR above the canopy, μmol m⁻² s⁻¹

Q _{b 1}(γ):

un-scattered direct PAR absorbed by the light-limited sunlit leaves, μmol m⁻² s⁻¹

Q _{ba_sun} :

un-scattered direct PAR absorbed by the big sunlit leaf as in the sun/shade model, μmol m⁻² s⁻¹

Q _bThreshold :

maximum un-scattered direct PAR absorbed by a light-limited sunlit leaf at canopy depth ℓ (see Fig. 1b), Q _bThreshold = max[Q _{b 1}(γ)], μmol m⁻² s⁻¹

ΔQ _bThreshold :

difference between the un-scattered direct PAR absorbed by the light-saturated sunlit leaves and Q _bThreshold (i.e., ΔQ _bThreshold = Q _b(γ) − Q _bThreshold), μmol m⁻² s⁻¹

Q _d(ℓ):

absorbed sky diffuse PAR at canopy depth ℓ, μmol m⁻² s⁻¹

Q _{d 0} :

incident sky diffuse PAR above the canopy, μmol m⁻² s⁻¹

Q _e :

effective amount of PAR contributing to P (Q _e = Q _{d 0} + kQ _{b 0}), μmol m⁻² s⁻¹

Q _p :

amount of direct PAR perpendicular to the solar beam, μmol m⁻² s⁻¹

Q _s(ℓ):

absorbed scattered direct PAR at canopy depth ℓ, μmol m⁻² s⁻¹

Q _sat :

the amount of Q _ta at canopy depth ℓ above which the quantum-use efficiency for absorbed PAR decreases (see Fig. 1b), Q _sat = Q _d(ℓ) + Q _s(ℓ) + Q _bThreshold, μmol m⁻² s⁻¹

Q _{t 0} :

incident total PAR above the canopy, μmol m⁻² s⁻¹

Q _ta :

absorbed total PAR, μmol m⁻² s⁻¹

Q _x :

Q _x = Q _{d 0} + xQ _{b 0}, used in Fig. 2 to test the effect of adding varying fractions of Q _{d 0} to Q _{b 0} on canopy P, when x = k, Q _x = Q _e, μmol m⁻² s⁻¹

r ² :

coefficient of determination

Rubisco:

ribulose-1,5-biphosphate carboxylase/oxygenase

RuBP:

ribulose biphosphate

s _c :

CO₂ mixing ratio, mol CO₂ mol⁻¹ of dry air

T _a :

air temperature, °C

V _{cmax 25} :

Rubisco capacity at 25°C as used in the sun/shade model, μmol m⁻² s⁻¹

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