Approximating the Photosynthesis Curve
by
Simon Woodward
AgResearch, Hamilton, Private Bag 3123

Fifty years of research into the photochemistry used by plants to convert atmospheric CO₂ into soluble carbohydrates has given us a simple non-rectangular hyperbola model for the photosynthesis of a leaf:

Pl(Jl) =   1 2\theta ì í î \alphaJl + Pm -    Ö   (\alphaJl + P m) -4\thetaJl Pm   ü ý þ

where P_l is the rate of photosynthesis of a leaf, J_l is the intensity of light on the leaf, P_m is the maximum rate of leaf photosynthesis, \alpha is the efficiency of photosynthesis at low irradiances, and \theta is a curvature parameter.

The daily gross photosynthesis of a whole plant canopy (P_d) is then given by the integral of this model over all of the leaves in the canopy:

Pd = ó õ L 0  (h - h0, se-kl)Pl(kJ0, de-kl) + h0, se-klPl(kJ0, s + kJ0, de-kl)  dl

where L is the leaf area index of the canopy, k is the Beer's Law extinction coefficient of the canopy, h is the daylight hours, h_{0, s} is the sunshine hours, J_{0, d} is the intensity of diffuse light at the top of the canopy, and J_{0, s} is the intensity of direct sunlight.

All of these non-linearities mean that calculation of canopy photosynthesis, which is needed if plant growth is going to be predicted, is computationally expensive. In this talk I will describe the successes and failures I have had in trying to arrive at an approximation for this integral that works with real data, in order to calculate pasture growth on New Zealand farms.

Date received: June 7, 1998