Instantaneous canopy photosynthesis: analytical expressions for sun and shade leaves based on exponential light decay down the canopy and an acclimated non-rectangular hyperbola for leaf photosynthesis

Analytical expressions for the contributions of sun and shade leaves to instantaneous canopy photosynthesis are derived. The analysis is based on four assumptions. First, that the canopy is closed in the sense that it is horizontally uniform. Secondly, that there is an exponential profile of light down the canopy with the same decay constant for light from different parts of the sky. Thirdly, that the leaf photosynthetic response to incident irradiance can be described by a three-parameter non-rectangular hyperbola (NRH). And lastly, that light acclimation at the leaf level occurs in only one parameter of the NRH, that describing the light-saturated photosynthetic rate, which is assumed to be proportional to the local averaged leaf irradiance. These assumptions have been extensively researched empirically and theoretically and their limitations are quite well understood. They have been widely used when appropriate. Combining these four assumptions permits the derivation of algebraic expressions for instantaneous canopy photosynthesis which are computationally efficient because they avoid the necessity for numerical integration down the canopy. These are valuable for modelling plant and crop ecosystems, for which canopy photosynthesis is the primary driver. Ignoring the sun/shade dichotomy can result in overestimates of canopy photosynthesis of up to 20 %, but using a rectangular hyperbola instead of a non-rectangular hyperbola to estimate canopy photosynthesis taking account of sun and shade leaves can lead to a similarly sized underestimate.