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Modelling the diurnal course of photosynthesis in oak leaves (Quercus robur L.) requires appropriate description of the dynamics of leaf photosynthesis of which diurnal variations in leaf conductance and in CO2 assimilation are essential components. We propose and analyse a simple photosynthesis model with three variables: leaf conductance (gs), the CO2 partial pressure inside the leaf (pi), and a pool of Calvin cycle intermediates (aps). The environmental factors light (I) and vapour pressure deficit (VPD) are used to formulate a target function G(I, VPD) from which the actual leaf conductance is calculated. Using this gs value and a CO2 consumption term representing CO2 fixation, a differential equation for pi is derived. Carboxylation corresponds to the sink term of the pi pool and is assumed to be feedback-inhibited by aps. This simple model is shown to produce reasonable to excellent fits to data on the diurnal time courses of photosythesis, pi and gs sampled for oak leaves.
Noe et al. (2004) studied this question.