Incorporating diurnal light variation and canopy light attenuation into analytical equations for calculating daily gross photosynthesis

Calculating daily gross photosynthesis for a crop growth model requires a technique to integrate the single-leaf photosynthetic response to light flux density through leaf canopy and diurnal light distribution patterns. The objective of this study was to derive analytical solutions of the rectangular hyperbola for calculating daily gross photosynthesis. The photosynthesis model was evaluated using two approaches for light variation within canopy. Combinations of the unattenuated or attenuated light flux density and one of three approximations of diurnal light distributions, namely constant, triangular or sine-curve distribution, were used in the evaluation. Five analytical solutions were derived from the six combinations. The approaches to diurnal light distributions were validated using recorded data, while validations of these equations were based on the comparison of the daily gross photosynthesis predicated from these approaches with that numerically calculated from recorded light flux density, i.e., experimental data of daily gross photosynthesis were not used. Triangular approximation was the most reliable among the three approaches, hence two analytical equations associated with this approach may be used for modelling. One was derived from the unattenuated light flux density which is applicable to the plant growth model when the leaf area index is small. A second derived from the light attenuation approach is the more general equation and can be incorporated into the model when light attenuation occurs.