A canopy photosynthesis model based on a highly generalizable artificial neural network incorporated with a mechanistic understanding of single-leaf photosynthesis

Crop productivity is largely dependent on canopy photosynthesis, which is difficult to measure at farming sites. Therefore, real-time estimation of the canopy photosynthetic rate (A_c) is expected to facilitate effective farm management. For the estimation of A_c, two types of mathematical models (i.e., process-based models and empirical models) have been used, although both types have their own weaknesses. Process-based models inevitably require many model parameters that are difficult to identify, while empirical models, including artificial neural network (ANN) models, have a low predictive ability outside of the range of training datasets. To overcome these weaknesses, we developed a hybrid canopy photosynthesis model that included components of both process-based models and ANN models. In this hybrid model, the single-leaf photosynthetic rate (A_L) and leaf area index (LAI) were first estimated from information easily obtainable at farming sites: A_L was estimated by the process-based model of A_L (i.e., the biochemical photosynthesis model of Farquhar et al. (1980)) from environmental data (photosynthetic photon flux density (PPFD), air temperature (T_a), humidity, and atmospheric CO₂ concentration (C_a)), and the LAI was estimated by an analysis of crop canopy imagery. As highly explainable information for A_c, the estimated A_L and LAI were input into the ANN model to estimate A_c. As such, the ANN model learned the logical relationships between the inputs (A_L and LAI) and the output (A_c). Detailed validation analysis using nine spinach A_c datasets revealed that the hybrid ANN model can estimate A_c accurately throughout the whole growth period, even when training and test datasets were obtained in different seasons under different CO₂ concentrations and based on training datasets of only three days. This study highlights the high generalizability of the hybrid ANN model, which is a prerequisite for practical application in environmentally controlled crop production.