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 (Ac) is expected to facilitate effective farm management. For the estimation of Ac, 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 (AL) and leaf area index (LAI) were first estimated from information easily obtainable at farming sites: AL was estimated by the process-based model of AL (i.e., the biochemical photosynthesis model of Farquhar et al. (1980)) from environmental data (photosynthetic photon flux density (PPFD), air temperature (Ta), humidity, and atmospheric CO2 concentration (Ca)), and the LAI was estimated by an analysis of crop canopy imagery. As highly explainable information for Ac, the estimated AL and LAI were input into the ANN model to estimate Ac. As such, the ANN model learned the logical relationships between the inputs (AL and LAI) and the output (Ac). Detailed validation analysis using nine spinach Ac datasets revealed that the hybrid ANN model can estimate Ac 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.
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