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 ($C_{\mathrm{a}}$)), 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.

作物生产力很大程度上取决于冠层光合作用，这在农田很难测量。因此，实时估计冠层光合速率 ( A _c ) 有望促进有效的农场管理。对于A _c的估计，有两种数学模型（即.、基于过程的模型和经验模型）已被使用，尽管这两种类型都有自己的弱点。基于过程的模型不可避免地需要许多难以识别的模型参数，而经验模型，包括人工神经网络 (ANN) 模型，在训练数据集范围之外具有较低的预测能力。为了克服这些弱点，我们开发了一种混合冠层光合作用模型，其中包括基于过程的模型和 ANN 模型的组件。在这个混合模型中，单叶光合速率 ( A _L ) 和叶面积指数 (LAI) 首先是根据在农田容易获得的信息估算的：A _L是通过基于过程的A _L模型估算的（即., Farquhar等人的生化光合作用模型。(1980)) 来自环境数据（光合光子通量密度 (PPFD)、气温 ( T _a )、湿度和大气 CO ₂浓度 ($C_{\mathrm{一个}}$))，并通过分析作物冠层图像来估计 LAI。作为A _c的高度可解释信息，估计的 A _L和 LAI 被输入到 ANN 模型中以估计A _c。因此，ANN 模型学习了输入（A _L和 LAI）和输出（A _c）之间的逻辑关系。使用九个菠菜A _c数据集的详细验证分析表明，混合 ANN 模型可以在整个生长期准确估计A _{c ，即使在不同季节获得不同 CO 2下的训练和测试数据集也是如此}浓度并基于仅三天的训练数据集。本研究强调了混合人工神经网络模型的高度概括性，这是在环境控制作物生产中实际应用的先决条件。