However, to date, no study has yet estimated leaf photosynthetic capacity using a DNN model based on leaf reflectance. Hence, the objectives of this study are to assess the feasibility of predicting the photosynthetic capacity from leaf reflectance in cool–temperate deciduous forests by employing DNN models; to assess the performance of DNN models across different leaf types and different temporal scales; to evaluate whether including other leaf traits would improve the estimation of leaf photosynthetic capacity using DNN models. This study explores the potential of deep learning for predicting photosynthetic capacities quantitatively in different leaf types and during different growing periods in cool–temperate deciduous forests. A DNN model is generally composed of an input layer, an output layer, and several hidden layers placed between them, and each layer contains a number of neurons. In this study, leaf reflectance data were considered as predictors of Vcmax and Jmax when constructing the deep neural network.

The workflow is illustrated in Figure 2. The entire dataset was then randomly divided into training data and test data , while the training dataset was further arranged to be in proportion to the validation data. Specifically, the networks had the following architecture: an input layer, seven hidden layers with 16, 32, 64, 128, 256, 128, and 64 neurons, respectively, and an output layer, with the nodes being fully connected. The loss and optimization functions selected were the mean square error and the Adam optimizer, respectively. The number of training epochs was defined using early stopping; the networks were trained for 500 epochs, with the patience equal to 20 epochs, to minimize the loss function until the minimum error was achieved to prevent overfitting. Furthermore, dropout , which is a regularization technique that randomly and temporarily removes a fixed proportion of different neurons and their respective connections from the network in each training step, was also used to avoid complex co-adaptations on training data, therefore reducing overfitting. The deep neural networks were builtand trained with the TensorFlow backend, using the Keras library in RStudio . To improve the generality and predictive performance of the DNN model, a bootstrap approach was applied for the training dataset in this study.

Bootstrapping is a resampling method that samples independently with replacement from a sample dataset with the sample size, which reduces biases and strengthens the robustness, especially when the number of samples is limited . Specifically, we randomly sampled the training set with replacement k times; the maximum k value was set to 50 and the best k value was selected based on the mean squared error. The DNN model was fitted using a bootstrap sample each time and prediction values fromFurthermore, we explored the robustness of the DNN models for predicting the photosynthetic capacity with different leaf groups. The modeling performances for Vcmax and Jmax of the DNN model for sunlit leaves were much higher than those for shaded leaves. The differences in leaf groups can be explained by the differences in their responses to the photosynthesis process and/or the changes in leaf properties such as the leaf mass per area, and the light environment throughout the vertical profile. Taking the sunlit and shaded leaf groups into consideration is helpful for improving the estimation of carbon and water fluxes. In addition, the performance using the DNN models in estimating Vcmax and Jmax was notably the best during the leaf flushing period, followed by the senescence period, with the poorest performance occurring during the maturity period.

As reported by previous studies, leaf flushing and senescence are accompanied by a strong increase and decline in photosynthetic capacity, while leaf maturity is relatively stable with minor changes . A more likely explanation is that the spectra–photosynthetic capacity linkages could vary with leaf age. The results suggest that including as many axes of variation as possible is critical in tracing the photosynthetic capacity using spectral information.Our results showed that using only leaf hyperspectral reflectance, it is possible to capture a large variety of photosynthetic traits. However, combining other leaf biophysical/biochemical traits could further improve the estimation accuracy of photosynthetic traits using DNN models, since our results clearly indicated that the estimation accuracy of Vcmax from reflectance using DNN models was much improved by the addition of the leaf chlorophyll content for sunlit leaves. Leaf chlorophyll is an important component of the photosynthesis machinery that harvests light and transports electrons to support the production of the biochemical energy necessary to drive photosynthesis , and it is an important indicator of physiological status .