A constrained depth-resolved artificial neural network model of marine phytoplankton primary production

Marine phytoplankton primary production is a process of paramount importance not only in biological oceanography, but also in a wider perspective, due to its relationship with oceanic food webs, energy fluxes, carbon cycle and Earth’s climate. As field measurements of this process are both expensive and time consuming, indirect approaches, which can estimate primary production from remotely sensed imagery are the only viable solution. We developed a depth-resolved model of marine phytoplankton primary production using an Artificial Neural Network, namely a three-layer perceptron trained with the Error Back-Propagation algorithm. Despite numerous variables could be useful to estimate primary production, we chose to use predictive variables that can be acquired by remote sensing in order to enhance the practical value of the model. Indeed, using exclusively this type of predictors in combination with a depth-resolved approach allows to expand the two-dimensional view from satellite images to the estimated three-dimensional distribution of phytoplankton primary production. Since the vertically integrated values of this process are the basis for any connection to other levels of the pelagic food web, it is worth noting that, once integrated, the primary production estimates of this depth-resolved model are more accurate than those obtained from a similar vertically integrated approach. We also tried to improve the accuracy of the primary production estimates using constraints during the training procedure. Those constraints were based on theoretical knowledge of the marine photosynthesis process. Accordingly, the training phase has been modified in order to add penalty terms to the solutions which were not compliant with the constraints. For instance, one of the constraints acts as a selection tool for the shape of the modelled production profile. The above-mentioned approach not only enhanced the ecological soundness of the artificial neural network predictions. In fact, the constrained version of the model also explained a larger share of variance than the original one