Developing an empirical model of phytoplankton primary production: a neural network case study (1998).

Michele Scardi° and Lawrence W. Harding, Jr.*

° Stazione Zoologica "A. Dohrn" di Napoli, Villa Comunale, 80121 Napoli, Italy
* University of Maryland, Horn Point Laboratory (UMCES) and Maryland Sea Grant, Box 775, Cambridge, Maryland 21613

During the last two years, several models of phytoplankton primary production (PP) have been developed by applying neural networks to shipboard data from Chesapeake Bay. The first models were intended as simple tests of the applicability of neural networks to modeling PP, whereas more recent models have been trained and validated on fairly large data sets encompassing seasonal and interannual variability of PP and environmental variables affecting PP. All the neural network models have a single hidden layer and were trained using the error-backpropagation algorithm with constant learning rate and no momentum term. Our results show that even the simplest neural network models provide superior results to those from more conventional empirical models of PP that are usually based on linear or multilinear relationships.

Phytoplankton biomass, surface irradiance and transparency (expressed as light extinction coefficient or as depth of the photic zone) were always used as predictive variables, whereas an estimate of phytoplankton PP was the only neural network output. Other variables that tend to co-vary with phytoplankton PP were added to this basic set during model development. Specifically, geographical coordinates, julian day, salinity, and depth of the water column were taken into account, as well as a few derived variables (e.g. the depth-integrated phytoplantkon biomass).

The final formulation of the neural network model has a 12-8-1 structure and uses log-transformed phytoplankton biomass and PP data. The model has been trained and validated on the basis of a data set that included 326 observations. One hundred of the observations were randomly selected to create the training set, whereas the remaining 226 observations were used as a validation set. Several techniques have been applied to obtain a generalized model and to prevent overfitting (training set sub-sampling, white noise addition, etc.). Finally, a sensitivity analysis of the neural network model was conducted to evaluate the relative importance of each predictive variable. Some examples of the neural network model application will be presented and compared with the results of more conventional models and with those of a simplified neural network model that only uses a subset of the predictive variables that can be obtained by remote sensing.