A neural network technique to improve computational efficiency of numerical oceanic models

A new generic approach to improve computational efficiency of certain processes in numerical environmental medols is formulated. This approach is based on the application of neural network (NN) techniques. It can be used to accelerate the calculations and improve the accuracy of the parameterizations of several types of physical processes which generally require computations involving complex mathematical expressions, including differential and integral equations, rules, restrictions and highly nonlinear emprical relations based on physical or statistical models. It is shown that, form a mathematical point of view, such parameterizations can usually be considered as continuous mappings (continuous dependencies between two vectors). It is also shown that NNs are a generic tool for fast and accurate approximation of continuous mappings and, therefore, can be used to replace primary parameterization algorithms. In addition to fast and accurate approximation of the primary parameterization, NN also provides the entire Jacobian for very little computation cost. Three successful particular of the NN approach are presented here: (1) a NN approximation of the UNESCO equation of state of the seawater (density of the seawater); (2) an inversion of this equation (salinity of the seawater); and (3) a NN approximation for the nonlinear wave-wave interaction. The first application has been implemented in the National Centers for Environmental Prediction multi-scale oceanic forecast system, and the second one is being developed for wind wave models. The NN approach introduced in this paper can provide numerically efficient solutions to a wide range of problems in environmental numerical models where lengthy, complicated calculations, which describe physical processes, must be repeated frequently