Some neural network applications in environmental sciences. Part II: advancing computational efficiency of environmental numerical models

A new generic neural network (NN) application-improving computational efficiency of certain processes in numerical environmental models-is considered. This approach 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 empirical relations based on physical or statistical models. It is shown that, from a mathematical point of view, such parameterizations can usually be considered as continuous mappings (continuous dependencies between two vectors) and, therefore, NNs 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. Four particular real-life applications of the NN approach are presented here: for oceanic numerical models, a NN approximation of the UNESCO equation of state of the sea water (NN for the density of the seawater) and an inversion of this equation (NN for the salinity of the seawater); for atmospheric numerical models, a NN approximation for long wave radiative transfer code; and for wave models, a NN approximation for the nonlinear wave-wave interaction. In all considered applications a significant acceleration of numerical computations has been achieved. The first two of these NN applications have already been implemented in the multi-scale ocean forecast system at NCEP. The NN approach introduced in this paper can provide numerically efficient solutions to a wide range of problems in numerical models where lengthy, complicated calculations, which describe physical, chemical and/or biological processes, must be repeated frequently.