5. NN Ensembles and Their Applications

In this chapter, various neural network (NN) ensemble applications including applications in data assimilation systems, nonlinear multi-model ensembles, ensembles with perturbed model physics, and others are introduced and discussed. It is shown that in many cases, NN ensemble approaches provide a better and more adequate emulation of the complex nonlinear mappings than a single NN. In this chapter, an NN ensemble approach is applied to introduce analytic approximations for highly complex functional dependencies and mappings between the model variables in an oceanic data assimilation system which enables 3-D assimilation of surface 2-D variables like the surface elevation. An NN ensemble approach is applied to derive a nonlinear multi-model ensemble for improving 24-h precipitation forecasts over the continental US (ConUS). Different possibilities for using the NN emulation technique in combination with the NN ensemble approach for generating stochastic or perturbed model physics and ensembles with perturbed model physics are considered. The chapter contains an extensive list of references giving extended background and further detail to the interested reader on each examined topic. It can serve as a textbook and an introductory reading for students and beginning and advanced investigators interested in learning how to apply the NN ensemble technique to various problems.