Inverse Projection of Vector Fields

Abstract

Vector fields play an essential role in a large range of scientific applications. They are commonly generated through computer simulations. Such simulations may be a costly process since they usually require an intensive computational time. When researchers want to quantify the uncertainty in such kind of applications, usually an ensemble of vector fields realizations are generated, making the process much more expensive. The main contribution of this paper is to present a new method, based on the inverse projection technique, to quickly and consistently generate 2D vector fields similar to the ones in the ensemble, which after an evaluation of a specialist could enlarge the ensemble in order to better represent the uncertainty. Through the Helmholtz-Hodge Decomposition, we obtain the divergence-free, rotational-free and harmonic components of a vector field. With those components and the original ensemble in hand, it is possible to derive new realizations from their projections into a 2-dimensional space. To do so, we propose the use of an inverse projection technique individually in each component projected space. Results are obtained in real-time, through an interactive interface. A set of multi-method wind forecast realizations were used to demonstrate the results obtained with this approach.