UCLA

A two-dimensional dynamic vector field is any system in which spatially separated values move over or through a diverse terrain. Examples of this include wind fields, ocean currents, gaseous systems, and the movement of people. With the exponential growth of these dynamic data sets, via environmental sensing satellites, smart cameras, and GPS enabled cell phones, there is an immediate need for new techniques.

Modeling dynamic vector fields not only entails measuring the spatial dependence between locations and variables, but also capturing the independent markers that signal directional flow changes. In order to capture this, the objective of this new technique was to break down the modeling process into several steps. Given that spatial dependence changes with directional flow, it is the first objective to cluster the training data set of vectors into several distinct flow regimes. The following step is to then build separate spatially dependent models for predicting

the value's strength and direction within each regime. By first grouping the data into clusters, we achieve subsets of data with spatial dependence structures that are more homogenous, reducing overall variance or mixed signals in our modeling training.

The process and interpretation of regime based cluster modeling will be demonstrated in the statistical downscaling of two-dimensional ten meter wind fields over the diverse coastal and mountainous terrain of Southern California. Southern California's coastal mountains provide the perfect example of topography changing spatial dependencies with the change of the overall wind direction. This statistical downscaling process helps local regions prepare for and understand possible

climate changes and leverages the growing number and importance of Global Climate Models.