Parsimonious Vector Field Analysis

Hi everyone,

I am beginning to design an analysis routine for vector field data: each point on the two-dimensional (x, y) grid has an associated (u, v) vector. I would like to analyze the vector field with the vectors in polar format (i.e., each point has a vector with angle [a] and magnitude [m]). I prefer this representation because conceptualizing the local and global structure of the field feels more intuitive with polar data.

My primary question is: Does the vector angle or magnitude depend on position?

• Linear regression can be used with m as a dependent and x and y as independent variables
• Is there a regression for circular dependent (a) and linear independent (x, y)?
• Is there a simpler way to instead analyze both vector angle and magnitude simultaneously across positions?

I'm a relative newbie to vector fields and am wary of using too many statistical tests when fewer could instead be used.

Thanks.