Vector data are not uncommon in geography, and include examples such as transportation flows, particulate transport, and cartographic distortion. The directional and vector means and variances of these types of data are easily computed using a complex-arithmetic extension of the equations for scalar mean and variance. The January surface wind field over the contiguous United States provides an example with which to compare the information provided by scalar, directional and vector-based statistics. Spatial patterns of the mean and variance of January wind velocity (the wind vector) resemble patterns of wind speeds and directions but are not a simple superposition of the two, and one cannot necessarily infer the nature of the velocity field from separately computed salar and directional statistics. However, scalar and directional means and variances can lend insight into the features contributing to the velocity mean and variance. Scalar, directional, and vector-based analyses thus provide complementary methods with which to examine the spatial patterns of wind, or of any flow field that can be represented as a vector.
Bibliographical noteFunding Information:
* I thank D. G. Baker, J. F. Hart, D. C. Hodge, and C. J. Willmott for comments on earlier versions of the paper, and M. B. Lindberg and the University of Minnesota Cartography Lab for drafting the final figures. Portions of this research were supported by the University of Minnesota and the Minnesota Supercomputer Institute.
- Directional statistics
- Surface wind field
- Vector statistics