Appendix A. Computation of change vector statistics using Tasselled Cap brightness (B), greenness (G), and wetness (W) for images from two dates. A pdf file is also available.
The equations to compute change vector
statistics using Tasselled Cap brightness (B), greenness (G), and wetness (W)
for images from two dates are: Finally, the mean direction angles are:
(1) Magnitude change, , where B, G, and W refer to the changes in image BGW between the two dates,
(2) Colatitude, , and
To compute the summary spherical statistics (such as the mean ¸ or for all for all forested pixels in a sub-basin), the direction cosines x, y, and z are computed for the B, G, and W dimensions for every pixel:
(4) , and .
These values are summed for all forested image pixels i in a sub-basin such that mean direction cosines are calculated as:
with in the numerator of and in the numerator of .
(6) , and
Equations 14 follow standard trigonometry and were derived from CRC Standard Tables and Formulae (Zwillinger 1995). Our application of change vector statistics follows from Allen and Kupfer (2000), but differs in implementation with Eqs. 2 and 7.
Finally, the mean direction angles are:
Allen, T. R., and J. A. Kupfer.
2000. Application of spherical statistics to change vector analysis of Landsat
data: Southern Appalachian spruce-fir forests. Remote Sensing of Environment
Fisher, N. I., T. Lewis, and B. J. J. Embleton. 1987. Statistical analysis of spherical data. Cambridge University Press, Cambridge.
Zwillinger, D., editor. 1995. CRC Standard Mathematical Tables and Formulae, 30th Edition. CRC Press, Boca Raton, Florida, USA.