Hello Madhu, aspect and slope are actually two "coordintes" showing the orientation of a surface in a polar coordinate system. Why not just switch to a Cartesian system instead? You could e.g. give the oriantation of a surface with its "northness" and "eastness", as the coordinates of the endpoint of the normal vector to that surface. Thus:
northness = cos(aspect)*sin(slope), eastness = sin(aspect)*sin(slope), or something similar, depending on exactly how you defined aspect and slope. This completely eliminates the probélems of circularity (however at the expense of using somewhat unusual predictors, the interpretation of which is still relatively straightforward...) A somewhat less elegant (but still frequently used) similar solution is to leave the slope alone, and just transform aspect: northness = cos(aspect) eastness = sin(aspect) slope = slope This way you will get 3 values to describe an intrinsically 2D entity, so the resulting "coordinates" will not be independent. Best regards, Bálint -- Bálint Czúcz Institute of Ecology and Botany of the Hungarian Academy of Sciences H-2163 Vácrátót, Alkotmány u. 2-4. HUNGARY Tel: +36 28 360122/137 +36 70 7034692 magyar nyelvű blog: http://atermeszettorvenye.blogspot.com/ On Mon, Jul 5, 2010 at 01:04, Madhu Srinivasan <[email protected]> wrote: > Hi all, > I am currently writing one of my dissertation chapters. I collected plant > community data in a grassland ecosystem along with environmental variables . > One of the questions I am addressing is: "How do the dominant grasses > respond to the aspect?" Aspect was the direction that the slope faced. In > the linked graphs (http://sweb.uky.edu/~mpsrin2/aspect_fig.pdf) I have > displayed aspect in two ways: (1) in degrees as measured by compass > bearings, Fig. 2,and (2) converted to linear scale using: > A' = cos (45 - A) + 1, where A is the aspect in degrees (Beers et al, 1966, > Journal of Forestry), Fig.3. The resulting index values range from 0 to 2 (0 > = SW, 1 = SE and NW, 2 = NE), see Fig. 1. I have fitted regression lines > after determining the appropriate fit. One of my concerns is: in Fig. 3, the > hump around A'=1.5 could either correspond to N or E, as both take the value > 1.5 (see Fig.1). So this index of aspect does not allow me to interpret if > the plants are more abundant at N or at E facing slopes. Fig 2. allows me to > distinguish data from the different aspects, and it is easier to explain; > but the explanatory variable here is circular, and I am concerned whether it > is correct to apply regressions on circular data. I showed these graphs to > some of my colleagues and I got mixed responses. I would like to know which > representation is more appropriate? Right now I am leaning towards Fig. 2, > but I am concerned about the statistical appropriateness. I will include the > explanatory Fig. 1 with either graph that I choose to finally use. > Also, if there is a better way to display/ analyze this, please let me know. > > Thanks, > Madhu Srinivasan > Department of Biology > University of Kentucky >
