# Transforming aspect values in order to use them in multiple regression models

I want to use aspect as an independent variable in a multiple regression model but I would like to transform the aspect values so that from degrees 180 to 360, I would get their equivalent to degrees from 0 to 180. How could I do that in ArcGIS or R?

• If you have aspect raster computed, why not to use con ("Aspect" >= 180,"Aspect"-180,"Aspect") in raster calculator – FelixIP Mar 11 '15 at 22:50
• The most straightforward way is to take the aspect modulo 180. As Dr. Evans' answer suggests, though, that should only be the start of your modeling procedure. – whuber Jun 22 '15 at 18:31

I have several methods available in our Geomorphometry and Gradient Metrics Toolbox (Evans et al., 2014). From your description it sounds like the "Linear Aspect" or "Classify Aspect" tools would work for you. However, I have found that, in regression models, other transformations are much more effective.

The Roberts & Cooper (1989) method unfolds and recenters aspect so that 0 represents north- northeast aspects, (typically the coolest and wettest orientation) and 1 represents hotter, dryer south-southwesterly aspects. The Stage (1976) transformations are an interaction between slope and aspect and have proven to be robust indicators of topographically driven a biotic ecological process. The McCune & Keon (2002) Heat Load Index also represents a slope/aspect interaction but is scaled to represent solar isolation.

The methodology for unfolding or "linearizing" aspect, in ArcGIS raster algebra, are:

``````tmp1=Aspect(dem)
tmp2=SetNull(tmp1 < 0,(450.0 - tmp1) / 57.296)
tmp3=Sin(tmp2)
tmp4=Cos(tmp2)
tmp5=FocalStatistics(tmp3,NbrRectangle(3,3,"CELL"),"SUM","DATA")
tmp6=FocalStatistics(tmp4,NbrRectangle(3,3,"CELL"),"SUM","DATA")
tmp7 = Mod(((450 - (ATan2(tmp5, tmp6) * 57.296)) * 100), 36000) / 100
outRaster = Con((tmp5 == 0) & (tmp6 == 0),- 1, tmp7)
``````

References

Evans JS, Oakleaf J, Cushman SA, Theobald D (2014) An ArcGIS Toolbox for Surface Gradient and Geomorphometric Modeling, version 2.0-0. Available: http://evansmurphy.wix.com/evansspatial.

McCune, B. & D. Keon., (2002). Equations for potential annual direct incident radiation and heat load index. Journal of Vegetation Science. 13:603-606.

Stage, A.R., (1976). An Expression of the Effects of Aspect, Slope, and Habitat Type on Tree Growth. Forest Science 22(3):457-460.

Roberts. D.W., and Cooper, S.V., (1989). Concepts and techniques of vegetation mapping. In Land Classifications Based on Vegetation: Applications for Resource Management. USDA Forest Service GTR INT-257, Ogden, UT, pp 90-96

• Thank you very much Jeffrey! So is it reclassification what you suggest? – Maria Karypidou Mar 11 '15 at 16:58
• Sorry, no I meant the "linear aspect" tool. I modified my answer to reflect this a provide the methodology to do this outside of my toolbox. – Jeffrey Evans Mar 11 '15 at 17:06
• I have applied what you suggested but I can't understand how this will is taking care of the issue of repeating values from 180 to 360 when I want to use the aspect values as an independent variable in my regression model. My values are from 1-359. – Maria Karypidou Mar 13 '15 at 12:58
• The variable is no longer circular. – Jeffrey Evans Mar 13 '15 at 13:35
• Yes, the formula is almost the same - consider to write it as a single r.mapcalc call using the eval() function which allows to concatenate several equations. – markusN Jun 22 '15 at 19:01