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Table 1 Definitions for the shape and topographic indices used to characterize unburned islands within fires in the Inland Pacific Northwest from 1984 to 2014. pij = perimeter (m) of patch ij. aij = area (m2) of patch ij. TPI and TRI were calculated with a seven by seven focal window (90 m in each direction). Aspect is azimuth in degrees

From: Characterizing persistent unburned islands within the Inland Northwest USA

Index Abbreviation Formula Notes Reference
Fractal Dimension Index FRAC \( \frac{2\ln \left(0.25\ {p}_{\mathrm{ij}}\right)}{\ln \left({a}_{\mathrm{ij}}\right)} \) Shape complexity, from less complex to more complex McGarigal and Marks 1995
Topographic Position Index TPI Difference between the value of a cell and the mean elevation of the surrounding cells Weiss 2001
Topographic Wetness Index TWI \( \ln \frac{upslope\ drainage}{\tan (slope)} \) Measure of hydrologic pooling potential Beven and Kirkby 1979
Terrain Ruggedness Index TRI Mean of the absolute differences between the elevation of a cell and the elevation of the surrounding cells Riley et al. 1999
Slope Slope Slope in degrees Steepness  
Cosine of the aspect CosAsp cos(Aspect) Gradient from north to south aspects  
Transformed aspect TRASP \( \frac{-\cos \left( Aspect-30\right)+1}{2} \) Gradient from northeastern to southwestern aspects Roberts and Cooper 1989