Citing and method overview

When using a method implemented in xDEM, one should cite both the package and the original study behind the method (if there is any)!

Citing xDEM

To cite the package, use the Zenodo DOI: .

Method overview

For citation and other purposes, here’s an overview of all methods implemented in the package and their reference, if it exists. More details are available on each feature page!

Terrain attributes

References for curvatures are detailed further below the other terrain attributes.

Method	Reference
Partial derivatives (slope, aspect, curvatures)	Horn (1981) or Zevenbergen and Thorne (1987) or Florinsky (2009)
Slope, aspect and hillshade	Horn (1981) or Zevenbergen and Thorne (1987)
Topographic position index	Weiss (2001)
Terrain ruggedness index	Riley et al. (1999) or Wilson et al. (2007)
Roughness	Dartnell (2000)
Rugosity	Jenness (2004)
Fractal roughness	Taud and Parrot (2005)
Texture shading	Brown (2010) and Allmendinger and Karabinos (2023)

Curvatures follow the recommended system of Minár et al. (2020). Where no direct DOI can be linked, consult this paper for the full citation. There are two ways of defining curvatures: either geometric (curvatures can be defined by the radius of a circle), or directional derivative (curvatures can be understood as directional derivatives of the elevation field). xDEM defaults to the geometric method.

Method	Geometric	Directional derivative
Profile curvature	Krcho (1973) and Evans (1979)	Zevenbergen and Thorne (1987)
Tangential curvature	Krcho (1983)	Zevenbergen and Thorne (1987)
Planform curvature	Sobolevsky (1932)	Sobolevsky (1932)
Flowline curvature	Minár et al. (2020)	Shary (1991)
Maximal/Maximum curvature	Shary (1995)	Wood (1996)
Minimal/Minimum curvature	Shary (1995)	Wood (1996)

Coregistration

Method	Reference
Nuth and Kääb	Nuth and Kääb (2011)
Dh minimization	N/A
Least Z-difference	Rosenholm and Torlegård (1988)
Iterative closest point	Besl and McKay (1992), Chen and Medioni (1992)
Coherent point drift	Myronenko and Song (2010)
Vertical shift	N/A

Bias-correction

Method	Reference
Deramp	N/A
Directional bias (sinusoids)	Girod et al. (2017)
Terrain bias (curvature)	Gardelle et al. (2012)
Terrain bias (elevation)	Nuth and Kääb (2011)
Vertical shift	N/A

Gap-filling

Method	Reference
Bilinear	N/A
Local and regional hypsometric	Arendt et al. (2002), McNabb et al. (2019)

Uncertainty analysis

Method	Reference
R2009 (nested ranges, circular approx.)	Rolstad et al. (2009)
H2022 (heterosc., nested ranges, spatial propag.)	Hugonnet et al. (2022)