Wind Shelter Index
wind.shelter is a function to be used with
focal.function to calculate a topographic wind shelter index from a digital elevation model, which is a proxy for snow accumulation on the lee side of topographic obstacles.
wind.shelter.prep performs some preparatory calculations to speed up repeated calls to
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square matrix of elevation data
numeric: quantile of slope values to be used in computing the wind shelter index; if
required argument: the result of a call to
radius (>1) of circle segment to be used (number of grid cells, not necessarily an integer)
wind direction: direction from which the wind originates; North = 0 =
wind.shelter implements a wind shelter index used by Plattner et al. (2004) for modeling snow accumulation patterns on a glacier in the Austrian Alps. It is a modified version of the algorithm of Winstral et al. (2002). The wind shelter index of Plattner et al. (2004) is defined as:
Shelter index(S) = arctan( max( (z(x0)-z(x)) / |x0-x| : x in S ) ),
S = S(x0,a,da,d) is the set of grid nodes within a distance
x0, only considering grid nodes in directions between
The present implementation generalizes this index by replacing
max by the
quantile function; the
max function is used if
prob=NULL, and the same result is obtained for
prob=1 using the
wind.shelter returns the wind shelter index as described above if a numeric matrix
x is provided. If it is missing, it returns the character string
wind.shelter.prep returns a list with components
dist. Both are square matrices with
2*(ceiling(radius)+1) columns and rows:
indicates which grid cell in the moving window is within the specified circle segment (value
the precomputed distances of a grid cell to the center of the moving window, in map units
The wind shelter index only makes sense if elevation is measured in the same units as the horizontal map units used for the
cellsize argument (i.e. usually meters).
wind.shelter.prep do not restrict the calculation to a circular area; this is done by
focal.function when used in combination with that function (assuming
Note that the present definition of the wind shelter index returns negative values for surfaces that are completely exposed toward the specified direction. This may make sense if interpreted as a "wind exposure index", or it might be appropriate to set negative wind shelter values to 0.
Plattner, C., Braun, L.N., Brenning, A. (2004): Spatial variability of snow accumulation on Vernagtferner, Austrian Alps, in winter 2003/2004. Zeitschrift fuer Gletscherkunde und Glazialgeologie, 39: 43-57.
Winstral, A., Elder, K., Davis, R.E. (2002): Spatial snow modeling of wind-redistributed snow using terrain-based parameters. Journal of Hydrometeorology, 3: 524-538.
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