Preferred Slope Algorithm
Three slope methods appear to have the broadest support:
- Four closest neighbors (FCU):
- Eight neighbors unweighted (ENU): present preferred
method in MICRODEM. Users must still be aware that this
method produces peaks that are too flat.
- Steepest Adjacent Neighbor (SAN): requires adjustments to
get reliable aspect distribution, and does not give a
smooth slope distribution. Preferred method in MICRODEM
until the summer of 2003, and there are still reasons to prefer it.
The Eight Neighbors Unweighted method became the default in
the summer of 2003, primarily because it produces the smoothest,
most realistic slope histograms, and reasonable aspect distributions It still has problems with
smoothing of slopes in valleys, peaks, and ridges.
Guth (1995) reviewed all the
independent slope and aspect algorithms he could find. He
suggested that the steepest adjacent neighbor provided the best
estimate of slope, and the 8 neighbors with even weights provided
the best estimate of aspect. This is modestly called the Guth
Hybrid slope algorithm.
More recent comparisons of slope algorithms include Hodgson (1998) and Jones (1998), but neither cited Guth (1995) and their dismissal of the
steepest adjacent neighbor does not appear completely valid.
Justification to use largest slope of 8 to adjacent elevations
- Each point is surrounded by 8 neighbors. Four are to the
N,S,E,& W, and 4 approximately NE,SE,SW,& NW. How
close those are depend upon the type of DEM and latitude;
it is exact at the equator where x and y spacing is equal
or using a UTM based DEM. The worst cases will be in the
vicinity of 50°, where just to the south the spacing is
60 and 90 m, and just to the north the spacing is 90 and
120 m. There the diagonal values are at 53 and 34°
instead of 45° (arc tan (120/90) and arc tan (60/90)).
- The direction of maximum slope can thus occur no more
than 28° away from the largest of the eight directional
slopes to nearest neighbors in the DTED grid (half of 56,
the complement of 34).
- If we assume a plane for the surface in the vicinity of
the greatest slope, we can use vector arithmetic to
project the slope in various directions. The projection
will be a function of the cosine. For the worst case, the
estimated slope to the DTED value in the closest
direction will be 87.9% of the true slope (cos(28) =
0.879), and that occurs only when the true maximum lies
directly between two grid values. At the equator, with
maximum error in estimating, the estimated slope is 92.4%
of its true value.
- Since maximum error is only about 10%, and given the
overall accuracy of the data to start with, we do not
feel it necessary to obtain the added rigor of fitting a
surface to the data points in the vicinity and then
computing the slope of the tangent surface.
- The other methods effectively compute the slope are a
region twice the size of the data spacing.
- See Guth (1995) for additional
details and a comparison on the effect of algorithm on
Maps showing where slope
Implemented slope methods
Last revised 10/20/2011