1 Spatial Modelling of the Terrestrial Environment - Georeferencial

Remotely Sensed Topographic Data for River Channel Research 123
magnified due to propagation of error through incorrectly matched points or interpolated
points. This would raise σ z and make the incorrect elevations more difficult to find: it is
vital to remove blunders before a surface is fitted to a dataset.
The user has to choose two main parameters: (1) the radius of the search error (r); and
(2) the SD tolerance (t). In the case of search radius, 5 values were explored: r = 5m,
r = 10 m, r = 15 m, r = 20 m and r = 25 m. The effects of search area upon SD is
shown in Figure 6.4(d) through (h) and it is clear that there is some relationship between
SD and the error that is clear in Figure 6.4(c). The use of a search radius means that a
larger area can be considered than the 3 × 3 elevation matrix used in the photogrammetric
software’s application of equation (6). This is important as it increases the reliability of
derived standard deviations due to the inclusion of a larger number of data points. In practice
then, the actual area chosen should reflect the topography of the surface being considered.
The greater the local rate of elevation change (i.e., with less local stationarity at order 2), the
smaller the search area that may be used for reliable SD estimation. However, there is a
trade-off here as with larger numbers of data points, the ability to detect individual points
that are in error, as opposed to clusters of data points, is reduced: highly localized errors
may not be detected by this method. Thus, we explore the effects of a number of different
search ranges to identify an optimal one for the dataset used here.
Three tolerance levels were tested (2 m, 1 m and 0.5 m). There is an a priori reason
for the choice of tolerance levels based upon the expected SD and the characteristics
topography of this type of river: relatively flat bar surfaces with breaks of slope between
bar surfaces of different elevation. The maximum possible expected standard deviation,
for a dataset within a given area, will occur when the break of slope falls exactly along
the diameter of each search radius, with 50% of elevations at the maximum value for the
surface and 50% of elevations at the minimum value for the surface. This results in an areaindependent
justification of all three tolerance values. If the surface topographic range is 2
m, then the maximum possible expected SD is 1 m, which was set as the median tolerance
value considered. The 2 m tolerance value was chosen to recognize that the SD is almost
certainly higher than this because of grain and bedform scale related elevation variation on
both high- and low-bar surfaces. The 0.5 m tolerance was chosen under two assumptions:
(1) the removal of too much data would not be a problem in a surface that already contained
so much data; and (2) that the 1 m tolerance is essentially the maximum possible standard
deviation.
Figure 6.5 shows the test results, plotted for different radii of curvature and tolerance
levels, as compared with check point data, for the test area shown in Figure 6.4. As expected,
there is strong interaction between search radius and tolerance. The search radius of 5 m
retains a large number of points and ME and SDE both remain high. Once the 10 m search
radius is reached, with the exception of the 2 m tolerance level, the SDE falls significantly,
to below 1 m. Optimal results are obtained with a 15 m or 20 m search radius. After this,
the SDEs for the 0.5 m and 2 m tolerances begin to rise again. The observations reflect
the point made above: as the search radius is increased, the SD becomes more reliable as
more good points will be included. However, at large search radii, the effects of points in
error upon the SD become too small for even the tolerances used here. Thus there is a link
between search radius and tolerance. This link will be surface dependent (in relation to
topographic variability) and error dependent (according to the level of point clustering).
The 0.5 m tolerance level consistently produces the lowest SDE for all radii of curvature