Methodology - Response of Flood Events to Land Use and Climate Change - page 56

Topo to Raster

Topo to Raster is a specific technique designed to convert the vector surface data,
in the form of contours, into a consistent DEM format hydrologically. It is based
on interpolation models and the Australian national university digital elevation
model (ANUDEM) program developed by Hutchinson [ 19 , 20 ], specifically
designed for the creation of hydrologically correct DEMs which are provided
within ArcGIS.
The interpolation procedure has been designed to take advantage of the types of
input data commonly available and the known characteristics of elevation surfaces.
This method uses an iterative finite difference interpolation technique.
It is optimized to have the computational efficiency of local interpolation
methods, such as IDW interpolation, without losing the surface continuity of
global interpolation methods, such as Kriging and Spline. It is essentially a dis-
cretized thin plate of Spline technique [ 19 - 21 ], for which the roughness penalty
has been modified to allow the fitted DEM to follow abrupt changes in terrain,
such as streams and ridges. It is also the only ArcGIS interpolator specifically
designed to work intelligently with contour inputs.
The roughness penalty is defined in function of the first- and second-order partial
derivatives of the interpolation function f by the following equations:

dxdy

J 1 ðÞ¼ Z

f x þ f y

ð 3 : 7 Þ

dxdy

J 2 ðÞ¼ Z

f xx þ 2f xy þ f yy

ð 3 : 8 Þ

where:
minimizing J 1 in its discretized form conduces to discretized minimum
potential interpolation, while minimizing J 2 conduces to the minimum curvature
interpolation of thin-plate splines in their discrete form. If only J 2 was minimized,
the resulting surface would be unrealistically smooth, whereas minimizing J 1 gives
rise to sharper local maxima and minima at data points as the grid resolution
becomes finer. Hutchinson [ 20 ] suggested the following compromise between J 1
and J 2 to define the roughness penalty in this algorithm:

J ð f Þ¼ 0 : 5 h 2 J 1 ð f Þþ J 2 ð f Þ

ð 3 : 9 Þ

where:
h is the cell resolution; this form of roughness penalty maintains trends beyond
data points as in minimum curvature interpolation, allows the definition of sharp
changes in slope occurring at ridges, and identifies points at rivers as sinks.

Kriging

Autocorrelation in spatial phenomena is a defining concept of Geostatistic inter-
polation methods. On the other hand, the data points which are located close
together tend to be more similar than the data points which are located far from