Methodology - Response of Flood Events to Land Use and Climate Change - page 52

data points within the range of known data points. They also mentioned that in the
fields of engineering and science there are often a number of data points obtained
by different methods such as sampling or experimentation. These methods try to
construct a function which is closely fitted to all those data points. This con-
structing of a function between the data points is called curve fitting or regression
analysis. Therefore, interpolation is a specific case of curve fitting, in which the
function must go exactly through the data points. According to Alkema and
Rahman [ 5 ], the interpolation methods are considered to be designed to create
statistically correct surfaces.
There are two main interpolation techniques:

1. Deterministic: This method is based on mathematical equations to predict the

new data points based on the assumption that the interpolating surface should
be influenced mostly by the nearby points and less by the more distant points.

2. Geostatistic: This method applies both mathematical and statistical approaches

to predict the new data points at unknown locations. This method is based on
the assumption that the interpolating surface should be influenced mostly by
the nearby points, and less by the more distant points. Nevertheless, it is also
based on the spatial autocorrelation among data points [ 4 , 6 ]. Geostatistical
techniques quantify the spatial autocorrelation among measured points and
account for the spatial configuration of the sample points around the prediction
location [ 7 ].

There are typical methods used to produce many of the DEMs in use today or to
correct errors. In this study, the main aim was to compare the quality of different
interpolation techniques available to derive DEMs from the point data. The
interpolation techniques were used also to determine DEM errors. The interpola-
tion methods compared were some common interpolation algorithms based on the
inverse distance weighted (IDW), Topo to Raster, and Spline as deterministic
methods. In Geostatistical analysis, Kriging (Spherical, Circular, Exponential,
Gaussian, and Stable) was selected. Figure 3.1 shows the process of DEM quality
control modeling based on different interpolation techniques.
Spline and Inverse Distance Weighting were chosen because they are com-
monly used now and were also used in earlier work, and they have been recom-
mended by many investigators [ 8 , 9 ]. The Topo to Raster method was selected
because it automatically removes spurious sinks, has advantages for faster com-
putation, lowers ''roughness penalty'' [ 10 ], and has a drainage enforcement
algorithm for preserving the natural sinks in the area [ 11 ]. The Kriging method
was found to produce the best results in general tests of interpolators. All methods
were implemented in the ArcGIS environment and were thus easy to access. The
interpolation methods applied in this research have different characteristics as the
following table outlines (Table 3.1 ).
The detailed interpretation with related equations for all the above-mentioned
techniques is described in the next section.