Results - Response of Flood Events to Land Use and Climate Change - page 130

Table 6.1 Accuracy values for the DEMs generated in the geostatistical analyst extension

Deterministic Geostatistic

IDW Topo Spline Circular Exponential Gaussian Stable Spherical

RMSE 17.55 17.62 17.54 1.51 .119 .005 .432 .000

Mean 4.18 4.08 4.16 2.98 .092 .003 .230 .000

Max 35.84 36.04 35.85 9.08 .036 .003 .627 .000

R square .982 .982 .982 1.000 1.000 1.000 1.000 1.000

1. RMSE is calculated for selected data points (randomly 1,000 points)
2. Mean error presents the arithmetic mean of the error values and reveals whether
the interpolation has a tendency to under or overestimate on average.
3. Maximum absolute error shows how large the errors can be in extreme cases
4. R-square is a statistical measure of how well a regression line approximates real
data points; an R-squared of ''1.0'' (100 %) indicates a perfect fit.

As a general conclusion, the results of statistical analysis showed that all DEMs
derived from different interpolation techniques were statistically significant. Going
into the details in terms of RMSE, better results in model accuracy were obtained
when Exponential, Gaussian, Stable, and Spherical models were used. On the other
hand, in Geostatistic analysis, the difference was slight and has no bearing on the
overall pattern of results. The mean errors in these methods were also close to
zero. This means that mean error is simply the arithmetic mean of the error values
and reveals whether the interpolation has a tendency to under or overestimate on
average. Maximum absolute error also shows that the errors are not so large. R-
square in all methods shows that the regression line is ''1'' or close to ''1'',
meaning that in terms of R-squared, the results obey a perfect fit especially in
Geostatistic methods. In principle, the spatial pattern of errors was similar in all
cases of Geostatistic methods. Inversely, in the results of deterministic methods,
especially in terms of RMSE, the errors are larger than Geostatistic methods.
Therefore, as an overall result, it could be concluded that Geostatistic techniques
show the strongest results compared to the deterministic. In between, the Spherical
and Gaussian showed better agreement with the observed data and represents the
smoothest and more accurate DEM. In terms of visualization pattern of errors
underestimation of elevation occurs where the slope is upwardly convex and where
a change in elevation is marked (Fig. 6.4 ). Hence, the largest errors occur along
narrow crest lines and at the convex change of slope at the tops of ridges. Large
convex areas, such as the tops of broad ridges, are estimated more successfully.
Conversely, overestimation occurs in areas that are upwardly concave.
Table 6.2 shows the frequency distribution of error values and Table 6.3
represents the standard error and P value of a significant level.
Tests for normality were run on all the distributions and a Kolmogorov-
Smirnov test showed that all considered DEMs are significantly different from the
original DEM, with a 0.008 P value for the Spline and zero for the rest of the
applied methods. The standard coefficient and standard error in Geostatistical