Results - Response of Flood Events to Land Use and Climate Change - page 132

values, and given the fact that interpolation itself is likely to produce similar
values for neighboring points. When the number of original data points is small,
there will be a very strong autocorrelation between the estimated elevations values
since neighboring values are essentially being estimated from the same data points.
The Q-Q plot (Fig. 6.5 ) quantifies and represents the estimated variable's
distribution against the original values more consistent. It could be concluded that
in Geostatistic methods the distribution of a variable matches very strongly with
the observed or original data distribution. On the other hand, the points cluster
around a straight line.
To test the accuracy of different interpolation techniques and to get more idea
about the achieved results, additional statistical analysis was estimated using spatial
analysis in macroecology (SAM). First, the predicted values for each method were
compared with original values of source data points. The minimum, maximum,
mean, and standard deviations for each method were calculated and the descriptive
statistical results are shown in Table 6.4 . These parameters are defined as following:
• Minimum absolute error shows how small the errors can be in case of consid-
ering lowest elevation in both observed and estimated value.
• Maximum absolute error shows how large the errors can be in case of consid-
ering highest elevation in both observed and estimated value.
• Mean error presents the arithmetic mean of the error values and reveals whether
the interpolation has a tendency to under or overestimate on average.
• Standard deviation shows how much variation or ''dispersion'' there is from the
average. A low standard deviation indicates that the data points tend to be very
close to the mean, whereas high standard deviation indicates that the data points
are spread out over a large range of values.
• ''Residuals'' are defined as meaning the spatially modeled component of vari-
ation not accounted for by the environmental variables, and that is why it has a
very strong spatial structure (because it is added when modeling the semi-
variogram). By doing this, it is ''released'', at the same time, the effect of the
spatial structure of data points.
In this test the best results also belong to Geostatistic-Spherical method, which
achieved the most accurate results with a value of \.001. A fundamental task in
many statistical analyses is to characterize the location and variability of a dataset.
A further characterization of the data includes skewness and kurtosis. To this
propose, the histogram of the residuals (Fig. 6.6 ), including the standard residual
diagnosis graphs (Fig. 6.7 ) was plotted for selected interpolated values. The
skewness and kurtosis value for all methods are represented in Table 6.5 .
It seems that the dataset for Circular, Exponential, and Gaussian is symmetric,
because the distribution is almost the same to the left and right of the center and
the skewness in these datasets is close to zero.
The negative values belong to Exponential with the value of -1.69. These
negative values indicate data that are skewed left. Skewed left means that the left
tail is long relative to the right tail. The positive values belong to Circular and
Gaussian. These positive values indicate data that are skewed right. Similarly,