Methodology - Response of Flood Events to Land Use and Climate Change - page 60

(a) (b)

(c) (d)

Fig. 3.4 Cross validation statistic; a Cross validation between measured and predicted values,
b Estimated error, c Standardized error, d Q-Q plot

apart. Thus, pairs of locations that are closer (far left on the x-axis of the semi-
variogram cloud) should have more similar values (low on the y-axis of the
semivariogram cloud). As pairs of locations become farther apart (moving to
the right on the x-axis of the semivariogram cloud), they should become more
dissimilar and have a higher squared difference (move up on the y-axis of the
semivariogram).
The implementation of Kriging begins with the calculation of the empirical
semivarigram. To do this, the empirical semivariance between each pair of data
points is calculated as:

h i

2

c ij ¼ 0 : 5 z ð s ðÞ z ð s j Þ

ð 3 : 14 Þ

With large datasets the calculation of all possible combinations of the points is not
feasible. Therefore, data points are grouped based on their distance and direction
from one another in a process called binning. To construct the empirical semi-
variogram graph, the average semivariogram value for all the pairs within each bin
is plotted against the average distance [ 7 ].
To fit a model to the empirical semivariogram, some functions such as
Spherical, Exponential, Stable, Gaussian, etc., should be selected, which rise at
first and then level off for larger distances beyond a certain range. From the model,
there are deviations of the points on the empirical semivariogram. Some points are
located above the model curve and some are located below. But if we add
the distance of each point, those located above the line, with those located below
the line, the two values should be similar. As mentioned before, there are different
functions and models. Selecting the best model is important and it influences the