Methodology - Response of Flood Events to Land Use and Climate Change - page 61

prediction of the unknown values, particularly when the shape of the curve near
the origin differs significantly. The steeper the curve is near the origin, the more
influence the closest neighbors will have on the prediction [ 7 , 25 ]. As a result, the
output surface will be less smooth. Each model is designed to fit different types of
phenomena more accurately. Model surfaces can be compared using cross vali-
dation statistics (Fig. 3.4 ). Cross validation is a technique for assessing how the
results of a statistical analysis will generalize to an independent dataset. It is
mainly used in settings where the goal is prediction, and one wants to estimate how
accurately a predictive model will perform in practice.

3.2.2 Statistical Analysis

In this part, the attempt was to quantify the achieved results from the previous
section based on some statistical analysis.
Root Mean Square: The root mean square error (RMSE) represents the dif-
ference between the measured control points data and the predicted control point
locations calculated by the transformation process.
It is expressed as:

s

P i ¼ 1 ð x i x j Þ 2
N 1

RMSE elev ¼

ð 3 : 15 Þ

where:
x i is the predicted elevation and x j is the observed elevation. N is the number of
sample points.
Although such a measure of the accuracy of elevations in a DEM is clearly
useful and sensible, there are still a number of limitations with RMSE to evaluate
the DEM quality as several investigators have already addressed [ 8 , 26 - 28 ]:
1. RMSE is a global measure and it does not refer to the spatial characteristics of the
error. However, it would be expected that the error in whole DEM varies. Many
investigations such as Gong et al. [ 29 ], Chang and Tsai [ 30 ], Carter [ 31 ], Bolstad
and Stowe [ 32 ] have addressed that the error is strongly linked to the nature of the
terrain surface, given the high spatial autocorrelation in elevation data. On the
other hand, the error is likely to be highly spatially autocorrelated. Additionally,
other researches, such as Albani and Klinkenberg [ 33 ], Brown and Bara [ 34 ],
Guth [ 35 ], Wise [ 7 ] and Wood and Fisher [ 36 ], emphasized that many DEM
creation methods produce distinctive artifacts that have a strong spatial signature.
2. Another limitation of RMSE was found by Florinsky [ 37 ] and Wise [ 28 ]. They
mentioned that small errors in predicted elevation data points can produce a
large range of errors in derived values.
3. The last limitation of RMSE is perhaps related to the criteria that RMSE is only
based on a small sample of known data elevation points [ 38 ].