Geoscience Reference
In-Depth Information
Keywords
DTM • ANN • IDW • GA • Interpolation • Elevations • Optimisation
1 Introduction
Three-dimensional modelling of the Earth is one of the most important tools for
studying in various fields of geology, meteorology, civil engineering, environmen-
tal engineering, and numerous engineering projects and it has many applications in
the Geospatial Information System (GIS) (Petrie and Kennie
1990
; Florinsky
2011
;
de Mesnard
2013
). GIS can generally be used to create the Digital Train Modelling
(DTM) to display topography and synthetic changes and all environmental parame-
ters such as temperature, air pollution, etc. (Kasser and Egels
2002
; Li et al.
2004
).
One of the most significant parameters in GIS is the topography elevation of the
Earth, which can be visualised in 3D digital form to represent the Digital Elevation
Model (DEM) (El-Sheimy et al.
2005
). In other words, DEM continuously displays
elevation changes of the Earth, which is directly proportional to the plane position
(x, y) (El-Sheimy et al.
2005
; Chaplot et al.
2006
; Miller and Laflamme
1985
).
Initially, 3D models were created physically from plastic, sand, clay, etc. (Li et al.
2004
). Today, however, computers are used to display the Earths' continuous sur-
faces in a digital form (Heesom and Mahdjobi
2001
).
One of the most important issues in the field of digital modelling is to generate
the DEM with high quality and precision and keeping minimum costs. To estimate a
continuous surface, due to the limited number of samples and the necessity of repro-
ducing altitude points, the mathematical interpolation functions are used to estimate
the elevation of midpoints (Abdul-Rahman and Pilouk
2008
). Interpolation meth-
ods are used to determine unknown altitudes of midpoints from the samples and as a
result, the coordinated points are reproduced and the digitally formed Earths' continu-
ous surfaces can be visualised. Since any interpolation has mainly errors, those errors
can be expanded through the calculations and processes. The results from interpo-
lation are achieved and the Standard Deviation (SD) of the facts is not acceptable.
Such errors transfer inaccurate assessments in the executable projects and convey the
financial losses and even their life threatening results (Eyvazi et al.
2007
; Mitas and
Mitasova
1999
). Therefore, one of the challenges in this method is to find an appro-
priate way in which the data source not only consists of accuracy and distribution
of sample points but also, contains geomorphological characteristic of the Earth's
Surface. The method in question for interpolation and the estimation of the middle
points' height, will affect the quality and the accuracy of DEM (Li
1990
,
1992
).
Numerous methods for the interpolation have been proposed (Hardy
1971
,
1990
; Larsson and Fornberg
2003
), which shows different results influenced by
the environment's conditions and data input. Usually, the optimal method of inter-
polation depends on the Root Mean Square Error (RMSE) of the output. In most
studies the comparison of interpolation methods and the selection of the optimal
methods are used to achieve higher accuracy (Yanalak
2003
; Amidror
2002
; Rees
2000
; Yang et al.
2004
; Li and Heap
2011
; Wagnera et al.
2012
).
