DIGITAL TERRAIN MODELING
3.1 Study Area Description
3.6.4 Volume computation
The merit of using TIN is the ability to represent the topographic information at a both small and large scale of resolution. Furthermore, by using TIN, it is also easy to define the volume ofthe DTM.
All volume computations in the TIN programs are based on simple mathematical formula of triangular prism [5 I]. The volume is determined by the multiplication of the medial high with the area. The formula is as follow;
where;
11
v
V;
F;
h ..
=
..'
: name of one triangle :number of all triangles
: height of each vertex of one triangle : medial height of one triangle
:volume of the object : volume of one triangle : area of one triangle
(3.2)
(3.3) (3.4)
In this method, the volume is computed above a certain reference plane. In this work, the reference plane was defined by referring the lowest height vrdue of the grid-point.
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3. 7 Quality Measure of DTM
One of the consequences of using DTM, especially in high accuracy applications, is the need to characterize the DTM quality. This is particularly a relevant issue in civil engineering where, beside the technical implications, a lack quality in the DTM can lead to important economic deviations during project execution. The quality control presented in this work is based on the common parameters used in civil engineering to determine the quality of a DTM [5], that are:
1. The height error analysis
11. The volumetric error analysis
The volumetric accuracy analysis is a simple yet useful method for DTM quality control.
This is based on the idea that DTM quality can be analyzed by the ability to estimate soil volumes. This criterion was introduced given the economic importance that the control of volume has in civil engineering applications. The consequence of this method is the need of a reference model to be used for volume comparison. This method allows a global analysis of the model but it does not allow us to determine the presence of systematic errors that, particu!<Jrly with the height v<Jiue have <1 great impact in the quality of the DTM. Hence, to avoid this problem the height error analysis was introduced to complement the volumetric error analysis.
1.7.1. The height error analysis
The height error analysis has several advantages:
1. It allows the characterization of height errors of the model
11. It serves as control over the volume estimation method
111. It needs only a set of strategic points to have a control over the models
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In this work, the height error analysis was carried out on all of the study areas. For Terrain- I, this was carried out over two profiles across the area. For Terrain-2 and Terrrain-3, it was performed over the grid-points. The analysis was conducted by analyzing the discrepancy between the value given by RTK GPS and total station survey.
The statistical measures used for this are:
where:
Em = mean error
Ema =absolute mean error
e; =individual error of one point u =total number of points.
(3.5) E
= I:le;l
lll:l (3.6)
u
The average error is a good indicator of the randomness of rhe errors to test the existence of important systematic errors in the height value [5]. Hence, the absolute mean error is the most suitable indicator of DTM accuracy. The fact that it is expressed in absolute terms has the advantage that errors with different signs will not cancel each other which allow a more rigorous characterization of errors.
3.7.2 The volumetric error analysis
The volumetric error analysis was performed by analyzing the difference of computed volume between the DTM generated from RTK GPS compared to the respective DTM based from TS data. Here, the latter was used as the reference model. This is due to some theoretical and practical reasons. Firstly, total station accuracy (0.3cm ± 3ppm) is relatively better than RTK GPS that is I em± I ppm for horizontal positioning and 1.5cm
± I ppm for vertical positioning. Secondly, it is free from errors contributed by
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surrounding or sky view whereas is an important parameter in RTK GPS survey. This is due to the fact that the quality of RTK GPS data normally depends on the sky view and the condition of the survey area. Hence, it is interesting to investigate of how far the sky view affects the accuracy of RTK GPS data and its influence to the generated DTM.
Beside, it is also important to approximate the workable and usable sky view for RTK GPS survey. These are specifically correlated with the efficiency and productivity as well as the accuracy of the RTK GPS. Practically, total station survey is the conventional technique that has been used for years. Hence, the RTI< GPS, which is a new method in term of DTM data collection, should be tested against the conventional method that is Total Station.
The volumetric accuracy analysis was performed based on DTMs of Terrain-2 and Terrain-3. This is intended to have a valid analysis since both of the DTMs are based on grid based sampling which uses exact grid-point. The volumetric error analysis is unlikely to be performed on DTM of Terrain-! which is based on composite sampling.
This is due to the fact that the RTK GPS and TS data gained from this sampling are different in term of spatial position since no exact same point can be used for the analysis. Hence, the DTM generated from RTK GPS survey data is totally a different model compared to the one generated from TS survey data.
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