A Study of DEM Accuracy according to Spatial Resolution
3.2 Slope Stability Accuracy
A slope stability analysis is popular application of DEM. Sometime we generate land slide risk map or slope failure risk map from DEM. The slope stability which means safety factor was calculated by a ratio between driving moment and residtance moment along the target profile. When the safety factor is calculated on every pixel, such risk map can be generated. Fellenius method as slope stability analysis was selected in this study. In this method, landslide type is assumed rotational slip (Figure 60a). A
landslide soil is divided into some slices in order to calculate moment along the critical circle (Figure 6-b). The driving moment (T) and resistance moment (N) on each slice are calculated by the following equation.
Figure 6-a Illustration of Fellenius Method and
Figure 6-b Illustration of Each Slice
T= R W. sin a
N = R(C.L. + tanf. W. cos a)
R Radius of Critical Surface I(m)
C cohesion (t/m2)
f Angle of Shearing Resistance (degree)
W Weight of Each Slice (t/m) (W=
Yt A)
Yt Wet Unit Weight of Soil (t/m3)
A Area of Slice (m2)
a Angle between Horizontal Axis and the Base of Slice (degree)
L Length of the Base of Slice (m)
Therefore safety factor (Fs) is calculated by the following equation.
Originally, parameters of soil mechanics (C, f, Yt) and radius of critical surface ® should be determined by experimental data and field survey data on each pixel. In this study, those parameters were given constant value as follows:
R = 200m, C = 2.0t/m2, f=10°,
Yt = 1.91/ m3
When profile at target pixel was drawn along the steepest direction, other parameters can be estimated by DEM. If this safely factor calculation applied every pixel, slope stability risk can be mapped.
Figure 7 shows histogram of difference between original sope stability data and resampled slope stability data of each grid size. The histograms show asymmetrical from that is shifted to left. It means the resampled safety factor. This situation will make serious problem because of under estimation. Figure 8 shows a relationship between grid size and percentages of correct pixels. In case of slope stability, correct pixel means difference with original data indicates inside of 0.2 (Fs). The nearest accuracy. However, each trend was very similar.
Figure 7 Accuracy of Safety Factor according to Spatial Resolution
Figure 8 Accuracy of Safety Factor according to Spatial Resolution
3.2 Drainage Pattern Accuracy
A runoff analysis or a drainage pattern generation is very popular application of DEM. Usually, such analysis can be carried out by using a grid series tank model . A precipitation is supplied to each DEM grid that is one of the tanks. An inlet content which means effective rainfall ofr dischargeis calculated by following equation.
Qin KiRL2
Qin : Inlet Conent (m
3)
Ki: Infiltration
R: Precipiation (m)
L: Grid Size (m)
The inlet contest must discharge to next grid according to slope aspect and velocity. That is to say flow tracking. The slope aspect can be calculated from DEM, the velocity can be estimated from slope inclimnation which is also calculated from DEM. And the flow in the grid can be expressed by a continuous equation as follows;
Qt+Dt =
(åqin-qout)Dt
Q: Remaining Content (m
3)
qin: Inlet (m
3/s)
qout: Qutlet (m
3/s)
Dt: Time (s)
By using previous equations, drainage pattern can be drawn. In this study, a parameetr of infiltration was given, 1.0, because purpose is just DEM evaluation.
Figure 9 shows histogram of difference between original runoff data and resampled runoff data os each grid size. The histograms show symmetrical form. Figure 10 shows a relationship between grid size and percentages of correct pixels. In case of runoff analysis, correct pixel means difference with original data I indicates inside of 20m3/s. the nearest neighbor sampling showed the highest accuracy, minimum value sampling showed the worst accuracy. The accuracy of runoff analysis indicates higher than slope stability analysis.
Figure 9 Accuracy of Drainage Pattern according to Spatial Resolution
Figure 10 Accuracy of Drainage Pattern according to Spatial Resolution
4.Conclusions
In this study, an accuracy of DEM according to spatial resolution was considered. Spatial resolution didn't influence a slope aspect very well. A slope aspect is not sensitive on spatial resolution surface generally undulate in even one pixel, so that such detailed retrain is neglected by resampling. This situation also influence slope stability analysis. The result showed under estimation in case of low resolution data. The inclination is one of the most important factor in a slope stability analysis. And almost terrain analyses use combination of slope aspect and inclination. So, we must take care to use low resolution DEM.
We tried to compare with each resamplign method. In those resampling method, nearest neighbor resampling showed the best method except slope aspect. Minimum value resampling showed the worst. Test area was selected from mountainous area. Minimum value makes flat, so that is was much different from original data.
In this study, the highest used resolution is 50m grid DEM. However, we will use less than 10m grid by commercial very high resolution satellite. In future, such very high resolution DEM must be evaluated. A spatial resolution was very important for any analysis.
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