International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
Similar procedure of simulation in PC Raster was applied to the
filtered-perturbed DEM. At the end of N,, simulation,
similarly, the statistics grids of DEM as well as of slope were
obtained. Due to computational limitations, for this method,
only DEM with 20 m cell size was used.
3.7 Assessment of Output
To comply with the objectives, the following statistics were
used to evaluate the level of uncertainty:
1) Grids of elevation RMSE and slope RMSE, which are
defined as:
RMSE:
where: Y, = estimator of the parameter Y. . In this study, the
y is the original data, DEM or slope.
N = number of simulations.
To avoid confusion between the RMSE as the input of assumed
error for perturbation layer with the RMSE as the statistics for
uncertainty, the term ‘initial DEM RMSE’ is used for the first
and ‘output RMSE ’ for the latter.
2) Average value of each RMSE grid (from 1) above) was
used to observe the trends and effects of tested parameters on
the variables of interests, i.e.:
- Effects of initial DEM RMSE on slope RMSE
- Effects of resolutions on slope RMSE
3) The average grids of slope at the end of N simulations were
also analyzed visually to see the resulting derived slope, and to
compare those resulted from unfiltered perturbation and from
filtered perturbation with the original DEM.
4. RESULTS AND DISCUSSION
From the elevation validation using GPS measurements, the
difference in clevation resulted was an RMSE of 10.7 m.
The simulations to determine N optimum for perturbation
simulations gave result that across different initial RMSEs, the
5% difference occurs between N =125 and N = 175. Therefore,
the number of simulations considered to be optimum was 150
(Figure 5).
—e— Difl 5% |
- Diff 1096 ||
|— - Din 15% ||
(TE Diff 205 |.
% o
LA CA
i
=
u
2s —
a
C
RMSE Difference (%)
Figure 5. N optimum of the simulation
4.1 Semivariogram Analysis.
The results of Semivariogram show that for the Upstream site,
similar behavior of the semivariance is shown within the
distance of approximately 375 m while for the Downstream site
it is within the distance of approximately 130 m (Figures 6 and
7). Those distances were then used as the distances of spatial
dependence (SDD) in filtering the random field to obtain
“weighted-mean” filter.
100% 10% T—— ——— BR SAL DURCH
140x103 I
120x103 /
100x103 / 7
80x10° /
60x 105 DES 1
+
g AC
40x10 -— —9— Omni
250 450
Semivariance
20x10? —^ - 90Deg
T
50
—-— 180Deg |
650 850 1050 1250
Distance Lag (m)
Figure 6. Semivariogram of the Upstream site
400 4
—9— Omni
—45Deg & |
—é - 90Deg 7 |
300 | — 180Deg A
: a
8 « .
$ 200 "€ sd
= x^ de — |
5 > | |
N "a. eT
100 e) a €
50 150. 250. 350 450 550 650
Distance Lag (m)
Figure 7. Semivariogram of the Downstream site
4.2 Sensitivity Analysis — effects of initial RMSE on slope
RMSE
The result shows that the increase of initial DEM RMSE affects
the increase of slope RMSE following linear trend (Figure 8).
For the higher resolution (5 m), the trend appears to be
curvilinear, as the slope of the graph is smaller for the higher
initial DEM RMSE.
When comparing the two sites, for each initial DEM RMSE and
each cell size, the slope RMSE is higher in the Downstream site
than in the Upstream site. This result shows perturbation has
stronger effects in adding variability to the original elevation
variability in the flat area than in the undulating area.
60 1——7———9—————————
— $— Up 5m cell
— Up iüm cell
S0 4 — a— Up 20m cell
——9—— Down 5m cell
——# Down 10m cell
——k— Down 20m cell
40
Slope RMSE
8
0 5 10 15
Initial DEM RMSE
Figure 8. Sensitivity of initial DEM RMSE on Slope RMSE
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