International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
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Figure 1. General location of the study site
Two contrasting sites within the subset were chosen: an
‘Upstream site’ with undulating terrain, and a ‘Downstream
site’ with relatively flat topography.
3. METHODS AND PROCEDURES
The overall methods in this study can be seen in the flow
diagram in Figure 2.
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Figure 2. Overall flow diagram of the study
The DEM was generated from aerial photos of 1:24,000, using
soficopy photogrammetry methods in the Orthoengine Module
of PCI Geomatica 8.2.3. The originally-generated DEM is in 5
m resolution.
3.1 Root Mean Square Error (RMSE)
Root Mean Square Error (RMSE) is measured from discrete
sample points and is commonly used to estimate error or
uncertainty in locations where crror was not measured directly
(Holmes, 2000). For DEM, RMSE refers to the degree of
differences between interpolated values and the “most
probable” elevation -- so as not to use the term “true” elevation,
which is normally considered unknown--. Methods for
obtaining the sample points include GPS measurements,
triangulation points, or a DEM of higher accuracy.
In this study, high accuracy GPS measurements were done with
carrier phase processing, utilizing Trimble Pro XR as the rover
and Trimble Base Station as the base station. The accuracy of
this method goes up to sub-meter for horizontal (GPS Tutor,
1998) and approximately 1-2 m for vertical accuracy
accordingly. Thirty-five high accuracy elevation points were
collected and a subset of 14 points was used to give an error
indication of the DEM generated.
3.2 DEM Perturbation using Monte Carlo Simulations
The number of GPS measurements is often limited due to time
or budgetary constraints. Modeling offers a way out to assess
the effects of error in elevation on the derived products.
To simulate the error over the whole surface of a DEM, a grid
of random errors (random field) was generated and perturbed to
the original DEM using Monte Carlo method. Monte Carlo
method can be loosely described as statistical simulation
method that utilizes sequences of random numbers according to
a certain statistical distribution. Any statistical distribution can
actually be used to generate the random errors, but the Gaussian
normal distribution is most commonly used. When additional
information is available about the structure of errors in a data
set, the Gaussian model should be replaced with a more
accurate representation (Hunter and Goodchild, 1997).
In this study, random fields were created with the same
geospatial extent of the DEM and with the properties based on
the statistics of the error indication of the DEM; mean - 0 and
standard deviation = RMSE obtained from validation ( p= 0, o=
RMSE). The random fields were created for N number of times
(N simulations) to perturb the DEM.
The 14 samples for elevation validation were considered
insufficient to represent the magnitude of error over the whole
study site. Therefore in generating the random fields for
perturbing the original DEM, instead of using only 10 m as the
elevation RMSE, a series of assumed elevation RMSE's of 5,
10, 15 and 20 m were used.
3.2.1 N Optimum. The optimum number of simulations was
derived from Wechsler (2000) based on the Law of Diminishing
Return. A grid of standard deviation values is obtained for each
N. From each standard deviation grid, a standard deviation is
calculated and kept. The observation is done on the increments
of 25. Once the difference of standard deviation estimated from
the sequential N falls at 596, the N optimum (N,y) is reached.
This procedure is applied across the perturbed DEMs with
different perturbation layers (different assumed RMSEs).
Five hundred simulations were run to each initial DEM RMSEs
(5, 10, 15, and 20 m) and then the average values of the
resulting RMSE grid for each 25 increments were taken out.
Observation was done to see when the 5% difference is reached.
3.2.2 Sensitivity Analysis. Various RMSEs were used as the
statistics for the random ficld. Sensitivity tests (Jorgensen,
1994) were then conducted to observe the effects of the variable
DEM RMSEs to the RMSEs of the derived products.
Two types of perturbation layers were used for the simulation,
ie. Random field and Spatially-dependent field. These
perturbation filters are explained in the following sections.
3.3 Random Field - Unfiltered
The first approach of perturbation assumes that error is
spatially-independent with a normal distribution and mean =
zero. The random field generated based on that assumption was
added to the original DEM as a single DEM realization to be
tested, of which N realizations would be simulated.
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