Good educational materia

1. Experiments with National
Digital Elevation Models
Yaron A. Felus, Robert C. Burtch, and Chad Schaeding
Surveying Engineering Department
Ferris State University, MI
http://btcsure1.ferris.edu/NGA/
915 Campus Dr. Swan 314, Big-Rapids, MI 49307
E-mail: felusy@ferris.edu or burtchr@ferris.edu

2. Presentation outline
• Introduction
• Existing National Digital Elevation Models
– National Elevation Data Set (NED) by USGS
– Shuttle Radar Topography Mission (SRTM)
• Experiments with the data
• Accuracy analysis with respect to standards
• Applications:
– Using free data to ortho-rectify aerial photographs.
• The FSU-NGA project
– Spatial interpolation, Kriging and Co-Kriging
• Conclusions

3. National Elevation Data Set (NED)
• The National Elevation Dataset is a new elevation
product assembled by the U.S. Geological Survey
(USGS).
• The development of NED began in the early 1990’s
and was completely assembled in 1999 by merging
and processing the individual 7.5 minute DEM (with
10 & 30 meter resolution at NAVD88 ).
• It was designed to provide national elevation data in
a seamless form with a consistent datum, elevation
unit, and projection.
• Data corrections were made in the assembly process
to minimize artifacts, permit edge matching, and fill
sliver areas of missing data.

4. Shuttle Radar Topography Mission (SRTM)
February 11, 2000, the Space Shuttle gathered topographic data
over approximately 80% of the land surfaces of the Earth.

5. Shuttle Radar Topography Mission
(SRTM) data
• The SRTM data were acquired by the National Geospatial-
Intelligence Agency (NGA) and the National Aeronautics
and Space Administration (NASA) using a radar system
that flew onboard the Space Shuttle Endeavour during an
11-day mission in February, 2000.
• Currently two products are available:
– One arc-second resolution (~90’) for the United States
and its territories
– Three arc-second (~270’) for all the areas between 60º
North and 56º South latitudes.
• The radar data underwent extensive processing and noise
filtering before they were released to the public. SRTM
DEM uses WGS84 datum and EGM96 geoid model.

6. • Download data from http://seamless.usgs.gov/
How to obtain the data

7. Accuracy of NED and SRTM
• NED (left) Vs. SRTM (right)
• SRTM is a Digital Surface Model and was filter extensively

8. Accuracy of NED and SRTM
• Smith and Sandwell (2003) performed spectral
analysis of the 1-arcsecond SRTM and NED data
and found that following
– Root Mean Squared (RMS) of the SRTM data is
2.7m
– Root Mean Squared (RMS) of the NED data
3.5m
• Reinartz et al (2005) conclude that SRTM data
accuracy decreases drastically in forest areas since it
neither represents the tree canopy or the ground.

9. Case study, the FSU golf course
• Evaluating the accuracy of SRTM/NED data
Comparing
• SRTM
• NED
• Photogrammetry
• GPS

10. • Even though USGS standards for DEM require only 20 check
points with at least eight scattered around the edge.
• More than 500 points were collected in Real-time Kinematic
(RTK) mode using the Big Rapids Continuous Operating
Reference Station (CORS) at a distance of less than 1mile.
Case study, the FSU golf course

11. Case study, results
Elevation
Evaluation
NED SRTM
Mean Error (m) 1.173 1.161
Minimum Error (m) -5.732 -3.536
Maximum Error (m) 6.434 6.106
RMSE (m) 2.944 2.097
Table 1: Accuracy comparison of the NED and SRTM data, with
respect to the GPS measured points
Slope Evaluation GPS35-NED35 GPS35-SRTM35
Mean Error (degrees) -0.464 -0.795
Minimum Error (degrees) -3.78 -4.418
Maximum Error (degrees) 3.976 1.918
RMSE (degrees) 1.557 1.645
Table 2: A comparison of the slope parameter of the different surfaces

12. Accuracy standards
National Map Accuracy Standards (NMAS)
• The NMAS defines the following two criteria to test the
vertical accuracy of a topographic map:
– “Vertical accuracy, as applied to contour maps on all
publication scales, shall be such that not more than 10
percent of the elevations tested shall be in error by more
than one-half the contour interval.” .
– “The accuracy of any map may be tested by comparing the
positions of points whose locations or elevations are shown
upon it with corresponding positions as determined by
surveys of a higher accuracy.”

13. Accuracy standards
American Society for Photogrammetry and Remote
Sensing (ASPRS)
• The ASPRS standard is using the Root-Mean-Square Error
(RMSE) statistic to evaluate the accuracy of a given spatial data.
• The RMSE is defined as:
Class 1 map should have a vertical RMSE of 1/3 the contour
interval for well-defined points and 1/6 the contour interval for
spot elevations.
Maps compiled within limiting RMSE errors of twice or three times
those allowed for Class 1 map shall be designated as Class 2 or
Class 3, respectively.
n
z
z
RMSE
t
i
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2
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(

14. COMPATIBLE MAP SCALES & CONTOUR
INTERVALS FOR AVERAGE TERRAIN
Imperial Units SI Units
SMap CI SMap CI
1”=50’ 1’ 1:500 0.5 m
1”=100’ 2’ 1:1000 1 m
1”=200’ 5’ 1:2000 2 m
1”=500’ 10’ 1:5000 5 m
1”=1000’ 20’ 1:10000 10 m

15. Is it good for floodplain plan?
Section 142 of Act No. 59 of the Public Acts of 1978, as amended, being S559.242 of
the Michigan Compiled Laws
• A flood plain plan when the condominium lies within
or abuts a flood plain area, showing all the following:
– The location of all condominium buildings and
improvements….
– The contours over the entire project shown at 2-foot intervals.
NO!

16. Using NED and SRTM data for
orthophotographs creation
Orthophotography is a
geometrically corrected
photograph created
from either aerial or
satellite imagery.
The most expensive part of
producing an
orhtophoto is generally
the creation of the
DEM.
1
4
3
Orthographic Projection

17. Case study, the FSU golf course
• Two orthophotographs were created using the Leica
Photogrammetry Suite from 1:10,000-scale photography taken at a
flight height of 1,582 meter above the average terrain and scanned at
ground resolution of 0.15 meters.
• The initial NED and SRTM DEMs were projected from their native
geographic coordinates to Michigan State Plane coordinate system to
create a 35x35 meter resolution DEM.
PTS
Max
Error RMSE NMAS
ASPRS,
class 1 Class 2 Class 3
NED 54 5.14 1.76 1:3400 1:7025 1:3513 1:2342
SRTM 54 4.51 1.36 1:2450 1:5500 1:2720 1:1814
Table 3: The accuracy of the NED and SRTM created orthophotographs
evaluated against the GPS points.

18. Orthophotography
accuracy
The errors were larger on
the edges of the
orthophotograph and
very small near the
center of the image
(nadir point).
Distance 0 200 400 600 800 1000 1200 1400 1600 1700
RMSE 0.15 0.17 0.25 0.38 0.57 0.82 1.12 1.48 1.89 2.12

19. From the results of experiments undertaken in this study, it is clear
that these government datasets can be used to create orthophotos
at a scale of 1:10,000 that meet acceptable industry standards
such as those developed by ASPRS.
This study found that the SRTM data had slightly better accuracy
than the NED data but it may not represent the terrain properly
and may have larger errors in computing slope and aspect
parameters. It is also important to note that the SRTM data is a
DSM while NED data is a DEM measuring ground topography.
SRTM data is current which is an important advantage providing a
proper model that can be used for many applications, even for
updating the NED.
Concluding remarks for the
experiments with DEMs

20. Multisource Data Fusion
Strategies and methods for integrating data from different
(and possibly diverse) sensors.
Process results maintain the highest accuracy and resolution
existing within the original data
Data set 1
high resolution and
accuracy
Data set 2
low resolution and
accuracy Nugget
Nugget
TLS Variogram
estimation
TLS Variogram
estimation
TLS
transforation
Sequential
kriging
+
Elevation grid with
improved resolution
Kriging variance
metadata report

21. Ellipsod
Geoid
Topogrphy
Ho
He
Point
Ho - Orthometric height
He- ellipsodial height
Ocean
Interpolation of the Geoid Undulation Surface
Geoid separation -N
The geoid separation is also termed geoid undulation
Ho = He - N
Interpolation procedure should be employed to obtain the geoid
undulation surface from measurements made in specific points.

22. Geoid 2003
What is the geoid undulation
in Michigan?

23. SPATIAL INTERPOLATION
Interpolation is the procedure of predicting the
value of an attribute at unsampled site from
the measurements made at point locations
within the same area or region.

24. SPATIAL INTERPOLATION
• Data close together in space (e.g. elevations, geoid
undulation) or time (e.g. temperatures) are likely to be
correlated (related).
• Many interpolation procedures and methods are being
used in different fields of science. These methods can
be classified into a few categories.
• Global/Local:
• Exact/Approximate Interpolators:
• Stochastic/Deterministic Interpolators
• Gradual/Abrupt Interpolators.

25. Geoid 2003
• USGG2003 is a gravimetric geoid file covering the
Conterminous United States.
• It improves the gravimetric geoid primarily along the East
Coast and especially in Florida (a reduction from 40 to 30
cm in misfit).
• The USGG2003 geoid undulations refer to a geocentric
GRS-80 ellipsoid.
• USGG2003 was computed on a 1 x 1 arc minute grid
(about 1 mile)
Interpolate the
value of geoid
undulation between
the grid values

26. Global/Local Interpolations
• Global:
• global interpolators determine a single function which is
mapped across the whole region
• a change in one input value affects the entire map
• Local:
• local interpolators apply an algorithm repeatedly to a
small portion of the total set of points
• a change in an input value only affects the result within
the window

27. Exact/Approximate Interpolations
• Exact:
• exact interpolators honor the data points upon which the interpolation is
based. the surface passes through all points whose values are known
• Approximate:
• approximate interpolators are used when there is some uncertainty about the
given surface values
• this utilizes the belief that in many data sets there are global trends, which
vary slowly, overlain by local fluctuations, which vary rapidly and produce
uncertainty (error) in the recorded values
• the effect of smoothing will therefore be to reduce the effects of error on the
resulting surface

28. Stochastic/Deterministic
Interpolations
• Stochastic:
• stochastic methods incorporate the concept of
randomness
• the interpolated surface is conceptualized as one of
many that might have been observed, all of which
could have produced the known data points
• Deterministic:
• deterministic methods do not use probability theory

29. Gradual/Abrupt Interpolations
• Gradual:
• a typical example of a gradual interpolator is the distance
weighted moving average
• Abrupt:
• it may be necessary to include barriers in the
interpolation process

30. Kriging techniques (Geostatistics)
• Professor Georges Matheron
(1930-2000) developed the formal
foundation of Geostatistics,
centered, in the beginning, on
estimating changes in ore grade
within a mine.
• However, the principles have
been applied to a variety of areas
in geology and then to other
scientific disciplines.
• Geostatistical interpolation is
known as kriging after D. G.
Krige.

31. Kriging assumptions
• Some spatial surfaces cannot be modeled using deterministic
methods that use smooth mathematical functions. Specifically if
data are sparse, for example ground-water modeling, gravity
data, soil mapping, water toxicity, air pollution, bathymetric data
etc.
• Kriging is a stochastic interpolation method in contrast with
deterministic methods (TIN, Inverse distance, trend
estimation).
• It attempts to statistically obtain the optimal prediction i.e. to
provide the Best Linear Unbiased Estimation (BLUE),
specifically when data are sparse Sparse =>kriging
Dense =>deterministic

32. Kriging assumptions
The basic assumption is that the spatial variation can be
expressed by the following summation:
z(s0) = m(s0) + x (s0) + e
where
m(s0) = deterministic function describing the ‘structural’
component of z
x(s0) = stochastic, spatially dependent residual from m(x)
e = Observational noise

33. Variogram / Covariance function
• Spatial dependence is usually expressed mathematically
in the form of a spatial coherency function such as the
semi-variogram, or the covariance function.
• The semi-variogram and the covariance function are
valuable tools in explanatory data analysis. Moreover
these functions control the way in which kriging weights
are assigned to data points during interpolation.
10.3
22.9
18
.3
480
420
240
170
260
2
1
.
1
31.9
Unknown
Covariance
Lag Distance

34. Ordinary kriging, Basic Steps
Steps in the kriging interpolation process:
1. Explanatory data analysis; identify and eliminate outliers
and trend ( compute m(s0) using Trend estimation )
2. Estimation of the variogram ( 2(h) )
3. Using the semi-variogram to perform kriging prediction
(1)
where is our interpolated point, z(si) are the sample points,
and λi are kriging coefficients
4. MSPE calculation and error analysis (cross validation)
)
(
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0 i
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z
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35. Interpolation Summary
• There is no 'best' interpolation algorithm that is
clearly superior to all others and appropriate for all
applications.
• The quality of the resulting DTM is determined by the
distribution and accuracy of the original data points, and
the adequacy of the underlying interpolation model (i.e.
a hypothesis about the behavior of the terrain surface);
• The most important criterion for selecting a DTM
interpolation method are the degree to which
(1) structural features can be taken into account, and
(2) the interpolation function can be adapted to the
varying terrain character.

36. Interpolation Summary
• Other criteria that may influence the selection of a
particular method are the degree of accuracy desired and
the computational effort involved
• Cross validation is the procedure where one data is
removed and the rest of the data is used to predict the
removed data. Thus an estimate of the accuracy is obtain
by:
Error = Predicted value - known value

37. Ferris State and Height
Modernization
The Best Surveying Students!
The support for this research from the National Geospatial-
Intelligence Agency under contract no. HM1582-04-1-2026 is
greatly acknowledged.