Date post: | 11-Nov-2018 |
Category: |
Documents |
Upload: | nguyenkhue |
View: | 215 times |
Download: | 0 times |
1
John Lloyd
MEA582 Fall 2011
Homework 7: Spatial interpolation and approximation: methods
October 11, 2011
ContentsTask ............................................................................................................................................................... 2
Approach ....................................................................................................................................................... 2
Results ........................................................................................................................................................... 2
GRASS ........................................................................................................................................................ 2
Computing Voronoi Polygons ............................................................................................................... 2
Interpolation using IDW ........................................................................................................................ 5
Experiment that elucidates the Impact of IDW Parameters ................................................................. 7
Computing DEM from Contours using Linear Interpolation ............................................................... 13
ESRI ArcMap ............................................................................................................................................ 15
Computing DEM based on Voronoi Polygons ..................................................................................... 15
Interpolate DEM using TIN .................................................................................................................. 17
Interpolate DEM using IDW ................................................................................................................ 18
Discussion ................................................................................................................................................... 19
Conclusion ................................................................................................................................................... 19
2
TaskThis assignment's tasks were to interpolate elevation surfaces using various approaches and understand
the differences and problems with each of the results.
ApproachI started with a dataset of points containing x, y, and z (elevation) coordinates. I then created elevation
rasters using Voronoi Polygons, Triangulated Irregular Networks (TIN), Linear Interpolation between
Contours, and Inverse Distance Weighting (IDW). I used a hillshade raster to emphasize the differences
in topology. I also viewed 3D representations of the rasters to further explore differences.
Finally, I devised an experiment to show the effects of varying the IDW algorithm’s number of points and
exponent parameters. The experiment varied one parameter at a time and then compared the rasters
both visually and statistically.
Results
GRASSI completed these tasks using GRASS GIS 6.4.2svn48509 (2011) on Windows7.
ComputingVoronoiPolygonsI computed Voronoi polygons from a set of random elevation points using the v.voronoi tool. The
attribute "value" associated with each polygon is the elevation of the point contained by the polygon.
From the polygons I used the v.to.rast tool to create an elevation raster and the r.slope.aspect tool to
create an aspect raster. The results are shown in Figure 1 Zoom in on portion of elev_vor showing
polygons, Figure 2 elev_vor_1m elevation raster, and Figure 3 asp_vor_1m aspect raster.
Figure 4 elev_voronoi with elevation, aspect, and points shows the resulting elevation map.
An aspect raster created from an elevation raster derived from Voronoi Polygons is unusable. Because
the entire polygon contains the same elevation value, the only points in the raster, where a slope exists
are the borders of the polygons. Hence, the majority of the cells will contain the “no slope” value.
Figure 5 Hole in Elevation Raster shows a hole in the elevation raster (and also the aspect raster but not
shown). There appear to be points inside the hole and it looks like a polygon was created, but no cells
were assigned the attribute values. This may be an indication of a bug.
Figure 6 elev_vor_1m viewed in nviz shows the nviz view of Voronoi Polygon derived elevation raster.
3
Figure 1 Zoom in on portion of elev_vor showing polygons
Figure 2 elev_vor_1m elevation raster
4
Figure 3 asp_vor_1m aspect raster
Figure 4 elev_voronoi with elevation, aspect, and points
5
Figure 5 Hole in Elevation Raster
Figure 6 elev_vor_1m viewed in nviz
InterpolationusingIDWI used the v.surf.idw tool to create an elevation raster using Inverse Distance Weighting (IDW)
interpolation. Then, I used the tool r.slope.aspect to create an aspect raster from the elevation raster.
The results are shown in Figure 7 elev_idw_1m elevation raster and Figure 8 asp_idw_1m aspect raster.
Figure 9 elev_idw with elevation, aspect, and points and Figure 10 elev_idw_1m in nviz show the
resulting elevation map.
6
Figure 7 elev_idw_1m elevation raster
Figure 8 asp_idw_1m aspect raster
7
Figure 9 elev_idw with elevation, aspect, and points
Figure 10 elev_idw_1m in nviz
ExperimentthatelucidatestheImpactofIDWParametersI first used the g.region command to zoom in on a one portion of the map allowing me to see smaller
differences in the rasters. I chose an area about 100m by 100m in the center of the map containing a
slope (See Figure 11 Grey patch indicates area of experiment and Figure 12 The experiment area with
default, p=2, npoint=12, parameters in nviz). Then, I reran the v.surf.idw command with the default
parameters, exponent p=2 and neighbor points npoint=12, to create an elevation raster covering only
my zoomed in area (Figure 13 Defaults p=2 np=12).
Then, I created four more elevation rasters varying one of the parameters at a time (Figure 15 p=0.5
npoint=12 to Figure 18 p=2 npoint=60). I created two rasters by varying the p value above and below the
8
default; decreasing p to 0.5 and increasing p to 5, and I created two rasters by varying npoint parameter
above and below the default; decreasing the npoint value to 5 and increasing npoint to 60.
I can see that by decreasing p from 5 (Figure 16 p=5 npoint=12) to 0.5 (Figure 15 p=0.5 npoint=12) I got a
smoother surface, which is as expected, since the farther points had a greater influence with the
decreasing p value. The histogram in Figure 21 p=0.5 npoint=12 Histogram contains less spikes than the
histogram in Figure 22 p=5 npoint=12 Histogram also indicating a smoother surface. Figure 27 nviz of
p=0.5 npoint=12 and Figure 28 nviz of p=5 npoint=12 show the same surfaces in nviz.
However, with my initial experiment it was difficult to see the influence of npoint, possibly because the
default, p=2, caused the additional points that were farther away to have little influence. I reran the
experiment with p=0.5 and varied the npoint from 5 to 60. This time I could see that increasing the
npoint parameter to 60 caused the elevation to blur in some places but also caused spikes and holes at
the extreme elevations as those points had less influence on the cells around them (Figure 20 p=0.5
npoint=60). The histogram in Figure 26 p=0.5 npoint=60 Histogram is more bunched in the middle
showing less influence of the extreme high and low elevations. Figure 29 nviz p=0.5 npoint=5 and Figure
30 nviz p=0.5 npoint 60 show the same results in nviz.
The results are shown in the figures below.
Figure 11 Grey patch indicates area of experiment
Figure 12 The experiment area with default, p=2, npoint=12, parameters in nviz
9
Figure 13 Defaults p=2 np=12
Figure 14 Defaults p=2 np=12 Histogram
Figure 15 p=0.5 npoint=12
Figure 16 p=5 npoint=12
Figure 17 p=2 npoint=5
Figure 18 p=2 npoint=60
10
Figure 19 p=0.5 npoint=5
Figure 20 p=0.5 npoint=60
Figure 21 p=0.5 npoint=12 Histogram
Figure 22 p=5 npoint=12 Histogram
Figure 23 p=2 npoint=5Histogram
Figure 24 p=2 npoint=60 Histogram
11
Figure 25 p=0.5 npoint=5 Histogram
Figure 26 p=0.5 npoint=60 Histogram
12
Figure 27 nviz of p=0.5 npoint=12
Figure 28 nviz of p=5 npoint=12
Figure 29 nviz p=0.5 npoint=5 Figure 30 nviz p=0.5 npoint 60
13
ComputingDEMfromContoursusingLinearInterpolationI first converted a vector line contour layer to a raster layer and, then, multiplied the cell (elevation)
values by 100 as seen in Figure 31 el_lid792_cont1m_100 contours multiplied by 100.
I used r.surf.contour to create elevation rasters from the contour rasters. The first raster (shown in
Figure 32 el_rcont elevation raster) was created from the contours without multiplying the contour
value. The second raster (shown in Figure 33 el_rcont_1 elevation raster) was created from a contour
raster after multiplying the contour value by 100 then dividing the elevation raster by 100 using
r.mapcalc in an attempt to gain better resolution.
I checked the results by creating a map with the elevation and aspect rasters for both the sets of results.
I set the aspect raster to 50% transparency, to make the elevation raster visible below. Figure 34
asp_rcont_1 and el_rcont_1 rasters and Figure 35 asp_rcont and el_rcont rasters show the results.
However, with the latest version of GRASS multiplying by 100 and dividing by 100 now has no effect on
the resolution. Previously, r.surf.contour only used integer arithmetic to interpolate the surface
between the contours. This tool has now been updated to use floating point
(http://trac.osgeo.org/grass/ticket/1168).
Figure 36 el_rcont in nviz shows the result in nviz.
Figure 31 el_lid792_cont1m_100 contours multiplied by 100
14
Figure 32 el_rcont elevation raster Figure 33 el_rcont_1 elevation raster
Figure 34 asp_rcont_1 and el_rcont_1 rasters
15
Figure 35 asp_rcont and el_rcont rasters
Figure 36 el_rcont in nviz
ESRIArcMap
ComputingDEMbasedonVoronoiPolygonsI used the Analysis Tool, Create Thiessen Polygons tool to read a set of points with an elevation attribute
and build the Voronoi polygons (Figure 37 Voronoi Polygons created around points) with the same
elevation attribute. I then used the Polygon to Raster tool convert the polygon vector shapefile to an
elevation raster.
16
To check the result I used the 3D Analyst, Raster Surface, Hillshade tool to create a hillshade raster and
superimposed this on the elevation raster. (I set the Cell Size Raster Analysis environment setting to 2m
to match the cell size used in the Polygon to Raster.) Figure 38 elev_vor2m elevation raster with
hillshade shows the result.
Figure 37 Voronoi Polygons created around points
Figure 38 elev_vor2m elevation raster with hillshade
17
InterpolateDEMusingTINI used the same set of points to create a Triangulated Irregular Network (TIN) using the 3D Analysis Tool,
TIN Management, Create TIN Tool. The TIN interpolates the elevation value using the points setting the
elevation attribute of the triangle to that of the point contained in the triangle. Figure 39 Zoom in on
TIN to show Triangles shows the triangles. Figure 40 TIN showing Topology shows the entire layer.
I then used the 3D Analysis, Conversion, From TIN, TIN to Raster tool to create an elevation raster. I
checked the result using a hillshade raster as seen in Figure 41 tinrast_2m Elevation Raster created from
TIN with Hillshade.
Figure 39 Zoom in on TIN to show Triangles
Figure 40 TIN showing Topology
18
Figure 41 tinrast_2m Elevation Raster created from TIN with Hillshade
InterpolateDEMusingIDWI again used the same set of points but with the Spatial Analysis Tools, Interpolation, IDW tool to create
an elevation raster. I checked the result using a hillshade as seen in Figure 42 elev_idw_2m Elevation
Raster with Hillshade.
Figure 42 elev_idw_2m Elevation Raster with Hillshade
19
DiscussionThere are various differences in the methods for creating elevation rasters that a researcher needs to
take into consideration. For example, the Voronoi polygon method creates a non‐continuous elevation
raster since the elevation within each polygon is constant. This will cause areas to appear flat or
stepped, when they are in fact on a slope.
With the TIN method elevation is continuous but the rate of elevation change is not continuous resulting
in sharp edges at the borders of the triangles.
The IDW method creates “bull’s eyes” or knobs around elevation extremes when the distance between
points is greater that cell size. This would make the topology look like it had more spikes and holes than
were actually present.
With IDW varying the interpolation algorithm’s input parameters can reduce these effects, but also
cause a side effect of bringing the extremes elevations closer to the middle (Figure 25 p=0.5 npoint=5
Histogram and Figure 26 p=0.5 npoint=60 Histogram). Depending on the application, the research must
choose between these trade‐offs.
Linear interpolation from contours may introduce additional error since there are two levels of
interpolation; one when creating contours from a set a points and a second from the contours to the
elevation raster. In addition, the points on lines between contours will all have the same slope making
the method bad of slope analysis.
While completing this assignment, I made an observation unrelated to interpolation of elevation rasters.
The ArcMap Spatial Analyst, Surface, Hillshade tool creates a raster of light intensity with an imaginary
light source at azimuth 315 degrees (default). This results in a raster with highest illumination values on
slopes with aspects of 315 degrees and lowest values on slopes 180 degrees opposite or 135 degrees. In
contrast the GRASS r.slope.aspect command in conjunction with the r.colors color=aspect command
causes the brightest cells to be those assigned the value of 180, but since cell values are assigned by
aspect starting at East equal 360 and decrease clockwise, 180 is assigned to cells with slope facing West
not North West as in ArcMap. The result is a different hillshade not necessarily what the viewer is
accustomed to.
ConclusionAs with many computer applications reading the manual and determining the commands and inputs is
the easy part. Understanding the details of the processing is much more difficult. Creating elevation
rasters is one of these applications. The various methods all create an elevation raster and that raster
may look correct when displayed, but knowing the inaccuracies in each representation will help the
researcher choose the correct method.