Introduction
Prior
to this lab each group was to create a terrain inside of a sandbox of about one
square meter (Figure 1), and then tasked to come up with a sampling scheme and technique
for the creation of a digital elevation surface. Due to the small size of the
study area, the grid scheme consisted of 6 X 6 cm squares and systematic point
sampling was used to gather elevation data from the X, Y intersections of each
square. In cases of sharp change in elevation within one square two
measurements were taken in one square, giving the X or Y a 0.5 decimal place in
the coordinating location. Data was manually recorded on a hand drawn grid
matching that of the one created over the sandbox. This method organized the
data and assisted in data normalization as it was entered into an excel
spreadsheet. Data normalization involves the input of data into a database so
that all related data is stored together, without any redundancy. Data for this
excel file was set to numeric, double to indicate the decimal values and keep
all data in the same format. X, Y, and Z data for each grid was entered
beginning at the first X column from bottom to top and so forth, this pattern
eliminated redundancy and kept all data inside one excel file. In total; 434
data points were collected in a relatively uniform pattern throughout the
entire study area, with some clustering of points in areas with rapid change in
elevation. These data points can be imported into ArcGIS or Arc Scene, where
interpolation can mathematically create a visual of the entire terrain based on
the know values.
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| Figure 1 |
Methods
To bring this process a
geodatabase was created and the excel file, which has been set to a numerical
data format, is imported into the database, brought into ArcMap as X, Y data,
and then converted into a point feature class. After a point feature class has
been made the data can be used to create a continuous surface using
interpolation methods. Four raster interpolations and one done in a vector
environment are experimented with to determine the ideal representation of the
terrain. The four raster operations are: Inverse Distance Weighted (IDW),
natural neighbors, kriging, and spline. The interpolation done in a vector
environment is called TIN.
IDW and spline methods are
deterministic methods, they are based directly on a set of surrounding points
or mathematical calculation to produce a smooth continuous surface. IDW
interpolation averages the values of known points in the area of the cells
being calculated to give them values based on proximity to the know values;
cells closer to known points are more influenced by the average than those
farther away. Influence of known points can be controlled by defining power, a
larger power will place more emphasis on near points and result in a more
detailed map, while a lower power will place emphasis on distant points as well
to produce a smoother map. Produced values can also be varied by manipulation
of the search radius to control for distance of points from the cell being
calculated. The IDW interpolation method would not be advantageous for random
sampling methods, areas with a higher density of samples would be more well
represented than areas with fewer points. Spline uses a mathematical function
and the resulting surface passes exactly through each sample point, making it
ideal an ideal method for large samples. The function used creates a smooth
transition from one point to the next and is ideal for interpolation of
gradually changing surfaces such as; elevation, rain fall levels, and pollution
concentration. Since this method passes through each sample point to create the
resulting surface, it is not ideal for sampling techniques that result in
clustered areas or fewer sample points in proportion to the entire area, such
as random and/or stratified.
Kriging is a multi-step,
geostatistical method of interpolation that creates a prediction of a surface
based on sample points and also produce a measure of accuracy of those
predictions. It assumes a correlation between points based on distance and
direction between them. Kriging is similar to IDW in the fact that it weights
points in a certain vicinity but it goes beyond IDW and takes spatial
arrangement of the sample points into account, in a process called variography.
While kriging goes a step beyond IDW to create a more accurate portrayal of a
surface, like IDW it is not an advantageous method for sampling techniques that
have resulted in clusters of sample points, such as random sampling.
Natural neighbor interpolation
utilizes a subdivision of known points closest to the unknown point to
interpolate and does not deduce patterns from the subdivision data. Hence if
the entered sample does not indicate the pattern of a ridge, valley, etc.; it
will not create this feature. Natural neighbor interpolation is advantageous
for samples that have been collected using a stratified sampling method due to
subdivisions within the study area. However
random sampling may result in poor representation of a specific surface and
thus natural neighbor would produce a poor representation of the surface as
well.
TIN, or triangulated irregular
network, uses an algorithm to select sample points in the form triangles and
then creates circles around each triangle throughout the entire surface. The
intersections of these are used to create a series of the smallest possible,
non-overlapping triangles. The triangle`s edges cause discontinuous slopes
throughout the produced surface, which may result in a jagged appearance and
TIN is not an advisable interpolation method for areas away from sample points.
Given the comprehensive and uniform
collection of sample points in the terrain, each of these methods should
produce a relatively accurate portrayal of the terrain. However, the areas with
more densely collected data may result in over-representation in those areas in
all interpolation methods except spline. Because of the fact that spline
interpolation passes the surface though each data point and produces a smoothed
surface in-between the points. Further reading in ArcGIS help indicates that
spline is also ideal for areas with large numbers of sample points and
gradually changing surfaces, like elevation. This indicated it would be the
most ideal method for the survey.
Results/Discussion
Prior to this activity, it
was necessary to create a sandbox terrain and spatially sample it for elevation
values. The entire terrain was slightly larger than one square meter and a
systematic point sampling of the entire terrain was feasible. Systematic sampling
done within an X, Y plane consisting of 361, 62 centimeters, quadrates
resulted in an excel spreadsheet with 434 data points (Link to excel file).
After the excel file was imported into ArcGIS as X, Y data and converted into a
point feature class (Figure 2A), it produced a collection of sample points that
were uniform throughout most of the terrain, with areas of sharp change in
elevation more densely sampled. Each of the five interpolation methods
described above were applied to the feature class to create different
continuous elevation surfaces and each analyzed for best fit for the survey.
For each method, the elevation from
surfaces option was set to floating on a custom surface with the custom surface
being set to the corresponding surface being interpolated and each was set to
shade areal features relative to the scene`s light position. Furthermore, other
than the TIN method, each scene was set to a stretched symbology with the same
color ramp. The TIN method only offers elevation symbology and did not offer
the same color ramp. All First, IDW
resulted in elevation changes that were relatively smooth and accurate but the
image appeared “dimply”, similar to that of a zoomed in view of a golf ball in
almost the entire image (Figure 3A). Kriging also accurately represented
elevation, but it appeared very geometric. It would most likely appear similar
to a fractal if each shape within the image were colored in differently (Figure 3B). The natural neighbor method is smooth in most places, but edges are rough
and smaller elevation changes are less pronounced (Figure 3C). TIN
interpolation produced a very detailed image, however it is very “blocky” with
angular curvature instead of a smooth surface appearance (Figure 3D). Finally,
the spline interpolation method produced smooth elevation transitions, with the
most pronounced representation of different elevations throughout the terrain. Based
on these results, the spline method appeared to be the interpolation most
appropriate for the survey taken (Figure 2B).
Before applying the interpolation
methods and having only researched sampling techniques and some about the first
geography law; it seemed the survey performed may have been slightly excessive.
However, on the other hand, a larger survey is ideal and the time taken to
perform the survey was not all that long. After experimenting with and reading
about each interpolation method, it can be concluded that the sampling
technique and grid scheme was not too excessive. The results from each
interpolation method captured most details of the original terrain, and it was
clear what was being portrayed in each image.
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| Figure 2 |
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| Figure 3 |
Summary/Conclusions
Field based surveys collect
essential spatial data needed to determine the relative data of unknown areas
within proximity to the collected data, in order to establish an acceptable
representation of the entire study area. This activity illustrated the basics
of the survey process on a much smaller scale than usual. Like this survey,
surveyors need to decide which sampling technique and tools are most suitable
for the task. However, the tools used in most field-based studies are go beyond
string and thumbtacks, some of the tools used include GPS receivers, total
stations, 3-D scanners, and UAVs. In larger survey areas, surveyors must also
consider temporal aspects. If a survey is to be done as a follow up to a
previous one, the surveyors need to consider whether it should be done in the
same temporal situation as the previous survey. Alternatively, if a new survey
is to be conducted, the surveyors need to determine the best temporal situation
for the survey. The detail given to this small scale survey is not always a
feasible option, resulting in a different collection of sample points. This is
where the other interpolations would yield a more accurate representation of
the survey in question.
Interpolation
is a useful tool for visualization of many things beyond elevation. Other
gradually changing phenomena’s such as water table levels and rain fall can be
interpolated or demographic data, such as a survey of HIV distribution in
Africa. Ecological surveys, such as forest type could also be interpolated. Interpolation
methods are crucial in many fields for the extraction of important information
otherwise extremely difficult or impossible to survey completely.
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