This lab is based off of a previous exercise performed earlier in the semester which involved measuring a 115 x 115cm sandbox to produce a hill, ridge, plain, depression and valley. After the terrain was molded, students created a grid system utilizing pins and strings in efforts to normalize the data. 576 sample points of the elevation model were recorded in order for the data to be normalized. This was essential to successfully project the data. Data normalization, according to Esri, can be defined as "the process of organizing, and cleaning data to increase efficiency for data use and sharing." The data points gathered from the sandbox were entered into a table in x,y,z-(elevation) format in order for it to be used in ArcMap. These points were converted into a grid system in ArcMap in order to display the elevation of individual data points gathered within the sandbox. The data sampling method chosen for these particular points was a systematic sampling technique. This method was found to be the most accurate and effective with gathering individual points on the grid. It has consistent intervals which are recorded at specific sampling points. The group which performed this sampling method created equal intersections with the string and utilized equal intervals of five centimeters along the x and y axis of the sandbox. The interpolation procedure in this lab helps in visualizing this data by displaying 3D models of the sandbox. These series of maps helped in representing the entire surface of the sandbox simply based off of the plots of each recorded point. Figure 1 below displays a section of the x, y, z data used for the data points.
Methods:
Once the data was normalized and a geodatabase was created, the x,y,z data points were imported into ArcMap by navigating to File-->Add XY Data. This was exported as a feature class within the geodatabase. Since the points were established in relation to a specific reference point at (0,0), a cadastral coordinate system was utilized without projecting the data. A grid was then established and ran through a series of different interpolation methods in order to determine advantages/disadvantages of each, as well as how realistic of a representation of the sandbox terrain each method produced. These methods (defined by ESRI) included Inverse Distance Weighted (IDW), Kringing, Natural Neighbor, Spline and Triangular Irregular Network (TIN).
The IDW tool uses a method of interpolation which calculates cell value by taking the average values of data points in the vicinity of each processing cell. The closer a point is to the center of a cell being estimated, the more influence it has in the averaging process.
The IDW tool seemed to provide a basic picture of what the original sandbox looked like, but is lacking specific definition. This is likely due to the fact that there are only 100 total input units available.
Natural Neighbor interpolation finds the closest subset of input samples to a query point and applies weights to them based on proportionate areas to interpolate a value. Since it only uses neighboring points, it is better suited for compact datasets and terrain that has higher elevation variability.
The Natural Neighbor seemed to created an elevation that was a little distorted with elevation variance, though it served well in revealing the peaks and valleys.
Kriging is an advanced geostatistical procedure that generates an estimated surface from a scattered set of points with z-values. More so than other interpolation methods, a thorough investigation of the spatial behavior of the phenomenon represented by the z-values should be done before you select the best estimation method for generating the output surface.
Besides a couple spikes in the surface model, the Kriging created a smooth and accurate representation of the original sandbox.
Spline interpolation method estimates values using a mathematical function that minimizes overall surface curvature, resulting in a smooth surface that passes exactly through the input points.
The spline tool created the smoothest surface out of all the models. During processing, the Regularized option was selected in order to create the most accurate replica of the recorded terrain.
TIN is a vector data structure that partitions geographic space into contiguous, non-overlapping triangles. The vertices of each triangle are sample data points with x-,y-, and z-values. These sample points are connected by lines to form Delaunay triagles. TINs are used to store and display surface models.
The tin model strongly illustrated the slopes in the terrain, but poorly reflected what the sandbox looked like in that it was jagged.
Once all 5 interpolation methods were completed, the resulting output rasters were imported into ArcScene in order to produce a floating 3D view of elevation change in the sandbox. When the raster is initially brought in, it's projected as a flat surface. It can be modified to 3D by selecting "floating under a custom surface" under layer properties. The 3D surface was then exported as a JPEG and brought into ArcMap to be used as a visual aid for the maps produced in the results section. A scale bar was established by navigating to data frame properties and selecting "centimeters".
Results/Discussion
Figure 2 displays the surface of the original sandbox.
Figures 3-7 below show the resulting maps of each Interpolation method.
IDW
Figure 3 below shows a map utilizing the IDW interpolation method. This map had a fair representation of surface elevation, but did not have a very smooth surface. This was uncharacteristic of the actual terrain of the sandbox, which wasn't nearly as bumpy.
Natural Neighbor
Figure 4 below shows a map utilizing the Natural Neighbor interpolation method. The peaks of each of the "hills" appear jagged, which is unrepresentative of the actual sandbox that was measured.
Kriging
Figure 5 below shows a map utilizing the Kriging interpolation method. Elevation changes are not as strongly pronounced, but the overall surface is considerably smoother than Natural Neighbor and IDW, having less pronounced variability from point to point.
Spline
Figure 6 below shows a map utilizing the Spline interpolation method. It is obvious that the surface of this model is considerably smoother than any of the other previous 3D representations. This is likely due to the fact that Spline utilizes a mathematical function which minimizes overall surface curvature.
TIN
Figure 7 below shows a map utilizing the TIN interpolation method. It is very geometric and pointy by nature due to the triangles generated, unlike the actual surface of the sand. Despite that distortion, it still represents the sandbox elevation well.
For this particular survey, the Spline interpolation method appeared to be the best survey technique for producing the most accurate representation of the sandbox. The mathematical function utilized to minimize surface curvature proved to be very effective.
Conclusion
This survey is related to other field surveys in that it collects elevation data over many points. What makes it unique is the fact that such recordings were made only inches apart. It is not always realistic to perform a highly detailed grid based survey, nor it it always necessary. Difficult terrain or private property may be factors that interfere with this. Interpolation be used for much more than just elevation models. Factors like temperature, wind speed and windchill could also be collected for a interpolation dataset, being that they're multiple factors that are all inter-related.
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| Figure 1: Segment of normalized data on Excel |
Methods:
Once the data was normalized and a geodatabase was created, the x,y,z data points were imported into ArcMap by navigating to File-->Add XY Data. This was exported as a feature class within the geodatabase. Since the points were established in relation to a specific reference point at (0,0), a cadastral coordinate system was utilized without projecting the data. A grid was then established and ran through a series of different interpolation methods in order to determine advantages/disadvantages of each, as well as how realistic of a representation of the sandbox terrain each method produced. These methods (defined by ESRI) included Inverse Distance Weighted (IDW), Kringing, Natural Neighbor, Spline and Triangular Irregular Network (TIN).
The IDW tool uses a method of interpolation which calculates cell value by taking the average values of data points in the vicinity of each processing cell. The closer a point is to the center of a cell being estimated, the more influence it has in the averaging process.
The IDW tool seemed to provide a basic picture of what the original sandbox looked like, but is lacking specific definition. This is likely due to the fact that there are only 100 total input units available.
Natural Neighbor interpolation finds the closest subset of input samples to a query point and applies weights to them based on proportionate areas to interpolate a value. Since it only uses neighboring points, it is better suited for compact datasets and terrain that has higher elevation variability.
The Natural Neighbor seemed to created an elevation that was a little distorted with elevation variance, though it served well in revealing the peaks and valleys.
Kriging is an advanced geostatistical procedure that generates an estimated surface from a scattered set of points with z-values. More so than other interpolation methods, a thorough investigation of the spatial behavior of the phenomenon represented by the z-values should be done before you select the best estimation method for generating the output surface.
Besides a couple spikes in the surface model, the Kriging created a smooth and accurate representation of the original sandbox.
Spline interpolation method estimates values using a mathematical function that minimizes overall surface curvature, resulting in a smooth surface that passes exactly through the input points.
The spline tool created the smoothest surface out of all the models. During processing, the Regularized option was selected in order to create the most accurate replica of the recorded terrain.
TIN is a vector data structure that partitions geographic space into contiguous, non-overlapping triangles. The vertices of each triangle are sample data points with x-,y-, and z-values. These sample points are connected by lines to form Delaunay triagles. TINs are used to store and display surface models.
The tin model strongly illustrated the slopes in the terrain, but poorly reflected what the sandbox looked like in that it was jagged.
Once all 5 interpolation methods were completed, the resulting output rasters were imported into ArcScene in order to produce a floating 3D view of elevation change in the sandbox. When the raster is initially brought in, it's projected as a flat surface. It can be modified to 3D by selecting "floating under a custom surface" under layer properties. The 3D surface was then exported as a JPEG and brought into ArcMap to be used as a visual aid for the maps produced in the results section. A scale bar was established by navigating to data frame properties and selecting "centimeters".
Results/Discussion
Figure 2 displays the surface of the original sandbox.
 |
| Figure 2 |
Figures 3-7 below show the resulting maps of each Interpolation method.
IDW
Figure 3 below shows a map utilizing the IDW interpolation method. This map had a fair representation of surface elevation, but did not have a very smooth surface. This was uncharacteristic of the actual terrain of the sandbox, which wasn't nearly as bumpy.
 |
| Figure 3 |
Natural Neighbor
Figure 4 below shows a map utilizing the Natural Neighbor interpolation method. The peaks of each of the "hills" appear jagged, which is unrepresentative of the actual sandbox that was measured.
 |
| Figure 4 |
Kriging
Figure 5 below shows a map utilizing the Kriging interpolation method. Elevation changes are not as strongly pronounced, but the overall surface is considerably smoother than Natural Neighbor and IDW, having less pronounced variability from point to point.
 |
| Figure 5 |
Spline
Figure 6 below shows a map utilizing the Spline interpolation method. It is obvious that the surface of this model is considerably smoother than any of the other previous 3D representations. This is likely due to the fact that Spline utilizes a mathematical function which minimizes overall surface curvature.
 |
| Figure 6 |
TIN
Figure 7 below shows a map utilizing the TIN interpolation method. It is very geometric and pointy by nature due to the triangles generated, unlike the actual surface of the sand. Despite that distortion, it still represents the sandbox elevation well.
 |
| Figure 7 |
For this particular survey, the Spline interpolation method appeared to be the best survey technique for producing the most accurate representation of the sandbox. The mathematical function utilized to minimize surface curvature proved to be very effective.
Conclusion
This survey is related to other field surveys in that it collects elevation data over many points. What makes it unique is the fact that such recordings were made only inches apart. It is not always realistic to perform a highly detailed grid based survey, nor it it always necessary. Difficult terrain or private property may be factors that interfere with this. Interpolation be used for much more than just elevation models. Factors like temperature, wind speed and windchill could also be collected for a interpolation dataset, being that they're multiple factors that are all inter-related.
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