In this week's lab, we were given a point shapefile containing the measurements of Biochemical Oxygen Demand in milligrams per liter at 40 sample points within the Tampa Bay. The goal was to utilize different interpolation models to develop the best representation of the distribution of BOC in the bay.
The first method I utilized was a simple non-spatial statistical analysis. This essentially examines all of the statistics (mean, max, min, standard deviation) of data and performs no spatial analysis. This gives us pertinent information but estimate values for unsampled areas. This means that quantifying the density of the BOC in specific locations is not possible.
The second method I used was the Thiessen Interpolation. This is where each location on the raster represents the same value as the nearest point. Essentially, polygons are created around each point base on their distance to the next point. Each location is incorporated into the polygon of the point it is closest to. These polygons are then transformed into a raster image. For the purpose of this lab, the data represented is far too general to be used in any in depth spatial analysis.
Thiessen Model:
The next model, and most effective I believe in this form of analysis, is the Inverse Distance Weighting Interpolation model. This is where each cell value is contingent on the value of nearby sampled values and their distance from the sample point. Essentially, each location is weighted by the value of their nearest recorded point. The closer the location is to a recorded point, the greater influence that value will have on the locations value.
Thiessen Model:
The next model, and most effective I believe in this form of analysis, is the Inverse Distance Weighting Interpolation model. This is where each cell value is contingent on the value of nearby sampled values and their distance from the sample point. Essentially, each location is weighted by the value of their nearest recorded point. The closer the location is to a recorded point, the greater influence that value will have on the locations value.
This appeared to be the best way to monitor BOC in the bay due to all of the values which are being represented existing within the range of the original data measurements. Other forms of interpolation, such as the Spline method, will generate estimates that may exceed values recorded in the sampling. Utilizing an IDW model shows a distance based differential of each location from each measured point and gives us the best representative relationship between all of data points within the actual range of values recorded in the field.
IDW:
The final method used was the aforementioned spline interpolation model. This method runs a curved line (more in the shape of a sheet since we are operating in 3 dimensions) through the center of each point. This connects them into a continuous display based on all of the points being connected by a curved surface. The curvature, however, must be reduced to the minimum possible curvature to attain greater accuracy.
This mode did not perform too well as the curvature of the line between points allows values that are not within the recorded range to be represented. Values for an area in between high valued points will have a curvature that overshoots recorded values (which can often be an amazing predictive tool) or overshoots low values depending on the shape of the curve and the surrounding points. This is a useful method for attributes such as elevation, however, it would be detrimental to our representative data to estimate that data values outside of the recorded range are occurring in swaths across our study area. A point of difficulty was reached when spline models from this method were not corresponding correctly in terms of value to the original points. This is because two data points existed within a similar geographic location, and due to these points needing to be connected by a sloped line, the line connecting to the subsequent point would illustrate a value far exceeding what was recorded and placing it in an unmeasured location on the map. To properly utilize a spline model, there should be no coinciding points in the data (tow measurements at the same geographic location).
This mode did not perform too well as the curvature of the line between points allows values that are not within the recorded range to be represented. Values for an area in between high valued points will have a curvature that overshoots recorded values (which can often be an amazing predictive tool) or overshoots low values depending on the shape of the curve and the surrounding points. This is a useful method for attributes such as elevation, however, it would be detrimental to our representative data to estimate that data values outside of the recorded range are occurring in swaths across our study area. A point of difficulty was reached when spline models from this method were not corresponding correctly in terms of value to the original points. This is because two data points existed within a similar geographic location, and due to these points needing to be connected by a sloped line, the line connecting to the subsequent point would illustrate a value far exceeding what was recorded and placing it in an unmeasured location on the map. To properly utilize a spline model, there should be no coinciding points in the data (tow measurements at the same geographic location).
We used two different forms of spline interpolation methos: tension and regulated. This difference is the polynomial used in the equation. Essentially, tension will give a much smoother surface due to the minimization of the curvature while regulated will produce a more jagged model.
Spline (regularized):
Spline (tension):
Spline (tension):
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