GIS 5935 Module 2.2 - Surface Interpolation

Module 2.2 of Special Topics in GIS was an exploration of surface interpolation and some of the different methods that can be employed to produce a dataset consisting of estimated values in between known [sample or testing] points. [Bolstad & Manson, 2022] define surface interpolation as a 'prediction of variables at unmeasured locations, and based on a sampling of the same variables at known locations [p. 510]. This was accomplished by the use of four different techniques and comparing the results to discern which model most accurately portrayed the data. 

The first exercise was a comparison of Digital Elevation Models produced by Inverse Distance Weighted [IDW] and Spline interpolation. The IDW Interpolation model is an estimation of unknown values inversely proportionate to the distance from known values at sample, or testing, points. Essentially, this equates to greater distanced from sample points equals less influence in determining that cell's estimated value. The Spline Interpolation model employs mathematical functions, or polynomials, to form a smooth curved surface between the known sample points [Bolstad & Manson, 2022]. 

After these models were constructed, the Raster Calculator geoprocessing tool was ran to determine the mathematical difference between the two; the results are shown in the map below.

As illustrated in the legend, areas that are shaded brown represent raster cells where the Spline model had a higher elevation, and areas that are shaded purple represent cells where the IDW had higher elevation values. It is noteworthy, that mostly all the white areas are places where sample points were collected. Also, mathematically, the ratio of purple to brown areas are 52% and 48%, respectively. 

The remainder of the lab was an analysis of the levels of Biochemical Oxygen Demand [BOD] levels in Tampa Bay, Florida using the following models: Nearest Neighbor [Thiessen Polygons], Inverse Distance Weighted, Regularized Spline, and Tensions Spline. While IDW and Spline were described above, we took spline interpolation one step further to explore the difference between Regularized and Tension. The difference between the two models is based on the weight parameter, where the Regularized Spline produces a smooth, continuous surface, while the Tension Spline is coarser, but manages to force the surface to exactly match the values at the sample points [ESRI, 2024]. The other model used was Nearest Neighbor, or Thiessen Polygon Interpolation. Mathematically speaking, this is the least intensive as it assigns a value for any unsampled location that is equal to the value found at the nearest sample location. [Bolstad & Manson, 2022, p. 516]. This method creates polygons that extend out [in all directions] from known sample points until the maximum distance is reached to the next sample point. The results for all four methods are shown in the maps below.

The interpolation method I would choose to best represent BOD concentrations of Tampa Bay would be the Spline Technique, specifically the Regularized Spline type. The reasoning behind this decision is due to the nature of any substance being diluted in water. Regardless of the substance, once introduced into a body of water, it will disperse evenly and continuously throughout the adjacent areas. The ISW method tends to create 'hot spots' with peaks occurring at the testing points while the Tension Spline type will create a continuous surface, but not a smooth surface. Finally, Nearest Neighbor will provide an estimated value of BOD concentrations, but these are generalized over discreet regions of the bay and will not provide a smooth, continuous interpolated model. However, the Regularized Spline type 'creates a smooth, gradually changing surface with values that may lie outside the sample data range' [ESRI, 2024]. This, in my opinion, would provide a much more accurate estimate of BOD concentrations in Tampa Bay than the other three methods discussed in this assignment.

Sources:

Bolstad, Paul & Manson, Steven. (2022). GIS Fundamentals: A First Text on Geographic Information Systems (7^th Edition). Eider Press.

Environmental Systems Research Institute. (2024). How Spline Works. https://pro.arcgis.com/en/pro-app/latest/tool-reference/3d-analyst/how-spline-works.htm