Interpolation is a way of making predictions based on known values. We interpolated the surface water quality of Tampa Bay using the BOD Mg/L variable from multiple sampling locations.
Interpolation methods explored were
- Spline (regular)
- Spline (tension
- IDW
- Thiessen polygons
IDW uses the distance of each data point to neighboring values to weight its predictions, whereas the Spline interpolation techniques fits through a set of input points to make its estimation. Spline is not constrained by the limits of the provided data and can give values greater or less than the highest and lowest data points, while IDW is constrained to the highest and lowest data point.
Thiessen interpolation creates a series of polygons with each data point associated with the central location of a polygon. Because of this the size of the polygons is variable and dependent on the distance from other sampling locations. Each polygon is given the value of the central point and there is not estimation or continuity to the data. This method was not ideal for measuring water quality.
In this exercise my regular spline interpolation ended up displaying values that were not mathematically possible, giving me large swaths of negative value areas. It is highly unlikely for water quality to be at 0, and impossible for it to be a negative number. The tension method was a more accurate and aside from a greater range of values, data was closer to that displayed by the IDW. I personally chose to map the data along standard water quality monitoring guidelines using the following table for analysis:
and when using these guidelines the spline (tension) method only slightly differed from the IDW with the majority of the data falling into the "very good" range for both data sets, but a slightly bigger circle area falling under "fair" in the spline tension map.
IDW: "Fair" data is mapped in yellow and "very good" data in green
Spline tension: "Fair" data is mapped in yellow and "very good" data in green
Finally, here is more thoroughly symbolized view of my IDW map with BOD estimates. Although I would not necessarily need to use these number for water quality estimation, they give a good visual of how the IDW interpolation method calculated the water quality with regard to the data points.