Lab 5 [GIS5935]: Surface Interpolation

 

In this lab we examined various interpolation methods to create a surface of water quality in Tampa Bay. Each method received as input a set of sample points containing Biochemical Oxygen Demand (BOD) values in milligrams per liter that were recorded from various points throughout the study region.

The interpolation methods used this case study included the following:

Thiessen

IDW

Spline - Regularized

Spline - Tension

This interpolation method is a special case of IDW where only the nearest water sample is used to estimate the BOD value at an unsampled location.

This interpolation method uses a preset number of nearest neighbors to estimate the BOD value at an unsampled location, and inversely weights the contributing strength of these neighbors based on their distances from the unsampled location.

Spline interpolation methods work to fit a smooth surface exactly touching the BOD sampled points, while also minimizing overall surface curvature between these points.

 

A regularized spline can produce values outside the sampled BOD data range.

A tension spline controls the surface generation to more closely align to the sampled BOD data range.

The screenshot below shows the results of interpolation using the Spline – Tension technique with 9 classes:

Values in red represent low BOD values and values in green represent high BOD values. This surface is more visually appealing due to its smooth transitions compared to the Thiessen method, where abrupt changes were observed at polygon boundaries. In addition, although the IDW-generated surface produced a smoother visualization (Bolstad, 2016, pp. 530) compared to the Thiessen method, the IDW result was not as successful at predicting valleys and peaks in the final visualization compared to the spline methods. Overall, the Tension-based spline technique performed best in terms of a smoothly created surface without significant amounts of  underestimating or overestimating throughout the study region.

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