Special Topics - Mod2.2 - Lab 5 - Interpolation

 Greetings and welcome to Lab 5!

Interpolation is how we apply values to unknown points based on sample points where we do have known information. These values are predictions based on what we do know. Several different methods of interpolation focus on different statistical or geometric calculations. We will discuss a few of them as they were applied to this week's lab. 

 Thiessen Polygons: these polygons represent an area in which all points contained are measurably closest to the representative data point contained within them. That is, all areas are physically closest to this sample data, not any other sample points. This is a nearest neighbor style analysis.

Inverse Distance Weighting (IDW): this method applies greater weight to nearby points than farther points. This assumes through spatial autocorrelation that a point closer is more alike than those farther. One problem is that it may not capture local variations depending on the effective distribution of the data. 

Spline: This method fits a line through all of the data points present in the set. It seeks to minimize the curvature of the surface, and is good for trying to represent gradual transitions. It can overshoot areas with abrupt changes, but as seen below can present a smoother surface between less harsh phenomena. 

These are only a few of the possible interpolation methods, and are the primary ones discussed in this lab. They were all used to look at a fictitious sample data set for a real place. Specifically, we are looking at points across Tampa Bay to measure Biochemical Oxygen Demand (BOD) in milligrams per liter (Mg/L).

Here is a look at two of the primary methods and how they visually compare: 

IDW:

The thing that I dont think is modeled well by this approach are the Green areas. That is, those areas with a lower concentration.  They are more like localized Low points, when I think they should be more of a balance and transition between the higher areas and lower. That is one thing that is captured better below in my opinion.

Spline: Regularized. 

While also not perfect, I think this presentation does a better job at highlight the transition in zone types. However, it may have missed larger areas that still have a high BOD concentration. 

Regardless, both of these are two different approaches with the same dataset. They seek to estimate the values for areas outside of the measured points. 

This lab further continues to solidify the importance of good sampling methodology. And really we only talked about a few methods, there are so many other choices with varying degrees of difficult calculations included. But as a taste for interpolation it is definitely interesting to see how much the same data set can vary by different presentation models. 

v/r

Brandon