Scale and Gerrymandering

 This week, we reviewed how scale affects our analysis and understanding of vector data and the basic resolution of raster data. With regards to vector data, as map scale moves from large scale to small scale, it has the effect of reducing our ability to be accurate and precise in measuring landscape features. The number of specific polygons, total length, and the area is reduced because it is much harder to accurately depict what is and is not a specific feature. You have to be much more general in your analysis and descriptions. It is also much easier to miss features altogether when viewing on a relatively small scale.

The images below help depict the effect of scale on vector data:

When it comes to raster data, our resolution is much worse at small scales and it forces you to be very general in your analysis for whatever purpose that may be.  If we generate a raster at a large scale, our precision and accuracy can be much greater.

The table below illustrates how resolution affects our interpretation of slope.  In general, the better the resolution, the better our ability to identify steep slopes and dynamic landscapes.

DEM Resolution	Average Slope (degrees)
1m	39.25
2m	38.98
5m	38.39
10m	37.47
30m	34.81
90m	30.31

The second part of our lab dealt with gerrymandering.  Gerrymandering is the redrawing of congressional districts in order to favor one party over another.  Gerrymandering generally increases divisions based on wealth and race.  The effects of gerrymandering can be measured mathematically using the Polsby-Popper score where a score closer to one indicates a more compact district shape.  Districts with a very low Polsby-Popper score indicate that it is drawn with purposes that are not impartial.  Below is an image of the district in the contiguous 48 states with the lowest Polsby-Popper score:

As you can see from the image, this district (congressional district 12) makes absolutely no sense in terms of how you might imagine a district if it were drawn to include an impartial representation.  There is clearly a motive behind drawing north Charlotte, and the interstate to Greensboro and Winstom-Salem.  One must question the motives behind any political actors who draw such a district.
  

Interpolation

 This week, we evaluated several methods of interpolation for efficacy in two different example scenarios: elevation and water quality. I will first describe briefly how these interpolation methods work.

According to Esri's help documentation, IDW (Inverse Distances Weighted) operates under the assumption that objects or things close together are more similar than things farther apart.  If we are interpolating what might be expected in a void, this method will assume the known data points closest to that void will be more similar that data points farther away. Each known data point has an influence that diminishes with distance.

According to Esri's help documentation on Spline interpretation, this method uses a mathematical function that attempts to create a smooth surface by minimizing overall curvature and passing through all known data points.  

For elevation, we evaluated the use of Spline and IDW from known elevation data points.  In this instance, Spline outperformed IDW in creating a more realistic display of the terrain.  The IDW method created many potholes and areas that did not seem to fit with what a natural landscape might be like.

For water quality analysis, we evaluated the use of non-spatial analysis, Thiessen interpolation, IDW and Spline (regularized and tension).  In this analysis, IDW was the most effective in presenting the data accurately and in a spatial distribution that reflects an intuitive sense of reality. This is represented in the table below:

Technique		Minimum	Maximum	Average	Standard Deviation
Non-Spatial		0.8	3.5	1.81	0.57
Thiessen		0.8	3.5	1.79	0.56
IDW		0.81	3.5	1.78	0.29
Spline
	Regularized	-1.7	3.64	1.67	0.65
	Tension	-9.79	9.64	1.81	0.76

Below is a representation of the most accurate method used in water quality analysis, the IDW interpolation:

And the same data represented by the regularized Spline method:

As you can see, there are some areas of contamination that are not really represented with the Spline method.  Because it wants to create a smooth surface, it overpowers the more anomalous known measurements in a way that ultimately creates an inaccurate representation.  It also assumes influence in perpetuity and is only cut off by the mask that we input manually.