Map Projections

 This week, we learned more about projections.  We learned how they work, how to identify the best projection for your intended purpose, how to create custom projections, and the science and history behind projections.  Below, I created a map of my home state of Nebraska.  I used the Nebraska State Plane Projection and added a grid and graticules.

This projection is appropriate because it is the only State Plane projection for the state of Nebraska and is therefore developed specifically for general use with the state.  This is a general use map where we wish to preserve shape and area as best as possible, so this selection makes the most sense.

Typography and Labeling of the San Francisco Bay Area

For this week's exercise, we were tasked with labeling various features in the San Francisco Bay area. Below is the map I created:

I chose Sitka font for this project because I felt like a serif font helped me read smaller type. For each respective category, I changed the font size from large to small depending on the relative size of the object being labeled within each category.  For example, when labeling the water features, I used the largest font on the Pacific Ocean, the next largest for the San Francisco Bay, and so on.  I used this same philosophy when naming all of the general features with the largest being San Francisco, Marin Peninsula, and so on.  I created a visual hierarchy by separating each category of feature by at least 2 font sizes with the water and general features. 

I used 8-point font on all parks and topographic names and 10-point font size for the Golden Gate Bridge.  I placed most every label on top of the respective feature and used halos or shadows with different colors to represent the various categories.  This helped each font stand out amongst a busy background. I used a white halo for the general category, a green halo for parks, and a yellow shadow for the geographic features.  I did not use a halo for the water features or the Golden Gate Bridge. I did use Italic font for the water features, however. I also used a callout for Lake Merced and the Golden Gate Bridge.

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.

TINs and DEMs

 This week, we explored Triangulated Irregular Networks (TINs) and Digital Elevation Models (DEMs).  The TIN is unique in that it allows you to evaluate slope, aspect and elevation in a way that is useful for certain types of landscape analysis and quick retrieval of information regarding these types of information.  An example of this is shown in the image below:

A quick click on any triangle and you can get the slope, aspect, and elevation of that area.  So they can act as a good quick reference for a landscape.  They can also give you a new perspective on landscape and allow you to think about your elevation analysis as it would apply to a DEM as well.

Below, I used a DEM and weighted overlay to give a visual analysis of ski slope suitability.  The DEM makes the appearance of elevation data appear more smooth and it better for general map making as it is pleasing on the eye.

Both elevation models are useful and have their place in the toolbox.  This week was a good exercise in understanding the tools and methods used in both applications.

Road Completeness

 This week, I completed an accuracy assessment of two road networks based on their relative completeness using 1km x1km grid for comparison.  The goal of this assessment was to determine which road network is more complete.  TIGER Roads or Street Centerlines, and to determine which locations are similarly accurate and which locations are more accurate with either of the two networks.  The method ology I used to achieve this is outlined below.

I first used the “Clip” tool to remove portions of each road network that were outside of the supplied grid network.  Once the roads outside of the grid area were clipped, I used the “Summarize Within” tool to calculate the lengths of the road system inside each grid polygon.  I specified the output in kilometers so as to eliminate the need to do a separate calculation to convert the results from feet.

Once I had the total feet for each grid and road dataset, I used the “Table to Excel” tool to export this information to Microsoft Excel and calculate the necessary statistics in order to produce the table and maps below.  Once the statistics were calculated, I used the “Excel to Table” tool to import the final Excel table back into ArcGIS.  Once in ArcGIS, I used the “Join Field” tool join the Percent Difference field I created in Excel to the Grid layer.  I then used this field and the Grid layer to generate the map.

As evidenced by the map, the completeness of the road network is within +/- 5%, but there are areas that diverge a lot based on the accuracy of each network as it relates to specific grids.  

TIGER_Roads total length in kilometers: 11,382.7

Street Centerlines total length in kilometers: 10,873.3

The TIGER Roads network is more complete based on this analysis.

Total Grid Cells	297
Cells Where Street_Centerlines is more complete than TIGER_Roads	134
Cells Where TIGER_Roads is more complete than Street_Centerlines	162

Horizontal Accuracy

This week, I tested the horizontal accuracy of two street datasets in Albuquerque, NM.  I tested the City of Albuquerque dataset and the StreetMap USA dataset. To complete this analysis, I overlaid the two street datasets on orthophotos of Albuquerque. I used the orthophotos to identify the true location of 20 intersections.  After establishing these reference points, I identified the location of those intersections within the Albuquerque streets dataset and the StreetMap dataset, added XY data for all points, and used the NSSDA datasheet to compute the accuracy of each dataset.  Please see the map below for the location of intersections used in the analysis.

The Albuquerque dataset proved to be much more accurate than the StreetMap dataset and the accuracy statements for each are listed below:

ABQ Streets

Positional Accuracy: Tested 13.15 feet horizontal accuracy at 95% confidence interval.

 

StreetMap Streets

Positional Accuracy: Tested 353.50 feet horizontal accuracy at 95% confidence interval.

The relative accuracy of these two datasets is not even close, and it is clear which dataset would best be used for navigating the streets of Albuquerque.