Scale Effect & Spatial Data Aggregation

Scale effects on vector data seem to be intuitive.  When you taking real earth and shrinking it down to fit on a page there will be details that will be lost or moved or changed.  Does your map scale allow for rivers, how about major creeks, does it show smaller tributaries?  The details that are not the focus are often eliminated the details that are the focus maybe included but require shifting of other features to get them to fit.

Resolution effects on raster data are also intuitive.  This is easiest demonstrated by a discussion of pixel.  The high the number of pixel for a photo the larger the picture can be made without looking blurry.  Raster data is contained in grids of cells.  At smaller cell size, 1m or 2m,  the more detail is available.  As the cell size gets to be larger (10m, 30m, 90m) the sample data is averaged in those cells.  The creates smoother data as the highs and lows are lost in the averaging.  And the imagery becomes more pixelated at finer resolution.

Modifiable Area Unit Problem (MAUP) exists for aggregation and zonation. Just because there are more area units does not mean the data is more specific and granular.  I can combine several areas to make larger areas and then put many many small areas into the mix.  I may end with more areas, but less detail than a lower number of evenly distributed area units.

Gerrymandering refers to odd shapes that can arise in political districts when the boundaries are manipulated for statistical properties.  Include this set of people and exclude those and we can raise or lower all kinds of statistics.  Determining the Polsby-Popper score results in a range 0-1.  The closer to 1 the more compact a polygon.  Polsby-Popper was calculated as 4*pie*area / perimeter^.  Below in red are the top 5 Congressional Districts in the Continental US that have lowest compact score, indicating the highest probability of gerrymandering.

Surfaces - Accuracy in DEMs

This week we examined vertical accuracy of DEMs.  We were provided with a raster file of high resolution bare earth DEM obtained through LIDAR and and excel file with field observations of ground elevation.  The field data contained 5 land cover types (a-e).  We utilized the Extract Multi Values to Points tool.  This tool grabs the elevation value of the pixel of the lidar raster directly beneath each sample point.  We added a field to the attribute table to convert feet to meters.  Accuracy was calculated for each land cover type and then the all the data combined.  We summarized the comparison in the table above.  The calculations in the table are the differences in meters from the DEM to the reference field data at 68%, 95%, RMSE, and Bias.

RMSE

• difference between DEM and reference for each point
• Square the difference for each point
• Average the squared differences (Sum the square difference/count of points)
• Square root of the average 

Bias as ME - is the average of the errors