Monday, September 08, 2008

Texas Statewide Historical Maps & Positional Accuracy Pt. 1

We have been undertaking a project, called the Texas Time Machine (TTM), which requires us to georeference statewide historic maps of Texas.

Brief overview of TTM:
Preparing historical materials for use within GIS for geographic analysis requires a large time commitment and high level of expertise. Once prepared, the researcher still needs to understand the fundamentals of operating a large desktop GIS application. TTM resolves this by (1) compiling a collection of prepared historic materials, and (2) enabling interaction with these materials within Google Maps and Google Earth (as well as desktop GIS applications).

TTM provides 4 ways to view geographically referenced maps, statistics, and images. (1) Via Google Map overlays, (2) Via downloadable Google Earth KMZ files, (3) Via downloadable GIS Data, and (4) Via downloadable un-georeferenced images.
I want to focus this post specifically on how we are georeferencing 150 year old maps whose geography encompasses over 250,000 square miles.

Georeference Scanned Map Image
  1. The intended coordinate system of the original cartographer needs to be determined. In consultation with our Cartographic Archivist Librarian, we discovered that for the majority of the maps dating int he 19th century a Mercator system was intended.
  2. Control points need to be used for georeferencing. For the first order, we use control points from the state outline, namely the Pan Handle, westernmost tip, easternmost tip, and southernmost tip. Then, we overlay a uniform 5x5 grid shapefile (25 standard polygon features) over the ungeoreferenced image within ArcMap. One city per cell is used as a control point. Cells without cities indicated on the scanned map will not contain control points.
NSSDA & Historical Measurements
We are adhering to the National Standard for Spatial Data Accuracy (NSSDA). The two primary resources we followed are:
  • ‘Geospatial Positioning Accuracy Standards, Part 3: National Standard for Spatial Data Accuracy’
  • ‘Positional Accuracy Handbook: Using the National Standard for Spatial Data Accuracy to measure and report geographic data quality’.
Both resources can be accessed here.

The first work above provides a general overview of the process and specific case studies where one can learn by those examples. There are two cases for measuring horizontal accuracy.
  • The first case is on page 3-10. This case demonstrates how to calculate error with 95% confidence when the x-axis error is equal to the y-error. RMSE(x) == RMSE(y). (Root Mean Square Error) I do not anticipate this as applicable as our maps are not consistently drawn to scale.
  • The second case is on page 3-11. This case is entitled ‘Approximating Circular Standard Error When RMSE(x) != RSME(y)’. However, the details of the case demonstrate how to calculate error when RMSE(min)/RMSE(max) is between 0.6 and 1.0. This implies an almost consistent error across the x- and y-axis.
    • The formula provided is: Accuracy ~ 2.4477 * 0.5 * (RMSE(x) + RMSE(y)). This is in effect the average of the two errors (added and divided by 2) and then multiplied by the full circle confidence of 95% as designated by the ‘Generalized Circular Probable Error’ table. (JSTOR access, page #170).
    • This case continues to explain that the circular standard error at 39.35% confidence may be approximated at 0.5 * (RMSE(x) + RMSE(y)).
    • The big question for us is how can these numbers be adjusted to accommodate where RMSE(min)/RMSE(max) is less than 0.6.
  • The second work above is a handbook/workbook that enables the easy use of the first case specified in the first work. Namely, where RMSE(x) == RMSE(y). As stated above, this is not the case with our maps because cartographers could not draw them to scale 150 years ago. However, this second work provides print and downloadable versions of a spreadsheet that modified for our uses, namely adjusting the modifier at the end based on the RMSE ratio.
  • Both works provide template language to include in the GIS metadata, as well as specific metadata fields where positional accuracy should be reported.
Our Geographic Accuracy Measurement Procedures
  • Ha! I am tired of writing at the moment and will lay out out specific in-house procedures tomorrow. I will also include some snippets from one of our metadata records.

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