About the VTM Plot Maps and Plot Points

The VTM plot maps show the locations of plots surveyed during the original VTM project. The original surveyors ran vegetation transects at each plot, collecting species richness and abundance data for trees and ground cover. The VTM plot maps mark the location of the plots with red numbered circles. To our knowledge these circles were stamped, and thus their size has no meaning.

NAMING CONVENTIONS

Each VTM plot map was divided into a grid, labeled alphabetically down the side and numerically across the top. The plots were numbered within each section of the grid, for example A13 for grid section A 1, plot 3. We assign each plot a unique identifier by prepending the quad number, i.e. 65A13 for quad 65, grid section A 1, plot 3.

SCANNING

We scanned all VTM plot maps on an Epson Perfection flatbed scanner at 600 dpi. We cropped and rotated the scans in Adobe Photoshop to prepare them for rectification.

GEOREFERENCING

In order to be useful in a geographic information system, scanned maps must be georeferenced. This involves applying geographic coordinates to the images and warping the maps to fit a standardized projection. The original VTM surveyors marked the plot locations on USGS topographic maps, which have a polyconic projection centered at the center of the map¹. Thus each individual quad has a unique projection. We georeference each plot map to reference data that have been projected to that map's unique projection. When complete, we reproject all our data in the California Teale Albers NAD 27 projection.

Simplified example of our georeferencing process. We georeference an uncut USGS topographic map of the same edition and reprint as the VTM map to modern USGS Digital Raster Graphics (DRGs), which we then in turn use as reference data for georeferencing the VTM plot map sections. For a normal map, we use more control points, including corners and graticule marks, and we collect checkpoints as an independent metric of the spatial error.

In order to georeference an image, one must select control points, locations on the target image that are present in some reference data that already have a projection and coordinates associated with them. One then applies the known coordinates of these points from the reference image to the target image, and warps (or rectifies) the target image to best fit these points. There are many kinds of marks that one could potentially use on a map, but we use road intersections, mountain peaks, and occasionally USGS and NGS benchmarks, because we assume they were more accurately surveyed than other geographic features, and more likely to remain the same between the publication of the original USGS topographic maps and the present. We try to select at least 10 points for each base map, preferably 16. We also use the 16 points from the 5' or 10' graticule on the map. We then select at least 4 check points, preferably 8-10. These are points that are only used to check the accuracy of the rectification model, and are not themselves used to warp the image. We try to select check points in parts of the map where there were plots, so the reported error more closely reflects the areas of interest. We test whether the feature points, the graticule points, or a combination yields the lowest RMS, and use the set of points that does to rectify the image.

On some base maps, there are large systematic errors that appear when georeferencing, most likely due to datum shift. To compensate for this, we take the average check point error along the X and Y axes and shift the control points by these values.

All the VTM plot maps were cut into eight sections and mounted on cloth to facilitate folding. This presents an additional challenge in georeferencing because each indivudal section rarely has enough good control points to rectify the image. We circumvent this problem by first georeferencing an uncut scan of the base USGS map (of the same edition and reprint, if available), using 7.5 minute (1:24,000) USGS Digital Raster Graphics (DRGs) as reference. Then we georeference the individual VTM plot sections using the georeferenced USGS base map as reference. Finally, we create a vector version of the point data by manually creating point features at the center of each red circle. We perform all georeferencing using first order polynomial models in Leica Geosystems' ERDAS IMAGINE 8.7, and all vectorization with ESRI's ArcGIS 8.

ERROR

Geospatial data is of little value without some knowledge of the spatial uncertainty or error associated with it, and this is especially true of historical geospatial data. Spatial error in the VTM plot maps begins with the USGS topographic maps the original surveyors used to mark their plots. We were unable to discover any USGS standards in spatial uncertainty prior to the National Map Accuracy Standards (NMAS) of 1947, so we have assumed that maps produced before then are at most as accurate. The USGS DRGs that we used as a reference when georeferencing the historical maps do follow the NMAS, and thus contribute about 20.32 m.

The VTM surveyors also introduced uncertainty in marking their plots on the maps. This is impossible to quantify since no one who might have remembered the locations of individual plots in the field is still alive. Instead, we use the size of the red circle as a proxy. We know that the size of the circle was not intended for this use, but we think it represents a maximum degree of error in the placement of the plot on the map. We selected plots at random from the set of georeferenced maps in December of 2004, 20 from the 30' maps and 20 from 15' maps, and averaged the radii of their red circles. 15' plots had an average circle radius of 112.46 m, and 30' plots had an average circle radius of 215.73 m.

The process of rectification also introduces error, but it does so in a quantifiable way. We recorded the total root mean squared (RMS) error for each rectification event (each base map, each VTM plot section). This was highly variable for the base maps, but amounted to about 2 pixels on average for the VTM plot sections.

We gauged error in manually digitizing each plot point by testing technicians involved in the georeferencing process for their ability to place single pixel at the center of a circle 39 pixels in diameter, the approximate size of the plot circle on a scanned VTM plot section. We measured the Euclidian distance of their point relative to the true center of the circle, averaged the error across technicians, and converted to meters for 30' and 15' maps.

We combined all sources of error by taking root of the sum of the squared error from all sources, as per Thapa and Bossler 1992². Since each individual plot section has its own error, this means that all the plot points on a particular VTM plot section have the same error value.

Works Cited

1. Birdseye, C.H. Topographic Instructions of the United States Geological Survey. Washington: United States Government Printing Office, 1928.
2. Thapa, Khagendra and John Bossler. "Accuracy of Spatial Data Used in Geographic Information Systems." Photogrammetric Engineering and Remote Sensing 58:6 (1992): 835-841.