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7.B.ii. Absolute Accuracy: Data from Cartographic Sources

Digital Chart of the World (DCW): The absolute vertical accuracy of the DCW, the vector source with the largest area of coverage, is stated in its product specification as ± 650 meters linear error at the 90% confidence level (Defense Mapping Agency, 1990). USGS's (1997b) experience while converting DCW to grids has shown that the grids derived from DCW data should (in many areas) be much more accurate than the 650-meter specification.

To better characterize the accuracy of areas derived from DCW vector hypsography, USGS compared its DCW grid to 30 arc-second DTED, which had been aggregated by averaging in selected areas of overlap with DCW coverage. By aggregating, the comparison could be done at the 30 arc-second cell size of the DCW grid. The comparison was done for portions of southern Europe and the Mideast, and all of Africa. Those areas of the DCW grid for which supplemental DTED point control had been included in the gridding process were eliminated from the comparison.

If the averaged DTED are thought of as the reference data set, the RMSE of the DCW grid is 95 meters. To get an idea of the overall absolute accuracy of the DCW grid, the relative error between the DCW and DTED can be combined with the known error of the DTED itself in a sum of squares. The root of that sum of squares is 97 meters. Using the assumptions about the error distribution cited above, a RMSE of 97 meters can be expressed as ± 160 meters linear error at 90 percent confidence. This number compares favorably with an expected vertical accuracy (linear error at 90 percent) of one-half of the primary contour interval of 1,000 feet (305 meters) for the topographic maps on which the DCW is based (USGS, 1997b).

AUSLIG Source Data: The accuracy of AUSLIG spot elevations in its source relief layer varies with the type of source material from which they were captured. AUSLIG provided the following table, giving estimates of vertical accuracy applicable to each source of point determination in terms of its standard deviation in meters:

tabSpot height: 5
tabSpot height inside depression contour: 5
tabSpot height on sand ridge: 5
tabPoint captured from 20m contour: 10
tabPoint captured from 40m contour: 20
tabWaterline (edge of sea): 25

NGDC's estimate of 10m linear error at the 90% confidence level from histogram analysis can be considered as an overall empirical estimate for the DEM derived from these sources, weighted by the volume of data from the various sources. The estimate was derived from the dominant implied contour interval in the grid of 20m, plus the dense coverage of source data compared to the 30o output grid.

Other Sources: The accuracy of the areas of GLOBE based on the other sources can only be estimated based on that which is known about each source. Using certain assumptions, the vertical accuracy of each source (and the derived 30 arc-second grid) can be estimated from the contour interval. One assumption is that the original map sources meet the commonly used accuracy standard which states that 90% of the map elevations are within ± 1/2 of the contour interval. It is unknown if any of these maps actually meet this standard. Also, map digitizing and elevation surface interpolation errors are unknown and therefore not included. However, histogram analysis of DEMs derived from cartographic sources of undocumented contour interval can often be used to estimate contour intervals from those original cartographic sources.

Table 2 (below) lists the estimated absolute vertical accuracy for the areas of GLOBE derived from each source, with the method of estimating the accuracy also identified. The RMSE numbers were calculated using the assumptions about the error distribution cited above (a Gaussian distribution with a mean of zero).

    Table 2. Estimated Absolute Vertical Accuracy for Areas of GLOBE              
 

Vertical accuracy (meters)
Source        L.E. at 90% RMSE           Estimation method

DEM for Japan        10      6       estimated from histogram analysis of DEM*
DEM for Australia    10      6       estimated from histogram analysis of DEM
DEM for Italy        13      8       estimated from 25-meter contour interval**
DEM for New Zealand  15      9       estimated from 100-foot contour interval
DTED                 30-200  18-120  product specification for lower figure; 
                                     higher figure estimated from DMA DTED 
                                     coverage map categorizing horizontal and 
                                     vertical accuracy by location
Maps for Brazil      50      30      estimated from 100-meter contour interval
DEM for Greenland    150     91      estimated from histogram analysis of DEM
DCW                  160     97      calculated vs. DTED  
Maps for Asia  
     and S. America  250     152     estimated from 500-meter contour interval
Map for Peru         500     304     estimated from 1000-meter contour interval
SCAR/USGS            500     304     estimated from histogram analysis of DEM

* Here is a description of our method of estimating vertical accuracy from histogram analysis of the DEM. Since traditional contour map production goals include vertical accuracy of 1/2 of the contour interval, the estimates above by USGS for contour maps equate 1/2 of the source map's contour interval to vertical accuracy. Histogram analyses of DEMs can often determine the likely contour values of source maps. These interpreted contour intervals were halved to estimate vertical accuracy of DEMs. In many cases, more than one contour interval appears to exist in DEMs, perhaps because the DEMs were produced from various types of maps, or perhaps because of supplemental contour intervals. In such cases, vertical accuracy was estimated conservatively.

** Just outside of Italy, but included in the Italian DEM, some sources had somewhat coarser contour intervals. In addition, histogram analyses within Italy suggests that different supplemental contour intervals were used (to 5 meters in low-gradient areas (Salvi, 1995)), and that some contour lines were decimated in mountainous terrain, especially in northern Italy. Nevertheless, the estimates noted above are probably reasonably accurate.

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