Significant Topographic Changes in the United States
SRTM – NED Vertical Differencing
Image differencing has long been used as an effective change detection technique for coregistered digital remote sensing datasets. One image is simply subtracted from another image on a pixel-by-pixel basis. As applied to gridded DEMs, the result of image differencing is a differential surface, which is a measure of the spatial distribution of mass displacement. In a differential surface, the areas of mass displacement are both located and quantified, and both are important for this study in which locating and describing (quantifying) topographic changes are primary goals. Thus, DEM differencing is the most appropriate change detection method.
DEM quality is another key aspect, and the processing described below measures and accounts for the accuracy of both of the input elevation datasets. To obtain the best results in an image differencing operation, the input datasets need to be precisely aligned. For vertical change detection with DEMs, the alignment of the input datasets is critical, especially in high-relief areas. Even for a single DEM, a registration error (horizontal offset) can introduce an apparent elevation error. In other words, even if an elevation measurement is without vertical error, if that observation is shifted horizontally from its true position the effect of the planimetric error is manifested in the vertical dimension. The only condition where this is not true is on flat ground, but the effect of a given horizontal error increases as the slope of the ground (a) increases:
Elevation error = tan a × horizontal displacement
In the case of a pair of DEMs, the horizontal displacement results from an offset in alignment between the two datasets, and in areas of higher relief the apparent change in elevation due solely to planimetric error can be falsely detected as topographic change. The below diagram presents an idealized case where the actual land surfaces have not changed and have been measured identically in each DEM, but a horizontal offset between the two DEMs results in an apparent vertical change in the difference grid, the magnitude of which is a function of the surface slope.
To minimize the chances of falsely detecting vertical changes because of misregistration, the NED and SRTM data were coregistered as precisely as possible prior to differencing. In their native formats, each dataset is in a geographic (latitude/longitude) coordinate system with a resolution of 1 arc-second. The SRTM data are referenced horizontally to the WGS84 datum, whereas the NED is referenced horizontally to the NAD83 datum. A transformation was done on the SRTM data to convert it to NAD83 referencing, but at the resolution of the data the difference between the datums is probably negligible.
The primary adjustment in the coregistration process was required to account for a difference in the way the NED and SRTM data are referenced to the geographic coordinate system in their native formats. NED uses “cell corner” referencing in which integer lines of latitude and longitude fall on the edges of a cell (pixel) along a 1x1-degree tile boundary. In contrast, SRTM uses “cell center” referencing in which integer lines of latitude and longitude fall at the center of a cell along a 1x1-degree tile boundary. This effectively results in a one-half pixel shift between the two datasets. Such a shift would not be a concern for some applications. However, as described above, this offset could result in false elevation changes in a difference grid in higher relief areas if left unadjusted.
The figure below shows a diagram of the NED and SRTM coordinate system referencing in their native formats.
The next figure shows how the one-half pixel shift is removed to bring the NED and SRTM into precise alignment. Prior to the adjustment, each NED pixel is centered on the intersection of four SRTM pixels. These four pixels are averaged and the resulting value is placed into the upper left position of the 2x2-degree window. The 2x2-degree window is then moved one column and the operation is repeated, each time averaging four original SRTM elevation values. The procedure is repeated until the entire 1x1-degree tile of SRTM data has been processed. The output grid is then shifted a distance of one-half pixel in both the x and y directions (by modifying the reference latitude and longitude coordinates) to bring the SRTM data into precise alignment with the NED grid. The averaging operation on the SRTM data has the added advantage of slightly reducing the high-frequency noise inherent in radar-derived elevation data.
The NED is referenced vertically to the NAVD88 datum, while the SRTM data are referenced vertically to the EGM96 geoid. NAVD88 is an orthometric (sea level referenced) datum, which is closely approximated by the geoid, thus the NED and SRTM elevations are essentially in the same reference system so no vertical transformations were required.
After coregistration, a difference grid was created for each 1x1-degree tile by subtracting the NED from the SRTM on a per pixel basis. In this manner, positive values in the difference grid reflect areas where the SRTM elevations are higher than NED, and negative values represent areas where SRTM elevations are lower than NED. In terms of topographic surface change, the positive differences may indicate areas of filling, and the negative differences may indicate areas of excavation, or cuts.
Below is an example of the NED, SRTM, and the derived difference grid for an area in eastern Kentucky that has experienced topographic change due to surface coal mining. A final step in this initial part of the data processing flow for the 1x1-degree tiles included generation of other coregistered grids needed for subsequent processing, such as shaded relief from the NED and SRTM data and land cover data from the NLCD.