Significant Topographic Changes in the United States
Significant Change Thresholds
The next step in the data processing procedure was to threshold the difference grids to isolate areas of significant change. This procedure is commonly done in the image differencing method of change detection, and the threshold is often based on the standard deviation value of the differences. As implemented for this study, the thresholding approach incorporated the inherent absolute vertical accuracy of each of the input elevation datasets, expressed as the RMSE, which is the statistical equivalent of the standard deviation for normal distributions. The accuracy values used are those determined in the accuracy assessment procedure described above. The individual absolute vertical accuracies for the NED and SRTM data, segmented by NLCD class, are used to determine the threshold for each land cover class with the following formula. The threshold, T, is defined by:
In recognition of the fact that the values in the tails of the distribution of difference values represent the likely changes, the root sum of squares is multiplied by a factor of three. The assumption here is that the differences approximate a Gaussian distribution. By using the RMSE for each elevation dataset, the multiplier of three effectively states that differences within the threshold bounds may be due solely to the combined inherent vertical errors (uncertainty) of the NED and SRTM data. Real surface changes are indicated by the most extreme difference values that are beyond three standard deviations above or below the mean difference value (see figure below).
Stated alternatively, difference values not exceeding the threshold may represent areas that have experienced topographic change, but there is no way to be certain in a statistical sense because the NED and SRTM data may each be in error by an amount that, when combined, result in a difference. Based on probabilities associated with a Gaussian distribution, there is less than a 1 percent chance that the error of SRTM and/or NED exceeds three times + or – the measured RMSE. In these rare cases, extreme errors in the elevation datasets could cause an area to be erroneously flagged as an area of topographic change. The range of difference values is a continuum, and the selection of thresholds sets an artificial point to segment change versus no change areas. This practical approach is necessary when the objective is change detection over a vast area, as is the case for this study.
The thresholds for each land cover class are listed in the table below.
When applied to the SRTM – NED difference grids on a per pixel basis, the difference values have to exceed the threshold to be identified as significant change. For example, in an area identified as low intensity residential in the NLCD, the vertical difference has to be greater than +14.32 meters or less than –14.32 meters for a pixel to be included in the change mask. In an area of evergreen forest, the difference has to be of a greater magnitude (fall outside of ±17.57 meters) to be labeled as significant change, which is indicative of the increased uncertainty of the SRTM data in forested areas. Note also that the overall change threshold is ±12.87 meters, which is lower than the threshold for 12 of the 19 NLCD classes. Thus, if a single change threshold had been applied without regard to land cover type, many areas could have been erroneously flagged as changed, especially vegetated areas subject to greater uncertainty in SRTM elevation measurements.
The lowest thresholds occur in agricultural areas (NLCD classes of pasture/hay, row crops, small grains, and fallow) that are generally located in lower relief areas. These areas likely had bare ground or short vegetation conditions during the February collection date for SRTM, so they provide a good measure of the best accuracy of elevation measurement that could be achieved by SRTM in the absence of reflective surfaces above ground level (trees or vegetation canopy). Some of the best accuracies for NED were also observed in these areas of agricultural land use/land cover, so the change thresholds are correspondingly lower for these features. Thus, the minimum detectable difference using the change detection approach applied here to the NED and SRTM data appears to be on the order of 10 meters. Real changes to the topographic surface may have a magnitude much less than 10 meters, especially in low relief coastal areas, but those changes would not be detected by the implemented approach using the NED and SRTM data. With the type of change detection approach used for this study, multitemporal elevation data with much better vertical accuracies would have to be used to detect geomorphic changes characterized by a vertical alteration of only 1 or 2 meters.
While developing, testing, and implementing the thresholding approach, it was noticed that in some areas, the land cover based thresholds eliminated areas from the change mask that had clearly experienced significant topographic surface modifications. The land cover based thresholds were developed on the basis of overall national accuracy statistics. Even though the reference control point dataset has points located throughout the conterminous United States, it is doubtful that it represents the full variability of terrain and land cover conditions across the study area. Consequently, exclusive use of the thresholds based on the derived accuracy statistics may also not capture the full extent of topographic changes.
In recognition of this, and in an attempt to include more local factors into the initial delineation of significant difference areas, the threshold approach was supplemented by including pixels from the difference grids that met certain criteria. The local mean and standard deviation of the difference grid were used to calculate an additional threshold for selecting areas for inclusion in the change mask. In this case, the thresholds were adapted for each 1x1-degree tile by setting them equal to three times the standard deviation above and below the mean difference for the tile. In this manner, the philosophy from the accuracy-based threshold approach of selecting only extreme difference values was carried through to the locally based threshold step. Pixels from the difference grid that met the local statistics-based thresholds were added to those that had previously been selected by having met the land cover based threshold criteria. By examining test results of using just the land cover based thresholds or the local statistics-based thresholds, it was determined that neither one by itself was completely satisfactory in flagging candidate topographic change areas. However, in combination as a two-step threshold process, they were effective in delineating areas of significant differences. The next major step in the data processing procedure involved extensive filtering and refinement of the change area mask (described below), and it was useful to have as input to that process a comprehensive set of candidate areas of statistically significant elevation differences.