Purpose and Scope

The purposes of this report are to document the methods and assessment techniques used to classify depressions in DEMs as likely or unlikely to exist; to delineate depressions, sinking streams, and their associated watersheds from multiple elevation data sources and digital hydrographic data within the karst areas of Tennessee and parts of surrounding States; to characterize the spatial distribution of these features within the area; and to present geospatial datasets of these features and their watersheds (Ladd, 2025). DEM analysis was used to delineate preliminary depressions derived from elevation source data such as topographic maps, lidar data, and photogrammetrically derived data. Depressions, sinking streams, and their watersheds were compiled into geospatial datasets, and the spatial distribution of depressions within each karst region in the study area was characterized.

Although subjective distinctions between depressions and karst features were made at field visit locations, the DEM analysis methods used for this study provide no distinction between sinkholes, man-made depressions, or natural depressions; such distinctions are beyond the scope of the study and this report. Many of the depressions in the geospatial datasets are considered compound or nested depressions, in which the boundary representing the area of internal drainage contains additional internal closed depressions; in these cases, only the outer boundary of the internally drained area is represented. In this regard, the geospatial datasets of depressions are not intended to represent every depression or sinkhole on the landscape. Depressions in the geospatial datasets represent areas of internal drainage that have the potential to store surface runoff. Some sinking streams that do not terminate in depressions, and therefore store no surface runoff, are included in the geospatial datasets, and watersheds for these sinking streams are included in the watershed datasets.

Study Area

The study area comprises approximately 61,800 square miles (mi²) in the eastern two-thirds of Tennessee and parts of Kentucky, Virginia, North Carolina, Georgia, Alabama, and Mississippi, and encompasses the Cumberland, Tennessee, Barren, and Conasauga River watersheds (fig. 1). Soluble carbonate rocks underlie most of middle Tennessee, large areas of east Tennessee, and parts of surrounding States (fig. 2). Wolfe and others (1997) divided the carbonate areas of Tennessee into eight karst regions based on geologic structure, stratigraphy, relief, regolith thickness, and karst landforms. The boundaries and names of these regions were modified to create eight karst regions for this report: (1) the Inner Nashville Basin, corresponding to the Inner Central Basin region from Wolfe and others (1997), (2) the Outer Nashville Basin, corresponding to the Outer Central Basin region from Wolfe and others (1997), (3) the Eastern Highland Rim, corresponding to the Eastern Highland Rim subregion of the Highland Rim region from Wolfe and others (1997), (4) the Western Highland Rim, corresponding to the Western Highland Rim subregion of the Highland Rim region from Wolfe and others (1997), (5) the Western Pennyroyal Karst Plain and Crawford-Mammoth Cave Uplands, corresponding to the Pennyroyal Plateau subregion of the Highland Rim region from Wolfe and others (1997), (6) the Cumberland Plateau Escarpment and Sequatchie Valley, corresponding to the Coves and Escarpments of the Cumberland Plateau region from Wolfe and others (1997), (7) the Ridge and Valley, corresponding to the Valley and Ridge region from Wolfe and others (1997), and (8) the Limestone Valleys and Coves, corresponding roughly to the Western Toe of the Blue Ridge region from Wolfe and others (1997) (fig. 2). The boundaries and names for the Inner Nashville Basin, Outer Nashville Basin, Eastern Highland Rim, Western Highland Rim, and Limestone Valleys and Coves were compiled from Level IV ecoregion data (U.S. Environmental Protection Agency, 2013). The Western Pennyroyal Karst Plain and Crawford-Mammoth Cave Uplands karst region and Cumberland Plateau and Sequatchie Valley region boundaries and names were compiled from combined Level IV ecoregions (U.S. Environmental Protection Agency, 2013). The Ridge and Valley region boundary and name were taken from the Ridge and Valley Level III ecoregion (U.S. Environmental Protection Agency, 2013).

Acquisition of Digital Elevation and Hydrography Data

The NED used in this study included USGS 1/3 and 1/9 arc-second DEMs. The contour-derived NED came from 1/3 arc-second (approximately 10 meters) DEMs (USGS, variously dated a), and the lidar-derived NED came from 1/3 arc-second and 1/9 arc-second (approximately 3 meters) DEMs (USGS, 2011–12, 2014a, b; fig. 1), which were in raster format when acquired. The 1/3 arc-second NED was updated with more current and higher resolution source data as they have become available (USGS, 2014a), often by incorporating data from the 1/9 arc-second NED (Evans, 2014; USGS, 2014b). The most current release of the 1/3 arc-second NED included more 1/9 arc-second lidar-derived NED source data than the version downloaded in June 2011 for this study (USGS, 2011, 2014b). To incorporate more current high-resolution elevation source data, 1/9 arc-second NED source data were downloaded in June 2013 and merged with the original NED used for this study (fig. 1). The photogrammetrically derived TNBMP elevation data, provided by the State of Tennessee in Triangular Irregular Network format, were derived from a combination of 1:1,200- and 1:4,800-scale mass points and accompanying break lines.

A hydrography dataset was compiled for the study area from 1:24,000-scale high-resolution NHD flowlines (USGS, variously dated b). Extensive checking and editing were conducted to ensure proper stream connectivity within the study area. After editing, the flowlines were separated into a connected stream network and disconnected streams, henceforth referred to as “sinking streams” (Ladd, 2025).

Elevation Data Preprocessing

In preparation for DEM analysis, a common raster format, coordinate system, cell size, and elevation unit were chosen for each elevation dataset. The 1/3 and 1/9 arc-second DEMs from the NED were in raster format when acquired. TNBMP elevation data were converted from Triangular Irregular Network format to raster format by using a natural-neighbor interpolation technique to meet the formatting requirements for this study. Each raster was projected to a Lambert Conformal Conic projection and resampled to a 30-foot (ft) cell size. Elevation values for the NED were converted to feet above the North American Vertical Datum of 1988.

Each formatted DEM was prepared by using methods similar to those described by Djokic (2008) to ensure that flow directions represent known drainage patterns and to reduce the occurrence of preliminary depressions near and within stream channels. The connected stream network derived from NHD flowlines was imposed onto each DEM using the AGREE method (Hellweger, 1997) with a 60-ft stream buffer, a 10-ft smooth drop from the buffer edge to the flowline, and a 1,000-ft flowline drop. After imposing the connected stream network, cells in connected stream locations were removed from DEMs, leaving only the stream buffer imposed onto the elevation data. The AGREE method (Hellweger, 1997) forces flow within the 60-ft stream buffer toward known stream locations from the NHD. Although practically all depressions within the 60-ft stream buffer are eliminated through this enforcement, the buffered area represents a relatively small part of the 61,800-mi² study area and was deemed appropriate for the spatial and technical scope of the project. DEMs with imposed streams from the connected NHD flowlines will be referred to as “hydroimposed DEMs” in the remainder of this report.

Delineation and Characterization of Preliminary Depressions

The NED and TNBMP hydroimposed DEMs were processed by using the ArcGIS Fill tool (Esri, 2017) to raise all depression elevations enough to remove all internal drainage from the rasters. The filled areas were converted to rasters representing preliminary depressions, with areas defined by the extent of contiguous cells with the same filled elevation. These preliminary depressions include all unlikely and likely depressions derived from each DEM.

Depression size and shape characteristics were determined for each preliminary depression by comparing filled-cell characteristics to the hydroimposed DEMs and through determining the general density of contiguous filled cells for depressions derived from each elevation data source. Size and shape characteristics were examined during the preliminary depression assessments to determine characteristic thresholds for separating unlikely and likely depressions. Depression-proximity characteristics were also determined for each preliminary depression, including depression proximity to closed 10-ft contours, which was examined as a potential indicator of likely depressions. Other proximity characteristics, such as proximity to transportation pathways, proximity to developed areas, and proximity to inundated areas or boundaries of man-made hydrologic structures, were also determined and used as filters to indicate that a preliminary depression is unlikely.

Size and Shape Characteristics of Depressions

Zandbergen (2010) determined that small and shallow depressions derived from digital elevation data are more likely to be artificial than large and deep depressions. Depression size characteristics such as area, maximum depth, and volume were determined for preliminary depressions from the NED and the TNBMP data by comparing the respective hydroimposed DEM elevations to the filled elevations for the preliminary depressions. A depression shape and size metric, termed “mean enclosure,” also was calculated for each preliminary depression. Mean enclosure was determined by calculating the number of depression cells within the immediate 3 x 3 cell neighborhood of each cell in a depression with the ArcGIS Focal Statistics tool (Esri, 2017), subtracting 1 from the sum of cells in the neighborhood (because the total sum includes the cell of interest), and then calculating the average value for all cells within a given depression (fig. 3). In general, small mean enclosure values for relatively large depressions can indicate oddly shaped or thin features (for example, a drainage ditch), providing evidence that such a depression is possibly artificial.

Proximity Characteristics of Depressions and Filters

If depressions can be identified in the source data for a DEM, then comparison of the source depressions to depressions derived from DEMs can provide a means to distinguish unlikely from likely depressions in DEMs (Lindsay and Creed, 2006). In topographic-contour maps, closed contours that are lower than neighboring contours can be identified as depressions. Digital contours derived from topographic-contour-based DEMs can be used as a surrogate for the source contours if they are unavailable. Closed 10-ft contours were delineated from each elevation dataset, and 30-ft buffers were created around each of the delineated preliminary depressions. Preliminary depressions whose buffers contained at least one closed 10-ft contour with an area of at least 900 square feet (ft²) that was delineated from the same preliminary depression source data were flagged and examined during assessments as an indicator of likely depressions. When contours are derived from digital elevation data such as rasters or Triangular Irregular Networks, small, closed contours with an area of less than 900 ft² (the size of one grid cell) can be spurious artifacts of the contouring process.

DEMs can include artificial depressions caused by objects elevated above the surrounding terrain such as transportation pathways, where routing of water through culverts, into drains, or beneath small bridges is not represented (Lindsay and Creed, 2005; Poppenga and others, 2010; Zandbergen, 2010; Wall and others, 2015; fig. 4). Artificial depressions can be particularly pronounced in lidar-derived data, where more detail is captured than in coarser elevation data (Poppenga and others, 2010), such as data derived from topographic contours. Without field inspection, determining which depressions are caused by “topographic barriers,” where water is routed beneath a road or bridge, can be difficult. In artificial depressions caused by topographic barriers, the lowest elevation within the depression, or depression bottom, would often be close to the barrier (Poppenga and others, 2010). Locations of preliminary depression bottoms were delineated based on the minimum elevations and were compared to locations of detailed street (TomTom North America, Inc., and Esri, 2013b), major road (TomTom North America, Inc., and Esri, 2013c), railroad (TomTom North America, Inc., and Esri, 2013d), and airport runway (TomTom North America, Inc., and Esri, 2013a) vector digital data. Preliminary depressions with bottoms within 200 ft of these features were flagged as unlikely.

Other off-terrain objects causing depressions include developed or impervious areas, where real depressions exist in the elevation data but are man-made or caused by development. Partly because of increased development and urbanization over time, this is a problem that is more pronounced in lidar-derived data than in data derived from topographic contours delineated decades ago. Raster cells designated as being in low-, medium-, or high-intensity developed areas from the 2011 National Land Cover Database (USGS, 2014c; Homer and others, 2015) were converted to polygon vectors. Preliminary depressions derived from the contour-based NED with bottoms that fall within polygons representing low- to high-intensity developed areas were flagged as unlikely. Preliminary depressions derived from the lidar-based NED and the TNBMP data with bottoms that fall within polygons representing low- to high-intensity developed areas were flagged as artificial.

Some preliminary depressions derived from the NED and TNBMP elevation data were located within inundated areas or boundaries of man-made hydrologic structures. Certain waterbody features and hydrographic landmarks from the NHD (USGS, variously dated b) were used to determine specific areas where preliminary depressions should be considered unlikely. These areas include (1) NHD lakes, ponds, or reservoirs intersecting connected streams derived from the NHD, (2) NHD hydrologic landmarks, such as dams or locks, and (3) sinking streams from the NHD upstream of their termination point. These features were extracted from the NHDWaterbody, NHDArea, and NHDFlowline feature classes (USGS, variously dated b), respectively. Preliminary depressions from all elevation data sources intersecting these features were flagged as artificial.

Assessment Methods for Preliminary Depressions

An assessment of preliminary depressions based on elevation accuracy and comparisons to topographic-contour source data was performed to determine proper depression-characteristic thresholds for distinguishing unlikely from likely depressions. This assessment included estimating the vertical accuracy of each elevation dataset, a numerical error propagation technique based on the estimated vertical accuracy of the elevation data in 10 test areas (fig. 5), and a comparison of preliminary depression locations to topographic-contour source data. Although all of the assessments were applied to depressions derived from each elevation dataset, different assessment methods were used to distinguish unlikely from likely depressions derived from the topographic-contour-derived NED than were used to distinguish unlikely from likely depressions derived from the lidar-derived NED and the photogrammetrically derived TNBMP data. Depressions delineated from the topographic-contour-derived NED could be assessed by using topographic-contour source data, which was in turn part of the process used to separate unlikely from likely digital depressions in the topographic-contour-based NED. The lidar-based NED and photogrammetrically based TNBMP data were derived from mass points with elevation data and break lines, which do not lend themselves to a visual or proximity-based detection of depressions.

Comparison of Preliminary Depressions to Topographic-Contour Source Data

Taylor and Nelson (2008) compiled karst geospatial data for the Interior Low Plateaus physiographic region (Fenneman, 1938) in the central United States, the extent of which is roughly equivalent to that of the Interior Plateau Level III ecoregion (U.S. Environmental Protection Agency, 2013) within the study area. The compilation of karst data includes points placed in apparent centroids of closed-depression contours from 1:24,000-scale topographic maps in parts of middle Tennessee and northern Alabama (Taylor and Nelson, 2008). A subset of these point locations (fig. 6) within a 17,739-mi² test area were compared to locations of topographic-contour-based preliminary depressions derived from the NED to determine depression proximity and size characteristics that might be used to distinguish unlikely from likely depressions. The centroid locations from Taylor and Nelson (2008) were compared to locations of depressions derived from the lidar-based NED and the photogrammetry-based TNBMP data to quantify how well the topographic-contour source data matched depressions derived from other sources used in the current investigation. Depressions derived from 1:24,000-scale topographic contours are more comparable to the closed-contour centroid locations from the karst compilation than are the depressions derived from other sources; depressions derived from the lidar-based NED and the TNBMP are not based on 1:24,000-scale topographic contours and would be expected to produce a different spatial distribution of depressions than the topographic-contour-based NED.

Field Validation

During May through July 2014, field validations of a subset of preliminary depression features in the study area were conducted at 91 sites (fig. 7) to apply a level of quantitative accuracy to depressions derived from each dataset. The subset of preliminary depression features examined during the field visits contained unlikely depressions and those deemed likely based on characteristic criteria determined during assessments and through proximity filters. Many sites contained clusters of depressions, and the number of depressions at each site varied among elevation data sources. Field visits were conducted in each karst region within the study area except the Limestone Valleys and Coves in the Blue Ridge Level III ecoregion (figs. 2 and 7). Field validations consisted primarily of “road observations” because most sites were on private property. To help ensure visibility from the vehicle, only selected sites within a 600-ft buffer of interstates, State highways, and U.S. highways (Tele Atlas North America, Inc., and Esri, 2008) were visited initially. The buffer was later altered to cover the area from 1,000 to 2,000 ft away from the interstates, State highways, and U.S. highways (Tele Atlas North America, Inc., and Esri, 2008). The altered buffer generally minimized the number of structure-related artificial depressions encountered during the field validations but also affected site access and visibility.

During the field visits, locations of preliminary depressions derived from all elevation sources were examined. At many sites, preliminary depressions from multiple data sources were available. In parts of the study area where the lidar-derived NED was merged into the topographic-contour-derived NED (fig. 1), elevation data derived from contours and from lidar covered the same area. At field visit locations where data were from both sources, preliminary depressions were derived from both sources to compare the preliminary depressions derived from the different elevation data sources for the NED. In all, 168 total preliminary depressions were visited at 91 sites: 66 were derived from the contour-based NED, 21 were derived from the lidar-based NED, and 81 were derived from the TNBMP data. Attempts were made in the field to determine whether each preliminary depression existed in the field and whether those existing in the field were karst depressions.

Reduction of Artificial Depressions Caused by Topographic Barriers

Prior to the delineation of the depressions that are included in Ladd (2025), methods similar to those described by Wall and others (2015) were used to approximate locations of flow pathways under topographic barriers to flow, such as roads and bridges, and enforce the pathways into the hydroimposed DEMs for each elevation dataset. In contrast to using preliminary depression proximity to topographic barriers as a filter for the identification of unlikely depressions, the methods described by Wall and others (2015) help reduce the number of artificial depressions caused by topographic barriers to flow in the DEMs by eliminating the barriers where flow is likely to cross.

Artificial depressions caused by topographic barriers are particularly prominent in DEMs derived from lidar, where more detail of the land surface is captured than in coarser elevation data (Poppenga and others, 2010), such as elevation data derived from topographic contours. Vector datasets of detailed streets (TomTom North America, Inc., and Esri, 2013b), major roads (TomTom North America, Inc., and Esri, 2013c), railroads (TomTom North America, Inc., and Esri, 2013d), and airport runways (TomTom North America, Inc., and Esri, 2013a) were acquired for the study area and were assumed to coincide with the transportation pathways that act as topographic barriers in the DEMs. In the parts of the NED derived from lidar data and in the TNBMP elevation data, where more detail of the land surface is captured than in parts of the NED derived from topographic contours, the detailed streets were used with the railroad and airport runway data to approximate locations of topographic barriers in the DEMs. The relatively less dense major road data were used with the railroad and airport runway data in the parts of the NED derived from topographic contours, where a visual inspection of the source topographic maps indicated that major roads more accurately represented topographic barriers to flow than did detailed streets. Because the set of connected streams derived from the NHD was enforced onto the hydroimposed DEMs, followed by removal of the DEM cells underlying the connected streams, connected streams already breached transportation pathways in the hydroimposed DEMs used for this analysis.

Sinking-stream features derived from the NHD were intersected with the transportation pathways. Intersections between the sinking streams and the airport runways created lines because the runways are represented by polygons; otherwise, points were created at the intersections for the remainder of the transportation pathway lines. A 100-ft buffer was created around the intersections, and the sinking-stream features were clipped to the buffers. The clipped sinking-stream features were converted to a grid, and the ArcGIS Zonal Fill tool (Esri, 2017) was used to find the minimum elevation from the hydroimposed DEMs along the boundary of the clipped sinking-stream grid within each buffered area. This minimum elevation value was assigned to the clipped stream grid segments, which acted as approximate culvert locations enforced onto the hydroimposed DEMs. The ArcGIS Fill tool (Esri, 2017) was used on the hydroimposed DEMs with enforced culvert locations to eliminate any depressions caused by transportation corridors. The ArcGIS Flow Direction tool (Esri, 2017) was used on the filled DEMs to assign a flow direction to each cell in the culvert-enforced hydroimposed DEMs, and the ArcGIS Flow Accumulation tool (Esri, 2017) was used to determine the number of cells that contribute flow to each cell in the culvert-enforced hydroimposed DEMs. From the flow accumulation grid, a synthetic stream grid of flow accumulation values of at least 5,000 cells (approximately 0.16 mi²) was generated, and the synthetic stream grid was converted to vector lines. The entire intersection, buffer, and culvert-enforcement process was repeated on the previously culvert-enforced and hydroimposed DEMs using the streamlines representing flow accumulation greater than 5,000 cells. The process was repeated a third time using streamlines representing flow accumulation greater than 120 cells (approximately 0.004 mi²) to create final culvert-enforced hydroimposed DEMs, termed “culvert-enforced DEMs” in the remainder of this report.

Delineation of Depressions, Sinking Streams, and Watersheds

Depressions were delineated by using the culvert-enforced DEMs for each elevation dataset. Depression characteristics were calculated by using the same methods used to delineate preliminary depressions. The final depressions derived from the culvert-enforced DEMs were depressions that (1) passed depression-characteristic thresholds to be deemed likely, and (2) passed the proximity filters required to remain in the depression dataset.

To delineate watersheds from each elevation dataset for depressions and sinking streams that were obtained by editing the NHD (USGS, variously dated b), custom flow direction grids were created from the culvert-enforced DEMs from each elevation dataset. The custom flow direction grids created for delineating watersheds of closed depressions from the NED and the TNBMP data were created using a different method than the one used for delineating watersheds of sinking streams. To create the custom flow direction grids for the delineation of depression watersheds, the sinking streams from the NHD were separated into two subsets composed of sinking streams that intersect depressions and those that do not. Grid cells in the culvert-enforced DEMs derived from the NED and TNBMP data were then removed from within the boundaries of depressions and from the locations of sinking streams that do not terminate within a depression, and elevation values at grid cells at the locations of sinking streams that intersect depressions were decreased by 1,000 ft. A fill process was run on the resulting grid, and a flow direction grid was created from the filled grid. To create a custom flow direction grid for delineating sinking-stream watersheds, grid cells were removed from the culvert-enforced grid derived from the NED at all sinking-stream locations. A fill process was run on the resulting grid, and a flow direction grid was created from the filled grid. The ArcGIS Watershed tool (Esri, 2017) was used to create watersheds for depressions and sinking streams from their respective custom flow direction grids. The geospatial datasets of depressions derived from the culvert-enforced DEMs, sinking streams derived from digital hydrographic data, and watersheds for the depressions and sinking streams are available in Ladd (2025).

Numerical Error Propagation Tests

Numerical error propagation tests were used to assign likelihoods to each preliminary depression within the 10 test areas (fig. 5). The likelihoods derived from the numerical error propagation tests were used to determine depression-characteristic thresholds for separating unlikely from likely depressions delineated from the lidar- and photogrammetry-based DEMs. Ideally, tests like numerical error propagation would be used across the entire study area, allowing depression probability to be the primary distinguishing factor for unlikely and likely depressions when elevation source data cannot be used to make such a distinction; however, the number of simulations required to calculate depression probabilities makes an application unfeasible for large areas. For this study, depression probabilities were compared to selected depression characteristics to determine combined characteristic thresholds that can be applied to make the distinction between unlikely and likely depressions in the remainder of the study area.

Determining a probability threshold for likely depressions is a subjective process (Lindsay and Creed, 2006). Previous applications of numerical error propagation to determine likely depressions have been done in several ways, including assigning the maximum cell probability within a depression to the entire depression delineated from elevation data (Lindsay and Creed, 2006) and using a cell probability threshold to define the extent of likely depressions (Zandbergen, 2010). Calculating the depression probability (P_dep) as the probability that at least one cell within a depression is likely, based on the Monte Carlo simulations as was done in this study, produces a depression probability value that is heavily influenced by cell depths and the area of each depression. A comparison of volume (a function of cell depth and depression area) to P_dep indicated that all elevation data generally produced depressions with a wide range of probabilities when depression volumes were less than approximately 17,000 cubic feet (ft³). When depression volumes were greater than 17,000 ft³, all depressions had probabilities of at least 0.99 (fig. 8A). Similarly, all preliminary depressions with areas greater than approximately 12,000 ft² had probabilities of at least 0.99 (fig. 8B), and all preliminary depressions with mean enclosure of five or more cells had probabilities of at least 0.99 (fig. 8C). The convergence of P_dep values above multiple depression-characteristic values lends credence to the choice of 0.99 as a proper threshold for high-likelihood depressions.

Because the numerical error propagation tests could not be conducted across the entire study area, depression-characteristic thresholds were determined for distinguishing unlikely from likely lidar-based NED and photogrammetrically derived TNBMP depressions. Zandbergen (2010) found that using a single depression characteristic, such as depth or area, would likely lead to many incorrect classifications of unlikely and likely depressions. For depressions derived from the lidar-based NED and the TNBMP data, multiple criteria were required to consider a depression likely. For the lidar-based NED, these criteria were (1) a minimum area, volume, and mean enclosure of 2,700 ft² (approximately 251 square meters [m²]), 31 ft³ (approximately 0.88 cubic meter [m³]), and 1.33 cells, respectively, (2) an area of at least 8,100 ft² (approximately 753 m²) or a volume of at least 12,000 ft³ (approximately 340 m³), and (3) a mean enclosure of at least 3 cells for depressions with an area of at least 8,100 ft² (approximately 753 m²; table 4). For depressions derived from the TNBMP elevation data, likely depressions required (1) a minimum area, volume, and mean enclosure of 2,700 ft² (approximately 251 m²), 161 ft³ (approximately 4.56 m³), and 1.33 cells, respectively, (2) an area of at least 7,200 ft² (approximately 204 m²) or a volume of at least 8,000 ft³ (approximately 227 m³), and (3) a mean enclosure of at least 3 cells for depressions with an area of at least 9,000 ft² (approximately 836 m²).

Depression-characteristic thresholds determined from the numerical error propagation tests were not used to distinguish unlikely from likely depressions in the topographic-contour-derived NED, but the depression-characteristic thresholds for depressions delineated from the topographic-contour-derived NED were used for comparison of numerical error propagation results across the various elevation data. For depressions delineated from the topographic-contour-based NED, thresholds determined from the numerical error propagation tests were (1) a minimum area, volume, and mean enclosure of 3,600 ft² (approximately 334 m²), 3 ft³ (approximately 0.08 m³), and 1.5 cells, respectively, and (2) an area of at least 6,300 ft² (approximately 585 m²) or a volume of at least 10,000 ft³ (approximately 283 m³; table 4).

The area, volume, and mean enclosure thresholds for the depressions derived from the lidar-based NED produced a false positive rate of 3.97 percent and a false negative rate of 11.9 percent within the four numerical error propagation test areas that contained lidar data (table 4). The thresholds for depressions derived from the TNBMP data produced a false positive rate of 4.68 percent and a false negative rate of 11.9 percent within the eight numerical error propagation test areas that contained TNBMP data. The thresholds for depressions derived from the topographic-contour-based NED produced a false positive rate of 5.99 percent and a false negative rate of 8.48 percent within the six numerical propagation test areas that contained contour-derived data.

Although the primary aim of threshold selection is the reduction of false positives and negatives, error reduction is not the only concern. The mean enclosure characteristic calculated for this study is a measure of how surrounded each depression cell is, on average, by other depression cells. Hence, the magnitude of mean enclosure is related to both the size and shape of a depression. An increase in depression area generally relates to an increase in mean enclosure up to a logical upper limit for mean enclosure of eight cells. Depressions with relatively large areas and relatively small mean enclosure values tend to be either long and thin or oddly shaped features and can often be characteristic of man-made features and drainage ditches truncated by off-terrain objects. The application of numerical error propagation tests can result in high probabilities for these and other artificial depressions caused by off-terrain objects, providing validation for the use of higher mean enclosure thresholds for depressions with large areas; however, removal of features with relatively low mean enclosure values and large areas can lead to an increase in false negative rates as determined here.

Differences in the depression density within the numerical error propagation test areas, the characteristic threshold values, and the error rates between depressions derived from the different elevation data sources are due in part to differences in the estimated elevation error term introduced into the numerical error propagation tests and differences in source-data resolution. The error term used in the numerical error propagation tests for the TNBMP data was 3 ft, as opposed to the 5-ft error term used in the lidar- and contour-based NED. Zandbergen (2010) reported that an increase in the error term in tests performed on the same elevation data generally leads to a decrease in the number of depressions and an increase in the size of the depressions, meeting a given probability threshold. In this study, this relation was not seen when comparing different elevation data sources. The TNBMP data produced fewer preliminary depressions, fewer high-likelihood depressions, and larger (generally in terms of area and volume) high-likelihood depressions on average than the lidar-derived NED in two shared test areas (tables 2 and 3). The TNBMP data produced more preliminary depressions than the contour-based NED in six shared areas and produced more high-likelihood depressions in five of the six shared areas, although neither dataset produced clearly larger high-likelihood depressions in the shared areas (tables 2 and 3). These comparisons indicate that source-data resolution and accuracy as well as the error term used in the numerical error propagation tests influence high-likelihood depression density and size, and the differences in depression density and size influence the chosen threshold values and error rates. Further study could help verify and quantify these effects.

Error Assessment of Depressions From Topographic-Contour Source Data

For depressions derived from topographic-contour-based DEMs, a comparison to the topographic-contour source data can be helpful in distinguishing unlikely from likely depressions in DEMs. If elevation data are derived from contours, a derived depression containing at least one closed contour of the same interval as the source data can be considered a likely feature. If a depression occurs in contour-based elevation data but there is no source contour to justify it, then the depression must have resulted from the interpolation process and can safely be considered artificial (Lindsay and Creed, 2006).

In large study areas where the source topographic contours are unavailable in a digital format, digital contours derived directly from the DEM can be used to help make the distinction between unlikely and likely depressions. In the comparison of closed-contour centroids identified by Taylor and Nelson (2008) to preliminary depressions, a false positive rate of depression delineation from a DEM could be estimated by determining the number of likely depressions not containing an identified closed-depression centroid. A false negative rate could be estimated by determining the number of closed-depression centroids that do not fall within a depression derived from the DEM, although a false negative rate calculated by using this method would likely be overestimated because many DEM-derived depressions contain more than one closed-contour centroid.

Approximately 93 percent of closed-depression centroid locations identified by Taylor and Nelson (2008) were within preliminary depressions derived from the topographic-contour-based NED. Only about 78 percent of the closed-depression centroids were within preliminary depressions derived from the contour-based NED that contained a closed 10-ft contour within a 30-ft buffer of the depression, indicating that the use of 10-ft contours as a qualifier introduced up to 15 percent of additional false negatives on top of the original 6.88 percent (table 5). When including only depressions that contained a closed 10-ft contour within a 30-ft buffer around the depression, preliminary depressions delineated from the contour-based NED produced false positive rates of 95.1 percent when no filtering was used and 1.43 percent when filters were applied. Adding a minimum depression volume threshold of 5,000 ft³, a minimum mean enclosure threshold of 4.5 cells, and the contour-containing requirement for depressions delineated from the contour-based NED reduced the false positive rate by 0.8 percent (from 1.43 to 0.63 percent). These additions only increased the false negative rate by 2.5 percent (from 22.5 to 25 percent), adding justification for volume and mean enclosure thresholds for likely depressions derived from the contour-based NED.

As expected, false positive and negative rates in preliminary depressions derived from the lidar-based NED and the photogrammetry-based TNBMP data were higher than those for the depressions derived from the contour-based NED. For depressions derived from the lidar-based NED, false positive rates were 99.7 percent when no filters were used, 2.90 percent when the 10-ft contour requirement was added, and 1.29 percent when the 5,000-ft³ volume and the 4.5-cell mean enclosure thresholds were added to the contour requirement (table 5). False negative rates for depressions derived from the lidar-based NED were 38.5 percent when no filters were used, 60.1 percent when the contour requirement was applied, and 62.6 percent when the volume and mean enclosure thresholds were added.

Error rates for preliminary depressions derived from the TNBMP data were lower than those derived from the lidar-based NED, with false positive rates of 98.5 percent when no filters were applied, 3.52 percent when the contour requirement was applied, and 2.21 percent when the volume and mean enclosure thresholds were applied (table 5). False negative rates for preliminary depressions derived from the TNBMP data were 40.1 percent when no filters were applied, 55.8 percent with the contour requirement, and 56.2 percent with the volume and mean enclosure thresholds.

When using a contour filter in depressions derived from the contour-based NED data, high error rates can occur. False positives can be caused by several factors. Some closed contours were omitted due to human error when constructing the closed-depression centroid dataset. Generally, in the 2008 study (Taylor and Nelson, 2008), closed-depression centroids were not placed in unlikely depressions caused by off-terrain objects, such as transportation pathways; however, these features often contain closed contours (fig. 4). Additionally, a 10-ft contour interval was chosen for the contour filter, but the contour interval of the source data in which the centroids were placed generally was 10 ft or greater within the test area. The inability of the DEM to accurately represent the contour source data would affect false positive and false negative rates. A DEM that does not accurately represent the source data could lead to (1) missing depressions, additional depressions, or inaccurately located depressions when compared to the source contours, and (2) missing contours, additional contours, or inaccurately located contours when compared to the source contours. Errors due to deriving contours from the DEM could be eliminated if digital source contours are available, but those related to human error, an inability to distinguish false depressions caused by off-terrain objects from likely depressions, and DEM inaccuracies in relation to the source data would remain.

Field Validation

Although numerical error propagation tests and comparisons to DEM source data can provide justification for whether a DEM-derived depression is unlikely or likely, field visits are the most reliable method for determining whether a depression actually exists in the natural landscape. Even if a DEM-derived depression is examined in the field, making determinations about whether the feature exists in the landscape and whether it is a karst feature is still a subjective and imperfect process (Lindsay and Creed, 2006). Determining the presence of depressions and karst features is particularly difficult in developed areas where the natural landscape has been modified. Recent development makes comparisons to depressions derived from topographic-contour-based DEMs especially difficult if the topographic-contour source data were mapped prior to development. Even in rural areas with mature karst, wooded areas can obscure easy viewing of depressions and limit the ability to verify the presence of depressions and karst features. Because of these difficulties, determinations could not be made at some of the field visit locations.

For preliminary depressions derived from each elevation source, comparisons were made between field determinations (including whether a depression exists in the field and whether existing depressions are karst features) and digital determinations for preliminary depressions (including whether a preliminary depression is likely based on depression-characteristic thresholds, and whether those depressions deemed likely based on thresholds are considered artificial and were removed from the dataset based on proximity filters; appendix 1). Agreement rates between field and digital determinations were calculated only for sites where a definitive field determination could be made.

For the preliminary depressions derived from the topographic-contour-based NED, the agreement between field determinations of whether a depression exists in the field and the digital determination of whether the depression is likely based on characteristic thresholds is 72.9 percent, and the agreement between field determinations of whether a depression is a karst feature and whether a depression is likely based on characteristic thresholds is 70.0 percent. After adding the proximity filters to the likely depressions derived from the contour-based NED, the agreements between the field determinations of a depression existing in the field and a depression being a karst feature also were 72.9 and 70.0 percent, respectively.

For the TNBMP-based preliminary depressions, the agreement between field determinations of whether a depression exists and the digital determination of whether the depression is likely based on characteristic thresholds is 98.6 percent, and the agreement between field determinations of whether a depression is a karst feature and whether a depression is likely based on thresholds is 79.7 percent. After adding the proximity filters to the TNBMP-based preliminary depressions, the agreements between the field determinations of a depression existing in the field and a depression being a karst feature were 82.6 and 71.9 percent, respectively.

The lidar-based preliminary depressions had the highest rate of agreement (100 percent) of all preliminary depressions between those that exist in the field and those that are deemed likely based on characteristic threshold requirements. However, the rate of agreement for whether a depression exists in the field and whether a depression is deemed likely after proximity filters are applied (63.2 percent), and the rates of agreement for whether a depression is a karst feature and whether a depression is deemed likely after characteristic thresholds (66.7 percent) and after proximity filters (53.3 percent) were applied, are all lower than rates for depressions from other sources. A few reasons could cause this discrepancy. All (100 percent) of the lidar-based preliminary depressions that were visited in the field met the characteristic thresholds to be deemed likely, which is the highest rate of visited depressions from all sources. Additionally, the visited lidar-based preliminary depressions had the highest rates of preliminary depressions deemed unlikely due to proximity to developed areas (38.1 percent) and proximity to likely depression-excluding objects in general (also 38.1 percent) compared to the visited depressions from other sources. The relatively high rate of lidar-based preliminary depressions that are influenced by development, combined with the inherent difficulty in making an accurate field determination of whether a depression is a karst feature in developed areas, likely led to a low agreement rate between whether a lidar-based preliminary depression was deemed likely after characteristic thresholds were applied and whether a depression was considered a karst feature, as well as low agreement rates between whether a lidar-based preliminary depression was deemed likely after proximity filters were applied and field determinations were made.

Reduction of Unlikely Depressions Caused by Topographic Barriers

To quantify the effect of the application of the flow pathway enforcement methods (Wall and others, 2015) in this study, the number of preliminary depressions deemed likely after passing characteristic thresholds and proximity filters and that have a bottom within 200 ft of detailed streets (TomTom North America, Inc., and Esri, 2013b), major roads (TomTom North America, Inc., and Esri, 2013c), railroads (TomTom North America, Inc., and Esri, 2013d), and airport runways (TomTom North America, Inc., and Esri, 2013a) were compared before and after the application of flow pathway enforcement. The flow pathway enforcement methods used to create the culvert-enforced DEMs used for this study led to the removal of 2,052 (10.2 percent) unlikely depressions that were caused by topographic barriers derived from the contour-based NED; 3,428 (36.7 percent) unlikely depressions derived from the lidar-based NED; and 14,330 (26.2 percent) unlikely depressions derived from the TNBMP data. The flow pathway enforcement methods will not remove all artificial depressions caused by topographic barriers from elevation data prior to the delineation of depressions (Wall and others, 2015). Quantification of the number of artificial depressions remaining in each dataset after the application of the flow pathway enforcement methods would require further study.

Depression Statistics Within Karst Regions

The depressions documented in Ladd (2025) were used to calculate statistics within each karst region in the study area. For each karst region, the density metrics and characteristics of depressions delineated from the contour-based NED, the lidar-based NED, and the TNBMP data were compared (table 6). Depressions delineated from the contour-based NED had lower densities, higher average areas, higher average volumes, and higher average mean enclosure values than the lidar-based depressions and the TNBMP-based depressions within all karst regions (table 6; fig. 9A, C–E). In general, average values of density and area within each karst region for depressions from the lidar-derived NED and the TNBMP data were more similar to one another than to the average values of density and area for depressions from the topographic-contour-based NED. DEMs derived from finely spaced mass-point data produce more depressions in general than DEMs derived from contours (MacMillan and others, 2003; Lindsay and Creed, 2005), so higher densities in depressions from the lidar-derived NED and the photogrammetrically derived TNBMP data compared to depressions from the contour-derived NED are expected. Additionally, increased surface roughness would generally lead to an increase in relatively small depressions, bringing the average depression size down in a given area.

Although average areas and volumes were smaller for depressions from the lidar-derived NED and the TNBMP data than for depressions from the contour-based NED, depressions from the lidar-based NED were generally smaller than those derived from the TNBMP data in most areas, including the Cumberland Plateau Escarpment and Sequatchie Valley, Inner Nashville Basin, Limestone Valleys and Coves, Ridge and Valley, and Western Highland Rim karst regions, as well as the parts of the study area that lie outside of a designated karst region (table 6; fig. 9C). The areal extent of depressions delineated from the contour-based NED composed a higher percentage of the Cumberland Plateau Escarpment and Sequatchie Valley, Inner Nashville Basin, and Western Pennyroyal Karst Plain and Crawford-Mammoth Cave Uplands karst regions than the lidar-based depressions, but the lidar-based NED covered less than 10 percent of these regions within the study area (table 6; fig. 9B), making density metrics for depressions derived from the lidar-based NED suspect in these areas. The areal extent of depressions delineated from the contour-based NED also composed a higher percentage of the Western Pennyroyal Karst Plain and Crawford-Mammoth Cave Uplands karst region than depressions delineated from the TNBMP elevation data, but the TNBMP elevation data also covered less than 10 percent of the Western Pennyroyal Karst Plain and Crawford-Mammoth Cave Uplands karst region (table 6; fig. 9B). Depressions from the lidar-derived NED were generally larger than those derived from the TNBMP data in the Outer Nashville Basin and Western Pennyroyal Karst Plain and Crawford-Mammoth Cave Uplands karst regions, but the lidar-derived NED and the TNBMP data composed less than 10 percent of the Western Pennyroyal Karst Plain and Crawford-Mammoth Cave Uplands karst region (table 6; fig. 9C, D).

The differences in criteria used to separate unlikely from likely depressions complicate the direct comparison of depression density and size among elevation data sources. However, apparent density and average size trends within depressions from multiple elevation sources across karst regions can provide more evidence for the existence of those trends. The Western Pennyroyal Karst Plain and Crawford-Mammoth Cave Uplands karst region has generally high densities, high percentages of depression area, and high average areas of likely depressions from all elevation data sources (table 6; fig. 9A–C). The Cumberland Plateau Escarpment and Sequatchie Valley karst region has relatively low densities of likely depressions and low percentages of depression area from all sources but also contains relatively high average areas and the highest average volumes of depressions from all sources (table 6; fig. 9A–D). The Eastern Highland Rim, where the lidar-derived NED is absent, has the highest average area values for depressions from the contour-derived NED and the TNBMP (table 6; fig. 9C). The lowest average volumes for likely depressions from the lidar-derived NED and the TNBMP data occurred in the Western Highland Rim karst region, where the average volume for depressions from the contour-derived NED were generally low (table 6; fig. 9D). The highest average mean enclosure values for likely depressions from the contour-based NED and the TNBMP data occurred in the Eastern Highland Rim, where depressions derived from lidar are absent (table 6; fig. 9E). The highest average mean enclosure value for likely depressions from the lidar-derived NED was in the Western Pennyroyal Karst Plain and Crawford-Mammoth Cave Uplands karst region, which also had the second and third highest average mean enclosure values for depressions from the contour-based NED and the TNBMP data, respectively.

Some general discrepancies in depression density and percentage of depression area exist when different elevation data sources are used. The highest density of depressions and percentage of depression area from the contour-derived NED and the lidar-based NED occurred in the Western Pennyroyal Karst Plain and Crawford-Mammoth Cave Uplands karst region, while the highest density of depressions and percentage of depression area from the TNBMP data occurred in the Inner Nashville Basin karst region (table 6; fig. 9A, B). The lowest densities of depressions and percentages of depression area from the contour-based NED and the lidar-based NED occurred outside of designated karst regions within the study area; the density of depressions and percentage of depression area from the TNBMP data were slightly lower in the Western Highland Rim karst region than outside of designated karst regions. Within the Limestone Valleys and Coves, the density of depressions and percentage of depression area from the lidar-based NED were relatively high compared to the density values for depressions and percentages of depression area from the contour-based NED and the TNBMP data.