DIGITAL ELEVATION MODEL (DEM) ACCURACY

The standards specified in this document pertain to the collection, processing, and quality control of USGS digital elevation model (DEM) data. These standards are intended to facilitate the interchange and use of DEM data. DEM collection and editing systems must produce data that are compatible with other production systems in government and private sector organizations, including international ones.

A number of factors affect gridding processes and the accuracy of the final DEM product:

Ø All DEM's where the companion map (of the same geographic extent) contour interval is 10 foot or less are gridded in vertical units of feet.

Ø A dependency exists between the scale of the source materials and the level of detail or grid refinement that is possible from a given source.

Ø During the process of changing scale, from large to small, some source data may be generalized or dropped out and, therefore, some features would not be available for formation of, or incorporation into, a grid at that scale.

Ø The process of forming a grid with regular spacing requires the transfer of precise point or vector data to generalized grid square corners using a process similar to taking a simple weighted average. This process may alter the apparent position upon display of point or vector source data, reducing the ability to recover positions of specific features whose dimensions are less than the internal grid cell spacing.

Ø The DEM collection process normally consists of successive stages of production through which errors may be cumulative: a highly accurate aerotriangulation solution, compilation of source data sets, and the final gridding process. In the case of derivation of DEM's from digital line graphs (DLG), the first two stages of production have their origins in the original compilation of the source map. If each stage of production satisfies accuracy criteria customarily applied to each intermediate product, then the maximum error that can be expected from all processes may be accumulated as a integral sum of all errors, such that the total error squared is the sum of the squares of the individual errors. So that each product in this production process may qualify to be used in the next step of the process, production personnel must make a strict accounting of accuracy for each production step leading to the final DEM.

Ø For cartographic-source DEM data, accuracy is highly dependent on original materials. Existing quadrangles that are used as source for hypsography and hydrography must conform to national standards. Further, USGS map digitizing accuracy must conform to Standards for Digital Line Graphs, when DLG data are used as input to USGS gridding algorithms that produce DEM's.

 

DEM data contain errors, mainly of three types: blunders, which are removed prior to entry in the data base; systematic errors, which occur in a system-specific or a procedure-specific pattern; and random errors, which are of a purely random nature and are completely unpredictable. Although all three types may be reduced in magnitude by refinements in technique and precision, they cannot be completely eliminated.

For DEM data, a blunder is a vertical error usually of major proportions often exceeding the maximum absolute error permitted (3 sigma) for each DEM level (see section 2.3) and as such is easily identifiable. Moreover, a blunder is an indication that the data collection process has deteriorated beyond the level of simple systematic or random errors. Blunders are mistakes caused by misreading contours, transposing numeric values, erroneous correlations, or careless observations. Wherever detected, errors caused by blunders must be removed.

Systematic errors are those errors that follow some fixed pattern or rule, are generally of constant magnitude or sign, are introduced by procedures or systems, and are typically predictable. These types of errors cause bias or artifacts in the final product. For DEM data, typical systematic errors include: vertical elevation shifts, either for the quadrangle as a whole or for individual local areas or profiles; fictitious features, such as phantom tops, ridges, benches, or striations; and improper interpretation of terrain surfaces due to the effects of trees, buildings, and shadows. Systematic errors can be eliminated or substantially reduced when the cause is known.

Random errors are those remaining after blunders and systematic errors have been removed. They result from accidental and unknown combinations of causes beyond the control of the observer. Random errors are classed as normally distributed and are characterized by: (1) variation in sign - positive and negative errors occurring with equal frequency, (2) small errors occurring more frequently than large errors, and (3) extremely large errors rarely occurring.

Edge matching is a process of matching elevation values along common quadrangle edges. Prior to edge matching, the majority of in-process DEMs may have noticeable edge breaks of approximately 1 to 3 vertical units of resolution (feet or meters). Under these conditions, enforcement of a simple edge matching filter extending approximately 5 rows or columns to both sides of the edge should produce adequate topographic definition. Instances of breaks in excess of 3 vertical units of resolution require more extensive editing. Edge matching along these edges may include conventional editing procedures such as recontouring of local areas or use of area smoothing or filtering to extend to a maximum of 30 rows or columns to both sides of the edge.

The intent of DEM production processes is to produce DEM data sets that are accurate representations of slope as well as elevation. Slope data are more critical to certain scientific applications than are elevation data. For this reason the DEM should be smooth within the grid and continuous from node to node except at natural break points such as streams, cliffs, and craters.

When a DEM is generated, it may contain areas of constant elevation derived from corresponding areas within the graphic or digital source containing estimated or false elevations. Three types of these areas may occur: void areas, suspect areas, and water bodies.

Void areas occur in the DEM as a result of interruptions to the contours of the source graphic or DLG (eg. photoimages overprinted onto a topographic map). Void areas are identified in DLG hypsographic data by using the void area code. Each DEM elevation post located within a void area is assigned a false negative value.

Suspect areas in the DEM result from corresponding areas on the graphic source that are shown as "disturbed surfaces." They are symbolized by contours that have been overprinted with photorevised or other surface patterns. Examples of disturbed surfaces are: lava flows, landslides, open pit mining, construction cut and fill, and land fill operations. An estimated elevation is supplied for suspect areas based on the presumed elevation at the time the DEM grid is generated. When an elevation cannot be estimated for a suspect area, the area is downgraded to a void area and assigned a false negative value.

Water body areas are naturally occurring areas of constant elevation. Oceans or estuaries at mean sea level are assigned an elevation value of zero. All other water bodies are assigned their known or an estimated elevation.

Water bodies contained in DEM data are edited when they conform to the following criteria:

Type: Ponds, lakes, reservoirs, and double-line drainage.

Size: Ponds, lakes and reservoirs exceed approximately ½ inch at map scale along the major axis.

Double-line drainage exceeds 1/4 inch at map scale in width.

To establish the water body elevation of each of the individual polygons of a double-line drain, assign the elevation of the contour crossing (or closure line) representing the lowest elevation of the polygon. Determine the correct horizontal and vertical position or elevation from published products or other office sources by procedures established by the mapping centers. Edit water body data using the map or orthophoto containing the most current water body information. Horizontal position and shape are as important as the elevation. Water bodies meeting type and size criteria but lacking a published elevation are assigned an interpolated elevation not to exceed the highest contour that closely approximates the shoreline of the water body. To derive this elevation interpolate one half the contour interval subtracted from the next higher naturally occurring contour elevation above the water body or substitute an elevation derived from various water control structures such as spillways and embankments. Sea level is set as an arbitrary value of zero in the DEM. The shoreline is defined as mean high tide. Local variations of tides are rarely tied to or coincide with absolute datums; therefore, as derived within the DEM, neither sea level or mean high tide are assumed to be related to standard datums. Extremely shallow land just interior to coastlines but not classified as swamp or otherwise inundated should have a higher elevation value than the sea by at least one unit of resolution to force land/water boundary portrayal. Water bodies must be depicted as flat and generally lower than the surrounding terrain and must have shorelines clearly delineated. Where water bodies join or merge with swamps or other areas that are inundated at the same elevation, the swamp or other area must be brought to conform to approximately the same elevation as the water body. Water bodies must not have striations or benches of any kind. Areas such as swamps that are normally inundated must be free of artifacts such as striations or benches so that the surface is interpretable as a hydrographic feature.

Quality control is an integral part of the production process and includes project planning and the use of proper hardware, software, and procedures. The following tests, inspections, and corrective actions are mandatory to ensure the accuracy and format of the DEM.

The vertical root-mean-square error (RMSE) statistic is used to describe the vertical accuracy of a DEM, encompassing both random and systematic errors introduced during production of the data. The RMSE is defined as:

RMSE – √[∑(Zi-Zt)²]/n

where

Zi = interpolated DEM elevation of a test point

Zt = true elevation of a test point

n = number of test points

The RMSE derived from the above accuracy computation is encoded in a record of the DEM. Accuracy is computed by a comparison of linear interpolated elevations in the DEM with corresponding known elevations. Test points should be well distributed, representative of the terrain, and have true elevations with accuracies well within the DEM accuracy criteria. Acceptable test points include, in order of preference: field control, aerotriangulated test points, spot elevations, or points on contours from existing source maps with appropriate contour interval. Care should be exercised in selecting bench mark or supplemental bench mark control points from map sources because many of these are on structures above the ground (freeway right-of-ways, overpasses, railroad bridges, etc.). When in doubt, don't use these points. A minimum of 28 test points per DEM is required to compute the RMSE, which is composed of a single test using 20 interior points and 8 edge points. Edge points are those, which are located along, at, or near the quadrangle neatlines and are deemed by the editor to be useful to evaluating the accuracy of the edge of the DEM.

All USGS DEM's are tested and assigned a vertical RMSE. Because of practical limitations inherent in all collection systems there will always be some artifacts such as benches, striations, patches, or some other anomaly that imparts some signature of the collection system in the data set. This coalescence should not be tolerated to the point where valid surfaces become unintelligible to the users of the data.

For example:

Ø Isolated tops must be depicted with their approximate size and shape.

Ø Flat trending surfaces must be depicted as generally flat trending without confusing patterns or striations.

Ø Water bodies must be flat, be lower than the surrounding terrain, and have shorelines clearly delineated.

Corrective actions must be taken to minimize these artifacts. For all DEM's, the grid spacing and spatial resolution results in data intervals that span terrain discontinuities, such as benches, tops, and drainage. Some features can be appropriately captured at a given grid spacing while other, smaller features are subdued or filtered out.

The USGS uses a computer software program, DEM VERIFY, to verify the logical and physical format as part of the data base entry procedure.

Additional testing is performed using a DEM Editing System to identify blunders such as irregularly gridded data, mistagging of tops and depressions, and spikes. These blunders are generally identified by displaying the DEM using options such as color banding of elevation gradients, stereoscopic viewing using anaglyphic filters, and shaded-relief enhancement. An elevation matrix is analyzed in suspect areas and corrected as required.

Verification includes:

1. Identification of the maximum and minimum elevations contained in the DEM and comparison with the maximum and minimum values represented by contours or spot elevations on the best available map product of the area. The maximum and minimum grid points must be within the stated error tolerances. The data and map should be examined to determine the reason for any discrepancy and the data edited.

2. Verification of all elevations below sea level according to the best available map product of the area and, if unsupported, adjustment to the surrounding terrain.

If it is judged economically feasible, the mapping control centers will reprocess the raw data. These edited or reprocessed DEM's will be resubmitted for quality review.

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