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June 24, 2019 Rich Mohr

Assessing Vertical Accuracy of Digital Elevation Models7

For numerous industries, and especially the flood hazard modelling Intermap specializes in, accurate digital elevation models (DEMs) are indispensable. And one of the most important aspects of a DEM is its vertical accuracy.

Vertical accuracy of elevation data is the possible height difference between the modelled height and the actual height of the land. Different methods of creating elevation data, such as LiDAR, photogrammetry or radar, produce different levels of accuracy. Of these methods, LiDAR is generally the preferred source for elevation modelling due to its excellent horizontal resolution and vertical accuracy, as well as its ability to subtract out features, such as buildings and vegetation, from the landscape. However, LiDAR is extremely expensive and, therefore, is typically flown just over the smaller, high-value areas like cities, with photogrammetry being used to collect large-scale data for other areas.

Considerations

There are many sources of elevation data available, and it seems like every supplier is claiming to be the “most accurate”. So how do you determine who really has the best accuracy?

Because of the wide variety of methods available to create digital elevation models, that’s not an easy answer. Assessing vertical accuracy can be as easy as a simple subtraction operation or as complicated as creating an entirely new DEM. First, let’s review some considerations to keep in mind when assessing vertical accuracy.

Absolute Vertical Accuracy vs. Relative Vertical Accuracy. Most DEM evaluations focus on absolute vertical, rather than relative vertical accuracy. Absolute vertical accuracy accounts for all effects of systematic and random errors, and relates the modeled elevation to the true elevation with respect to an established vertical datum (geo-referenced). Relative accuracy is a measure of the point-to-point vertical accuracy within a specific dataset, e.g. the vertical difference between two points is measured then compared to the difference in elevation for the same two points within a reference dataset.

Vertical Accuracy is Related to Horizontal Resolution. In an elevation model, elevations are an average over the chosen area. As such, post spacing strongly influences the ability to hold precision. For a flat area or plateau, the effects of post spacing is minimal; however, in hilly terrain, errors can be greatly magnified in lower resolutions. The small the post spacing, the higher the resolution.

Vertical Accuracies Can Vary between DSMs and DTMs of the Same Resolutions. Digital terrain models (DTMs) are typically derived by removing ground features (vegetation, buildings, roads, etc.) in post processing. The number of uncertainties, or errors, increase as the terrain complexity increases, as in urban areas. As such, vertical accuracy is typically lower for DTMs than for digital surface models (DSMs).

Metrics & Terminology. Common metrics used to assess vertical accuracy include the absolute mean difference, root mean square error (RMSE), and linear error (LE) expressed in terms of confidence levels (e.g.,95%). These calculations will relate to post spacing , datums used, and the geographic area covered.

Methodology

Selection of test site is important to judging the validity of an accuracy assessment. Assessments should occur over a number of test sites, and each of those test sites should consist of a variety of terrains. At Intermap, our selection is typically limited areas to those where United States Geological Survey (USGS) LiDAR data was available at high resolution.

The type of methodology approach, such as point-based, profile-based, or surface-based, is also important. It varies, based upon what type of data you start with.

  • Point-Based. If the reference data is provided as a set of scatter points with accurate 3D positional information, the point-based approach is usually the best approach to take. In this approach, elevation errors are independently calculated for each point and the vertical accuracy can be only assessed for the entire set.
  • Profile-Based. If the reference data is collected along a linear feature (e.g., roads, river banks), a profile-based approach will provide more insights to the quality of your DEM. In this approach, vertical accuracy can be assessed for each profile. Additionally, a meaningful relative vertical accuracy can be calculated along each profile after removing the errors of the starting point. It is also helpful to determine whether your data is capturing the details of the elevation variations and whether your data has unexpected systematic errors along the profiles.
  • Surface-Based. If the reference data is provided as a grid, the surface-based approach is more appropriate. In this approach, a difference surface is usually calculated and a validity mask is usually used to exclude anomalies in any of the input datasets or any differences due to temporal changes.

Regardless of what methodology approach is used, vertical datum alignment is a critical step. Before you start your assessment, you will have to know the vertical datum of your DEM and that of your reference data. If the datums are different, you will have to determine the differences between them and make adjustment to them. A misalignment of the vertical datum can result in misleading conclusions.

Finally, a “difference” surface is created by subtracting the reference data (typically LiDAR) from the corresponding. Then the elevation errors are categorized using slope and surface height information, and confidence of accuracy is charted.

Independent Verification of Intermap’s Accuracy

Intermap has posted a white paper that describes, in detail, the validation process for our NEXTMap One™ elevation models. More importantly, this assessment has been independently verified by the Digital Photogrammetry Group at Purdue University.

For more information on Intermap’s digital elevation products, click here.

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