# From the Ground Up

It has taken some time for these new standards to gain wide acceptance. It was rare to see requirements for the ASPRS Accuracy Standards from our clients a year or two ago. Most clients still requested maps meeting the NMAS. Today, requests for maps meeting the ASPRS standards are much more commonplace. Yet there are still a lot of misconceptions regarding these accuracy standards—and a lot of questions from professionals trying to compare the newer ASPRS standards to the NMAS. What are the major differences between the NMAS and ASPRS Accuracy Standards? Should a map compiled to meet the requirements of the ASPRS standards be more accurate than the same map compiled under the NMAS requirements? Should one map cost more than the other?

The standards are fairly straightforward. The answers to these questions are also fairly straightforward, once a clear understanding of the standards is gained.

## Map Accuracy

Identify a feature shown in a map and determine its position from your CAD system. What kind of accuracy should you expect from the coordinate values of that feature? Some error should be expected in the position of map features. The error comes from several different sources. Although GPS technology has lead to great improvements in photo control, the ground control is by no means perfect. Additional errors arise from the capture of the imagery and the resulting extraction of features in the map compilation processes.With both the NMAS and ASPRS standards, the accuracy of a map is directly related to the final map scale and contour interval. Determine the position of a planimetric feature in a map compiled for 1"=100' mapping. Now assume you have a second map of the same area compiled for 1"=200' mapping. You should expect twice the error in the coordinate values for that same feature determined from the 1"=200' mapping. The same holds true for elevation data. All other things being equal, you should expect elevation data taken from a map compiled for a 1-foot contour interval to be twice as accurate as a map compiled for a 2-foot contour interval.

The ASPRS Accuracy Standards for large scale maps define the tolerances differently than the older NMAS. The ASPRS standards place limits on the root mean square error (RMSE) for individual position components—northing, easting and elevation. This is very different from the NMAS. The NMAS do not require an evaluation of the northing and easting errors independently. Instead, the NMAS looks at the individual horizontal (combination of northing and easting errors) and vertical errors and places two limits for the checkpoints. The first limit applies to 90 percent of the points checked. A less restrictive limit applies to the remaining 10 percent of the points.

The limiting horizontal RMSE for large scale class 1 maps as defined under ASPRS is 0.01" at map scale. Therefore, the limiting RMSE for the x and y components in a map compiled for 1"=100' mapping would be 1.0 foot. Similarly, the limiting RMSE for the x and y components of a map compiled for 1"=500' mapping would be 5.0 feet. Compare the map coordinates for a number of planimetric features to the coordinates of these same features on the ground. Determine the RMSE for all features compared. The resulting RMSE for the individual x and y components should not exceed 1.0 foot for 100' scale maps or 5.0 feet for 500' scale maps.

The limiting RMSE for elevation data under the ASPRS standards is 1/3 the indicated contour interval. Spot elevations are restricted to an RMSE of 1/6 the contour interval.

While these are pretty simple concepts, there are still a number of misunderstandings relating to these tolerances. Many people confuse the “limiting RMS errors” with a maximum error in the x, y or z component. In fact, the “limiting RMS error” is just that: a limit on the statistical value for the collection of differences taken as a whole. It is possible for individual differences determined for the points checked to exceed the limiting RMS error while the overall RMSE meets the accuracy specification. Review the table below where the results for 20 checkpoints are summarized. The discrepancies define the differences between the map coordinates and the values determined from an accurate ground survey. In this case, the mapping was compiled for 1"=100' mapping with a 2-foot contour interval.

Remember that the horizontal RMSE limit for 100' scale mapping for the x and y components is 1 foot. Notice that several individual values for the discrepancies in the x and y components are outside of the range from –1 to +1 feet. The RMSE for both the x and y components in this example, however, are 1.00 feet. Therefore, the ASPRS Accuracy Standards for the horizontal components are met.

Also remember that the vertical RMSE limit for a map prepared with a 2-foot contour interval is 0.67 feet. Again, several of the individual discrepancies for the vertical components exceed the range of –0.67 to +0.67 feet. The RMSE for the vertical component in this example is 0.66 feet. Therefore, the ASPRS Accuracy Standards for the vertical component are met.

## Root Mean Square Error

The statistical root mean square error as defined in the ASPRS accuracy standards is simply the square root of the average of the squared individual errors. An RMSE is computed for all components of the position—northing, easting and elevation. For example, the RMSE in the elevation component is computed as:As an example, assume the elevations of four points were extracted from a map and compared to the elevations gained from an accurate field survey on the ground.

The table below lists the elevations for these four points and the discrepancy (difference) between the two elevations. The RMSE for these four checkpoints would be determined as follows:

The RMSE for the

*x*and

*y*components would be calculated in the same fashion.

## Comparing the NMAS and ASPRS Standards

Both standards call for a minimum of 20 checkpoints within a map for a valid evaluation of the accuracy found in the map. Discrepancies in the map positions—the differences between accurately determined field positions and positions gained from the mapping—are computed. From there, the two standards differ significantly. Under the NMAS for large scale maps, 90 percent of the horizontal points checked had to fall within 1/30" at map scale. The remaining 10 percent of the points could be in error up to twice that amount, or 1/15" at map scale. Go back to our example for 100' scale maps. The limits under the NMAS would be 3.33 feet for 90 percent of the points and 6.67 feet for the remaining 10 percent. Remember, however, that the NMAS evaluates the total horizontal error, not the individual*x*and

*y*components of this horizontal error. The limiting RMSE under the ASPRS standards would be 1.0 foot for both the

*x*and

*y*components.

What about elevation data? The limiting RMSE for the elevation under the ASPRS standards is 1/3 the indicated contour interval. Spot elevations are restricted to 1/6 the contour interval. Under the NMAS, 90 percent of the points checked in the field must be within 1/2 the contour interval. The remaining 10 percent of the points checked can be in error up to the contour interval.

When maps are compiled to meet the accuracy standards as required by the ASPRS, the map should include the following note in the title block:

THIS MAP WAS COMPILED TO MEET THE ASPRS STANDARD FOR CLASS 1 MAP ACCURACY.

If the map was checked and subsequently found to meet the requirements of the ASPRS Accuracy Standards, the following note should be added to the title block:

THIS MAP WAS CHECKED AND FOUND TO CONFORM TO THE ASPRS STANDARD FOR CLASS 1 MAP ACCURACY.

## Conclusion

A mapping professional carefully considers the accuracy requirements while planning a project. A higher level of expected accuracy places increased demands on the project. The newer ASPRS standards for class 1 maps are more rigorous than the older NMAS. The ASPRS also defines two other classes of large scale maps: class 2 and class 3 maps. The limiting RMS errors for class 2 maps are twice that of class 1 maps. Likewise, the limiting RMS errors for class 3 maps are three times that of class 1 maps.Now back to the questions posed at the beginning of this article. Should you expect a higher level of accuracy from a map compiled to meet the ASPRS Accuracy Standards for Class 1 Maps as opposed to the same map compiled to meet the requirements of the NMAS? The answer is, of course, yes. Should you expect to pay more for this higher level of accuracy? Hopefully you also recognize the answer to this question is yes. More rigorous planning and exacting controls will be required to meet the more stringent standards.