| PHOTOGRAMMETRY
Two Foot Contours from 1"=800' Photography
pAre We Fooling Ourselves? or Worse Still: Are We Fooling Our Customers?
By John Thorpe The tendency among some of the leading aerial survey companies in the U.S. toward using 1"=800' scale photography for city or county mapping with 2-foot contours is damaging to the industry. With the advent of airborne GPS technology there is an unhealthy tendency to reduce the number of ground control points beyond what is prudent to meet required contour accuracy. This article attempts to describe the reasons why, in the author's opinion, the accuracy standards for 2-foot contours cannot be met under normal conditions using 1"=800' scale photography. Note that in this article we will only refer to vertical accuracy standards, while horizontal accuracy is not considered.
There are three different standards laid down by federal authorities1:
1. Office of Management and Budget (OMB) United States National Map Accuracy which specifies that 90 percent of independent check points must lie within one half of the contour interval, in this case 1.0 ft.
2. American Society of Photogrammetry (ASP) Specifications for Aerial Surveys and Mapping by Photogrammetric Methods for Highways, which is the same as item 1 above, with the additional specification that the accuracy of spot elevations shall be twice as high as contours. This makes sense when the objective is to obtain precise cross-sections for calculation of cut and fill earthwork quantities, but may not make sense for general city or county mapping.
3. American Society of Photogrammetry and Remote Sensing (ASPRS) Standards for Large Scale Maps, which specify that the rms (root mean square error) must be less than one third of the contour interval, in this case 0.67 feet.
Note that items 1 and 3 are almost identical from the statistical point of view. The author's recommendation is that the ASPRS Class I specifications from item 3 be used at all times. History
The practice of using 1"=800' (1:9600) scale photography for 2-foot contour photogrammetric mapping in the United States is almost certainly a spin-off of the Public Land Survey system. Most of the country was surveyed using one-mile square sections of land, often having roads constructed along section lines. 1'=800' photography, using a 27 percent side overlap between adjacent flight lines, fits very nicely, thank you, over one row of sections. Not only is the flight navigation made easy by flying between the roads, but more importantly, the ground control which is necessary along the side overlap between flight lines to maintain vertical accuracy, was much easier and less expensive when the traverses could be run along the existing roads.
It is interesting to observe that the use of this photography scale predominates in the mid-western part of the country where the ground is sectionalized. In the eastern part of the U.S., where the 'metes and bounds' method of survey was originally used and there are no sections, the common (and much better) practice is the use of 1"=500' (1:6000) scale photography for 2-foot contours. Technical Considerations
What are the technical reasons inhibiting contouring accuracy?
Actually, there are many, including film and camera lens distortion, atmospheric refraction, Earth curvature, ground control quality and distribution, aerial triangulation procedures, airborne and ground GPS techniques, stereoplotter type and calibration, and observational accuracy of the elevation measurements made by the human operator. A detailed examination of all these error sources is beyond the scope of this article, but they are described in some detail in a paper published in 1982 entitled "CPS: Computed Photo Scale."2
All of the errors resulting from these sources increase with higher altitude photography, so other things being equal, the higher the flight altitude, the less accurate will be the contours.
While we are discussing accuracy, let's talk a little about some other lesser known criteria. The rms or root mean square error is a statistical term commonly used in least squares adjustment theory, and amounts to roughly two thirds of the 90 percent confidence level. The other thing to remember is that any error greater than three times the rms is considered to be a 'gross' error, and is unacceptable, so this three times criterion is termed a 'maximum' error (although in least squares theory no maximum error exists; theoretically, 99.9 percent of errors will be within three time the rms). In the example under discussion, the following numbers apply for 2-foot contours; but please bear in mind that they are approximate:
The NMAS for Highways specification deals with the accuracy of spot elevations, which are prescribed to be twice as accurate as the contours. In this case 90 percent of spot elevations must be within 0.5 feet which implies an rms of 0.33 feet, and no error may be larger than 1.0 feet . The author contends that this specification is not consistent with county-wide mapping, and is unachievable unless large photo scales, e.g. 1"=400', are used.
Let's take a quick look at some of the more significant error sources: Earth curvature and atmospheric refraction
Strictly speaking, these are not errors, but conditions which create systematic displacements of the images. Both are predictable and removable (in a computer controlled analytical stereo-plotter) and both create radial displacements relative to the center of the photograph.
An 'educated guess' of the extent of this error would be an rms of 0.2 feet. Lens distortion
Until about 10 years ago, this was a major source of error in photogrammetry. With modern design of camera lenses, it is minimal and correctable.
An 'educated guess' of the extent of this error would be an rms of 0.2 feet. Film distortion
When the film is being transported through the camera and later through the development and fixing process, it is subjected to stresses and major temperature changes which cause some distortions which are unpredictable. However, modern cameras have eight carefully calibrated "fiducial marks" at the corners and the centers of sides of the image, so the amount of film distortion can be measured and corrected (once again, only in an analytical stereo-plotter).
An 'educated guess' of the extent of this error would be an rms of 0.2 feet. Distribution of ground control
This is a critical issue, and the practice of commercial companies varies widely. Lessening the number of vertical control points saves cost but results in poorer accuracy. The simple fact is that in the subsequent aerial triangulation (control densification) process, substantial systematic errors build up from a combination of actual systematic tendencies (such as Earth curvature), and also what is called a 'double summation of random errors' by academics. The further you go between control points, the more systematic error is possible. For 2-foot contours, not more than four photographs should be 'bridged' between control points, but the author has personally seen instances where apparently reputable companies have bridged as many as 10 photographs!
An 'educated guess' of the extent of this error would be an rms of 0.4 feet. Airborne GPS (AGPS)
This is a new technology which has been used in practice for only four or five years, and is proven for the production of two foot contours, but only where great care is taken with the ground control layout. The aircraft carries a GPS receiver on board which receives satellite signals along with simultaneous reception by another GPS receiver on a nearby ground station, resulting in the calculation of the coordinates of the exact center of the camera lens being obtained at the instant of exposure of each photograph, to an accuracy of about 10 cm or 4 inches. Note that this gives a control point for every photograph which limits the systematic build-up described above, but also note that 4 inches of error is already a significant proportion or the allowable rms of 0.67 feet!
However, this technology requires the full understanding of the evaluation of what is called the 'geoidal model'. It is essential to measure the elevations of existing leveled benchmarks inside the mapped area with the GPS unit as well, to calculate the difference between the leveled and the GPS elevations, and use these to model the geoid in that particular area, so that all the air stations used in the final aerial triangulation can be adjusted accordingly. The differences between regional published geoidal models, e.g. GEOID96 published by NGS, and local geoidal effects, vary up to 30 feet in some parts of the country. Clearly, non-attention to this detail will result in non-compliance with the specifications. While it is true that only four ground control points are necessary when AGPS is used for planimetric mapping, if accurate contours are required, far more points must be surveyed by a competent geodesist who fully understands the issues.
A study done on a GIS mapping project in Georgia3 shows that using airborne GPS, adequate ground control and proper processing of the geoidal model, 2-foot contouring accuracy can be achieved from 1"=600' (1:7200) scale photography using about one bench mark per four or five square miles for the geoidal modeling. To the author's knowledge, no similar tests have ever been done using 1"=800' (1:9600) scale photography.
An 'educated guess' of the extent of this error would be an rms of 0.4 feet. Aerial triangulation
This is a complex subject involving understanding of least squares adjustment principles, a subject which is not well understood by many users. However, the software available from several different suppliers contains many quality control features, and fortunately, most specifications demand the use of good principles and good aerial triangulation bundle adjustment software. What is not well understood or practiced is the weighting of ground control points, but that is a discussion outside the scope of this article.
An 'educated guess' of the extent of this error would be an rms of 0.3 feet. Stereoplotters
There are four recognized classes of stereoplotters, grouped as follows:
These are roughly grouped according to their size, accuracy and cost, and each group has a basic accuracy better than the next. Group 2 has largely been displaced by Group 1, while Group 4 is never used (we hope!) on accurate projects. Of Group 3, the PG2 is still fairly widely used in the U.S., and while it has excellent vertical accuracy, it can not equal that of Group 1 instrumentation. The CPS article referenced below contains a discussion on the vertical accuracy capabilities of these instruments.
Digital stereoplotters using raster (digitally scanned) photographs will become more common in the future, but in the author's opinion they belong only in the future, as they are not yet functional enough to be used extensively for contour mapping in the commercial marketplace. Certainly, another developing practice in commercial mapping, i.e. using automatic correlation of digital terrain models, should never be used without extensive manual editing for 2-foot contouring except perhaps in the desert or semi-desert where no vegetation obscures the smaller terrain differences.
No 'educated guess' of the extent of this error is included, as hopefully everybody compiling 2-foot contours from 1"=800' would use analytical plotters. Observational accuracy of the instrument operator
In an instrument with excellent optics, the rms accuracy of repeated elevation observations in perfect conditions is about 1:20,000 or 0.05 per thousand parts of the flying height of the aircraft above the ground. For 1"=800' photography, which has a flying height of 4,800 ft., this amounts to 0.24 ft, and the 90 percent criterion is therefore nearly 0.4 ft. This should not be confused with the 1:10,000 criterion which often appears in accuracy specifications, which refers to the required accuracy on the used control points; this is a ridiculous specification as the control points can be weighted to get any result that a knowledgeable user would want to prove!
An 'educated guess' of the extent of this error would be an rms of 0.3 feet.
The only way to check vertical accuracy compliance is through the use of independent ground check control points. Practical Considerations
Eight different sources of error or distortion have been briefly described above. While it is almost impossible to statistically examine the cumulative error occurring in a given situation (as many of them are non-identifiable at the time), it is easy to see that to expect to meet National Mapping Standards when flying at extreme altitudes, is unreasonable.
If the 'educated guesses' given above are valid, the cumulative effect or total error propagation would amount to 0.81 feet, which is too high. A photo scale of 1"=660' would give a proportionately large error of 0.67, while 1"=600' scale which is very widely accepted for 2-foot contouring, would give an error of 0.61 feet, which gives just a little room for error.
Some years ago the author's company was extensively checked with 700 check points on a 20 sq.ml. project using 1"=660' scale photography, field-leveled control points at 3-4 model intervals, and analytical stereoplotters. Only 87 percent of the points fell within 1.0 feet! If we couldn't meet the specs from 1"=660', then the author considers it extremely doubtful that anyone could meet them from 1"=800'. The remainder of that project was re-negotiated at 1"=600'. Recommendations
What is the answer? The only way to ensure that the accuracy standards have been met is to check the contours in the field, by running vertical traverses whose accuracy is beyond doubt (rms of less than 0.1 feet, so GPS should not be used), plotting the points on the maps and interpolating the elevations from the contours. The differences from the field-measured elevations are calculated and the rms calculated using the following formula:
where vv are the squares of the vertical errors and n is the number of independent check points measured. The rms should not be greater than 0.67 feet, 90 percent of the errors should be less than 1.0 feet, and no error should be greater than 2.0 feet.
If the ASPRS standards apply, only the rms needs to be calculated.
Note: The check points should be surveyed by an independent registered land surveyor. They should number at least 20 and be well-distributed in an area as far from the used ground control as feasible. Summary
Until someone proves that this practice actually works, any mapping or GIS manager will be taking huge risks by allowing the use of 1"=800' photography for 2-foot contouring on their project. The only justification is cost saving, and since many future GIS users will expect that specified accuracy standards have been met, the decision-makers at the design stage of the mapping process will have to bear the responsibility if the contours prove later to be inaccurate.
And where does the ASPRS stand on this issue?
To return to the title of this article: Fooling ourselves may be understandable, but fooling our customers is unacceptable! Acknowlegements:
The author would like to express his thanks to Roger McKee of Analytical Surveys Inc., whose help on this topic was invaluable. References
1. Corps of Engineers Document EM 1110-1-1000 (FINAL DRAFT), 31 Jan., 1992.
2. CPS: Computed Photo Scale - John A. Thorpe, PE&RS, November 1984.
3. Assessment of the Economic Advantages of Airborne GPS in Support of Large Scale Mapping in Dekalb Co., GA - Measurement Science, Inc., 303-799-1989, May 1995, unpublished. About the Author:
John Thorpe is chairman and chief technical officer at Analytical Surveys, Inc, in Colorado Springs, Colo. He may be reached at 719-593-0093. Back |
