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6.1 INTRODUCTION Factors such as human limitations, instrument imperfec- tions, and instabilities in nature often render measured val- ues inexact. There are many potential sources of error asso- ciated with maps and photos used in the comparison techniques and with the method, precision, and accuracy of the mea- surements. The overlay techniques have their limitations, in part, because of these potential sources of error (Wolf and Dewitt, 2000). Understanding the occurrence and treatment of errors requires an understanding of the concepts of accuracy and pre- cision. Accuracy pertains to the degree of conformity to the true value. The level of accuracy can be assessed by checking against an independent, higher accuracy standard. Precision is the degree of refinement of a quantity. Repeated measure- ments to check the consistency of values are used to assess the level of precision. An error is the difference between a partic- ular value and the true or correct value. Most measurements of a continuous physical quantity (such as distance) contain some amount of error (Wolf and Dewitt, 2000). Errors are categorized as mistakes, systematic errors, and random errors. Mistakes are gross errors caused by careless- ness. Mistakes can often be avoided through careful proce- dures, or they can be detected and eliminated or corrected using quality control checks. Systematic errors are errors that follow some mathematical or physical law. A correction can be calculated and the sys- tematic error can be eliminated if the conditions causing the error are measured and properly modeled. Shrinkage or expan- sion of photographs, camera lens distortions, and atmospheric refraction distortions are examples of systematic errors in photogrammetry. Errors that are not mistakes and systematic errors are ran- dom and are dealt with according to the mathematical laws of probability. Random errors are usually small and are often compensated for naturally. 6.2 MAP AND AERIAL PHOTO ERRORS AND LIMITATIONS 6.2.1 Errors The principal errors associated with aerial photos, and ulti- mately with maps, are systematic errors. The major sources of these errors are the following: 26 ⢠Film distortions because of shrinkage, expansion, and lack of flatness; ⢠Failure of fiducial axes to intersect at the principal point; ⢠Lens distortion; ⢠Atmospheric refraction distortions; and ⢠Earth curvature distortion. A detailed description of the causes of these sources of error is beyond the scope of the Handbook, but such a description can be found in most textbooks on photogram- metry (e.g., Wolf and Dewitt, 2000). Depending on the pre- cision and accuracy requirements of a given project, correc- tions can be applied to eliminate the effects of these systematic errors. The primary sources of map error are associated with the vertical and horizontal accuracy and the age of the map. Most federal maps are required to meet rigorous standards for accu- racy. The National Map Accuracy Standards, which were issued in 1941, apply to all federal agencies that produce maps. The following is a partial list of the standards of accu- racy for published maps defined by the federal government (U.S. Bureau of the Budget, 1941, 1943, 1947 [available at http://geography.usgs.gov/standards/]): ⢠Horizontal accuracy. For maps on publication scales larger than 1:20,000, not more than 10 percent of the points tested shall be in error by more than 1/30 in., mea- sured on the publication scale; for maps on publication scales of 1:20,000 or smaller, 1/50 in. These limits of accuracy shall apply to positions of well-defined points only. Well-defined points are those that are easily visible or recoverable on the ground, such as the following: mon- uments or markers, such as bench marks, property bound- ary monuments; intersections of roads and railroads, etc.; corners of large buildings or structures (or center points of small buildings); etc. In general what is well-defined will be determined by what is plottable on the scale of the map within 1/100 in. Thus while the intersection of two road or property lines meeting at right angles would come within a sensible interpretation, identification of the inter- section of such lines meeting at an acute angle would obviously not be practicable within 1/100 in. Similarly, features not identifiable upon the ground within close lim- its are not to be considered as test points within the limits quoted, even though their positions may be scaled closely CHAPTER 6 SOURCES OF ERROR AND LIMITATIONS
27 upon the map. In this class would come timber lines and soil boundaries, etc. ⢠Vertical accuracy, as applied to contour maps on all pub- lication scales, shall be such that not more than 10 percent of the elevations tested shall be in error more than one-half the contour interval. In checking elevations taken from the map, the apparent vertical error may be decreased by assuming a horizontal displacement within the per- missible horizontal error for a map of that scale. ⢠The accuracy of any map may be tested by comparing the positions of points whose locations or elevations are shown upon it with corresponding positions as determined by surveys of a higher accuracy. Tests shall be made by the producing agency, which shall also determine which of its maps are to be tested, and the extent of the testing. Although the federal standards for accuracy may seem rea- sonable, the accuracy of topographic maps may be insufficient or problematic when using the comparison techniques for defining and predicting meander migration. For example, if the potential horizontal error of the topographic map used in the comparison is a significant percentage of the actual channel width, then there could be a substantial discrepancy between the mapped bankline position and the true bankline position for the same time period and between time periods. The map error may also be problematic if comparisons are made with historic survey data. Comparison of newer maps and aerial photos with older maps may also pose a problem because the older maps may have been compiled before the use of aerial photos. These maps are based on physical ground surveys, field notes, sur- veyor descriptions, and sketches made in the field. Therefore, the accuracy of historic maps decreases with increasing age. Maps that are georeferenced may not match the positions of georeferenced aerial photos. This can occur if georeferenced digital maps are obtained from sources other than the USGS and used in conjunction with georeferenced digital aerial pho- tographs compiled by the USGS or other agencies. The authors of the Handbook have encountered this problem many times. There may also be problems associated with the use of dif- ferent horizontal âdatums.â A datum is a system of reference using precisely surveyed control monuments to specify the relative positions of points used for surveying and mapping purposes. The most common horizontal datums used in the United States are the North American Datum of 1927 (NAD27), the North American Datum of 1983 (NAD83), the World Geodetic System of 1984 (WGS84), various statewide high-accuracy reference networks (HARNs), and the Inter- national Terrestrial Reference Framework (ITRF). In addi- tion, the U.S. Army Corps of Engineers, local levee districts, and other state and local agencies may have different datums. Therefore, comparisons of maps, aerial photos, and survey data from different sources should be evaluated for different datums. Transformations from one datum to another have become commonplace with the increasing use of GISs. Soft- ware (NADCON) to convert NAD27 to NAD83 is readily available from the National Geodetic Survey via the World Wide Web (http://www.ngs.noaa.gov). 6.2.2 Limitations There are several potential limitations to the use of aer- ial photos and maps in the comparison techniques and in the evaluation of meander migration. Scale can be a sig- nificant limitation to the use of aerial photos and maps. There are potential problems associated with major scale differences between maps and photos and changes in scale on a given photograph because of distortion across the photo. In some cases, only high-altitude aerial photographs (scales of 1:40,000 or 1:60,000) may be available for a particular site. A comparison of bankline positions from high-altitude photos with those from topographic maps may be difficult because of the significant scale difference. In some cases, an enlargement of the aerial photo may provide an image of sufficient resolution or clarity to be used in the compar- ison. However, this is also dependent on the relative size of the channel with regard to the scale at which it is being evaluated. Often, the enlargement of high-altitude photos using a copier or a flatbed scanner in conjunction with photo-editing software yields images with poor resolution. Even though an aerial photo can be scanned at a high resolution, the quality of the resolution and the amount of visible detail is greatly depen- dent on the original image quality and clarity. Moreover, the quality of an enlarged scanned image degrades rapidly after the image has been enlarged to more than two or three times its original size. The resolution of an older aerial photograph will generally be lower than the resolution of a newer aerial photograph because of changes in technology over time. In contrast, digital images such as those found on the TerraServer Web site can be downloaded at various scales and resolutions. Brightness and contrast also play a role in the usability of an aerial photo. Photos can be too dark or too light, and the contrast may be so coarse that the banklines of a channel may be difficult or impossible to identify. The time of the year or the time of day during which the aerial photo is taken is also important and can affect the usability of a photo. Long shad- ows, dense vegetation, and cloud coverage may partially or totally obscure the bankline or the entire channel. Aerial pho- tos that were taken at midday and during winter months with little cloud coverage are optimal. Photos taken during early spring, prior to leaf-out, may be useful, but spring floods may obscure the tops of the banks. Photos taken during summer months can be used if the density of the bankline vegetation is sparse enough to allow the user to adequately define the bankline. Otherwise, bankline positions will need to be esti- mated based on the locations of the crowns of the trees grow- ing at the bankline, as described in Section 5.2. In this case, the accuracy of the measurements is questionable. The age of an aerial photo and map may also limit their usefulness. Old maps and photos may not have the same
identifiable geographic features or landmarks found on newer maps and photos, so finding identifiable landmarks that can be used as registration points may be difficult. In addition, the township, range, and section lines found on newer topographic maps, whose intersections could be used as registration points, may not be in the same location or may not be available on older maps. 6.3 MEASUREMENT ERROR As with any methodology that requires the physical mea- surement of a quantity, the accuracy and precision of the measurements conducted under the comparison techniques described in the Handbook can limit the usefulness of the acquired data. Obviously, those measurements made visually using a ruler or engineering scale will be less accurate than those made using a computer. Also, repeated measurements should be made the same way each time. Scale plays an important role in measurement error as well. Large-scale images (e.g., 1:10,000) show ground features at a larger, more detailed size, and small-scale images (e.g., 1:50,000) show ground features at a smaller, less detailed size. Thus, using identical measurement techniques, measurements made on large-scale maps and photos generally will be more accurate than those made on smaller-scale maps and photos. Meander bends are rarely perfectly round with smooth banklines. They often are oddly shaped, and their banklines are irregular. As a result, fitting a circle to the channel centerline or outer bank can be very difficult. As a rule, the circle should be fit to the bend centerline or outer bankline between the crossings or at the point where the bend begins to straighten or where there is a major inflection in the channel. As much of the circle as possible should intersect the bankline or center- line, and the amount of area outside the circle should match the amount of area inside the circle as closely as possible. The radius of curvature of a bend centerline or bankline can be sig- nificantly different depending on how the circle is fit to the bend, especially on smaller channels. Defining meander bends with best-fit circles is discussed in greater detail in Chapter 7 and Appendix B. 6.4 LIMITATIONS OF OVERLAY TECHNIQUES Overlay techniques require the availability of adequate maps and aerial photos that cover a sufficient period of time to be useful. Another requirement is the ability to identify and delineate a sufficient number of registration points common to each map and photo. It is not necessary to find all the registra- tion points on all the maps and photos, but an adequate num- ber of registration points identified on each map or photo should match those on the previous or following map or photo. The registration points should bracket the area of interest (this would require at least four common registration points) and should not change significantly in size over time. Even when a sufficient number of registration points are available, photo distortions or inaccuracies in mapping may not allow for an 28 accurate registration of the images. In these cases, the user will need to decide whether âcloseâ is good enough or if the image should be abandoned. Excessive or very limited movement of the channel, cutoffs, and bank erosion countermeasures will also limit the useful- ness of the comparison techniques. An analysis of the rate and extent of historical movement may be useless if excessive meander migration is a problem (as with meander Class F in Figure 3.2). Depending on the scale of the overlays, the amount of migration may be so small as to be undetectable, or the overlays may be at such a small scale that the movement is not measurable. Countermeasures to halt bank erosion or protect a physi- cal feature within the floodplain can also have an impact on the usefulness of the overlays. These features should be iden- tified prior to developing the overlays. Anomalous changes in the bend or bankline configuration or a major reduction in migration rates may suggest that bank protection is present, especially in areas where the bankline is not completely visible or on images with poor resolution. Geologic features in the floodplain, such as clay plugs or rock outcrops, can also limit the usefulness of the overlays because they can have a significant influence on migration patterns. Bends can become distorted as they impinge on these features, and localized bankline erosion rates may decrease significantly as these erosion resistant features become exposed in the bank. Where the channel encounters a geologic control or man-made feature, the channel may intersect the feature at a sharp or abrupt angle and migrate more rapidly down valley along the feature, or the channel may become highly distorted. An example of this might be where a channel encounters geo- logic controls, bank protection, or levees that run parallel to the valley direction. In some cases, the channel may encounter a very localized outcrop or hard point in the bank creating an irregular bankline or causing the bend to deform around it. In these cases, deter- mining the radius of the outside bankline of a bend may be very difficult. Because any evaluation of meander migration requires an assessment of, among other things, changes in bend radius, the user will need to use judgment in determining the radius of the bend, and possibly the bankline, by defining it with a best-fit circle of known radius (see Section 7.2). Where the channel makes a sharp or abrupt turn, mud flats or bars may develop along the outer bank in the upstream half of the bend, and the delineation of the outer bankline on a photo or map may be difficult at best. In this case, there are two methods of defining an approximate outer bankline radius. The first method is to identify the radius of the inner bankline by inscribing a best-fit circle on it and then determining the aver- age channel width at the crossings in the reach. Then, the user can add 1.5 to 2 average channel widths to the inner bankline circle to define the outer bankline radius. Once this is accom- plished, the user will need to evaluate how well the estimated outer bankline fits relative to the actual channel position, to similar bends that may be located in the reach, and to other features along the channel at the bend.
29 The second method requires the use of the edge of water at the outer bankline of the channel on the photo or map. This should provide a relatively close approximation of the outer bankline radius of curvature. Although both of these methods can contain significant error, they may provide the only rea- sonable approximation of the outer bankline and radius of curvature necessary to make a prediction of future bankline position. In reaches where geologic controls are exposed predomi- nantly in the bed of the channel, migration rates may increase dramatically because the channel bed is not adjustable, which may cause the channel to migrate rapidly across the feature. A fundamental assumption of the overlay techniques based on aerial photo or map comparison is that a time period sufficient to âaverage outâ such anomalies will be available, making the historic meander rates a reasonable key to the future.
