Then, using a conservative tilt estimate of 2°, the following maximum scale 

 error was determined. 



0.152 - 0.0889 sin 2° _ 1 



max 547.2 - 5 3,641 



3,600 - 3,641 , 1 



A<; = <; - s = — =1.1 percent 



^^max ^ ^max 3,600 ^'^^^•^ 



Similarly, using average values and 2° of tilt, an average scale error can be 

 computed 



= 3,611 - 3,600 ^03 ^^^^^^ 

 '^^9 3,600 ^ 



Because these errors were minimized by the procedure used, ^^avq ^^ probably 

 the more realistic error. This amoiont of error can be converted to distance, 

 D, by using the maximum distance measured between the reference line and the 

 bluff line (52 meters) . 



AD^„ = 0.03 X 52 = 1.56 meters 



Therefore, a reasonable assuraption is that the amount of error for a single 

 measurement will lie between + 1.56 and - 1.56 meters and be normally distrib- 

 uted about a zero mean. A consequence of this assunption is that 99.7 percent 

 of the errors for all measurements lie within three standard deviations of the 

 mean error. . The standard deviation of the error, a^, can then be estimated 

 as 1/6 of the total range, or in this case 



a^ = 2 X — ^ — = 0.52 meter 



and the variance 



a? = 0.27 square meter 



Another error inherent in vertical aerial photos is relief displacement. 

 Figure A-1 shows that the location of the top of an object of height h will 

 appear to be farther from the nadir than it actually is. This difference in 

 distance, dR, depends on both the height of the object, h, and its radial 

 distance from the nadir, R. The amount can be calculated as 



dR = R ^ CA-4) 



Relief displacement is an important error in any area that has considerable 

 relief, e.g., the bluffs. However, the procedure used allowed relief displace- 

 ment errors to be neglected. This was possible because of the optical matching 

 and because the reference line was selected close to the bluff line and at a 

 similar elevation. Since the quantity of interest is the amount of bluff re- 

 cession, calculated as the difference between two measurements at a single sta- 

 tion, the only source of relief displacement error affecting this quantity is 

 a change in position of a measurement station, relative to the nadir, between 

 photo sets. Even this is minimized by using reference points near the bluff 

 to optically match the photos. 



70 



