Since the nominal scale of all the photos was the same, and since the distances 

 were approximately equal, 



a2 - a2 = 0.91 



Di 02 



V(6) = 0.91 + 0.91 = 1.82 

 a^ =1.35 meters 



Therefore, a change in bluff position can be determined to an accuracy of ±1.35 

 meters. Tliis error is quite large and makes it difficult to measure small 

 amounts of change. 



In bluff recession rate determinations, the accuracy improves for long- 

 period data and decreases for short periods. For example, a bluff recession 

 amount of 20 ± 1.4 meters over 4 years reduces to an annual rate of 5 + 0.3 

 meter per year. 



Measurements were also made to the toe of the bluff and the shoreline. The 

 accuracy of these measurements is considerably less than for the bluff measure- 

 ments becaiise of increased relief displacement and line definition problems. 

 Changing water levels also affected the accuracy of shoreline measurement and 

 of comparing successive measurements. 



Stoker (1976) reported on the difficulty of properly identifying the vari- 

 ous beach and bluff features out to the offshore bar and indicated that inter- 

 pretation was the major source of error. 



3. Number of Measurement Stations . 



The errors given above pertain to one station and are too large to detect 

 small changes in bluff recession rates; therefore, measurements were taken every 

 30.5 meters. This allows mean changes to be specified as small as ±a/^ (de- 

 fined as the standard error of the mean) where n is the number of stations and 

 a is the standard deviation of the rate of bluff change. For example, using 

 the bluff recession along reach A for four 1-year intervals (see Table 5) , the 

 mean recession rate varied from 3.6 to 6.0 meters per year with the standard 

 deviation varying from 1.9 to 3.8 meters per year. With 57 stations within the 

 reach, those values give a standard error between ±0.3 to ±0.5 meter per year. 

 An empirical evaluation was made to determine the minimum number of stations 

 needed to obtain a mean recession rate which was within ±0.3 meter per year of 

 the mean value determined using all stations. This was done by first removing 

 the linear trend from the 1- and 4-year recession rate data from reach A. Sub- 

 samples of n stations were then obtained .by systematically sampling (Cochran, 

 1963) all the stations at equal increments of k stations such that nk - 57. 

 For each year and for each value of k, k unique subsamples were obtained. 

 Means were calculated for each subsaraple and the maximum difference between 

 sample mean (x ) selected from the set of 4 x k subs ample and the population 

 mean (Xgy) was plotted versus the number of stations in a sample (see Fig. 

 A-2). The figure also shows a similar line (based on k samples) computed 

 for a rate per year using data over a 4-year interval which has a significantly 

 lower standard deviation than the 1-year data. 



73 



