^ 1 , V, n 2D(L + W - 2D) 

 Proportion of lake in shallow zone = 



LW 

 where 



D = the average distance from shore to the 15 -foot depth line as projected from measured 



bank slopes 

 L = length of lake 

 W = width of lake . 



The formula is derived on the assumption that each lake is a perfect ellipse .'^ Formula esti- 

 mates of shallow zone area were within ±25 percent of field measurements 69 percent of the 

 time (35 out of 51, table 1, page 21). 



Formula -derived estimates of shallow area averaged somewhat less than field estimates. 

 An adjustment factor may be used to improve accuracy if field measurements are available for 

 a few sample lakes. The factor is the result of dividing the average field -measured proportion 

 of total lake area to shallow area by the average formula -estimated proportion. Each formula 

 estimate is then multiplied by this factor to obtain an adjusted formula estimate. In the test 

 study, an average factor for the three interpreters was used (1 . 16) . The adjusted estimates 

 were within ±25 percent of field measurements 75 percent of the time (38 out of 51). Because 

 estimates tend to differ from one photo interpreter to another, slightly better accuracy can be 

 obtained by using a separate adjustment factor for each photo interpreter . 



The accuracy of the four methods may be summarized according to percent of estimates 

 coming within ±25 percent of values based on field measurements as follows: (1) 80 percent 

 accurate (41/51) --plotting of 15-foot depth contour with parallax measurements; (2) 75 percent 

 accurate (38/51) --adjusted formula estimation; (3) 69 percent accurate (35/ 51) --unadjusted 

 formula estimation; and (4) 47 percent accurate (16/34) --contour plotting without parallax meas- 

 urement. (The estimates on which these percentages are based are given in table 1, page 21.) 



®If the lake is an ellipse, then the shallow zone area equals the total lake area minus the 



deep zone area. Thus, 



Total lake area 



Deep area 



nLW 



4 _ _ 

 3t(L - 2D) (W - 2D) 



4 



Shallow area = total area - deep area 



_ «LW jt(L - 2D) (W - 2D) 



which reduces to 



_ 2jtD(L + W - 2D) 



This must be divided by the total area of the lake to convert it to the proportion of lake in 

 shallow zone. 



_ 2jtD(L + W - 2D)/4 2D(L + W - 2D) 



Shallow area 



3tLW/4 LW 



NOTE: In order to convert a proportion obtained by the formula method to acreage of shallow 

 area, when no dot count of total lake area has been made, the total area can be calculated by 

 the formula jtLW/4. 



11 



