each 25 xX 12.5m in area centered on a survey lane. Investigation 
of the various errors associated with the depth measurements, 
positioning ranges, and tide height corrections determined a 
standard error (s,) for the depth value of any given cell to be 
approximately 0.15 meters. The standard error of a mean depth over 
the entire grid (s,) equals: 
S. 
S\San Se (1) 
JN 
where N = the number of grid cells in the survey. 
In order to calculate the difference in the volume of 
material between two surveys, one determines the number of grid 
cells at the left and right boundaries of the grid that are assumed 
not to have experienced changes in depth (ambient bottom). Because 
these cells are then defined as having the same depth in both 
surveys, equation (1) is modified to: 
2\(Ss)eaee(Sse) ia 2 1 
aS + =e) Sk —_ + — (2) 
n m n m 
where m= the number of cells on ambient bottom and assumed 
to be identical and 
n= the remaining cells (n = N =- m) over the area 
suspected of changes in depth. 
The standard error on the volume difference is calculated as: 
Bp SS, 6 kh ()) 
where A = the area of the survey in square meters. 
For the present volume difference calculations, the 900 
x 900 m survey area (A = 810,000 m?) had 37 x 72 cells (N = 2664). 
A total of 25 cells on each lane was determined to be on ambient 
bottom (m = 25 x 37 = 925) leaving 47 cells on each lane (n = 47 
x 37 = 1739) to be compared for differences in depth. 
Then, 
2 1 2 1 
Sas te Oley) + = 0.0071 m 
n m 1739 925 
and s, = s, x A = 0.0071 m x 810,000 m’ = 5739 n’. 
Therefore, the volume difference (V,) of 17,000 m? for 
these surveys, calculated as the sum of the volume differences of 
each cell, had a standard error of 5739 m°. To insure the 
reliability of this estimated volume difference, 95% confidence 
16 
