ERDC TN-DOER-T6

September 2004

subtracting light ship displacement (weight) from loaded ship displacement, has the largest effect

of the four variables in the TDS equation. As would be expected, if the hopper weight is over-

estimated, the TDS value is likewise inflated, but when the hopper volume value is over-

estimated, the TDS value is calculated below its "true" value.

Besides impacts on measurements being caused by the water density inside the hopper, the

density of water surrounding the vessel can also impact TDS accuracy because of its influence

whether this error is systemic or random in nature.

the calculation of dredging quantities has some error or uncertainty associated with it. The

equation for calculating TDS production is a function of multiple variables (measurements and

physical quantities), each contributing some error. These errors propagate through the data

reduction equation to the final calculation. It is essential that the error associated with each

variable is accounted for, and that the individual error contribution to the total error is

recognized. Equations are introduced in Scott (2000) that describe production for both pipeline

and hopper dredges. An uncertainty analysis expression is derived for each equation. Scott

applies the general uncertainty analysis technique in a step-by-step manner to show the

derivation of the uncertainty analysis expression. Example dredging situations are introduced in

Scott (2000) to demonstrate the uncertainty analysis application. Numerical solutions show the

error contribution of each variable, and the effect of uncalibrated instruments and unmeasured

sediment and water properties on the accuracy of production calculations.

The results of Scott's example uncertainty calculations for TDS (Table 1) show that the error

potential is greatest for the case of poorly calibrated instruments (40 percent for Case 3), because

the average density measured in the hopper is dependent on two measured variables. The water

density contributes significant error when the instruments are properly calibrated. The error in

hopper production calculations ranged from a low of about 10 percent for calibrated instruments

and known sediment and water properties (Case 1), to over 40 percent for a worst case of

uncalibrated instruments and unknown material properties (Case 4) (Scott 2000).

2

1

0.05

2.15

2.78

4.00

8.98

23

0.22

11.26

1.62

2.33

15.43

34

0.01

0.49

15.90

22.90

39.30

5

4

0.08

4.21

15.15

21.81

41.25

1

Information taken from Scott (2000). Percent uncertainty contributed by variable to total.

2

Case 1 - All instruments calibrated and sediment properties measured.

3

Case 2 - All instruments calibrated and sediment properties estimated.

4

Case 3 - Instruments out of calibration and sediment properties measured.

5

Case 4 - Instruments out of calibration and sediment properties estimated.

Scott presents this example only as a guide for applying the uncertainty analysis method for

determining the accuracy of this type of production system calculation. It should be apparent

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