94

A. Bayram et al. / Coastal Engineering 44 (2001) 7999

Table 3

Summary of accuracy of all the formulas

Formula

Scatter

Trend

Clustering

Data with discrepancy ratio distribution

between 1/5 and 5

(DUCK85 +

(SANDYDUCK)

(DUCK85 +

(SANDYDUCK)

SUPERDUCK)

SUPERDUCK)

rrms

(%)

Bijker

0.868

0.608

2

1

32

8

Engelund Hansen

0.705

0.519

4

3

29

18

Ackers White

0.812

0.724

4

3

20

22

Bailard Inman

0.659

0.485

2

4

16

24

Van Rijn

0.662

0.518

3

4

19

16

Watanabe

0.864

0.349

2

1

38

4

BI and VR formulas yielding ratios of 8% and 16%,

points around qp/qm = 1.0. As a measure of the scatter,

respectively. Taking an average for all experimental

the rms error was calculated according to,

cases, the VR formula produces the lowest discrep-

31=2

2

ancy ratio, whereas the other formulas yield compa-

X

N

2

rable ratios.

logqp logqm 7

6

7

6 1

7

6

2

rrms

7

6

N 1

5

4

6. Conclusions

The VR formula gave the most reliable predic-

tions over the entire range of wave conditions

where N is the number of data points. The computed

(swell and storm) studied, based on criteria involv-

rrms values for all formulas are listed in Table 3,

ing the scatter, trend, and clustering of the predic-

where a smaller rrms value implies a smaller scatter.

tions around the measurements. The AW formula

From the table it can be seen that the BI formula

gave satisfactory results for all conditions, but

shows the smallest scatter for the DUCK85 and

scatter was marked both for swell and storm.

SUPERDUCK data, followed by the VR and EH

Regarding the scatter, the BI formula yielded

formulas. The W formula shows the smallest scatter

improved predictions compared to AW, although

for the SANDYDUCK data, followed by the BI and

the transport was systematically overestimated dur-

VR formula. Taking an average for all data, the VR

ing swell and underestimated during storm. The EH

and BI formulas display the least scatter.

formula displayed similar tendency as the AW

Based on visual observations (Fig. 15), the for-

formula, producing reasonable results over the

mulas were subjectively ranked from 1 (i.e., weak) to

entire range of wave conditions investigated, but

5 (i.e., strong) concerning trends and clustering (see

displaying significant scatter. The W formula

Table 3). Also, a relative rating of the predictions was

yielded the best predictions for the storm condi-

assigned to the formulas utilizing a mean discrepancy

tions, but markedly overestimated the transport rates

ratio, given by the percentage of the measurement

for swell waves. Finally, the B formula systemati-

points lying between 1/5 to 5 of the predictions by the

cally overestimated the transport rates for all con-

formulas (this value was subtracted from 100% to

ditions.

yield a small number for good agreement). The BI

The coefficient values in the sediment transport

formula produce the smallest discrepancy ratio (16%)

formulas employed were the original ones as recom-

for DUCK85 and SUPERDUCK experiments, fol-

mended by the authors. In most cases, these values

lowed by the VR and AW formulas (19% and 20%,

were derived based upon laboratory data or data from

respectively). For the SANDYDUCK cases, the W

a river environment, involving no or limited field

formula has a discrepancy ratio of only 4% with the