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
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