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

mulas are assessed, as well as their limitations, using

1. Introduction

various statistical measures. Finally, the conclusions

of the study are presented in Section 6.

During the past three decades, numerous formulas

and models for computing the sediment transport by

waves and currents have been proposed, ranging from

quasi-steady formulas based on the traction approach

2. Longshore sediment transport formulas

of Bijker, and the energetics approach of Bagnold, to

Longshore sand transport is typically greatest in

complex numerical models involving higher-order

the surf zone, where wave breaking and wave-induced

turbulence closure schemes that attempt to resolve

currents prevail, although a pronounced peak can be

the flow field at small scale. There are relatively few

found in the swash zone as well (Kraus et al., 1982).

high-quality field data sets on the cross-shore distri-

Typically the total (or gross) longshore sediment

bution of the longshore sediment transport rate avail-

transport rate is computed with the CERC formula

able to evaluate existing predictive formulas. Kraus et

(SPM, 1984) in engineering applications. However, as

al. (1989) and Rosati et al. (1990) measured the

ability to predict the surf zone hydrodynamics has

longshore transport rate across the surf zone using

improved, the need for reliable formulas that spatially

streamer traps (i.e., DUCK85 and SUPERDUCK field

better resolves the sediment transport rate has

experiments). Miller (1999) measured the cross-shore

increased, both concerning the cross-shore distribu-

distribution with optical backscatter sensors (OBS)

tion of the transport rate and the concentration dis-

combined with current measurements (i.e., SANDY-

tribution through the water column.

DUCK field experiment). The measurements reported

In this investigation, the skill of six published

by Miller (1999) covered a number of storms, thus

formulas proposed for calculating the cross-shore

complementing the measurements by Kraus et al.

distribution of the longshore sediment transport rate

(1989) and Rosati et al. (1990) that were made in

was investigated. Transport rates were calculated for

milder swell waves.

the utilized cases using standard coefficient values (as

The objective of the present study is to evaluate the

given in the literature) without calibration. In the

predictive capability of six well-known sediment

present comparison the formulas proposed by Bijker

transport formulas, adapted to calculate the cross-

(1967, 1971), Engelund and Hansen (1967), Ackers

shore distribution of the longshore sediment transport

and White (1973), Bailard and Inman (1981), Van

rate, based upon the above-mentioned three field data

Rijn (1984), and Watanabe (1992) (as they chrono-

sets. We selected formulas that have gained world-

logically appeared in the literature) were employed,

wide acceptance in confidently predicting longshore

representing the most common approaches for calcu-

sediment transport rates. This, however, should not be

lating the time-averaged net sediment transport rate.

interpreted as a sign of disagreement or a lessening of

The Bijker and Van Rijn formulas also calculate the

the importance of formulas not discussed here. Only

suspended sediment concentration distribution

sand transport was investigated in this study, and

through the water column, which allowed for addi-

focus is on computing the time-averaged net long-

tional comparisons for these two formulas with some

shore transport rate.

of the field cases for which concentration measure-

Background to the investigated sediment transport

ments were made. This will be discussed in a forth-

formulas are given in Section 2 and their main

coming paper (Larson et al., in preparation).

characteristics are summarized (the equations used

The six formulas are summarized in Table 1, where

to calculate the transport rate are given in Appendix

the formulas, coefficient values, and wave and beach

A). Next, in Section 3, the longshore sediment trans-

conditions of the data originally used for verification

port data sets are described. In Section 4 are shown

of the formulas are listed. Further details regarding the

the results of the comparisons between the formulas

equations are given in Appendix A. This is necessary

and the field data including a wide range of wave and

because some variants of the formulas have appeared

current conditions. An overall discussion of the results

in the literature. In the following, a short background

from the comparisons is provided in Section 5, where

to the formulas is presented together with their main

the strength and weaknesses of the investigated for-

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