Table B.9. Discrepancy Ratios and Correlation Coefficients for Posada and Kodoatie
Equations, Data from Group 1.
Posada
Kodoatie
Cc
Cc
RD
RD
Silt-bed rivers
0.12
0.8393
0.88 0.8018
Very fine to fine sand-bed rivers
0.33
0.6843
1.00 0.7242
Medium to very coarse sand-bed rivers
1.12
0.7274
1.00 0.8146
Gravel-bed rivers
312.46
0.2175
1.00 0.7625
Table B.10. Discrepancy Ratios and Correlation Coefficients for Posada and Kodoatie
Equations, Data from Group 2.
Posada
Kodoatie
Cc
Cc
RD
RD
Silt-bed rivers
0.18
0.8393
0.88 0.8018
Very fine to fine sand-bed rivers
0.33
0.7845
1.01 0.8239
Medium to very coarse sand-bed rivers
1.12
0.7511
1.07 0.8006
Gravel-bed rivers
13.516
0.8357
0.47 0.9591
B.4 LAURSEN AND MODIFIED LAURSEN EQUATIONS
B.4.1 Laursen Equation (1958)
Laursen (1958) working with Rouse developed the following equation. This relationship was
modified by several scientists in an attempt to improve it by several scientists.
7/6
τ′
V
d
o - 1f *
C t = 0.01γ p i i
(B.7)
ω
τ
d
i
ci
i
B.4.2 Modified Laursen Equation by Madden (1985) and Copeland and Thomas (1989)
Madden (1985) modified Laursen's concepts by utilizing Arkansas River data. The
modification by Madden permitted the analysis of bed material transport by size fraction. The
U.S. Corps of Engineers' (1988) adopted this methodology for computing the transport in
rivers with a mixture of sand and gravel forming the bed. Madden's modification to Laursen's
methodology was based on three sets of sediment measurements made in the Arkansas
River. The first two sets were gathered near Dardanelle in June-July 1957 and in April 1958.
The third set was gathered near Morrilton in April 1958. Madden utilized the Missouri River
data collected by Bondurant (1958) to validate the rating curves for the Arkansas River. The
data sets resulted in best-fit curves that were parallel, but the two data sets did not overlap.
The reader is reminded that the two sets of data were from two different rivers and even
though they were sand-bed rivers, the methodologies produced by Bondurant and Madden
were developed for specific rivers and are not generally applicable to other river systems.
B.19
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