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<br />HYDRAULIC ENGINEERING '94
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<br />verifications of roughness values for 78 reaches of New Zealand rive.. where the
<br />discharges ranged from low flows 10 floods,
<br />Several investigators (Limerinos, 1970; Bray, 1979; Griffiths, 1981, and1arrett,
<br />1984) have used multiple regression methods to define equations relating n and the
<br />hydraulic characteristics of the channel, Equations for calculating n are attractive
<br />because they remove the subjectivity of the traditional approach, Data upon which to
<br />base such relations. however, are difficult to obtain and are sparse, Consequently,
<br />these slOdies, excepting that of Bray (1979), included data from low and moderate
<br />discharges as weD as from floods, Bray used data for the 2-year recurrence-intelVaI
<br />flood (QV in natural gravel.bed river reaches and limited the application of the
<br />equations 10 relatively high in-bank flows, The other authors did not limit the
<br />application of their equations based on the relative magnitudes of the discharges,
<br />The purpose of this paper is 10 delermine whether Ihe equations are equally
<br />applicable for the entire range of discharges, The issue is not whether relations fil the
<br />data upon which they were based -- clearly, they do, The question is if the data are
<br />SlIatified by relative flood magnitude, is there bias?
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<br />Previoml Shlll~
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<br />Two generaJ approaches have been used to develop equations for n, One
<br />approach has been 10 use Iaboratoty and field data 10 relate n 10 some measure of
<br />relative smoothness, usually stated as a ratio of a measure of hydraulic depth 10 a
<br />characteristic bed-particle size, The other has been 10 directly relate n 10 various
<br />measures of channel and reach characleristics, The principal difference in the two
<br />approaches is in the final fonn of the resulting equations; both approaches use a fonn
<br />of ClllVe fitting 10 define the constants in the relatinns.
<br />Umerinos (1970) used data from 50 measurements of discharge at II stream
<br />reaches in California, U,S,A., to define relations between n and hydraulic radius, R,
<br />and the ratio of R 10 intennediate bed-material diamete.., dso and d84' equalling or
<br />exceeding 50-percent and 84-percent of the streambed particles, respectively -n".. SO
<br />measurements included discharges that ranged from low-flow cond'''''"" to
<br />approximately~, Bed material for the Streams in Limerinos' study included gravel,
<br />cobbles. and boulders, and slopes ranged from 0,00068 10 0.024,
<br />Bray (1979) developed varions equations for estimating n based on data for 67
<br />natural gravel-bed river reaches in Alberta, Canada Slopes of the reaches ranged
<br />from 0,00022 10 0,015 with about one half the reaches having slopes of more than
<br />0,002, Bray's preferred equation was similar in fonn 10 those of Umerinos, Bray,
<br />however, used the mean depth, D, rather than the hydrauJic radius. R, in aU relations,
<br />noting that for the reaches in his study D was not more than 3 percent greater than R,
<br />Griffiths (1981) used data from 186 measurements of gravel-bed rivers in the
<br />United States, England, and New Zealand 10 develop an equation similar in fonn 10 the
<br />equations of Umerinos, Although the discharge frequencies were not given, some of
<br />the data are for low or moderate discharges.
<br />1arrett (1984) used data from 75 measurements made on 2] high-gradient
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<br />BIAS IN MANNING'S N
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<br />729
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<br />th 0002) in Colorado, U,S,A" to define an equatio~ for n as
<br />streams (slopes,8':"ater an S' d h draulic radius, Jarrett's data included discharges
<br />a function of frichOl1 slope, ,an y 'a1 flood
<br />' from low flow 10 about a lO-year recurrence-m.erv ,
<br />rangmg ,
<br />The equations defined are,
<br />O,\I3Rv. ,
<br />Limerinos- n = R '
<br />1.16 + 2,OIog (d..)
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<br />O,\I3D1/6 ,
<br />D '
<br />UJ9 + 2,210g (d.. )
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<br />n ~ 0.32s"3'R-o,I.,
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<br />Umerinos -- n =
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<br />O,1I3R1/6 ,
<br />R '
<br />0,35 + 2,OIog ( d )
<br />so
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<br />Bray--
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<br />O,1I3R1/6
<br />Griffiths -- n ~ R
<br />0,76+ 1.9810g(dso)
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<br />n~
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<br />Janett--
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<br />. th tions of Bray and Umerinos are
<br />If D and R ,are equiv~ent, differe:~~;nDl: eq~.::. R/d84)' The equations yield
<br />a function of differences 10 the I valu f DId (:: R/d84) of 2, However, for a given
<br />essentially the same n:sult, for va ~es 0 ields ~ values that are smaller than those of
<br />value of D (or R), Bray s eq~::on 110 and by 5,9 percent for D/d84 of ]00. ~
<br />Limennos by 4.2 percent for D ~ ~ than those amounts however. because R 1S
<br />difference will actually be somc:w,:Cts:. difference hetwe'en the Griffiths' and
<br />actually smaller, th~ D, Sl,nn ;' of RId with Griffiths' equation consistently
<br />Limerinos' equauons IS a fURCbon on .Y I SUof R The differences range from 30
<br />producing smaller values for n for a gIven va ue .
<br />percen. for R/dso of 2 to 6,6 percent for R/dsu of 200,
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<br />Data AnaJvgig
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<br />,,, aI ati s 10 flood discharges are
<br />Data for testing the applicabilIty of n-v ue equ ~ and about one
<br />limited. The data for A]bena (Bray, ]979) ~ ~or r::::::~~ contain only
<br />half of Barnes' (1967) data is for fl~~ e ts o;rBames (1%7), Lim:.nnos (]970),
<br />limited dala for floods, Therefore" k w: ~ (1991) were combined 10 form .
<br />Bray (1979), Jarrett (]984), and Hic s sed though il used D instead of R, ThslS
<br />composite data "':" B?,y's,data sel was u ev~ nl difference between D and R
<br />against the equanons 10 thIS study show thaI ~ 3 perce the ranges of R tested in this
<br />will produce less than a ]-pen:enl diff-=.ce m::r::'tion about Q,. and recurrence
<br />paper, Griffiths' data set was - used __~":'I I ailable Jarrett did nol use 3 of his
<br />' aI f ured discharges was not ROW y av, 'a1
<br />IOlerv so meas 'nil need by overhanging vegetation; this slOdy so
<br />75 measurements because n was 1 ue Zealand data of Hicks and Mason were
<br />excluded those 3 measurements, The New , '
<br />limited 10 reaches tha~ ap~ared 10 be free ~W;:;:~;::~~~":~ian annual
<br />~harges (Q) 10 thl~ ~per were ';;sons between rive.. of different sizes, Where
<br />peak discharge (Qm) to facilItate comp 'tion No significance is attached
<br />Qrn was not available. <h was used as an approxnna .
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