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of flows. The results are plotted as a histogram. The bed-materialload histogram should display a continuous distribution with asingle mode (peak). If this is the case, the effective dischargecorresponds to the mean discharge for the modal class (that is thepeak of the histogram). If the modal class cannot be readilyidentified, the peak of a smooth curve drawn through the tops ofthe histogram bars can be used to estimate the effective dischargeby interpolation.3.5.4 OverviewAll three approaches (bankfull estimate, discharge of aselected return period, or effective discharge) for estimating thechannel-forming flow or dominant discharge present challenges.The selection of the appropriate method will be based on dataavailability, physical characteristics of the study stream, level ofstudy, and time and funding constraints. It is recommended that allthree methods be used and the results cross-checked to reducethe uncertainty in the final estimate of the channel-forming flow. Ifthe effective-discharge method is used, then it is recommendedthat the standardized procedure presented herein be followed.3.6 RELATIONSHIPS INRIVERSGiven the evident complexity of fluvial processes and theinteractions with stream morphology, it is perhaps surprising thatthe characteristic forms adopted by alluvial rivers are limited innumber and are frequent in occurrence. For example, theplanforms of meandering rivers display clear similarity inproportions. Brice (1984) suggested that the similarity of meandersaccounts for the fact that, if scale is ignored, all meandering riverstend to look alike in plan view. It is the familiar and almostubiquitous nature of the forms and features displayed by alluvialstreams of different sizes, in widely varying landscapes, whichmakes these complex systems amenable to description byrelatively simple empirical relationships. For example,relationships developed by Williams (1986) illustrate how Brice’srecognition of the similarity of meanders may be expressedquantitatively through empirical relationships relating the geometricproperties of stream meander to one another (Table 3.3).40 Fundamentals of Fluvial Geomorphology and Stream Processes
Table 3.3 – Meander GeometryEquations (Williams 1986;adapted from FISRWG 1998)EquationNumberEquationApplicableRangeInterrelations between meander features2 L m = 1.25 b 18.0 < L b < 43,600 ft3 L m = 1.63B 12.1 < B < 44,900 ft4 L m = 4.53R c 8.5 < R c < 11,800 ft5 L b = 0.8L m 26 < L m < 54,100 ft6 L b = 1.29B 12.1 < B < 32,800 ft7 L b = 3.77R c 8.5 < R c < 11,800 ft8 B = 0.61L m 26 < L m < 76,100 ft9 B = 0.78L b 18.0 < L b < 43,600 ft10 B = 2.88R c 8.5 < R c < 11,800 ft11 R c = 0.22L m 33 < L m < 54,100 ft12 R c = 0.26L c 22.3 < L b < 43,600 ft13 R c = 0.35B 16 of channel size to meander features141.53A = 0.0094L m 33 < L m < 76,100 ft151.53A = 0.0149L b 20 < L b < 43,600 ft16 A = 0.021B 1.53 16 < B < 38,100 ft171.53A = 0.117R c 7 < R c < 11,800 ft180.89W = 0.019L m 26 < L m < 76,100 ft190.89W = 0.026L b 16 < L b < 43,600 ft20 W = 0.031B 0.89 10 < B < 44,900 ft210.89W = 0.81R c 8.5 < R c < 11,800 ft220.66D = 0.040L m 33 < L m < 76,100 ft230.66D = 0.054L b 23 < L b < 43,600 ft24 D = 0.055B 0.66 16 of meander features to channel size26 L m = 21A 0.65 0.43 < A < 225,000 ft27 L b = 15A 0.65 0.43 < A < 225,000 ft28 B = 13A 0.65 0.43 < A < 225,000 ft29 R c = 4.1A 0.65 0.43 < A < 225,000 ft30 L m = 6.5W 1.12 4.9 < W < 13,000 ft31 L b = 4.4W 1.12 4.9 < W < 7,000 ft32 B = 3.7W 1.12 4.9 < W < 13,000 ft33 R c = 1.3W 1.12 4.9 < W < 7,000 ft34 L m = 129D 1.52 0.10 < D < 59 ft35 L b = 86D 1.52 0.10 < D < 57.7 ft36 B = 80D 1.52 0.10 < D < 59 ft37 R c = 23D 1.52 0.10 < D < 57.7 ftRelations between channel width, channel depth, and channel sinuosity38 W = 12.5D 1.45 0.10 < D 59 ft39 D = 0.17W 0.89 4.92 < W < 13,000 ft40 W = 73D 1.23 K -2.35 0.10 < D < 59 ft &1.20 < K < 2.6041 D = 0.15W 0.50 K 1.48 4.9 < W < 13,000 ft & 1.20 < K < 2.60Derived empirical equations for river-meander and channel-size features:A = bankfull cross-sectional area L b = along-channel bend lengthW = bankfull widthB = meander belt widthD = bankfull mean depth R c = loop radius of curvatureL m = meander wavelength K = channel sinuosityFundamentals of Fluvial Geomorphology and Stream Processes 41
Page 6 and 7: materials. Also, the threshold mobi
Page 8 and 9: ank of a large river. From an engin
Page 10 and 11: eddies in a stream do not scale on
Page 12 and 13: aiding. Braid bars are sediment fea
Page 14 and 15: Sinuosity (P) is a commonly used pa
Page 16 and 17: outcrops, other non-erodible materi
Page 18 and 19: continent (Inglis 1941, 1947, 1949)
Page 20 and 21: instances where the bankfull discha
Page 22 and 23: uses readily available mean daily f
Page 26 and 27: Similarly, in regime theory the con
Page 28 and 29: 3.7 STREAM STABILITY ANDINSTABILITY
Page 30 and 31: It should be noted that the map coo
Page 32 and 33: and slope of the reach are not sign
Page 34 and 35: (a) Bed and Bank InstabilityFigure
Page 36 and 37: the downstream limit of the system
Page 38 and 39: dam, where degradation was expected
Page 40 and 41: Figure 3.13 - Channel PatternClassi
Page 42 and 43: definition of a graded stream in wh
Page 44 and 45: midwestern experience, while Rosgen
Page 46 and 47: Schumm et al. (1981, 1984) and thei
Page 48 and 49: ut at a much reduced rate. The sedi
Page 50 and 51: • integration of results into eng
Page 52: 68 Fundamentals of Fluvial Geomorph

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