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Rivers andFloodplains
Forms, Processes, andSedimentary Record
John S. BridgeProfessor of Geological SciencesBinghamton University, P.O. Box 6000,Binghamton, NY 13902–6000, USA
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RIVERS AND FLOODPLAINS
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For my family
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Rivers andFloodplains
Forms, Processes, andSedimentary Record
John S. BridgeProfessor of Geological SciencesBinghamton University, P.O. Box 6000,Binghamton, NY 13902–6000, USA
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Library of Congress Cataloging-in-Publication DataBridge, J. S.
Rivers and floodplains : forms, processes, and sedimentary record / John S. Bridge.p. cm.
Includes bibliographical references (p. ).ISBN 0–632–06489–7 (pbk. : alk. paper)1. Rivers. 2. Floodplains. 3. Sedimentation and deposition. I. Title.
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Preface ix
1 Overview of river systems 1Geometry of river systems 1Origin and evolution of river systems 5Water supply 7Sediment supply 12Controls on geometry, flow, and sedimentary processes of river systems 13
2 Fundamentals of water flow 17Parameters and units 17Reference material 17Definition of fluid motion 17Forces acting on stationary and moving fluids 18Fluid forces and equations of motion 25Turbulent boundary layers in steady, uniform flows 26Turbulent boundary layers in steady, non-uniform flows 39Subcritical and supercritical flow 41Unsteady flows 42
3 Fundamentals of sediment transport 44Parameters and units 44Drag on sediment grains 45Settling of grains in fluids 46Drag and lift on bed grains 49The threshold of transport of cohesionless sediment 49The threshold of transport of grains of mixed sizes, shapes, and densities 51The threshold of transport of cohesive sediment (mud) 54Bed load and suspended load 55Effect of sediment transport on flow characteristics 57Sediment transport rate (capacity) 60Sorting and abrasion of grains during transport 67Erosion and deposition 69Dissolved load 76Sediment gravity flows 76
Contents
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vi C O N T E N T S
4 Bed forms and sedimentary structures 78Parameters and units 78Bed states in cohesionless sediment 79Ripples 79Lower-stage plane beds 83Dunes 86Flow and sediment transport over ripples and dunes 97Grain sorting during sediment transport over ripples and dunes 103Cross stratification formed by ripples and dunes 104Upper-stage plane beds 117Planar lamination associated with upper-stage plane beds 118Antidunes and chutes-and-pools 120Cross stratification formed by antidunes and chutes-and-pools 125Hydraulic criteria for the existence of equilibrium bed states 129Theories for the origin and geometry of bed states 131Erosional structures in cohesionless sediments 139Bed forms and sedimentary structures in cohesive sediments (muds) 139
5 Alluvial channels and bars 141Evolution of initially straight alluvial channels 141Description and classification of the plan geometry of channels (channel patterns) 147Controls of channel pattern 153Geometry of alluvial channels at the bar-bend scale 162Flow in alluvial channels at the bar-bend scale 181Sediment transport in alluvial rivers at the bar scale 188Bed configurations on bars 192A model of equilibrium water flow, sediment transport, and bed topography in curved
alluvial channels 193Models of equilibrium water flow, sediment transport, and bed topography in braided rivers 199Erosion and deposition at the channel and bar scale 202Effect of vegetation on flow and sedimentary processes in rivers 211River and floodplain engineering and restoration 211Depositional models for channel and bar deposits 214
6 Floodplains 260Geometry 260Flow and sediment transport 261Flood frequency and the nature of floodplain deposition 269Nature of floodplain deposits 270Soils 279
7 Along-valley variations in channels and floodplains 296Long profiles of rivers and valleys 296Effects of tectonism on along-valley variation of rivers and floodplains 297Alluvial fans and deltas 301
8 Channel-belt movements across floodplains 310Observations of the nature of avulsion 310Avulsion and anastomosis 313
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C O N T E N T S vii
Effect of sedimentation rate on avulsion 314Effects of base-level change on avulsion 315Effect of climate change on avulsion 315Effects of tectonism on avulsion 315Theoretical models of avulsion 316Effects of avulsions on erosion and deposition 324Non-avulsive shift of channel belts across floodplains 326
9 Long-term, large-scale evolution of fluvial systems 328Process-based models of alluvial stratigraphy 329Long-term, large-scale erosion in rivers and floodplains 339Stochastic models of alluvial stratigraphy 343Effects of tectonics on long-term, large-scale fluvial deposition and erosion 347Effect of climate change on long-term, large-scale fluvial deposition and erosion 358Effect of relative base-level change on long-term, large-scale fluvial deposition and erosion 363Case study of effect of sea-level rise, climate change and tectonism on the Holocene lower
Mississippi Valley and Delta Plain 367Case study of effect of tectonism, climate, and sea-level change on the Tertiary Siwaliks
of northern Pakistan 369
10 Fossils in fluvial deposits 374Preservation of terrestrial and aquatic organisms in fluvial deposits 374Fossils in different fluvial sub-environments 379Time and space resolution of fossils in fluvial deposits 388Changes in fluvial fossils over time 388
Appendix 1 Methods of measuring water flow, sediment transport, bed topography,erosion, and deposition in rivers 390
Measurement of water flows 390Measurement of sediment transport rate 395Measurement of flow and sediment transport over bed forms 397Measurement of bed form geometry and kinematics 397Methods of sampling bed-surface sediment 398Measurement of erosion and deposition 400Sampling deposited sediment 401Laboratory rivers and floodplains 402
Appendix 2 Methods of describing and interpreting sedimentary strata 404Description of sediments and sedimentary rocks: data sources 404Recognition of distinctive rock types: facies definition 410Age determination 411Stratigraphic correlation 412Interpretation of origin of sedimentary deposits 414Interpretation of different scales of strata 415Depositional facies models 416Interpretation of fluvial deposits from subsurface data 416
References cited 417Index 487
Plate section faces p. 266
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Rivers and floodplains are of interest to most people in one way or another, because most of uslive near rivers and floodplains and rely on them forwater supply, food, power, transport, recreation,waste disposal, and as a source of raw materials.Earth scientists and civil, environmental, and agricul-tural engineers must understand rivers and flood-plains in order to deal with problems such as floods,water supply, design and construction of artifi-cial channels, river-bank erosion, sedimentation inreservoirs and navigated waterways, restoration offreshwater habitats, and remediation of pollutedsurface water and groundwater. Earth scientists(particularly physical geographers and sediment-ary geologists) also study modern rivers and flood-plains in order to understand how water flows,transports, erodes, and deposits sediment, and howthese processes control the form of hill-slopes, riverchannels, floodplains, alluvial fans, and deltas. Sedi-mentary geologists are particularly interested in thenature of modern deposition in rivers and flood-plains, as this knowledge must be used to inter-pret the origin of ancient river deposits. Ancientriver deposits contain a record of past landscapes, earth movements, and climates. An understandingof ancient river deposits is essential for effective exploration, development, and management of eco-nomically important resources contained withinancient river deposits, such as water, oil, gas, placerminerals, and coal. Therefore, hydrogeologists, en-vironmental geologists, petroleum geologists, andengineers must understand the deposits of riversand floodplains. This broad interest in rivers andfloodplains has resulted in such a vast and disparateliterature that it is very difficult to obtain a compre-
hensive view of rivers and floodplains as a generalbackground for work in a more specialized field.Therefore, my purpose in writing this book is tobring together the literature on rivers and flood-plains in a way that will appeal to a broad audienceof students, teachers, and practicing professionalsin the fields of geology, geography, and engineering.
The book is concerned with the origin, nature,and evolution of alluvial rivers and floodplains.Following a brief overview of river systems, themain part of the book is concerned with the geo-metry, water flow, sediment transport, erosion, anddeposition associated with modern alluvial riversand floodplains, and how this information is used tointerpret deposits of ancient rivers and floodplains.These topics are considered in order of increasingspatial and time scale. There is a section on inter-pretation of the types and lifestyles of ancient land-dwelling organisms from organic remains influvial deposits. Throughout the book, there is spe-cific reference to human interactions with rivers and floodplains, and associated environmental andengineering concerns. There is also frequent refer-ence made to economic aspects of fluvial deposits.Methods of studying rivers and floodplains andtheir deposits are discussed at the end of the book.
The approach taken in this book is to emphasizebasic principles, but also to discuss some of themore important details. These principles and detailsare supported by many examples, but I have triedto avoid a catalogue of case studies. A basic aim is to foster understanding of the nature of modernrivers and floodplains, and to illustrate that thisunderstanding is required before any problemsconcerning rivers and floodplains, past or present,
Preface
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x P R E F A C E
cussions and collaboration with many colleagues,including: Jan Alexander, Kay Behrensmeyer, JimBest, Mike Blum, Rick Cheel, Richard Collier, SergioGeorgieff, Rob Gawthorpe, Jack Jarvis, DerekKarssenberg, Mike Leeder, Jim Lorsong, RudySlingerland, Norman Smith, Bo Tye, and TorbjornTornqvist. My graduate assistants have also beensources of inspiration as well as great friends. I particularly want to mention Sean Bennett, DaveDominic, Sharon Gabel, Suzanne Leclair, Ian Lunt, Scudder Mackey, Brian Willis, and MikeZaleha. All of these people have also encouragedme in this endeavor. Some of the photographs in the book were graciously provided by: Peter Ashmore, Sean Bennett, Henk Berendsen, Jim Best, Mike Blum, Doug Cant, Sharon Gabel, SteveHasiotis, Esther Stouthamer, Brian Willis, and MikeZaleha. Anne Hull and Dave Tuttle have also helpedenormously in the preparation of many of thefigures. Jim Best undertook the overwhelming task of editing the first version of the manuscript. I am eternally grateful to Jim for his typically con-scientious and unselfish efforts. My wife Heatherprovided moral support, cups of tea, and othertreats.
can be addressed rationally. I have not included aseparate historic review of the literature on riversand floodplains. Such a review would necessarilybe very long and distract attention from the mainaim of the book. However, I have attempted to givedue credit to the originators of the main ideas in thefield. I do not consider bed-rock rivers.
There is a long list of references at the end of thebook. I consider such a long list to be essential inorder to enable readers to go beyond the level oftreatment in this book, and to give due credit to thelarge number of contributors to the field. Never-theless, this list constitutes a small fraction of thethousands of books and articles written on this sub-ject: a number that appears to be growing expon-entially. It would be an impossible task to cite all of these references, or even to read all of those in the list of references cited. Therefore, it is becom-ing increasingly necessary to rely initially on booksand articles that review the literature (includingthis book). I apologize in advance if I have offendedany authors by not citing their work sufficiently oraccurately.
Over the years during which the ideas in thisbook evolved, I have benefited greatly from dis-
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Fig. 1.1 is composed of: (i) a mountain belt withsteep valley walls, narrow floodplains, and riverchannels bounded by both bed-rock and coarse-grained alluvium; (ii) an alluvial fan where the mainchannel emerges from the mountain belt, wherethe channels may be both distributive and tributive(i.e. anastomosing); (iii) broad alluvial valleys withfloodplains and alluvial channels with a tributivedrainage pattern; and (iv) a delta where the main
Geometry of river systems
River system is the term used here for the system ofconnected river channels in a drainage basin (e.g.Fig. 1.1 and Plate 1.1). The drainage basin (or catch-ment area) is the area that contributes water andsediment to the river system, and is bounded by adrainage divide. The plan geometry (or drainagepattern) of the hypothetical river system shown in
Overview of riversystems1
Drainage divide separatesdrainage basin from others
Mountain belt with steep valleywalls, bedrock channels, alluvialchannels, and narrow floodplain
Alluvial fan as main channelemerges from mountain belt
Broad, low-relief valleys withalluvial channels and floodplains
Tributary
Main channel
DistributaryDelta
Lake or sea
Fan
Fig. 1.1 Plan geometry of ahypothetical river system. See also Plate 1.1.
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2 C H A P T E R 1
number and geometric properties of successively lower orders increase or decrease as geometricseries. The bifurcation ratio (Fig. 1.2) depends onthe degree of dissection of the drainage basin, andis commonly in the range 2 to 5 (Leopold et al.1964; Knighton 1998). Length ratio and area ratio (Fig. 1.2) are commonly in the ranges 1.5 to 3 and 3 to 6, respectively, for most drainage systems(review in Knighton 1998). The limited range of values of these ratios may be a consequence of theordering scheme itself. Furthermore, the ratios arenot clearly related to the physical controls on riversystem geometry, such as water and sediment sup-ply (Richards 1982; Knighton 1998).
channel flows into a lake or the sea, and where thechannels form a distributive pattern. Many otherdrainage patterns are possible (e.g. Miall 1996;Rodriguez-Iturbe & Rinaldo 1997; Rinaldo et al.1998; Dodds & Rothman 2000; Schumm et al.2000).
A river system consists of channel segments ofdifferent size (Fig. 1.2). Each segment has its owndrainage basin. The relative geometry of the vari-ous segments and drainage basins is orderly and fol-lows morphometric laws. One way of describingthe relative geometry of different sized stream seg-ments is to assign a numerical stream order (e.g.Horton 1945; Strahler 1952, 1957; see Fig. 1.2). The
Smaller divide separating 3rd order basins
Divide of 4th order basin contributeswater to 4th order stream
Stream orders1st order stream segments are smallest unbranchedsegments as seen on a map2nd order segments are those formed by joining togetherof 1st order segments3rd order segments are those formed by joining togetherof two 2nd order segments
Morphometric laws
bifurcation ratio Nn = ( ) m−nNn
Nn+1
m = highest order segmentNn = number of segments of order n
length ratio Ln = ( )nLn+1
LnLn = mean length of segments of order n
slope ratio Sn = ( )m−nSn
Sn+1Sn = mean slope of segments of order n
area ratio An = ( )nAn+1
AnAn = mean drainage area of segments of order n
Number and geometric properties of stream segments of successively lower ordersincrease or decrease as geometric series
Bifurcation ratio is 2.5–7.0 for natural basins.
11
1
1
1
1
1
1
1
1
11
1 2
2
2
22
3
4
3
Large river
3
DFDF
AC
AC
DF
AC
DF
AC
Fig. 1.2 Stream orders and morphometric laws of the drainage basin.
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O V E R V I E W O F R I V E R S Y S T E M S 3
drainage systems are not really random, dependingin detail on geology and antecedent conditions (seebelow and Knighton 1998). Furthermore, objectivedefinition of stream segments is difficult becauseidentification of stream segments of the smallestorder of magnitude is very much dependent on themap scale and on the discharge condition of thestreams when the map was constructed.
Drainage density (defined as the total channellength/drainage basin area) is a measure of thedegree of dissection of the drainage basin. Thedrainage density increases directly as the averagedistance between adjacent channels decreases.Also, the closer the stream heads are to the drainagedivides, the greater the drainage density. Drainagedensity depends on the precipitation rate (minusevaporation rate), the permeability of the surfacematerials, the resistance to erosion of the surfacematerial, and the degree of protection by vegeta-tion. Drainage density tends to be high in semi-arid regions (on the order of tens to hundreds ofkilometers per square kilometer) because of tem-porally concentrated precipitation (and runoff)and lack of protective vegetation. Drainage densityis lower in humid temperate regions (less than tenkilometers per square kilometer) because of thevegetation cover.
The drainage basin area, A, increases with channel length, L, in moving down valley from theheadwaters, according to
L = coefficient Aexponent (1.3)
where the coefficient and exponent vary fromregion to region (Hack 1957; Knighton 1998). Theexponent is generally close to 0.6 (ranging from 0.5to 0.7), meaning that the length of drainage basinsincreases with drainage basin area more than theirwidth does. Dodds and Rothman (2000) discusshow the exponent varies with different types of ide-alized drainage patterns.
The position and orientation of river channels indrainage basins are in fact controlled by geologicalstructure, the areal distribution of different types of surface material, and antecedent drainage con-ditions (e.g. radial, dendritic, rectilinear drainagepatterns shown in Fig. 1.4a; review by Schumm et al. 2000). Most of the world’s largest rivers have
An alternative way of describing the relativegeometry of stream segments is to assign a streammagnitude (Shreve 1966, 1967; Fig. 1.3). A streamsystem of magnitude n has n segments of magni-tude 1 and n − 1 segments of magnitude greaterthan 1, giving 2n − 1 segments in total. Accord-ing to Shreve (1966), channel systems develop by random combination of segments that have randomlengths and drainage areas, such that there is no sys-tematic variation of segment length or area withposition in the basin (in the absence of climatic,geological or topographic constraints). However, a range of topologically distinct channel systemscan be created by successively joining a given num-ber of segments of magnitude 1. According to thismodel, mean segment length and drainage area arerelated by
A ≈ 1.5F2 (1.1)
The total drainage area, A, is therefore given by
A = A(2n − 1) ≈ 1.5F 2(2n − 1) (1.2)
There are various other measures of channel-systemgeometry based on stream magnitude (Richards1982). Although Shreve’s approach predicts real-istic values of bifurcation ratio and of the relation-ship between stream length and drainage basin area,
Magnitude, n = 13n exterior segments2n − 1 total segments
1
1
11
11
1
1
1
1
12
2
4
5
82
1
16
4
2
13
Fig. 1.3 Definition of stream magnitude.
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4 C H A P T E R 1
time. River diversions are common and are causedby changes in local valley gradients associated, forexample, with tectonism, deposition, erosion, andice dams (e.g. Jackson et al. 1996; Gupta 1997;Friend et al. 1999; Schumm et al. 2000; Fig. 1.4b).
Long profiles of river valleys (graphs of height ofvalley floor plotted against down-valley distance)are commonly reported as being concave upward,or a series of valley segments of constant slopebetween major tributaries, with slopes decreasingdown valley. This is much too simplified a view,especially in areas of active tectonism, and in riversystems where discharge does not increase downvalley (Fig. 1.5 and Chapter 7).
It is also commonly stated that the down-valleyparts of river systems are areas of net deposition,whereas the up-valley parts are mainly erosional
valleys in long established (many millions of years)structural lows (Potter 1978; Miall 1996). Manyrivers flow either parallel or transverse to the mainstructural grain of the landscape (e.g. Fig. 1.4). Miall(1981, 1996) has classified drainage basins based onwhether the main channel flows parallel or trans-verse to the structural grain of the landscape, andon whether the depositional area at the mouth ofthe river (e.g. the delta) is dominated by fluvial,wave, or tidal currents. Such a classification fails to consider the temporal and spatial variability ofthe geometry and processes of river systems. Forexample, a main channel may flow parallel andtransverse to structural grain, and different parts ofa delta may be dominated by fluvial or wave or tidalcurrents at a given instant in time. Furthermore,drainage patterns are dynamic and change with
A Dendritic B Parallel
C Trellis D Rectangular
E Radial F Annular
(a) (b)
Ghaghraplain
82° 84° 86° 88°
27°
26°Indo-gangetic plain
InterfanGandakmegafan
Interfan
Ganges river
Kosimegafan
PiedmontMFTMBT
N
km
0 100
Tibetanplateau
Fan Fan Fan Fan
Diversion
Thrust-foldgrowth
Megafan
Fig. 1.4 (a) Drainage patterns (after Howard 1967) controlled by topography and geology. Dendritic patterns form on slopes underlain by homogeneous material. Trellis and rectangular patterns are controlled by fracture patterns or dippingsedimentary strata of unequal resistance to erosion. Radial dendritic patterns form on topographic domes formed ofhomogeneous material (e.g. ash cones). Annular patterns form on topographic domes with either concentric fracture patterns or rocks with unequal resistance to erosion. AAPG © 1967. Reprinted by permission of the AAPG whose permissionis required for further use. (b) Modification of Himalayan rivers by progressive growth of anticlines associated with thrustfronts (from Leeder 1999, after Gupta 1997). Upper left figure shows present day drainage system. MFT is the Main FrontalThrust, and MBT is the Main Boundary Thrust. Lower left figure shows postulated courses of rivers (arrows) prior to formationof thrust-related drainage divide. Right-hand figure shows how river courses are modified by growing structural topography.
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O V E R V I E W O F R I V E R S Y S T E M S 5
discussed further below, after a review of howdrainage systems originate and evolve.
Origin and evolution of river systems
Studies of the origin and evolution of river systemshave involved fieldwork, analysis of sequential mapsor aerial photographs, laboratory experiments, and theoretical approaches. In general, the inability to make detailed, long-term observations of the origin and evolution of river systems in geologicallyrealistic settings has hampered our understanding of river systems and our ability to test theoreticalmodels (Knighton 1998).
Initiation of a channel requires a surface waterflow to develop sufficient power to locally erodeand transport surface material. In order for a sur-face flow to develop such power, it is necessary tohave sufficient water discharge and slope, whichrequires a critical source basin area and slope. Thewater may be supplied by overland flow and byshallow subsurface flow. The local concentrationof flow power required to initiate a channel headmay be associated with a local concentration of
(Schumm 1977). This notion may have arisen fromstudies of mid-latitude rivers that have experienceda major relative sea-level rise during the Holocene,accompanied by unloading of glacial ice andchanges in climate and vegetation in upland areas.However, some modern, near-coastal valleys arecurrently experiencing erosion, and many areaswithin and immediately adjacent to upland areashave major amounts of deposition, especially intectonically active regions.
The geometry of the drainage system is appar-ently adjusted to maintain the continuity of waterand sediment supplied from the valley sides. Forexample, the surface area of the whole drainagebasin is normally proportional to the volume of waterthat must be discharged per unit time (Leopold et al. 1964; Richards 1982). The cumulative drain-age area commonly increases discontinuously withdistance down valley, and this partly controls thetiming and magnitude of flood peaks in differentparts of the basin. Stream networks with largedrainage density commonly have relatively shortdistances of overland flow, and thus relatively rapidincreases in discharge and large peak dischargesduring times of high precipitation. These points are
Trisuli(Chi-lung Ho)
Chenab
10
0
MBTMCT
MCT?T MBT T
T P
SutlejP
10
0
10
0
10
0
10
0
MCT?
MCTMBT P
PMBT
Ganges-Alaknanda
KarnaliBheri
T
T
TT
MBT
MCTT
KarnaliBheri
10
0
MCTMBT P
Kali Gandaki(Ko-liho)
10
0
10
0
10
0
MCT
MCTT
TKali Gandaki
MBT
TSunkosi
MBT P Arun
Arun
Sun Kosi(Po Ho)
km5
00
15
10
5
Thousandfeet
Vertical exaggeration = 16x
50 200100 150
km
Fig. 1.5 Long profiles of Himalayanrivers showing zones of high gradientand convex-upward profile associatedwith major thrust fronts (T ) such as the Main Central Thrust (MCT ) and the Main Boundary Thrust (MBT ).(Modified from Seeber & Gornitz1983). © 1983, with permission fromElsevier Science.
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6 C H A P T E R 1
subparallel and closely spaced rills flowing down aplanar surface into a master rill by a process knownas micropiracy (Horton 1945). Subsequently, rillsdeveloped on the valley slopes of the initial masterrill, and new master rills developed as tributaries tothe initial master rill, and so on. This theory does notagree with observational data. Dunne (1980, 1990)developed a theory for the evolution of channelsystems from an initial stream head produced at alocal groundwater seepage. Headward extension of the stream head increases groundwater flow con-vergence into the channel. Tributaries also origin-ate by seepage erosion of “susceptible” zones in thevalley sides. Tributaries develop until their drainageareas become insufficient to produce the ground-water discharge required for further seepage ero-sion. Clearly, all channel networks are not producedby seepage erosion. Willgoose et al. (1991a, b, c)developed a quantitative, deterministic theory forthe development of drainage systems (Fig. 1.6).Channels continue to extend headward as long as a channel initiation function (proportional to functions of water discharge and slope) exceedssome specified threshold. Headward extension and development of tributaries ceases when thechannel initiation function decreases below thethreshold because the drainage areas contribut-ing water to the channels progressively decrease.Other deterministic approaches to development ofdrainage basins include those of Howard (1994)and Izumi and Parker (1995). Stochastic models ofdrainage systems involve random headward growthof channels and tributary branching (Leopold &Langbein 1962; Howard 1971a, b; Stark 1991).
The development of drainage systems has alsobeen approached from the point of view of theenergy required to transport water and sedimentfrom the land as efficiently as possible. Drainagesystems are most efficient (require the least energyexpenditure) when flow resistance due to bound-ary friction is at a minimum. The best way of min-imizing flow resistance is to have channel flowinstead of overland (sheet) flow, and to have a relat-ively small number of large channels. However,channel initiation requires a certain amount of overland and/or shallow subsurface flow, which isassociated with high flow resistance. According to Rodriguez-Iturbe et al. (1992) and Rinaldo et al.
discharge related to surface topography or to a zoneof high permeability in the shallow subsurface. Itmay also be related to a local increase in down-stream slope. In order for progressive erosion tooccur, the transporting power and sediment trans-port rate must increase downstream. Resistance ofsurface material to erosion depends greatly on itstexture (e.g. grain size and shape) and on thedegree of cohesion brought about by degree oflithification, clays, and vegetation. Spatial variationin the erodibility of surface material will also con-tribute to the localization of erosion required forinitiation of channels.
Channel initiation has been associated with ero-sion by overland flow, by localized groundwaterseepages, and by shallow landslides that producelocal slope increases and unvegetated surfaces thatare relatively easily eroded (Montgomery & Dietrich1988, 1989, 1994; Dietrich et al. 1993; Dietrich &Dunne 1993; Kirkby 1994). As mentioned above,channel initiation requires threshold basin sourcearea and valley slope. Different modes of channelinitiation may be associated with different area–slope combinations. For example, shallow land-slides generally require relatively large slopes.Erosion associated with groundwater seepages maynot require as much drainage area as overland flow.However, it is unlikely that any of these processesof channel initiation acts independently, and theactual area–slope combination when channel headsform is greatly dependent on the materials thatneed to be eroded.
Experimental and field studies of the initiation andevolution of channel systems on freshly exposed,regular surfaces composed of homogeneous mater-ial demonstrate that channel systems evolve byheadward extension (elongation) of channels anddevelopment of branches (e.g. Schumm 1956;Morisawa 1964; Flint 1973; Parker 1977; Fig. 1.6).The relative timing of headward extension anddevelopment of branches depends on particularexperimental conditions, such as initial slope andspatial variations in slope (review by Knighton1998). During the early stages of river system evo-lution, drainage density increases rapidly, but laterchanges little with time.
Early theories for the evolution of drainage systems involved the transformation of numerous
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O V E R V I E W O F R I V E R S Y S T E M S 7
Water supply
Water is supplied to rivers from precipitation in thedrainage basin (catchment area). Some of the pre-cipitation is returned to the atmosphere by evapora-tion and evapo-transpiration, but the remainderflows under the influence of gravity over the surfaceor through the ground towards rivers, floodplains,and lakes (Fig. 1.7). Overland flow is commonlysubdivided into infiltration-excess overland flow
(a)
Initialconditions
Mode 1Slope = 0.43°
Base-level loweredbefore each run
Mode 2Slope = 1.83°
Base-level not loweredbefore each run
Incr
easi
ng ti
me
t = 500
t = 2000
t = 6000
t = 13,000
(b)
(1992, 1998), drainage networks are developedsuch that the energy expenditure in any stream seg-ment and in the whole system are at a minimum,and the energy expenditure per unit bed area isconstant. Although these assumptions regarding dis-tribution of energy expenditure can be argued with,this theory agrees with the morphometric laws dis-cussed above. The subject of energy distribution inrivers will be returned to in Chapter 5, where weconsider the geometry of individual river channels.
Fig. 1.6 (a) Experimental study of drainage evolution (afterParker 1977). The number of first-order streams increasesmore quickly in the mode 1 experiments. (b) Theoreticalsimulation model of drainage evolution (after Willgoose et al. 1991a, b). t is non-dimensional time. © by theAmerican Geophysical Union.
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8 C H A P T E R 1
examples given in Figs 1.8 and 1.9 show the typicalasymmetrical shape of flood hydrographs, with thepeak discharge lagging behind peak precipitationbecause of the time it takes for water to movethrough and over the surface of the ground. Floodhydrographs are commonly separated into quick-flow (or stormflow) and delayed flow (or base-flow) (Fig. 1.8). Quickflow originates mainly fromoverland flow (but also from fast, shallow subsur-face flow), whereas delayed flow is due to slowflow through the ground. The relationship betweenwater discharge and net precipitation is commonlyexpressed in terms of the response factor, R =(quickflow discharge/catchment area)/(rainfall −evaporation). Response factors are typically on the
(due to precipitation rate exceeding infiltrationcapacity of the ground) and saturation-excess over-land flow (due to the fact that the ground is satur-ated with water). The relative importance of thesetwo types of overland flow depends on the pre-cipitation rate relative to the permeability of theground. Water may flow through the ground relat-ively rapidly near the surface (called throughflowor subsurface storm flow) or more slowly deeperdown (groundwater flow). As water flows downslope, the potential energy of the water is con-verted to kinetic energy. However, kinetic energydoes not necessarily increase with loss of elevation,because the water flow is resisted by friction at itssolid boundaries (the ground surface or the sides ofpore spaces).
Hydrographs
Water supply to rivers and floodplains varies inspace and time. Water supply increases in the down-valley direction as tributaries join, unless water is lostby evaporation and/or by infiltration. Changes inwater supply in time occur over various time scales,associated, for example, with: daily and seasonalvariations in snowmelt, individual storms, seasonalprecipitation, sunspot cycles, drainage diversions,and Milankovitch cycles. A hydrograph is a graphof time variation of water discharge in a river. The
Infiltration
Watertable
Groundwater flowStream flow
(and floodplain flow)
Overland flow
Evaporation and Evapotranspiration
Precipitation
Fig. 1.7 Movement of water on and through the ground.
Waterdischarge
Rainfall peak
time to peaktime base
baseflow
stormflow
Dischargepeak
arbitrary separation line
Time
Fig. 1.8 Definition of flood discharge hydrograph.
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O V E R V I E W O F R I V E R S Y S T E M S 9
precipitation and temperature) or on statistical ana-lyses of hydrographs.
Unit hydrographs are used to compare hydro-graph shapes between drainage basins. The unithydrograph is defined as the hydrograph of 10 mmof quickflow from a storm of a specific duration. Itis defined by three parameters (time base, time topeak discharge, and peak discharge: Fig. 1.8) thatare related to catchment properties. Unit hydro-graphs are used to predict hydrographs in ungagedcatchments, but there are many limitations relatedto lack of understanding of processes responsiblefor the hydrograph shape, different hydrologicalconditions in different catchments, and the lack ofconsideration of antecedent conditions. There arenow much more sophisticated ways of modelinghydrographs in a given drainage basin (review byFawthrop 1996).
It is common for the time of peak discharge fol-lowing a storm to occur progressively later in thedown-valley direction, and for the shape of thehydrograph to change down valley. The translationand modification of a flood wave can be treatedusing the equations of motion for unsteady, non-uniform flow, but with difficulty. Storage of theinflow to a reach of river, such as during overbankflow or the filling of a lake, leads to attenuation anddelay of the flood peak in moving down valley. Inorder to predict hydrograph shape as a function oftime and space in a drainage basin, it is thus neces-sary to consider antecedent conditions, the timeand space variations in effective precipitation, over-land flow and groundwater flow, and the routing ofriver and overbank flow through the system. This isnot a simple task.
Long-term discharge records for selected riversin the USA (Fig. 1.10: Leopold et al. 1964) showhow discharge varies in time and space. Most ofthese hydrographs show a steady decline in dis-charge in the first half of the twentieth century, dueto the climate becoming warmer and drier. Manyhydrographs also show a cyclicity with a period of 8 to 13 years, possibly associated with sunspotcycles. The tendency for wet or dry years to occurin groups was called the persistence effect by Hurst(1950).
Streamflow hydrographs are continuous timeseries, and records of daily, monthly, or annual
order of 10−2 to 10−1. High values are associatedwith impermeable or previously saturated ground(hence high proportion of overland flow), whereaslow values are associated with large amounts ofinfiltration and groundwater flow.
Differences in the shapes of flood hydrographs ata point depend on: (i) the time and space distribu-tion of precipitation; (ii) the relative amount ofoverland flow and groundwater flow before reach-ing the river, as determined by geology, soil type,vegetation, land use, and antecedent conditions;and (iii) the drainage system geometry, which con-trols the amount of overland flow and groundwaterflow relative to channel flow. The sharp-peakedhydrograph in Fig. 1.9 may be due to a high rate ofrainfall or snowmelt over a short period of timeand/or a high proportion of overland flow relativeto groundwater flow due to impermeability, highwater table, or lack of the retarding effects of vegeta-tion. The broad hydrograph in Fig. 1.9 may be dueto precipitation distributed over time and/or highgroundwater flow/overland flow due to high per-meability, low groundwater table, or the presenceof a vegetation cover. High drainage density andsteep valley slopes tend to result in highly peakedhydrographs, because of the relative speed withwhich overland flow can reach the channels. Theeffect on hydrographs of water flow on and belowhillslopes relative to that in channels decreaseswith distance down valley. Hydrograph shapes havebeen classified by several workers (e.g. Pardé 1947;Beckinsale 1969; Gustard 1996). These classifica-tions are based either on relating a particularhydrograph shape to climate (seasonal variations in
Waterdischarge
Rainfall peak
Time
a
b
Fig. 1.9 Schematic hydrographs.
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10 C H A P T E R 1
of one year. After removal of the trend and oscillat-ory component, the remaining, or residual, series may be independent or dependent stochastic vari-ables. In general, these stochastic variables are notindependent, because the discharge of one day ormonth is related to that of the previous day ormonth. To model this situation, a second-order, lin-ear autoregressive (Markov) model can be used(e.g. Quimpo 1968), in which the discharge for oneday or month is linearly dependent on the two pre-vious days or months. Then, the remaining part ofthe time series can be represented by an independ-ent stochastic variable, which typically follows aGaussian, log-Gaussian, or Gamma distribution. Oncethe structure of the time series has been estab-lished, sequential stream flow data are generatedusing Monte-Carlo techniques. Particular types ofstream-flow time series can be classified and relatedto climate, vegetation, basin geometry, and geology.
discharges are discrete time series. Such time seriesare commonly analyzed in order to recognize trends,cycles, and random fluctuations in discharge (e.g.Chow 1964). Mathematical models of hydrolog-ical time series are used for sequential generation of stream-flow data for simulation purposes (e.g.Roesner & Yevjevich 1966; Quimpo 1968; Rodriguez-Iturbe 1968; Adamowski 1971). Such mathematicalmodels are commonly considered to contain adeterministic component and a stochastic compon-ent. The deterministic component may be com-posed of a trend and an oscillatory (or periodic)component. The trend may be recognized usingpolynomial regression, for example. The oscillatorycomponent may be modeled using Fourier analysis,where the means and standard deviations of thedaily or monthly discharges are represented by anumber of harmonics (sine and cosine functions).One of the harmonics will normally have a period
1.0
0.5
DIS
CH
AR
GE,
IN T
HO
USA
ND
CU
BIC
FEE
T PE
R S
ECO
ND
1880
ROARING FORK AT GLENWOODSPRINGS, COLORADO
MISSISSIPPI RIVER AT KEOKUK, IOWA
1900 1920 1940 1960
1900 1960
1900 1920 1940 19601880 1900 1920 1940 1960
1880 1900 1920 1940 1960
1900 1920 1940 1960
1880 1900 1920 1940 1960
2.0
1.5
1.0
100
75
50
25
1900 1920 1940 19603.5
3.0
2.5
1.5KINGS RIVER AT PIEDRA,
CALIFORNIA
250
200
150COLUMBIA RIVER NEARTHE DALLES, OREGON
1.6
1.4
1.2
40
30
PEMIGEWASSET RIVER ATPLYMOUTH, NEW HAMPSHIRE
VERDE RIVER BELOW BARTLETT DAM,ARIZONA
SUSQUEHANNA RIVER AT HARRISBURG,PENNSYLVANIA
2.5
2.0
1.5CHATTAHOOCHEE RIVER NEAR
ROSWELL, GEORGIA
1920 1940
Fig. 1.10 Long-term discharge hydrographs for selected rivers in the USA (from Leopold et al. 1964). © 1964 by WH Freemanand Company. Used with permission.
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O V E R V I E W O F R I V E R S Y S T E M S 11
Figure 1.12 is an example of an analysis of annualmaximum discharges. A partial duration seriesis a series of independent flood discharges thatexceed some specified threshold. It is analyzed inthe same way as an annual series, but the floodreturn period can be less than one year.
Frequency distributions of extreme events suchas annual maximum discharges are normally posit-ively skewed (i.e. mode displaced towards smallervalues) and can be described by functions such asexponential, gamma, lognormal, Gumbel EV1, orPearson type III. The Gumbel EV1 function isfavored, and its distribution function is given by
f(x) = exp (−exp (−(x − u)/α)) (1.7)
where u is the mode, the mean = u + 0.5772, andthe standard deviation is 0.78α . According to theGumbel EV1 function, the probability of exceedingthe mean annual flood is 0.43, and its recurrenceinterval is 2.33 years. The modal (most probable)annual flood has a recurrence interval of 1.58 years.If a series of annual maximum discharges followsthe Gumbel EV1 function, a plot of annual max-imum discharge versus cumulative probability orrecurrence interval (with a special type of loga-rithmic scale) will be a straight line (e.g. Fig. 1.12).There are plenty of other functions to choose from,and it is commonly difficult to decide which onebest fits the flood frequency data. In order to fit
Flood frequency
The frequency with which water discharge of agiven magnitude occurs at a particular point on ariver is commonly represented on a duration curve(e.g. Fig. 1.11: Dalrymple 1960; Chow 1964). Aduration curve shows the percentage of time that aparticular discharge is exceeded or equaled. If thefrequency distribution of discharge is lognormal,the duration curve will be a straight line when plotted on normal probability paper (Fig. 1.11). Aflow duration curve with a relatively low negativeslope implies a large discharge range (i.e. flashy),whereas a high negative slope implies less dis-charge variability.
The distribution of annual maximum dischargesthat occur over a period of years is called theannual series. The mean of the annual series iscalled the mean annual flood. If there are N yearsof record, and these maximum annual dischargesare ranked, with the largest having rank m = 1 andthe smallest having rank m = N, then the probabil-ity of an annual flood of magnitude x exceeding onewith magnitude m is
p(x) = m/(N + 1) (1.4)
The mean return period of this flood event is
T = 1/p(x) (1.5)
and the cumulative probability is
f(x) = 1 − p(x) (1.6)
Mea
n da
ily d
isch
arge
(m3
s−1)
10
1
0.5
5
0.5 5 10 50 95 99.5
Time a given discharge is equalled or exceeded (%)
(a)
7.6
Fig. 1.11 Example of flow duration curve (after Knighton1998).
Ann
ual m
axim
um d
isch
arge
(m3
s−1)
50
0.020.050.10.20.50.670.80.950.9870
20
60
50
40
30
Mean annualflood = 38 m3 s–1
201052.331.51.251.01.02 2
Recurrence interval (years)
EXCEEDENCE PROBABILITY
(b)
Fig. 1.12 Example of flood frequency curve (after Knighton1998).
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12 C H A P T E R 1
composition of the dissolved species, in rivers asgroundwater flow starts to add to quickflow. Incontrast, the concentration of dissolved materialdecreases as water discharge increases, because ofthe decreasing importance of groundwater flow.However, the total dissolved load increases withdischarge (Leopold et al. 1964; Knighton 1998).
The sediment supply to rivers and floodplainsvaries in space and time for the same reasons as thewater supply. There is more variability in the caseof sediment supply, because of discrete mass move-ments such as debris flows and landslides. Peaks insediment supply commonly lag behind peaks inwater supply because sediment requires a thresh-old gravity and/or fluid force to initiate down-slopemovement, and sediment travels more slowly thanthe fluid (unless it is suspended load). Furthermore,sediment from mass wasting is commonly storedtemporarily at the outer edges of floodplains.
Sediment yield from drainage basins has beenestimated based on measurements of suspendedload and dissolved load in rivers, and rates of de-position in reservoirs (e.g. Langbein & Schumm1958; Fournier 1960; Leopold et al. 1964; Douglas1967; Ahnert 1970, 1984; Wilson 1973; Dunne1979; Jansson 1988; Pinet & Souriau 1988; Milliman& Syvitski 1992; Summerfield & Hulton 1994;Hovius 1998; Hooke 2000). These yields amount todenudation rates on the order of 0.01 to 1 mm peryear. The average global denudation rate is 0.055mm per year based on suspended solids and 0.01mm per year based on dissolved material: how-ever, these rates vary greatly across the globe(Knighton 1998). Estimates of sediment yield arelikely to be very inaccurate, partly because bed-load is not considered. As sediment loads are veryvariable in time and space, the accuracy of the estimates is greatly dependent on the sampling fre-quency and extent in time and space. It is also likelythat humans have had a large impact on sedimentyields in some regions, as a result of deforestation,agriculture, construction, and mining. Sedimentyields may actually underestimate denudation ratesof hillsides because much eroded sediment may bestored on floodplains. Therefore, great care mustbe exercised in extrapolating both sediment yieldsand derived denudation rates to the geological past.
such functions to data it is necessary to have a longperiod of records and no progressive changes inflood discharge, as, for instance, brought about byhuman interference.
In ungaged catchments, flood discharge of agiven frequency may be estimated using multivari-ate statistical techniques. Flood discharge is relatedempirically to catchment characteristics such as cli-mate (rainfall), land use, soil type, basin geometry(area, slope), and drainage density (Richards 1982;Fawthrop 1996; Knighton 1998). Problems withthis approach include bias caused by the samplesused to derive the statistical relationship and corre-lations among the independent variables. There arealso physically based models for predicting flooddischarges, but these are fraught with uncertaintybecause of the complicated nature of problem.
Sediment supply
Sediment is supplied by weathering of exposedrocks and by down-slope movement of the loosematerial, with or without the assistance of overlandwater flow. The rate of weathering and the textureand composition of weathered material are con-trolled by at least: (i) the nature of the exposedrocks (their composition, texture and structure);(ii) the amount of precipitation; (iii) temperaturevariations; and (iv) the presence of vegetation.These are in turn controlled by topography and cli-mate. Relatively coarse weathered material tends to be most common in cold climates and wherethere are steep slopes. Clays (produced by chem-ical weathering) are voluminous in warm humid climates. Organic material makes its maximum con-tribution to the sediment supply in humid climates.The rate of mass wasting (down-slope movement of loose material under the influence of gravity)depends on the texture and composition of theloose material, the availability of water, the pres-ence of vegetation, slope angle, and ground motionsassociated with earthquakes.
Dissolved material comes from rainfall, thegroundwater, and human sources. Thus solute com-position reflects the geology of the drainage basinas well as external sources. It is common to observepeaks in solute concentration, and changes in the
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O V E R V I E W O F R I V E R S Y S T E M S 13
part by the supply of water and sediment, whichare controlled in turn by the nature of the drain-age basin and, ultimately, by regional climate andtectonics. Other controls on the geometry, flow,and sedimentary processes within alluvial systemsinclude changes in topography and “accommoda-tion space” associated with tectonism and relativebase-level changes. The interactions between thevarious independent and dependent variables occurover a range of time and space scales (Table 1.1).There are time lags between changes in independ-ent variables and responses of dependent variables,controlled by the rates and magnitudes of changesin independent variables, and the ability of thedependent variables to change.
Adjustment of dependent variables such as channel width and depth to changes in independ-ent variables requires erosion and deposition. It isnormally assumed that most erosional and deposi-tional activity in alluvial rivers is accomplished at relatively high flow stages, and therefore the geometry of alluvial rivers is also controlled by high discharges. However, it is necessary to con-sider the frequency as well as the magnitude ofdepositional and erosional events (Wolman & Miller1960; Leopold et al. 1964; Nash 1994; Knighton1998). The dominant discharge or channel-forming
Estimated sediment yields plotted as a function of mean annual effective precipitation (Fig. 1.13)suggest that maximum yields occur where annualprecipitation is around 300 mm. Arid climates havelittle protective vegetation, but relatively low run-off. Very wet climates have dense forest vegeta-tion to protect the surficial material from erosion.However, Fig. 1.13 shows the effect on sedimentyield of only one factor: effective precipitation.Other factors, such as seasonality of precipitationand temperature, topographic relief, seismicity,soil type, and land use, are expected to have aninfluence on sediment yields, as all of these factorsinfluence weathering rate, hillslope erosion, andriver transport (Hooke 2000). Humans have had adramatic effect on sediment yields, as mentionedabove.
Controls on geometry, flow, and sedimentaryprocesses of river systems
Figure 1.14 summarizes the relationship betweenmaterials, processes, and landforms in alluvial riversystems. Specifically, the geometry, water flow,sediment transport, erosion, and deposition inrivers, floodplains, fans, and deltas are controlled in
Sedi
men
t yie
ld (t
onne
s km
−2yr
−1)
1000
800
600
400
200
020001000500 1500
(mm)Precipitation (A)Mean annual runoff (B)
A2
B2
B110°C 20°C
A1
Fig. 1.13 Various relationships of sediment yield to mean annualprecipitation (Fournier 1960, curveA1), effective precipitation (Langbein& Schumm 1958, curve A2) and runoff(Douglas 1967, curve B1; Judson & Ritter 1964, curve B2). Runoff values represent precipitation lessevapotranspiration and infiltration.(from Richards 1982).
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14 C H A P T E R 1
In reality, all discharges that are capable of trans-porting sediment will have some effect on channelgeometry, even if not a dominant one. Actual adjust-ments of channel geometry to changes in water andsediment supply will depend on the rates and mag-nitudes of the changes, and the ability of the channelto change its form through erosion and deposition.These interactions among variables are illustratedbelow with several simple qualitative examples.
If the flood (bankfull) discharges of water andsediment in a river did not vary appreciably overtime spans on the order of decades, the channel
discharge (see Fig. 1.15) is commonly taken as nearthe bankfull discharge; that is, the discharge thatjust fills the channel. Bankfull discharge commonlyhas a return period of between 1 and 2 years(Wolman & Leopold 1957; Woodyer 1968; Dury1973; Williams 1978). The return period of bank-full discharge actually varies markedly along thelength of a given river and between different riversbecause of differences in shape of flood hydro-graphs. Furthermore, the return period of bankfullstage in aggrading rivers is less than that in incisingrivers.
Supply of waterand sediment
Geometry, water flow, sediment transport,erosion and deposition in rivers,
floodplains, fans, and deltas.Preservation of deposits depends onavailability of space, deposition rate,
and subsequent erosion.
Redistribution of massresults in changes in slope,
isostatic adjustment
Geology, topography,local climate, vegetation
of drainage basin
Tectonics andclimate
Tectonics, climate,and eustasy
Water and sedimentto sea and lakes
Fig. 1.14 The relationship betweenmaterials, processes, and landforms inalluvial river systems.
Table 1.1 Independent and dependent variables in alluvial river systems as a function of time.
Variable Decreasing time span
Geology Independent Climate Independent Vegetation Dependent IndependentTopography Dependent Independent Water and sediment supply Dependent IndependentChannel geometry Dependent IndependentChannel flow, sediment transport, Dependent
erosion and deposition
Source: Modified from Schumm and Lichty (1963).
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O V E R V I E W O F R I V E R S Y S T E M S 15
geometry, flow, and sedimentary processes wouldbe adjusted to the flood discharges, with relativelyminor changes associated with changing flow stage.This adjusted condition is referred to as dynamicequilibrium (also graded or regime). If there wasa major change in the flood discharge of water andsediment in a river, caused, for example, by an ex-ceptional (e.g. 1000-year) flood, earthquake, chan-nel diversion, or human activity (e.g. dams, mining,overgrazing), there would most likely be a major,regional change in the river’s geometry, flow, andsedimentary processes. Such exceptional (evencatastrophic) short-term changes in the river sys-tem would cause it to be in disequilibrium withprevious “normal” flood discharges, and a finite lagtime would be required to re-establish dynamicequilibrium with subsequent “normal” conditions(see Fig. 1.16). Whether or not the system is
Magnitudeor
frequency
Dischargefrequency
Sedimenttransport rate
Product ofsediment transport rate
and frequency
Variable
Waterdischarge
Time
Channelwidth
Disequilibrium
Equilibrium
Equilibrium Disequilibrium Equilibrium
Waterdischarge
Flowdepth
Time
(a)
(b)
Fig. 1.16 Definition of equilibriumand disequilibrium in streamgeometry. (a) Channel width variescongruently with water discharge (i.e.equilibrium) until extreme dischargethat causes excessive bank erosion andchannel widening. The channel is indisequilibrium with subsequent waterdischarge and requires a finite lag timeto regain equilibrium (by deposition).(b) Flow depth varies incongruentlywith water discharge over seasonalfloods (disequilibrium), but flow depthand water discharge averaged overseveral floods are both constant (inequilibrium). There are correlationsbetween width, depth, and dischargeover various time intervals, whether ornot equilibrium exists. Recognition of equilibrium and disequilibriumrequires observations at sufficientlysmall time intervals.
Fig. 1.15 Dominant discharge defined by the magnitudeand frequency of sediment transport associated with a range of water discharge (from Wolman and Miller 1960).
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16 C H A P T E R 1
in the supply of water and sediment to rivers and floodplains. Dynamic equilibrium may well beattained at any location, but the whole river systemwould be changing gradually and probably imper-ceptibly over time spans of decades to centuries.More details of these interactions between the geo-metry, flow, and sedimentary processes in alluvialsystems, and their controls, are discussed in sub-sequent chapters.
regarded as in equilibrium or disequilibrium de-pends on the time interval of measurement relativeto the lag time (Fig. 1.16). In order to establish this,it is necessary to have measurements of the depend-ent and independent variables at short intervals butover long periods of time, which are very difficultto obtain. Long-term (longer than 10,000 years),regional-scale changes in climate, tectonic activity,or relative sea level will probably result in changes
RAFC01 11/03/2009 17:13 Page 16
Reference material
Well known books on turbulent flows are those of Batchelor (1970), Bradshaw (1971), Cebeci andBradshaw (1977), Hinze (1975), Lamb (1966),Prandtl (1952), Rodi (1993), Schlichting (1979),Townsend (1976), and Tritton (1977). Referencebooks on open-channel flows include ASCE (1975),Chang (1988), Chow (1959), French (1985),Henderson (1966), Jansen et al. (1979), Nezu andNakagawa (1993), Raudkivi (1990), Van Rijn(1990), Yalin (1992), and Yalin and Ferreira da Silva(2001). Recent compilations of research papers on turbulent water flows include Ashworth et al.(1996), Carling and Dawson (1996), and Clifford et al. (1993). The information in this chapter drawsupon these sources of reference.
Definition of fluid motion
Consider a water flow in which the cross-sectionalarea varies downstream, but the discharge is con-stant in space and time (Fig. 2.1). Assuming that thefluid is incompressible (constant density), an expres-sion for the conservation of mass (and volume) is
Q = U1a1 = U2a2 (2.1a)
∂(Ua)/∂x = 0 (2.1b)
where x is the downstream direction. Equation 2.1is also known as the (one-dimensional) equation ofcontinuity. Flows that do not vary along stream in their velocity or cross-sectional area are called
Parameters and units
In order to understand the movement of water and sediment in geophysical systems like rivers and floodplains, it is necessary to describe the sys-tems precisely and numerically using well definedunits of measurement. The fundamental physicalquantities of concern are mass, length, and time.Quantities such as velocity, acceleration, force, andmomentum are composed of combinations of thesefundamental quantities. The preferred system ofunits of measurement of physical quantities is theSI system, in which the units of mass, length, andtime are kilograms, meters, and seconds, respect-ively. The units of force, pressure, power, andenergy are the Newton, Pascal, Watt, and Joule,respectively. Other systems of units of measure-ment that have been used are the CGS (centimeter,gram, second) and FPS (foot, pound, second) sys-tems. They should not be used today. Some physicalparameters have no units (e.g. a gradient), and arecalled dimensionless. Quantities that have magni-tude only are called scalars (e.g. mass, density),whereas those that have magnitude and directionare called vectors (e.g. velocity, force). When rep-resenting physical quantities in mathematical equa-tions, it is common to use standard symbols, as seenin Table 2.1.
Important physical properties of water includeits density, temperature, and viscosity. The para-meters used to describe the flow of water includedepth, cross-sectional area, velocity, discharge, bedshear stress, Reynolds number, and Froude num-ber. The units and standard symbols used to repres-ent these parameters are given in Table 2.1.
Fundamentals of water flow2
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18 C H A P T E R 2
laminar flow, where the magnitude and directionof the velocity vectors do not change with time attime scales of seconds or less. Flows in which watervelocity does not change in time are called steady,whereas those in which velocity varies with timeare called unsteady. Natural turbulent flows arestrictly unsteady, but this definition depends on thetime scale over which the flow velocity is measuredand averaged. For example, if the flow velocity isaveraged over a period of one hour (such that tur-bulent fluctuations in velocity are not considered),the flow may appear steady for periods of days.
Water motion can be shown graphically usingdifferent kinds of flow lines. One of the most import-ant is the streamline, an imaginary line parallel to the local mean flow direction. Streamlines areparallel in uniform flow, but not in non-uniformflows. Velocity increases as streamlines converge,and decreases as they diverge. An important stream-line, the skin-friction line, is that very close to thebounding surface of a water flow, i.e. the sedimentbed. This line shows the direction of the near-bedvelocity or bed shear stress. Another important typeof flow line is the path line. This is the trajectory ofa single moving fluid particle, as shown, for instance,by inserting a drop of neutrally buoyant dye in a flow.
Forces acting on stationary and moving fluids
Definition of forces
Force is defined as the rate of change of momen-tum, that is the product of mass and acceleration(units are Newtons, where N = kg m/s). Forces may
uniform flows. Velocity must increase as the waterflows into a narrower cross section (convective ac-celeration), and must decrease as the cross sectionexpands (convective deceleration). Flows wherevelocity and cross-sectional area vary along streamare called non-uniform flows. Most natural flowsare strictly non-uniform, but can be approximatedas uniform over certain spatial scales, simplifyingtheir analysis considerably. Non-uniform, spatiallydecelerating flows tend to be associated with deposi-tion, whereas spatially accelerating flows tend to beassociated with erosion, as shown in a later section.
The water flows of interest here are turbulent,whereby the magnitude and direction of the flow-velocity vectors at any point in the flow changewith time over time intervals of fractions of a sec-ond to seconds. Water particles travel in curved,swirling motions called turbulent eddies. This typeof flow contrasts with the straight-line flow paths of
Uniform flow
Non-uniform flow
Uniform flow
a2
U2
Q = U1a1 = U2a2
U1
a1
Fig. 2.1 Definition of uniform andnon-uniform flow.
Table 2.1 Flow parameters.
Parameter Units Symbol
Mass kg mDensity kg/m3 rMolecular viscosity kg/m/s mKinematic viscosity m2/s ν = m /rDepth m dCross-sectional area m2 aVelocity m/s u, v, w, U, V, WDischarge m3/s QBed shear stress N/m2 (Pa) τoShear velocity m/s U* =Reynolds number none ReFroude number none Fr
τo /r
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