River Morphology

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ISBN (13) : 978-81-224-2841-4

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Preface

Rivers have been the focus of human activity since the early civilizations. Even in modern times a large number of activities of the engineers such as water supply, irrigation, water quality control, power generation, flood control, river regulation, navigation and recreation are centered around rivers. Hence considerable interest has been evinced in the society about various aspects of rivers such as their formation, hydraulics and sediment transport, erosion and sedimentation, and effect of natural and human interferences on rivers.

Books have been written on rivers by geologists, geomorphologists, hydraulic engineers, hydrologists and geographers. Even though all of them have attempted to understand the behaviour of rivers that have carved their channels through the material deposited by them, the emphasis of each one of them is different from that of the other depending on his background, objectives of writing the book and the targeted readership. Yet fewer attempts seem to have been made to synthesize the contributions of these scientists into a coherent text that takes a balanced view of the subject of river morphology. To fill this gap is the objective in writing this book. Hence, the text covers history of fluvial hydraulics and geomorphology, drainage basin characteristics, erosion, fluvial morphology, hydraulics of alluvial and gravel-bed rivers, river bed and channel changes, fluvial palaeo hydrology, analytical and numerical modeling of fluvial processes, morphology of some Indian rivers, rivers and environment, and data needs for morphological studies. The text can be used for teaching a course on river morphology to graduate and undergraduate students in civil engineering and geology, and as a reference material for engineers engaged in planning and management of rivers.

My interest and involvement in the study of alluvial rivers and associated problems started with late Prof. E.W. Lane, and Profs. M.L. Albertson, D.B. Simons and E.V. Richardson of the Colorado State University, Fort Collins (U.S.A.). Over four decades of teaching and research in fluvial hydraulics, and association with colleagues at the University of Roorkee (now I.I.T. Roorkee) India, have helped me in looking at rivers in a much broader perspective. My association with Central Water and Power Research Station at Pune over the last decade further enriched my association with the rivers problems.

While preparing the manuscript of the book, valuable assistance has been rendered by my former colleagues Profs. K.G. Ranga Raju and U.C. Kothyari who have gone through the draft of the book and given valuable suggestions for its improvement; most of these have been incorporated. I am indebted to Profs. Rajiv Sinha of I.I.T. Kanpur, Brahma Parkash and Pradeep Kumar of I.I.T. Roorkee, and V.S. Kale of the University of Poona for making their publications available to me. I

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am thankful to Dr. Z.S. Tarapore and subsequent directors of CWPRS for allowing me to work at the research station for the past thirteen years. I am particularly thankful to M.S. Shitole, Joint Director, D.N. Deshmukh, J.D. Prayag, R.A. Oak, Hradaya Prakash, Pradeep Kumar, Mukund Deshpande, Y.N. Karanjikar and others whose assistance has been valuable in finalizing the manuscript of the book. Lastly, I am thankful to my wife Vidya and daughter Rashmi for the patience shown by them while I was preparing the manuscript.

December 2005 R. J. Garde

R-1 Sankul Condominium Near Deenanath Hospital Evandavane, Pune-411004

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a₁,a₂,a₃ coefficients/exponents

A area of cross-section, area of basin

A_b area at bankful stage, area corresponding to bed

A_f area of fan

A_u area of basin of order u

A_u mean area of basin of order u

A_w area of corresponding to wall

b exponent

B width of rectangular channel

BI Brice braiding index

C Chezy’s coefficient, suspended sediment concentration at a point, climate index

C_a reference suspended sediment concentration

C_D drag coefficient

C_L lift coefficient

C C_B, bed material concentration in ppm by wt., total load concentration

d_* dimensionless sediment size

d, d₅₀ median size of bed material, rain drop size

d₁₆, d₅₀, d_84, d₉₀ sediment size such that 16,50,84,90 percent material is finer than this size respectively

d_a arithmetic mean size

d_i any size fraction

d_max maximum size of sediment

D depth of flow (WD=A)

D_C depth at the centre

D_d drainage density

D_max maximum depth

E kinetic energy of storm

E_R entrenchment ratio

f Darcy-Weisbach resistance coefficient

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f ¢ friction factor corresponding to grain roughness f¢¢ friction factor corresponding to form roughness

f₁ Lacey’s silt factor

F stream frequency

F_b Blench’s bed factor

F_bo value of F_b when bed load is negligible

F_D drag force

F_e erosion factor

F_L lift force

Fr Froude number (= U/ gD)

F_s Blench’s side factor

g gravitational acceleration

G transport rate of any section

G_e equilibrium transport rate

G_¥ sediment transport rate at infinity

DG change in G

h_b head loss in bend

h_s saltation height

H average height at ripple or dunes, bars; relief

i index

I intensity of rain fall

I₃₀ maximum 30 minute intensity during storm

j index

k_s roughness parameter

K erodibility index, diffusion coefficient, wave number (= 2pD/L)

K_o theoretical diffusion coefficient

l length, distance, length of aggradation

L average length of ripples or dunes, length of stream up to drainage divide

l_s saltation length

L_u total length of streams of order u

Lu mean length of streams of order u

m exponent

M percent of silt-clay in perimeter, Kramer’s uniformity coefficient, dimensionless velocity bed or water wave

M_b meander belt

M_L meander length

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n index, exponent, Manning’s n

n_b Manning’s n with respect to bed

n_s Strickler’s n

N_u number of streams of order u

n_w Manning’s n with respect to wall

p_i per cent

P perimeter, annual rainfall

P_max average monthly maximum precipitation

q discharge per unit width

q_b bed load transport rate in weight/width

q_Bv volumetric bed load transport rate per unit width q_c critical water discharge per unit width

q_s suspended load transport rate per unit width

q_T total sediment transport rate in volume per unit width q_Tv total volumetric sediment transport rate per unit width

q_* dimensionless discharge (= q/ gd3)

q¢ lateral inflow per unit length on both sides

Q, Q_w water discharge

Q₁ = Q_b/d2 gd

Q₂ = Q_bS/d2 gd

Q₃ = Q_b/d2 gd S

Q_2.33 flood discharge of return period 2.33 years

Q_b bankful discharge

Q_B bed-load discharge

Q_ma mean annual discharge

Q_maf mean annual flood discharge

Q_r runoff rate per unit area

Q_S suspended load discharge

Q_T total sediment transport rate in weight or volume

r radius

r_c centre line radius of bend

r_i, r_o inner and outer radius of bend

R hydraulic radius, annul run off, run off parameter

R_A area ratio

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R_b¢, R_b¢¢ R_bwith respect to grain and form roughness respectively

R_e Reynolds number

R_L length ratio of Horton

R_m mean radius of meander bends

R_o*2 = Dg_sd3/r n_f 2

R_s bifurcation ratio for slope

R_W hydraulic radius corresponding to walls

R_* particle Reynolds number u_*d/v

S, S_o slope, bed slope, slope at x = o

S¢ slope corresponding to grain roughness

S¢¢ slope corresponding to form roughness

S_a annual erosion rate in cm (absolute)

S_f energy slope, fan slope

S_i sinuosity

S_W water surface slope

S average catchment slope

S_u average slope of segments of order u

SDR sediment delivery ratio

SE super-elevation

t_p time to peak

T number of years, also dimensionless excess shear {= ( 't -t₀_c)/t₀_c}

TE trap efficiency of reservoirs

u local velocity in x direction, order of stream ¢

u2 r.m.s. value of velocity function in x direction

u_d velocity at the top of particle

u_dcr critical velocity at particle level u_* shear velocity (= t r₀/ _f)

u*¢ shear velocity corresponding to grain roughness u*¢¢ shear velocity corresponding to form roughness

U average velocity

U_cr average critical velocity

U_g average velocity of particle moving as bed load

U_W average velocity of bed form or wave

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¢

v2 r.m.s. value of velocity fluctuations in y direction

v_q velocity in q direction

v_max maximum velocity at any vertical

v_r velocity in r direction

V_cp average velocity in the vertical

w local velocity in z direction, mean width of rib ¢

w2 r.m.s. value of velocity fluctuations in z direction

W average width (WD = A); weight of the particle

W_av average unit weight over T years

W_b bankful width

W_o unit weight value of sediment

W_s water surface width

x distance in x direction, a dimensionless coefficient

y distance from the wall

Y₁ hydraulic mean depth (=A/W_s)

z lateral distance from the origin,

Z actual slope of suspended sediment distribution curve, elevation of bed at given x and t; side slope of channel (Z hor.: 1 vert.)

Z_o theoretical value of suspended distribution curve; bed elevation at x = 0

a energy correction coefficient

a1,a2,a3 exponents

b es/em ratio of sediment transfer coefficient to the momentum transfer coefficient

gs, gf specific weights of sediment and fluid

d lag distance

d¢ thickness of laminar sub-layer

Dgs difference in specific weights of sediment and fluid

Îm momentum transfer coefficient

Îs sediment transfer coefficient

h dimensionless distance in the vertical

q angle

k Karman constant (actual)

k0 Karman constant (clear water)

l porosity, wave length

m dynamic viscosity of fluid

n kinematic viscosity of fluid

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rf mass density of fluid

rs mass density of sediment

s arithmetic standard deviation

sg geometric standard deviation

t shear stress

to average shear stress on the bed

t0c critical shear stress for sediment

tr, tq components of shear stress on the bed along r and q direction

t* dimensionless shear stress

t*c dimensionless critical shear stress

j angle of repose

jB, jS, jT dimensionless bed-load, suspended load and total load transport rate respectively

y = Dg_sd₃₅/t0

y¢ = Dg_sd₃₅/t0¢

w fall velocity

w0 fall velocity under ideal conditions

Subscripts and superscripts

Subscripts

* dimensionless quantity

c pertaining to critical condition

1, 2 pertaining to section 1, 2.

Superscripts

' corresponding to grain roughness

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Below is given meaning of some terms occurring in the text. (adapted from Easterbrook 1969)

Abrasion: wearing away of particle due to friction

Aggradation: rise in bed level of the stream over large length

Alluvium: unconsolidated sediment deposited by river; sediment deposited in river bed, floodplains,

lakes, alluvial fans etc.

Alluvial fan: cone shaped accumulation of debris or sediment deposited by the stream as it descends

from steep slope to a plain where the material deposits in the form of a fan

Avalanche: mass of snow sliding down the mountain Avulsion: shifting of a river course

Base level: the level below which a land surface cannot be reduced by running water Bed-load: material moved on or near the bed due to tractive force of the flow

Bed-forms: features developed on the bed of the river due to interaction between flowing water and

river bed sediments

Bed-load: material moved on or near the bed due to tractive force of the flow

Bed material load: material transported by the stream which has the stream bed or banks as its origin Beheaded stream: lower portion of the stream from which water has been diverted due to stream piracy Braided stream: a stream divided into a number of channels by island formation, which may join and

bifurcate again and again

Cirque: a deep steep walled recess in a mountain caused by erosion due to glaciers

Colluvium: unconsolidated deposits, usually at the foot hills or cliff, brought down by gravity Creep: slow down-slope movement of rock fragments and soil

Crevasse: a fissure formed in glacial ice due to various strains

Degradation: general lowering of stream bed over large length due to deficiency of sediment load as

compared to its sediment transport capacity

Delta: a triangular shaped alluvial deposit formed when a stream enters lake or sea

Diastrophism: the process or processes by which the crust of the earth’s surface is deformed

Glossary of Some Terms in

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Divide: a ridge between the streams; a line of separation between drainage basins Drainage basin: the area drained by a system of rivers

Eolian: deposits which are due to transporting action of the wind

Ephemeral stream: the stream which flows only in direct response to precipitation; it receives no water

from ground water

Escarpment: relatively steep slope or cliff separating gently sloping tracts Eustatic: pertaining to simultaneous world wide changes in sea level

Floodplain: relatively flat land strip on one or both sides of a stream built by sediment deposits during

flooding. It is sometimes called active flood plain

Fluvial: produced by the action of rivers

Geomorphic cycle: erosion cycle during which land forms are evolved which change from youth to

maturity to old, each of which is characterized by distinctive features

Geologic structure: it includes not only folding, faulting and uplift of the crust but also includes other

factors related to the physical and chemical characteristics of rocks, relative resistance to weathering, dip, strike, jointing, stratification etc.

Glacial drift: material transported by glaciers

Glacial trough: U-shaped valley produced by glacial erosion

Hanging valley: a tributary valley whose floor is higher than that of the main valley at the junction due

to degradation of the main valley

Incised meander or entrenched meander: a deep sinuous valley cut by a rejuvenated stream

Levee: natural or man-made embankment above the general level of floodplain which confines the

stream channel

Loess: fine sized particles deposited by wind

Mass-wasting: the down-slope movement of rock debris under the influence of gravity

Meander scar: crescent-shaped cut in a valley side made by lateral planation of the outer part of a

meander

Meandering stream: a stream that follows sinuous or crooked path

Misfit stream: a stream whose meanders are either too small or too large, compared to valley width Monadnock: a residual hill or mountain standing above a peneplain

Oxbow: a crescent-shaped lake formed in an abandoned river bend by a meander cutoff Palaeosol: a buried soil

Peneplain: a landscape of low relief formed by long continued erosion Periglacial: region beyond the margin of a glacier

Piracy: diversion of one stream by the other Pleistocene: the last Ice Age

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Regimes of flow: characteristics of bed and water surface produced by water flowing on a loose alluvial

bed

Rejuvenation: activation of erosion of a stream by uplift, climatic changes or change in base level Relief: the difference between high and low points of the land surface

Saltation load: material bouncing along the bed or moved directly or indirectly by the impact of

bouncing particles

Scour: local lowering of the bed of the stream usually due to presence of a hydraulic structure in the

stream

Suspended load: that part of the sediment load carried by the stream that is kept in suspension by

turbulent fluctuations

Talus: an accumulation of loose rock mass at the base of a cliff

Terrace: a flat or gently sloping surface bordered by an escarpment, it is composed of alluvium or bed

rock. It is flooded so rarely that it does not grow by sediment deposition

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1

C H A P T E R

Introduction

1.1 INTRODUCTION

A river carries water, sediment and solute from the drainage area to the sea and is thus of interest to hydraulic engineers, geomorphologists and sedimentologists. This is important to engineers because water is used for a variety of purposes by humanity; water courses are used as navigation channels, and also erosion, transportation and deposition of sediment cause a number of problems in the river and in the catchment that must be solved pragmatically. The direct effect of transportation of sediment and water from the geologist’s and geomorphologist’s point of view is that the structure and form of the river and adjoining areas are continually changed due to erosion and sedimentation. The rates of this change are variable. While geologists and geomorphologists are concerned about changes taking place in 103 to 106 years or more, engineers are concerned with changes in a river during a relatively short period, say 10–20 years to probably 50–100 years. These channel changes can be in the form of size, shape, composition of bed material, slope and plan-form. The engineer’s primary objective is to understand the basic mechanisms of erosion, transportation and deposition of sediment by flow in the river and develop qualitative and quantitative methods for prediction of river behaviour. The approach followed by engineers is called fluvial hydraulics or river dynamics and this approach has been developed during the past 200–300 years.

The other approach taken by geologists and geomorphologists is primarily qualitative even though, in recent years some quantitative methods have been used. Morphology is defined as the science of structure or form. Hence according to Worcester (1948) geomorphology is the science of landforms; it is the interpretive description of the relief features of the earth. It thus describes the surface of the lithosphere, explains its origin and interprets its history. To understand geomorphology one should know in detail the composition and structure of the rocks of the earth and the processes which act on it. Geomorphology recognises that the earth’s surface has changed in the past and is changing at present due to internal and external processes. The internal processes are those, which originate within the earth itself and include diastrophism and volcanism. External processes shaping the earth’s surface include running water, weathering, waves and shore currents, glaciers, avalanches, and plant, animal and human

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activities. It may be mentioned that most of the changes taking place in the earth’s surface are slow, even though a few may be catastrophic. Conventional texts in geomorphology would deal in detail about the internal and external processes which cause changes in the landform and then deal with the topography produced by streams in humid regions, by winds in arid and semiarid regions, glaciers, shore processes, ground water, volcanoes etc. Geomorphology is sometimes called physiography. This latter term, as used particularly in Europe, includes climatology, meteorology, oceanography and mathematical geography. Inasmuch as these are not addressed in this book, the term geomorphology is preferred to physiography.

The word “fluvial” means produced by river action. Hence fluvial morphology means the science of landforms as produced by river action. It can also be called river morphology; it is a branch of geomorphology and it would deal with form of the streams and adjoining areas as brought about by erosion, transportation and deposition of sediment by the running water. Both river morphology and geomorphology are descriptive sciences based mainly on careful observation and interpretation of natural phenomena. In the last century hydraulic engineers, hydrologists and geographers have also made contributions to river morphology.

1.2 SOME PROBLEMS IN RIVER MORPHOLOGY

Since the dawn of civilization, mankind has used rivers for supporting and sustaining life. This has been done by harnessing and controlling rivers for the benefit of people. In doing so the regime or stability of the river is invariably disturbed. In discussing these problems caused by disturbance in the stability of rivers, it is desirable to define what geomorphologists call a graded stream (Mackin 1948). A graded stream, poised stream, balanced stream or a stream in equilibrium is defined by Mackin as the one in which channel dimensions and slope are so adjusted over a period of time that it carries incoming sediment load and water without appreciable erosion or deposition.

In geologic time frame no river can be graded because of the natural tendency of land mass and rivers to erode gradually towards sea level. In a true dynamic sense also no river can be in true equilibrium since the discharge changes continuously. However, it may be mentioned that the changes related to geomorphic erosion are very slow and hence if one considers a time period of a few years to some decades, most of the streams can be considered to be in equilibrium, except a few rivers such as the Kosi, the Brahmaputra and the Yellow river which are truly unstable.

This equilibrium of the stream is disturbed by natural or man-made interferences in one or more of the conditions that maintain the equilibrium. A few of these instances are discussed below.

i. When a large dam is constructed across the river to store water for irrigation, water supply, flood control, generation of water power, navigation or recreation, the sediment transport capacity upstream of the dam is reduced thereby causing aggradation in the main reservoir and also in the tributaries on the upstream. This has many undesirable effects including depletion of reservoir capacity and flooding of the upstream areas. In some cases such as the Imperial dam on the Colorado river and Bhakra dam on the Sutlej in India sediment deposition has been found to occur 70-80 km upstream of the dam.

The water released from the reservoir is almost sediment free and hence it picks up sediment from the bed and banks of the stream causing degradation over long reaches of the stream. It

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may also lead to channel widening or change in the planform of the river. Needless to emphasise, degradation has many undesirable effects.

ii. It has long been recognized that water transport is comparatively much cheaper than road or rail transport and hence many streams such as the Danube, the Volga, the Rhine, the Mississippi, the Yangtze, the Ganga, the Brahmaputra and the Nile have been used for navigation since ancient times. Making the river navigable year around involves construction of dams, locks, channel widening, channel straightening and channel contraction using spurs or jetties and bank stabilization. It may also involve dredging and releasing additional water during low flows. These changes affect the stability of the river and hence executions of such changes need consideration from hydraulic and morphologic points of view.

iii. Barrages, canal head works, sediment excluders and extractors in irrigation canals are constructed for withdrawing relatively sediment free water for irrigation and water supply purposes. This disturbs the equilibrium of the stream causing aggradation in the downstream reaches. Similarly, aggradation takes place when rivers are used for dumping mining wastes hoping that the stream will safely carry the dumped material downstream. However, the stream can carry this excess load only with increased slope, which is achieved by aggradation. This happened, for example, on the Yuba river in California (U.S.A.) during gold-rush period in the latter half of the 19th century.

iv. Similarly, when sand and gravel are mined from the river bed to meet the ever increasing demand of the construction industry, the river downstream is found to degrade creating many problems in that reach. Such degradation in the river causes similar effects in the tributaries and sub-tributaries on the downstream side.

v. In order to have equitable distribution of water throughout the country large scale transfer of water from one basin to the other is either contemplated or is being executed. This is likely to disturb the equilibrium of the streams because the balance between water distribution and sediment load distribution is likely to be disturbed.

vi. Construction of flood control works such as embankments, reservoirs, channel straightening, meander cut-offs and channel improvement also tend to disturb the equilibrium of the stream and needs careful study.

vii. Large scale dredging carried out along the river for navigation purposes also disturbs the sediment balance and hence the stream equilibrium.

There are other less obvious factors that affect the stability of the stream, i.e., they affect channel slope, plan-form, cross-section, and alignment. Some of these are the following: viii. Change in drainage basin characteristics due to change in land use such as deforestation,

reforestation, agricultural land development, road construction, urbanization, and building of dams and check-dams disturb the river equilibrium by changing runoff and sediment load and trigger changes in the channel characteristics.

Ruhe (1971) has described the case where straightening of a channel had repercussions throughout the basin. In the Willow river (Crawford County, Iowa, USA) straightening led to channel deepening and widening. In addition, new deeply entrenched gullies extended for many kilometres up the tributary system and developed hill slides, disrupting agricultural lands and public roads.

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When urbanization takes place large-scale changes are induced in the catchment, its hydrological characteristics and the sediment yield. Because of breaking of new grounds, removing of vegetation, and use of construction equipment, the runoff and storm flow increases and hence land erosion is accelerated. As a result the sediment load of the streams is often increased dramatically. Wolman and Schick (1967) recorded up to 50,000 tons/km2/yr sediment load at one site, as compared to 80-200 tons/km2/yr under normal conditions.

After the urban area is developed, infiltration is reduced and ground water levels may be lowered. Untreated waste including sewage may be discharged into the streams causing pollution, which in turn, may be lethal for the aquatic life and detrimental to the use of the water in downstream reaches for drinking and recreational purposes. Due to urbanization there is an encroachment on the flood plain and hence channels are confined resulting in higher flood levels.

ix. Long term changes in the climate or hydrologic regime lead to significant changes in discharge, type of sediment load and its quality which lead to change in channel dimensions, change in river course and/or change in plan-form or meander characteristics. In extreme case the river can cease to exist.

x. Earthquakes and active tectonic movement such as subsidence or upheaval are found to influence the river stability.

Earthquake of magnitude greater than 4 on Richter scale can trigger a number of landslides through out the region and earthquake of magnitude 8 or larger is capable of triggering tens of thousands of land slides throughout the region that extends to more than 400 km from the fault (Wilson and Keefer 1985). Heavy rainfall following such landslides can bring enormous amount of material in the stream and can change its regime. Gee (1951) has reported the damage caused by 15 August 1950 earthquake in Brahmaputra valley that was of 8.6 intensity on Richter scale. He found that 75 percent of hills in 4 3000 km2 area were mutilated by landslides. Small and large rivers became blocked by material that fell in them and some even ceased to flow. Flood following the earthquake burst these dams and large quantity of sediment and rock material was carried downstream. The rivers Dibang and Subansiri twice changed their courses. The Brahmaputra got considerably silted up near Dibrugarh, and the bed level rose by a few metres; it took several years for the excess sediment to move downstream.

In engineering literature little attention has been paid to active neo-tectonic movement as a factor influencing river morphology. The rates of surficial deformation in certain region may vary from less than 10 mm/yr to more than 10 mm/yr for seismic deformation. When considered over a few decades such deformation can affect valley slope enough to affect the river morphology. If at a particular section along the river there is uplift there is aggradation on upstream and downstream side while in between there is degradation.

1.3 HISTORICAL DEVELOPMENTS IN FLUVIAL HYDRAULICS

(GARDE 1995)

Even though mankind has been living with sediment problems for the past several centuries, relatively little progress was made in our knowledge about sediment movement up to 16th century A.D. Earlier civilizations in the valleys of the Indus, the Tigris, the Euphrates, the Nile and the Yellow rivers were

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using canals for supplying water for irrigation through unlined channels. These canals either took off from a weir or they were inundation canals. The common problem with these canals was silting and hence frequent sediment removal was necessary. Locating the canals on the outer side of the bend of a stream to reduce sediment entry into canal seems to have been practised. The Chinese had made considerable progress in controlling large rivers, flood diversion, and similar other problems. The Romans had made progress in water supply and sewerage. The Greeks knew about the fall velocity of different sediment particles.

During 1600–1800 A.D. relatively more progress was made in understanding the physics of flow in open channels. The basic equations governing the flow, viz. the continuity equation and the equations of motion were developed during this period. d¢ Alembert (1717–1783) gave the differential equation for continuity of flow which was generalized by Leonard Euler (1707–1783). It was also during this period that the equations of motion, commonly known as Euler’s equations were established. The French engineer Chezy (1718–1798) gave the resistance equation U=C RS where U is the average velocity, R the hydraulic radius, S the channel slope and C is Chezy coefficient. Some basic ideas about river hydraulics were initiated by Dominico Guglielmini (1655–1710) and Paul Frizi; both wrote books on rivers. Du Buat (1734–1809) gave scouring velocities for materials of different sizes.

Much more progress was made during 19th century. Bouniceau, Grass, Lechalas, Suchier and Deacon conducted studies and critical velocities for different sized materials were recommended. Brahm showed that the critical velocity is proportional to (submerged particle weight)1/6. D.F. duBoys (1847-1924) gave a simple model for bed-load transport and reached the conclusion that q_B ~

to (to – toc) were qB is the rate of bed-load transport, and to and toc are the average bed shear stress and

critical shear stress for given size of bed material respectively. During this period two new resistance equations, which are now commonly used, were proposed. These are

Darcy-Weisbach equation: h_f = f L D U g 2 2 and Manning’s equation U = 1 2 3 1 2 nR S / / _...(1.1)

Here h_f is the head loss in length L of pipe diameter D, R is the hydraulic radius, S is the slope and f and n are friction factor and Manning’s roughness coefficient respectively. In the latter half of 19th century O. Fargue (1827–1910) who was closely associated with the developmental work of the river Garonne, gave what are popularly known as “Fargue’s rules” of river behaviour. Finally equations of motion for laminar flow and turbulent flow, commonly known as Navier-Stokes equations and Reynolds equations were developed. Similarly Sternberg gave his law for the reduction of sediment size along the river by the combined action of grinding and sorting. It was also at the fag end of 19th century that Kennedy proposed the method for design of stable channels based on canal data from India that was later modified by Lacey and others.

The first half of the twentieth century witnessed all round progress in fluvial hydraulics. G.K. Gilbert (1843–1918) performed extensive laboratory experiments and studied modes of sediment

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transport, and observed various bed-forms. Different investigators later used the hydraulic data collected by Gilbert to study resistance and sediment transport in channels. As regards channel resistance, Strickler analysed Swiss river data and for plane beds with coarse material proposed the equation

n = d1 6₅₀/ /21 ...(1.2)

where d₅₀ is expressed in metres. Exner tried to explain formation of bed undulations using the equations of motion. During this period a number of investigators conducted experiments in the laboratory and developed empirical equations for critical shear stress (i.e., shear stress at which sediment of a given size just starts moving) as a function of sediment size d and the difference in specific weight between sediment and water Dg_s. However, the credit for developing the rational criterion for incipient motion that is based on sound principles of fluid mechanics goes to A.F. Shields (1908–1974). Using sediments of different relative densities and sizes, he obtained a unique curve between t_oc/Dg_sd and t r_oc/ _f. /d n. Here t_oc is critical shear stress for sediment of size d and n is the kinematic viscosity of fluid. The term t r_oc/ _f = u_*c is known as critical shear velocity.

In a similar manner a number of empirical equations were developed by different investigators relating rate of bed-load transport to (t_o – t_oc), (q – q_c) or (U – U_c) where q is the discharge per unit width, U is the average velocity of flow, and quantities with subscript c refer to their values at incipient motion conditions. However, these equations were of limited use. In 1948 E. Meyer-Peter and R. Müller proposed an empirical equation for bed-load transport which is based on a wide range of sediment sizes and flow conditions and which is used often even today. A. Kalinske and H.A. Einstein developed bed-load equations using statistical nature of sediment movement.

Simultaneously progress was made in developing the theory of suspended sediment transport. The German meteorologist Schmidt gave the equation

woC s dC

dy

+ Î = 0 ...(1.3)

for distribution of suspended sediment in the vertical. Here C is the concentration of sediment of fall velocity w_o at a distance y from the bed and Î_s is sediment transfer coefficient. This equation was integrated independently by Rouse and by Ippen using equation for velocity distribution obtained by Karman and Prandtl, and the integrated form was verified by Vanoni and Ismail. Simultaneously, bed-load and suspended bed-load samplers were developed and tested in Europe and U.S.A., which greatly helped in collecting valuable data on sediment transport by rivers.

As regards the resistance to flow, Karman and Prandtl’s equations for velocity distribution for turbulent flow in pipes were adapted to open channel flow and velocity distribution laws for hydrodynamically smooth and rough surfaces were established. Einstein (1904–1963) suggested a method for separating grain resistance and form resistance of bed undulations while Einstein and Barbarossa proposed a method for predicting resistance to flow in alluvial streams.

Lastly on the basis of a large volume of data from stable mobile bed alluvial channels and building on the advances made by Kennedy, Lindley, King and others, G. Lacey (1887–1980) proposed a method of channel design according to which for given Q and bed material size, the channel depth, width and

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slope are uniquely fixed. Also data were collected about the geometry of alluvial rivers and equations have been developed to predict width and depth as a function of bankful discharge and sediment size.

The last half of the twentieth century has seen considerable progress in fluvial hydraulics. The characteristics of different bed-forms have been studied and criteria for their prediction established. A number of equations have been developed to predict the resistance and sediment transport rates of uniform and non-uniform sediments.

Kennedy, Engelund, Hansen and Fredsoe, have studied stability of mobile bed subjected to small disturbances to explain the formation of dunes, antidunes and plane bed. Similarly, Hansen, Callander, Parker, Hayaski and Ozaki, Engelund and Skovgaard and others have carried out stability analysis to determine the conditions under which streams meander.

And finally, with the availability of high speed computers the equations of motion in alluvial streams have been solved to develop methods of prediction of bed levels in unsteady non-uniform flows such as silting of reservoirs, aggradation caused by increase in sediment load or decrease in discharge and degradation caused by increase in flow. Simultaneously field data are being collected to test various softwares developed for solving such problems. Also experimental data are being collected to study some basic problems such as armouring and pickup function.

There has also seen considerable activity in understanding the hydraulics of gravel-bed rivers, their hydraulic geometry and sediment transport and scour.

1.4 HISTORICAL DEVELOPMENTS IN GEOMORPHOLOGY

(Tinkler, 1985)

From the Greek writings one can extract three basic principles regarding the rational investigations of landforms; these are (i) the concept of infinite time, (ii) reality of denudation i.e., loss of mass or material from the landscape and (iii) acceptance of the principle of conservation of mass. Herodotus (485– 425 B.C.) recognized the importance of yearly increments of silt and clay deposition by the Nile. He also anticipated the idea of changing sea levels that is of great significance in geomorphology. Aristotle (384 – 322 B.C.) thought that rainfall might produce a temporary torrent, but doubted that it could maintain flow in a river. Strabo (54 B.C.–25 A.D.) noted examples of local sinking and rise of the land. He also mentioned about the effect of ebbs and tides on the growth of delta. Both Strabo and Seneca (B.C.– 65 A.D.) recognized the role played by volcanic activity and earthquakes on the landforms.

During the many centuries that followed the decline of the Roman Empire, there was little or no progress of scientific thought in Europe; however, some learning process continued in Arabia. During 941–982 A.D. there is reference to erosion and transportation of sediment by the streams and wind and weathering in the four-volume tretise on discourses of the Brothers of Purity.

Little progress was made in Europe between the first century and beginning of the 16th century. During the fifteenth, sixteenth and seventeenth centuries landforms were explained by the philosophy of catastrophism, according to which the features of the earth were created as a result of violent catastrophic actions. Leonardo da Vinci (1452–1519 A.D.) had very advanced ideas about geologic thinking for his time. He recognized that streams cut the valleys and that the streams carried sediment from one part of the earth and deposited at other places. The Frenchman Baffon (1707–1788) thought

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that erosion by streams would eventually reduce the land to the sea level. He was also the first to suggest that the age of the earth was not to be measured in terms of a few thousand years. Another Frenchman Guetthard (1715– 1786) also discussed about the degradation of mountains by streams and emphasized that not all the material removed by the stream would immediately be carried to the sea but a part would also deposit on the flood plains. The Swiss De Saussure (1740– 1799) recognized the ability of glaciers to carry out erosional work.

James Hutton (1726– 1797) who entered the university at the age of 14 to study humanities was more interested in chemistry and geology. Finally, he was educated as a physician. However, instead of practising medicine he gradually switched over to agriculture and travelled through Southern England during which time he developed his interest in geology. Hutton is known for propounding the concept that “the present is the key to the past”, thus establishing the doctrine of uniformitarianism. His writings clearly express the concept of a river system and its geomorphic significance. Some other important concepts introduced by Hutton are:

i. A vast portion of the present rocks is composed of bodies, animals, vegetables and minerals of more ancient formation.

ii. All present rocks are going to decay and their material going to deposit in the sea. iii. The morphological process requires indefinitely long geological time.

iv. There is a conceptual possibility of relative change between land and sea levels leading to upheaval.

Hutton’s friend John Playfair (1748–1819) who was Professor of Mathematics and Philosophy at Edinburgh was in contact with Hutton, Joseph Black, and Adam Smith. After the death of Hutton in 1797 Playfair published “Illustrations of Huttonian Theory of Earth” in 1802 for he had realized how confused and repetitive were the writings of Hutton; Playfair’s work was smaller, cheaper, and precise with great clarity and beauty of expression. Playfair presented Hutton’s ideas and conclusions clearly. Playfair also proclaimed the ability of glaciers to erode their valleys deeply.

Sir Charles Lyell (1797–1875) wrote a number of textbooks to spread the geologic knowledge. He was somewhat doubtful about the immense ability of running water to carve the valleys. It was during 19th century that there was recognition of an ice age during which much of North Europe was covered with ice sheets. Playfair had sensed the possibility of large boulders being transported by glaciers. Louis Agassiz (1807-1873), Venetz of Switzerland in 1821, Bernardi of Germany in 1832 and Jean de Charpentier in 1836 supported this concept of glaciation in Europe. In the later part of 19th century books were written to describe the principles of landform development. These were by Peschel, Richthofen and A. Penck.

The basic foundation of geomorphology was laid in America in the later half of 19th century by Major J.W. Powell (1834-1902), G.K. Gilbert (1843-1918) and C.E. Dutton (1841-1912). Powell’s studies of Unita Mountains emphasized the importance of geologic structure in the classification of landforms. He also introduced the concept of the limiting level to which the land-level would reduce and called it the base level. Col. George Greenwood earlier used this concept in Europe in 1857. Powell recognized that the process of erosion, if carried undisturbed on land, would reduce it eventually to a level little above sea level. He was able to correctly interpret that various unconformities in rocks in the Grand Canyon, Colorado (U.S.A.) correspond to ancient periods of land erosion.

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G.K. Gilbert’s contribution in experimental work carried out in California has already been described. He was a pioneer in studying hydraulic mining and its effect on stream morphology. His other contributions include recognizing the importance of lateral planation by streams in the development of valleys and his explanation of Henry Mountains of Utah (U.S.A.) as the result of erosion of intrusive bodies. Dutton gave a penetrating analysis of individual landforms. Gilbert and Dutton are given credit for initiating the concept of erosional unloading of the earth’s crest technically known as isostasy. W.M. Davis (1850–1934) had greater impact on the development of geomorphology than any one else. Of all the contributions to geomorphology, Davis is remembered for introducing the concept of geomorphic cycle. According to this concept in the evolution of landscapes there is a systematic sequence that enables one to recognize the stages of development of landforms. This sequence is called by him as youth, maturity and old age. These landsforms are explainable in terms of differences in geologic structure, geomorphic processes and the stage of development. In the development of the idea of geomorphic cycle Davis had assumed that there is a relatively rapid uplift due to diastrophism which is followed by a relatively long period of standstill which permits the erosion cycle to run its course. W. Penck and his followers questioned Davis’ idea of geomorphic cycle during 1920’s and 30’s. In spite of these objections the Davisian geomorphic cycle is still considered a reasonable model primarily because of the absence of a plausible reasonable alternative.

Recent Contributions

Since the end of the Second World War a large number of aspects about river morphology have been or are being studied. These include channel geometry, mathematical modelling, effect of neo-tectonics and mass movements on channels, fluvial systems, experimental fluvial morphology, palaeo climatic and palaeo hydrologic effects and gravel-bed rivers. Scientists working at U.S. Geological Survey have studied short-term morphology of river channels; they include W.B. Langbein, L.B. Leopold and M.G. Wolman. S.A. Schumm, M.P. Mosley and W.E. Weaver studied fluvial systems and performed experiments in the laboratory to study river morphology. J.R.L. Allen from U.K. has done extensive work on the character and classification of bed forms and sedimentary structures with respect to deltas, meanders and floodplains. Many investigators including K.J. Gregory, J. Lewin, V.R. Baker and L. Starkel have studied Palaeo climatic and palaeo hydrologic effects on river channels. Geographers in U.K. have given impetus to the research in gravel-bed rivers and this work is now continued in Canada, U.S.A. and New Zealand.

1.5 SCOPE

The text takes a balanced view of the contributions made by engineers, geologists, geomorphologists and geographers to fluvial morphology.

Introduction, morphologic problems, and history of fluvial hydraulics and geomorphology are discussed in the first chapter. The second chapter is devoted to the discussion about drainage basin and channel networks. The third chapter deals with erosion from the catchment in humid regions where erosion due to water action predominates. The fourth chapter presents basic concepts from geomorphology such as geomorphic cycle, stages of landform and rivers and discusses the erosional and depositional features developed by rivers. Chapter five deals with the hydraulics of alluvial rivers while chapter six deals with the hydraulic geometry and plan-forms in alluvial streams. The seventh chapter

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deals with gravel-bed rivers. Chapter eight deals with fluvial paleo hydrology while chapters nine and ten are devoted to changes in bed level and plan-form. Chapters eleven and twelve deal with analytical and numerical models used in studying the transient flows in rivers. Chapter thirteen is devoted to the discussion of morphology of the Kosi and the Brahmaputra rivers in India. Chapter fourteen deals with rivers and environment, and the fifteenth chapter dicusses the data requirements for morphological studies.

References

Garde, R.J. (1995) History of Fluvial Hydraulics. New Age International (P) Ltd., Publishers, New Delhi. Gee, G.P. (1951) The Assam Earthquake of 1950. Jour. Bombay Natural History Society, Vol. 50, pp. 629–638. Mackin, J.H. (1948) Concept of the Graded River. Bul. Geological Society of America, Vol. 59, pp. 463–512. Ouchi, S. (1985) Response of Alluvial Rivers to Slow Active Tectonic Movement. Bul. Geological Society of

America, Vol. 96, Apr, pp. 504–513.

Ruhe, R.V. (1971) Stream Region and Man’s Manipulation - in Environmental Geomorphology (Ed. D.R. Coates). Publication in Geomorphology, State University of New York, Binghamton, U.S.A.

Thornbury, W.D. (1969) Principles of Geomorphology. John Wiley and Sons Inc., New York, 2nd Ed. Chapter 1. Tinkler, K.J. (1985) A Short History of Geomorphology. Croom Helm (P) Ltd., U.K., 1st Edition.

Wilson, R.C. and Keefer, D.K. (1985) Predicting Areal Limits of Earthquake–Induced Land Sliding. In Evaluating Earthquake Hazards in the Los Angeles Region (Ed. Ziony, J.I.). USGS Professional Paper 1360, pp 317–345 Wolman, M.G. and Schick A.P. (1967) Effects of Construction on Fluvial Sediment Urban and Sub-urban Areas of

Maryland. Water Resources Research, Vol. 3, pp. 451–464.

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2

C H A P T E R

Drainage Basins and Channel

Networks

2.1 INTRODUCTION

Drainage basin is an area drained by the stream and its tributaries. It is bounded by a divide. Drainage basin is also sometimes called watershed or catchment area. It can be thought of as an open system that receives energy or input from the atmosphere and sun over the basin and loses energy or output through the water and sediment mainly through the basin mouth or outlet (Strahler 1964). The present form of any drainage basin is the result of the processes that have operated in the past on the material available locally. These processes at the basin level are the precipitation and runoff, sediment yield and rate of erosion. However, these processes in the past may not be the same in their relative importance as the ones that operate in the drainage basin at present. The importance of studying the drainage basin characteristics derives from the need of studying forms of channels and channel networks as they are related to physical characteristics of the drainage basin, and also from the need of relating physical characteristics of the basin to flow characteristics and sediment yield.

The drainage pattern is the arrangement and length of small, medium and large streams in the basin. Two aspects of the development of drainage basins have been studied. In earlier years, the drainage pattern development in relation to the structure and lithology of the underlying rocks was studied. This was essentially qualitative in nature. In the recent times drainage patterns have been treated more as geometric patterns and attempts have been made to derive relationships for them (Horton 1945). The drainage pattern acquired at any time is the result of the combined effect of lithology, precipitation pattern and climate, and their variation with respect to space and time. Since the sediment eroded from the drainage basin along with water causing erosion, flows through the tributaries and the main stream, the drainage net is intimately associated with the hydraulic geometry of the stream channels and their longitudinal profile. As suggested by Schumm (1977) the drainage basin is primarily a sediment production area where climate, diastrophism and land use act as the upstream controls.

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Glock (1932) assumed that the drainage pattern is initiated on an essentially smooth plane due to the uplift. According to him the drainage pattern goes through the following developmental stages: initiation, elongation (headward growth of the main stream), elaboration (filling in of the previously undissected areas by small tributaries), maximum extension (the maximum development of the drainage pattern) and abstraction (loss of tributaries as the elevation is reduced through time). This sequence takes a long time in geologic sense. During this sequence the sediment yield first increases to a maximum and then decreases. However, such erosional development cannot be observed. Hence several drainage basins in different stages of development are studied at a given time. Thus what is to be observed in time domain is studied in space domain assuming the process to be ergodic.

The topographic characteristics of the drainage basin can be visualised either for the basin or for the drainage network. The most important topographic characteristics for the basin are its area, length, shape and relief. The corresponding characteristics for the drainage network are area tributary to stream channels, drainage density, stream length, network shape or drainage pattern, and network relief.

2.2 DRAINAGE PATTERNS AND TEXTURE

Drainage pattern is the general arrangement of channels in a drainage basin. Drainage patterns reflect the influence of such factors as initial slope, inequalities in rock hardness, structural controls, recent diastrophism, and recent geomorphic and geologic history of the drainage basin. Because drainage patterns are influenced by many factors, they are quite useful in the interpretation of geomorphic features and their study represents one of the more practical approaches to the understanding of the structural and lithologic controls on landform evolution. Looking at them in the most general manner, one can classify drainage patterns into the following categories:

Figure 2.1 (a) shows dendritic or branch-like pattern that is probably the most common drainage pattern. This is characterised by irregular branching of tributary streams in many directions and at almost any angle usually less than 90o. Dendritic patterns develop on rocks of uniform resistance and indicate a complete lack of structural control. This pattern is more likely to be found on nearly horizontal sedimentary rocks or on areas of massive igneous rocks. They may also be seen on complex metamorphosed rocks.

Trellised or lattice-like pattern shown in Fig. 2.1 (b) displays a system of sub-parallel streams, usually along the strike of the rock formations or between parallel or nearly parallel topographic features recently deposited by wind or ice.

Radial pattern shown in Fig. 2.1 (c) is usually found on the flanks of domes or volcanoes and various other types of isolated conical and sub conical hills.

Parallel drainage pattern shown in Fig. 2.1 (d) is usually found in regions of pronounced slope or structural controls that lead to regular spacing of parallel or near parallel streams.

Rectangular drainage pattern shown in Fig. 2.1 (e) has the main stream and its tributaries displaying right-angled bends. This is common in areas where joints and faults intersect at right angle. The streams are thus adjusted to the underlying structure.

Deranged drainage pattern, see Fig. 2.1 (f) indicates a complete lack of structural or bed rock control. Here the preglacial drainage has been affected by glaciation and new drainage has not had enough time to develop any significant degree of integration. It is marked by irregular stream courses that flow into and out of lakes and swamps and have only a few short tributaries.

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Centripetal pattern shown in Fig. 2.1 (g) is encountered locally. Here the drainage lines converge into a central depression. These are found on sinkholes, craters and other basin like depressions.

Highly violent pattern shown in Fig. 2.1 (h) is characteristic of areas of complex geology.

The complex drainage patterns observed in nature are a result of differing lithology, regional slopes, presence of joints and faults, and geologic activities such as glaciation, volcanism and limestone solution. Zernitz (1932), Howard (1967) and Thornbury (1969) have given full description of commonly occurring drainage patterns and their interpretation.

Drainage Texture

An important geomorphic concept about the drainage pattern is the drainage texture by which one means relative spacing of drainage lines. Drainage texture is commonly expressed as fine, medium or coarse. Climate affects the drainage texture both directly and indirectly. The amount and type of precipitation influence directly the quantity and character of runoff. In areas where the precipitation

Fig. 2.1 Various drainage pattern

b) Trellis or lattice like pattern a) Dendritic pattern

f) Deranged pattern e) Rectangular pattern

d) Parallel pattern c) Radial or concentric pattern

h) Highly violent pattern g) Centripetal pattern

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occurs primarily in the form of thunder showers, a larger percentage of rainfall will result in runoff immediately and hence, other factors remaining the same, there will be more surface drainage lines. The climate affects the drainage texture indirectly by its control on the amount and types of vegetation present which, in turn, influences the amount and rate of surface runoff. With similar conditions of lithology and geologic structure, semiarid regions have finer drainage structure than humid regions, even though major streams may be more widely spaced in semiarid than in humid regions. It is also noticed that drainage lines are more numerous over impermeable materials than over permeable areas. The initial relief also affects drainage structure; drainage lines develop in larger number upon an irregular surface than on the one that lacks conspicuous relief.

Bad-land topography promotes fine drainage structure. Impermeable clays and shales, sparse vegetation and existence of thundershowers are responsible for very fine drainage structure. Coarse drainage structure is in particular found on sand and gravel outwash plains. Gravel plains have fewer drainage lines on them than adjacent till plains underlain by relatively impermeable clay till.

The drainage structure can be qualitatively related to a parameter known as drainage density (see section 2.9) first defined by Horton (1932) as total length of streams per unit of drainage area. Drainage density varies from about 0.93 km/km2 on steep impervious areas to nearly zero for highly permeable basins. It varies from about 2.0 to 0.60 km/km2 in humid regions. As indicated by Smith (1950) and Strahler (1957), coarse drainage structure corresponds to drainage density less than 5.0 km/km2, medium drainage structure to drainage density value between 5 and 15 km/km2 and fine drainage structure to drainage density between 15 and 150 km/km2.

2.3 STREAM ORDER

A stream net or river net is the interrelated drainage pattern formed by a set of streams in a certain area. A junction is the point where two channels meet. A link is any unbroken stretch of the river between two junctions; this is then known as the interior link. If it is between the source and first junction, it is called the exterior link.

Quantitative analysis of the stream network really started with Horton (1945). This analysis has been developed to facilitate comparison between different drainage basins, to help obtain relations between various aspects of drainage patterns, and to define certain useful properties of drainage basins in significant terms.

According to Horton (1945) the main stream in the river net should be denoted by the same order number all the way from its mouth to its headwaters. Thus, at every junction where the order changes, one of the lower order streams is renumbered to the higher order and the process repeated. Thus in Fig. 2.2 (a) the main stream is shown as the fourth order stream right back to its source. The third order streams which are tributary to the fourth order stream are also extended back to their farthest source as the third order streams and so on. The streams joining the third order stream are second order stream and they can be extended backward. It can be immediately realized that a certain amount of subjectivity is involved in the ordering of streams according to Horton’s method.

In Strahler’s (1952) system, see Fig. 2.2 (b), the headwater streams that receive no tributary are called first order streams. Two first order streams unite to give a second order stream. Two second order streams unite to give a third order stream and so on. When two streams of different order unite, the combined stream retains the order of the higher order stream. A combination of two streams of lower

River Morphology - Garde - India

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Preface

Glossary of Some Terms in