Sorting out river channel The Author(s) 2010 patterns · 80115, 3508 TC Utrecht, The Netherlands...

Article

Sorting out river channelpatterns

Maarten G. KleinhansUtrecht University, The Netherlands

AbstractRivers self-organize their pattern/planform through feedbacks between bars, channels, floodplain andvegetation, which emerge as a result of the basic spatial sorting process of wash load sediment and bedsediment. The balance between floodplain formation and destruction determines the width and pattern ofchannels. Floodplain structure affects the style and rate of channel avulsion once aggradation takes place.Downstream fining of bed sediment and the sediment balance of fines in the pores of the bed sedimentprovide the ‘template’ or sediment boundary conditions, from which sorting at smaller scales leads to theformation of distinct channel patterns. Bar patterns provide the template of bank erosion and formationas well as the dynamics of the channel network through bifurcation destabilization. However, so far we havebeen unable to obtain dynamic meandering in laboratory experiments and in physics-based models that canalso produce braiding, which reflects our lack of understanding of what causes the different river patterns.

Keywordsbank erosion, bar pattern, floodplain sedimentation, riparian vegetation, river channel pattern

I Introduction

This review is concerned with river morphology

at a scale of, say, tens of bar or meander lengths,

at which the channel pattern is the most striking

characteristic. The storyline of this paper is the

effect of various sorting processes on channel

patterns that emerge as channels and floodplains

form, erode and reform. Rivers sort the sedi-

ments that they receive from their hinterlands

at sorting scales from particle size to river

length. From mountains to the sea the bed sedi-

ment may fine from cobbles to mud. Across the

river valley mud is found in floodplains and sand

and gravel in the channels. Styles of sorting out

sediments differ between channel patterns, but

channel pattern strongly depends on the flood-

plain sediment and vegetation properties as well.

This is partly linked to bed sediment sorting

through the transition of fines from wash load

to bed material load. From bars to channels and

through bends the bed sediment may vary

horizontally from sand to gravel, which affects

their morphodynamics and the steering of flow

against banks by the bars. In short, morphologi-

cal and sedimentological (sorting) patterns of

rivers emerge as the result of interactions and

feedbacks between the smallest turbulence and

particle-scale processes up to reach-scale flow

dynamics, sedimentation, erosion and vegeta-

tion patterns.

The aim of this review is to unravel connections

between various subjects related to river channel

patterns, including bar theory, bank erosion,

Corresponding author:Faculty of Geosciences, Utrecht University, PO Box80115, 3508 TC Utrecht, The NetherlandsEmail: [email protected]

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floodplain sedimentation, and interactions with

vegetation. Interactions between morphology,

sorting of fines and coarse sediment, as well as

vegetation, are collected into a grand picture.

Whether correct or not, I will argue that the time

is ripe for making such connections quantitatively

in integrative experiments and physics-based

numerical models, which are already starting to

accelerate our progress in the understanding of

channel patterns. With the storyline of sorting

I stress the intimate relation between channel and

floodplain, and I will argue that this relation is the

outstanding problem to be solved for better

understanding of the morphogenesis of rivers.

As a necessary prelude to the core of this paper,

I will argue how and why combining field study,

experiments and numerical modelling will lead

to rapid progress in the coming decade. The next

section is therefore devoted to basically different

logical explanation structures of Quaternary

geologists, sedimentologists, geomorphologists,

engineers and so on.

The main part of this paper, section III, is

devoted to channels and channel patterns and

how they emerge as the result of floodplain

dynamics and channel dynamics and the basic

size-sorting of sediment that may lead to this

division. Furthermore, a strong link between

the fractional bed sediment balance and the

floodplain sediment balance and hence channel

pattern is identified.

II Prelude: Three pillars of theEarth sciences

Quaternary geologists, fluvial sedimentologists,

fluvial geomorphologists, civil engineers and

so on use three very different approaches that

have their own aims, weaknesses and strengths.

The basic logical explanation structure of

Quaternary geology, for instance the reconstruc-

tion of the avulsion history of the Rhine-Meuse

delta (Berendsen and Stouthamer, 2000), is

completely different from the logical structure

of physics-based modelling of river bifurcations

(Kleinhans et al., 2008), and from systematic

experimentation on laboratory-scale deltas and

fans (Bryant et al., 1995; Hoyal and Sheets,

2009), although they all refer to exactly the same

natural phenomenon. Weaknesses of both logi-

cal structures and scope for progress will be dis-

cussed in the next section. The research methods

are also very different: fieldwork, modelling or

experiments. How and why these methods are

fruitfully combined is explored in the following

section.

I hope this paper will clear up common blind

spots and misconceptions of workers in different

fields and promote mutual understanding

and collaboration by providing a vocabulary.

No straw man is slain here: misunderstanding

between Quaternary geology and geomorphol-

ogy has been reported (eg, Baker, 1996; Rhoads

and Thorn, 1996) and nothing short of fear of

being overwhelmed with facts or equations has

been experienced on both sides. As further

evidence, many papers have been written about

the need for interdisciplinary approaches to

prediction of Earth surface dynamics (eg, Paola

et al., 2006), and the need for more quantitative

physics-based work in the predominantly

descriptive geographical sciences (Church,

2005). Finally, there remain many opportunities

for Earth scientists to collaborate with geophysi-

cists and civil engineers all over the world.

1 Earth scientists as detectives ... ‘Purededuction, my dear Watson’?

When asked what basic logical explanation

structure is used in natural science, many scien-

tists will answer ‘deduction and induction’. But

this is incomplete. There are three logic compo-

nents in our explanations: causes, effects and

laws. Thus there are three ways to derive

one component from the other two (Figure 1;

Kleinhans et al., 2010a).

a Deduction. For deduction, the initial condi-

tions (causes) are combined with laws of nature

288 Progress in Physical Geography 34(3)



to predict the effects. This is what happens in

analytical solutions for linear stability analyses

and physics- or chemistry-based modelling

(except ‘reduced-complexity’ modelling; see

later discussion). Although deduction is a solid

form of logic, its Achilles’ heels are the choice

of relevant laws included in the model, the

inclusion of generalizations rather than laws,

numerical issues, and the initial and boundary

conditions for the model which must be based

on measurements that may be incomplete or con-

tain errors (Oreskes et al., 1994). Deduction is

also what happens in 1:1 and scale experiments.

The limitation of experiments differs from that of

models (illustrating their complementary bene-

fit). The materials, and the implicit laws that

come with it, are in a sense more real than in

models (Morgan, 2003), but scale effects may

Figure 1. The three logical explanation structures based on causes, effects and laws, two of which arenecessary to arrive at the third. Each has its own weakness (see text).Source: Kleinhans et al. (2010a)

Kleinhans 289



limit the validity. This limit can be explored by

proper non-dimensional analysis of relevant

parameters as well as modelling on experimental

and real scales (Peakall et al., 1996).

b Induction. Induction leads to (statistical)

generalizations based on both causes and

effects. Empirical hydraulic geometry relations

between some measure of flow discharge and

cross-sectional properties of natural river

channels or stable canals are obvious examples

(Ferguson, 1987). Also experimental relations

between a measure of flow strength and

sediment transport rate fall in this category,

although relations of similar form have been

derived from physics with some rigour. Further-

more, generalizations about avulsion based on

field data of (sub)recent fluvial systems are

inductive (Aslan et al., 2005; Stouthamer and

Berendsen, 2007).

The problems of induction are well known:

the validity range of empirical relations is deter-

mined by the range and bias of the data included,

and the amount of data is obviously never large

enough to create a universally valid generaliza-

tion – that is, law. Nevertheless empirical

relations somehow contain knowledge about

reality and have shown the way to underlying

mechanisms in the past.

c Abduction. In abductive inference, final

conditions, facts and so on are (often implicitly)

combined with laws or generalizations of

nature, to arrive at the best of a limited number

of hypotheses that explain the observations. For

example, crime scene investigations yield

several clues that, combined with ‘laws’ of

human behaviour and biology (blood and DNA

evidence), all converge to the best explanation

that Moriarty was the murderer. Pure deduc-

tion? No, Sherlock, this is an example of abduc-

tion, which Earth scientists commonly employ

too (for background and historical references,

see Baker, 1996; Kleinhans et al., 2005).

For instance, present-day landforms and

conditions, in short, effects, are (often implicitly)

combined with laws of nature and geoscientific

generalizations – that is, major premises – to

infer the best from a limited number of hypoth-

eses that explain the observations, such as past

conditions. Thus, the avulsion history of the

Rhine delta was explained by a time-varying

combination of sea-level rise, tectonics, climate

change and autogenic processes (Stouthamer and

Berendsen, 2000). Also the inference of

formative conditions and processes from similar

rivers as modern analogues is abductive.

The major limitation of abduction is that one

cannot be certain that all possible hypotheses,

including the correct one, have been conceived.

The right hypothesis might be one that no one

thought of. Furthermore the geoscientific ‘laws’

of nature are often tacit so that it is far from pro-

ven that the inference to the best explanation

does not contradict the laws of nature. For

instance, a tacit law could be that climate change

leads to a transition from braided river to mean-

dering river, but as the precise reasons remain

unclear this is far from a universal law.

d Mature explanation structures. Deduction,

induction and abduction are used complementa-

rily to great benefit to answer different questions.

For instance, channel pattern discriminators pro-

vide empirical knowledge that points towards

underlying physical causes. Abductive infer-

ences to historical causes use generalizations or

laws. The latter are tested with (scale) experi-

ments or physics-based modelling to confirm that

the inferred initial conditions indeed lead to the

observed phenomena. Models produce diagnos-

tic features that were hitherto not recognized or

misinterpreted from images. In general, Earth

scientific explanations appear to have an abduc-

tive structure with many inductive and deductive

elements in it (Kleinhans et al., 2005).

Note that various other explanation structures

have been ignored, notably functional and teleo-

logical explanation. Functional explanation




refers to the laws of past evolution of life. For

instance, certain riparian reeds are flexible as

they would otherwise break in the current. This

trait of the species evolved in the past from

mutations, was transmitted and lived on through

genes, because it increased the chance of sur-

vival for the individuals that bear the trait. Tele-

ological explanation refers to future-directed

actions of man. For instance, the height of dikes

along a river is explained by the fact that they

were built with the intention to mitigate future

flooding risk.

Two things became clear in the discussion

above. First, all three types of logical explana-

tion commonly used in the Earth sciences have

serious weaknesses; none is better than the other.

Second, observations are somehow combined

with experiments and modelling in natural sci-

ence in general and by river researchers in spe-

cific. Why?

2 Complementarity of field data,experimentation and modelling

Observations (including satellite imagery,

measurements and so on) and experiments and

models represent nature in different ways and

have different weaknesses and strengths. The

following discussion aims to provide a founda-

tion for the truism that observation of nature,

experimentation and modelling are complemen-

tary and should be combined where possible. By

understanding why and how they are comple-

mentary, their application to the problem of river

patterns will become more efficient and focused.

a The story of an Earth scientist’s life: Fieldworkand underdetermination. Earth scientific the-

ories and hypotheses, ranging from mechanisti-

cal theories to explanatory reconstructions of

past conditions, usually are underdetermined

by the available evidence. That is, there is insuf-

ficient available evidence to choose one theory

over its rivals. Typical examples of underdeter-

mination problems are:

� Measurement techniques may disturb the

observed processes.

� The timescale of human observation is

(much) shorter than that of the phenomenon

under study.

� Many processes and phenomena cannot

(yet) be observed directly or even indirectly.

Erosional and sedimentary landforms of the

past may have been obliterated by later ero-

sion, and phenomena may not be accessible

in practice.

� The relatively simple laws of physics can

seldom be applied directly to the initial con-

ditions to check whether they explain the

observations, because they may be applied

in models in many different ways that pro-

vide conflicting answers.

� Many processes are intrinsically random or

chaotic, and may be very sensitive to initial

conditions. This means that inference to the

best explanation – that is, the most plausible

combination of formative processes and ini-

tial conditions – may be impossible.

Practising Earth scientists very often face situa-

tions in which theories are underdetermined by

the available evidence, perhaps in contrast to

physicists. In fact, it is hard to find papers that

do not contain at least a paragraph on the way

underdetermination was dealt with in practice

(although it is usually not explicitly referred to

as underdetermination).

For example, consider a research project that

aims to construct a spatiotemporal description

and an explanation of the course of the river

Rhine in the past 10,500 years (Berendsen and

Stouthamer, 2000). The hypothesis that the

Rhine has been present in the Netherlands is

obviously practically unassailable. But what

we really want is a description, and an explana-

tion of the course of events (their order in

time and their specific characteristics) that is

generalizable to other, comparable river deltas

in comparable circumstances. For such an expla-

nation, much more detailed evidence is needed

Kleinhans 291



to distinguish between competing theories on,

for instance, causes (initial conditions), relevant

circumstances, and principles of evolution of

bifurcations and avulsion. However, empirical

data often leaves room for a wide range of differ-

ent, often incompatible, hypotheses. In sum, the

inferences are hampered by problems of under-

determination (Kleinhans et al., 2005).

b Physics-based modelling. A physics-based

model may be used to test whether a hypothesis

does not conflict with the laws of physics. But a

model contains various sets of laws, of which

some at best are derived from physics, but even

then are simplified to allow numerical solutions.

Also, for many problems it is not obvious which

laws apply, and to what extent simplification is

possible. Thus one cannot be certain that a mis-

match between model results and observations

is not due to the simplifications and numerical

techniques or the initial and boundary condi-

tions used in the model (Oreskes et al., 1994).

For instance, conservation of momentum and

conservation of mass are simple physical laws

that apply to fluid flow. These simple laws are

the basic components of the Navier-Stokes equa-

tions that describe fluid flow, but cannot be

solved analytically. These equations are there-

fore implemented in so-called mathematical or

physical computer models. There is a trend in

geomorphology at present to develop ‘reduced-

complexity models’ (discussed later), but clearly

every model reduces the complexity of reality. In

this paper the focus is on physics-based model-

ling rather than rule-based modelling.

For physics-based numerical models to work

in practice, the equations have to be simplified,

and discrete timesteps and grid cells must be

used to model the flow in space and time. The

discretization brings a host of necessary numer-

ical techniques to ensure conservation laws and

to minimize numerical (computer-intrinsic)

error propagation. When initial or boundary

conditions are specified for this model, certain

laboratory or field conditions can be simulated.

In this way, a model is used to test whether a

hypothesis does not conflict with the laws of

physics, and the model results can then be

compared to the observations.

As such, models are not very useful for simu-

lating the details of a concrete existing case,

because then the initial and boundary conditions

must be specified in great detail so that it is no

longer clear whether the results are due to these

empirical parts or due to autogenic modelled

behaviour. Nevertheless this is common practice

in river and coastal engineering, which is clearly

justified because of the societal need, and is fur-

ther justified by using established models, and is

commonly (but unfortunately not universally)

complemented by healthy mistrust and careful

specification of prediction uncertainties.

Furthermore, models can be tested thoroughly

if not verified on highly detailed experimental

data of simple setups, as is increasingly done for

morphodynamics and CFD codes (Hardy et al.,

2003; Lesser et al., 2004). This removes some

of the need for detailed initial conditions,

although boundary conditions still present prob-

lems, because they were relatively simple in the

experiments compared to a field verification

case.

However, models are very useful to present

results of complicated sets of equations that the

unaided human mind cannot comprehend,

sensitivity to certain parameters and to explore

scenarios (Oreskes et al., 1994; Kleinhans

et al., 2005). As such, models are used to med-

iate between theory, based on physics, biology

and perhaps chemistry, and nature (Morrison

and Morgan, 1999).

c Experiments. Many different types of experi-

ments represent reality in one way or another

(Peakall et al., 1996), and all have limitations

similar to those listed above for models, in

particular the simplified initial and boundary

conditions. One important additional problem

is that of scale effects. In Froude-scaled models

it is attempted to obtain a Froude number and a




Shields mobility number as close as possible to

the prototype, but, as one depends on velocity

and the other on velocity squared, it is impossi-

ble to satisfy both requirements. The Reynolds

number may be lower but this is considered to

have small effects on the mobile bed as long

as the flow remains turbulent. Moreover, the

sediment can usually not be scaled down with

the same factor as the length of the model

because of cohesion problems with finer sedi-

ments. The sediment mobility scale problem is

commonly solved by applying a higher bed

slope to the model, called distortion, so that the

relatively coarser is equally mobile (Peakall

et al., 1996). But then scale problems arise, such

as in the reproduction of alternating bars

(Struiksma et al., 1985). It has been attempted

to forego the necessity of distorting the model

by using lightweight sediments such as bakelite,

but this appeared to give other scale effects, for

instance in the transverse bed slope (de Vries

et al., 1990). For the scale modelling of suspen-

sion, however, lightweight sediments may still

be necessary, but this is in its infancy.

It matters which aspects are under scrutiny

whether scale effects are really problematic.

Against experiments with vegetation on braided

rivers it has been argued that the stems of the

plants scale like Sequoia gigantea. In terms of

size this may be correct, but size does not matter

here. The relevant properties of the plants are

their hydraulic resistance as well as the strength

their roots provide to the sediment (Tal and

Paola, 2007). This added strength can be quanti-

fied with geotechnical experiments.

In analogue experimental models the scale

factor may be much larger. Consequently the

aforementioned scale effects prohibit a straight-

forward quantitative comparison to the natural

system. Seen from the perspective of a quantita-

tive replication of the detailed morphology of a

prototype, analogue experiments are therefore

poor tools. In particular, the particle sizes are

ridiculously large compared to water depth.

Highly subcritical flows and meandering are

nearly impossible to obtain because the flow is

commonly near-critical or supercritical (Peakall

et al., 1996). It could then be argued that such

experiments represent braided gravel systems

well. However, in the lab the flow is commonly

hydraulically smooth (Postma et al., 2008)

which leads to other bedforms and bar patterns

as well as unrealistically deep scour holes. Thus,

the mean grain size of the sediment should be

larger than about 0.5 mm, or the conditions

should be made hydraulically rough by the

presence of larger sizes in a mixture.

However, for somewhat different aims

analogue experiments are excellent tools. The

sediment can be seen as the material that builds

up stratification. Given the large scale factor,

time is very much compressed so that long peri-

ods can be studied. The detail at the particle

scale is irrelevant for such sequence stratigra-

phy, which is more referring to geometry of sedi-

ment package stacking and sediment budget

than to the detailed sediment transport and mor-

phodynamics of how the sediment got there

(Paola et al., 2001; van Heijst et al., 2001).

Moreover, analogue experiments can be stud-

ied as interesting cases of natural systems in

themselves. They are, after all, composed of the

same material as in nature: water and sediment.

The simple fact that many patterns in nature are

similar over a wide range of scales suggests that

the basic factors controlling their nature are sim-

ilar (Paola et al., 2001). For a number of relevant

systems and aspects we know this to be true:

alluvial fans and fan deltas occur in nature at the

scale of hundreds of kilometres as well as at

the scale of 1 m on the bank of a river or on the

beach. Their autogenic processes of incision,

sheet flow and avulsion as well as response to

allogenic forcing (changing boundary condi-

tions or simulated tectonics) can well be studied

in experiments (Bryant et al., 1995; Ashworth

et al., 2004; Hoyal and Sheets, 2009; van Dijk

et al., 2009). With carefully chosen materials

of different density, large-scale sorting along

sedimentary basins can also fruitfully be studied

Kleinhans 293



(Paola et al., 2001). This is not to say there are no

scale problems at all, but they are not fatally

problematic.

d Twisting a lion’s tail. Lord Bacon once stated

that scientists want to twist the lion’s tail. That

is, we want to manipulate reality to see what

will happen, so that we find out how the

beast works. This is unwanted, dangerous or

impossible in many Earth scientific cases. Large

rivers were avulsed by man for warfare pur-

poses, which cost many lives (Parker, 1999;

Slingerland and Smith, 2004). In lowlands such

as the Netherlands great effort has been put into

preventing such disasters for centuries, with

some success.

But we can twist the tails of representatives of

lions (Figure 2). We can twist our qualitative

images of lions, albeit myopic, bald and three-

legged ones, as we reconstruct the workings and

the past of rivers. But then we run the risk of

twisting our own imagined tail rather than the

real tail. We can twist tails of downscaled rela-

tives of lions (kittens) in a variety of ways to

experiment systematically. There are scale

effects: when the experimental lion size reduces

to that of a beetle, their mode of locomotion dra-

matically changes. We can play exhaustively

with model lions, albeit simplified. But then

there are numerical problems, particularly with

rectangular model lions representing rounded

real lions, and their behaviour is limited by the

experiment

conceptual model, description

numerical model

reality

Figure 2. ‘To twist the lion’s tail’ and observe what would happen, Lord Bacon’s view on doing empiricalscience, is not commonly possible with large rivers because it is dangerous. Instead, we twist tails ofrepresentatives of lions. These all have shortcomings and limitations, calling for combination of the threepillars of the Earth sciences: observations, experiments and modelling. (Note: whatever the cartoonistwants the reader to believe, the author does not have a tattoo.)




laws we apply a priori. Henceforth any feeling

of superiority of modellers or fieldworkers or

experimentalists can therefore safely be

abandoned.

Now to be serious. This is my answer to the

fundamental question of why and how we fruit-

fully combine fieldwork, experimentation and

modelling. Field data is as close as possible to

reality, but may be seriously hampered by

incompleteness, inaccessibility and other prob-

lems of underdetermination. Experimentation

allows a much larger control and accessibility

while maintaining materiality, but may suffer

from scale problems. Modelling allows full con-

trol over boundary conditions and laws, but the

representativeness of reality is considerably

decreased. The only hope is to base such models

on the laws of physics, chemistry and perhaps

biology so that they can be used to test whether

hypotheses derived from field data and experi-

ments are not in disagreement with established

laws. There are many more roles for models, but

this is the most important for basic research.

Most importantly, when the results from all three

epistemic approaches converge, we foster hope

that we possess good explanations for natural

phenomena.

III Riverland: Patterns of self-formed channels and floodplains

Natural rivers on plains and deltas can have

distinctive planforms such as meandering and

braided. Why these patterns emerge is only qua-

litatively understood. Their self-organization

involves feedbacks between channel morphody-

namics and channel migration, and the evolution

and subsequent erosion during floods of

floodplains including the vegetated levees that

flank the river as natural dikes. This dynamic

self-organizing landscape and its sedimentation

patterns will simply be called ‘riverland’ in this

paper.

In this section, problems of classical classifi-

cations and explanations for channel patterns

will be reviewed as well as the potential for bar

theories, bank erosion and floodplain formation

to contribute to a comprehensive explanation.

Recent work on experimental channel patterns

and on modelling will be reviewed to identify

where progress can be made in the near future.

For clarity, some matters were simplified; for

example, channel patterns other than meander-

ing and braiding (Figure 3) are not thoroughly

considered. It is to be expected, however, that

a more complete understanding will also cover

anabranching, anastomosing, wandering rivers

and so on.

1 Classifications

Many qualitative classifications have been for-

warded in the past. Leopold and Wolman

(1957) emphasized that a braided river is defined

by the number of active channels being larger

than one, while each individual channel may

meander as in single-thread rivers. More impor-

tantly, Leopold and Wolman emphasized that a

continuum of channel patterns with many inter-

mediate classes represents natural rivers better

than a hard discrimination between meandering

and braiding such as they induced.

Schumm (1985) distinguished straight, mean-

dering and braided classes from suspended

load-dominated to bedload-dominated and from

low to high flow strength at the same time, from

small to large width/depth ratios and high to low

pattern stability. Since then, anastomosing, ana-

branching, wandering and many other patterns

have been identified. Ferguson (1987) reinter-

preted the qualitative channel pattern classifica-

tion of Schumm (1985) in terms of streampower

on the one hand, and amount and size of bedload

as well as width/depth ratio and channel instabil-

ity on the other (Figure 4). Interesting groups of

patterns then emerge. For sand and increasing

streampower, straight, meandering and ana-

branching patterns emerge. For gravel, straight,

slightly sinuous with alternating bars, and

braided rivers emerge.

Kleinhans 295



Figure 3. Examples of rivers of various patterns and flow strength versus bank strength ratios. From topto bottom: Brahmaputra River, India (10 km wide braid plain), Rakaia River, New Zealand (1.7 km widebraid plain), Allier River, France (0.8 km wide meander belt), Koyukuk River, Alaska (10 km wide meanderbelt), Columbia river, Canada (2.1 km wide fluvial valley), Escalante River, Utah (60 m wide channel) andNanedi Valles, Mars (2 km wide channel).Source: Google Earth and Mars (accessed May 2009)




Alabyan and Chalov (1998) showed how every

known pattern can be described as a combination

of three main configurations (straight, meandering

and branched) on three main relief or structural scale

levels (low water channel, flood channel and valley

bottom). Thus, a single discharge is no longer used;

rather, the pattern is determined at a range of dis-

charges involving larger scales. Moreover, the effec-

tiveness of a discharge, expressed by the product of

sediment transport rate and frequency of occurrence,

was shown to exhibit more than onepeak forRussian

plain rivers, only one of which is near the mean

annual flood and one other determines where the riv-

ers appear to be branching. Two classes of factors

emerge that determine the channel pattern: flow

strength and sediment characteristics. A similar dis-

tinction between pattern at bankfull and flood condi-

tions was found useful in the Brahmaputra River

(Thorne et al., 1993), where weak meandering of the

entire braid belt in its valley was found.

2 Classical explanations for channelpatterns

Ferguson (1987) provides an insightful review

of the state of the art c.1987 and presents an

important new insight. Two classical explana-

tions were given for channel pattern that are still

debated: (1) pattern changes with flow strength;

(2) pattern changes with sediment feed rate.

a Flow strength and sediment feed. The first

explanation is that the pattern changes from

meandering to braiding with increasing flow

strength. Flow strength is determined by

channel-forming discharge and energy gradient,

which can be combined in a (unit) streampower

or a bed shear stress. Many discriminators

between meandering and braiding rivers have

been proposed based on flow strength (Leopold

and Wolman, 1957; Ferguson, 1987; van den

Berg, 1995). Note, however, that all these work-

ers stress that there are no hard thresholds;

rather, gradual transitions exist between channel

patterns, indicated by a discrimination line.

Various modifications were proposed on how

exactly the necessary parameters should be deter-

mined in practice. This is not a trivial problem.

For instance, energy gradient depends on channel

pattern (the more sinuous, the lower) and can

therefore not be used as an independent predic-

tive variable. Valley gradient, on the other hand,

is independent of the timescale over which chan-

nel pattern may change (Ferguson, 1987; van den

Berg, 1995). For instance, the field determination

of reach-averaged channel-forming discharge,

width and depth is difficult and somewhat sub-

jective in natural rivers (see Soar and Thorne,

2001, for an impressively complete review).

The second classical explanation for channel

pattern is that it depends on supply and type of

sediment (Ferguson, 1987). The type of sedi-

ment is relevant for bank stability (discussed

later): sinuosity has been found to decrease with

increasing proportions of silt and clay or vegeta-

tion in the channel banks and bed. Changes in

the supply of bed sediment feed to a channel had

been observed to provoke changes in the channel

pattern. Overloading a river with more sediment

than transport capacity may result in braiding

Figure 4. Typification of channel patternsSource: After Ferguson (1987)

Kleinhans 297



whereas reduced load may result in meandering

(Church, 2006).

But again practical problems proved difficult

to overcome: for instance, the definition of a rep-

resentative particle size is not straightforward as

it varies rapidly and strongly over short dis-

tances; sediment transport is notoriously difficult

to measure, and, moreover, the overloading or

underloading suggests disequilibrium of the

longitudinal profile. A disequilibrium between

sediment feed and sediment transport capacity

would lead to deposition near the sediment

source rather than overloading along a consider-

able length of the river. Yet equilibrium meander-

ing and braiding rivers are found; in particular

the latter have been reproduced in laboratory

experiments.

An important problem applying to both

classical explanations is that there appear

many different channel pattern classifications

(Leopold and Wolman, 1957; Schumm,

1985), pointing at a deeper source of uncer-

tainty of what exactly the deterministic charac-

teristics of channel patterns are – for example,

whether braid bars are vegetated or not, how

many braids there may be, what the minimum

sinuosity is for meandering, at which flow

stage bars should (not) be emergent, and

whether there is channel sediment or flood-

plain sediment in between the channels (eg,

Leopold and Wolman, 1957; Knighton and

Nanson, 1993). The obvious answer is that

channel patterns should be considered along

a morphological continuum rather than as sep-

arate classes, and are moreover likely to be

continuously but hysteretically adapting to

changing boundary conditions rather than in

equilibrium (Leopold and Wolman, 1957; Fer-

guson, 1987; Vandenberghe, 1995), but this

still leaves unclear how the patterns should best

be characterized.

b Experimental channel patterns. Lack of

experimental evidence was another major

problem for both explanations, as it proved very

difficult to produce self-formed dynamic mean-

dering in the laboratory, while braided channels

are relatively easily reproduced in laboratory

experiments (Ashmore, 1991). This either

reflects a lack of understanding of the basic con-

ditions in which a self-formed dynamic meander-

ing river emerges, or reflects serious scale

problems that, once understood, could lead to

better understanding of meandering.

Only three sets of experiments have repro-

duced aspects of dynamic meandering rivers with

floodplains. Friedkin (1945), Schumm and Khan

(1972), Jin and Schumm (1987) and Smith et al.

(1998) produced meandering channels in cohe-

sive sediment. The major advance of these

experiments was that meandering was produced

at all and the strength of the banks was found to

be a crucial factor. In Friedkin’s experiments the

channels usually developed into braided channels

Figure 5. Experimental river with pattern between braided and meandering (at St Anthony FallsLaboratory, 10 m long, 2 m wide). Bars are less mobile due to vegetation and the number of active channelsis reduced.Source: Tal and Paola (2007; 2010)




through the process of chute cutoff; in Schumm’s

experiments the channels remained straight with

low-sinuous thalwegs or eventually removed the

emplaced cohesive floodplain that was not self-

formed; and in Smith’s experiments channels

ultimately became (nearly) static as they had

cohesive sediment in the bed as well as in the

floodplain. However, natural meandering rivers

are dynamically meandering by continuous cre-

ation, expansion and translation and cutoff of

meander bends (eg, Camporeale et al., 2005).

Peakall et al. (2007) produced one dynamical

low-sinuosity meandering channel in sediment

ranging from fine gravel to silt (silica flour),

whereby the silt appeared to add strength to the

banks. Many features of meandering rivers were

observed in the experiment, such as point bar

formation and chute cutoff. Discharge was kept

constant. Gran and Paola (2001) and Tal and

Paola (2007) seeded alfalfa to an initially

braided experimental river in non-cohesive

uniform sediment during low flow. A dense

vegetation resulted in a static stream or slowly

wandering rivers whereas less dense vegetation

resulted in single-thread sinuous channels with

some characteristics of meandering, such as

point bar formation and chute cutoff (Figure 5;

Tal and Paola, 2010). Meandering has also been

obtained from an initially straight channel using

alfalfa and a lightweight sediment that filled in

lower areas of the floodplain so that recapture

was prevented (Braudrick et al., 2009). In both

cases three combined factors leading to mean-

dering probably were the reduction of floodplain

flow strength by the hydraulic resistance of

vegetation and the concurrent increase of focus

and strength of channel flow, the increased

strength of eroding banks, and the filling of

abandoned channels and lows by vegetation

and lightweight floodplain sediment, so that

multiple channels and reoccupation were

prevented.

c Flow strength and bank strength. Ferguson

(1987) qualitatively clarified that the ratio of

flow strength and bank strength determines

channel pattern and how this would explain

many observations (Figure 6). Nanson and

Croke (1992) based their classification of chan-

nel pattern on the cohesion of floodplains in

relation to flow strength. Indeed spectacular

results were obtained in the experiments by

adjusting the supply of silica flour or plants

(Peakall et al., 2007; Tal and Paola, 2007).

Thus, the key to producing self-formed dynamic

meandering is a proper scaling of bank strength

Figure 6. (a) Relation between channel pattern,flow strength (unit streampower) and bankstrength. (b) Relation between channel pattern,streampower based on valley slope and bankfulldischarge, and channel bed sediment size.Source: (a) After Figure 6.4c in Ferguson (1987); (b) van denBerg (1995)

Kleinhans 299



relative to flow strength. Conversely, the key to

producing self-formed dynamic braiding is by

having very weak banks. This explains the

following observations qualitatively (Ferguson,

1987):

(1) sand-bed rivers braid at lower slopes than

gravel-bed rivers of similar discharge

because sand is more easily entrained;

(2) braiding requires a larger gradient than

meandering, given a discharge, because

braiding involves a greater amount and

rate of channel modification and bank

erosion;

(3) changing bank vegetation correlates to

pattern changes along rivers and in time,

because vegetation often increases bank

strength;

(4) inactively meandering channels have such

strong banks that they cannot be eroded;

this would include a number of the earlier

experiments (Smith et al., 1998) as well as

many small rivers in glacial tills, meander-

ing channels on intertidal mudflats and so

on (Ferguson, 1987; Fagherazzi et al.,

2004; Kleinhans et al., 2010a).

Quantitatively the two classical explanations

had not been unified at the time of Ferguson’s

review. This is still true because it has remained

difficult to quantify bank strength and because a

physics-based explanation for channel and bar

pattern is lacking. In addition diagrams such as

those in Figure 6 are empirical and have dimen-

sional parameters on their axes. Further progress

requires that such parameters are more rigor-

ously based on physics and perhaps appropri-

ately non-dimensionalized. But this is the key

difficulty we face; for instance, it remains

unclear how exactly something complicated as

vertically varying bank strength could be

expressed in a meaningful physical parameter.

We will turn to a physics-based theory for bar

pattern in the next section and discuss bank

erosion later.

3 Role of channel bars in channel pattern

Flow over non-cohesive sediment almost never

creates a plane, a smooth surface or a straight

plain-floored channel. On the contrary, pat-

terns emerge at many scales. The reason is that

sediment transport rate depends on flow shear

stress to a power higher than unity. A slight

local irregularity on the bed surface causes

flow deceleration and local curvature, which

then leads to a relatively large local gradient

in sediment transport that may grow into bed-

forms, bars, channels, sand waves and so on.

This tendency is predicted even when flow and

sediment transport equations are dramatically

simplified and linearized. Linear stability anal-

ysis explores how this fundamental instability

mechanism causes infinitesimal perturbations

to grow to regular patterns (eg, Federici and

Seminara, 2003).

a Bar theory. For clarity, we start with cases in a

straight channel. The length and celerity of bars

can be predicted from stability analyses to

depend most of all on the width/depth ratio of

the channel and to a lesser extent on friction

and on sediment mobility (Parker, 1976;

Struiksma et al., 1985). For very narrow and

deep channels, a perturbation would result in

alternating bars but their amplitude decreases,

so that a plane bed develops. For somewhat

wider and shallower channels, alternating bars

grow.

At some point, higher mode bars appear – that

is, mid-channel bars emerge in between the

alternating bars (Crosato and Mosselman,

2009). This can be called braiding, but it is

important to realize that these bar patterns

already appear in a constant flow discharge so

that the bars would be submerged at all times,

however far they grow up to the water surface,

so that the river appears straight rather than

braiding. More importantly, the width/depth

ratio is used as independent parameter in these

analyses and cannot be predicted.




Conceptually, bars can be divided into

free and forced bars. Free bars grow from

perturbations. If they migrate, then their migra-

tion rate depends on their size. Forced bars grow

from a local channel constriction or a change in

curvature of the channel. Free and forced bars

are not entirely mutually exclusive; mixed forms

exist in low-sinuosity channels (Seminara and

Tubino, 1989). But the more prominent the

forced bars, the less likely free bars are to exist.

Forced bars occur in most real rivers because

they have curved banklines (Crosato and

Mosselman, 2009). Very large free bars may

move so slowly that they effectively form the

forcing for smaller-scale bars.

b Alternating bars and incipient meandering. In

meander bends, bars are forced to their positions

by the bends. It is therefore tempting to infer

that alternating bars lead to alternating bank

erosion so that meandering rivers emerge. Many

meander simulation models were set up from

bar theories (Camporeale et al., 2007) with the

condition that bank erosion was matched on

the other bank by an equal amount of sedimen-

tation so that the channel maintains a constant

width. As such, meander simulation models

reproduce many properties of meandering rivers

(Camporeale et al., 2005; Crosato, 2007). But a

physics-based explanation that independently

predicts channel pattern may not be that

straightforward: alternating bars in an initially

straight channel migrate so fast that over time

the banks will be eroded everywhere (Seminara

and Tubino, 1989). The channel then widens so

that the pattern evolves towards braiding.

An obvious solution for the high bar celerity

is that vegetation or cohesive sediment on the

bars and banks would retard bar migration rate

and at the same time reduce bank erosion so that

meandering rivers might form. Alternatively,

alternating bars in meandering gravel or cobble

bed rivers may be covered by very coarse sedi-

ment at their surface – that is, armoured – to such

extent that their celerity is reduced because only

extreme floods would mobilize such armour

layers (van den Berg, personal communication,

2009). A third possibility is that large alternating

bars are no longer forced to migrate, because the

upstream sediment feed is no longer fluctuating

strongly over the width (as is the case in braided

rivers) but rather follows the alternating pattern

(Crosato and Mosselman, personal communica-

tion, 2009).

Either way, bar theory provides one element

that was missing from the classical explanations

of channel patterns: it predicts whether alternat-

ing bars focus bank erosion or whether braid bars

develop that shave the banks more uniformly.

With weak banks natural and experimental

channels commonly evolve into wide and shal-

low rivers with irregular bars that form the braid-

ing pattern (Parker, 1979; Xu, 2002). Rivers

with strong banks and bar surfaces become nar-

row and deep (Hey and Thorne, 1986; Soar and

Thorne, 2001; Xu, 2002; Parker et al., 2007),

and as a result have alternating bars (Struiksma

et al., 1985; Camporeale et al., 2007). Stronger

flow in pools between alternating bars cause

only localized bank undercutting (Johannesson

and Parker, 1989; Camporeale et al., 2005;

Crosato, 2007) and mass wasting during

floods (Osman and Thorne, 1988; Thorne and

Osman, 1988; Darby et al., 2000; 2007) which

may lead to meander bend growth, migration

and cutoff.

In short, the balance between floodplain for-

mation and bank erosion determines channel

width, and channel width determines bar pattern,

which in turn determines where the banks are

eroded, while floodplain formation or armouring

on the bars as well as resistive floodplain mate-

rial in the banks reduces bar migration. Depend-

ing on these processes and feedbacks, different

channel patterns emerge. Before we turn to

floodplain formation and destruction, first the

effect of bed sediment sorting on the bar

dynamics must be discussed.

Kleinhans 301



4 Effect of bed sediment sorting onmorphology

Sorting of bed sediment affects the morphology

of rivers and channel patterns in a variety of

ways (see Powell, 1998, for a review) at different

scales, in particular at the length scale of bars

and beyond the length scale of channel patterns.

The sorting itself is a result of mobility differ-

ences related to flow-particle interaction (dis-

cussed below). Thanks to the usually high

efficiency of sediment sorting processes, much

of past fluvial morphology and engineering

could progress by considering only uniform

channel or floodplain sediment, as attested by

a large body of literature on sediment transport

predictors and morphodynamic modelling for

uniform sediment. Nevertheless the importance

of sorting has long been recognized and has been

unravelled in fluviosedimentological geological

studies. Recent progress by the powerful combi-

nation of geological and process field studies,

experiments and numerical modelling has made

clear that further progress requires consideration

of the entire particle size distribution and the

sorting processes (for reviews, see, for example,

Powell, 1998; Bridge, 2003; Parker, 2004;

Blom, 2008; Frings, 2008).

Sorting has direct relevance for the morphol-

ogy at the bar scale. Two categories of sorting

mechanisms can be distinguished: particle-

particle interactions and flow-particle interac-

tions. These two categories will be reviewed and

their effect on bar dynamics will be discussed.

a ‘Shaken and stirred’: Particle-scale sorting andlarge-scale effects. Particle-particle interactions

comprise granular effects that would also occur

in still water or vacuum. When a sediment mix-

ture is in motion due to stirring, flow shear, or

gravity-driven sediment flow, the sediment

expands and the pore space increases because

of the extra space taken by the individual and

colliding particles. The fine sediment is able

to move into the pores between the large

particles under the influence of gravity, mean-

while working up the coarse sediment because

that cannot move into the pores. This promotes

a coarsening upward sorting. A related phenom-

enon is percolation, which occurs when gravel

particles rest on each other and have empty pore

spaces, so the fine sediment may fall through the

pores even if the gravel is immobile (Kleinhans,

2004; Gibson et al., 2009).

In any sediment mixture, a range of larger

sizes contribute to the bed structure, whereas a

range of smaller sizes partially fill the pores but

could be removed without a drop in bed level.

For a bimodal sediment with much gravel, the

gravel is bed structure sediment whereas the

sand is pore-filling sediment. When the relative

amount of sand increases, the pores become

filled entirely so that the sand contributes to

the bed structure. Adapting a model from chem-

ical engineering, Frings et al. (2008) were

able to predict the porosity of an arbitrary non-

cohesive sediment mixture from the particle size

distribution. Moreover, a cutoff size is predicted

at which the abundance of a certain size is such

that this size no longer contributes to the struc-

ture of the sediment. That is, sediment finer than

the cutoff size only partially fills the pores of the

coarser sediment. When more is added up to the

point where this fine size starts to participate in

the structure, the cutoff size becomes smaller.

This behaviour may very well explain the differ-

ence in incipient motion dynamics between sand

and gravel in mixtures. Wilcock and Crowe

(2003), for instance, arbitrarily attribute a cutoff

size of 2 mm to the two behaviours, but applica-

tion of the Frings et al. (2008) model by Vollmer

and Kleinhans (2008) showed that a cutoff size

of 1.4 was more likely. Also rapid changes from

gravel-bed to sand-bed rivers can be explained

by the filling of gravel pores by sand (Frings et

al., 2008; Frings, 2008).

In the past the pore-filling sand in gravel-bed

rivers was ignored as ‘wash load’, and silt and

clay in sand-bed rivers was likewise ignored as

‘wash load’. Recently the sand received much




more attention because of its relevance for sal-

mon spawning and invertebrates in view of fine

sediment release from dam lakes and in case of

dam removal. In highly bimodal sediments the

sand percolates a certain depth into the gravel

bed depending on the coarse tail of the sand dis-

tribution and the fine tail of the gravel distribu-

tion (Cui et al., 2008; Frings et al., 2008;

Wooster et al., 2008). There are large-scale

effects of this sorting behaviour on incipient

motion, bar dynamics and, most importantly,

downstream fining.

b Incipient motion. Incipient motion and the

transport rates of particles of different sizes

have been studied for half a century (see

Egiazaroff, 1965; Parker et al., 1982; Wilcock,

1998; Kleinhans and van Rijn, 2002; Wilcock

and Crowe, 2003; Vollmer and Kleinhans,

2008). The differences in mobility of the parti-

cle sizes in a mixture have been described

empirically in hiding functions, where ‘hiding’

refers to smaller particles that are hidden in the

lee of larger particles. There are, unfortunately,

about as many hiding functions as there are

experiments or field data sets. The entrainment

of the size fractions depends on the drag and lift

forces on the particles. Calculation of these

forces must include effects of flow turbulence,

pressure fluctuations into the bed, bed slope and

the exposure of particles above the average bed.

Models based on various combinations of these

factors have been presented (eg, Bridge, 1981;

Wiberg and Smith, 1987; Zanke, 2003; Vollmer

and Kleinhans, 2007; 2008), but a large number

of issues remain to be resolved. In particular, the

structure of turbulent flow over rough beds

requires a more sophisticated formulation than

the law of the wall (Nikora et al., 2001).

Furthermore, the configuration of particles on

the bed (Buffington et al., 1992; Aberle and

Nikora, 2006) require attention. The incipient

motion models may now contain more

physics of the flow, but merely displace the

empiricism to the particle-particle interactions

and water-working history that lead to the

particle configuration.

The mobilization of sand from within a gravel

layer and the relative mobility of sand and gravel

in any mixture has been studied in isolation from

the infiltration problem. The connection

between the two issues lies in the exposure of

particles to the flow, where ‘flow’ includes tur-

bulent pressure fluctuations in the bed that may

mobilize sediment that is not exposed to direct

flow. Infiltrated sand is negatively exposed but

may nevertheless be entrained in some condi-

tions (Vollmer and Kleinhans, 2008). Thus, inci-

pient motion models based on force balances

and near-bed and in-bed flow parameterization

promise to provide physics-based explanations

and models for the hitherto empirical hiding

functions. However, for further progress the par-

ticle configuration of water-worked beds must

be described first – perhaps partly based on the

porosity model of Frings et al. (2008) combined

with the percolation model of Cui et al. (2008).

c Sorting versus morphodynamics of bars. Local

sorting on the bed affects the dynamics of bars

because the sorting changes the mobility of the

sediment. In particular, the bed surface may

react in two ways to a gradient in flow shear

stress and sediment transport: by changing bed

elevation and by changing bed surface particle

size distribution (Hirano, 1971; Parker and

Klingeman, 1982; Dietrich and Whiting, 1989;

Mosselman et al., 1999). In morphodynamic

models, sorting has been modelled with the active

layer concept (Hirano, 1971; Parker, 2004; Blom,

2008), but the balance between changing bed ele-

vation and changing bed surface composition is

extremely sensitive to the thickness of the active

layer. Hence, the effects of armour layers (Parker

and Klingeman, 1982) and dunes (Kleinhans,

2001; Blom, 2008) on large-scale morphology

is significant but as yet not well enough under-

stood. A promising model concept is to replace

the active layer with a continuous (but numeri-

cally discretized) distribution of bed elevation

Kleinhans 303



and a vertical sorting function (Blom and

Kleinhans, 2008; Blom, 2008).

Vertical growth of bars is not only limited by

water depth but also by the increase of the effect

of gravity on particles on increasing transverse

slopes. The first effect is that particles on a

transverse or longitudinal slope are more easily

mobilized (Parker et al., 2003; Vollmer and

Kleinhans, 2007). The second effect is that grav-

ity pulls the moving particles down the slope

while the flow drags the particles along a slope.

In bends, near-bed inward directed flow due to

the helicoidal motion of flow in bends counter-

acts this effect. The transverse slope effect can

be used for the prediction of channel bed

morphology (Odgaard, 1981; Struiksma et al.,

1985; Talmon et al., 1995; Parker et al., 2003),

but the different formulations appear to have a

considerable effect on the morphology, includ-

ing the bar properties and channel depths in

braided rivers and estuaries. It is by no means

resolved how transverse slope models can be

extended to sediment mixtures. The helicoidal

flow in bends drags particles upslope towards

the inner bend while gravity pulls particles

downslope towards the outer bend. As drag

depends on the surface area of particles while

gravity depends on the volume, the balance turns

out to give the classical bend sorting of coarser

sediment in deeper outer bends and finer sedi-

ment towards the shallower inner bends (Parker

and Andrews, 1985; Bridge, 2003).

But transverse slope models are, in particular,

poorly developed for cases where dunes are

present (Talmon et al., 1995), although for plane

bed in bedload there is progress (Parker et al.,

2003). The actual bed slopes on the dunes differ

much from the spatial average slope through the

bend, and dunes sort sediment vertically as well

and modify near-bed flow. Ideally, the Blom

(2008) model must be incorporated somehow

in a 2D or 3D model in combination with a sub-

model for fractional sediment transport on trans-

verse slopes. Furthermore, these models must be

integrated with the incipient motion and particle

configuration models discussed above. This is

necessary to predict bar pattern, dimensions and

dynamics for the entire range of sand-bed to

gravel-bed rivers and single-thread to multi-

mode bar rivers.

d Downstream fining as a template for channelpattern. Many rivers show a downstream fining

pattern from gravel to sand. Coarse gravel-bed

rivers and fine and medium sand-bed rivers are

abundant, but rivers with intermediate sizes

such as pea gravel are rare (Parker, 1991; van

den Berg, 1995). Downstream fining in gravel-

bed rivers is caused by selective transport pro-

cesses as well as abrasion of sediment, as is well

known (eg, Parker, 1991; Hoey and Ferguson,

1994; Paola and Seal, 1995). Downstream fin-

ing in sand-bed rivers is much less well under-

stood (Frings, 2008), but may be related to a

reduction in suspended bed sediment transport

capacity caused by concavity of the long profile

of rivers (Wright and Parker, 2005). Mixtures of

sand and gravel as well as intermediate sizes

might be abundant locally where the river

transforms from gravel-bed to sand-bed. The

gravel-sand transition may be rapid or gradual

depending on lithology, sediment mobility and

particle size distributions (Sambrook Smith and

Ferguson, 1996; Cui and Parker, 1998; Frings

et al., 2008; Frings, 2008), but it is by no means

clear how and why exactly. Furthermore, the

downstream fining trend can be broken at points

where tributaries contribute different sediments

(Rice, 1999).

One ramification of particle-scale sorting

(and the resulting division between bed structure

particles and pore-filling particles) for down-

stream fining is that the transition from gravel-

bed river to sand-bed river depends strongly on

the sediment composition: bimodal sediment

may have a sudden transition whereas unimodal

sediment may have a more gradual transition

(Frings et al., 2008; Frings, 2008). Indeed Iseya

and Ikeda (1987) found experimentally that the

transition is sudden for bimodal sediment, which




also causes a sudden change in water surface

slope, mobility of the sediment and sediment

transport. More generally, although the pore-

filling sediment does not contribute to bed level

change, it does contribute to the formation of

floodplains and the downstream fining pattern

that affects the morphology along the river. This

means that all particle size fractions of the

upstream sediment feed should be considered

in the mass balance of one-dimensional morpho-

logical models with sediment mixtures even if

they do not contribute to morphological change

locally. One way of adapting the current models

is by allowing bed sediment porosity to vary

(Frings et al., 2008).

5 Bank erosion and channel geometry

Having elaborated on the roles of bars and sort-

ing, the key element that is still missing from a

comprehensive theory for channel pattern is how

floodplains form and how they are destroyed

when the channel banks erode. Clearly, there is

a strong link with another classical problem of

fluvial geomorphology: that of hydraulic geo-

metry, where it has been found that coefficients

determining channel dimensions were correlated

to the nature and strength of the channel banks.

I first turn to hydraulic geometry to see what can

be learned from it before the review continues on

bank erosion.

a Channel-forming discharge. Most hydraulic

geometry relations predict channel width and

depth from discharge, from which a third rela-

tion obviously follows for the flow velocity

(eg, Lane, 1935; Leopold and Maddock, 1953;

Hey and Thorne, 1986; Knighton, 1998). The

number of empirical hydraulic geometry rela-

tions is about as large as the number of empiri-

cal sediment transport predictors and is likely

even more uncertain in its predictions. Coeffi-

cients were derived by semi-analytical deriva-

tions and by fitting to data sets. Implicitly a

friction relation is then also present in the

coefficients. Furthermore, some relations

include a particle size parameter and some

include the mud fraction of the banks (Fergu-

son, 1987; Soar and Thorne, 2001) which is

empirically better for some data sets but has

no more universal validity. Thus, it has empiri-

cally been shown that hydraulic geometry

depends partly on bank strength, caused by

cohesive sediment or vegetation (Leopold and

Maddock, 1953; Parker, 1979; Hey and Thorne,

1986; Soar and Thorne, 2001; Xu, 2002;

Church, 2006; Eaton and Church, 2007; Parker

et al., 2007).

Many workers attempted to provide physical

justification for hydraulic geometry relations

by extremal hypotheses, assuming that channel

flow friction is minimized, sediment transport

in the channel is maximized, etc (for an

overview, see Knighton, 1998). The key argu-

ment was based on the Least Action Principle

and has been extended to channel pattern expla-

nation (Huang and Nanson, 2007; Nanson and

Huang, 2008). Even if the least action principle

is valid for water and sediment, which is heavily

debated, then it remains to be seen whether

vegetation adheres to the principle. Just as a fri-

volous note, there is a Harvard law of animal

experimentation which says that under highly

controlled laboratory conditions laboratory

animals do just as they please. This may well

be true for laboratory plants as well.

b Channel-forming Shields mobility number. As

an alternative to the hydraulic geometry

relations based on a formative discharge, Parker

et al. derive an elegant non-dimensional set of

hydraulic geometry relations for bankfull

single-thread gravel-bed rivers without bank

vegetation (Parker et al., 2007) and for sand-

bed rivers with floodplains with cohesive sedi-

ment and/or vegetation (Parker et al., 2008).

The basic idea evolved from the concept of a

threshold channel: when the banks of a river are

composed of the same non-cohesive sediment

as the bed, the banks will be eroded by flow until

Kleinhans 305



the river is so wide and shallow that both banks

and bed are barely mobile (Parker, 1978a;

1978b; 1979). The parameters discharge, width

and depth are made dimensionless with median

particle size of the bed surface and gravitational

acceleration, perhaps inspired by the Shields

and Einstein non-dimensionalizations in sedi-

ment transport relations. The coefficients were

derived from the Manning-Strickler flow resis-

tance equation, a nearly constant critical Shields

parameter, a sediment transport relation and a

channel-forming relation expressed in terms of

bankfull Shields number to critical Shields

number. As these relations are not exactly uni-

versal, the resultant coefficients in their hydrau-

lic geometry relations are also approximations.

Hence Parker et al. (2007) present their relations

as ‘broad brush’, although it is fair to say that they

are much less broad brush than the purely empiri-

cal hydraulic geometry relations of the past.

The use of a channel-forming Shields number

(Paola et al., 1992; Parker et al., 1998) differs fun-

damentally from the use of a channel-forming

discharge as in most other relations. Empirically,

sand-bed rivers have a bankfull Shields number

well above the threshold for suspension, and

gravel-bed rivers have a bankfull Shields number

slightly above the critical Shields number. The

simple fact that gravel and sand are both abundant

but intermediate particle sizes are not (Smith,

1996; Frings, 2008) permits the use of a constant

channel-forming Shields number for sand-bed

rivers and a constant for gravel-bed rivers. These

are then not valid for pea-gravel rivers and rivers

with sand-gravel mixtures.

To generalize the relations to both sand- and

gravel-bed rivers, the channel-forming Shields

number can be expressed as a bank strength sur-

rogate parameter times the critical Shields num-

ber. This means that the bank strength of all

sand-bed rivers is lumped into one single value,

and another value for gravel-bed rivers. Paola

et al. (1992) used this for the derivation of a dif-

fusive sediment transport law applicable to

gravel- or sand-bed rivers for the purpose of

long-term and large-scale sedimentary basin

modelling. For such purposes small-scale details

such as channel pattern are less relevant. Parker

et al. (1998) explicitly mention that factors like

cohesive banks and vegetation cause uncertainty

and variation in the empirical coefficients of their

relations. For our purpose, unfortunately, bar pat-

tern is very sensitive to width/depth ratio so that

these relations will not be very useful for explain-

ing channel patterns. We must therefore dive

deeper into the detailed processes of bank erosion

and the floodplain formation that precedes it.

6 Floodplain formation and destruction

The term ‘floodplain formation’ covers a suite of

very different processes that lead to the sorting-

out of fine and coarse sediment in different

locations. Hence various combinations and

intensities of these processes lead to very

different floodplains. The detailed structure of a

cut-bank in a floodplain, in turn, determines the

erodibility of the bank.

a Floodplain formation by overbanksedimentation and vegetation. Fine sediment

is deposited on growing inner-bend bars, which

transform into levees (Brierley et al., 1997).

Natural levees grow during floods by sediment

diffusion from channel onto banks (Pizzuto,

1995), sediment advection in focused overbank

flow (Middelkoop and Asselman, 1998;

Nicholas and Walling, 1998) and crevasse

splays growing from levee breaches (Walling

and He, 1997; Cazanacli and Smith, 1998). Pio-

neer vegetation settles on the higher and better

drained grounds (or perhaps on the wetter

near-channel grounds in semi-arid regions) and

successes into riparian forest (Johnson, 1994;

Tal and Paola, 2007; 2010; Perucca et al.,

2007), causing hydraulic resistance, sediment

trapping and added strength. The vegetation

on inner-bend bars promotes the transition from

bar to levee by reducing flow velocity, adding

strength and trapping sediment so that the




channel maintains its width (Johnson, 1994;

Darby, 1999; Baptist et al., 2006; Geerling et

al., 2006). Furthermore it transforms bars into

islands in a multi-thread channel (Gurnell and

Petts, 2002; Tal and Paola, 2007).

Levees in turn control natural flooding fre-

quency and overbank sedimentation (Wolman

and Leopold, 1957; Brierley et al., 1997).

Further away from the channel fines settle in

the floodplain to form cohesive sediment

(Middelkoop and Asselman, 1998; Nicholas and

Walling, 1998). Sediment compaction and

vegetation succession (Geerling et al., 2006)

strengthen floodplain deposits over time, provid-

ing bank strength when eroded in a meander

bend. Thus, discharge regime and flooding

frequency of a river determine the deposition

of levees, of cohesive fines and the settling of

vegetation, which in turn determine width and

depth of self-formed channels, while the flood-

ing frequency is determined by the dimensions

of the self-formed channels (Wolman and

Leopold, 1957).

b Floodplain destruction by bank erosion.Floodplain is simultaneously formed and

destroyed. Floodplain destruction occurs not

only by bank erosion but also by channel cut-

ting. Both are strongly affected by the composi-

tion of the sediment, which may have layers of

different composition and strength, and by

vegetation including peat. Channel cutting will

be discussed later in the context of avulsion.

Bank erosion occurs in two steps: bank under-

cutting by fluvial erosion and bank failure by

mass wasting.

First, banks are undercut by fluvial erosion at

the base and lower portion of the banks (Thorne

and Tovey, 1981; Osman and Thorne, 1988;

Thorne and Osman, 1988; Darby et al., 2000;

Simon et al., 2000; Simon and Collinson,

2002; Darby et al., 2007). This depends on the

flow shear stress and the strength of the sediment

at the base of the banks. If this is cohesionless

sediment similar to the bed sediment of the river,

then the angle of repose and lateral sediment dif-

fusion are important (Parker, 1978a; 1978b).

Although shear stress can be argued to increase

with depth, the flow pattern in bends, particu-

larly sharp bends, has not been clarified to such

extent that it is clear how exactly banks are

eroded. Channel bends lead to secondary flow

patterns as has been known for a long time (van

Bendegom, 1947; Allen, 1978). The basic rea-

son is that flow is faster near the water surface,

so that conserved momentum of a flow through

a bend leads to a developing helicoidal motion

of which the magnitude depends on water depth,

bend radius and friction (de Vriend, 1977;

Blanckaert and de Vriend, 2003). In sharper

river bends, however, a smaller counter-

rotating cell develops near the outer bank water

surface, which leads to a reduction of flow

strength and turbulence at the bank and possibly

to a reduction in bank erosion (Thorne et al.,

1985; Blanckaert and Graf, 2001). In very sharp

bends the flow separates from the inner-bend

channel boundary and impinges directly on the

bank on the opposite side of the channel (Leeder

and Bridges, 1975; Ferguson et al., 2003), which

leads to a very different bank erosion and bar

formation pattern. This style is likely associated

with channels with relatively very strong

banks and limited to no dynamical meandering

(Ferguson, 1987; Kleinhans et al., 2009). For

simplicity, we will further assume that a good

model would provide sufficient detail and rea-

lism in the flow for modelling the bank erosion

but this clearly deserves more work. This detail

would be needed for the coupling of bank erosion

to the flow in realistic cases (Mosselman, 1998;

Duan and Julien, 2005; Darby et al., 2007).

The second step in bank erosion is the mass

failure of the bank (Thorne and Tovey, 1981;

Osman and Thorne, 1988; Thorne and Osman,

1988; Darby et al., 2000; 2007; Simon et al.,

2000; Simon and Collinson, 2002). This process

is more akin to mass wasting in mountainous

areas than to other fluvial processes. There are

various failure mechanisms that occur

Kleinhans 307



depending on bank height, bank oversteepening

due to the fluvial undercutting, composition and

layering of the bank material, presence, nature

and age of vegetation (Pollen, 2007), and history

of water levels and groundwater level. Once a

failed block deposits on the river bed, it modifies

the morphology and the flow locally. Eventu-

ally, it will be eroded by the flow. The composi-

tion and possible vegetation in it determine how

long the block remains in place and to what

extent it protects the bed (Fagherazzi et al.,

2004). The influx of material different from the

bed sediment means that various particle size

fractions and their properties must be included

in the prediction of morphology.

Channel pattern stability is intuitively associ-

ated to a balance between sediment import and

export from a reach. However, the volume of

floodplain sediment eroded from banks is likely

larger than the deposited volume of this sedi-

ment on point bars, because the flow energy on

the point bars is higher than on the floodplain

and because their proportion of length along the

channel is smaller than that of the eroded outer

banks (Wolman and Leopold, 1957). This means

that, for a system to be really balanced, the

excess eroded floodplain sediment must be

deposited in oxbow lakes and on the overbanks

(Lauer and Parker, 2008). The layering of

the bank material is basically a ‘memory’ of

floodplain processes that affects the channel

dynamics. Furthermore the flood history deter-

mines groundwater level and outflow, which is

well known to be very important for bank stabi-

lity. The fact that advanced morphodynamics

models have barely been coupled to advanced

bank erosion models may therefore well be

explained by full awareness of the apparent

arbitrariness and spatial variation in bank

layering as well as the intricacies of coupling

of groundwater flow and open channel flow.

But to progress with riverlands we must

understand and model them, so we now turn to

future modelling of this complicated set of

processes.

7 Physics-based modelling of self-formedchannels and channel patterns

Rivers self-organize their pattern/planform

through feedbacks between channels, floodplain

and vegetation, which emerge as a result of the

basic spatial sorting process of wash load sedi-

ment and bed sediment that leads to channels

and floodplains. The balance between floodplain

formation and destruction determines the width

and pattern of channels. The role of the compo-

sition of banks was already acknowledged in

classical explanations for channel geometry and

channel patterns. Past work was based on bank-

full flow in channels, but floodplains are not

formed during bankfull flow; floods are essen-

tial. This shift in emphasis from channel to

floodplain dynamics is significant. It leads to a

system of processes and feedbacks that is so

complicated that it can no longer be compre-

hended by the unaided human mind. The

practical consequence is that a comprehensive

computer model and an experimental scaling

strategy are urgently wanted.

The time is ripe: the variables governing

floodplain dynamics that were once hidden in

empirical coefficients can now be addressed in

advanced models for three-dimensional flow

and bar dynamics, bank erosion and floodplain

sedimentation and vegetation. These are all

relatively well understood on their own, and

comprehensive models could be used to explore

the feedbacks between components of the self-

organizing riverland. Then it remains to be

explained how this suite of processes and their

interactions lead to the emergent empirical prop-

erty that channel dimensions and pattern are well

correlated to bankfull flow.

a Meander models or braided models. Since

the advent of the computer, simulation models

have been constructed for meandering rivers

and for braided rivers. Meander simulation

models based on advanced bar theories strongly

simplify the bank erosion and levee and




floodplain formation in stark contrast to the

modelled complexity for channel morphology

(Ikeda et al., 1981; Johannesson and Parker,

1989; Camporeale et al., 2005; Crosato,

2007). Moreover, the width is specified as a

constant which implies that bank and floodplain

formation exactly mirror bank erosion. This

ignores the feedbacks with antecedent deposits

and vegetation that determine channel width,

pattern, floodplain dynamics and, in short, the

entire riverland self-organization.

Braided river simulation models based on cel-

lular automata (Murray and Paola, 1994; 2003)

strongly simplify the channelization process. In

many such models the channels are one grid cell

wide. The models can easily be adapted to

include vegetation and other aspects, but the

behaviour remains the result of rules that are

only distantly related to the laws of physics that

govern flow and sediment transport. Although

these models reproduced many characteristics

of these rivers, braided river simulation models

cannot produce meandering, and meandering

simulation models cannot produce braiding.

Hence transitions from one to another river

pattern cannot be modelled, which reflects our

lack of understanding of either pattern and

illustrates that essential riverland elements

are still missing from these relatively simple

models.

b Future development of channel patternmodels. Future models should be able to allow

channels to form autogenically and form their

own geometry as well as pattern. At present,

two- or three-dimensional codes model channel

processes well but only within fixed banks

(Figure 7) and at local reach scales for short

periods (eg, Lesser et al., 2004; Kleinhans

et al., 2008). Nevertheless, with increasing com-

puter power, such models can soon be applied to

large braided rivers over periods of millennia.

Furthermore, the predicted bathymetry, when

stored in small increments, allows the creation

Figure 7. Braided river emerging in a morphody-namic model calculation (using Delft3D; Lesser etal., 2004; Kleinhans et al., 2008) after 30, 50, 70, 90and 110 years, loosely based on the river Rhine. Theinitial quasi-regular mode 4 bar pattern (four barsacross the width) is also predicted by linear stabilityanalysis (Crosato and Mosselman, 2009). The largealternating bars nearly stabilize after several dec-ades despite the lack of vegetation or floodplainsediment. Discharge 2500 m3s�1, gradient 1�10�4,particle size 2 mm. Flow is from bottom to top.Channel width is 2000 m and length is 40 km.White-to-black scale indicates sedimentation-erosion relative to original bed (scale –5 to 1.5 mfor left image and –10 to 3 m for later steps).Discharge was based on time series of the Rhinewith 5% random noise along the upstreamboundary, and initial bed level was seeded with afew centimetres of random noise. More noise orlarger fluctuations on the discharge would lead tomore bar migration. Sediment transport wascalculated with the Engelund-Hansen formulation.

Kleinhans 309



of geological profiles (Figure 8) that provide

another way to combine models and field data.

Flow has been modelled in this context at

many levels of details, from gradually varied

flow to Large Eddy Simulation. Much has been

said about computational fluid dynamics

modelling elsewhere (Bates et al., 1996; Hardy

et al., 2003; Keylock et al., 2005). The issue here

is how much detail in the turbulence is necessary

to obtain the flow structures that cause bank ero-

sion and floodplain deposition at the scale of

channel patterns. Secondary circulation is

Figure 8. Portion of a geological profile of the braided river modelled in Figure 7 (near top), automaticallycreated by comparing bed levels in four timesteps. The dotted line indicates initial bed level and the bartops are only just submerged. Darker colours are old, while lighter colours are young. The four lowerpanels show channel planform in four timesteps (covering 110 years; black is deep and light grey is shallow),while the black horizontal line in the panels indicates the position of the profile.




relatively easily resolved in quasi-3D codes

(Lesser et al., 2004) and even parameterized in

2D codes (Struiksma et al., 1985; Blanckaert and

de Vriend, 2003) but the extra near-bank cell as

well as near-bank flow pattern is not (Blanckaert

and Graf, 2001).

Two-dimensional or quasi-three-dimensional

flow models with k-e-type turbulence closures

have the advantage of computational efficiency

and have proven in the past capable of prediction

bar and sorting patterns as well as compound

channel flow with vegetated floodplains (Darby,

1999; Baptist et al., 2006). Large Eddy Simula-

tion, on the other hand, can now resolve flow

structures that simpler models cannot resolve

(Hardy et al., 2003; Keylock et al., 2005), but

implementing sediment transport and morphol-

ogy in such models has barely begun (Ferguson

et al., 2003; Keylock et al., 2005). It remains to

be seen how much detail in the flow models is

needed for floodplain dynamics.

Bank erosion has been modelled well in a sin-

gle cross-section (Simon and Thomas, 2002;

Darby et al., 2007) but the antecedent river

deposits that strongly determine bank erosion

had to be specified exhaustively as initial and

boundary conditions. Relatively simple bank

erosion has been implemented in a 2D

morphodynamic model surprisingly long ago

(Mosselman, 1998; Darby et al., 2002) but

demonstrated significant discrepancies between

data and model. Similarly, Duan and Julien

(2005) modelled incipient meandering in specta-

cular agreement with the Friedkin (1945) experi-

ments, but evolution beyond incipient

meandering is not yet possible because the

floodplain formation was not included. The

same was true of Friedkin’s experiments.

Furthermore, a serious numerical problem arises

(Mosselman, 1998; Darby et al., 2002; Duan and

Julien, 2005): that of the representation of a

curved channel with a cut bank on a grid. A reg-

ular rectangular grid produces many cut cells.

A curvilinear grid may follow the bank lines

much better and can be deformed as the banks

erode, but cannot become too curved as

orthogonality is required. Moreover, it is hardly

possible to model chute or neck cutoffs. An irre-

gular unstructured grid may follow bank lines

well and allow bend cutoffs, but still incremental

bank erosion will result either in small cells near

the bank or in numerical diffusion due to fre-

quent regridding. A porosity treatment of par-

tially filled grid cells may also allow the use of

regular grids with irregular banklines without

the need to remesh (Keylock et al., 2005; R.

Hardy, personal communication).

Levee and overbank formation were so far

ignored but should be the result of sediment sort-

ing over bars as well as in floodplains. This will

require adaptation of the active layer concept so

that it includes the routing of pore-filling particle

size fractions including sand, silt and clay as dis-

cussed earlier. It also requires more work on

sand-mud interaction. Vegetation development

in relation to river morphodynamics is in its

infancy, but a number of things are clear from

the bank erosion studies reviewed above.

Considering that a comprehensive model would

run long enough for vegetation to develop,

existing models of vegetation succession could

be integrated (eg, Temmerman et al., 2003;

Geerling et al., 2006) in combination with rules

of the tolerance of vegetation to duration of

flooding, as well as rules for peat growth, seed

banks and perhaps even delivery of large woody

debris (Gurnell and Gregory, 1995). Perhaps the

hydraulic resistance of vegetation is sufficient to

describe the interaction between vegetation and

sedimentation, but this obviously needs to be

explored.

c Increasing computational capacity: The sky isnot the limit. Regardless of the immediate chal-

lenges for numerical models, application of a

riverland model including bank erosion and

floodplain formation over periods of millennia

will require much more computational power

than is typically available in the geomorphology

community. Perhaps as a result of this

Kleinhans 311



limitation, there is an ongoing debate on the fea-

sibility of the micro-reductionistic stance. The

question is whether we need to incorporate as

much physics and detail into models as possible

to reproduce as many relevant aspects of reality

as possible. Or perhaps it is feasible to simulate

aspects of reality with rule-based, so-called

‘reduced complexity’ models, as long as addi-

tion of rules is not arbitrary (Murray and Paola,

2003). For example, can we simulate river

channel patterns with such reduced complexity

models or do we need to address the full set of

processes and conservation laws deemed

relevant? Reduced complexity models have the

obvious advantage over physics-based flow and

morphodynamics models that they are computa-

tionally much more efficient. The obvious

disadvantage is that ad hoc rules and empirical

constants replace well-established (conserva-

tion) laws of physics and well-established

semi-empirical relations, so it can by no means

be ascertained that reduced complexity models

correctly reproduce the dynamics of natural

systems for the correct reasons. It is therefore

essential to ground models on the truth by

evaluating model output quantitatively against

real data, while allowing for errors in the latter.

While the debate rages on, it is useful to con-

sider one argument: computational efficiency. In

the Earth sciences, models are run on single per-

sonal computers or perhaps clusters of tens of

PCs. Now imagine that we could use the super-

computers with hundreds or thousands of paral-

lel processors that are presently used and

developed further for Global Circulation Models

and models for galaxy formation and astronom-

ical data processing. These disciplines have

already paved the way for full complexity mod-

els in our discipline. The reduced complexity

models would remain useful, if only for organiz-

ing thoughts, teaching and inspiration, but

increased complexity models could – within

years – provide us with increasingly powerful

tools to test whether our hypotheses agree with

the laws of physics, and to explore the parameter

space of riverlands that is only sparsely filled

with real rivers on Earth, and perhaps on Mars

and Titan (Irwin et al., 2008; Kleinhans, 2010).

d Grounding models on the truth. To verify

model results, data on channel patterns is

required. The recent explosion of data types

such as lidar DTMs and remote sensing imagery

will allow not only for qualitative comparison of

river patterns and quantitative comparison of

morphometrics, but also for new techniques

such as pattern recognition. After all, patterns

are emergent characteristics that are easily but

subjectively recognized by the human mind,

while physics-based numerical models that pro-

duce patterns, or pixel-based images of rivers,

do not involve recognition of any pattern. Data

are increasingly available at many spatial and

temporal scales. To date, about 40 years’ worth

of satellite imagery have been collected. Aerial

photographs have been available for much

longer, and in some cases historical maps have

been available since about AD 1600. Also digital

terrain models are often available from stereo

photography, surveying and lidar. In principle

this creates new opportunities for excellent

specification of initial conditions and for testing

models.

But a point-by-point comparison of model

results and real rivers is not sensible for several

reasons. First, the details in the real system can-

not have been covered by the model if the initial

and boundary conditions have not been supplied

in endless detail, perhaps much more than in the

new techniques, as argued at the beginning of

this paper. Second, important processes that

slightly modify the morphology may not be

included, such as size-sorting of the sediment.

Third, the physics for, eg, bars may be about cor-

rect but the empirical constants in the model may

not be exactly correct (in the transverse slope

components, for instance). If we were to follow

the point-by-point approach, a morphodynamics

model would modify the initial topography of a

braided river until it fitted the wavelengths and




other properties emerging only from the

specified physics and constants, and would then

dramatically fail the test of comparison to a ter-

rain model collected at a later date. But this is

neither fair nor fruitful: the model may have

done very well in terms of bar dimensions and

dynamics but a slightly different wavelength

would render the point-by-point comparison

useless.

Instead, general characteristics of rivers must

be compared, such as dimensions and deriva-

tives of bars, bends, channels, networks, etc.

This has been moderately successful in the study

of the largest rivers on Earth (Thorne et al.,

1993; Klaassen et al., 1993; Latrubesse, 2008)

and for experiments (Egozi and Ashmore,

2008), but also suggests that general statistics

are not critical enough. Parameters such as

braiding indices are usually binary (channel/no

channel) and strongly depend on stage. We need

quantifiers for subtle patterns to reveal structure

objectively, which has been a major challenge in

many natural sciences for decades. Two promis-

ing approaches with spectacular recent progress

are pattern recognition in remote sensing images

and network analysis.

Objects can be recognized by spectral signa-

ture and heterogeneity of the spectral signature

(Addink et al., 2007). Such objects can then be

classified with shape parameters, such as com-

pactness, roundness and convexity. This has

already successfully been used to distinguish

river channels, thaw lakes and oxbow lakes (van

der Werff and van der Meer, 2008). Combina-

tions of pixel-based and object-based classifica-

tion result not only in present water-filled

channels but also in former channels, oxbow

lakes and fills with bare sediment as well as vege-

tation cover (Addink and Kleinhans, 2008). It is

conceivable that these techniques yield semi-

automated maps of various channel and flood-

plain elements, in which patterns and structure

can quantitatively be explored. Furthermore,

evolution over time can be explored through

changes in subsequent images, particularly for

the largest rivers of the world as the image reso-

lution of the earlier imagery is limited.

The evolving channel network structure could

be studied with techniques developed for the

world wide web, the internet, road networks,

neurological networks, food webs and social

networks including that of scientists, expressed

in their citing behaviour (for a review, see

Strogatz, 2001). River networks may be similar

to other networks, or completely different,

which would tell us something as well. Complex

networks may be scale-free, random, regular or

something in between random and regular called

small-world, which come with varying degrees

of clustering and connectivity. From this per-

spective, a river channel network is nearly regu-

lar, nearly chain-like because a channel splits

into two or at best three channels at a node

(or bifurcation), and directional because the

water obviously flows only in one direction

(although it would be interesting to apply this

to deltas with tides). Fluvial plains are character-

ized by an equal number of bifurcations and con-

fluences, whereas deltas are characterized by

more bifurcations than deltas. Temporally,

channel networks evolve, so that the network

may change, and links between nodes may have

time-varying proportions of the total flow and

sediment flux. Ideally, the usefulness of network

characterization will be tested on rivers that

changed their pattern over time. Given the lim-

ited number of good data sets available, there

is a clear role for experiments.

8 Dynamics of riverlands

Channel patterns may change. A certain channel

pattern may be stable in some characteristics, but

the pattern itself is usually dynamic, even if no

net aggradation takes place. Channels migrate,

meander or form new braid bars and channels,

crevasse splays form, vegetation grows, and

channels avulse over the fluvial plain so that it

starts all over again while the old channel fills

up and is buried. Avulsion is an autogenic

Kleinhans 313



process – that is, an intrinsic result of the

dynamics of riverlands while the allogenic con-

trols, or boundary conditions to use a non-

geological term, are constant and tectonics is

insignificant. To understand channel patterns

and changes in patterns, the style of autogenic

avulsion must be understood as well, so this will

be the focus of the next section.

Channel patterns may also change more dra-

matically. Braided rivers are known to have tran-

sitioned to meandering at timescales of centuries

to decades. In geology the reasoning that braided

rivers change to meandering at the transition

from glacial to interglacial is still occasionally

heard. Such changes may be allogenically

forced, or, in non-geological terms, be forced

by a change in boundary conditions that has

nothing to do with the internal dynamics of riv-

erlands. Two fundamental problems will be dis-

cussed in the latter part of this section. First, the

reaction of a river to changes in forcing is

strongly affected by the history of a river as

stored in the sediments and surface morphology.

Second, perhaps there exist thresholds in the

river systems that, when crossed, lead to a sudden

dramatic change in pattern, and, when crossed in

the reverse direction, lead to hysteresis.

a Splitting rivers at their seams: Avulsion andbifurcations. Avulsion means the shift of the

course of a river over a considerable length –

say, several meander bend wavelengths. At

bifurcations, water and sediment are divided

over two downstream branches. An avulsion

site is at least temporarily a bifurcation because

the new channel develops while the old one is

still active. The terms avulsion and bifurcation

are derived from medicine, where they are used

for blood vessel topology and change thereof.

Avulsion and bifurcations are found on allu-

vial fans and coarse-grained fan deltas, fluvial

plains and lowland deltas. Braided rivers are

characterized by many bifurcations, bars and

confluences within a single channel. Anasto-

mosing rivers may have bifurcations that are

stable in a nearly symmetrical division of flow

and sediment for a relatively longer time. Occa-

sionally trifurcations, with three downstream

branches, are found in nature, particularly in

deltaic environments.

Avulsion wreaked havoc for society (Parker,

1999; Slingerland and Smith, 2004; Kleinhans

et al., 2010b) in the recent past. Furthermore the

rate and style of avulsion determine fluvial

architecture, in particular connectivity between

sandy bodies, which is relevant for hydrocarbon

exploration. It is therefore surprising that avul-

sion and bifurcations barely received attention

until two decades ago.

Avulsions can be divided into four classes

(Slingerland and Smith, 2004): avulsion by

annexation of a small active or abandoned

channel (eg, Stouthamer and Berendsen, 2007);

avulsion by incision and formation of a new

channel (eg, Stouthamer, 2005); avulsion by

progradation of splays or lacustrine deltas

through which a dominant channel may eventu-

ally develop (eg, Smith et al., 1989); and

avulsion following the formation of a mouth bar

with an unstable bifurcation (eg, Edmonds and

Slingerland, 2007). These four classes have dis-

tinct initial conditions, distinct processes and

different relative control of upstream and

downstream conditions.

Several conditions are known to be necessary

for avulsion (for reviews, see Slingerland and

Smith, 2004; Stouthamer and Berendsen,

2007), in particular a gradient advantage of the

new course over the old course, and slight under-

feeding of the new channel with sediment. The

gradient advantage should here refer to energy

gradient, which is often not understood. Even

if the bed gradient along a crevasse (across a

channel belt) into a flood basin is much larger

than the bed gradient along the channel, then the

flow into the flood basin may still pond so that

sediment deposition clogs up the crevasse chan-

nel and the avulsion fails (Aslan et al., 2005).

Hence, long flood basins and breached flood

basins would promote avulsion. Ponding is




basically a backwater effect and therefore a

downstream control, even though it may seem

as if the sediment feed conditions at the crevasse

entrance matter more (Slingerland and Smith,

1998). A slight underfeeding of the new course

is necessary so that the new channel enlarges.

This is an upstream control. Key factors are the

size of the crevasse, the absence of resistive

layers in the old channel bank and under the dee-

pening new channel, the suspended sediment

concentration of the flow entering the channel

(Slingerland and Smith, 1998) and the presence

of an upstream bend in which helicoidal flow

modifies the direction of the sediment just

upstream of the bifurcation (Kleinhans et al.,

2008).

The formation of a mouth bar and bifurcation

is akin to that of splay formation. A body of sedi-

ment is formed where the flow expands

(Edmonds and Slingerland, 2007), after which

the body is in the way of the flow so that the flow

decelerates through the backwater effect. If the

flow decelerates on the upstream side of the

mouth bar, then it grows in the upstream direc-

tion (Kriele et al., 1998; Hoyal and Sheets,

2009; van Dijk et al., 2009; Kleinhans et al.,

2010b). Furthermore, the channel with the two

bifurcates in it is lengthened compared to other

main channels, so that a gradient disadvantage

occurs. Continued long enough, the entire

channel upstream of the mouth bar aggrades,

reducing its flow capacity compared to other

channels, and avulsion occurs on the delta.

In all avulsion types, there is, averaged over a

period longer than a few avulsions, net sedimen-

tation. There is hardly opportunity for avulsion

in incised rivers (Stouthamer and Berendsen,

2000). A gradual rise of flood levels above the

surrounding floodplain is another necessary con-

dition for avulsion, fulfilled by a slight overload-

ing of the upstream feeder channel with

sediment (upstream allogenic control; Bryant

et al., 1995; Ashworth et al., 2004), or with

general progradation of a delta or fluvial plain

(downstream autogenic control; van Dijk et al.,

2009), or with base level rise (downstream allo-

genic control; Stouthamer and Berendsen,

2000), or with tectonics (allogenic control;

Stouthamer and Berendsen, 2000), or with com-

paction of floodplain sediment and floodplain-

filling peat (autogenic control; Aslan et al.,

2005; Stouthamer and Berendsen, 2007).

Morphodynamics models have reproduced

various emergent phenomena, including

upstream-driven avulsion on fans, mouth bar

formation and upstream migrating sedimenta-

tion causing upstream avulsion (Edmonds and

Slingerland, 2007; Kleinhans et al., 2010b).

Potentially, a comprehensive morphodynamic

model for channels and floodplains, as described

above, could autogenically create avulsions. To

include tectonics and compaction is relatively

straightforward, although differential vertical

movement of the bookkeeping grid for sediment

composition may provide another numerical

challenge.

b Avulsion, bifurcations and channel pattern.Bifurcations are rarely stable, so that the

number of active channels does not increase

ad infinitum because they silt up. The period

over which a bifurcation becomes unbalanced

– in other words, avulsion duration – depends

on the length of the downstream bifurcates, the

difference in gradient, and presence of upstream

bars or bends (for reviews, see Slingerland and

Smith, 2004; Kleinhans et al., 2008). It can be

postulated that single-channel systems exist in

principle when the average interavulsion period

is larger than the avulsion duration, and

alternatively multi-channel systems such as

anabranching and anastomosing rivers exist. If

activity of a channel is defined as having signif-

icant bed sediment transport (say, more than a

fifth of the transport integrated over all chan-

nels), then many seemingly anastomosing rivers

are in fact single-channel systems wherein the

abandoned branches convey a limited portion

of the flow discharge, in particular during floods

(Makaske et al., 2002; Kleinhans et al., 2008).

Kleinhans 315



The pattern of wandering gravel-bed rivers,

also confusingly called anabranching rivers, is

thus related to bifurcation stability. New chan-

nels are sometimes cut into the floodplains at

flood or into abandoned channels, when the flow

has been diverted by very large floods, log jams,

sediment waves or ice dams (Burge, 2006).

The relation between avulsion parameters and

pattern raises the question of whether large ana-

branching rivers, such as the Russian plain rivers

(Alabyan and Chalov, 1998) and the Ganges-

Brahmaputra system are simply single-channel

systems with recently abandoned flood-

conveying branches or multi-channel systems

in which the interavulsion period is larger than

the avulsion duration. One argument against this

is the existence of relatively stable, vegetated

and inhabited islands (chars) in the Brahmaputra

(Thorne et al., 1993). No megariver with a

discharge larger than 17000 m3 s�1, except the

Mississippi, satisfies the usual discriminators

between braiding and meandering, possibly

because there exists a stable state of anabranch-

ing (Latrubesse, 2008). Interestingly, some of

these megarivers have straight, sinuous or

braided channels within the larger-scale ana-

branching, which would argue for a separate

explanation as suggested by Alabyan and

Chalov (1998), rather than one at the same level

as meandering and braiding. Latrubesse (2008)

suggests that the Least Action Principle (Huang

and Nanson, 2007) explains the emergence of

islands and hence anabranching because narrow-

ing channels would be the only way to transport

all the sediment at such small energy gradients.

As megarivers cannot well be scaled in experi-

ments, anabranching must urgently be explored

with physics-based models for an explanation.

c Changes in channel patterns: Thresholds andtransitions. Channel patterns are known to have

changed, sometimes called metamorphosed

(Schumm, 1985). An increase of vegetation

density on bars transformed a braided river into

a transitional river (Schumm, 1985; Johnson,

1994; Tal and Paola, 2010). Changes in the hin-

terland as well as human interference such as

gravel dredging led to incision of a braided river

which then transformed to meandering (van den

Berg, 1995). Climatic change, both in the hin-

terland and the fluvial plain, transformed a large

braided river into a meandering and straight

river in the transition from interglacial to glacial

(Vandenberghe, 1995; Berendsen and Stoutha-

mer, 2000).

A simple correlation between cold climate

and braided rivers or warm climate and mean-

dering rivers has been used and debated in the

past. The key explanation is discharge regime

and coupled sediment feed to the river. In a cold

climate there may be one large spring melt flood

event causing a large discharge peak, whereas

in a temperate climate there may be several rel-

atively smaller rainfall-generated flood events,

and in a tropical climate the monsoon provides

a different flood regime again. The annual dis-

charge may still be the same but the distribution

over the year changes, with shorter and higher

peaks in the cold climate case. Thus the effective

channel-forming discharge in a cold climate

may be larger. The sediment feed rate and vege-

tation respond to climate change as well, so that

a suite of changes may cause a transition of river

pattern (Vandenberghe, 1995; Busschers et al.,

2007). It would be extremely interesting to study

the effect of each individual factor in a physics-

based model capable of producing different river

patterns.

Careful geological reconstructions have led

general hypotheses for the relation between

channel pattern and climate to move away from

the cold-braided and warm-meandering simpli-

city. In particular, the tardy reaction of vegeta-

tion, destruction of strong interglacial soils and

permafrost to climate change causes out-of-

phase changes in supply of water and sediment

(Vandenberghe, 1995; Busschers et al., 2007).

Furthermore, it takes time to convey coarse sedi-

ment, generated by strong physical weathering,

to downstream fluvial plains so that its delivery




may be delayed to the end of a glacial (Busschers

et al., 2007). Before this arrival of different sedi-

ment the local sediment is therefore reworked.

Thus, both irregularity of discharge and sedi-

ment supply are thought to cause channel pattern

change. The period of instability could be short,

so that the pattern is braided only some time after

the onset of a glacial period (Bogaart and van

Balen, 2000; Vandenberghe, 2003). In some

climates, however, the adaptation period may

be much larger (Church and Slaymaker, 1989).

The transition from meandering to braiding

is poorly recorded, whereas the braiding-

meandering transition is well preserved. The

preservation potential of the braided river depos-

its is much larger than that of the meandering

deposits because braided rivers tend to erode

widely, removing the former meandering river

floodplain, while meandering rivers erode

deeply (Vandenberghe, 2008), although some-

times a large-scale avulsion allows for some

preservation of meandering channels (Busschers

et al., 2007).

As an example, the following interpretations

were given for the transition from braiding to

meandering of the river Rhine (Busschers

et al., 2007). In the Last Glacial maximum

(before 21,000 BP) the river was braiding and

incising. This strongly supported observation

may conflict with the idea that sediment over-

loading causes braiding, but part of the incision

is due to isostatic effects so that the overloading

with sediment basically occurs from below the

entire river. While the warming initiates

18,000 BP, the transition from braided to mean-

dering is first observed 14,500 BP. Both far

downstream in the Rhine basin (Netherlands)

and upstream (Upper Rhine Graben in Germany)

the meandering initiates in the larger channel or

channels of the braided river. Two or three chan-

nels were active over several millennia, although

it is not known whether one or all of the channels

had most of the discharge and sediment trans-

port. So, initially the braided river temporarily

forces characteristics onto the meandering river

(Busschers et al., 2007; Erkens et al., 2009),

which is important to take into consideration

when quantifying and explaining measures such

as meander length over the transition. By 8000

BP there is only one active meandering channel.

But what exactly caused these channel pattern

changes? To answer this question, the channel

patterns first require explanation in their own

right as argued in most of this paper. Once such

understanding has been gained, abductive

inference could lead to answers that are better

constrained. At present, a number of causes have

been forwarded, including climatic change in the

hinterland, deforestation and sea-level change.

But climatic change and deforestation may mean

a change in annual flow discharge, flow dis-

charge regime, upstream sediment feed and the

composition of the upstream sediment supply,

all timed differently because of their different

timelags, and all with delayed effects because

the inherited channel pattern belonging to past

conditions is only slowly modified. Once a com-

prehensive model and an experimental scaling

strategy have been developed, these questions

can be addressed systematically.

9 Towards understanding river channel andpattern formation

The following questions emerge from this

review.

� What is the role of flow strength and varia-

tion in flooding magnitude and frequency on

the pattern?

� What is the effect of nature, magnitude and

variation of upstream sediment feed on

patterns?

� Is added bank strength due to sorting of fines

and bed sediment a sufficient condition for

meandering, and is vegetation also a suffi-

cient condition? What extra interactions and

feedbacks on channel pattern would arise if

both occur?

Kleinhans 317



� What is the role of bar pattern and sorting at

the bar scale? Is the emergence of fixed

alternate (complex) gravel bars a sufficient

condition for meandering in gravel-bed riv-

ers? To what extent do small-scale sorting

processes cause large-scale sorting patterns

relevant for channel pattern?

� In what parameter space of vegetation, fine

sediment deposition (density, size, thick-

ness) and flooding (magnitude, frequency)

do transitions between river patterns take

place?

� In what manner, to what extent and why do

channel patterns and their causes in sand-

bed and in gravel-bed rivers differ?

� In what manner, to what extent and why do

channel patterns and their causes in small

rivers (1 m width) differ from those in large

rivers (10 km width)?

Fieldwork successfully helped raise these

questions but will not alone answer them.

A quantitative experimental scaling methodol-

ogy must be developed and a comprehensive

physics-based model must be developed in

which the various river channel patterns emerge

as a result of different initial and boundary con-

ditions of water and sediment. The challenge for

experimenters is clear: a systematic geotechni-

cal study of scaling relations of bank strength

must be done. The precise process that causes

bank strength in silica flour or vegetation must

also be studied in order to be able to develop

new scaling rules. With such scaling rules, var-

ious combinations of vegetation (like vegetation

in reality; Tal and Paola, 2007), silica flour (like

suspended sediment; Peakall et al., 1996) and

polymer (like cohesive floodplain sediment;

Hoyal and Sheets, 2009) could be pursued to

combine the best of all and create the richest

experimental riverlands.

The challenge for modellers is also clear: to

combine physics-based models that produce

accurate three-dimensional flow, bar patterns

with (preferably) physics-based models for

floodplain sedimentation, including the effects

of cohesive sediment and of vegetation, and a

submodel for the erosion and failure of channel

banks. In short, hydrodynamics, sediment trans-

port of particle sizes ranging from cohesive fines

to the coarsest bed sediment, effects of vegeta-

tion and morphodynamics must be fully coupled.

The obvious way to do this is to implement a

bank erosion model into a hydrodynamics and

morphodynamics code as has already been done,

but perhaps with more advanced 3D flow, with a

solution for the deforming grid problem and

capability to deal with fine sediment transport

and settling and vegetation. The time is past that

such a reductionistic modelling approach is

unrealistic. In short, a greater engagement with

fundamental mathematical and physical princi-

ples is both required (Church, 2005) and feasible.

Once experimental and model tools have

been developed, modelled evolution of fluvial

landscapes at longer timescales can be compared

to geological studies that reconstruct environ-

mental and climate conditions and change. Then

questions such as the following can fruitfully be

asked.

� What are necessary conditions and time-

scales for transitions between river patterns

in response to changes in forcings?

� How do channel patterns develop when the

initial condition is another channel pattern

rather than a hypothetical plane valley?

� Are there hard thresholds (rather than transi-

tions) that the system can cross during

changing forcings and due to extreme

events? Can such threshold crossings lead

to hysteretic or irreversible change due to

vegetation or inherited floodplain structure?

Significant progress can be made in the next

decade by modelling and experimentation.

Existing models can be combined for bed and

floodplain sediment dynamics and morphody-

namics, rules for vegetation and bank erosion

into a comprehensive physics-based model.




Experimental floodplain and channel processes

can be enriched with essential characteristic by

adding vegetation, fines and polymer to the sedi-

ment mixture. While following such a physical

reductionistic approach, the empirical concepts,

relations, diagrams and geological reconstruc-

tions developed in the past will provide necessary

verification data, constraints, exceptional cases

and realistic boundary conditions.

Acknowledgements

As for most reviews, the author is indebted to many

colleagues in the Geoscience faculty and all over the

world for exchanges and discussions. In particular, I

thank Janrik van den Berg and Gary Parker for their

inspiring guidance in the past that, to my initial sur-

prise, echoed on while I move from sorting into

channel patterns. I thank Christopher Keylock and

Wietse van de Lageweg for comments on the draft;

Piet Hoekstra for his ongoing support and comments

on an earlier version of this review; and Gilles

Erkens, Kim Cohen, George Postma and Wim Hoek

for their attempts to hammer some geological sense

into my thinking. I also thank the MSc students who

did so much work to chase the fundamental questions

raised here. Fred Trappenburg of Geomedia, Utrecht

University, painted and virtually modelled two

representative lions and seduced a third to have its

tail twisted (gently) on camera; Kimberlee Kessler

Design granted permission for the use of their

real lion photograph. MGK is supported by the

Netherlands Organisation for Scientific Research

(NWO) (grant ALW-Vidi- 864.08.007).

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