sorting out river channel the author(s) 2010 patterns · 80115, 3508 tc utrecht, the netherlands...
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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
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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)
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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
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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
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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
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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
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(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.)
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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.
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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)
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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)
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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)
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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)
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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.
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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.
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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
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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
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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
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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
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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
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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
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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
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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.
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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.
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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
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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
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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
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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
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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).
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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
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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
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� 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.
318 Progress in Physical Geography 34(3)
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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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