numero 2-2007 - Géomorphologie : relief, processus, environnement

Géomorphologie : relief, processus, environnement, 2007, n° 2, p. 145-158
A history of the systems approach in geomorphology
Une histoire de l’approche systémique en géomorphologie
Richard Huggett*
Abstract
A systems approach in geomorphology has a long and varied history that tracks developments in physics, chemistry, biology, and ecology. Four related stages started with classical mechanics and moved through classical thermodynamics and open systems to
non-equilibrium thermodynamics and dissipative systems. New ideas emerged in each of the stages that led to fresh concepts about the
dynamics of geomorphic systems. Classical mechanics and classical thermodynamics promoted the idea of equilibrium, open systems
thermodynamics fostered the idea of steady state and dynamic equilibrium, and non-equilibrium thinking generated the linked ideas of
complexity and chaos.
Key words: geomorphology, steady state, dynamic equilibrium, open system, dissipative system, chaos.
Résumé
L’approche systémique en géomorphologie possède déjà une histoire longue et variée, dont les développements suivent plus ou moins
ceux de la physique contemporaine. Quatre étapes peuvent être distinguées, depuis la mécanique et la thermodynamique classiques jusqu’à la physique des systèmes ouverts de la thermodynamique des états de non-équilibre et des systèmes dissipatifs. À chacune des
étapes, des idées nouvelles ont émergé et conduit à de nouveaux concepts en matière de dynamique des systèmes géomorphologiques.
La mécanique classique et la thermodynamique des systèmes fermés ont promu l’idée d’équilibre, la thermodynamique des systèmes
ouverts a stimulé les idées de régime stationnaire et d’équilibre dynamique, et la physique des situations de non-équilibre a permis le
développement des idées relatives à la complexité et au chaos.
Mots-clés : géomorphologie, état stationnaire, équilibre dynamique, système ouvert, système dissipatif, chaos.
Version française abrégée
Cet article retrace le développement du concept de système
en géomorphologie. L’idée de système dont a hérité la géomorphologie est issue de la physique, de la chimie, de la biologie et de l’écologie. Les physiciens identifient trois genres
principaux de systèmes : les simples, les non-organisés et les
complexes organisés. Les systèmes des deux premiers genres
ont déjà une longue et illustre histoire. En géomorphologie,
quelques rochers à flanc de colline constituent un système
simple, alors que l’ensemble des particules en déplacement
sur le versant d’une colline se comporte comme un système
complexe mais désorganisé. Le troisième et plus récent type
de système correspond à des objets en interaction forte produisant des ensembles de nature complexe et auto-organisée.
Ce genre de système et son extension aux états de non-équilibre fermés a dominé l’approche systémique en géomorphologie depuis les années 1970, bien que les idées antérieures
en matière de systèmes aient toujours leur importance.
Les premiers systèmes étudiés en science se sont composés
d’un petit nombre d’objets décrits par quelques variables.
Les équations déterministes du mouvement, par exemple
celles qui sont utilisées dans la mécanique classique, décrivent le mouvement de chaque composant du système dans un
modèle mécanique simple, comme celui des boules de billard
se déplaçant sur une table ou des planètes tournant autour
du soleil. En géomorphologie, la conception newtonienne de
la dynamique s’est avérée une méthode utile et puissante
d’analyse des systèmes simples. La littérature traitant des
processus et de la dynamique des systèmes géomorphologiques en termes de mécanique classique est vaste.
La thermodynamique classique implique l’étude de la chaleur, donc de la collision et de l’interaction des particules à
l’intérieur de grands systèmes fermés au sein desquels on
s’approche des états d’équilibre. La dynamique newtonienne
ne peut pas aborder des systèmes de cette complexité parce
qu’il y a trop d’équations à manipuler. Les prévisions faites
par cette branche de la thermodynamique classique s’appliquent aux systèmes fermés à l’équilibre ou très proches de
l’état d’équilibre. En géomorphologie, en partie à cause des
enseignements de la thermodynamique classique, la notion
d’équilibre est devenue une idée directrice pendant la pre-
*School of Environment and Development, University of Manchester, Manchester M13 9PL. E-mail: [email protected]
Richard Huggett
mière moitié du XXe siècle. Par exemple, la théorie davisienne du développement stadiaire des formes du relief dans le
paysage s’inspire des principes de la thermodynamique classique parce qu’elle semble fonctionner à certains égards
comme un système fermé tendant vers l’entropie maximum
(Chorley, 1967). Plus tard au XXe siècle, l’application de la
notion de système complexe désorganisé aux systèmes géomorphologiques a ouvert une ligne d’enquête intéressante et
puissante reposant sur des principes de comptabilité de
l’énergie et de matériaux. Les applications principales en ont
été des équations géomorphologiques de bilan de matière et
de transport (par exemple, Dietrich et Perron, 2006).
Les systèmes complexes organisés sont des systèmes ouverts qui échangent de l’énergie avec leur environnement,
en importent, ou les deux à la fois, et qui montrent un comportement non-linéaire. Apparue en écologie dans les années 1940, l’approche focalisée sur les systèmes ouverts a
trouvé de larges et nombreuses applications dans les
sciences de la vie et de la terre, y compris la géomorphologie. La notion d’équilibre est restée aussi centrale qu’elle
l’avait été dans les travaux précédents, mais elle a subi une
réinterprétation en termes d’état stationnaire et d’équilibre
dynamique. Bien que Gilbert (1877) ait eu le premier l’idée
de recourir à la notion de système en géomorphologie, c’est
à Strahler (1950, 1952) que reviennent l’introduction et le
développement de la théorie des systèmes ouverts dans cette
discipline. L’approche par les systèmes ouverts a abouti à
une nouvelle typologie des systèmes, proposée d’abord par
Chorley et Kennedy (1971), ensuite adoptée et adaptée par
Strahler (1980). Selon ces auteurs, il existe plusieurs niveaux des systèmes : des systèmes morphologiques (forme),
des systèmes en cascade (flux), et des systèmes de réponse
aux processus (processus-forme). Les systèmes morphogénétiques ou de forme sont des ensembles de variables morphologiques en relation significative d’interdépendance,
tant du point de vue de l’origine du système que de sa fonction. Les systèmes en cascade sont des réseaux de transport
et de stockage d’énergie, de matière, ou des deux ensembles
(Strahler, 1980). Les systèmes de type processus-réponse
correspondent à des systèmes d’écoulement d’énergie interagissant avec un système morphologique de telle manière
que les processus à l’œuvre dans ce dernier puissent en
changer la forme et que, inversement, tout changement de
forme dans le système affecte en retour le fonctionnement
des processus en jeu dans celui-ci.
La large acceptation de l’idée de non-équilibre (ou de
déséquilibre) marque le début de la troisième période de
l’histoire des systèmes en géomorphologie. Howard (1965) a
noté que les systèmes géomorphologiques pouvaient posséder des seuils séparant deux modes de fonctionnements assez
différents dans leur économie interne. Schumm (1973, 1977)
a introduit les notions d’équilibre métastable et d’équilibre
métastable dynamique. Il a prouvé que, dans un système fluvial, des phénomènes de seuil dynamique affectent l’état
moyen du système. Dans l’équilibre métastable dynamique,
les seuils déclenchent des changements épisodiques des états
d’équilibre dynamique. Un système soumis à des contraintes
s’éloigne de l’état d’équilibre pour atteindre un nouvel état
146
stationnaire. Si les contraintes sont fortes, le système peut
passer sans à-coup dans un autre domaine de la thermo-dynamique et atteindre par bifurcation un état de non-équilibre
pour lequel le théorème de la production minimum d’entropie s’applique toujours. Au delà de ce seuil, les solutions des
équations régissant la dynamique du système peuvent ne plus
être uniques : ce dernier peut connaître un ou plusieurs nouveaux régimes. Les systèmes qui possèdent des bifurcations
peuvent être décrits par des équations déterministes de diffusion et de réaction, mais la présence de bifurcations implique
que la dynamique du système dépende d’événements contingents ou fortuits. La théorie de la bifurcation permet au
même système de passer par une série d’états différents et,
dans un sens, introduit donc une dimension historique dans
le développement du système. La théorie de la bifurcation a
été appliquée par quelques géomorphologues aux systèmes
géomorphologiques vers la fin des années 1970 et au début
des années 1980.
Les vues sur le déséquilibre ont par la suite mené aux
idées sur la dynamique chaotique. La recherche classique
sur les systèmes ouverts se caractérise par l’étude des relations linéaires entre variables au sein de systèmes proches
de l’équilibre. La dynamique chaotique (chaos déterministe) se caractérise par l’identification de relations non-linéaires à l’intérieur des systèmes. En géomorphologie, la
non-linéarité signifie que les sorties du système (ou ses réponses) ne sont pas proportionnelles aux entrées (ou forçages) dans le système, quelle que soit l’étendue de la
gamme des entrées. Les relations non-linéaires produisent
une dynamique riche et complexe au sein de systèmes fort
éloignés de l’état d’équilibre, qui montrent un comportement périodique et chaotique. Phillips (1999, 2006) est assurément le partisan le plus enthousiaste et actif en matière
de dynamique non-linéaire appliquée à l’étude des systèmes
de la surface terrestre. Phillips montre que la convergence
et la divergence dans un système, lorsque ces tendances sont
calibrées par une métrique comme par exemple l’altitude ou
l’épaisseur d’un régolithe, constituent des indicateurs significatifs de la stabilité d’un système géomorphologique. La
balance entre convergence et divergence est d’importance
cruciale pour une appréciation de la dynamique géomorphologique de systèmes. Phillips se montre également persuasif lorsqu’il explique que ce sont les enquêtes de terrain
qui doivent éclairer les études de dynamique non-linéaire en
géomorphologie, car ce n’est qu’en reliant les systèmes
d’idées aux paysages, aux processus et aux scénarios réels,
et qu’en recherchant sur le terrain des traces des dynamiques chaotiques et des autres phénomènes non-linéaires,
que les géomorphologues pourront tester la pertinence de la
théorie des systèmes en géomorphologie.
En conclusion, il s’avère que les impacts des sciences physiques, biologiques, et chimiques sur la pensée systémique en
géomorphologie n’ont pas été toujours directs. D’ailleurs,
les géomorphologues qui ont adopté le langage et le formalisme d’une approche systémique ont adapté les concepts aux
spécificités des systèmes qu’ils ont étudiés. Il est possible que
l’approche systémique en géomorphologie soit sur le point
d’établir un lien décisif entre les deux traditions, jusqu’à
Géomorphologie : relief, processus, environnement, 2007, n° 2, p. 145-158
Systems in geomorphology
présent quelque peu disjointes, de la géomorphologie dynamique et de la géomorphologie historique.
Introduction
This paper traces the development of systems concepts in
geomorphology. It submits that (1) they have closely followed developments in physics, chemistry, biology, and
ecology; and (2) that they each represent a radically different way of thinking about geomorphic systems, all of which
still have currency in geomorphological research.
A ‘system’ is a whole compounded of many parts, or ‘a
meaningful arrangement of things’ (Schumm 1977). By
this definition, a hillslope is a system consisting of ‘things’
(rock waste, organic matter, and so forth) arranged in a
particular way, the arrangement being meaningful because
it is understandable in terms of physical processes. Other
definitions of systems refer to a set of objects, and attributes of the objects, standing together to form a regular
and connected whole. Chorley and Kennedy wrote: ‘A system is a structured set of objects and/or attributes. These
objects and attributes consist of components or variables
(i.e. phenomena which are free to assume variable magnitudes) that exhibit discernible relationships with one
another and operate together as a complex whole, according to some observed pattern.’ (Chorley and Kennedy,
1971).
Geomorphology has inherited the idea of systems from
physics, biology, and, to a lesser extent, chemistry. Physicists
recognize three main kinds of system: simple systems, complex but disorganized systems, and complex and organized
systems. The first two conceptions of systems have a long
and illustrious history of study. Since at least the sixteenthcentury revolution in science, astronomers have referred to a
set of heavenly bodies connected together and acting on each
other in accordance with certain laws as a ‘simple’ system:
the solar system is the Sun and its planets; the Jovian system
is the planet Jupiter and its moons. In geomorphology, a few
boulders resting on a hillslope is a simple system. The conditions required to dislodge the boulders and their fate once
they have been dislodged are predictable from mechanical
laws involving forces, resistances, and equations of motion,
in much the same way that the motion of planets around the
Sun can be predicted from Newtonian laws.
In the complex but disorganized conception of systems, a
vast number of objects interact in a weak and haphazard
manner. An example is gas in a jar. This system could
consist of more than 1023 molecules colliding with each
other. In the same way, the countless individual particles in
a hillslope mantle are viewable as a complex but somewhat
disorganized system, even if the hillslope mantle as a whole
does have an organization. In both the gas and the hillslope
mantle, the interactions are rather haphazard and far too
numerous to study individually, so aggregate measures must
be employed.
In a more modern notion of systems, which has its roots
in biology and ecology, objects interact strongly with one
another to form systems with a complex and organized natu-
re. Most biological systems and ecosystems are of this kind,
but many other structures at the Earth’s surface display high
degrees of regularity and rich connexions and may be
thought of as complexly organized systems. Hillslopes,
rivers, and beaches are examples. This kind of system, and
its extension to non-equilibrium cases, has dominated systems thinking in geomorphology since the 1970s, although
earlier systems ideas are still important.
Simple systems and classical
mechanics
The first systems studied in science consisted of a few
objects described by a few variables. The study of such
simple systems dominated science until late in the nineteenth
century. Deterministic equations of motion describe the
motion of each system component as in simple mechanical
system, say a few billiard balls moving on a billiard table or
planets revolving around the Sun. These equations define the
exact movement of the balls or planets with respect to the
forces acting upon them. In the case of the billiard balls, just
four variables are needed for each ball – position and velocity in a plane. Taken together, the equations for individual
balls form a set of simultaneous differential equations which
enable the prediction, for a given initial distribution of balls
and known forces applied from outside by a billiard cue, of
system changes, of the future location of all balls. The dynamics of virtually all simple systems, including balls rolling
down inclined planes, levers, cogwheels, bodies colliding
with each other, and billiard balls bouncing off cushions, can
be studied and predicted using the classical methods of Newtonian mechanics (Waddington, 1977).
In geomorphology, the Newtonian conception of dynamics has proved a useful and powerful method of analysing
simple systems. Its application to the study of the movement
of material at the surface of the Earth has been particularly
rewarding. Geomorphologists commonly regard erosion and
weathering as the result of external forces or stresses applied
at the Earth’s surface and internal forces resisting them.
Strahler (1952) classified Earth materials according to their
response to an applied stress caused by either gravity or by
molecular processes. His groundbreaking work spawned a
generation of Anglo-American geomorphologists who
researched the small-scale erosion, transport, and deposition
of sediments in a mechanistic framework (Martin and Church, 2004). The literature dealing with the mechanics and
dynamics of geomorphic systems is extensive. An early
example is Nye’s (1951) application of plasticity theory to
the flow of ice sheets and glaciers. Another case is the work
of Bagnold, including his classic study of the physics of
blown sand and desert dunes (Bagnold, 1954), his classic
paper on the bedload stresses set up during the transport of
cohesionless grains in fluids (Bagnold, 1956), and his
approach to the problem of sediment transport from the
viewpoint of general physics (Bagnold, 1966). Other
examples are Yalin’s (1977) treatment of the mechanics of
sediment transport and Graf’s (1971) account of the hydraulics of sediment transport.
Géomorphologie : relief, processus, environnement, 2007, n° 2, p. 145-158
147
Richard Huggett
Systems of complex disorder and
classical thermodynamics
Nineteenth-century physicists invented classical thermodynamics, which is the study of heat transformation and exchange. Classical thermodynamics involves the study of
heat (and so with the collision and interaction of particles)
in large and closed systems in, or near, equilibrium states. A
large system in classical thermodynamics contains a huge
number of interacting particles (for example, colliding molecules in a gas or a huge number of billiard balls on a big
billiard table for instance). Newtonian dynamics cannot
tackle systems of this complexity because there are too
many equations to handle. In the late nineteenth century,
Boltzmann and Gibbs showed that systems that are complex
but disorganized can be studied using a new kind of mathematics to find certain quantities of interest. The new mathematics was statistical averaging or, more technically, entropy maximizing (Wilson, 1981). These methods cannot predict the behaviour of any one particle of gas, or one billiard
ball among many. However, they can predict the distribution
of particles among energy states and aggregate measures
such as the pressure and temperature of a gas, and the distribution of velocities of billiard balls and the average rate at
which a ball strikes a cushion. The predictions made by this
branch of classical thermodynamics apply to closed system
at, or very near to, equilibrium.
Regarding geomorphic systems as systems of complex
disorder opens up an interesting and powerful line of enquiry that applies principles of energy and materials
accounting. Although the principles of accounting are
simple, they can lead to sophisticated methods such as
input-output analysis. They can also lead to statements of
energy conservation and mass conservation that, in conjunction with principles of classical dynamics, assist in the study
a variety of geomorphic systems. To be sure, the laws of
Newtonian dynamics and thermodynamics are widely used
in geomorphology. These laws cover four kinds of basic
equations: balance equations, physical–chemical state equations, phenomenological equations, and entropy balance
equations (Isermann, 1975).
Balance equations
These equations represent the laws of conservation. They
indicate that what goes into a system must be stored, come
out, or transform into something else; in other words, matter, energy, and momentum cannot suddenly appear or
disappear in an unaccountable manner (Huggett, 1980). For
mass transactions, the principle of the conservation of mass
applies, giving a mass or materials balance equation:
dt
148
= M in − M out
∂ρ
∂t
=−
∂ρu
∂x
+
∂ρv
∂y
+
∂ρw
∂z
(2)
where ρ is fluid density and u, v, and w are velocity components in the x, y, and z directions. Geomorphologists apply
this ‘equation of continuity’ to all cases of mass balance, and
not just fluid balances. Kirkby (1971) used it in hillslope
models. Applied to mass transactions on a hillslope, the
continuity equation states that if more material enters a
slope section than leaves it, then the difference must be
represented by aggradation; conversely, if less material
enters than leaves, then the difference must represent net
erosion. The same principle of continuity of sediment transport applies to other geomorphic systems, including rivers
(e.g., Dietrich and Perron, 2006).
Physical–chemical state equations
Energy and mass conservation in systems
dM
where M is mass, t is time, Min is mass input, and Mout is
mass output. Conservation of mass is a general principle of
Nature and applies to all models of geomorphic systems that
keep account of materials transactions. It applies to smallscale, short-lived systems such as deltas, to medium scale
systems such as sedimentary basins, and to global-scale systems such as the sedimentary cycle and world biogeochemical cycles. Applied to hydrodynamic systems, the law of
mass conservation is expressed as the continuity equation as
first developed by Laplace. In rectangular co-ordinates and
in differential form, the continuity equation is
(1)
These equations express the dependence of one state variable upon another. A classic example is the gas law of
Boyle and Gay-Lussac, which states that PV=RT, where P
is pressure, V is volume, R is a gas constant, and T is absolute temperature. Some researchers have applied physical–chemical-state equations for heat to landscapes. Leopold and Langbein (1962) and Scheidegger (1964) drew an
analogy between temperature and height and between change of heat and change of mass. The rationale behind this approach is a general analogy of the landscape with ideal isolated and closed systems (Chorley, 1962; Scheidegger,
1964; Karcz, 1980), the intrinsic randomness of geomorphic
processes such as soil creep (Culling, 1963), and the aggregate randomness of complex landscape systems in which a
large number of individually deterministic relationships interact (Leopold et al., 1962). Leopold and Langbein (1962)
saw a direct analogy between landscape variables and thermodynamic variables. They equated height of the land surface above a base line with temperature, and equated mass
with heat, which enabled them to equate change in landscape entropy with change in mass divided by height. Scheidegger (1964, 1967, 1991; Lechthaler-Zdenkovic and Scheidegger, 1989) elaborated this analogy, showing that for a
steady state in a landscape, entropy production must be at a
minimum. For such systems, this condition leads to a process–response concept, insofar as, if disturbed, an equilibrium system responds through the adjustment of the state
variables to a new equilibrium configuration (Scheidegger,
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Systems in geomorphology
2004). It is probably fair to remark that the thermodynamic
analogy for equilibrium systems has not contributed vastly
to the understanding of landscape evolution. It suggested
that the general direction of landscape development is always in the direction of relief equalization, as high areas
lower and low areas build up. It also prompted Scheidegger
(1992) to conclude that the systems approach in geomorphology is chiefly limited to purely exogenic processes, and
cannot deal with underlying endogenic processes.
Systems of complex order
Phenomenological equations
The thermodynamics of open systems
These equations describe irreversible processes. The word
‘phenomenological’ refers to the fact that changes in observed macroscopic variables are described without trying to
see what concomitant changes are occurring in atoms, molecules, or electrons. All phenomenological laws describe
processes that tend to equalize the value of macroscopic
variables throughout a system. They relate to the second law
of thermodynamics, which is concerned with irreversible
processes. The second law determines that heat will not flow
from a colder to a hotter body without assistance. In other
words, heat flow occurs spontaneously in a ‘downhill’ direction, but the performance of work must drive the process to
make it flow ‘uphill’ from a cold body to a hot body. The
phenomenological equation describing heat flow is Fourier’s
law of heat conduction, that describing the flow of water in a
porous medium is Darcy’s law, and that describing the flow
of a solute is Fick’s first law of diffusion. In geomorphology,
the first applications of homegrown phenomenological equations dealt with diffusion-like transport processes, such as
soil creep, over hillslopes (e.g., Culling, 1960, 1963, 1965;
Luke, 1972; Hirano, 1968, 1975). Scheidegger (2004) pointed out that such transport equations are derivable from the
analogy between thermodynamics and geomorphic systems
being extended to non-equilibrium cases (see also Tomkoria
and Scheidegger, 1967).
A closed system in classical thermodynamics does not
exchange energy or material with it surroundings. Some
authorities define a closed system as one that exchanges
energy but not matter with its environment and an isolated
system as one that exchanges neither energy nor matter with
it environment. In closed systems, the total amount of energy, E, is always conserved (as stipulated by the first law of
thermodynamics), the amount of available energy inevitably
decreases to zero (as dictated by the second law of thermodynamics), and the entropy, S, of the system (the amount of
unusable energy) increases to a maximum. Around the
middle of the twentieth century, the theory of irreversible
processes and open systems, which physicists, chemists, and
biologists developed, led to a new thermodynamics. Open
systems exchange energy or matter (or both) with their surroundings and can exhibit nonlinear behaviour. The
immensely potent idea of open systems was the brainchild
of von Bertalanffy (1932). From about 1932, von Bertalanffy explored the implications of viewing organisms as open
systems, and, building on the groundbreaking work of Lotka
(1924, 1954), which drew on chemical reaction theory, couched the dynamics of biological systems in terms of
simultaneous differential equations (e.g., Bertalanffy, 1950).
This work was the inspiration for the eventual injection of
open systems concepts into geomorphology.
Lotka had developed equations of ‘physical biology’ to
describe ‘the mechanics of systems undergoing irreversible
changes in the distribution of matter among several components of such systems’ (Lotka, 1924). He had used the reaction equations:
Entropy balance equations
These simply keep account of energy changes – the entropy balance – caused by irreversible processes in a system.
Classical thermodynamics and equilibrium
views in geomorphology
In part owing to the teachings of classical thermodynamics, equilibrium became a preceptive idea in geomorphology during the first half the twentieth century. Classical thermodynamics saw the Universe inexorably winding down to
an ultimate ‘heat death’ (Brush, 1987). It is claimed that Davis’s theory of landscape development follows classical thermodynamic principles in that it ‘seems to operate in some
respects like a closed system tending towards maximum entropy’ (Chorley, 1967), although not all geomorphologists
agree with this interpretation and counter that Davis in point
of fact regarded landscapes as open systems (e.g., Ollier,
1968). Charles Darwin’s (1859) evolutionary worldview also
influenced it, providing the ‘developmental’ terms - youth,
maturity, and senility - for the ‘geographical cycle’ (Chorley,
1965a; see also Stoddart, 1966). The word ‘developmental’
here implies a change toward a stable endpoint (Drury and
Nisbet, 1971), as seen in the putative sequence of transformation from youthful landscape to senile peneplain.
dX i
dt
= F i ( X 1 , X 2 , ... X n ; P , Q )
(3)
to define the kinetics of evolving systems (defined by
variables – the Xs – and constrained by parameters – the Ps
and Qs) (Lotka, 1924). Lotka had noted three interesting
properties of the equations. First, where velocities of change in such a system are zero, an equilibrium or, to be more
exact a steady state, obtains. Second, where the parameters
change slowly, a moving equilibrium (or what geomorphologists now call a dynamic equilibrium) results. Third,
where a change in the system’s environment causes a displacement from equilibrium, Le Châtelier’s principle comes
into operation, which means that the system equilibrium
Géomorphologie : relief, processus, environnement, 2007, n° 2, p. 145-158
149
Richard Huggett
shifts to minimize the effects of the change; in other words,
the system absorbs the change by making as few adjustments as possible.
A note of caution is necessary here. The term ‘dynamic
equilibrium’ is problematic. When first used in chemistry, it
meant equilibrium between a solid and a solute maintained
by solutional loss from the solid and precipitation from the
solution running at equal rates. The word equilibrium captured that balance and the word dynamic captured the idea that,
despite the equilibrium state, changes take place. In other
words, the situation is a dynamic, and not a static, equilibrium. It could be argued that Gilbert used the term in this
sense. Later geomorphologists have used the term to mean
‘balanced fluctuations about a constantly changing system
condition which has a trajectory of unrepeated states through
time’ (Chorley and Kennedy 1971), which is similar to Lotka’s idea of moving equilibrium (cf. Ollier, 1968, 1981).
Building on Lotka’s foundations, von Bertalanffy established several important properties of open systems not
possessed by closed systems. First, owing to the second law
of thermodynamics, an open system will eventually attain
time-independent equilibrium state - a steady state - in which
the systems and its parts are unchanging, with maximum
entropy and minimum free energy. In such a steady state, a
system stays constant as a whole and in its parts, but material
or energy continually passes through it. Second, as a rule,
steady states are irreversible. Third, closed systems cannot
behave equifinally (that is, arrive at equilibrium from different starting positions), but open systems, exchanging energy
or matter with their environment, can do so with the steady
state being independent of the starting conditions. An outcome of von Bertalanffy’s investigations was the emergence in
the early 1950s of a general systems theory, which caught the
attention of some geomorphologists (e.g., Chorley, 1962), at
the core of which was the idea of open systems.
Prigogine (1947) extended and generalized the thermodynamic theory of open systems. He famously wrote the total
change in entropy, dS, in an open system as:
dS = deS+diS,
diS≥0
(4)
where deS denotes transfer of entropy across the boundaries
of the system (entropy exchange between the system and its
environment), and diS denotes the production of entropy within the system due to irreversible processes (such as chemical reactions, diffusion, and heat transport). Only irreversible processes contribute to entropy production in a system
and give time a sense of direction, sometimes metaphorically called ‘time’s arrow’.
Starting with its introduction to ecology by Tansley (1935)
and Lindeman (1942), an open systems approach found
widespread applications within the Earth and life sciences,
including geomorphology. Biological and ecological applications preceded geomorphological ones, but ideas from the
two disciplines (and from pedology) began to cross-fertilize
during the 1960s, when applications in the social sciences
also emerged (e.g., Forrester 1961, 1969, 1971). The idea of
equilibrium remained as dominant a focus as it had been in
150
previous work, but it underwent reinterpretation in terms of
steady state and dynamic equilibrium.
Open geomorphic systems
Strahler (1950, 1952; see also 1980) introduced open systems theory to geomorphology, though Gilbert first mooted
the idea of a system in the subject, and in doing so took an
open systems approach in his concept of dynamic equilibrium: ‘The tendency to equality of action, or the
establishment of a dynamic equilibrium, has already been
pointed out … but one of its most important results has not
been noticed: … in each basin all lines of drainage unite in
a main line, and a disturbance upon any line is communicated through it to the other main line and thence to every
tributary. And as any member of the system may influence all
others, so each member is influenced by every other.’ (Gilbert, 1877).
Thus, Gilbert saw equilibrium landforms adjusting to
geomorphic processes (Chorley, 1965b).Strahler’s low-key
comments on geomorphic systems ushered in a revival of
Gilbertian thinking in geomorphology. Melton (1958), Hack
(1960), Chorley (1962), Howard (1965), Schumm (1977)
and many others took up his call to action. For example,
Hack (1960) abandoned the cyclic theory of landform development (as proposed by Davis) and instead adopted
Gilbert’s concept of dynamic equilibrium as a philosophical
base for interpreting erosional topography in the Central
Appalachians, USA. In this conception, ‘The landscape and
the processes molding it are considered a part of an open
system in a steady state of balance in which every slope and
every form is adjusted to every other. Changes in topographic form take place as equilibrium conditions change, but
it is not necessary to assume that the kind of evolutionary
changes envisaged by Davis ever occur.’ (Hack, 1960). ‘The
concept [of dynamic equilibrium] requires a state of balance between opposing forces such that they operate at equal
rates and their effects cancel each other to produce a steady state, in which energy is continually entering and leaving
the system. The opposing forces might be of various kinds.
For example, an alluvial fan would be in dynamic equilibrium if the debris shed from the mountain behind it were
deposited on the fan at exactly the same rate as it was removed by erosion from the surface of the fan itself. Similarly a
slope would be in equilibrium if the material washed down
the face and removed from its summit were exactly balanced
by erosion at the foot’ (Hack, 1960).
Open systems thinking led to a new typology of systems,
as first proposed by Chorley and Kennedy (1971), and adopted and adapted by Strahler (1980). According to these authors, there are several levels of systems: morphological
(form) systems, cascading (flow) systems, and process–response (process–form) systems (the terms in parenthesis are
Strahler’s). Morphological or form systems are conceived as
sets of morphological variables which are thought to interrelate in a meaningful way in terms of system origin or system function. An example is a hillslope represented by variables pertaining to hillslope geometry, such as slope angle,
Géomorphologie : relief, processus, environnement, 2007, n° 2, p. 145-158
Systems in geomorphology
slope curvature, and slope length, and to hillslope composition, such as sand content, moisture content, and vegetation
cover, all of which are assumed to form an interrelated set.
Cascading systems or flow systems are conceived as ‘interconnected pathways of transport of energy or matter or both,
together with such storages of energy and matter as may be
required’ (Strahler, 1980). An example is a hillslope represented as a store of materials: the weathering of bedrock and
wind deposition both add materials to the store, slope processes transfer materials through the store, and erosion by
wind and fluvial erosion at the slope base remove materials
from the store. Other examples of cascading systems include the water cycle, the biogeochemical cycle, and the sedimentary cycle, all of which may be identified at scales ranging from minor cascades in small segments of a landscape,
through medium-scale cascades in drainage basins and seas,
to mighty circulations involving the entire globe. Processresponse systems or process-form systems are conceived as
an energy flow system linked to a morphological system in
such a way that system processes may alter the system form
and, in turn, the changed system form alters the system processes. A hillslope may be viewed in this way with slope
form variables and slope process variables interacting. Thus
Small and Clark (1982) saw a hillslope as a natural system
within which there are numerous complex linkages between
‘controlling’ factors, processes, and form.
Some geomorphologists passionately and persuasively
promulgated an open systems approach (e.g., Chorley and
Kennedy, 1971). Other researchers applied the open system
concept to soil-landscape units, so linking pedology and
geomorphology (e.g., Walker and Ruhe, 1968; Ruhe and
Walker, 1968; Huggett, 1975, 1982). However, the rise of a
non-equilibrium systems paradigm ended the open systems’
period of celebrity in geomorphological research, although
it persists as a teaching tool. Perhaps its chief legacy is the
identification of negative and positive feedback links in geomorphic systems (e.g,. Phillips, 2006).
Non-equilibrium: chaos and
complexity
Equilibrium questioned
Widespread acceptance of the idea of non-equilibrium (or
disequilibrium) started the third period of systems thinking
in geomorphology. From the 1960s onward, some practitioners began questioning simplistic notions of equilibrium and
steady state. Howard (1965) noted that geomorphic systems
might possess thresholds that separate two rather different
system economies. Schumm (1973, 1977) introduced the
notions of metastable equilibrium and dynamic metastable
equilibrium. He showed that thresholds within a fluvial system cause a shift in its mean state. The thresholds are not
part of a change continuum, but show up as dramatic
changes resulting from minor shifts in system dynamics,
such as caused by a small disturbance. The thresholds may
be extrinsic or intrinsic (see also Chappell, 1983). In metastable equilibrium, static states episodically shift when
thresholds are crossed. In dynamic metastable equilibrium,
thresholds trigger episodic changes in states of dynamic
equilibrium.
Bifurcations and catastrophe models
A system with constraints imposed upon it is driven away
from equilibrium towards a new steady state. If the
constraints are weak then the system will respond in a linear
manner. If the constraints are strong then the system may
change smoothly along a thermodynamic branch into nonequilibrium states in which the theorem of minimum entropy production still applies. At a certain distance from equilibrium, called the thermodynamic threshold, non-linear relationships emerge and the steady states along the branch
are not of necessity stable. Beyond the threshold, the solutions of the equations governing the dynamics of the system
may no longer be unique: the system may enter one of several new regimes. The threshold is therefore a bifurcation
point. The path followed by the thermodynamic branch
beyond the threshold may involve further thresholds and
hence bifurcations. In passing through a bifurcation point,
the system loses its structural stability and undergoes a sudden or catastrophic change to a new form.
The implications of bifurcation theory are profound. Systems that possess bifurcations are describable by deterministic reaction-diffusion equations (similar in form to Lotka’s equations with diffusive terms included), but the presence of bifurcations implies that the dynamics of the system involves a chance element. When driven to some critical value the system can move in more than one way. The
route taken is probably, in essence, a matter of chance fluctuation. The theory of bifurcations permits the same system
to pass through a different series of states and, in a sense, introduces an historical dimension to system development (cf.
Prigogine, 1980).
Some geomorphologists applied bifurcation theory to geomorphic systems in the late 1970s and early 1980s. They
based their arguments on catastrophe theory, which is a special branch of bifurcation theory developed by Thom (1975).
Thom’s elegant treatment of bifurcations and structural stability applies only to systems with a finite number of degrees
of freedom and described by ordinary, rather than partial,
differential equations. So its application to geomorphic systems, where partial differential equations describing changes
in space and time are of paramount importance, seemed unpromising (Karcz, 1980). Undeterred, geomorphologists
tried to use Thom’s ideas (his cusp catastrophe proved a favourite) to explain certain processes at the Earth’s surface.
Examples included Chappell’s (1978) cusp catastrophe
model expressing relationships between wave energy, water
table height relative to a beach surface, and erosion and accretion; Graf’s (1979, 1982) model of the condition at
stream junctions in the northern Henry Mountains of Utah;
and Thornes’s (1983) model of sediment transport in a river.
Indeed, systems may possess multiple equilibrium points,
connected by bifurcations. Thornes (1983) saw catastrophe
theory as promising to produce major new insights into his-
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151
Richard Huggett
torical problems such as river terrace formation, drainage
initiation, and drainage basin evolution. The cusp catastrophe model still has currency, being used for example to
explain the instability of a slip-buckling slope (Qin et al.,
2001).
All these intimations of complex dynamics and non-equilibrium within systems found a firm theoretical footing with
the theory of nonlinear dynamics and chaotic systems that
scientists from a range of disciplines developed, including
geomorphology itself.
Chaotic systems
Classical open systems research characteristically deals
with linear relationships in systems near equilibrium. A fresh
direction in thought and a deeper understanding came with the
discovery of deterministic chaos by Lorenz in the 1963. Technically speaking, this was a rediscovery as Poincaré had dealt
with similar issues in nonlinear mechanics (e.g., Poincaré,
1881-1886). However, deterministic chaos did not make a
grand entrance into the scientific mindset until the 1960s (for
general reviews see Prigogine and Stengers, 1984; Gleick,
1988; Gribbin, 2004). The key change was the recognition of
nonlinear relationships in systems. In geomorphology, nonlinearity means that system outputs (or responses) are not
proportional to systems inputs (or forcings) across the full
gamut of inputs (cf. Phillips, 2006).
Nonlinear relationships produce rich and complex dynamics in systems far removed from equilibrium, which display periodic and chaotic behaviour. The most surprising
feature of such systems is the generation of ‘order out of
chaos’, with systems states unexpectedly moving to higher
levels of organization under the driving power of internal
entropy production and entropy dissipation. Systems of this
kind, which dissipate energy in maintaining order in states
removed from equilibrium, are dissipative systems. It is perhaps useful to distinguish ‘simple’ evolving system, such as
planets, stars, and galaxies, from complex adaptive systems
that learn or evolve by utilizing acquired information, as
when a child learns his or her native language, a strain of
bacteria becomes resistant to an antibiotic, and the scientific
community tests new theories (Gell-Mann, 1994).
In dissipative systems, non-equilibrium is the source of
order, with spontaneous fluctuations growing into macroscopic patterns. The Bénard convective cell is an instructive
example (Prigogine, 1980). Imagine a horizontal layer of
fluid at rest between two parallel planes. Warm the bottom
plane and hold it a higher temperature than the top plane.
When large enough, the temperature gradient between the
two planes causes the state of rest to destabilize and convection begins. Entropy production increases because the
convection is a new mechanism for heat transport. In more
detail, while the fluid is at rest and below the threshold temperature gradient, small convection currents appear as fluctuations from the average state but they are damped and disappear. Above the critical temperature gradient, some of
the fluctuations amplify to produce a macroscopic current.
In effect, the fluctuations trigger an instability that the sys152
tem accommodates by reorganizing itself. The macroscopic
convective cell stabilizes by exchange of energy with the
system’s environment. The general circulation of the atmosphere works on the same principle.
The theory of complex dynamics predicts a new order of
order, an order arising out of, and poised perilously at the
edge of, chaos. It is a fractal order that evolves to form a hierarchy of spatial systems whose properties are holistic and
irreducible to the laws of physics and chemistry. Geomorphic
examples are flat or irregular beds of sand on streambeds or
in deserts that self-organize themselves into regularly spaced
forms – ripples and dunes – that are rather similar in size and
shape (e.g., Baas, 2002). Conversely, some systems display
the opposite tendency – that of non-self-organization – as
when relief reduces to a plain. A central implication of chaotic dynamics for the natural world is that all Nature may
contain fundamentally erratic, discontinuous, and inherently
unpredictable elements. Nonetheless, nonlinear Nature is not
all complex and chaotic. Phillips (2006) sagely noted that
‘Nonlinear systems are not all, or always, complex, and even
those which can be chaotic are not chaotic under all circumstances. Conversely, complexity can arise due to factors
other than nonlinear dynamics’.
One of the most remarkable features of complex systems is
their behaviour. Complex systems are sensitive to initial
conditions, a notion popularized as the Butterfly Effect (in
which a butterfly fluttering its wings in England causes a
hurricane in Australia). They obey simple deterministic laws,
but their behaviour is irregular. Indeed, it may be so irregular that it looks random. However, chaotic behaviour is not
random; it is a cryptic, random-like pattern generated by
simple deterministic laws. So, contrary to the traditional
view that simple causes must produce simple effects (and the
implied corollary that complex effects must have complex
causes), chaos theory predicts that simple causes can create
complex effects. Because of this, knowledge of the simple
deterministic rules governing the behaviour of a complex
system does not guarantee success in predicting the system’s
future behaviour. However, it does mean that, for instance,
landscape models do not need to become increasingly complex to give useful predictions (Favis-Mortlock and de Boer,
2003). Significantly, a system displaying chaotic behaviour
through time usually displays spatial chaos, too. Thus, a
landscape that starts with a few small perturbations here and
there, if subject to chaotic evolution, displays increasing spatial variability as the perturbations grow (Phillips, 1999).
Culling (1985, 1987) recognized the potential importance
of nonlinear dynamics for geomorphic thinking (see also
Huggett, 1988). Phillips is surely the most dogged and industrious proponent of nonlinear dynamics in Earth surface
systems. From his studies, he drew up eleven principles of
Earth surface systems, which illustrate the potency of the
non-equilibrium paradigm (see also Huggett, 2003). More
recently, he has stressed the importance of confronting nonlinear complexity by ‘problematizing nonlinear dynamics
from within a geomorphological context’, rather than applying analytical techniques derived from mathematics, statistics, physics, and other disciplines that use experimental
Géomorphologie : relief, processus, environnement, 2007, n° 2, p. 145-158
Systems in geomorphology
laboratory techniques and numerical models (Phillips, 2006).
To this end, and rooting his arguments in field-based studies,
he discussed methods for detecting chaos in geomorphic systems, explored the idea of unstable and non-equilibrium systems versus stable system achieving a new equilibrium following a change in boundary conditions, and shed a new
light on the question of space and time scales. Convergence
versus divergence of a suitable system metric (elevation or
regolith thickness for instance) is a hugely significant indicator of stability behaviour in a geomorphic system. In landscape evolution, convergence associates with downwasting
and a reduction of relief, whilst divergence relates to dissection and an increase of relief. More fundamentally, convergence and divergence underpin developmental, ‘equilibrium’
conceptual frameworks, with a monotonic move to a unique
endpoint (peneplain or other steady-state landform), as well
as evolutionary, ‘non-equilibrium’ frameworks that engender
historical happenstance, multiple potential pathways and
end-states, and unstable states. The distinction between instability and new equilibria is critical to understanding the
dynamics of actual geomorphic systems, and for a given
scale of observation or investigation, it separates two conditions. On the one hand is a new steady-state equilibrium governed by stable equilibrium dynamics that develops after a
change in boundary conditions or in external forcings. On the
other hand, is a persistence of the disproportionate impacts of
small disturbances associated with dynamic instability in a
non-equilibrium system (or a system governed by unstable
equilibrium dynamics) (Phillips, 2006). The distinction is
critical because the establishment of a new steady-state equilibrium implies a consistent and predictable response throughout the system, predictable in the sense that the same
changes in boundary conditions affecting the same system at
a different place of time would produce the same outcome. In
contrast, a dynamically unstable system possesses variable
modes of system adjustment and inconsistent response, with
different outcomes possible for identical or similar changes
or disturbances. Several indicators potentially allow the identification of newly stable equilibria and dynamically unstable
system states in field situations (tab. 1). Scale is of crucial
importance to an appreciation of systems dynamics (e.g., de
Boer, 1992). As Phillips (2006) put it, ‘Stability, chaos, and
other manifestations of nonlinear dynamical systems are
emergent – that is, they appear or disappear as time frames,
spatial resolutions, and levels of detail are changed’ (tab. 2).
At the conclusion of his review, Phillips (2006) argued that
field-based investigations must inform studies on nonlinear
dynamics in geomorphology, for only by relating system
ideas to real-world landscape forms, processes, and histories,
and by researching on-the-ground signs of chaos and other
nonlinear phenomena, can the geomorphologists test the systems theory. Therein lies a major challenge for future research into geomorphic systems.
Concluding thoughts
This paper has argued that ideas from physics, biology,
and chemistry have strongly influenced geomorphological
thinking. However, to conclude the essay, I would stress two
points. First, I would argue that the impacts of the physical,
biological, and chemical sciences have not inevitably been
direct. Second, I would point out that those geomorphologists who have adopted the language and formalization of a
systems approach, have fashioned their own ideas on system
structure and function, devising applications befitting the
geomorphic systems they study, some of which have been
adopted by scientist in other disciplines. I would end by speculating a little on the future of the systems approach in
geomorphology.
It is probably the case that geomorphologists have imported many systems ideas from biology and evolutionary
ecology, rather than directly through physics and chemistry.
Strahler’s exposure to the open system concept, which set
the systems bandwagon in geomorphology rolling, was
through the writings of von Bertalanffy, a biologist. Interestingly, Strahler introduced the open systems model to
geomorphology when its ramifications were being explored
in many other sciences: Prigogine published his book on the
thermodynamics of open system in 1947, and Denbigh
published a book on the kinetics of open reaction systems in
industrial chemistry in 1951. There again, the source of
ideas about non-linear dynamics in geomorphology is more
population ecology (e.g., May 1973) and meteorology (e.g.
Lorenz 1963) than it is physics.
Geomorphologists have borrowed some terms and
concepts but they have adapted them to uniquely geomorphic settings to create original contributions to geomorphological enquiry. Scheidegger’s (1983) instability principle is
a case in point. This principle rests on the idea that equilibrium in geomorphic systems is commonly unstable equilibrium and any deviation from the equilibrium state may be
self-reinforcing, causing the deviation to grow. This principle ultimately links to the analytical framework of nonlinear partial differential equation systems, but field observations of increasing irregularity over time (such as cirques
tending to grow, karst sinkholes tending to increase in size,
valleys tending to develop steps) moved Scheidegger to propose it. The instability principle is an example of a homegrown systems idea in geomorphology. Another important
example is the work that identifies networks of flows and interactions, representing them as box-and-arrow models or
interaction matrixes and modelling them, which scientists in
other disciplines have found useful.
The above two points show that the evolution of systems
ideas in geomorphology is complicated. As with most general developments in scientific thinking, parallel and overlapping lines of thought in many disciplines characterize the
systems approach. Geomorphology has contributed to systems thinking in science, but equally, developments in physics, chemistry, biology, and ecology have strongly influenced systems thinking in geomorphology. So do systems ideas
in geomorphology have a future? My feeling is that they do
and that, ironically, their greatest contribution may be to help
reunite the geomorphological traditions of process geomorphology and historical geomorphology. Undoubtedly, the
systems approach has proved salutary in some branches of
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153
Richard Huggett
have armed them with a powerful
teaching tool. On the other hand,
most historical geomorphologists
Time series analysis,
have deemed the systems approaphase-space plots,
ch an irrelevance. This may be
Old and new system
qualitative asymptotic
Stability
Dynamic instability
states are stable
stability analysis,
partly because systems models
landscape entropy,
deal with steady states and relatidivergence indices
vely short-term transient states –
Magnitude and duration
they do not have a long-term hisMagnitude and duration
of responses
Divergence index,
torical dimension that involves
of responses proportional
disproportionately large perturbation magnitude
Proportionality
to the change or
unique events. It may also partly
compared with the
index
disturbance
result from the ‘Davis bashing’
change or disturbance
practised by many of the systems
Qualitative commonalities
Multiple modes of
pioneers in geomorphology, inof response – all parts of,
adjustment and
and locations within, a
cluding Chorley and Hack, which
divergence (e.g., different
system display
undeservedly denigrated much of
reaches of a river
Convergence,
qualitatively similar
Davis’s work. With historical sturespond to increased
Field evidence of
divergence, and responses (e.g., in
flows by various
commonality or multiple
dies fast resurging, the future of
commonality
response to increased
combinations of
response
the systems approach may seem
of response
flow, a river widens its
widening, deepening,
channel and increase its
uncertain. However, early discusvelocity an slope
meander amplitude in all
sions of non-linear dynamical
increases, and meander
reaches of similar bed
systems intimated that some geogrowth)
and bank composition)
morphic systems contain determiTable 1 – Criteria for distinguishing equilibrium and non-equilibrium system changes nistic elements and probabilistic
(Based on the discussion in Phillips, 2006.
elements. Deterministic elements
Tableau 1 – Critères pour distinguer des changements d’état rattachés à une situation d’équi- derive from the universal and necessary operation of geomorphic
libre et de non-équilibre (d’après discussion in Phillips, 2006).
laws, which apply in all landscapes at all times, though owing
Timescale
to thresholds, they may not operate in all landscapes at all times;
Short timescale
Long timescale
Spatial scale
Medium timescale
probabilistic elements derive
(seconds to about
(more than a million
(1,000 years to
from historical happenstance and
1,000 years) - Process
years) - Landscape
1,000,000 years)
mechanics
evolution
contingency (e.g. Huggett, 1988).
The latest expansion of this idea
Depends on strength of
suggests that because of their imLandscape scale
weathering–erosion
manent deterministic–contingent
(more than
feedbacks: weak
Unstable
Unstable
1,000,000 m2,
feedbacks aid stability,
duality, the study of non-linear
often much more)
strong feedbacks aid
geomorphic systems approach
instability
may help to bridge the gap betDepends on strength of
ween process and historical stuProbably stable
Probably stable
weathering–erosion
dies (Phillips, 2007). The arguIntermediate scale
(depends on strength of feedbacks: weak
(depends on strength
ment is that geomorphic systems
2
(100 to 1,000,000 m ) weathering–erosion
feedbacks aid stability, of weathering–erosion
have multifarious environmental
feedbacks)
feedbacks)
strong feedbacks aid
instability
controls and forcings, which acting in concert can produce
Local scale
Unstable
Unstable
Stable
many different landscapes. What
2
(less than 100 m )
is more, some controls and forcings are causally contingent
Table 2 – Stability–instability relationships in weathering systems (adapted from a diagram in
and specific to different times
Phillips, 2006).
and places. Dynamical instability
Tableau 2 – Relations de stabilité–instabilité dans les systèmes d’altération (d’après un
creates and enhances some of this
diagramme in Phillips, 2006).
contingency by encouraging the
effects of small initial variations
geomorphology, especially to those that prosecute a geo- and local disturbances to persist and grow disproportionamorphic process approach. Systems formulations have tely big, as established in Scheidegger’s instability prinaided the research of many process geomorphologists and ciple. Now, the combined probability of any particular set
Criterion
154
Equilibrium changes
Non-equilibrium
changes
Determinative measures
Géomorphologie : relief, processus, environnement, 2007, n° 2, p. 145-158
Systems in geomorphology
of global controls is low, and the probability of any set of
local, contingent controls is even lower. As a result, the likelihood of any landscape or geomorphic system existing at
a particular place and time is negligibly small – all landscapes are perfect, in the sense that they are an improbable
coincidence of several different forces or factors (Phillips,
2007). This fascinating notion, which has much in common
with Ollier’s (1981, 1992) ‘evolutionary geomorphology’,
dispenses with the view that all landscapes and landforms
are the inevitable outcome of deterministic laws. In its
stead, it offers a powerful and integrative new view that
sees landscapes and landforms as circumstantial and
contingent outcomes of deterministic laws operating in a
specific environmental and historical context, with several
outcomes possible for each set of processes and boundary
conditions. It remains to be seen if this implication of dynamical systems theory can reconcile different geomorphological traditions. Should it do so, it would be a huge success for the systems approach.
Dedication
I should like to dedicate this paper to the memory of the
late Professor R.J. Chorley, whose work fired my original
interest in a systems approach, and who was always supportive of my own efforts in that field of research.
Acknowledgements
I should like to thank J. Phillips for his perceptive review
of a draft of this paper, and C. Giusti for his careful editing
and thoughtful queries. Their contributions have greatly
improved the quality of the essay.
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Article soumis le 15 juin 2006, accepté le 18 mai 2007.
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