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Geomorphology and 

General Systems Theory

GEOLOGICAL SURVEY PROFESSIONAL PAPER 500-B
Geomorphology and 

General Systems Theory

By RICHARD J. CHORLEY

THEORETICAL PAPERS IN THE HYDROLOGIC AND 

GEOMORPHIC SCIENCES

GEOLOGICAL SURVEY PROFESSIONAL PAPER 500-B

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1962
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington 25, D.C.
CONTENTS

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Abstract_ __________________________________________________________________________________________________ Bl

Geomorphology and general systems theory__--_-__-__..-_.______________________________________________________ 1

Acknowledgments__ _-_--------_--__-__--__-_---_.._______--_________________________-________-_________-_-- 9

Eef erences._--_-__-____-----------_--_-------_-_-_.._--____-_____-_________-_--______---____-_____-__-_-__ -- 9

in

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THEORETICAL PAPERS IN THE HYDROLOGIC AND GEOMORPHIC SCIENCES

GEOMORPHOLOGY AND GENERAL SYSTEMS THEORY

By EICHARD J. CHORLET

"[Nature] * * * creates ever new forms; what exists has nover existed before, what has existed returns not again everything Is new 

and yet always old * * *. There is an eternal life, a coming into 

being and a movement in her; and yet she goesi not forward." (Goethe: 

Essay on Nature).1

ABSTRACT

An appreciation of the value of operating within an appropriate general systematic model has emerged from the recognition that the interpretation of a given body of information 

depends as much upon the character of the model adopted as 

upon any inherent quality of the data itself. Fluvial geomorphic phenomena are examined within the two systematic models 

which have been found especially useful in physics and biology 

closed and open systems, for which simple analogies arei given. 

Certain qualities of classic closed systems, namely the progressive increase in entropy, the irreversible character of operation, 

the importance of the initial system conditions, the absence of 

intermediate equilibrium states and the historical bias, permit 

comparisons to be made with the Davisian concept of cyclic 

erosion. The restrictions which were inherently imposed upon 

Davis' interpretation of landforms thus become more obvious. 

It is recognized, however, that no single theoretical model can 

adequately encompass the whole of a natural complex, and that 

the open system model is imperfect in that, while embracing the 

concept of grade, the progressive reduction of relief cannot be 

conveniently included within it. The open system characteristic of a tendency toward a steady state by self-regulation is 

equated with the geomorphic concepts of grade and dynamic 

equilibrium which were developed by Gilbert and later "dynamic" workers and, despite continued relief reduction, it is 

suggested that certain features of landscape geometry, as well 

as certain phases of landscape development, can be viewed profitably as partially or completely time-independent adjustments. 

In this latter respect the ratios forming the bases of the laws of 

morphometry, the hypsometric integral, drainage density, and 

valley-side slopes can be so considered. The relative values of 

the closed and open systematic frameworks of reference are 

recognized to depend upon the rapidity with which landscape 

features can become adjusted to changing energy flow, and a 

contrast is made between Schumm's (1956) essentially open 

system treatment of weak clay badlands and the historical approach which seems most profitable in treating the apparently 

ancient landscapes of the dry tropics.

1 Goethe, Fragment liber die Natur (1781-82) : Translated from 

Goethe's samtllche Werke, Jubilaumsausgabe, Stuttgart and Berlin, v. 

39, p. 3-4, undated.

Finally, seven advantages are suggested as accruing from 

attempts to treat landforms within an open system framework:

1. The focusing of attention on the possible relationships between form and process.

2. The recognition of the multivariate character of most geomorphic phenomena.

3. The acceptance of a more liberal view of changes of form 

through time than was fostered by Davisian thinking.

4. The liberalizing of attitudes toward the aims and methods of 

geomorphology.

5. The directing of attention to the whole landscape assemblage, 

rather than to the often minute elements having supposed 

historical significance.

6. The encouragement of geomorphic studies in those many 

areas where unambiguous evidence for a previous protracted erosional history is lacking.

7. The introduction into geography, via geomorphology, of the 

open systematic model which may prove of especial relevance to students of human geography.

GEOMORPHOLOGY AND GENERAL SYSTEMS THEORY

During the past decade several valuable attempts 

have been made, notably by Strahler (1950,1952A, and 

1952B), by Culling (1957, p. 259-261), and by Hack 

(1960, p. 81,85-86; Hack and Goodlett, 1960), to apply 

general systems theory to the study of geomorphology, 

with a view to examining in detail the fundamental 

basis of the subject, its aims and its methods. They 

come at a time when the conventional approach is in 

danger of subsiding into an uncritical series of conditioned reflexes, and when the more imaginative modern 

work in geomorphology often seems to be sacrificing 

breadth of vision for focus on details. In both approaches it is a common trend for workers to be increasingly critical of operating within general frameworks of thought, particularly with the examples of the 

Davis and Penck geormorphic systems before them, and 

"classical" geomorphologists have retreated into restricted historical studies of regional form elements, 

whereas, similarly, quantitative workers have often

Bl
B2 THEORETICAL PAPERS IN THE HYDROLOGIC AND GEOMORPHIC SCIENCE®

withdrawn into restricted empirical and theoretical 

studies based on process.

It is wrong, however, to confuse the restrictions 

which are rightly associated with preconceived notions 

in geomorphology with the advantages of operating 

within an appropriate general systematic framework. 

Tho first lead to the closing of vistas and the decrease 

of opportunity; the second, however, may increase the 

scope of the study, make possible correlations and associations which would otherwise be impossible, generally 

liberalize the whole approach to the subject and, in 

addition, allow an integration into a wider general conceptual framework. Essentially, it is not possible to 

enter into a study of the physical world without such a 

fundamental basis for the investigation, and even the 

most qualitative approaches to the subject show very 

strong evidence of operations of thought within a logical general framework, albeit a framework of thought 

which is in a sense unconscious. Hack (1960), for example, has pointed to the essential difference between 

the approaches to geomorphology of Gilbert and Davis, 

and in this respect the fundamental value of the adoption of a suitable general framework of investigation 

based on general systems theory becomes readily 

apparent.

Following the terminology used by Von Bertalanffy 

(1950 and 1960), it is possible to recognize in general 

two separate systematic frameworks wherein one may 

view the natural occurrence of physical phenomena; 

the closed system and the open system (Strahler, 1950, 

p. 6T5-676, and 1952A, p. 934-935). Hall and Fagan 

(1956, p. 18) have defined a system as "* * * a set of 

objects together with relationships between the objects 

and between their attributes." In the light of this definition, it is very significant that one of the fundamental 

purposes of Davis' approach to landf orms was to study 

them as an assemblage, in which the various parts 

might be related in an areal and a time sense, such that 

different systems might be compared, and the same system followed through its sequence of time changes. 

Closed systems are those which possess clearly defined 

closed boundaries, across which no import or export of 

materials or energy occurs (Von Bertalanffy, 1951). 

This view of systems immediately precludes a large 

number, perhaps all, of the systems with which natural 

scientists are concerned; and certainly most geographical systems are excluded on this basis, for boundary 

problems and the problems of the association between 

areal units and their interrelationships lie very close to 

the core of geographical investigations.

Another characteristic of closed systems is that, with 

a given amount of initial free, or potential, energy 

within the system, they develop toward states with

maximum "entropy" (Von Bertalanffy, 1951, p. 161- 

162). Entropy is an expression for the degree to which 

energy has become unable to perform work. The increase of entropy implies a trend toward minimum free 

energy (Von Bertalanffy, 1956, p. 3). Hence, in a 

closed system there is a tendency for leveling down of 

existing differentiation within the system; or, according to Lord Kelvin's expression, for progressive degradation of energy into its lowest form, i.e. heat as undirected molecular movement (Von Bertalanffy, 1956, 

p. 4). This is expressed by the second law of thermodynamics (Denbigh, 1955) which, in its classic form, is 

formulated for closed systems. In such systems, therefore, the change of entropy is always positive, associated with a decrease in the amount of free energy, or, to 

state this another way, with a tendency toward progressive destruction of existing order or differentiation.

Thus, one can see that Davis' view of landscape development contains certain elements of closed system 

thinking including, for example, the idea that uplift 

provides initially a given amount of potential energy 

and that, as degradation proceeds, the energy of the system decreases until at the stage of peneplanation there 

is a minimum amount of free energy as a result of the 

leveling down of topographic differences. The Davisian peneplain, therefore, may be considered as logically homologous to the condition of maximum entropy, 

general energy properties being more or less uniformly 

distributed throughout the system and with a potential 

energy approaching zero. The positive change of 

entropy, and connected negative change of free energy, 

implies the irreversibility of events within closed systems. This again bears striking similarities to the 

general operation of the geomorphic cycle of Davis. 

The belief in the sequential development of landforms, 

involving the progressive and irreversible evolution of 

almost every facet of landscape geometry, in sympathy 

with the reduction of relief, including valley-side 

slopes and drainage systems, is in accord with closed 

system thinking. Although "complications of the geographical cycle" can, in a sense, put the clock back, 

nothing was considered by Davis as capable of reversing the clock. The putting back of the clock by uplift, 

therefore, came to be associated with a release, or an 

absorption into the new closed system, of an increment 

of free energy, subsequently to be progressively dissipated through degradation.

Also, in closed systems there is the inherent characteristic that the initial system conditions, particularly 

the energy conditions, are sufficient to determine its 

ultimate equilibrium condition. This inevitability of 

closed-system thinking is very much associated with the 

view of geomorphic change held by Davis. Not only
GEOMORPHOLOGY AND GENERAL SYSTEMS THEORY B3

this, but the condition of a closed system at any particular time can be considered largely as a function of the 

initial system conditions and the amount of time which 

has subsequently elasped. Thus closed systems are 

eminently susceptible to study on a time, or historical, 

basis. This again enables one to draw striking analogies between closed-system thinking and the historical 

approach to landform study which was proposed by 

Davis.

Finally, it is recognized that closed systems can reach 

a state of equilibrium. Generally speaking, however, 

this equilibrium state is associated with the condition 

of maximum entropy which cannot occur until the system has run through its sequential development. In 

addition, it is impossible to introduce the concept of 

equilibrium into a closed-system framework of thought 

without the implication that it is associated with stationary conditions. The only feature of the cyclic 

system of Davis which employed the general concept 

of equilibrium was that of the "graded" condition of 

stream channels and slopes which, significantly, Davis 

borrowed from the work of Gilbert, who had an entirely 

noncyclic view of landform development (Hack, I960, 

p. 81). Characteristically, the concept of grade was 

the one feature of Davis' synthesis which seems least 

well at home in the cyclic framework, for it has always 

proved difficult to imagine how, within a closed system 

context, a graded or equilibrium state could exist and 

yet the associated forms be susceptible to continued 

change namely, downcutting or reduction.

The foregoing is not meant to imply that it is unprofitable to consider any assemblage of phenomena 

within a closed system framework, or, as Davis did, to 

overstress those aspects or phases which seem to achieve 

most significance with reference to the closed system 

model. It is important, however, to recognize the 

sources of partiality which result, not from any inherent 

quality of the data itself, but from the general systematic theory under which one is operating. In reality, no 

systematic model can encompass the whole of a natural 

complex without ceasing to be a model, and the phenomena of geomorphology present problems both when 

they are viewed within closed and open systematic 

frameworks. In the former, the useful concept of 

dynamic equilibrium or grade rests most uncomfortably ; in the latter, as will be seen, the progressive, loss 

of a component of potential energy due to relief reduction imposes an unwelcome historical parameter.

A simple, classic example of a closed system is represented by a mass of gas within a completely sealed, and 

insulated container. If, initially, the gas at one end 

of the container is at a higher temperature than that at 

the other, this can be viewed as a condition of maximum

segregation, maximum free energy, and, consequently, 

of maximum ability to perform work, should this thermal gradient be harnessed within a larger closed system. 

This is the state of minimum entropy. It is obvious, 

however, that this state of affairs is of a most transient 

character and that immediately an irreversible heat 

flow will begin toward the cooler end of the container. 

This will progressively decrease the segregation of mass 

and energy within the system, together with the available free energy and the 'ability of this energy to 

perform work, bringing about a similarly progressive 

increase of entropy. While the system remains closed 

nothing can check or hinder this inevitable leveling 

down of differences, which is so predictable that, knowing the initial energy conditions, the thermal conductivity of the gas and the lapse of time, one could 

accurately calculate the thermal state of the system 

at any required stage. Thus the distribution of heat 

energy and the heat flow within the system have a 

progressive and sequential history, the one becoming 

less segregated and the other ever-decreasing. Nor is 

it possible to imagine any form of equilibrium until 

all the gas has attained the same temperature, when 

the motion of the gas molecules is quite random and the 

static condition of maximum entropy obtains.

Open systems contrast quite strikingly with closed 

systems. An open system needs an energy supply for 

its maintenance and preservation (Keiner and Spiegelman, 1945), and is in effect maintained by a constant 

supply and removal of material and energy (Von Bertalanffy, 1952, p. 125). Thus, direct analogies exist 

between the classic open systems and drainage basins, 

slope elements, stream segments and all the other formassemblages of a landscape. The concept of the open 

system includes closed systems, however, because the 

latter can be considered a special case of the former 

when transport of matter and energy into and from the 

system becomes zero (Von Bertalanffy, 1951, p. 156). 

An open system manifests one important property 

which is denied to the closed system. It may attain a 

"steady state" (Von Bertalanffy, 1950; and 1951, p. 

156-157), wherein the import and export of energy and 

material are equated by means of an adjustment of the 

form, or geometry, of the system itself. It is more difficult to present a simple mechanical analog to illustrate 

completely the character and operations of an open 

system but it may be helpful to visualize one such system as represented by the moving body of water contained in a bowl which is being constantly filled from 

an overhead inflow and drained by an outflow in the 

bottom. If the inflow is stopped, the bowl drains and 

the system ceases to exist; whereas, if the inflow is 

stopped and the outflow is blocked, the system partakes
B4 THEORETICAL PAPERS IN THE HYDROLOGIC AND GEQMORPHIC SCIENCE'S

of many of the features of a closed system. In such an 

arrangement, changes in the supply of mass and energy 

from outside lead to a self-adjustment of the system to 

accommodate these changes. Thus, if the inflow is increased, the water level in the basin rises, the head of 

water above the outflow increases, and the outflow discharge will increase until it balances the increased inflow. At this time the level of water in the bowl will 

again become steady.

Long ago, Gilbert recognized the importance of the 

application of this principle of self-adjustment to landform development:

The tendency to equilibrium of action, or to the establishment 

of a dynamic equilibrium, has already been pointed out in the 

discussion of the principles of erosion and of sculpture, but one 

of its most important results has not been noticed.

Of the main conditions which determine the rate of erosion, 

namely, the quantity of running water, vegetation, texture of 

rock, and declivity, only the last is reciprocally determined by 

rate of erosion. Declivity originates in upheaval, or in the displacement of the earth's crust by which mountains and continents are formed: but it receives its distribution in detail in 

accordance with the laws of erosion. Wherever by reason of 

change in any of the conditions the erosive agents come to have 

locally exceptional power, that power is steadily diminished by 

the reaction of the rate of erosion upon declivity. Every slope 

is a member of a series, receiving the water and the waste of the 

slope above it, and discharging its own water and waste upon 

the slope below. If one member of the series is eroded with 

exceptional rapidity, two things immediately result: first, the 

member above has its own level of discharge lowered, and its 

rate of erosion is thereby increased; and second, the member 

below, being clogged by an exceptional load of detritus, has its 

rate of erosion diminished. The acceleration above and the 

retardation below diminish the declivity of the member in which 

the disturbance originated: and as the declivity is reduced, the 

rate of erosion is likewise reduced.

But the effect does not stop here. The disturbance that has 

been transferred from one member of the series to the two 

which adjoin it, is by then transmitted to others, and does not 

cease until it has reached the confines of the drainage basin. 

For in each basin all lines of drainage unite in a main line, and 

a disturbance upon any line is communicated through it to the 

main line and thence to every tributary. And as a member of 

the system may influence all the others, so each member is influenced by every other. There is an interdependence throughout 

the system. (Gilbert, 1880, p. 117-118).

This form-adjustment is brought about by the ability 

of an open system for self-regulation (Von Bertalanffy, 

1952, p. 132-133). Le Chatelier's Principle (originally 

stated for equilibrium in closed systems) can be expanded also to include the so-called "Dynamic Equilibrium" or steady states in open systems:

Any system in * * * equilibrium undergoes, as a result of a 

variation in one of the factors governing the equilibrium, a 

compensating change in a direction such that, had this change 

occurred alone it would have produced a variation of the factor 

considered in the opposite direction. (Prigogine and Defay, 

1954, p. 262.)

A geomorphic statement of this principle has been given 

by Mackin (1948):

A graded stream is one in which, over a period of years, slope 

is delicately adjusted to provide, with available discharge and 

with prevailing channel characteristics, just the velocity required for the transportation of the load supplied from the 

drainage basin. The graded stream is a system in equilibrium; 

its diagnostic characteristic is that any change in any of the 

controlling factors will cause a displacement of the equilibrium 

in a direction that will tend to absorb the effect of the change.

The cyclic adaptation of the concept of grade did not 

give sufficient importance to the factors, other than 

channel slope, which a stream system can control for 

itself, and in this respect Davis' ignorance of the significance of the practical experiments of Gilbert (1914) 

is most evident. A stream system cannot greatly control its discharge, which represents the energy and mass 

which is externally supplied into the open system. 

Neither can it completely control the amount and character of the debris supplied to it, except by its action of 

abrasion and sorting or as the result of the rapport 

which seems to exist regionally between stream-channel 

slope and valley-side slope (Strahler, 1950, p. 689). 

However, besides adjusting the general slope of its 

channel by erosion and deposition, a stream can very 

effectively and almost instantaneously control its transverse channel characteristics, together with its efficiency 

for the transport of water and load, by changes in depth 

and width of the channel. As Wolman (1955, p. 47) 

put it:

The downstream curves on Brandywine Creek * * * suggest 

that the adjustment of channel shape may be as significant as 

the adjustment of the longitudinal profile. There is no way in 

which one could predict that the effect of a change in the independent controls would be better absorbed by a change in 

slope rather than by a change in the form of the cross section.

It may be, therefore, that a stream or reach may be 

virtually always adjusted (Hack, 1960, p. 85-86), in 

the sense of being graded or in a steady state, without 

necessarily presenting the smooth longitudinal profile 

considered by the advocates of the geomorphic cycle as 

the hallmark of the "mature graded condition." The 

state of grade is thus analogous to the tendency for 

steady-state adjustment, it is perhaps always present 

and, therefore, this presence cannot be employed necessarily as an historical, or stage, characteristic. It is interesting that the concept of the vegetational "climax," 

which has often been compared to that of grade, has 

passed through a somewhat similar metamorphosis. 

The original idea of a progressive approach to a static 

equilibrium of the ecological assemblage (Clements, 

1916, p. 98-99) has been challenged by the open system 

interpretation of Whittaker (1955, p. 48), with an historical link being provided by the "individualistic
GEOMORPHOLOGY A1JD GENERAL SYSTEMS THEORY B5

concept" of Gleason (1926-27; 1927), much in the same 

way as Mackin's concept of grade links those of E'avis 

and Wolman.

The forms developed, together with the mutual adjustment of internal form elements and of related systems, are dependent on the flow of material and energy 

in the steady state. The laws of morphometry (Chorley, 1957) express one aspect of this relationship in 

geomorphology. In addition, adjustment of form elements implies a law of optimum size of a system and 

of elements within a system (Von Bertalanffy, 1956, 

p. 7). This is mirrored by Gilbert's (1880, p. 134-135) 

symmetrical migration of divides and by Schumm's 

constant of channel maintenance (1956, p. 607), and is 

illustrated by Schumm's (1956, p. 609) contrast between basin areas of differing order.

Although a steady state is in many respects a limeindependent condition, it differs from the equilibrium 

of closed systems. A steady state means that the aspects 

of form are not static and unchanging, but that they 

are maintained in the flow of matter and energy traversing the system. An open system will, certain conditions presupposed, develop toward a steady state and 

therefore undergo changes in this process. Such 

changes imply changes in energy conditions and, connected with these, changes in the structures during the 

process. The trend toward, and the development of, 

a steady state demands not an equation of force: and 

resistance over the landscape, but that the forms within 

the landscape are so regulated that the resistance presented by the surface at any point is proportionate to 

the stress applied to it.

Erosion on a slope of homogeneous material with uniform 

vegetative cover will be most rapid where the erosional power 

of the runoff is greatest. This nonuniform erosional process 

will in time result in a more stable slope profile which would 

offer a uniform resistance to erosion. (Little, 1940, p. 33.)

In this way the transport of mass and energy (i.e., water 

and debris) is carried on in the most economical manner. With time, landscape mass is therefore being removed and progressive changes in at least some of the 

absolute geometrical properties of landscape, particularly relief, are inevitable. It is wrong, however, to 

assume, as Davis did, that all these properties are involved necessarily in this progressive, sequential 

change. To return briefly to the analogy of the bowl. 

If the rush of water through the outflow is capable of 

progressively enlarging the orifice, the increasing discharge at the outflow, uncompensated at the inflow, will 

cause the head of water in the bowl to decrease. This 

loss of head will itself, however, constantly tend to 

compensate the increasing outflow, but, if the enlargement of the outflow orifice proceeds, this is a losing

battle and an important feature of the system will be 

the progressive and sequential loss of head. However, 

not all features of this system will reflect this progressive change of head, and, for example, the structure 

of the flow within the bowl will remain much the same 

while any head of water at all remains there. The 

dimensionless ratios between landscape forms, similarly, seem to express the steady state condition of adjusted forms from which mass is constantly being removed. The geometrical ratios which form the basis 

of the laws of morphometry, and the height-area ratios 

involved in the dimensionless, equilibrium hypsometric 

integral are examples of this adjustment:

In late mature and old stagesi of topography, despite the 

attainment of low relief, the hypsometirc curve shows no significant variations from the mature form, and a low integral results 

only where monadnocks remain * * *. After monadnock masses 

are removed, the hypsometric curve may be expected to revert 

to a middle position with integrals in the general range of 

40 to 60 percent. (Strahler, 1952B, p. 1129-1130.)

In a drainage basin composed of homogenous material, 

in which no monadnocks would tend to form, it seems 

possible, therefore, that the dimensionless percentage 

volume of unconsumed mass (represented by the hypsometric integral) may achieve a time-independent 

value. It has been suggested, however, that the construction of the hypsometric curve may be so inherently 

restricted as to make the hypsometric integral insensitive to variations of an order which would be necessary 

to recognize such an equilibrium state (Leopold, written communication, 1961). This steady state principle 

has been tentatively extended by Schumm (1956, p. 

616-617) to certain other aspects of drainage basin 

form:

* * * the form of the typical basin at Perth Amboy changes 

most rapidly in the earliest stage of development. Relief and 

stream gradient increase rapidly to a point at which about 25 

percent of the mass of the basin has been removed, then remains 

essentially constant. Because relief ratio [the ratio between 

total relief of a basin and the longest dimension of the basin 

parallel to the principal drainage] elsewhere has shown a close 

positive correlation with stream gradient, drainage density, and 

ground-slope angles, stage of development might be expected 

to have little effect on any of these values once the relief 

ratio has become constant.

In the steady state of landscape development, therefore, force and resistance are not equated (which would 

imply no absolute form change), but balanced in an 

areal sense, such that force may still exceed resistance 

and cause mass to be removed. Now, as has been 

pointed out, removal of mass under steady-state conditions must imply some progressive changes in certain 

absolute geometrical properties of a landscape, notably 

a decrease in average relief, but by no means all such 

properties need respond in this simple manner to the
B6 THEORETICAL PAPERS IN THE HYDROLOGIC AND GEOMORPHIC SCIENCES

progressive removal of mass. The existence, for example, of the optimum magnitude principle for individual 

systems, or subsystems, implies that if the available 

energy within the system is sufficient to impose the optimum magnitude on that system, this magnitude will be 

maintained throughout a period of time and will not 

always be susceptible to a progressive, sequential 

change. Thus, Strahler (1950) has indicated that erosional slopes which are being forced to their maximum 

angle of repose by aggressive basal stream action will, 

of necessity, retain this maximum angle despite the 

progressive removal of mass with time.

Total energy is made up of interchangeable potential 

energy and flux, or kinetic, energy (Burton, 1939, p. 

328) and even if the potential energy component decreases within an open system due to its general reduction, in other words along with a continual change in 

one aspect of form (i.e., relief), the residual flux energy 

may be of such overriding importance as to effectively 

maintain a steady state of operation. In practice the 

steady state is seldom, if ever, characterized by exact 

equilibrium, but simply by a tendency to attain it. 

This is partly due to the constant energy changes which 

are themselves characteristic of many open system operations, but the steady state condition of tendency 

toward attainment of equilibrium is a necessary prerequisite, according to Von Bertalanffy (1950, p. 23; 

and 1952, p. 132-33), for the system to perform work 

at all. Now, once a steady state has been established, 

the influence of the initial system conditions vanishes 

and, with it, the evidence for a previous history of the 

system (Culling, 1957, p. 261) (i.e., was our bowl full or 

empty at the start?). Indeed, in terms of analyzing 

the causes of phenomena which exhibit a marked steadystate tendency, considerations regarding previous history become not only hypothetical, but largely irrelevant. This concept contrasts strikingly with the historical view of development which is fostered by closedsystem thinking. Wooldridge and Linton (1955, p. 3) 

have gone so far as to say that:

Any such close comprehension of the terrain can be obtained 

in one way only, by tracing its evolution.

An even more extreme statement of the same philosophy has been made by Wooldridge and Goldring (1953, 

p. 165):

The physical landscape, including the vegetation cover, is the 

record of processes and the whole of the evidence for its evolution is contained in the landscape itself.

The whole matter hinges on the rapidity with which 

landscape features become adjusted to energy flow, 

which may itself be susceptible to rapid changes, particularly during the rather abnormal latest geologic 

period of earth history. Obviously, most existing features are the product of both past and reasonably contemporary energy conditions, and the degree to which 

these latter conditions have gained ascendancy over 

the former is largely a function of the ratio between 

the amount of present energy application and the 

strength (whatever this may mean) of the landscape 

materials. Thus, the geometry of stream channels 

(Leopold and Maddock, 1953) and the morphometry 

of weak clay badlands (Schumm, 1956) show remarkable adjustments to contemporary processes on whatever time level the action of these processes may be 

denned (Wolman and Miller, 1960) whereas, at the 

other end of the energy/resistance scale, erosion surfaces cut in resistant rock and exposed to the low present energy levels associated with the erosional processes 

of certain areas of tropical Africa can only be understood on the basis of past conditions. Between these 

two extremes lies the major part of the subject matter 

of geomorphology including considerations of slope development, and it is here where the apparent dichotomy 

between the two systematic approaches to the same 

phenomena, termed by Bucher (1941; see also Strahler, 

1952A, p. 924r-925) "timebound" and "timeless," is most 

acute. In a related context, the problem of timeboundversus-timeless phenomena becomes especially obvious 

when rates of change and the ability to adjust are 

underestimated, as when vegetational assemblages have 

been correlated with the assumed stages of geomorphic 

history in the folded Appalachians by Braun (1950, p. 

241-242) and in Brazil by Cole (1960, p. 174-177).

One can appreciate that in areas where good evidence 

for a previous landscape history still remains, the historical approach may be extremely productive, as exemplified by the work of Woolridge and Linton on southeastern England. However, in many (if not most) 

areas the condition is one of massive removal of past 

evidence and of tendency toward adjustment with 

progressively contemporaneous conditions. It is an impossibly restricted view, therefore, to imagine a universal approach to landform study being based only 

upon considerations of historical development.

Another characteristic of the open system is that 

negative entropy, or free energy, can be imported into 

it because of its very nature. Therefore, the open 

system is not defined by the trend toward maximum 

entropy. Open systems thus may maintain their organization and regularity of form, in a continual exchange of their component materials. They may even 

develop toward higher order, heterogeneity, hierarchical differentiation and organization (Von Bertalanffy, 

1952, p. 127-129). This is mirrored in geomorphology 

by the characteristic development of interrelated drainage forms, and goes along with a concept of progressive
GEOMORPHOLOGY ANE> GENERAL SYSTEMS THEORY B7

segregation (Von Bertalanffy, 1951, p. 148-149). This, 

to a minor extent, militates against the general view 

of adjustment previously discussed, insofar, as, with 

time, rates of interactions between form elements in 

an open system may tend to decrease. Therefore, it 

is quite reasonable to assume that mutual adjustments 

of form within geomorphic systems might be more 

difficult of accomplishment and delayed where the relief, through its influence over the potential energy of 

the system, is low rather than where there is a higher 

potential energy in the system.

Steady-state conditions can be interrupted by a disturbance in the energy flow or in the resistance, leading 

to form adjustments allowing a new steady state to be 

approached. These adjustments, however, do imply a 

consumption of energy and there is a "cost of transition" from one steady state to another (Burton, 1939, 

p. 334, 348). A particular geomorphic instance of this 

dissipation might be presented by the phenomenon of 

"overshooting" where active, but sporadic, processes are 

operating on weak materials, as instanced when the failure of steep slopes reduces them to inclinations very 

much below their repose angles, and by the excessive 

cutting and subsequent filling of alluvial channels associated with flash floods.

The dynamic equilibrium of the steady state manifests itself in a tendency toward a mean condition, of 

unit forms, recognizable statistically, about which 

variations may take place over periods of time with 

fluctuations in the energy flow. These periods of time 

may in some instances be of very short duration, and the 

fluctuations of transverse stream profiles are measurable in the days, or even minutes, during which changes 

of discharge occur. These constant adjustments to new 

steady-state conditions may be superimposed on a general tendency for change possibly associated with the 

reduction of average relief through time. This general 

relief change, however, does not imply a sympathetic 

change of all the other features of landscape geometry. 

As has been demonstrated by Strahler (1958) and 

Melton (1957), for example, drainage density is controlled by a number of factors of which relief is only 

one. Eecent work seems to be indicating that relief 

(naturally including considerations of average land 

slope) probably has only a relatively small influence 

over drainage density, which may be masked or negated 

altogether by the other more important factors (for 

example, rainfall intensity and surface resistance) 

which are not so obviously susceptible to changes with 

time. Denbigh, Hicks and Page (1948, p. 491) have 

pointed out that:

Quite large changes of environment may take place, without 

the need for more than a small internal readjustment.

Horton (1945) did not believe, as did Glock (1931), 

that drainage density could be employed as a measure 

of landscape "age," and, indeed, it is not difficult to 

entertain the possibility that certain features of landscape geometry may be relatively unchanging, in actual 

dimensional magnitude as well as in dimensionless 

ratio, throughout long periods of erosional history.

For many landscape units, changes on either level are 

slow, or in some instances nonexistent. Under steady 

state conditions, therefore, corresponding local morphometric units will, as regards their form and magnitude, tend to crowd around a very significant mean 

value, imparting to a geomorphic region its aspects of 

uniformity. Strahler's (1950, p. 685) "law of constancy of slopes" is an expression of one phase of this 

adjustment. It is interesting that the general principle of the operation of a steady state condition was 

intuitively recognized long ago by Play fair (1802, 

p. 440) :

The geological system of Dr. Button, resembles, in many respects, that which appears to preside over the heavenly motions. 

In both, we perceive continual vicissitude and change, but confined within certain limits, and never departing far from a certain mean condition, which is such, that in the lapse of time, the 

deviations from it on one side, must become just equal to the 

deviations from it on the other.

Often the achievement of exact equilibrium in nature 

occurs only momentarily as variations about the mean 

take place (Mackin, 1948), and in these instances the 

existence of the steady state can only be recognized statistically (Strahler, 1954). In the study of landscape, 

the steady state condition indicated by discrete, close 

and recognizable statistical groupings of similar units, 

is characteristic of regions of uniform ratios between 

process and surface resistance.

Davis' view of landscape evolution was that the passage of time, of necessity, imprinted recognizable, significant and progressive changes, on every facet of 

landscape geometry. The recognition, however, that 

landscape forms represent a steady-state adjustment 

with respect to a multiplicity of controlling factors 

obliges one to take a less rigid view of the evolutionary 

aspects of geomorphology. When a geometrical form 

is controlled by a number of factors, any change of form 

with the passage of time is entirely dependent upon the 

net result of the effect of time upon those factors. Some 

factors are profoundly affected by the passage of time, 

others are not; some factors act directly (using the term 

in the mathematical sense) upon the form, others inversely ; some factors exercise an important control over 

form aspects, others a less important one. Thus, if a 

particular geometrical feature of landscape is primarily controlled by a factor the action of which does not 

change greatly with time, or if the changes of factors
B8 THEORETICAL PAPERS IN THE HYDROLOGIC AND GEOMORPHIC SCIENCES

having direct and inverse controls tend to cancel out 

the net effect of the changes, then the resulting variation in geometry may itself -be small perhaps insignificant.

A last important characteristic of open systems is 

that they are capable of behaving "equifinally" in 

other words, different initial conditions can lead to 

similar end results (Von Bertalanffy, 1950, p. 25; and 

1952, p. 143). Davisian (closed system) thinking is 

instinctively opposed to this view, and the immediate 

and facile assumption, for example, that most breaks 

of stream slope are only referable to a polycyclic 

mechanism is an illustration of the one cause-one effect 

mentality. The concept of equifinality accentuates the 

multivariate nature of most geomorphic processes and 

militates against the unidirectional inevitability of the 

closed system cyclic approach of Davis. The approach 

contrasts strikingly with that of Gilbert:

Phenomena are arranged in chains of necessary sequence. In 

such a chain each link is the necessary consequent of that which 

precedes, and the necessary antecedent of that which follows 

* * * If we examine any link of the chain, we find it has 

more than one antecedent and more than one consequent * * * 

Antecedent and consequent relations are therefore not merely 

linear, but constitute a plexus; and this plexus pervades nature. 

(Gilbert, 1886, p. 286-287.)

To sum up, the real value of the open system approach to geomorphology is:

Firstly, that it throws the emphasis on the recognition of the adjustment, or the universal tendency 

toward adjustment, between form and process. Both 

form and process are studied, therefore, in equal measure, so avoiding the pitfall of Davis and his more recent 

associates of the complete ignoring of process in 

geomorphology:

In a graded drainage system the steady state manifests itself 

in the development of certain topographic form characteristics 

which achieve a time-independent condition * * * Erosional 

and transportational processes meanwhile produce a steady 

flow (averaged over a period of years or tens of years) of water 

and waste from and through the landform system * * * Over 

the long span of the erosion cycle continual adjustment of the

components in the steady state is required as relief lowers and 

available energy diminishes. The forms will likewise show a 

slow evolution.

Applied to erosion processes and forms, the concept of the 

steady state in an open system focuses attention upon the relationship between dynamics and morphology. (Strahler, 1950, 

p. 676.)

The relation between process and form lies close to 

the heart of geomorphology and, in practice, the two 

are often so intimately linked that the problem of cause 

and effect may present the features of the "hen and the 

egg." Approach from either direction is valuable, 

however, for knowledge of form aids in the understanding of process, and studies of process help in the clearer 

perception of the significant aspects of form.

The study of form may be descriptive merely, or it may become analytical. We begin by describing the shape of an object 

in the simple words of common speech: we end by defining it 

in the precise language of mathematics; and the one method 

tends to follow the other in strict scientific order and historical 

continuity * * * The mathematical definition of a "form" 

has a quality of precision which was quite lacking in our 

earlier stage of mere description * * * [employing means 

which] are so pregnant with meaning that thought itself is 

economized; * * *.

We are apt to think of mathematical definitions as too strict 

and rigid for common use, but their rigour is combined with 

all but endless freedom * * * we reach through mathematical 

analysis to mathematical synthesis. We discover homologies 

or identities which were not obvious before, and which our 

description obscured rather than revealed: * * *

Once more, and this is the greatest gain of all, we pass 

quickly and easily from the mathematical concept of form 

in its statical aspect to form in its dynamical relations: we rise 

from the conception of form to an understanding of the forces 

which gave rise to it; and in the representation of form and in 

the comparison of kindred forms, we see in the one case a 

diagram of forces in equilibrium, and in the other case we 

discern the magnitude and the direction of the forces which 

have sufficed to convert the one form into the other * * *.

* * * Every natural phenomenon, however simple, is really 

composite, and every visible action and effect is a summation 

of countless subordinate actions. Here mathematics shows her 

peculiar power, to combine and generalize * * *.

A large part of the neglect and suspicion of mathematical 

methods in * * * morphology is due * * * to an ingrained 

and deep-seated belief that even when we seem to discern a 

regular mathematical figure in an organism * * * [the form] 

which we so recognise merely resembles, but is never entirely 

explained by, its mathematical analogue; in short, that the 

details in which the figure differs from its mathematical prototype are more important and more interesting than the features 

in which it agrees; and even that the peculiar aesthetic pleasure 

with which we regard a living thing is somehow bound up with 

the departure from mathematical regularity which it manifests 

as a peculiar attribute of life * * *. We may be dismayed 

too easily my contingencies which are nothing short of irrelevant compared to the main issue; there is a principle of 

negligibility * * *.

If no chain hangs in a perfect catenary and no raindrop is 

a perfect sphere, this is for the reason that forces and resistances other than the main one are inevitably at work * * *, 

but it is for the mathematician to unravel the conflicting forces 

which are at work together. And this process of investigation 

may lead us on step by step to new phenomena, as it has done 

in physics, where sometimes a knowledge of form leads us to 

the interpretation of forces, and at other times a knowledge of 

the forces at work guides us towards a better insight into 

form. (Thompson, 1942, p. 1026-1029.)

Secondly, open-system thinking directs the investigation toward the essentially multivariate character of 

geomorphic phenomena (Melton, 1957; Krumbein, 

1959). It is of interest to note that the physical, and 

the resulting psychological, inability of geographers to
GEOMORPHOLOGY AND GENERAL SYSTEMS THEORY B9

handle successfully the simultaneous operation of a 

number of causes contributing to a given effect has beon 

one of the greatest impediments to the advancement of 

their discipline. This inability has prompted, at worst, 

a unicausal determinism and, at best, an unrealistic 

concentration upon one or two contributing factors at 

the expense of others. Davis' preoccupation with 

"stage" in geomorphology has been paralleled, for example, by an undue emphasis on the part of some economic geographers upon the factor of "distance" in 

many analyses of economic location.

Thirdly, it allows a more liberal view of changes of 

form with time, so as to include the possibility of nonsignificant or nonprogressive changes of certain aspects 

of landscape form through time.

Fourthly, while not denying the value of the historical approach to landform development in those 

areas to which the application of this framework of 

study is appropriate, open-system thinking fosters, a 

less rigid view regarding the aims and methods of 

geomorphology than that which appears to be held by 

proponents of the historical approach. It embraces 

naturally within its general framework the forms possessing relict facets, those indeed which form the basis 

for the present studies of denudation chronology, under 

the general category of the "inequilibrium" forms of 

Strahler (1952B). There is no uniquely correct method 

of treatment for a given body of information, and Postan (1948, p. 406) has been at pains to demonstrate the 

purely subjective distinction which exists between alternative explanations of phenomena on an immediately 

causal or generic basis, as against an historical or biographical one:

For the frontier they draw separates not the different compartments of the universe but merely the different mental attitudes to the universe as a whole. What makes the material fact 

a fit object for scientific study is that men are prepared to treat 

it as an instance of a generic series. What makes a social 

phenomenon an historical event is that men ask about it individual or, so to speak, biographical questions. But there is no 

reason why the process should not be reversed; why we should 

not ask generic questions about historical events or should not 

write individual biographies of physical objects. Here Spinoza's 

argument still holds. The fall of a brick can be treated as a 

mere instance of the general study of falling bricks, in which 

case it is a material fact, and part and parcel of a scientific 

enquiry. But it is equally possible to conceive a special interest 

in a particular brick and ask why that individual brick behaved 

as it did at the unique moment of its fall. And the brick will 

then become an historical event. Newton must have been confronted with something of the same choice on the famous day 

when he sat under the fabulous apple tree. Had he asked himself the obvious question, why did that particular apple choose 

that unrepeatable instant to fall on that unique head, he might 

have written the history of an apple. Instead of which he asked 

himself why apples fell and produced the theory of gravitation. 

The decision was not the apple's but Newton's.

Davis was metaphorically struck by landscape and 

chose to write a history of it.

Fifthly, the open-system mentality directs the study 

of geomorphology to the whole landscape assemblage, 

rather than simply to the often minute elements of 

landscape having supposed evolutionary significance.

Sixthly, the open-system approach encourages rigorous geomorphic studies to be carried out in those 

regions and perhaps these are in the majority where 

the evidence for a previous protracted erosional history 

is blurred, or has been removed altogether.

Lastly, open-system thinking, when applied to geomorphology, has application within the general framework of geography; for geomorphology has always 

influenced geographical thinking to a great, and possibly excessive, degree (as, for example, that of Whittlesey, 1929; Darby, 1953; Beaver, 1961). Opensystem thinking is characteristically less rigidly 

deterministic in a causative and time sense than the 

closed-system approach. The application of this 

closed-system approach to problems of human geography is extremely dangerous because, of its nature, it 

directs the emphasis toward a narrow determinism, and 

encourages a concentration upon closed boundary conditions, upon the tendency toward homogeneity and 

upon the leveling down of differences. Open-system 

thinking, however, directs attention to the heterogeneity of spatial organization, to the creation of segregation, and to the increasingly hierarchical differentiation 

which often takes place with time. These latter features are, after all, hallmarks of social, as well as biological, evolution.

ACKNOWLEDGMENTS

The author would like to thank Professor Ludwig von Bertalanffy of the University of Alberta and Dr. Luna B. Leopold 

of the United States Geological Survey for critically reading 

this manuscript and for making many valuable suggestions both 

regarding the general methodology and the application of general systems theory to geomorphology.

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