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1/5
G e o m o r p h o l o g y 5 ( 1 9 9 2 ) 2 1 3 - 2 1 7 2 1 3
E l s e v i e r S c i e n c e P u b l i s h e r s B . V . , A m s t e r d a m
imi ta t ions o f the sys tem approach in geomorph ology
A E
S c h e i d e g g e r
Technische Universi t ii t Wien Ins t i tu t J~r Theoret ische G eo d~ ie und Geophysik Abtei lun g Geophysik Gusshausstrasse 27 -29
A-1040 Wien Austr ia
( Re c e iv e d Au gu s t 1 3 , 1 9 91 ; r e v i s e d De c e m b e r 2 3 , 1 9 91 ; a c c e p te d J a n u a r y 6 , 1 99 2 )
A B S T R A C T
S c h e id e gge r , A . E . , 1 9 9 2. L im i ta t io n s o f th e s y s te m a p p r o a c h in ge o mo r p h o lo gy . I n : J . D . P h i l l ip s a n d W . H R e n w ic k ( E d i -
t o r s ) , G e o m o r p h i c S y s t e m s . Geomorphology 5 : 2 1 3 - 2 1 7 .
A s y s t e m i s d e f i n e d a s a s e t o f i n t e r r e l a t e d e l e m e n t s w h i c h f u n c t i o n t o g e t h e r a s a w h o l e . F o r a s t a t i s t i c a l- m e c h a n i c a l
a p p l i c a t i o n o f s y st e m t h e o r y , i t i s a s s u m e d t h a t t h e n u m b e r o f e l e m e n t s i s l a rg e a n d t h a t t h e i n t e r re l a t i o n s a r e c o m p l e x s o
t h a t t h e i n d i v i d u a l i n t e r a c t i o n s c a n n o t b e f o l l o w e d i n d i v i d u a l l y in d e t a i l . U n d e r s u c h c i r cu m s t a n c e s , t h e i n d i v i d u a l p r o -
c e s s e s c a n b e c o n s id e r e d a s q u a s i - r a n d o m , i . e. a s i f t h e y were s t o c h a st i c a n d , b y t h e u s e o f t h e l i m i t t h e o r e m s o f p r o b a b i li t y
t h e o r y , s t a t e m e n t s c a n b e m a d e r e g a rd i n g t h e e x p e c t e d b e h a v i o r o f t h e s y s te m . T h i s a p p r o a c h , h o w e v e r , h a s i t s l im i t a t i o n s :
t h e a s s u m p t i o n t h a t t h e i n d i v i d u a l p r o c es s e s a r e q u a si - s to c h a s t i c d o e s n o t n e c e s s a ri l y ho l d . T h e r e a r e m a n y i n s t a n c es w h e n
t h e i n d i v i d u a l p r o c e s s e s a re u n i f o r m a n d c o r r e la t e d ; i n t h i s c as e , th e y c a n n o t u n d e r a n y c i r c u m s t a n c e s b e c o n s i d e r e d a s
q u a s i - r a n d o m . T h i s a p p l i e s i n g e o m o r p h o l o g y m a i n l y i n c o n n e c t i o n w i t h s t r u c t u r a l a n d ( n e o ) t e c t o n i c p r e d e s i g n . T h e
a p p l i c a t io n o f s y s te m th e o r y in s u c h c i r c u m s ta n c e s l e a d s to f a u l ty r e su l t s .
Introduction
D u r i n g t h e l a s t 3 0 y e a r s , t h e s y s t e m a p -
p r o a c h h a s b e c o m e v e r y p o p u l a r i n g e o m o r -
p h o l o g y : al l k i n d s o f g e o m o r p h i c f e a tu r e s h a v e
b e e n r e g a r d e d a s systems a n d t h e r u l e s o f c o m -
p l e x s y s t e m d y n a m i c s a n d s y n e r g e t i c s h a v e
b e e n a p p l i e d t o t h e m . I n t h i s i t w a s o f t e n f o r -
g o t t e n t h a t s y s t e m d y n a m i c s a r e b a s e d o n a s e t
o f r a t h e r s p e c if i c a s s u m p t i o n s w h i c h m a y o r
m a y n o t a p p l y i n c o n n e c t i o n w i t h s p e c if i c g e o-
m o r p h o l o g i c a l p r o b l e m s . T h u s , t h e a i m o f th e
p r e s e n t p a p e r is to r e v i e w s o m e o f t h e b a s i c
p r in c i p le s o f s y s te m d y n a m i c s a n d o f l a n d -
s c a p e e v o l u t i o n , a n d t h e n t o c o m p a r e t h e f o r-
m e r w i t h t h e l a t t e r . I t w i ll b e s e e n t h a t n o t a l l
g e o m o r p h i c f e a t u re s c a n b e t r e a t e d b y s y s t e m
Correspondence to : A . E . S c h e i d e g g e r , T e c h n i s c h e U n i v -
e rs it ~ it W i e n , I n s t i t u t f t i r T h e o r e t i s c h e G e o d ~ i s i e u n d
G e o p h y s i k , A b t e i l u n g G e o p h y s i k , G u s s h a u s s t r as s e 2 7 - 2 9 ,
A - 1 0 4 0 W i e n , A u s t r i a .
t h e o r y , b u t t h a t s o m e d e f i n i te l y h a v e t o b e d e a l t
w i t h b y o t h e r m e t h o d s .
P r i n c i p l e s o f sy s tem th eory
Concept of a system
T h e c o n c e p t o f a s y s t e m h a s b e e n i n t ro -
d u c e d b y B e r t a l a n f f y ( 1 9 3 2 ) . A c c o r d i n g l y , i n
o r d e r t o s p e a k o f a s y st e m , o n e n e e d s
( 1 ) a s e t o f e l e m e n t s id e n t i f i e d w i t h s o m e
v a r i a b l e a t t r i b u t e s ,
( 2 ) a s e t o f r e l a t i o n s h i p s b e t w e e n a t tr i b u t e s ,
( 3 ) a se t o f r e l a t i o n s h i p s b e t w e e n a t t r ib u t e s
a n d t h e e n v i r o n m e n t .
T h u s , a s y s t e m i s a se t o f i n t e r r e l a t e d e l e m e n t s
w h i c h f u n c t i o n t o g e th e r as a n e n t it y e m b e d d e d
i n an e n v i r o n m e n t . T h e l a st c o n d i t i o n a b o v e
a s s u m e s t h a t t h e s y s t e m i s o p e n t o s o m e e x te r -
n a l e n v i r o n m e n t . I n e f f e c t , t h e d i s t i n c t i o n o f
w h e r e t h e s y s t e m p r o p e r e n d s a n d t h e e n v i r o n -
0 1 6 9 - 5 5 5 X / 9 2 / $ 0 5 . 0 0 1 9 9 2 E l s e v i e r S c i e n c e P u b l i s h e r s B . V . A l l r i g h t s r e s e rv e d .
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214 -x.~. SCHEIDEGGER
ment begins is arbitrary. A natural delimita-
tion occurs only ifa system is completely closed
within itself. However, most geomorphic sys-
tems are open in the sense that mass and en-
ergy enter at one instance, cascade through the
system and exit at ano ther instance.
Quasi stochastic approach
Formal system theory is, in fact, a mathe-
matical discipline. Gene rally it is involved with
statistical methods. In co mmon usage, the term
sys tem is often take n more loosely: a sys-
te m is simply represented by the interplay of
some parts, such as a hi-fi sys tem which is
represente d by the interplay of a CD-player, an
amplifier and loudspeakers. This loose con-
cept, however, does not lend itself easily to for-
mal analysis. The usefulness of formal system
theory is evident if the number o f elements in
the set is large and the relationships between
their attributes complex. By large and
complex is mea nt that it is no longer feasible
to consider each element and every relation-
ship separately and to calculate explicitly the
combined effect of these relationships on the
behavior of the whole.
In geomorphology, one deals essentially with
mechanical systems. The elements are me-
chanical entities (particles, river courses, slope
angles, etc. ) which interact in a c omplex way.
The state of the system is then defined by giv-
ing all the attribute-values of all the elements;
the set of all attribute-values can be repre-
sented by a point in a multi-dimensional phase-
space. During the evolution of the system, this
point will describe a trajectory in phase space.
As noted, it is assumed that the number of
elements is large and tha t the attribute values
of each element can be ascertained in detail.
Therefore, there is a quasi-probability distri-
bution of phase points which represents the
position likelihood of the system in phase space
within the limits of one's ignorance. This prob-
ability distribution can be taken as the basis for
statistical predictions of the behavior of the
system. Within the limits of one's ignorance, a
whole ensemble of states is possible. Because
of some fundame nta l natural laws, e.g. conser-
vation of mass (or energy), not all thinkable
states in phase space are possible, but these may
be restric ted to certain regions.
An observable quantity is generally a gross
characteristic built on a conglome rate function
of attributes. The expectation value for this
observable quantity is the average of the con-
glomera te over all states of the system that are
possible. On occasion, the conglomerate func-
tion has been calculated for those attributes
that correspond to the most probable state of
the system, but this is not in conformity with
the pr inciples of statistical physics as they were
developed by Boltzmann and Gibbs in connec-
tion with gas dynamcs (see e.g. Sommerfeld,
1964 ). Thus, most probable and expe cted
characteristics are not the same; it is logically
evident that ensemble averages have to be
taken of the attributes and not those attributes
for the most probable state of the system.
The approach presented above has been
called quasi-stochastic. The word quasi in-
dicates that the evolut ion of a large system (e.g.
landscape ) is not in reality a stochastic process
at all, but a well determined mechanical one.
This is also the case tbr thresholds in systems
where one or mor e parameters possess one or
several critical bifur cati on values at which
the structure changes of the control parame ter
lead to further hierarchically arranged bifur-
cations which may be run through until a quasi-
stationary state of complete chaos is reached
(Schuster, 1984; Brun, 1986; Harrison and
Biswas, 1986 ). The latter is also, in principle,
completely defined; however, the knowledge of
the details of the processes is so incomplete that
it is conveni ent to treat them, within the limits
of one's ignorance, as if they werestochastic.
Equilibrium conditions
In equilibrium conditions the basic proba-
bilities are stationary. In phase-space, this is
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LIMITATIONSOF THE SYSTEM APPROACH IN GEOMORPHOLOGY
215
e x p r e s se d b y t h e c o n f i n e m e n t o f t h e p h a s e
p o i n t s t o c e r t a i n f i x e d r e g i o n s . I f t h e r e i s a c o n -
s t a n t o f th e m o t i o n H , t h i s r e g i o n is r e p r e -
s e n t e d b y t h e s u b s p a c e t h a t h a s t h e e q u a t i o n :
H = c o n s t . ( 1 )
I f t h e i n t e r a c ti o n s a r e m a n y a n d c o m p l e x , th e
p h a s e p o i n t w i l l m o v e i n t i m e ; b e c a u s e w e s u p -
p o s e e q u i l i b r i u m c o n d i t i o n s , a l l p o i n t s o f t h e
s u b s p a c e w i l l , i n t i m e , b e e q u a l l y c l o s e l y a p -
p r o a c h e d b y t h e p h a s e - p o i n t : t h i s i s t h e e r -
g o d ic t h e o r e m e m b o d y i n g t h e i d e a th a t t h e
t i m e a v e r ag e s c a n b e r e p l a c e d b y e n s e m b l e a v -
e r a g e s ( c f . e .g . S o m m e r f e l d , 1 9 6 4 ) .
I f t h e s y s t e m c o n s i st s o f a la r g e n u m b e r o f
s u b s y s t e m s w h i c h f l u c t u a t e a n d c o n t r i b u t e
p a r t -v a l u e s H t o t h e c o n s t a n t o f t h e m o t i o n H ,
t h e n t h e d i s t r i b u t i o n P o f t h e s e v a l u e s i n ca -
n o n i c a l ( c f. e .g . S o m m e r f e l d , 1 9 6 4 ) f o r m i s :
P i H ~ ) = 1 / Z ) e x p ( - H i / k T ) ( 2 )
w h e r e Z i s t h e p a r t i t i o n f u n c t i o n r e q u i r e d f o r
n o r m a l i z a t i o n a n d
k T
a p a r a m e t e r . T h i s i s a
c o n s e q u e n c e o f t h e l i m i t t h e o r e m s o f p r o b a b i l-
i ty t h e o r y u n d e r t h e a s s u m p t i o n t h a t t h e i n t e r -
a c t i o n s b e t w e e n s u b s y s t e m s a r e m a n y a n d u n -
c o r r e l a t e d . O n t h i s b a s i s , i t is p o s s i b l e t o s e t u p
a c o m p l e t e a n a lo g y b e tw e e n t h e r m o d y n a m i c s
a n d l a n d s c a p e s ; o n e c a n d e f i n e a n a l o g s o f al l
t h e t h e r m o d y n a m i c f u n ct io n s ( n o t a b ly t h e e n -
t r o p y ) a n d c o r r e s p o n d i n g la n d s c a p e v a r i a b le s
( S c h e i d e g g e r , 1 9 6 7 ) . I t is c l e a r t h a t t h e c o n -
s t a n t o f t h e m o t i o n is m a s s ( t h is i s c o n s e r v e d
i n t h e l a n d s c a p e p r o c e s s ) , t h e t e m p e r a t u r e
e q u i v a l e n t i s t h e t o p o g r a p h i c h e i g h t h , a n d f o r
t h e e n t r o p y a n a l o g S o n e h a s :
d S = d M / h 3 )
T h e a n a lo g y b e tw e e n t e m p e r a t u r e T a n d
t o p o g r a p h i c h e i g h t h a n d t h e c o r r e s p o n d i n g
d e f i n i ti o n o f g e o m o r p h i c e n t r o p y S h a d b e e n
p o s t u l a t e d e a r l i e r b y L e o p o l d a n d L a n g b e i n
( 1 9 62 ) o n e n t i r e l y h e u r i s t i c g r o u n d s , f r o m t h e
a n a l o g y w i t h a h e a t e n g i n e . T h e s e a u t h o r s o b -
s e r v e d t h a t t h e t h e r m o d y n a m i c p r i n c i p l e a p -
p l i e d to t h e l a n d s c a p e a n a l o g s o f th e t h e r m o -
d y n a m i c v a r i a b l e s l e d t o v a l i d s t a t e m e n t s
r e g a r d i n g l a n d s c a p e d e v e l o p m e n t . T h e s ta ti s-
t i c a l j u s t i f i c a t i o n o f t h e s e a n a l o g i e s l e n d s a
m u c h b e t t e r f o u n d a t i o n t o t h e l a t te r .
A n e x t e n s i o n o f t h e e q u i l i b r i u m c a s e is to t h e
s t e ad y s t a te , f o r w h i c h t h e e n t r o p y p r o d u c t i o n
r a te a m u s t b e a m i n i m u m :
I h
a = - ~ T J d x = m i n ( 4)
w h e r e J i s t h e m a s s f lu x p e r u n i t t im e . F r o m
t h e a b o v e e q u a t i o n s , i t i s p o s s i b le t o c a l c u l a t e
e q u i l i b r i u m r i v e r p r o f il e s , e tc .
T h e e q u i l i b r iu m t h e o r y i m m e d i a t e l y le a d s to
t h e p r o c e s s - r e s p o n s e c o n c e p t : a s s o o n a s a n
e q u i l i b r i u m is d i s tu r b e d , t h e s y s te m r e s p o n d s
b y t h e a d j u s t m e n t o f t h e r e m a i n i n g v a r ia b l e s
t o a n e w e q u i l i b r i u m c o n f i g u r a ti o n .
N o n e q u i l i b r i u m c o n d i t i o n s
T h e a n a l o g y c a n b e e x t e n d e d t o n o n e q u i l i b -
r i u m c a s es . I f t h e ( l a r g e ) s y s t e m p o s s e ss e s a
l a r g e n u m b e r o f s u b s y s t e m s i n w h i c h a n o n -
n e g a t i v e q u a n t i t y i s t r a n s f e r r e d b y a s t a t i s t i -
c a l l y f l u c t u a t i n g t r a n s f e r p r o c e s s w h o s e e x a c t
n a t u r e i s u n s p e c i f i e d , t h e n t h e c e n t r a l l i m i t
t h e o r e m o f p r o b a b i l i t y t h e o r y l e a d s to a d i f f u -
s i v i t y e q u a t i o n f o r t h e n o n - n e g a t i v e q u a n t i t y ,
p r o v i d e d t h e f l u c tu a t i o n s a r e l i n e a r ly a d d i t i v e
( T o m k o r i a a n d S c h e i d e g g e r , 1 9 6 7 ) . T h i s i m -
m e d i a t e l y l e a d s t o a n u n d e r s t a n d i n g o f t h e
d e g r a d a t i o n o f l a n d s c ap e s .
andscape evolution
Q u i t e a p a r t f r o m t h e d i s c u s si o n a b o v e , l a n d -
s c a p e e v o l u t i o n h a s b e e n d e s c r i b e d b y a se t o f
h e u r i s t i c f u n d a m e n t a l p r i n c i p l e s ( S c h e i d e g -
ge r , 1 9 87 ) ; t h e s e w i l l b e b r i e f l y d e s c r i b e d .
P r i n c ip l e o f a n t a g o n i s m
T h e m o s t f u n d a m e n t a l o f t h e l a n d s ca p e
p r i n c ip l e s i s t h a t o f th e a n t a g o n i s m o f e n d o -
g e n i c ( o r i g i n a t i n g i n s i d e t h e s o l i d E a r t h , i . e .
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21 6 A.E. SCHEIDEGGER
t e c t o n i c ) a n d e x o g e n i c ( o r i g i n a t i n g o u t s i d e t h e
s o l i d E a r t h ) p ro c e s s e s . I n th i s , t h e c o n d i t i o n o f
t h e s u r f a c e o f t h e E a r t h r e p r e s e n t s t h e i n s t a n -
t a n e o u s r e su l t o f th e a c t i o n o f t h e s e t w o t y p e s
o f p r o c e ss e s : u p l i f t ( t e c t o n i c ) a n d d e g r a d a t i o n
( e x o g e n i c ) .
T h e
intensity
o f th e a n t a g o n i s m d e t e r m i n e s
t h e c h a r a c t e r o f t h e l a n d s c a p e : i f t h e u p l i f t -
d e n u d a t i o n r at e is m i l l i m e t re s p er y e ar ( m m /
a ) , o n e h a s a y o u t h t y p e , if i t i s 0 . 5 r a m / a , a
m a t u r e - t y p e , a n d i f i t i s < 0 .1 m m / a , a n o l d
a g e ty p e l a n d s c a p e. T h e p r i m a r i l y e n d o g e n e t i -
c a ll y c a u s e d f e a t u r e s a r e m o r p h o l o g i c a l l y sy s -
t e m a t i c , t h e e x o g e n e t i c a l ly c a u s e d o n e s a r e
m o r p h o l o g i c a l l y r a n d o m ( S c h e i d eg g e r , 1 9 7 9 ) .
Principle o f instability
T h e p r i n c ip l e o f a n t a g o n i s m d e s c ri b e s im -
p o r t a n t f e a tu r e s o f la n d s c a p e e v o l u t i o n . H o w -
e v e r , i t d o e s n o t a c t a l o n e . T h e a n t a g o n i s t i c a c-
t i o n o f e n d o g e n i c a n d e x o g e n ic p r o ce s s e s
e f fe c t s a f u n d a m e n t a l i n s t a b i l i ty o f a l a n d -
s c a p e. T h u s , w e a r r i v e a t a p r i n c i p l e o f in s t a -
b i l i ty . T h i s i n s t a b i l i t y e x p r e s s e s i t s e l f i n t w o
w a y s : f i r s t , m a n y i n d i v i d u a l l a n d s c a p e e l e -
m e n t s a r e i m p e r m a n e n t , a l t h o u g h t h e i r g e n -
e r a l c h a r a c t e r a p p e a r s a s p e r m a n e n t . T h e b e s t-
k n o w n e x a m p l e o f t h is t y p e i s t h e m e a n d e r i n g
o f ri v er s : th e m e a n d e r s c h a n g e c o n s t a n t l y , b u t
t h e m e a n d e r c h a r a c t e r s t a y s e s s e n t i a l l y t h e
s a m e . T h e s e c o n d a s p e c t o f t h e i n s t a b i l i t y is
t h a t t h e i n d i v i d u a l l a n d s c a p e e l e m e n t s ar e n o t
o n ly i m p e r m a n e n t , b u t a ls o r e m o v e t h e m -
s e lv e s f r o m t h e s t a te o f u n i f o r m i t y : s t r a i g h t
r i v e r s b e c o m e c u r v e d , b r o o k s e n d u p a s a s e -
q u e n c e o f r i f f l e s a n d p o o l s , v a l l e y s b e c o m e
s t e p p e d . I t i s a s i f t h e r e w e r e a p o s i t i v e f e e d -
b a c k b e t w e e n a n o n u n i f o r m i t y a n d i ts g ro w t h
( S c h e i d e g g e r , 1 9 8 3 ) .
atena principle
A f u r t h e r p r i n c i p l e i s r e l a t e d t o t h e i n s ta b i l -
i t y p r i n c i p l e ; t h i s i s t h e c a t e n a p r i n c i p l e
( S c h e i d e g g e r , 1 9 8 6 ) . I t s t a te s t h a t a s l o p e c o n -
s is ts o f f l a t - s t e e p - f l a t e l e m e n t s . T h i s i s a c o n -
s e q u e n c e o f th e i n s t a b i l it y p r i n c ip l e , i n a s m u c h
a s t h e e r o s i o n r a t e i n c r e a s e s w i t h t o p o g r a p h i c
g r a d i e n t ( p o s i t i v e f e e d b a c k ) l e a d i n g t o a c h a r -
a c t e r i s t i c d e v i a t i o n f r o m u n i f o r m i t y .
Selection principle
A p r i n c i p l e o f a c o m p l e t e l y d i f f e r e n t n a t u r e
i s t h e s e l e c t io n p r i n c i p l e ( G e r b e r , 1 9 6 9 ) . I t
s t a t e s t h a t i n e x o g e n i c p r o c e s s e s , t h e s t a t i c a l ly
s t a b l e f o r m a t i o n s a r e s e l e c t e d f o r p r e s e r v a -
t i o n . O n e h a s h e r e a d i r e c t i v i t y i n t h e e r o s i v e
a c t i o n w h i c h is t o w a r d s t a b le f o r m s .
Principle of tectonic control
F i n a ll y , t h e p r i n c i p l e o f te c t o n i c c o n t r o l
s t a te s t h a t m a n y l a n d s c a p e f e a t u r e s a r e c o n d i -
t i o n e d b y d e e p - s e a t e d t e c t o n i c p r o c e s se s . S u c h
f e a tu r e s a r e m o r e c o m m o n t h a n h a d b e e n u s u -
a ll y t h o u g h t . T h u s , t h e U - s h a p e o f gl a ci a l v al -
l ey s ( H a n t k e , 1 9 78 , p . 7 0 ) , t h e o r i e n t a t i o n
p a t t e r n s o f r iv e r n e t s ( S c h e i d e g g e r , 1 9 8 2, p p .
2 8 - 3 1 ) a n d t h e d i r e c t i o n s o f l a n d s li d e s
( S c h e i d e g g e r a n d A i , 1 9 8 7 ) a r e p r i m a r i l y
p r e d e s i g n e d b y e n d o g e n i c p r o c e ss e s a n d n o t b y
e x o g e n i c o n e s a s u s u a l l y t h o u g h t . I t i s t h e r e -
f o r e a p p r o p r i a t e t o e l e v a t e t h e s e o b s e r v a t i o n s
t o a p r i n c i p l e o f t e c t o n i c c o n t r o l o f l a n d -
s c a p e e v o l u t i o n ( S c h e i d e g g e r a n d A i , 1 9 8 6 ) .
ppl i cabi l i ty of system theory in landscape
evolution
F i n a l ly , o n e c a n i n v e s t i g a t e t h e a p p l i c a b i l i ty
o f t h e s y s t e m a p p r o a c h i n l a n d s c a p e e v o l u t i o n ,
t h e l a t t e r b e i n g d e s c r i b e d b y t h e h e u r i s t i c p r i n -
c i p l e s o u t l i n e d i n t h e l a s t s e c t i o n .
The funda me ntal features of the system
approach
W h e n w e r e v i e w t h e s y s t e m a p p r o a c h w e
n o t e t h a t t h e m o s t i m p o r t a n t f e a t u r e o f t h e l at -
t e r i s t h a t t h e r e a r e m a n y e l e m e n t s r e l a t e d b y
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c o m p l e x r e l a t i o n s . A l l o f s y s t e m t h e o r y , t h e n ,
i s e s s e n t i a ll y b a s e d o n p r o b a b i l i s t i c c o n s i d e r a -
t i o n s . F o r t h i s , o n e n e e d s i n d e e d m a n y e l e -
m e n t s a n d u n c o r r e l a t e d r e l a ti o n s s o t h a t a v e r -
a g es c a n b e ta k e n a n d t h e a s s u m p t i o n o f qu a s i-
s t o c h a s t ic i t y h o l d s . I f t h e s e a s s u m p t i o n s , m a n y
e l e m e n t s a n d q u a s i - r a n d o m n e s s , a r e n o t c o r -
r e c t , t h e s y s t e m a p p r o a c h l e a d s t o f a u l t y r e su l t s.
T h u s , t h e u s e fu l n e ss o f t h e s y s t e m a p p r o a c h
i s p r i n c i p a l l y l i m i t e d t o p u r e l y e x o g e n i c p r o -
c e s s e s ; r e g a r d i n g e n d o g e n i c p r o c e s s e s t h e u n -
d e r l y in g t e c to n i c p r o c e ss e s m u s t b e d e s c r i b e d
b y e x p l i c i t d e t e r m i n i s t i c m e c h a n i c s . I t i s t h e
m a i n a r g u m e n t o f t h i s p a p e r t h a t t h e s y s te m -
a t ic e n d o g e n i c p r e d e s i g n i n g e o m o r p h o l o g y i s
f ar m o r e w i d e s p re a d th a n c o m m o n l y a s su m e d .
rinciples o f landscape evolution and system
theory
e f e r e n c e s
W e s h al l n o w r e v i e w t h e f u n d a m e n t a l l a n d -
s c a p e e v o l u t i o n p r i n c i p l e s i n t h e l i g h t o f a p o s -
s ib l e c o rr e c t n e ss o f t h e b a s i c a s s u m p t i o n s o f
s y s t e m t h e o r y .
E v i d e n t l y , t h e p r i n c i p l e o f a n t a g o n i s m a p -
p l i e s t o a l a n d s c a p e c o n s i s t i n g o f m a n y e l e -
m e n t s t h a t a r e c o m p l e x l y r e la t e d . S o d o e s t h e
p r i n c i p l e o f i n s t a b il i ty a n d t h e c a t e n a p r i n c i p le .
H o w e v e r , th e s e l ec t io n p r i n c i p le e m b o d i e s a
d i r e c t i o n a l i t y b a s e d o n w e l l - d e f i n e d s t a ti c c o n -
s i d e r a t i o n s : c e r t a i n f o r m s a r e p r e f e r r e d w h o s e
c o n f i g u r a t i o n s h a v e n o t h i n g t o d o w i t h r a n -
d o m i n t e r a c t i o n s . T h i s i s e v e n m o r e t h e c a s e
i n c o n n e c t i o n w i t h t h e p r i n c i p l e o f t e c t o n i c
p r e d e s i g n . H e r e , t e c t o n i c c o n d i t i o n s , s u c h a s
t h e i n t r a p l a t e s t re s s f ie l d , a c t o n l a r g e n u m b e r s
o f la n d s c a p e p o i n t s a n d t h i s a c t i o n i s a n y t h i n g
b u t u n c o r r e l a t e d a n d q u a s i - r a n d o m . I n p r in c i -
p l e, th e s y s t e m a p p r o a c h c a n n o t b e e x p e c t e d t o
w o r k i n c o n n e c t i o n w i t h s t r u c t u r a l l a n d -
s c a p e s , o r t e c t o n i c l a n d s c a p e s : T e c t o n i s m
i s w e l l - o r d e r e d a n d a c ts o v e r d i m e n s i o n s t h a t
a r e o f t h e o r d e r o f t h o se o f t h e t e c t o n i c p l a te s .
T h u s , i n e a r l ie r s ta t e m e n t s o f th e p r i n c i p l e o f
a n t a g o n i s m ( S c h e id e g g e r , 1 9 79 ) i t w a s n o t e d
t h a t t h e e n d o g e n i c a l l y c o n d i t i o n e d f e a tu r e s a r e
not
r a n d o m . I t i s o n l y t h e e x o g e n i c p r o c e s s e s
t h a t a c t i n a q u a s i - r a n d o m f a s h i o n . I n e f f e c t ,
t h is m a y o n l y b e a q u e s t i o n o f sc al e: w a t e r a n d
a i r al so m o v e i n a c o m p l e t e l y m e c h a n i s t i c w a y ,
b u t t h e u n i f o r m i t y s ca l e i n t h e m o t i o n is o f t h e
o r d e r o f c m ; i n t e c t o n i c p r o c e s se s , t h e i r o r d e r
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