Limitations in system approach in geomorphology.pdf

8/10/2019 Limitations in system approach in geomorphology.pdf

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


5/5

L I M IT A T I ON S O F T H E S Y S T EM A P P R O A C H I N G E O M O R P H O L O G Y

217

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

m a y b e s e v er al h u n d r e d s o r t h o u s a n d s o f km .

Berta lanffy, L.V., 1 932. Th eore t ische Biologie. Spr inger,

Berlin, 1 70 pp .

Brun , E ., 19 86 . Ordnun gs-Hierarch ien . N eujahr sb la t t

N aturfo rsch . Gesellsch. Ziirich, 188. Stiick Orell-Fiissli,

Ziirich, 40 pp.

Gerbe r , E . , 1969 . Bi ldung v on G ratg ip fe ln und Felsw~in-

d en i n d en A lp en. Z . G eo m o r p h . Su p p ., 8 : 9 4 - 1 1 8 .

Han tke , R. , 1978. E iszei ta lter , 1 . Ot t , Thu n , 468 pp .

Har r i son , R.G . and Biswas, D .J . , 1986 . Chao s in l igh t.

Nature , 321 : 394-401 .

Leopold , L .B. and L angbein , W.B. , 1962 . The c oncep t o f

en t rop y in landscape evo lu t ion . U .S. Geo l . Surv . Prof .

Pap . , 500A: A1-A20.

Scheidegger , A .E ., 1967 . A comple te therm ody nam ic

analogy fo r l andscap e evo lu t ion . Bul l . In t . Assoc . Sci .

Hydro l . , 12(4) : 57-62 .

Scheidegger , A .E ., 1979 . Th e p r incip le o f an tago nism in

the E ar th ' s evo lu t ion . Tectonophys ics , 55 : 7 -10 .

Scheidegger , A .E . , 1982 . Pr incip les o f Geo dyna mic s , 3d

ed. Spr inger , Ber l in , 395 pp.

Scheidegger, A.E., 1983. Th e instab il i ty pr inciple in geo-

mo rph ic equ i l ib r ium. Z . Geom orph . , 27( l ) : 1 -19 .

Scheidegger , A .E . , 1986 . Th e ca tena p r incip le in geom or -

phology . Z . Ge om orph . , 30 (3 ) : 2 57-273 .

Scheidegger , A .E . , 19 87 . The fu ndam enta l p r inc ip les o f

landscap e evo lu t ion . Ca tena Suppl ., 10: 149-210.

Scheidegger, A.E. and A i, N.S., 1986. Tec tonic process an d

geom orphologica l des ign . Tec tonophys ics , 12 6 : 28 5-

300.

Scheidegger, A.E. an d Ai, N.S., 1987. Clay sl ides and de-

br i s - f lows in the W udu-Reg ion and the i r t ec ton ic im-

plicat ion . Sci . Explor . (Be jing) , 7( 1 ) : 253-26 4.

Schuster, H .G . , 1984 . De termin is t ic C haos . Phys ik , Ber -

l in , 220 pp.

So m m er f e ld , A . , 1 9 6 4 . T h e r m o d y n a m i cs an d S t a t is t ica l

Mechanics. Lec tures of The oret ic al Physics, 5 . Aca -

dem ic Press , Ne w York , 401 pp .

Tom kor ia , B.N. and Scheidegger , A .E ., 1967 . A com plete

therm ody nam ic analogy fo r t r ansp or t p rocesses. Can .

J . Phys. , 45: 3569-3587.

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