Hydro-ecolog}':
Linking Hydrology and Agnatic
UK. July 1999). IAHS Publ. no. 266, 2 0 0 1 .
Ecology* (Proceedings of Workshop MW2 held at Birmingham,
113
In-channel metamorphosis in a semiarid, mixed
bedrock/alluvial river system: implications for
Instream Flow Requirements
M. W. R O U N T R E E
Centre for Water in the Environment,
Department
of Animal, Plant and
Environmental
Sciences,
University
of the Witwatersrand,
Johannesburg
2050, South
Africa
e-mail: markr@,gecko.biol.wits.ae.za
G. L. H E R I T A G E
Telford Institute of Environmental
Manchester
M5 4WT, UK
Systems,
Department
of Geography,
University
of Sal ford,
K. H. R O G E R S
Centre for Water in the Environment,
Depart ment of Animal, Plant and
Environmental
Sciences,
University
of the Witwatersrand,
Johannesburg
2050, South
Africa
Abstract Semiarid river systems have been shown to experience phases of
sedimentation interspersed with flood related sediment stripping. In 1996 a
high magnitude flood in the Olifants River, South Africa, snipped most of the
vegetation and sediment from the channel, exposing extensive areas of the
underlying bedrock template. A 50-year aerial photographic record of the
stripping and accumulation phases was examined to elucidate pathways of
river landscape change in the 100 km study reach. Thirteen channel type states
were identified from a study of the 57 channel segments. The pattern of
change between the various states was used to develop a conceptual model of
in-channel metamorphosis. Preferential pathways of change suggest that the
underlying bedrock template plays an important role in predetermining the
pathway of change. However, the multiple pathways of change identified
show that this template does not exclusively control the change pathway. The
mixed (alluvium and bedrock) anastomosing channel type was shown to have
a highly stable planform, but in most channel types in-channel metamorphosis
appears to be the rule rather than the exception. This is particularly apparent in
the mixed pool-rapid and mixed braided channel types where switching
between these two states was common and frequent. These changes have
implications for the selection of sites for Instream Flow Requirement
determination and long-tenn monitoring sites. The desired future states for the
management of South African rivers do not explicitly allow for the inherent
channel changes identified in this study. Therefore the definition of desirable
geomorphological states and change need to be reassessed.
K e y w o r d s b e d r o c k i n f l u e n c e ; g e o m o r p h i c c h a n g e ; i n s t r e a m flow r e q u i r e m e n t s ; s e m i a r i d r i v e r
INTRODUCTION
In arid and semiarid areas the variation in discharge between rare floods and more
frequent floods (such as the 2-year event) is much higher than in temperate climates
and change in river morphology seldom conforms to the Wolman & Miller (1960)
114
M. W. Rountree et al.
uniformitarian principle (Baker, 1977). Instead, episodic stripping of sediments has been
used to explain fluvial changes in several semiarid rivers of Australia, India and North
America (Womack & Schumm, 1977; Baker, 1977; Nanson, 1986, Kochel, 1988; Gupta
et al, 1999; Bourke & Pickup, 1999). Episodic stripping occurs when gradual aggrada­
tion (deposition) is set back by extreme stripping (erosional) events (Nanson, 1986).
Episodic stripping is believed to occur also in the mixed bedrock/alluvial
influenced semiarid river systems of the Kruger National Park, South Africa. In 1996
extreme high magnitude floods occurred throughout the region and exposed the
bedrock template underlying the various channel types of the Olifants River. The
floods left the river in the most bedrock-influenced state on record. Under the episodic
stripping scenario, extreme floods would periodically scour the river to a condition
similar to that of 1996 (i.e. down to the bedrock template).
Previously studies of episodically stripped rivers have tended to focus on changes
resulting from the stripping event. The prolonged accumulation periods between
stripping events have seldom been considered or explicitly studied. Since channel
changes during the prolonged accumulation periods are not well documented, we know
very little about the long-term stability of channel types or planforms. This information
Witbank
®
Cape Town'
Fig. 1 Location of the study area.
In-channel metamorphosis in a semiarid, mixed bedrock/alluvial river system
115
is crucial for the determination of the Instream Flow Requirement (IFR) of rivers, and
for monitoring the efficacy of the recommended IFR.
In South Africa the Instream Flow Requirement is determined using the Building
Block Methodology (King & Louw, 1998). To determine the IFR, cross-sections of the
channel are needed to estimate the discharges required to inundate different habitats.
These selected sites would also be monitored later to validate and monitor the delivery
of the IFR. Sites that offer stable cross-sectional profiles, with a range of habitats, should
therefore be chosen. In mixed bedrock/alluvial river systems, this is often the pool-rapid
channel type because it presents the bedrock as a control feature and intuition would
suggest that bedrock sections are less likely to change than alluvial sections in the same
river. The pool-rapid channel type would therefore provide good future monitoring sites,
and the stage-discharge relationship is relatively easier to model in this channel type.
This study was initiated to determine medium- to long-term channel type
metamoiphosis in the Olifants River, a semiarid, mixed bedrock/alluvial river system,
and assess the implications of the results for IFR site selection and river monitoring.
STUDY SITE
The Olifants is one of South Africa's largest rivers—740 1cm long with a catchment of
54 800 k m (Carter & Rogers, 1995). The section of the river examined in this study is
in the lower reaches as it runs through the Kruger National Park (KNP) (Fig. 1). There
have been no previous studies on the geomorphology of this section, but considerable
geomorphological research has been conducted on a morphologically similar section of
the nearby Sabie River (Heritage et al, 1999). Both rivers have highly variable flow
regimes and channel-in-channel physiographies with the inner channel carrying flow
most of the time (Fig. 2). The larger "macro-channel" acts as a restrictive flood plain,
outside of which floods have very infrequent and limited influence.
2
In addition to the variable flow regimes and relatively high sediment loads, these
rivers are also characterized by a high degree of bedrock influence. The macro-channel
floor has generally eroded down to the bedrock template, although the bedrock can be
concealed by deep alluvial deposits. The variable underlying geology results in rapid
changes in slope and associated sediment deposition patterns. A geomorphological
classification developed for the Kruger National Park rivers (van Niekerk et al, 1995)
identified four basic channel types: single-thread, braided, pool-rapid and
anastomosing. These four basic types can be further classified according to the
proportion of bedrock and alluvial influence in the channel segment. Therefore channel
types may be either fully alluvial, of mixed influence or fully bedrock controlled
channels with very little alluvial influence. In the Sabie River four dominant channel
types were found (Heritage et al, 1996): alluvial braided, mixed pool-rapid, mixed
anastomosing and bedrock anastomosing (Table 1).
METHODS
Aerial photographs from 1944, 1965, 1974, 1986 and (post-flood) 1996 were used to
analyse geomorphological change at the channel type scale. The 1996 aerial
116
M. W. Rottntree et al.
Anastomosing channel type
Macro-channel
Active channels
/ l
L\
Single thread channel t y p e
Macro-channel
— —
Active channel
I
Braided channel type
_
. <|
Macro-channel
\
-
Active channels
WÊÊÈlMmÊmMlmËÊÈÊÉlÊËËÈlF.
j
! Bedrock
•••
/ium
Fig. 2 The macro-channel and active channels which flow within it.
photographs were used as the initial condition of the river. The accumulation phase is
thus represented by the 1996/44/65/74/86 aerial photograph sequence (Fig. 3), showing
the development of more alluvial channel types upon an initially highly bedrock
influenced template.
Table 1 Characteristics of the four dominant channel types in the Sabie River, Kruger National Park
(from Heritage et al, 1999).
Channel type
Alluvial
braided
Geomorphological characteristics
(after Heritage et al., 1999)
Average low flow water
surface slope (after
Birkheade/a/.,2000)
Confined braiding within the macro-channel. No bedrock
0.0020
influence due to very deep alluvial deposits. Narrow macrochannel.
Mixed pool- A series of deep, mixed bedrock and alluvial influenced pools 0.0029
rapid
separated by rapids usually free of sediment. Narrow macrochannel.
Bedrock
Multiple channels in the macro-channel flowing over resis0.0089
anastomosing tant bedrock. These steep segments were expected to inhibit
sediment deposition and make this channel type highly stable.
Macro-channel typically 3-4 times the average width.
Multiple bedrock, mixed and alluvial channels in the macroMixed
0.0023
anastomosing channel separated by long, wide, largely alluvial bars
colonized by reeds (Phragmites mauritanus). Macro-channel
the widest in this channel type.
In-channel metamorphosis in a semiarid, mixed bedrock/alluvial river system
Time
117
•
Fig. 3 Dates of aerial photographs represent the condition of the Olifants River during
an accumulation phase and a stripping event.
The channel type classification system developed for the Sabie River (van Niekerk
et al., 1995) was applied to the Olifants River. The delimitation and classification of
the channel segments (channel type units) were determined independently by two of
the authors for each set of aerial photographs. The independent classifications were
correlated revealing 57 channel segments in the 100 km length of the KNP section of
the Olifants River. The results from the five sets of aerial photographs were then used
to examine channel state changes during the accumulation phase.
R E S U L T S AND D I S C U S S I O N
Nine channel types and four transitional channel type states (transitional between two
channel types) were identified in the KNP section of the Olifants River. The transitional
states could not be reliably classified as a specific channel type because of the unusual
mix and proportion of their morphological units, upon which the channel type classifi­
cation is based. Four channel types—the mixed braided, mixed pool-rapid, mixed
anastomosing and bedrock anastomosing state—were dominant (representing 42 of the
57 segments in 1996). This paper focuses on the results from these four channel types.
Mixed braided
The mixed braided state is an alluvial dominated channel type similar to the alluvial
braided state described for the Sabie River, but has minor exposures of the underlying
bedrock template. There were two dominant patterns of change during the
hypothesized accumulation period. The first was from the mixed bedrock/alluvial
toward the fully alluvial braided state (Fig. 4). The initial condition (1996) represented
the scoured state of these segments. During the accumulation phase, progressive
M. W. Rountree et al
118
Channel Types
Bedrock influence
BA
B S T
M A
BA/PR
<
MA/BR M A / S I
• Alluvial influence
BI'R
MPR
MPR/BR M B R
A B R
A S T
M S T
Fig. 4 Classification changes through the accumulation phase of the 14 segments
initially classified as mixed braided. Each single thin line represents a single segment.
The channel type states are:
BA bedrock anastomosing
BST bedrock single thread
MA mixed anastomosing
BPR bedrock pool-rapid
MPR mixed pool-rapid
MBR mixed braided
ABR alluvial braided
AST alluvial single thread
MST mixed single thread
MPR/BR transitional MPR/braided
BA/PR transitional BA/pool-rapid
MA/BR transitional MA/braided
MA/ST transitional MA/single thread
sedimentation resulted in a total loss of the bedrock influence and the development of
the alluvial braided state.
The second pattern of change observed was a strong trend towards the mixed
anastomosing state, with the development of stable reed covered bars. The assumption
that the initial (1996) condition of the river represents the most scoured condition of
the river is not true in some isolated segments. Womack & Schumm (1977) showed
that whilst episodic erosion may be the normal course of events in some rivers, it was
difficult to identify periods of cutting which had affected the entire river at one time,
possibly due to local gradient or tributary influences. In the Olifants River, large
volumes of sediment deposited during the flood in former mixed anastomosing
segments resulted in the development of highly active braiding segments, thus
accounting for the observed trend.
Mixed pool-rapid
Frequent switching between mixed pool-rapid and more alluvial braided states (Fig. 5)
was the dominant partem of change in this channel type. These changes did not occur
in phase—between 1944 and 1965 change to both more and less alluviated states
occurred. The frequent state changes suggest that the mixed pool-rapid channel type is
inherently unstable, responding to very small local changes in the hydraulic and
sediment regime of the river.
119
In-channel metamorphosis in a semiarid, mixed bedrock/alluvial river system
Bedrock anastomosing
Most bedrock anastomosing segments changed to the more alluviated mixed
anastomosing state as the accumulation phase progressed (Fig. 6). Changes to highly
alluviated channel states, resulting in a total loss of bedrock influence, also occurred.
Despite the steep gradients and high energy slopes, this channel type was not resistant
to alluviation during the accumulation phase.
Channel Types
Bedrock influence
BA
BST
MA
<
BA/PR MA/BR MA/ST
• Alluvial influence
BPR
M PR
MPR/BR MBR
A BR
AST
MST
Fig. 5 Classification changes through the accumulation phase of the eight segments
initially classified as mixed pool-rapid. Each single line represents a single segment.
Refer to Fig. 4 for the channel type abbreviations.
Fig. 6 Classification changes through the accumulation phase of the 11 segments
initially classified as bedrock anastomosing. Each thin line represents a single
segment. Refer to Fig. 4 for the list of channel types and abbreviations.
120
M. W. Rountree et al.
Mixed anastomosing
Only one of the seven segments classified at the beginning of the accumulation period
as mixed anastomosing changed, and then only to a transitional mixed anastomosing/
braided state before changing back to its original state (Fig. 7). The mixed anastomosing
channel type was therefore the most stable channel type during the accumulation phase.
This was partly due to its unique character, and partly to the manner in which "change"
has been assessed. Field evidence strongly suggests that bars in mixed anastomosing
channel type segments grow by vertical accretion. Flood plains formed in an episodic
or cyclical process of vertical accretion and catastrophic erosion have been described
before (Schumm & Litchy, 1963; Burkham, 1972; Nanson, 1986). Vertical accretion
would be aided by the extensive reed growth on the anastomosing bars in this channel
type, since reeds promote sediment deposition (Tsujimoto et al., 1996). Alluvium
storage changes can only be inferred from area changes when using aerial photographs,
hence increased sediment storage by vertical accretion cannot be detected.
The confinement of low and medium flows to the numerous distributaries would
maintain these channels and the exposed bedrock within them. During extreme high
flow events, the stage of the flood would increase above the capacity of the distributary
channels, spreading out and over the extensive reed beds of the wide macro-channel.
With the flow depth reduced and roughness greatly increased by the reeds, sediment
deposition would result in the vertical accretion of the anastomosing bars. Thus despite
their stable planform, sediment storage is also increasing in this channel type during
the accumulation phase.
Not all segments of the mixed anastomosing channel type began the accumulation
phase in the mixed anastomosing state. After the stripping event some segments were
in the mixed braided state as a result of large sediment deposits in these segments. It
would therefore appear that channel types are not totally constrained by their
underlying bedrock templates.
Channel Types
Alluvial influence
Bedrock influence
BA
BST
o
o
1944
o
o
1965
o
o
1974
0
o
1986
o
0
nitial
( 1 ')%)
MA
BA/PR MA/BR MA/ST BPR
i
/
•
M PR MPR/BR M BR
ABR
AST
MST
0
O
o
o
o
o
o
o
©
0
O
G
o
o
©
o
o
o
o
o
j>o
0
o
0
O
0
o
o
o
o
0
o
o
0
O
0
0
0
o
0
o
o
o
o
o
o
o
o
o
Fig. 7 Classification changes through the accumulation phase of the seven segments
initially classified as mixed anastomosing. Each thin line represents a single segment.
Refer to Fig. 4 for the list of channel types and abbreviations.
In-channel metamorphosis in a semiarid, mixed bedrock/alluvial river system
121
Continuum of channel types
Specific bedrock channel type templates were exposed by the stripping event but exami­
nation of the patterns of change during the accumulation phase showed that channel type
metamorphosis was not exclusively predetermined by this underlying template. The
mixed braided state developed in segments that were initially mixed pool-rapid, mixed
anastomosing or even bedrock anastomosing. Similarly, the mixed anastomosing state
developed in segments that were initially mixed braided or mixed pool-rapid, although
most developed from bedrock anastomosing states. Thus, although some pathways of
change are more probable, any channel state can potentially develop from any other,
depending on local hydraulic and sediment delivery controls.
<
Gradient
•
Fig. 8 Multiple pathways of change identified during the analysis of high probability
transitions between channel type states. See Fig. 4 for the list of channel types and
their abbreviations.
A conceptual model of in-channel metamorphosis (Fig. 8) has been constructed
showing the likely changes between channel states using the high probability changes
observed on the Olifants River and the morphological characteristics and slope data of
the channel types found on the Sabie River (Birkhead et ai, 2000).
During a stripping event channel states rapidly change to steeper, more bedrock
influenced states as sediment is scoured out and the underlying bedrock exposed.
Sedimentation during the prolonged accumulation period results in channel states
gradually changing towards the more alluvial channel types as sediment is deposited
on bedrock features.
IMPLICATIONS F O R IFR D E T E R M I N A T I O N A N D RIVER M O N I T O R I N G
IN SEMIARID RIVERS
Much of the classic unifonnitarian theory has become entrenched in both the
conceptualization and analysis of river geomorphological change. Therefore the
122
M. W. Rountree et al.
recognition of a continuum of channel types, where there is continuous grading
between different states, as opposed to discrete channel types, will require a
fundamental shift in thinking and monitoring of semiarid river change.
Insneam Flow Requirements in South Africa are determined using the Building
Block Methodology (King & Louw, 1998). The Building Block Methodology (BBM)
determines the timing and magnitude of flows required to "aid maintenance of the
natural channel structure" and maintain the river "in some pre-defined desired state"
(King & Louw, 1998 page 112). Sensitive areas likely to change with future flow
manipulation are identified as part of this methodology (Rowntree & Wadeson, 1998).
In a field where managers seldom have geomorphological expertise, these
statements could be taken to imply that channel change is inherently undesirable and
this could entrench the common assumption (Ferguson, 1987) that an equilibrium state
exists. This study has shown that no such equilibrium state exists. The pool-rapid
channel type, frequently chosen as study sites in IFR determinations, is highly
susceptible to rapid, frequent state changes. The frequent alternations between the
mixed pool-rapid and mixed braided states, with state "switching" occurring in 10
years or less, suggest that there is no major threshold change between these two
channel types. Similar changes were recorded between single thread and braided
channel types in the Sabie River (Heritage et al, 1999).
The recognition of these highly dynamic channel complexes as opposed to two
separate channel types has important implications for river management. Frequent state
changes may not be catered for in the desired state of the river if an equilibrium
philosophy has been adopted and monitoring might thus perceive changes in the river
morphology as undesirable.
The switching pool-rapid/braided state would also have implications for the flow
determination. Under the current scenario, two very different IFRs would be developed
for the same segment depending on whether it was in a braided or pool-rapid state. A
case in point is the Sabie River IFR, where three different IFRs resulted from the
simultaneous but independent analyses of three different channel types (Tharme,
1997). A study of a flood-driven system in India (Gupta et al, 1999) revealed similar
results. At the scale of the alluvial and bedrock channel types, specific flow volumes
affected different channel types. W e could thus expect particular channel types to
respond to particular flows, especially in semiarid areas where the flow variability and
channel type diversity are both high.
This study demonstrates that channel metamorphosis could be the rule rather than
the exception in semiarid rivers. The results also suggest that channel type complexes
may be more appropriate than the current concept of distinctive channel types in the
classification, monitoring and management of semiarid rivers. The B B M process is
open to subjective bias because of the reliance on professional judgement and
specialist experience of the river system (Tharme, 1996). Therefore greater
understanding of spatial and temporal channel type change in rivers with highly
variable discharges is urgently required if management of such rivers is to be
successful.
Acknowledgements The authors wish to thank the South African National Parks
Board personnel for logistical support, and in particular Holger Eckhardt for assistance
In-channel metamorphosis in a semiarid, mixed bedrock/alluvial river system
123
with aerial photograph acquisitions. Financial support from the Andrew Mellon
Foundation, who provided the funding for this research and a grant to Mark Rountree
to study in the U K for four months, is gratefully acknowledged. Comments of earlier
drafts from Martin Thorns and Chris James were extremely helpful.
REFERENCES
Baker, V. R. ( 1 9 7 7 ) Stream-channel response to Hoods, with e x a m p l e s from central T e x a s . Geo/. Soc. Am. Bull. 8 8 , 1 0 5 7 1071.
Birkhead, A. L., Heritage. G. L., James, C. S., Rogers, K. 11. & van N i e k e r k , A. W. (2000) Geomorphological
Change
Models for the Sahie River, Kruger National Park. Report no. 7 8 2 / 1 / 0 0 , vol. 1, Water Research C o m m i s s i o n ,
Pretoria.
Bourke, M. C. & Pickup, G. ( 1999) Fluvial form and variability in arid central Australia. In: Varieties
of Fluvial
Form (ed.
by A. J. Miller & A. G u p t a ) , 2 4 9 - 2 7 2 . Wiley. Chichester, UK.
Burkham, D. E. (1972) Channel changes of the Gila River in Safford Valley, Arizona, 1 8 4 6 - 1 9 7 0 . In: 1986. Episodes
vertical
accretion
and catastrophic
stripping:
a model of disequilibrium
flood-plain
development
(ed.
of
by
G. C. N a n s o n ) . Geol. Soc. Am. Bull. 9 7 , 1 4 6 7 - 1 4 7 5 .
Carter, A. .1. & Rogers, K. H. (1995) A Markovian
Park Rivers.
Approach
to Investigating
Landscape
Change
in the Kruger
National
Report no. 2 / 9 5 , Centre for Water in the Environment, University of the Witwatcrsrancl, Johannesburg.
Ferguson, R. ( 1987) Hydraulic and sedimentary controls of channel pattern. In: River Channels:
Environment
and
Process
(ed. by. K. Richards), 1 2 9 - 1 5 8 . Blackwell, Oxford, UK.
Gupta, A., Kale, V. S. & Rajaguru, S. N . (1999) T h e N a r m a d a River, India, through space and time. In: Varieties
Fluvial
of
Form (ed. by A. .1. Miller & A. G u p t a ) , 1 1 3 - 1 4 4 . Wiley, Chichester, UK.
Heritage, G. L„ van Niekerk, A. W., M o o n , B. P., Broadhurst, L. J., Rogers, K. II. & James, C. S. (1996) The
Geomorphological
Response
to Changing
flow Regimes of the Sabie and Letaba River Systems.
Report no.
3 7 6 / 1 / 9 6 . Water Research C o m m i s s i o n , Pretoria.
Heritage, G. I,., van Niekerk, A. W. & Moon, B. P. (1999) G e o m o r p h o l o g y of the Sahie River: an incised bedrockinfluenced channel. In: Varieties
of Fluvial
Form (ed. by A. J. Miller & A. Gupta), 5 3 - 8 0 . Wiley, Chichester, UK.
King, .1. & Louvv, D. ( 1 9 9 8 ) Instream flow assessments for regulated rivers in South Africa using the Building Block
Methodology. Aquatic
Ecosystem
Health and Management
1, 1 0 9 - 1 2 4 .
Kochel, R. C. ( 1 9 8 8 ) G e o m o r p h i c impact of large Hoods: review and new perspectives on magnitude and frequency. In:
Flood Geomorphology
(ed. by V. R. Baker, R. C. Kochel & P. C. Patton), 1 6 9 - 1 8 7 . Wiley-lnterscience, N e w York.
N a n s o n , G. C. ( 1 9 8 6 ) Episodes of vertical accretion and catastrophic stripping: a model of disequilibrium Hood-plain
development. Geol. Soc. Am. Bull. 9 7 , 1 4 6 7 - 1 4 7 5 .
Rovvntree, K. M. & Wadcson, R. A. ( 1 9 9 8 ) A geomorphological
requirements. Aquatic
Ecosystem
Health and Management
framework
for the assessment of instream
How
1, 1 2 5 - 1 4 1 .
S c h u m m , S. A. & Litchy, R. W. ( 1 9 6 3 ) Channel w i d e n i n g and Hood-plain construction along Cimarron River in
southwestern Kansas. In: Pluvial Forms and Processes:
a New Perspective
(ed. by D. Knighton). Arnold, London.
UK.
J harme, R. E. ( 1996) Review of International
Methodologies
for the Quantification
of the Instream Flow Requirements
of
Rivers.
Department of Water Affairs and Forestry, Pretoria, South Africa.
T h a r m e , R. ( 1 9 9 7 ) Instream
Flow Requirements
of the Sahie-Sand
River System
(Proc. IFR W o r k s h o p , Aan de Vliet.
August 1996). Final report submitted to the Department of Water Affairs and Forestry, Pretoria.
I'sujimoto, T., Kitamura, T. & M u r a k a m i , S. ( 1 9 9 6 ) Basic morphological processes due to deposition of suspended
sediment affected by vegetation. In: Proceedings
of the 2nd lAHR Symposium on Habitai Hydraulics.
Ecohydraulics
2000 (cd. by M. Leclerc) (June 1996, Q u e b e c ) , A 3 9 5 - A 4 0 5 . I N R C - E a u , Quebec,
van Niekerk, A. W., I leritage, G. I... & Moon, B. P. ( 1 9 9 5 ) River classification for m a n a g e m e n t : the g e o m o r p h o l o g y of the
Sabie river in the eastern Transvaal. 5. Aft: Geogi: J. 7 7 ( 2 ) , 6 8 - 7 6 .
W o l m a n , M. G. & Miller, J. P. ( 1960) M a g n i t u d e and frequency of forces in geomorphic processes. J. Geol. 68, 5 4 - 7 4 .
W o m a c k , W. R. & S c h u m m , S. A. ( 1 9 7 7 ) Terraces of Douglas Creek, northwestern C o l o r a d o : an e x a m p l e of episodic
erosion. Geology 5, 7 2 - 7 6 .