Landscape Evolution

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Landscape evolution models

Frank J. Pazzaglia

Department of Earth and Environmental Sciences, Lehigh University, 31 Williams,

Bethlehem, PA 18015, USA; [email protected]

Introduction

Geomorphology is thestudy of Earths landforms andthe pro-

cesses that shape them. From its beginnings, geomorphology

has embraced a historical approach to understanding land-

forms; the concept of evolving landforms is firmly ingrained

in geomorphic thought. Modern process geomorphologists

use the term landscape evolution to describe the interactions

between form and process that are played out as measurable

changes in landscapes over geologic as well as human

time scales. More traditionally defined landscape evolution

describes exclusively time-dependent changes from rugged

youthful topography, through the rounded hillslopes of ma-turity, to death as a flat plain. Bridging the considerable gulf

in these different views of landscape evolution is the task of a

different paper altogether. Rather, this chapter provides some

historical perspectives on landscape evolution, identifies the

key qualitative studies that have moved the science of large-

scale geomorphology forward, explores some of the new nu-

meric models that simulate real landscapesand real processes,

and provides a glimpse of future landscape evolution studies.

In 1965, the year of the last INQUA meeting held in the

United States, thoughts on landscape evolution were still

dominated by the classic, philosophy-based arguments of

William Morris Davis, Lester King, and John Hack. Geomor-

phology, on the other hand, had become more quantitative

and the number of process studies was growing rapidly(Leopold et al., 1964). Systems theory was on still on the

horizon, but a landmark paper bySchumm & Licthy (1965)

had laid the framework for scaling the coming generation

of process and physical modeling studies into the landscape

context. In 1965, landscape evolution models were becoming

stale; process studies were viewed as more scientifically

rigorous and more directly applicable to human dimension

problems. At the same time, plate tectonics was emerging and

thought at the orogen scale enjoyed growth and acceptance

in the structure-tectonics community. Decades later that

community would begin questioning basic characteristics of

active orogens such as: what limits mean elevation or mean

relief of a landscape or what controls the rate that an orogen

erodes? Orogen-scale geomorphology became relevantagain to geologic and tectonic questions about the uplift and

erosion of mountains. Particularly in the past decade, interests

shared by the structure-tectonics community and the geomor-

phic community have inspired new thinking at the orogen

scale and a new generation of landscape evolution models.

Landscape evolution models come in two basic flavors,

qualitative and quantitative, that can be applied across a

wide range of spatial and temporal scales. This chapter will

primarily consider models that address large-scale landforms

andprocesses over the graded andcyclic scales ofSchumm &

Licthy (1965)(spatial dimensions equivalent to an orogen or

physiographic province, temporal dimensions equivalent to

104 to106 years). This scale of observation is usefulbecause it

encompasses investigations common to physical geography,

process geomorphology, paleoclimatology, and geodynam-

ics. Qualitative models are well known to most students of

geomorphology and they form the basis for the more quanti-

tative approaches.Louis Agassiz (1840)is best figured as the

grandfather of all landscape models. Agassizs approach to

understanding the impact of glaciation on landscapes forcedhim to think in terms of form and process as well as irre-

versible changes in the overall configuration of landforms as

a function of time. Ironically, Agassizs integrated approach

diverged with the next generation of geomorphologists and

landscape evolution models. By the late19th century William

Morris Davis had published his two seminal papers on the ge-

ographic cycle (Davis, 1889, 1899a) and Grove Karl Gilbert

laid the foundation for process-oriented approaches with his

influential chapter on land sculpture in his monograph on the

Henry Mountains (Gilbert, 1877). The middle part of the 20th

century saw the blossoming of physical analogue models

and more aggressive pursuit of process-oriented studies,

particularly with respect to hillslope hydrology (e.g.Horton,

1945) and fluvial geomorphology (e.g.Leopoldet al., 1964).Growth of interdisciplinary studies in the latter part of

the 20th century allowed the qualitative and quantitative

approaches to begin to find common ground, spurring a

proliferation of numeric approaches (e.g. Willgoose et al.,

1991) and ultimately, the coupled geodynamic-surface

process model (e.g.Beaumontet al., 1992; Koons, 1989).

This chapter begins by defining terms and suggesting a

taxonomy for types of landscape evolution models. It then

discusses the classic qualitative paradigms of landscape

evolution as a basis for explaining where the science is

today. It follows with an exploration of physical models

where the physical bases for geomorphic processes were

first explored. Finally, it summarizes four different types of

numeric landscape evolution models.

A Taxonomy of Landscape Evolution Models

Any organization of the various types of landscape evolution

models necessarily begins with a definition of some terms. A

landform is a feature of topography that exerts an influence

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248 Frank J. Pazzaglia

on, and is in turn shaped by surficial processes. A hillslope, a

river valley, a sand dune, anda colluvialhollow arelandforms.

A landscape is an aggregate of landforms for a region. The

evolution of a landscape here is not restricted to long-term

changes in topographic metrics, but rather is more generally

applied to describe any change of form-process interactions of

constituent landforms. This chapter organizes landscape evo-

lution models into three broad categories: qualitative, physi-

cal, and surficial process models.

Qualitative landscape models tend to describe the long-

term changes in the size, shape, and relief of landforms over

continental or subcontinental regions. They are not rooted

in the principles of physics and they are strongly colored

by the geography of their origin. Nevertheless, the quali-

tative models that endure are based on good, reproducible

field observations that must represent a common suite of

geodynamic and surficial processes that shape topography.

Close inspection of the several main qualitative models

reveals that they have much more in common then their often

incorrectly celebrated differences. Qualitative models tend

to be heavily skewed towards the influence of numerical

age on the resulting landforms. For cyclic time and space

scales in a decaying orogen setting, the age dependenceis warranted. But for landscape evolution at the scale of

individual watersheds, the resulting landforms many depend

less on numerical age than on the time scale of response and

adjustment to driving and resisting forces (e.g. Bull, 1991).

Physical models are scale representations of landforms. A

flume is a good example of a physical model used extensively

to understand channel form and process and there have been

remarkable accomplishments in the understanding of natural

channels based on flume studies (Schumm et al., 1987).

Well-known criticisms of physical models, based on the fact

that it is difficult to correctly scale for material properties

(Paola et al., 2001; Schumm et al., 1987), should not be

viewed as dismissing the potential insights from physical

experiments. For example, it would be easy to build a modelriver channel in a flume with scaled down grain size and den-

sity (coal dust) and a fluid other than water with a similarly

scaled down viscosity (acetone). The problem lies in the fact

that the resulting acetone-like fluid does not erode the coal

dust substrate by any process resembling what happens in

a real channel, not to mention that acetone volatilizes and

coal dust has high electrostatic charges. By retaining sand

and water for the flume, what is lost in the scaling is more

than made up for by retaining similar processes of grain

entrainment and erosion observed in natural channels.

Surface process models are rooted in the principles of

physics and chemistry. Good surface process models are

both inspired by and verified by field observations. Surficial

process models can focus on a specific landform, such asa hillslope or river channel, they can explore the linkages

between landforms, and/or they can consider the feedbacks

between surface and tectonic processes. A example that

focuses on a single landform is surface process modeling

of the evolution of hillslopes in a humid environment. Field

observations reveal these hillslopes to be concavo-convex in

cross-section. Their regoliths originate near the slope crest

and creep downslope. Evolution of the hillslope profile, if

not the regolith itself, is elegantly modeled by diffusion

where the diffusivity is a function of the regolith material

properties. As outlined in detail below, the rate of diffusion

is proportional to the slope, so form and process mutually

adjust. Numeric surface process modeling opens the door for

exploring the linkages between landforms and/or surficial

and tectonic processes. Numeric models are constructed by

determining the appropriate mathematical proxy for all, or at

least the major processes acting on a landscape. Typically, the

processes are landform specific such that one mathematical

equation describes the dominant hillslope process, another

describes regolith production, and another describes fluvial

transport. The surface process model reconstructs long-term

changes in a landscape by integrating simultaneously across

these different process using a large number of time steps in

a computer program. The simplest kinds of numeric models

deal with mass balances and cannot truly reconstruct the

complexity of a real landscape but rather attempt to track

some metric of that landscape, such as mean elevation. More

complex models are typically 1-, 2-, or 3-D finite difference

or finite element code that actually attempt to build and

shape a synthetic landscape. Numeric surface process modelshave been successfully linked with geodynamic models.

Such linked models are used to understand the feedbacks

between surficial and tectonic processes in active orogens.

Qualitative Models: Classic Paradigms of Long Term

Landscape Evolution

It has been said that the study of landscape evolution is first

and foremost a study of hillslope form and process (Carson

& Kirkby, 1972; Hooke, 2000). This is not to say that rivers

do not play an important role in the shaping of landscapes or

in limiting the overall rate of landscape evolution (Howard

et al., 1994; Whipple & Tucker, 1999). But across widelyvariable climates, rock types, and rates of rock uplift, rivers

tend to respond relatively quickly to driving forces and their

forms lack a memory of the changes in driving forces. Hill-

slopes respond more slowly on average and as a result, retain

a richer memory of the changes in process and driving forces

expressed in their forms, especially in landscapes underlain

by rock types of different erodibility.

Observations from a large number of field studies

conclude that most hillslopes generally have rounded convex

summitsand areseparated from streamvalleys at their base by

shallow concave reaches. The degree of convexity or concav-

ity, the linear separation between summits and the base, and

average slope angle constitute the differences in overall form.

Both the upslope convexity and downslope concavity are theresult of transport-limited processes. The former results from

weathering, creep, and rainsplash (Gilbert, 1909; Schumm,

1956) and the latter from hillslope retreat, not necessarily

at the same angle, by surface wash and solution (Schumm,

1956; Schumm & Chorley, 1964), or from deposition. The

remaining slope profile between the upper convexity and

lower concavity is called the main slope and its form is


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Landscape Evolution Models 249

primarily a result of weathering limited processes such as

mass movement and surface wash. The main slope can either

retreat parallel to itself, decline by laying back about a fixed

hinge point at its base, or shorten by having the upper convex-

ity extend downward to join the lower concavity. These three

main behaviors vary with rock type, layering of rock types of

variable resistance, and climate. The behaviors are common

to the important qualitative models of long-term landscape

evolution.

Base Level, Erosion, and Landscape Genesis Powell

(1875)

John Wesley Powell, a Civil War hero of the Battle of Shiloh

in which he lost an arm, is the true father of the genetic prin-

ciples of landscape evolution, many of which are incorrectly

attributed to William Morris Davis. Powells views on land-

scape evolution are vividly described in the accounts of his

expeditions through the river gorges of the Rocky Mountains

and Colorado Plateau (Powell, 1875). The concepts of base

level and widespread erosion of great mountain ranges to low

elevation and relief are the cornerstones of Powells work.These ideas were a natural consequence of the features that

Powell sawduring his river trips: great gorgescarved by rivers

attempting to lower their gradients, great torrents of sediment-

laden water resulting from material washing off steep hill-

slopes, and perhaps most influential, the Great Unconformity

of the Grand Canyon. More than any other feature, the Great

Unconformity forced Powell to appreciate the enormity of

erosion that must have occurred across a once lofty mountain

range to produce the strikingly horizontal boundary between

deformed Precambrian and flat-lying Paleozoic rocks. That

unconformity marked the beveling of a former world and it

is this point that most influenced the peneplain concept of

William Morris Davis. River gorges carved through variable

rock types led Powell to consider a genetic classification ofstreams, hinging primarily on their broad tectonic setting. The

concepts of antecedent, consequent, subsequent, and super-

imposed drainages have their origin in Powells writings, but

weregreatly popularized andfurther defined by Gilbert (1877)

andDavis (1889).

Form and Process Gilbert (1877, 1909)

The work of Grove Karl Gilbert has had perhaps the most

lasting impact on modern geomorphology (Yochelson, 1980).

The core of Gilberts work on landscape evolution was ele-

gantly laid out in his monograph on the geology of the Henry

Mountains, Utah (Gilbert, 1877). Chapter V in that mono-graph is entitled Land Sculpture and it is here that Gilbert

begins the science of modern process geomorphology. The

overall message in Chapter V is that there is an interaction

between form and process, or in Gilberts words, an equality

of action. In this view, the landforms of the Henry Mountains

reflect their underlying rock type, the tectonic processes that

uplifted, emplaced (in the case of laccoliths) and deformed

Fig. 1. Sketch, modified from Gilbert (1877), of monoclinal

shifting. Gilbert noted that when channels traverse dipping

sedimentary rocks of variable resistance (a), their courses

adjust to maximize interaction with soft rocks and minimize

interaction with hard rocks (b).

them, and the predominant surficial processes of weathering

and transport. This represents a wholly modern view of pro-

cess geomorphology andit is ironic that it lay largely dormant

forseveral decades following Gilberts monograph, only to be

rediscovered a half a century ago (Hack, 1960).

Gilbert built his ideas on the foundation laid by John

Wesley Powell (Powell, 1875) and on pioneering work of

European engineers, particularly Du Buat (1786), Dausse

(1857), Beardmore (1851) and Taylor (1851). Gilberts

genius was applying the results of these earlier studies to

the long periods of time represented by landscape evolu-

tion. Particularly noteworthy are Gilberts ideas about theprocesses and rates of erosion, land sculpture (landform

evolution), and drainage adjustment (Fig. 1). For Gilbert,

erosion encompasses mechanical and chemical weathering

in soils as well as during transport. Erosion rates are most

rapid where slopes are steep a concept not fully popularized

untilAhnert (1970). Because such erosion would produce a

landscape with a single slope angle, it is clear that rock type

must play a primary role also in determining erosion rates.

Gilbert cast the role of climate in controlling erosion rates in

the context of competing interests of effective precipitation

and vegetation with semi-arid landscapes having the highest

rates of erosion an idea not fully appreciated untilLangbein

& Schumm (1958). Fluvial channels erode in proportion

to their slope-discharge product, and sediment transportin a channel depends on the shear stress on the bed. Most

impressively, Gilbert was the first to describe the concave-up

profile of rivers as graded, improving upon the original

definition by European engineers by attributing the graded

condition to a balance between available discharge and

capacity for adjacent reaches. Gilbert described drainage

divides in the context of opposing and interacting graded


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Fig. 2. Sketch of a hillslope profile fromGilbert (1909)show-

ing the zone of creep (light shading) andtwo hillslope profiles

(solid lines) separated by a period of erosion. Gilbert rea-

soned that the prism of material between 1 and 2 had to be

carried past 2 during the period of erosion in the same way

that the prism between 2 and 3 was carried past 3 over the

same period of time. The quantity passing 2 and 3 is propor-

tional to the distance to the summit (point 1) if the creeping

layer is of uniform thickness and velocity of the creeping ma-

terial is proportional to slope.

profiles. Divides are strictly fluvial features in this description

and thus should migrate in the direction of their more gentle

side. In this respect, Gilbert was perplexed as to why the law

of divides seem to be violated in certain badlands where

opposing slopes were not concave up, but rather distinctly

convex. He surmised that it has something to do with a

transition from hillslope processes at or very near the divideto fluvial processes further downslope. This hunch proved to

be the correct answer which is ultimately laid out in a later

paper (Gilbert, 1909) that describes modern understanding

of transport and weathering limited hillslopes, creep as a

hillslope process, and the basis for hillslope transport pro-

portional to slope (Fig. 2). These contributions later form the

basis for Hortons zone of no fluvial erosion (Horton, 1945).

Gilberts findings were only slowly appreciated in terms

of long-term changes in the landscape. Part of the problem is

that Gilbert did not philosophically cast his observations into

a temporal framework. He focused on current interactions

between form and process with little regard for how those in-

teractions would play out over long periods of time to change

a landscape from its current form, to something different.Ironically, understanding the interactions between form and

process and casting them into mathematical equations is the

basis for numeric surface process modeling that has proven

to be a powerful tool for predicting long-term landscape

evolution.

Fig. 3. The geographic cycle of Davis

showing (a)a simplifiedversionof theorig-

inal figure from the 1899 paper and (b)

a modified interpretation of the original

figure (from Summerfield, 1991). Stages

1 through 4 in (a) refer to uplift, valley

bottom deepening, valley bottom widening,and finally interfluve lowering. Upper line

denotes mean elevation of interfluves and

lower line, mean elevation of valley bot-

toms.

The Geographic Cycle Davis (1889, 1899a, 1932)

The most influential paradigm on long-term landscape evolu-

tion comes from thework of theAmerica physical geographer

William Morris Davis. Much has been written regarding the

obvious differences between the Davisian approach with re-

spect to Gilberts process approach. There is a place for both

approaches in modern views of longterm landscapeevolution.

The Davisian approach provides the temporal framework and

the recognition that all landscapes are palimpsests, overwrit-

ten by numerous tectonic and climatic processes (Bloom,

2002). A Pennsylvanian by birth, Davis summered with his

family in the Pennsylvania Ridge and Valley, a landscape that

would forever color his geomorphology views. Davis fully

appreciated the best geologic interpretations of his day and

used these to constrain his models of landscape evolution.

He was also careful to point out that his model was idealized.

He never intended concepts like an instantaneous, impulsive

uplift, or completion of the geographic cycle to be attained in

every case or to be taken and applied literally (Davis, 1899b).

Unfortunately, these andother idealizations of his model have

been taken literally by many outside of the field of geomor-

phology, leading to muchconfusionand stifling reconciliationof his ideas with modern process-oriented thought.

Among Daviss numerous publications, three define

and apply the concept of the geographic cycle to a range

of landscapes. The first paper is The rivers and valleys of

Pennsylvania (Davis, 1889) which focuses on the develop-

ment and evolution of the current drainage of Pennsylvania.

Basic observations of accordant summits, wind gaps, and

water gaps routing the master streams transverse to structure

in the Ridge and Valley anchor the justifications for repeated

landscape uplift and beveling. The second paper is The

geographic cycle (Davis, 1899a) where the Davisian model

for long term landscape evolution is described. The third

paper is Piedmont benchlands and Primarrumpfe (Davis,

1932) where Davis confronts a major alternative paradigmto the geographic cycle and the formation of peneplains

presented by the ideas ofWalter Penck (1924).

The geographic cycle (Fig. 3) is a simple, but compelling

treatment of how mean elevation and mean relief change as a

landscape erodes. It also places a large emphasis on transport


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limited processes for the overall erosion and lowering of hill-

slopes. The geographic cycle has four major stages. In stage

1, a landscape is born by rapid, if not impulsive uplift of both

rocks and the land surface above sea level. The uplifted land-

scape has a high mean elevation, but low mean relief. Erosion

is initially concentrated in the river which leads to the carving

of deep, narrow valleys. The landscape passes into stage 2

where it is youthful in appearance, it has both a relatively

high mean elevation and high relief. Valleys rapidly lower to

base level, at which point they begin to widen laterally. At the

same time, hillslope erosion becomes important as interfluves

are rounded. Hillslopes take on a concavo-convex form and

weathered material is moved across this form to the river

valley predominantly by creep. These conditions describe

stage 3, the mature landscape. Both mean elevation and mean

relief steadily decrease, and valleys continue to widen. Stage

4 is reached when valleys can no longer deepen or widen and

all landscape lowering is accomplished by the progressive

rounding and lowering of interfluves by hillslope creep. The

completely beveled landscape resulting from the completion

of the geographic cycle, the penultimate plain, is called a

peneplain. Davis envisioned the peneplain being formed at

different rates depending on the size of the landscape beingbeveled and the relative erodibility of the rocks. Resistant

islands of high standing topography are called monadnocks

(for Mt. Monadnock in southern New Hampshire), and

evidence of partial peneplains is common on softer rocks.

Davis fully envisioned the difficulty in running the cycle

to completion. He inferred that renewed tectonic uplift of a

landscape occurs often enough to interrupt the cycle. This

realization led to the preoccupation with finding peneplains

and partial peneplains in the landscape, essentially an attempt

to define an landscapes erosional stratigraphy. Time was the

critical factor in determining a landscapes mean elevation

and relief; no interactions between form and process or

driving and resisting forces are considered. The concept of

the peneplain proved the most controversial part of the geo-graphic cycle (Davis, 1899b). Ironically, Davis never claimed

ownership of the term. In his view, he was just giving a name

to a process and a feature described by geologists before him,

most notable, Powells descriptionof the Great Unconformity

in hisExploration of the Colorado River(Powell, 1875).

The Geographic Cycle makes little reference to hillslope

processes and what references do exist are considered

together under the concept of agencies of removal. Here

Davis suggests that the hillslopes are shaped by a myriad

of processes that include surface wash, ground water,

temperature change, freeze-thaw, chemical weathering, root

and animal bioturbation. These collectively drive creeping

regolith downslope. Relative amounts of weathered products

and exposed bedrock are considered in the context of whetherthe slope is steep and youthful, or old and rounded.

An important idea that has survived from the geographic

cycle is that slopes in tectonically active landscapes rapidly

attain steep, almost straight profiles, then more slowly decay

into concavo-convex, sigmoid-shaped profiles as tectonism

wanes, valleys reach their base level of erosion, and divides

are lowered. Davis also suggested several modifications to

the geographic cycle model. Most notable are the ideas about

cyclic erosion in arid landscapes (Davis, 1930). In this paper,

Davis introduces elements of slope retreat into his model.

From this model Bryan (1940) and later King (1953) describe

and expand upon the role that retreating escarpments play in

long-term landscape evolution. Unfortunately, Davis appears

to abandon his view of slope form and process being a

consequence of climate in his 1932 paper where he returns

only to the ideas originally espoused in the Geographic Cycle

as a defense against the ideas of Walter Penck (see below).

The triumph of the geographic cycle is that it was

almost a century ahead of its time in showing how mean

elevation and mean relief might evolve in a landscape. Only

recently, with the realization that surficial and geodynamic

processes arelinked in orogenesis (Molnar& England, 1990),

has the broader geologic community come to appreciate the

lag times and feedbacks between rock uplift and erosion. The

four stagesof thegeographic cycleresemble modernconcepts

about growing, steady-state, and decaying orogens (Hovius,

2000). Furthermore, the erosional response to impulsive up-

lift described by the geographic cycle is completelyconsistent

with the observed flux of material from disturbed Earth sys-

tems across a wide range of space and time scales (Schumm& Rea, 1995). This flux follows a distinct exponential decay

after an impulsive increase. Over cyclic time scales, uplift

and the initial erosional response are in fact impulsive, and

the landscape response in terms of lowering mean elevation

and mean relief is most simply described by an exponential

decay function. The tragedy of the geographic cycle is that

individual parts of it have been accepted too literally. A prime

example is equating meandering streams with Daviss wide,

low gradient valleys of mature landscapes. Meandering chan-

nels do not necessairly indicate landscape maturity. Rather,

meandering reflects the interaction of driving and resisting

forces such as watershed hydrology, prevailing grain size,

bank stability, and rock type erodibility in a fluvial system.

Slope Replacement Penck (1924, 1953)

The most influential European geomorphologist in the

early part of the 20th century and a direct challenger to the

Davisian model was Walter Penck. Penck was influenced by

field observations made in Germany, particularly the Rhine

graben area, in northern Argentina, and to a lesser degree,

in Africa. Like Davis, Penck envisioned long term landscape

evolution occurring in stages from youth to old age, when

all relief in a landscape was beveled by erosion. And despite

the assertions that Penck was the original proponent of slope

retreat (King, 1953), he like Davis, believed in the flattening

of slopes through time. Misunderstandings arose from hisobscure writing style (Simons, 1962), and from Daviss

incorrect translation of some of his work (Davis, 1932). But

unlike Davis, Penck was more process oriented, actually

making measurements in the field, and he focused his process

studies on hillslopes.

Penck recognized concavo-convex hillslopes similar

to what Davis was observing in eastern North America.


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Fig. 4. The Penck model. (a) Diagram showing slopereplacement(upper profile)caused by successiveretreat of an infinite number

of inclined valley bottoms leading to a smooth concave profile (lower concave profile). Penck envisioned an initially steep linear

cliff (t0), being replaced by progressively more gentle slope segments (t1 t3). (b) Pencks original figure, misinterpreted by

Davis (1932), illustrating Pencks cycle of erosion. Much like Daviss model, this diagram shows that Penck considered erosion

to be concentrated in river valleys first (t0), then extended to hillslopes (t1 t2). If adjacent, ever-widening concave valley

profiles meet at an interfluve (t3), that interfluve becomes rounded and lowered (modified from Carson & Kirkby, 1972).

However, the Penckian model for their origin was altogether

different. Penck is the father of slope replacement as a

mechanism for hillslopes evolution (Fig. 4). Whereas Daviss

hillslopes are transport limited and always covered with a

creeping regolith mantle, Pencks hillslopes are predomi-

nantly weathering limited with little to no regolith cover,

except, implicitly at their base where regolith transported

downslope is allowed to accumulate. Originally steep and

straight slope profiles weather parallel to themselves except

for a small, step-like flattening at the base of the slope, the

haldenhang, which is presumably controlled by the angle

of repose of the hillslope debris. Retreat of the haldenhang

results in an even lower-gradient basal slope called theabflachungshang. The process continues with successive

abflachungshang retreating, each leaving a basal slope of

lower angle than itself. The integrated result is a concave-up

slope that has replaced the original steep, straight slope.

Penck went on to propose mechanisms of how the upper

part of the concave profile would flatten to produce an upper

slope convexity using arguments similar to those used by

Gilbert (1909).

The concept of waxing and waning slopes is not as much

a part of Pencks original model as it is Daviss interpretation

of it. But Pencks views on the effects of base level change

on slope form are notable. Penck argued that given a stable

base level, a hillslope will attain a characteristic profile deter-

mined by the erodibility of underlying rock. Steep slopes areunderlain by hard rocks whereas gentle slopes are underlain

by soft rocks. Furthermore, Penck was influenced by his

studies in the Alpine foreland, where it appeared certain

that orogeny was protracted and occurred at variable rates,

rather than being impulsive as in the Davisian model. These

observations led Penck to believe that base level fall, if linked

to orogeny, starts slow, accelerates to a maximum (waxing),

and decelerates back to stability (waning). Hillslopes adjust

to that base level fall throughout the waxing and waning

cycle. A fall in base level causes that segment of the hillslope

immediately adjacent to the base level fall to steepen, and that

steepened hillslope segment then causes the next segment

upslope to steepen and so on. The result is the replacement of

a gentle slope with a more steep one as the base level fall sig-

nal is translated upslope. If base level fall is a one-time event,

the steep hillslope segment propagates upslope, and in turn is

replaced by a less gentle segment downstream. But if the base

level fall continues or accelerates, there is a downslope trend

of progressively steeper slope segments, such that the hills-

lope becomes convexin profile. Alternatively under base levelrise or long-term stability, there is a downslope shallowing of

slope segment gradientsand thehillslope is concave in profile.

The Penckian model predicts convex hillslopes when base

level is actively falling (waxing slopes) as part of a youthful

landscape; the Davisian model predicts concavo-convex

hillslopes where base level is stable and a mature landscape is

slowly being beveled. In summary, Penck viewed base level

changes (uplift) as long-lived, rather than impulsive, and the

overall landscape response to those changes as having short

lag times.

Even though Pencks ideas on landscape evolution dif-

fered significantly from the Geographic Cycle, his landforms

are still time-dependent features (Fig. 4). The Penck model

holds that landscapes are born from a base level fall thataffects a low relief landscape called a primarrumpf, resulting

in stream incision and convex hillslopes. Acceleration in

the rate of base level fall increases hillslope convexity and

results in the formation of benches (piedmottreppen) near

drainage headwaters that have not been affect by the slope

replacement process. Eventually, base level fall decelerates

and stops completely. Slopes are replaced to lower and lower


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Fig. 5. The pediplanation model ofKing (1953)(modified fromSummerfield, 1991). Pencks model stresses the development of

concave-up slopes that retreat faster than interfluves lower, resulting in widespread pediments that coalesce into a pediplain.

Note that mean elevation decreases in this model, but relief persists along escarpments or inselbergs.

declivities until the relatively straight profiles of base level

stability retreat headward leaving a beveled plain called

an endrumpf with large, residual inselbergs at the drainage

divides.

Pediplanation L.C. King (1953, 1967)

Drawing upon work conductedprimarilyin Africa, but versed

on landscapes worldwide, Lester King championed a modelfor long term landscape evolution very similar to the geo-

graphic cycle, but differing in the dominant mode of hillslope

evolution (King, 1953, 1967). Like Davis, King envisioned

impulsive uplift and long response times of landscape ad-

justment. King never accepted the Davisian concavo-convex

slope; instead, he favored Pencks view of concave hillslopes

and slope replacement. In fact, King took the Penckian model

of slope replacement literally, to conclude that the landscape

assumes the form of a series of nested, retreating escarpments

(Fig. 5). King called the low-gradient footslope extensions of

the steep escarpments pediments and the flat beveled surface

they leave in their retreating wake a pediplane. Such a re-

stricted interpretation of the Penckian model is unwarranted

because Penck made it clear that the rates of slope modifi-cation are proportional to gradient, a relationship that would

continually produce slope replacement, not parallel retreat. In

fact, Kings model is based more on the earlier work ofKirk

Bryan (1922, 1940)than it is on Penck.

The notionof a landscapedominated by pediments should

not come as a surprise to a geomorphologist influenced by

South African landscapes. But King was wholly convinced

that these landforms are not restricted to just the arid and

semi-arid climates of his homeland. Rather, he argued, Davis

himself had described precisely the same features in New

England where Mt. Monadnock, the supposed type locality of

a remnant, rounded, concavo-convex hillslope has a concave-

up pediment profile. To Kings credit he built upon the earlier

work of Penck in making measurements in the field andincorporating the process work on pediment formation from

other noted geomorphologists includingKirk Bryan (1922).

King proposed that once pediments form, that they persist

indefinitely until consumed by younger retreating escarp-

ments following renewed base level fall. The base level fall

in Kings model is inherently episodic because it occurs on

passive margins, which at the time, were thought to respond

isostatically to episodes of erosional unloading and offshore

deposition (Schumm, 1963) a concept viewed today as

untenable.

King summarizes his pediplane model as well as his over-

all views on landscape evolution in fifty canons, published in

the1953 paper. Of these canons, thefollowing areparticularly

insightful, and research continues on many of them: (No. 1)

Landscape is a function of process, stage, and structure;

the relative importance of these is indicated by their order.

(No. 3) There is a general homology between all (fluviallysculpted) landscapes. The differences between landforms of

humid-temperate, semiarid, and arid environments are dif-

ferences only of degree. Thus, for instance, monadnocks and

inselbergs are homologous. (No. 6) The most active elements

of hillslope evolution are the free face and the debris slope. If

these are actively eroded, the hillslope will retreat parallel to

itself. (No. 9) When the free face anddebris slope are inactive,

the waxing slopebecomes strongly developed and may extend

down to met the waning slope. Such concavo-convex slopes

are degenerate. (No. 42) Major cyclic erosion scarps retreat

almost as fast as the knickpoints which travel up the rivers

transverse to the scarp. Such scarps therefore remain essen-

tially linear and lack pronounced re-entrants where they cross

the rivers.

Dynamic Equilibrium Hack (1960)

The simple, embodying concept of driving and resisting

forces the interaction between form and process proposed

by Gilbert (1877) was rediscovered and presented as an

alternative to the time-dependent paradigms of landscape

evolution by J.T. Hack of the U.S. Geological Survey ( Hack,

1960). By his own admission, Hack had been carefully study-

ing the same Appalachian landscape of Davis and making

a conscious effort to seek alternatives to cyclic theories of

landscape evolution. The alternative favored by Hack is that

landscapes arein a state of dynamic equilibrium (Fig.6). Theyare in equilibrium in the sense that given the same driving

and resisting forces over a long period of time, a time-

independent characteristic landscape will emerge. This is a

landscape where the rivers and hillslopes are all graded and

the processes acting on the interfluves and channel bottoms,

although different, are lowering their respective parts of the

landscape at the same rate. The landscape is dynamic in


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Fig. 6. Attainment of a near time-invariant relief and mean

elevation of a dynamic equilibrium landscape (a) attained

over graded time during a protracted period of decay (cyclic

time) and (b) attained as a flux steady-state between the input

of rocks by tectonic processes and output by erosion.

the sense that climate, tectonics, and rock type change as

subaerial erosion progresses so there is a constant adjustment

between the principal driving and resisting forces such that

true equilibrium is probably only asymptotically reached.

Strictly speaking, a truely characteristic or steady-state

landscape cannot exist, except in a tectonically active setting

where the mass flux in and out of the orogen is conserved

(Pazzaglia & Knuepfer, 2001; Willett & Brandon, 2002). In

a decaying orogen, mean elevation and mean relief must be

reduced, as Davis surmised, because isostatic rebound of

a low density crustal root only recovers 80% of what is

removed via erosion.

Hacks concept of dynamic equilibrium can be usedto describe the origin of the same landscape that Davis

worked in, but without cycles of erosion and peneplains. The

Hack model predicts accordant summits among resistant

rock types because the similar processes have established

themselves on slopes of similar declivity, and on rocks

sharing similar structure over a long period of time. Hack did

not propose an erosional stratigraphy in landscapes. Rather,

he proposed that all landscapes are essentially modern and a

reflection of modern processes. Truly flat landscapes are not

erosional, but rather aggradational. At the time, Hacks paper

was only the most recent of a long list of cycle of erosion

critics to point out the conspicuous global lack of peneplains

at or near sea level.

Hacks contribution very much refocused the geomor-phologic community back towards process and as such,

helped to lay the foundation upon which modern analogue

and surface process models are built. This is not to say that

process geomorphology was absent before Hack. But his

concept of dynamic equilibrium moved geomorphology back

into the wider geologic arena of basic principle chemical,

and biologic principles that govern landscape evolution.

Process Linkage Bull (1991)

Several decades of process studies (e.g. Leopold et al.,

1964), watershed hydrology (Dunne, 1978; Horton, 1945),

and the Hack tradition of dynamic equilibrium (Hack, 1960)

collectively form the basis for understanding landscape

evolution from the perspective of linked processes. This

view of landscape evolution, colored by the dramatic

effects of Quaternary climate change, is best representedin the textbook Climatic Geomorphology (Bull, 1991).

Many geomorphologists in North America and elsewhere

contributed to a modern understanding of process linkage.

But it was Bill Bull, working in the American southwest

and with colleagues abroad, particularly in Israel, who led

this effort.

Process linkage refers to the direct and indirect ways

in which individual components of a watershed mutually

respond to an external driving force, the two most obvious

being tectonics and climate. Implicit in the linkage among

individual components is the realization that there may not

be a unique response for a given external stimuli. Such

non-unique responses arise because thresholds (Patton

& Schumm, 1975) are embedded in most geomorphicprocesses, and because a large external stimulus is required

to elicit the same response in multiple watersheds.

Process linkage has a particular focus on landscape

change as a function of the creation and routing of sediment

thorough a watershed. In this respect, it differs from other

models of landscape evolution that focus on the evolution

of hillslope forms. Climate change, an important control on

sediment creation and routing affects watersheds at all spatial

scales and has been particularly acute during Pleistocene

glacial-interglacial cycles (Pederson etal., 2000, 2001). Qua-

ternary stratigraphy, like that of an alluvial fan, commonly

reveals relatively brief pulses of deposition interspersed

with longer periods of landscape stability and pedogenesis.

The Bull model considers weathering, the production rateof regolith, the liberation of that regolith off hillslopes, the

response time, thresholds, and equilibrium all interacting

in the watershed as the primary controls on the resulting

alluvial fan stratigraphy (Fig. 7). Although many factors in-

cluding rock type, climate, seasonality, relief, and vegetation

influence the hydrology and the unique response of a given

watershed, a simple, representative scenario best illustrates

Bulls model.

Particularly in arid and semi-arid climates, regolith

production is thought to be maximized under relatively cool,

moist climatic conditions when vegetative cover on the hills-

lope accelerates chemical and physical weathering. Stripping

of that regolith occurs when a switch to drier, warmer con-

ditions leads to the loss of the vegetative cover, leaving theregolith prone to gulling and removal by overland flow. Even

without much loss of vegetation, changes such as an increase

in precipitation seasonality or the lowering of infiltration

rates in well-developed, mature soils can eventually provoke

loss of a hillslopes regolith to increased overland flow. The

time between the climatic perturbation and the beginning of

hillslope stripping involves crossing a geomorphic threshold


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Fig. 7. Reaction time, relaxation time, and response times of

theBull (1991)process-response model (modified fromBull,

1991).

and is called the reaction time (Fig. 7). The time needed to

achieve a new equilibrium condition between the new climate

and hillslope process is called the relaxation time. The sumof the reaction time and relaxation time is the response time

(Brunsden & Thornes, 1979). Whipple & Tucker (1999)

describeda similar definitionof theresponsetime as it applies

to channel headwaters adjusting to changes in the rate of

rock uplift.

The transition from the reaction to relaxation times of

when the hillslopes begin to liberate regolith is affected

by the overall climatic regime (arid, semi-arid, semi-arid

and glaciated) of the watershed (Ritter et al., 2000). That

regolith is delivered to the fluvial system which moves it

out of the watershed. The hydraulic geometry may change

as sediment is routed through them, and the streams may

aggrade or incise depending on the sediment flux from the

hillslopes. Even so, the residence time of sediment in thefluvial system is typically short compared with the residence

time of regolith on the hillslopes. The sediment is delivered

to a basin where its depositional architecture retains clues

about climatically influenced transport processes as well as

the weathering processes in the source (Smith, 1994). Some

watersheds have very short response times between the

hillslopes, channels, and depositional basin where a direct

temporal link can be established between the climatic event

that affected the hillslopes and the depositional response

far downstream (Fig. 7). In other cases, long response times

between the hillslopes and depositional basin make it far

more difficult to link a climate change to the depositional

response.

Among the numerous studies that view process linkageas an important agent of landscape evolution, three are

noteworthy in illustrating the relative influences of rock type

(Bull & Schick, 1979), pedogenesis (Wells et al., 1987),

and climate-watershed hydrology (Meyer et al., 1995). The

Bull & Schick (1979) study is one of the first to show the

response of two adjacent watersheds in an arid environment

to the same climate change. The watersheds are underlain

by different rock types, leading to different regoliths, soil

infiltration rates, and response times to late Pleistocene

and Holocene climate change. Some watersheds continue

to deliver sediment from hillslopes as a response to late

Pleistocene to Holocene climate change, so that alluvial fans

at the mouths of these watersheds have a primarily aggrada-

tional history. In contrast, other watersheds cease liberating

sediment from their hillslopes and the corresponding alluvial

fans pass into a period of incision as the sediment supply

wanes.

Wells et al. (1987)showed how the landscape evolution

of an alluvial fan surface, including the location of fan

deposition, is strongly controlled by the linked factors of

soil genesis and how those soils control runoff. Alluvial

fan deposition is initially affected by the late Pleistocene-

Holocene climate change with the watershed hillslopes

being the dominant source of sediment delivered to the

fan. Subsequent Holocene fan deposition reflects a change

in the source from the hillslopes, where runoff has been

reduced by renewed colluvial mantle development, to the

piedmont where runoff has been increased by development of

progressively impermeable clay and calcic horizons in eolian

soils.Meyer et al. (1995) described the landscape evolution

of rugged montane valleys in the Rocky Mountains, where

liberation of sediment from hillslopes is influenced by large

slope-clearing fires as well as climate. The fires recur at

intervals that average approximately 200 years. Relatively dry

climate over a period of years increases the chances of large,

destructive, slope clearing fires. Drier climatic conditions

also correlate with relatively small winter snowpacks and

intense summer convective storms. The hydrology associated

with these relatively dry climatic conditions favors debris

flow activity in burned regions during the summer. Sediment

accumulates in debris fans along the valley margins and the

fluvial system has flashy discharges in a braided, incised

channel with a low base flow. Wet years, in contrast, arecharacterized by a climate with heavy winter snowpacks,

depressed summer convective storm activity, and decreased

numbers of fires and debris flows. The result is a meandering

stream fed by the high, stable base flows and ample sediment

supply recruited from the debris fans as the channel mean-

ders across a widening valley floor. The transition between

relative dry and relatively wet climatic conditions occurs at

the millennial scale. In their long-term evolution, hillslopes

and rivers in this setting are clearly linked, but there is a

millennial-scale response time of the river system following

the initial reaction time of the hillslope to the climatic

perturbation.

Geodynamic and Surficial Process Feedbacks Molnar

& England (1990)

A new way of thinking about orogen-scale landscape evolu-

tion, in terms of surface processes that limit rates of tectonic

deformation and the uplift of rocks originated withMolnar

& England (1990)who linked the building of high-standing


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Fig. 8. Changes in mean elevation and mean

localreliefin response to erosionthat deepens

and widens valleys. Rocks are uplifted as an

isostatic response to this erosion because the

topography is compensated by a low-density

crustal root protruding into the mantle.

Despite rock uplift and surface uplift of the

summits, the mean elevation of the landscape

decreases as the crustal root is consumed

(modified fromBurbank & Anderson, 2001).

mountains to cool climates. The idea of coupled surficial

and geodynamic processes is not new, extending back as

least as far as the original considerations of isostasy and

erosion (Ransome, 1896). More recently,King (1953)argued

that nested, inset pediments were the result of epeirogenic

upheavals caused by the unloading effects of retreating es-

carpments. Schumm (1963) forwarded a similar argument foruplift in the Appalachians caused by erosion crossing an iso-

static threshold after which the land surface would rapidly re-

bound. Thesearguments of episodic uplift(or subsidence) due

to erosion have largely been shown to be incorrect ( Gilchrist

& Summerfield, 1991), but the general idea that uplift and

erosion are linked persists.

The central idea in coupled geodynamic-surficial pro-

cesses is best illustrated by the simple Airy isostatic case of

a mountain range where the topography is supported by a

low-density crustal root protruding into the mantle (Fig. 8).

Uniform erosion across the range results in isostatic rebound

of the root proportional to the density difference between

the mantle and the crust, but the land surface and mean

elevation are lowered with respect to sea level. Airy isostaticrebound recovers approximately 80% of the mass removed

by erosion; a column of rock 5 km thick must be consumed

to reduce mean elevation by a kilometer. The shape of a

mountain range responds dramatically to the rebound if the

erosion rate is not uniform across the range. When erosion

is concentrated in valleys and interfluves are lowered much

more slowly than valley bottoms, local relief is increased

and the resulting isostatic rebound pushes the interfluves

(mountain peaks) higher even though mean elevation has

been lowered (Fig. 8). The effect is muted below the flexural

wavelength of the lithosphere (Small & Anderson, 1998)

but it still may be an important source of recent surface

uplift.

Feedbacks between surficial and geodynamic processesgo beyond simple consideration of surface uplift by isostasy.

The concept encompasses climatically controlled limits on

mean elevation (Brozovicet al., 1997), the width of orogens

(Beaumont et al., 1992), the metamorphic grade of rocks

exposed in ancient orogens (Hoffman & Grotzinger, 1993),

the dominant river long profiles and hillslope erosion pro-

cesses (Hovius, 2000), the structure of convergent mountain

belts (Willett, 1999), and a geomorphic throttle on orogenic

plateau evolution (Zeitler et al., 2001). Consideration of

surficial-geodynamic feedbacks releases geomorphic think-

ing from viewing landscape evolution at the large scale as

only reacting, rather than interacting to impulsive climatic

or tectonic changes. At the scale of the orogen, landscapes

evolve as a consequence of both tectonics and climate and theevolutionary path itself plays a role in defining the feedbacks

between the two.

Physical Models

Physical models of landscape evolution existed in parallel

with, but originally did not enjoy the spotlight focused on

the philosophical approaches. A history of the rise and

development of physical models is provided by Schummetal. (1987). Daubree (1879) wasamongthe first to recognize

that experiments can reveal basic relationships and general

hypotheses to guide field studies. Early experiments focused

on formation of drainage networks (Hubbard, 1907), theerosional evolution of an exhumed laccolith (Howe, 1901),

the downslope movement of scree (Davisson, 1888a, b),

fluvial transport of sediment (Gilbert, 1914, 1917), and

behavior of channel meanders (Jaggar, 1908). Evolution

of drainage networks within a given watershed were first

simulated byGlock (1931)andWurm (1935, 1936).

There are three broad classes of physical models: (1)

segments of unscaled reality, (2) scale models, and (3) analog

models (Chorley, 1967). A segment of unscaled reality does

not imply that the model is constructed at some scale very

different than what is found in nature. Rather, it refers to

a model that can actually be of a natural system, like the

segment of an alluvial river channel that is considered repre-

sentative of a broader range of river channels in form, process,and geography. Simple sand bed flumes or stream tables

also illustrate unscaled reality. There are particularly useful

applied geomorphology practices where data from segments

of unscaled reality have led to important policies in land man-

agement. An example widely used by agricultural engineers

is the Universal Soil Loss Equation (Wischmeier & Smith,

1965), which wasderived from both field studies andphysical


11/28


models of soil erosion. Commonly, space and time are substi-

tuted in segments of unscaled realitymodels so that processes

that unfold over millions of years in large watersheds can

be investigated over a period of years. For example, Ritter

& Gardner (1993)linked dependence of infiltration recovery

with channel development on mined landscapes in a physical

model that plays out over a period of years to mimic the

evolution of larger watersheds. In the process, the model

provides insight as to how climate change affects basin

hydrology.

Scale models make an attempt to reproduce natural

landforms in such a way that ratios of significant dimensions

and forces are equal to those found in nature. True scale

models are difficult to construct because of the limited range

of fluid and substrate material properties that are practically

available to maintain ratios of dimension and force. Jurassic

Tank at the University of Minnesota St. Anthonys Falls

laboratory illustrates a scale model dedicated to the study

of depositional landforms and their resulting underlying

stratigraphy (Paola et al., 2001).

Analogue models are designed to mimic a given natural

phenomena without having to reproduce the same driving

forces, processes, or materials. Examples include modelingthe flow of glaciers using oatmeal (Romey, 1982) or mod-

eling landslides using a flume filled with beans ( Densmoreet al., 1997).

Physical models typically isolate one part of the geomor-

phic system, or even one part of a watershed and, as a result,

rarely show the behavior of an alluvial channel, for example,

in the context of broader landscape change. Fortunately, vir-

tually all geomorphic processes produce erosion which phys-

ical models can reproduce as a general proxy for landscape

change. Erosion, channel incision, and sediment transport,

common to many physical models, are considered below.

Drainage Networks

Drainage networks have attracted a great deal of attention in

the overall evolution of a watershed. Given the growing ap-

preciation for the rate of fluvial incision and characteristic

drainage density in limiting rates of rock uplift and erosion

in tectonically active landscapes, the initiation and evolution

of drainage networks remains a central pursuit in landscape

evolution models. There are three main hypotheses regard-

ing drainage network evolution: (1) network growth by over-

land flow (Horton, 1945); (2) headward growth of established

channel heads (Howard, 1971; Smart & Moruzzi, 1971); and

(3) dominance of rapidly elongated channels (Glock, 1931).

The Glock model incorporates components of both overland

flow andheadwardretreat. In this model, a trunk channel initi-ates, rapidly elongates, elaborates, and then abstracts, settling

into a characteristic drainage density consistent with the pre-

vailing infiltration characteristics of contributing hillslope. In

fact, it is the evolution of infiltration characteristics on the

hillslope that determines the speed at which the network pro-

gresses through the various stages. Predictions of the Glock

model have been directly observed in field studies (Morisawa,

1964; Ritter & Gardner, 1993) and have been reproduced and

refined with other physical models (Parker, 1977).

Hillslopes

Physical models are common in studies of hillslope form and

process. Geological engineering and watershed hydrology

literature is rich in examples of physical models designed

to understand landslides, earthflows, and debris flows. The

U.S. Geological Survey debris flow experimental flume (e.g.

Denlinger & Iverson, 2001; Iverson & Vallance, 2001) is

an example of recent approaches that have greatly advanced

the understanding of Coulomb and granular dispersion

processes in hyperconcentrated and debris flows. However, it

is typically more difficult to reproduce scale representatives

of hillslopes in the laboratory, so many physical models

are actually carefully controlled field monitoring studies

designed to isolate one process acting over a limited area.

The fall of Threatening Rock, a well-documented example

of slab-failure processes, is one such field study that passes

for a physical model (Schumm & Chorley, 1964). This study

revealed that movement of the slab away from the cliffface accelerated exponentially approaching the moment of

failure. The rates were fastest in the winter months, probably

because of frost action. Studies of hillslope creep are another

class of physical models, typically conducted in the field.

Creep experiments consider a column or known shape of

regolith or soil periodically measured with respect to fixed

reference points. The measurements may include markers or

lines on the surface of the regolith, or horizontal pins inserted

in the free face of a Young Pit (Young, 1960).

Weathering and rock disaggradation in the hillslope envi-

ronment are easily simulated by repeated mass and volume

measurements of representative rock samples under different

weathering environments. Rates of disintegration and mass

loss depend on whether the rock sample remains exposed atthe surface, or if it remains buried in a soil profile, exhumed

only for the purpose of measurement. Such experiments may

influence the resulting measured rates, but they do provide

insights into processes. The classic experiment of this type

was conducted on sandstone collected from cliff faces in the

Colorado Plateau (Schumm & Chorley, 1966). The results

from measurements over a period of two years, showed

that granular disintegration, rather than fracturing into small

pieces, was the dominant weathering process. Steep cliff

faces are probably maintained in the Colorado Plateau as

the rock disintegrates and is blown away; little accumulates

against the cliff base.

There are at least two recent examples of small-scale

physical models with applications to long-term hillslope evo-lution based on the study of avalanches. Field studies support

creep processes to be dominant on low-gradient hillslopes

or for the convex upper slope portion, whereas landslides

dominate steep hillslopes or on the steep, straight main slope.

A physical model using dried beans of various sizes and

shapes (Densmoreet al., 1997) helps show the genesis and

role of landslides on the steep main slope. The apparatus used


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in these experiments wasa narrow flume made of clear acrylic

walls 2.5 cm apart. The front of the flume could be lowered to

simulate base level fall. The flume was alternately filled with

red, oval-shaped beans or white, more spherically-shaped

beans. Base level was lowered andthe fluxof beans shed from

the flume was measured for each base level lowering step.

The beans are thought to represent strong, coherent blocks

of rock with weak grain boundaries and as such, collectively

approximate rock behavior where strength is a function of

both zones of weakness andblock anisotropy. Results showed

that base level lowering caused a step to develop at the toe

of the slope. As the step grew, the slope above it destabilized

and was swept clear of a layer of beans in a slope-clearing

landslide. The landslides happened at irregular intervals and

their frequency depended on bean anisotropy. The slope

clearing events, analogous to landslides, accounted for 70%

of the total mass removed from the model hillslope. In real

landscapes, the steep inner gorges in mountainous topogra-

phy may be analogous to the lower step seen in the model.

The applicability of this model to real landscapes has been

questioned because subsequent experiments demonstrate

that the narrow width of the flume may have influenced the

initiation of the inner gorges and slope-clearing events (Aaltoet al., 1997). Nevertheless, the study does underscore the im-

portance of both creep and landslide processes on hillslopes

have creep and landslide components of mass removal.

Creep and landslide removal of mass from a hillslope

has been treated as linear and non-linear diffusive processes

respectively (Martin, 2000). Non-linear sediment transport

from model hillslopes was investigated by a physical model

(Roering et al., 1999, 2001) consisting of a plexiglass box,

with open ends, filled with a hill of sand. The sand was

subjected to acoustic vibrations that caused the outermost

layer of grains to vibrate, dilate, and creep downslope,

simulating the biologic and freeze-thaw turbation of regolith

on real hillslopes. A key result of the experiment is that the

flux of sediment from this model hillslope approximate alinear diffusive behavior when gradients were low (


13/28


Many iterations of solving the equations lead to changes

in cell height that mimic real time-dependent changes in

landscape elevation and relief. Numeric models provide

alternatives to cumbersome physical models where scaling

relationships may be violated. They also facilitate the focused

investigation of an individual process or suite of processes.

There is a certain elegance and level of objectivity to numeric

approaches because the outcome of a good model is the result

of independent equations based on physical laws. Lastly, and

perhaps most importantly, numeric models can be used to

test paradigms of landscape evolution and to predict future

changes in the landscape, using the modern topography as a

starting point. However, erroneous interpretations result if the

boundary conditions processes are not properly identified and

defined.

There are several different types of numeric models

that have been developed over the past three decades. Their

rapid expansion into studies of landscape evolution has

been greatly enhanced by computers. There are at least five

reviews or compilations of numeric landscape models from

the past ten years: the Tectonics and Topography special

volume published in the Journal of Geophysical Research

(Merritts & Ellis, 1994), Koons (1995), Beaumont et al.(2000),Landscape erosion and evolution modeling (Harmon

& Doe, 2001), and the Steady-State Orogen special volume

published by the American Journal of Science (Pazzaglia

& Knuepfer, 2001). The Beaumont et al. (2000) paper is

particularly noteworthy for its attempt to categorize numeric

models based on relative complexity. The organization and

explanations of numeric models in this chapter borrows heav-

ily upon these sources. The interested reader is directed to

them for detailed descriptions of the models describedherein.

The three major types of numeric landscape evolution

models are surrogate models, multi-process models, and

coupled geodynamic-surface process models. A surrogate

model typically tracks a single metric of the landscape, such

as mean elevation or mean relief, and does not discriminateamong the myriad of processes that redistribute mass in real

landscapes. The multi-process model attempts to isolate and

represent all processes that contribute to the redistribution of

mass with individual mathematical equations. A recent trend

is to link a robust multi-process model with a geodynamic

model of rock deformation in the Earths crust, to yield a

coupled geodynamic-surface process model. A true coupled

model is one where the surface process model predicts

lateral mass fluxes throughout the model landscape and the

corresponding geodynamic model calculates the solid earth

mass fluxes in response to the surface processes and as a

consequence of tectonic forces or velocity fields (Beaumont

et al., 2000). Such coupled models are particularly intriguing

because their results provide insights into the feedbacksbetween geodynamic and surficial processes.

All numeric models share the common goal of represent-

ing erosion of the landscape, either explicitly or implicitly as

a key component of landscape evolution. Nearly all models

treat erosion as proportional to local relief, mean elevation

(Fig. 9), or local gradient and hydrology. There are separate

justifications for all three. Erosion proportional to mean

relief is supported by studies that show a correlation between

river suspended sediment yields and relief (Ahnert, 1970).

Erosion proportional to mean elevation is supported by

Ruxton & McDougall (1967) and Ohmori (2000) among

other studies, and a correlation between mean elevation and

mean relief has been established for landscapes with well

integrated drainages (Ohmori, 2000; Summerfield & Hulton,

1991). An important caveat to models that appeal to relief

dependent erosion is that they can only be applied to decaying

landscapes. Constructional or steady-state landscapes may

exhibit no correlation between mean elevation, mean local

relief, and rate of erosion. Erosion proportional to local

gradient and hydrology is predicated on the field and lab

studies that began with Gilbert (1877, 1909) and continues

with experiments like those ofRoeringet al. (2001).

Another feature commonly shared by numeric models is

the concept of landscape response time. This numeric formal-

ization of the response timeofBull (1991) is typically derived

from linear system behavior. Response times are particularly

important in coupled geodynamic-surface process models

because the tectonic forcing in these models is commonly

treated as a step function. Linear system behavior treats the

system response to a step-like forcing as an exponential andthe response time (sometimes also called the characteristic

time) is defined as (1 1/e) where e = 2.71828. In other

words, the response time indicates the amount of time needed

to accomplish 63% of the landscape change or adjustment

following a perturbation. Response times are sensitive to

climate, model rock type, and the spatial-temporal scale of a

model tectonic forcing. In real orogens that are well-drained,

the response time scales approximately with the size of the

orogen. Small orogens like Taiwan have short response times

on the order of millions of years. Large orogens with orogenic

plateaux like the Himalaya mayhaveresponse times in excess

of 100 million years. Linear system behavior is supported

by real observations of how perturbed Earth systems liberate

sediment as they seek new equilibria (Schumm & Rea, 1995).Flumes, watersheds, and orogens all show an exponential de-

cay in sediment yield following the perturbation. In the case

of a whole orogen, theresponsetimes are long enoughthat the

simplest explanation for exponential reduction in sediment

yield is a decrease inthe mean elevation and meanrelief ofthe

source. At cyclic space and time scales, the Davisian cycle of

erosion is probably an appropriatelandscape evolution model.

Analytical solutions to the landscape response timehavebeen

proposed byWhipple & Tucker (1999)andWhipple (2001).

Surrogate Models

The goal of the surrogate landscape model is to track a metricof the landscape, such as mean elevation above base level, or

evolution of a single landscape component like a streamchan-

nel (Howard et al., 1994; Whipple & Tucker, 1999), using a

physically based equations or established functional relation-

ships between a landscape metrics or processes. Erosion rate

is commonly indexed to mean elevation (Fig. 9). Several early

models use an elevation-erosion rate relationship to solve for


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Fig. 9. (a) Correlation between mean local relief (measured in a circular window 10 km in diameter) and mean denudation rate,

calculated from suspended sediment yield data from large, mid-latitude, well-drainage watersheds (modified from Pazzaglia

& Brandon, 1996). (b) Correlation between mean elevation and mean local relief for well drained landscapes (modified from

Summerfield & Hulton, 1991).

rockuplift, evolution of mean elevation, and flexural deforma-tion of thelithosphere(Moretti & Turcotte, 1985; Stephenson,

1984; Stephenson & Lambeck, 1985). Such models have also

simulated critical taper on an emergent accretionary wedge

(Dahlen & Suppe, 1988), predicted the height limit of moun-

tains (Ahnert, 1984; Slingerland & Furlong, 1989; Whipple

& Tucker, 1999), and predicted the thermal structure of an

eroding crustal column (Batt, 2001; Zhou & Stuwe, 1994).

Surrogate landscape models are not designed to capture

the full range of changes in the landscape as it is eroded, but

rather are useful in exploring the relative scaling relation-

ships between landscape metrics and driving and resisting

forces. For example,Pitman & Golovchenko (1991)justified

an erosion proportional to mean elevation relationship to

define the necessary and sufficient conditions for generatingpeneplains in the Appalachian landscape. Pazzaglia &

Brandon (1996)followed a similar approach to reconstruct

the evolution of mean elevation of the post-rift central

Appalachians (Fig. 10a). The erosion rate was reconstructed

from known quantities of sediment trapped in the Baltimore

Canyon Trough, and a simple linear equation was solved

for the general relationship between the flux of rocks into

the mountain belt and erosional flux out of the belt. The

results of a tectonic model, in which the flux of rocks into

the belt was allowed to vary, but climate (rock erodibility)

was held constant shows that three kilometers of rock would

have to be fluxed through the belt in the past 20myr to

account for the recent offshore sediment volumes. Mean

elevation of the range would have had to increase from nearsea level before the Miocene to 1100 m, before diminishing

to its present value of about 350 m. Tested by, for example,

thermochronology, such predictions help place limits on the

range of landscape responses that might be expected from a

tectonic or climatic perturbation.

A less common surrogate approach is to apply a stochastic

technique where landscape change is determined by the

Fig. 10. (a) Reconstruction of rock uplift (source, triangles),

mean elevation (squares), and total erosion (inverted trian-

gles) for the post-rift Appalachian mountains (modified fromPazzaglia & Brandon, 1996). This simple single-process

landscape model provides insights to the scaling relation-

ships between mean elevation and rock uplift to explain the

known volume of sediment delivered to offshore basins. (b)

Illustration of detrital mineral age spectra during exhumation

of the landscape to the steady-state relief condition (modified

fromStock & Montgomery, 1996).


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mean and variance of landscape slope elements (Craig,

1982, 1989). This particular type of model is one of the

few that carefully incorporates map-scale considerations

of the influence of structure, rock type, and stratigraphy

on landscape evolution. One-kilometer-long slope elements

called draws are constructed between adjacent cells in a

DEM where the rock type underlying the cells is noted. The

mean and variance of draws for any particular rock type

pair is calculated and recorded. The slope of the draws is

assumed to be well adjusted to the rock type and structure.

The model can only be applied in settings where driving and

resisting forces approach a dynamic equilibrium. Erosion is

introduced as a random perturbation by lowering one cell.

All adjacent cells are adjusted randomly by choosing a new

draw that falls within the variance limits of all possible draw

slopes developed between specific rock type pairs. The result

is a diffusive rippling effect of slopes adjusting away from

the perturbation. Relief can increase or decrease depending

on the rock types encountered or uncovered. Erosion stops

when the landscape has been lowered to base level.

Another type of surrogate model involves inversion

techniques to estimate paleoelevation or paleorelief using

thermochronology in the source and/or detrital grain ages(e.g. Bernet et al., 2001; Brandon & Vance, 1992; Garver

et al., 1999; Stock & Montgomery, 1996; Fig. 10b). Con-

ceptually these models assume a relief or elevation depen-

dence on the exhumation of bedrock in the source. Mineral

isochrons commonly increase in age with elevation especially

where isotherms are a horizontally subdued reflection of to-

pography. Measurable mineral age gradients are apparent in

landscapes with moderate relief (3 km) and erosion rates

around0.5 mm/yr. Thenumerical ages of theminerals depend

on relief, the geotherm, and erosion rate. If erosion is uniform

across the landscape and relief remains more or less steady as

the landscape is unroofed, the vertical distribution of mineral

ages in a depositional basin essentially reflects that unroofing

process with a constant age gradient. If relief instead changesas the land erodes, the age gradients in the depositional basin

also change. An inversiontechnique hasbeen proposed to con-

vert that change in age gradient to changes in relief (Fig. 10b;

Stock & Montgomery, 1996). The technique requires high

precision single-grain ages, no change in mineral age during

transport and deposition, mixing of the eroded sediment, and

minimal sediment storage between source and sink.

Multi-Process Landscape Models

A multi-process landscape model considers two or more

mutually interacting geomorphic processes that sculpt real

landscapes. The model mathematically describes these pro-cesses, links the mathematical descriptions together in such a

way that the continuity of mass is maintained, provides inputs

of rock type, climate, and tectonics, and predicts the resulting

landscape evolution (Slingerlandet al., 1994). Multi-process

landscape models differ from the surrogate models in that the

former actually strives to simulate the form and process of

real landscapes, as opposed to simply exploring the scaling

relationships among landscape metrics. Two generations of

multi-process landscape models are recognized, the second

borrowing heavily on the first. First generation multi-process

models include attempts to mathematically capture bedrock

weathering, hillslope creep, landsliding, fluvial transport

of sediment, and channel initiation (Ahnert, 1976, 1987;

Anderson & Humphrey, 1990; Armstrong, 1976; Chase,

1992; Gregory & Chase, 1994; Kirkby, 1986; Musgrave etal.,

1989; Willgoose et al., 1991). Second generation models

specifically explore broader, more complex interactions

among processes by introducing, for example, climatic

perturbations (Tucker & Slingerland, 1997) or migration of

drainage divides (Kooi & Beaumont, 1994).

The basic physical principle underlying all multi-process

models is the conservation of mass. Mass rates into and out

of model cells are driven by the geomorphic processes acting

on the landscape (Fig. 11). These include but are not limited

to bedrock weathering, hillslope creep, hillslope landsliding,

glacial erosion, bedrock channel erosion, alluvial channel

erosion, and sediment transport. A simple multi-process

model collapses all hillslope processes into one mathematical

equation that treats them collectively as diffusion. Similarly, it

treats all fluvial transport processes collectively as advection,with sediment transport proportional to unit streampower (the

discharge-slope product;Howard, 1994). More sophisticated

approaches consider non-linear processes such as hillslope

landsliding. A fine example of a robust multi-process land-

scape model, GOLEM, with examples of the various model

inputs is discussed in detail inSlingerlandet al. (1994).

Bedrock weathering is typically modeled as an alter-

ation front that penetrates downward at a rate inversely

proportional to the thickness of the regolith cover (Ahnert,

1976; Anderson & Humphrey, 1990; Armstrong, 1976;

Rosenbloom & Anderson, 1994). The justification for this re-

lationship is that soil genesis is a self-limiting process. Thick,

well developed soils (or regoliths) tend to influence infiltra-

tion rates and generate runoff resulting in overland flow thatstrips the upper horizons. Regolith thickness approximates

a steady state when the rate of stripping equals the rate of

descent of theweathering front (Heimsath etal., 1999; Pavich

et al., 1989).

Hillslope creep is typically modeled as a linear diffusive

process where sediment transport is proportional to slope.

Diffusion has attracted the greatest attention of all modeled

geomorphic processes both within and outside the modeling

community because of its simplicity and its apparent veri-

fication from slope degradation studies (e.g. Culling, 1960,

1963; Hanks et al., 1984; Nash, 1980). On any uniformly

eroding hillslope, it has been long known that sediment

flux must increase systematically away from the hilltop

(Gilbert, 1909). If the sediment flux is dependent on theslope, the combination of a slope-dependent transport law

and the continuity equation leads to mathematical equation

that looks like linear diffusion (Culling, 1960; Nash, 1980).

However, this equation describes change in the hillslope

profileand is not meant to describe the downslope transport

of individual particles of sediment, a process that is probably

non-diffusive. The diffusion constant or diffusivity in the


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Fig. 11. Schematics showing (a) the arrangement of cells in a traditional 2-D, multi-process model where flow is directed down

the steepest paths between rectilinear cells and (b) the major processes that are represented mathematically in model landscapes

(both modified fromTucker & Slingerland, 1994). Most models now employ a triangulated network, rather than rectilinear cells.

diffusion equation is a scale dependent parameter that

implicitly includes climate and substrate characteristics.

The idea of simple hillslope diffusion is complicatedby field observations and physical models of slope-clearing

landslides as important agents for removing mass from

hillslopes, especially in steep landscapes undergoing tectonic

uplift. Multi-process models that account for landsliding

typically assign a threshold slope angle, below which

sediment is transported by diffusion, and above which,

sediment is transported by slope-clearing landslides until the

slope diminishes to a threshold angle (Kirkby, 1984). More

soph

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Landscape Evolution