Models of Slope Development

• Slope evolution is the change of hillslope and valley-side form through time, and a model of slope development explains which processes and controls produce a given profile and how that profile changes.
• Each model addresses the same core questions: do slopes retreat parallel to themselves and keep their angle, or do they decline progressively in angle; and is the landmass lowered by downwasting (lowering from above) or backwasting (retreat sideways)?
• Two classical schools grew from the contrasting ideas of William Morris Davis and Walther Penck; later workers added field measurement, cliff geometry and computer-based process-response models.
• The profile units these models work with are the slope elements: waxing crest, free face, debris slope and waning foot.

Approaches and Types of Slope Evolution

Three Ways of Studying Slopes

• Theoretical (deductive) models: reason from assumed processes to expected forms.
  • Davis, Penck, Wood and King worked this way.
• Experimental models: reproduce slope change under controlled conditions, from laboratory set-ups to computer simulation.
• Empirical models: measure real slopes and infer how they evolve.
  • R. A. G. Savigear and Arthur Strahler led this approach.

Three Types of Slope Evolution

• Anthony Young (1972) grouped all theories of slope development into three types; the table splits parallel retreat into two rows, as he did.

Type	Maximum slope angle	What changes	Final form	Main proponents
Slope decline	Decreases steadily	Convexity above and concavity below both grow	Gentle convexo-concave slope	W. M. Davis
Slope replacement	Decreases	Gentler units replace steeper ones from below; concavity takes most of the profile	Concave (smooth or segmented) profile	W. Penck
Parallel retreat (with free face)	Stays constant	Free face and debris slope keep their length; basal concavity lengthens	Broad pediment and pediplain	A. Wood, L. C. King
Parallel retreat (without free face)	Stays constant	Rectilinear slope retreats; concavity lengthens	Extended concave foot	A. N. Strahler

• In parallel retreat, the angle at any fixed height on the concavity decreases over time, even though the upper units keep theirs.

Classical Deductive Models

Slope Decline Model: William Morris Davis

• William Morris Davis built his slope ideas into his cycle, from “The Convex Profile of Bad-Land Divides” (1892) and “The Geographical Cycle” (1899) to his reply to Penck, “Piedmont Benchlands and Primärrümpfe” (1932).
• Assumptions: rapid uplift followed by a long period of crustal stability, a humid temperate climate, and base level fixed during the cycle.

Stages of Slope Decline

Stage	Dominant process	Slope form	Slope angle
Youth	Rapid downcutting; little slope retreat	Steep, convex valley sides	Steep, may even increase
Maturity	Lateral erosion and downwasting of divides	Smooth curve; graded rectilinear middle	Declining
Old age	Continued lateral erosion; relief much lowered	Broad concave slopes with low convex crests	Only a few degrees

• The slope becomes steadily gentler, longer and more curved: the radius of curvature of both the summit convexity and the basal concavity grows with time.

Three Features Davis Explained

• Rounded summit convexity:
  • Caused by soil creep, driven by alternate swelling and shrinking of the soil under gravity.
  • Near divides creep dominates over wash, because surface wash only builds up in volume downslope; creep yields rounded crests.
• Graded waste sheet:
  • The mantle of weathered debris that moves slowly downslope is graded when the ability of the transporting agents to do work equals the work they have to do.
  • At every point, removal just copes with the waste weathered there plus the waste arriving from upslope.
  • Grading starts at the slope base and spreads upslope; by old age the whole profile carries a sluggish, continuous waste cover.
  • With time the graded slope becomes gentler, and its debris becomes finer and thicker.
• Graded valley sides: summital convexity above and basal concavity below both lengthen, so valley sides flatten along with the interfluves.
  • The same idea of balance between energy and load underlies the graded river.

Evaluation

• Strengths:
  • Internally consistent and flexible; it makes slope form time-dependent, which can in principle be tested in the field.
  • Convexo-concave slopes do dominate many soil-mantled humid landscapes, such as the old rounded hills of the Peninsular gneissic uplands.
• Weaknesses:
  • It depends on prolonged crustal stability, which active regions rarely enjoy.
  • It is qualitative, and it treats form as a function of stage rather than of measured process rates.
  • Similar forms can arise from different histories, so “stage” cannot be read directly from a profile.

Slope Replacement Model: Walther Penck

• Walther Penck (1888–1923) set out his model in Die morphologische Analyse (1924), published by his father after his early death.
• Why he was long misunderstood:
  • His work was unfinished and written in dense German with loosely defined terms.
  • Davis’s reviews presented him as the champion of simple parallel retreat.
  • The English translation (1953) by Hella Czech and Katharine Cumming Boswell was criticised as imperfect, and M. Simons (1962) later re-read the original.
  • Only then was his idea recognised as slope replacement, not parallel retreat of the whole slope.

Penck’s Morphological System

• Aim: to read the tectonic (diastrophic) history of a region from its present landforms, since form reflects the balance between uplift and denudation.
• He related seven properties of form to three properties of process, stressing mass movement above other processes.

Properties of form	Properties of process
Degree of reduction (how finely the regolith is broken)	Reduction: comminution by weathering, controlled by rock, climate and exposure
Mobility of regolith	Denudation: removal of regolith downslope (Penck’s sense, not erosion)
Thickness of regolith (rises with reduction, falls with removal)	Renewal of exposure: fresh rock laid bare once regolith is removed
Exposure of rock under regolith
Rock properties (lithology, structure)
Climate (only its effect on reduction and removal)
Slope angle (independent at first, later partly dependent)

• Anthony Young (1972) recast these links as a process-response system:
  • He separated dependent from independent variables and paired the closely linked properties (reduction–mobility, thickness–exposure, denudation–renewal of exposure).
  • He grouped effects by time: short term (a year or less), medium term for regolith (1,000–10,000 years) and long term for slope form (10,000–100,000 years).

Basic Premises

• Slope form depends on the relative rates of stream incision at the base and denudation (removal of debris) on the slope.
• Slope processes do not shape the form directly; they remove debris and expose rock to weathering.
• Weathering acts at a uniform rate; removal begins once the regolith is mobile enough and then keeps pace with weathering.
• Steeper units retreat faster, and every unit retreats parallel to itself until it is replaced from below.
• “Flattening of slopes always takes place from below upward.”

The Deductive Model: Böschung and Haldenhang

• Initial condition: a steep rock face of uniform rock, capped by a level surface, above a river that neither erodes nor deposits but removes all debris arriving at the foot.
• Mechanism:
  • In each unit of time a layer of equal thickness is loosened on every part of the face, and the loosened particles fall away because the face is too steep for them to rest.
  • Every part of the steep unit (the Böschung or Steilwand) therefore retreats parallel to itself.
  • The lowest part cannot shed its debris, because its angle is too gentle for the required mobility, so a new unit of lower angle forms at the foot.
  • Repeated over many intervals, these small units join into a continuous basal slope of gentler gradient, the Haldenhang, which extends upslope at the expense of the steep face.
• Outcome: “a steep rock face, left to itself, moves back upslope, maintaining its original gradient; and a basal slope of lesser gradient develops at its expense.”
  • The stepped profile in diagrams is only a device of dividing time into intervals; in the field it becomes a smooth, concave profile under a uniform debris cover.
• Interfluves: once the steep units on both sides have been consumed, the divide is downwasted, and the slope then declines.
• Debris-covered slopes:
  • Penck applied the same logic to regolith-mantled slopes: debris moves only once the basal slope reaches the mobility it needs.
  • A still gentler unit then forms below and replaces it, so replacement repeats at ever lower angles.
• Indian example: on the Bhander plateau (Madhya Pradesh) the massive sandstone free face retreats parallel to itself while the shale slope beneath extends upslope; outliers that have lost their sandstone cap show convexo-concave profiles.

Rate of Stream Erosion and Slope Form

Rate of basal (stream) erosion	Penck’s term	Resulting valley-side form
Accelerating	Waxing development (aufsteigende Entwicklung)	Convex slope
Constant	Uniform development	Rectilinear slope
Decelerating	Waning development (absteigende Entwicklung)	Concave slope

• An abrupt rise in the erosion rate gives a convex break of slope, and the steeper unit below then works upslope, replacing the gentler one above.
  • Penck did not claim that a smoothly accelerating rate produces an angular break; that reading came from his commentators.

Evaluation

• Strengths:
  • It links form to process rates and tectonics, not to time alone.
  • It explains concave basal slopes and scarp-and-footslope profiles seen in the field.
• Weaknesses:
  • Rockfall with instant removal cannot simply be carried over to regolith-covered slopes.
  • Parts of the basal slope are not equally exposed to weathering: exposure is longest at the foot and falls to zero at the junction with the unit above.
  • Uniform weathering over the whole face is doubtful, and the model fails where debris is removed in pulses rather than continuously.
  • His text is ambiguous on whether development is stepwise or continuous, and whether the profile stays segmented or becomes a smooth concavity; his later work on the Black Forest favours the concave reading.
• Current view: in Penck’s scheme, parallel retreat operates only on an initial rectilinear slope; once replacement is continuous, no part of the concave slope retreats parallel to itself. Gentler slopes succeed steeper ones, but by a route quite unlike Davis’s decline.

Slope Evolution Model: Alan Wood (1942)

• Alan Wood presented his model in “The Development of Hillside Slopes” (1942), which named the four slope elements: waxing slope, free face, constant (debris) slope and waning slope.
• Key ideas: parallel retreat of the free face, and a balance between the rate of weathering and the rate of removal of the weathered debris.

Mechanism

• Initial form: a cliff (free face) produced by faulting or by erosion.
• Retreat: weathering makes the free face retreat parallel to itself.
• Scree build-up: the debris gathers at the foot as talus, which Wood treated as the local base level for weathering.
  • In the ideal case the scree is not weathered and has the same volume as the parent rock.
  • The scree protects the lower face, buries it progressively and reduces its height.
  • Beneath the scree a convex rock core is left behind as the face retreats.
• Constant slope: the scree surface stands at a constant angle, the constant slope; it grows until it buries the free face completely.

• Departures from the ideal case:
  • Real scree occupies more volume than the parent rock because of its pore spaces, so it grows upward faster and the buried face is steeper, though still convex.
  • If fines are washed out, the scree grows more slowly and the buried face is gentler.
  • Coarse-debris rocks build scree faster than rocks that yield fine debris.
• With a stream at the foot:
  • If the stream removes everything that arrives, the debris slope stays the same length while the free face keeps retreating.
  • The retreat leaves a denudational (bare) constant slope, a rectilinear slope of transportation, above the lower aggradational debris segment.
• Later stages:
  • Once the free face disappears, the crest is rounded into a waxing (convex) slope, and the foot turns concave as a waning slope.
  • The profile becomes convex–rectilinear–concave, then convexo-concave as the rectilinear unit is consumed from above and below.
  • Relief then slowly declines by wasting.
• Wood held that no single path applies everywhere: climate, structure and conditions at the slope foot decide the outcome.

Evaluation

• It is a clear geometric model and the source of the slope-element terms used ever since.
• It gives no convincing reason why convexity and concavity appear only late.
• Turning the constant debris slope into a concavity is acceptable, but the buried convex rock core becoming concave is an unsupported step.

Parallel Retreat Model: Lester Charles King

• Lester Charles King, working from South Africa, built his hillslope cycle into a wider scheme of landscape evolution, set out in “Canons of Landscape Evolution” (1953) and The Morphology of the Earth (1962).
  • He drew on Alan Wood, T. J. Fair, Walther Penck and Robert Elmer Horton (1945).
• Assumptions:
  • Semi-arid and savanna (sub-humid) regions, not humid temperate lands, show “normal” landscape development, because mid-latitude landforms were reshaped by Pleistocene glaciation and periglacial processes.
  • The basic controls of landscape are the same in all climates short of frigid or extremely arid, a direct challenge to climatic geomorphology.
  • A standard hillslope has all four elements (waxing crest, free face or scarp, debris slope, and a concave pediment), formed by running water, mass movement or both.
  • All four develop fully only where strong rock and bold relief exist; otherwise a waning convexo-concave slope forms.

Mechanism: Scarp Retreat and Pedimentation

• The scarp retreats parallel to itself by weathering and backwasting, and this retreat governs the whole hillslope.
• Supply equals removal on the debris slope and at the crest, so neither grows: the debris slope never buries the free face, unlike in Wood’s model.
• A pediment of concave profile extends at the foot as the scarp and debris slope recede.
• Pediments from opposite sides coalesce once the upper elements are consumed, producing a pediplain with residual inselbergs; this sequence is the pediplanation cycle.
• Where there is no scarp (weak rock, low relief), the maximum angle decreases and broad convexo-concave slopes form.
  • King regarded such slopes in the northern temperate lands as relict, inherited from past periglacial processes rather than shaped by present ones.

Evaluation

• Strengths: a bold global synthesis; parallel scarp retreat and pediments are widely seen in dry and savanna shield lands.
• Weaknesses:
  • It is not original in its parts: it combines Wood, Fair, Penck and Horton.
  • It rests on reconnaissance, with no measurement of either form or process.
  • Key claims are asserted, not tested, for example that turbulent flow on the upper slope gives way to laminar flow on the pediment.
  • Contrary field evidence is set aside as “not normal”; the model is best read as a set of hypotheses to test.
• Indian examples:
  • Scarps of jointed, massive sandstone over weaker shales and siltstones show parallel retreat by backwasting along the Kaimur range, Rohtas plateau, Rewa plateau and Bhander plateau, and on the margins of the Chotanagpur plateau.
  • The Bhander escarpments carry all four elements, and detached sandstone-capped mesas are retreating on all sides.

Empirical and Process-Response Models

R. A. G. Savigear (1952): Carmarthen Bay, South Wales

• R. A. G. Savigear measured cliff profiles at the head of Carmarthen Bay and concluded that both parallel retreat and slope decline occur, even side by side.
• Setting: sand accumulation progressively cut the old sea cliffs off from wave attack, so profiles along the coast record successive stages of development (substituting space for time).

Part of the bay	Basal condition	Profile	Mechanism
Active cliffs	Waves remove all debris at the foot	Basal free face, rectilinear slope at about 32°, small summit convexity	Parallel retreat
Abandoned cliffs	Sea withdrawn; debris piles up at the foot	Convex–rectilinear–concave	Slope decline

• Conclusion:
  • A rectilinear slope keeps its angle only while debris is removed from its base.
  • Once removal stops, accumulation protects the lower slope while the upper part keeps retreating, so the angle declines.
  • Summit convexity forms late in the sequence.
• Lithology can have the same effect: on the Bhander plateau, sandstone-capped scarps retreat parallel while nearby hills that have lost their cap are downwasted.

Arthur Newell Strahler (1950): Equilibrium Slopes

• Arthur Newell Strahler (1950) analysed frequency distributions of maximum slope angles measured in areas of uniform climate, vegetation, relief and tectonic history in California.
• Questions tested: whether rock type, aspect (exposure to sun and weather) and freedom from basal erosion change slope angles.
• Method: he found the mean maximum slope angle of an area and measured how far individual slopes deviated from it.
• Findings:
  • Deviations were small, so slopes in a locality develop at roughly the same angle, the one that lets creep, slumping and wash remove debris steadily.
  • Such equilibrium slopes are adjusted to channel gradient, climate, vegetation, soil, bedrock and initial relief; a change in any factor forces readjustment.
• Three inferences:
  1. Retreating slopes in one locality share a uniform maximum angle.
  2. They need not be of the same age.
  3. Slopes with uniform maximum angles more likely undergo parallel retreat than decline.
• Slope–channel relation:
  • Valley-side slope is positively correlated with channel gradient: steep sides deliver more debris, and the channel is steep enough to carry it. Near stream heads the side slopes do not steepen with channel gradient.
  • A bare slope yields more load than a vegetated one at the same angle, so the channel below it is steeper.
  • If the channel is steepened by rejuvenation or by a climatic shift in the discharge–load ratio, valley sides steepen rather than retreat; where base level controls a slowly lowering landscape, decline is possible.
  • Where the stream undercuts the slope foot, the slope is steep; where the stream lies away from the foot, debris accumulates and the slope is gentler.
• Like Savigear’s, his results make basal removal the switch between parallel retreat and decline.

Fisher–Lehmann Cliff Recession Model

• Osmond Fisher (1866) first modelled the recession of a chalk cliff; Andrew Cowper Lawson (1915) deduced the same process, and Otto Lehmann (1933) added variables: cliff angle, scree angle and the rock-to-scree volume ratio.
• Assumptions: a rectilinear free face of given height and angle, flat ground above and below, and a layer of uniform thickness weathered off the whole exposed face in each unit of time.
• Mechanism:
  • The weathered layer falls and forms scree at the foot at an angle below the cliff angle.
  • The face retreats parallel to itself and loses height as scree climbs it.
  • A convex rock core is left buried beneath the scree: its lowest point is tangent to the original cliff angle, and its highest point is tangent to the scree angle when the face is gone.
• Controls on the core:
  • The scree angle matters most: a steeper scree gives a steeper core.
  • A steeper initial cliff (up to 90°) also gives a steeper convexity.
• If all scree is removed, the exposed rock surface is a rectilinear denudational slope.
• The model gives Wood’s buried convex core a precise geometric basis and is used to date cliffs and scarps; marine cliffs are its classic case.

Process-Response Models: Anthony Young and Frank Ahnert

• Anthony Young (1963) and Frank Ahnert (from 1966) independently built mathematical process-response models, computing slope change step by step from assumed process laws rather than from measured rates.
• Common starting point: unimpeded basal removal of debris without basal erosion, except in Model 6.

Model	Dominant process (assumption)	Result
1	Soil creep: transport proportional to sine of angle and distance from crest	Crest rounded; convexity extends to the base; no concavity; maximum angle falls
2	Surface wash: transport rises with distance downslope	Convexity above, concavity in late stages
3	Solution loss (direct removal proportional to sine of angle)	Dominantly parallel retreat
4	Creep plus solution (models 1 and 3 combined)	Long, pediment-like concavity
5	Weathering and transport tied to regolith thickness	Regolith thickens slowly on the convexity, fast on the concavity
6	Creep with impeded basal removal	Debris accumulates; basal concavity forms

• Time scales: with dimensions and rates added, the time for a given change can be estimated.
  • At a creep rate of 0.5 cm³/cm/year, rounding a 10 m slope takes about 1.5 million years, and a 100 m slope about 150 million years.
  • Time rises with the square of height; a faster rate of 3.0 cm³/cm/year cuts these to about 260,000 and 26 million years.
• Significance: form follows process, not stage. Creep makes convexity, wash and accumulation make concavity, and removal controls whether slopes retreat or decline.

Comparison of the Models

Model	Year	Approach	Mechanism	Maximum angle	Characteristic profile
W. M. Davis	1899	Deductive	Slope decline, downwasting	Decreases	Convexo-concave, flattening
W. Penck	1924	Deductive	Slope replacement from below	Decreases	Concave, footslope-dominated
A. Wood	1942	Deductive	Free-face retreat; element growth	Free face constant, then declines	Four elements, then convexo-concave
L. C. King	1953	Deductive	Parallel scarp retreat	Constant	Scarp and pediment, then pediplain
R. A. G. Savigear	1952	Empirical	Retreat or decline by basal condition	Constant or declining	Cliff or convex–rectilinear–concave
A. N. Strahler	1950	Empirical, statistical	Equilibrium slope	Constant in a locality	Adjusted to channel gradient
A. Young / F. Ahnert	1963–66	Mathematical	Process laws	Depends on process	Creep convex; wash concave

Current View and Slope Failure

Present Understanding of Slope Evolution

• No single path: slope evolution is more complex than the classical decline, replacement and retreat; one area can show all three, depending on basal removal, rock strength, climate and uplift rate.
• Process laws replaced stage:
  • Grove Karl Gilbert (1909) tied convex hilltops to creep, and W. E. H. Culling (1960) expressed creep as diffusion, giving parabolic convex crests in steady state.
  • Michael Kirkby (1971) showed that each process mix yields a characteristic form, carrying forward the idea of dynamic equilibrium in landform development.
  • Roering, Kirchner and Dietrich (1999) showed that transport rises non-linearly as slopes steepen towards a critical angle, producing planar lower slopes below rounded crests.
  • Heimsath and colleagues (1997) measured, with cosmogenic nuclides, that soil production falls as the soil mantle thickens, supplying the “reduction” and “exposure” link Penck had assumed.
• Threshold hillslopes: in the north-western Himalaya, Douglas Burbank and colleagues (1996) found hillslope angles along the Indus steep and independent of erosion rate, even where the river cuts 2–12 mm per year.
  • Landsliding keeps the slopes at a limiting angle, which is Strahler’s equilibrium slope at its extreme.
• Tools: LiDAR topography, cosmogenic dating and numerical landscape models now test the old deductive schemes directly.

Hillslope Processes and the Forms They Build

Process	Nature	Typical effect on form
Soil creep	Slow mass movement of moist soil	Convex crests
Rainsplash	Raindrop impact; weak under vegetation	Loosens soil for wash
Overland flow (surface runoff)	Sheet flow once rainfall exceeds infiltration	Concave lower slopes
Throughflow (interflow)	Lateral flow below the surface; can form pipes	Slumping and collapse
Rills and gullies	Concentrated linear flow; parallel on steep slopes, dendritic on gentle	Dissection of bare slopes

• Indian example: devegetated lower slopes from the Himalaya to the Western and Eastern Ghats are heavily rilled and gullied.

Slope Failure

• Slope failure is the displacement and downslope movement of slope material when shear stress exceeds shear strength.
• Causes:
  • Steep angles and jointing, weak or complex rock, and pore-water pressure from rain or meltwater infiltration.
  • Weathering, and human action such as deforestation, road cutting, construction, dams, mining and blasting.
• Types:
  • Falls: rock, debris and earth falls, and toppling.
  • Slides: block glides, rock and debris slides, slumps.
  • Flows: earth, debris and mud flows.
  • Creep: soil, rock and talus creep.
  • Spreads.
• Indian evidence:
  • The Landslide Atlas of India (ISRO–NRSC, 2023) mapped about 80,000 landslides from 1998 to 2022, concentrated in the Himalaya and the Western Ghats; Rudraprayag and Tehri Garhwal rank highest for exposure.
  • Joshimath (Uttarakhand, 2023): land subsidence cracked hundreds of buildings on an old landslide-debris slope.
  • Wayanad (Kerala, 30 July 2024): debris flows after extreme rain killed more than 200 people.