Table of example LEM studies

Table layout

To review all the findings of researchers who have used LEMs is a near impossible task, such has been the rate of increase in the use of LEMs over the last twenty years. The author has therefore taken examples from the literature to demonstrate the range of topics in geomorphology to which LEMs have been applied, and these are summarised in Table 1. The table also includes some studies with numerical slope evolution models, as these models work in an equivalent way to LEMs, and indications of equifinality in such studies would indicate that similar results in LEM studies are possible.

The table is divided into columns so as to distinguish between the simulation scenarios and variables, listed in column 2, and the main influences exhibited in the simulations, listed in column 3. The information in column 2 also highlights both the relative frequency of certain research themes in LEM studies generally, and the main variables of interest used in each of the listed studies. The information in column 3 is a summary of the results from each study, thus allowing variables and results to be seen side by side. It should be noted, however, that in summarising model results in column 3, the author’s focus on influences of the variables gives the results a different emphasis to that given to them by the original authors. This is deliberate, for the purposes of introducing the equifinality problem, and is not meant to detract in any way from the work as it was originally reported. Another difference from the original papers is that each study is summarised in terms of the

‘influences’ of the variables, rather than their ‘effects’. This is also deliberate, as the term ‘effect’ is used in a specific way in this thesis, particularly from Chapter 3 onwards, and this is rather different from the way effects are commonly described in LEM studies. Finally, before turning to the particular variables and influences listed in the table, it is also helpful to comment on the temporal focus of the studies and certain aspects of the presentation. For convenience here, references are cited by using the reference numbers in the table

Table 1: Examples of studies with LEMs and slope evolution models, summarising the main variables and their influence on model output.

Reference Main variables or scenario Main influences on results 1. Ahnert (1987) Process rate parameter values,

geology

Differences in balance between processes and rates at different places strongly influences resulting forms. 2. Armstrong (1987) Different initial slope forms,

process classes and rates, rates of basal removal

Large differences in the initial form have a strong influence on the evolution of transient slope forms.

Combinations of different processes can produce very similar transient forms, suggesting equifinality and convergence. Low weathering rates limit erosion and strongly influences slope form evolution; high rates have little or no influence. Rate of basal removal influences eventual slope forms and the depth of lower slope sediments.

Different erosion processes produce different patterns of deposition on lower slopes, whatever the eventual slope form. 3. Bogaart et al. (2003a) Climate and process parameters Climate strongly influences surface runoff generation, areas draining into channel heads, and sediment yield.

Change of climate from cold to warm reduces sediment yield.

Change of climate from warm to cold increases drainage density, and sediment yield until ready supplies are exhausted. 4. Bogaart et al. (2003b) Climate and process parameters Variables have a strong influence on hillslope erosion, fluvial sediment transport, deposition and related output measures.

Strength of influences changes over time. 5. Braun & Sambridge

(1997)

Cell geometries, size and number Cell grid scheme influences routing of channels and sediment, sinuosity, drainage density, and over time, topography. 6. Clevis et al. (2003) Bedrock erodibility, rate of thrust

displacement, temporal tectonic and sea level (base level) fluctuations

Bedrock erodibility strongly influences sedimentation rates, although effect changes over time.

7. Coulthard & Macklin (2005)

Different study sites, same long term general climate signals per site

Shifts to a wetter climate have a strong and almost immediate influence on sediment yield from the catchment as a whole. Land cover (forest) influences peaks in the sediment yield in response to the same climate conditions.

Pattern of sediment movement within catchments is strongly determined by location.

Responses over time of erosion and sedimentation to the same climate forcing are ‘noisy’, with possible pulsations. 8. De Boer (2001) Rainstorm area in inverse relation

to rainstorm frequency

Frequency of rainstorms strongly influences the total sediment yield from the basin. (Note 1.)

Area of storms influences the sediment yield, whereas position of storms influences the formation of relief and topography. 9. Fagherazzi et al.

(2004)

Sea level oscillations, climate (runoff), initial topography

Oscillation amplitude of sea level change strongly influences river mouth incision.

Small amplitude oscillations in sea level have little influence on lowering of river beds, whereas larger amplitude oscillations have a stronger influence, causing the formation of knickpoints that propagate upstream.

Climate (via as an increase in runoff) strongly influences formation of new incisions and sediment delivery to the shelf. Initial topography strongly affects position of initial channels and subsequent development of channels and topography. 10. Fischer et al. (2004) Uplift and tectonic rebound coupled

to a surface process model (LEM)

Fluvial removal processes, rebound and base level changes together strongly influence formation of realistic relief. 11. Gargani et al. (2006) Long term climate shifts, base level Pattern of climate change strong affects sediment yield and fluvial erosion.

Base level changes have little influence on fluvial erosion at certain stages of the climate cycle. 12. Gasparini et al.

(1999)

Runoff, sediment classes and proportions thereof

Variations in runoff, slope and sediment characteristics influence downstream fining in eroding networks.

Initial proportions of sediment classes have little influence on pattern of downstream fining that eventually emerges. 13. Gasparini et al.

(2004)

Climate, uplift, grain sizes and mixing again

Sediment grain size strongly affects channel concavity and relief.

Table 1 (cntd): Examples of studies with LEMs and slope evolution models, summarising the main variables and their influence on model output.

Reference Main variables or scenario Main influences on results 14. Hancock (2003) Erosion parameters, catchment

aspect ratio

Erosion parameters and aspect ratio both influence hypsometric curve, area-slope relationship, channel width function and cumulative area distribution, although influence of some parameters/variations is greater than others.

15. Howard (1994) Uplift and climate scenarios, and different erosion law formulations

Form of fluvial erosion law has strong influence, in the presence of uplift, on locations and rates of stream erosion in transient landscapes

16. Kirkby (1989) Different climatic conditions, initial forms, time periods, process classes and process rate parameters, land management systems

Combinations of land management practices and climate strongly influence the evolution of slopes and sediment profiles. Responses to different temperature, hydrology, land cover and weathering are made more complex depending upon type of main climate being applied.

Influence of new climate or new land use on an otherwise near-stable soil profile may be strong and non-linear 17. Kooi & Beaumont

(1996)

Forms of process law; also uplift and transport/erosion rates

Response time of the landscape (as determined by process rate coefficients, laws and so on) and tectonics have important influences on patterns of landscape evolution.

18. Lancaster et al. (2001)

Numerous process parameters and site variables, including woody debris supply

Debris dams have little influence on sediment yield from a catchment, but absence of dams or a low supply of wood strongly influences the degree of pulsing of sediment through the system and the formation of terraces.

Combined influences of debris flows, wood supply and in-channel sediment storage may be complex and counter-intuitive. 19. Martin (2000) Weathering rates, diffusivities,

process formulations

Weathering strongly influences transport by mass movement on steep slopes, low rates limiting erosion by creep and slides. Diffusivities (incorporating both creep and slide) strongly influence slope forms, subject to limiting weathering rates. 20. Moglen & Bras

(1995)

Soil erodibility, expressed as ‘softness’

Variability in soil ‘softness’ strongly affects sinuosity and convex-concave slope variability.

Vertical variation strongly affects shape of hypsometric curve, whereas horizontal variation strongly influences relief. 21. Niemann et al.

(2001)

Uplift Uplift rates strongly affect the vertical migration rates of knickpoints. 22. Rinaldo et al. (1995) Cyclic variation in τc (surface

resistance), to effect climate change

Change in climate over time has complex (lagged) influences on drainage density, valley density and (fractal) topography. Evidence of past climates is complicated by uplift, slope-dependent processes and amplitude of the changes. (Note 2) 23. Rosenbloom &

Anderson (1994)

Diffusivities, weathering, forms of process law, stream incision parameter

Hillslope diffusivity rates have a strong influence on evolution of realistic forms. Weathering rates have little influence on slope evolution unless they are low and limiting. Stream incision parameter has a strong influence on the stream profile.

24. Schlunegger et al.

(2001)

Climate and geology, tectonic response to unloading following erosion

Change in climate strongly influences erosion and sediment yield; sediment yield also changes with time. Different geologies/strata strongly influence re-routing of drainage network.

Tectonic response to erosion (unloading) influences re-routing of channels, drainage density and sediment yield. 25. Tucker (2004) Climate and uplift, use of threshold

law

Over long time scales, absence of a threshold has a strong effect on pattern of slope retreat

A threshold in the erosion-transport laws strongly influences scarp evolution response to tectonic and climate forcing. Influence of the erosion threshold appears to be greater where fewer than 50% of flood events can mobilise sediment. 26. Tucker & Bras

(1998)

Contrasts between different process classes and formulations

Different process classes and formulations have strong but different influences on landscapes and produce different equilibrium or final forms.

27. Tucker & Bras (2000)

Short term climate – intensity, frequency, variability

Table 1 (cntd): Examples of studies with LEMs and slope evolution models, summarising the main variables and their influence on model output.

Reference Main variables or scenario Main influences on results 28. Tucker &

Slingerland (1994)

Process classes and formulations, uplift, initial forms, process rate parameters

Different process formulations strongly affect characteristic evolution of the landscape and drainage system, particularly where the weathering rate is limiting.

The slope failure angle and bedrock erodibility strongly influence the pattern of scarp retreat.

Uplift and rebound help to maintain steeper channel gradients and hillslopes near the highest part of the escarpment. 29. Tucker &

Slingerland (1996)

Uplift scenarios, variable geology (bedrock erodibility functions)

Variable geology strongly influences sediment yields, drainage density, patterns of erosion and sedimentation within the basin or range, and consequently affects the evolution of relief; uplift and rebound exert additional influences.

30. Tucker & Slingerland (1997)

Changes in intensity of runoff, overall runoff and erosion threshold (τc).

Runoff intensity strongly influences erosion, deposition, channel heads, drainage density, and hillslope gradients over time. Change in erosion threshold also influences the above, but less markedly than changes in runoff intensity.

Weathering and sediment supply to channels exert a limiting influence under some climate conditions. 31. Tucker & Whipple

(2002)

Influence of slope exponent in detachment-limited erosion law

Value of slope exponent in detachment-limited stream erosion law strongly influences form of slope retreat, rates and locations of erosion, positions of knickpoints and eventual slope profiles.

32. Whipple & Tucker (1999)

Uplift rate, ratio of m/n in stream erosion law.

Ratio of m/n has a strong influence on relationship between elevation and distance from the divide in equilibrium forms. Slope exponent n and uplift rate together have strong influence on response time of landscape to sudden base level changes. 33. Willgoose (1994a) Contrast dynamic and declining

equilibrium (rate of base level change)

Rate of uplift determines slope-area relationship as the landscape approaches dynamic equilibrium or declining relief. Area and slope exponents (m and n) in transport laws also influence the area-slope relationship and the position in the curve indicating where dominance shifts from diffusive (hillslope) to fluvial processes.

34. Willgoose (1994b) Uplift rates, including step changes; also climate

Slope-area relationship is sensitive in different ways to various uplift and climate change combinations, some of these combinations influencing the form of the curve more strongly than others.

35. Willgoose et al. (1991c)

Uplift and climate; also process parameters.

Balance between diffusive and fluvial processes strongly influences form of the area-slope relationship under dynamic equilibrium. Transient influences also noted.

36. Willgoose et al. (1991d)

Implemented distinct channels, contrasted different channel formation rules and influence of perturbations in initial landscape

Distinct channels influence sediment routing and evolution of morphology.

Perturbations in initial landscape (elevation) strongly influence channel location and direction along which they extend. If fluvial processes are dominant, then increasing aridity has little influence on non-dimensional form of landscape, whereas if diffusive processes are dominant, then combinations of different uplift and diffusivity may produce similar, non-

dimensional landscape forms. 37. Willgoose and

Hancock (1998)

Uplift, process parameters High diffusivities have a strong influence on the shape of the hypsometric curve in steady state or declining relief landscapes, whereas lower diffusivities have little influence.

The aspect ratio influences the hypsometric curve in steady state landscapes.

Subtler, more detailed influences of the erosion process exponents m and n also noted. 38. Willgoose et al.

(2003)

Different parameter values and output metrics

Influences of different parameter values on a single output metric are too small to allow its sole use as a calibration measure, and the use of suites of output statistics is recommended in calibration work. (Note 3)

Notes:

1. De Boer applied a rule whereby the frequency of a storm of a particular size was inversely related to its area.

2. Rinaldo et al’s paper is an interesting example of a study where the focus is on changes taking place over time. The implementation of their climate variation is considered again as part of the discussion, in subsection 7.4.3.

Temporal focus and use of variables in the example studies

Looking at the variables listed in column 2, and the research themes in more detail, many of the studies have been focused on the development of landscapes to a state of dynamic equilibrium or steadily declining relief, although there are also a selection of studies which can clearly be related to short term evolution and transient landforms (e.g. 1- 3, 7, 8, 15, 16, 18, 22, 27 and 30). Also, whereas some authors refer to both transient and equilibrium conditions in the same paper (e.g. numbers 22 and 35), the more general approach is to report the pattern of landscape evolution over time, rather than to concentrate on the state of the landscape at any one particular time, whether it be in the short or long term. This

probably accounts in part for the way variables are used in the reviewed studies, namely that only a limited number of variables are changed, generally perhaps four or five at most in any one study (e.g. 1-4, 6, 24 and 30), and often fewer than this. Authors also draw on their wider knowledge and experience to comment on the influence of some variables, for

example climate and uplift, rather than present results from specific simulations in which these variables are changed so that their influences can be identified. Table 1, therefore is intended to include all the important variables and their inferred influences, taking into account the original authors’ comments and not simply whether an individual variable was changed in the experiments or not.

With these points made, it is now possible to consider the main research themes, variables and influences.

In document Exploring equifinality in a landscape evolution model (Page 32-36)