Morphology

• the study of earth surface from is inherently spatial, because landforms generally change slowly over time
• geomorphologists have widely accepted the concept of equifinality ("same final result") or convergence, that a given landform can have different origins
• however, equifinality may mostly reflect imprecision in the description of form or applies to the development of the same landform from the same process(es) acting on landforms of different initial conditions
• as form is described and measured with greater precision, there is greater potential for identifying unique forms and relating these to individual processes
• the feasibility of linking process and form also depends on reaction and relaxation times
  
  
  • if they are short, then form may be characteristic (equilibrium) and reflect contemporary observable processes
  • if however they are long, then establishing links between (relict) form and contemporary process is problematic such that the description of form has a weak theoretical foundation
  
  
• even though the study of form is central to geomorphology, in recent decades it has not pursued with the same vigour and rigour as process geomorphology
• thus morphological concepts are more formally defined in other earth science, for example, in sedimentology and soil science, where formal measures of particle shape (e.g. Zingg shape classes, soil structures, Krumbein sphericity, blockiness) are used to interpret pedogenesis or depositional environments

Qualitative morphology: geomorphological mapping

• recognition of basic landscape units that are easily identified in the field, on aerial photographs or from maps
• the basic unit is scale-dependent; a landform is a single unit at one scale and an assemblage of units at a larger map scale
• thus scale and objective (e.g., hazard mapping, surficial deposits/ aggregate resources, terrain analysis) determine the content of a geomorphic map
• some maps are entirely morphological (descriptive), but most include an interpretation of the origin and / or age of landforms or deposits
• detailed geomorphic maps tend be misleading in their precision which hides the subjectivity behind mapping
• mapping is an activity that can be of greater benefit to the mapper than the user by forcing the mapper to recognize and contemplate the complexity of a landscape (sketches serve a similar purpose)
• slope profile surveying is a similar activity that provides great appreciation for the subtleties of hillslope form profiles are useful in a variety of contexts and thus there are manuals and preferred methods

Quantitative morphoplogy: geomorphometry

• geomorphometry refers to the measurement of earth shapes as opposed to other spatial features (e.g., cultural features, leukemia cells)

general geomorphometry

• form of landscapes
• defining and measuring parameters that reflect fundamental characteristics of landscapes
• the popular approach is statistical involving the sampling of elevation (usually on a square matrix) and derivation of
• slope gradient, the derivative of distance perpendicular to contours
• slope curvature, the derivative of slope
• aspect, the first derivative of distance along a contour and cross-slope curvature, the derivative of aspect
• other geomorphometric parameters include wavelength and amplitude (relief) along topographic profiles, complexity or roughness, and the hypsometric integral, reflecting the volume between the land surface and an arbitrary elevation
• two limitations of this approach are the failure to represent sequence in either time or space, and the difficulty of interpreting complex landscapes (palimpsest or polygenetic) from statistical data

specific geomorphometry

• form of individual landforms
• involves delimitation of landforms and thus all the subjectivity associated with landform boundaries plus the interpretation of genesis which generally accompanies the recognition of individual landforms
• the problem of boundary delimitation is critical but not unique, because the parameters in general geomorphometry also are sensitive to the location of boundaries
• but specific geomorphometry requires that landforms be defined numerically and thus it is usually applied only to classic landforms
• most geomorphometry is geometrical (shape parameters) but some is topological (relationships, ratios) especially with respect to streams
• data sources and sampling is critical since these can influence parameter values
• originally most data were derived from maps with the realization that these are the product of interpretation
• present geomorphometric research deals with the design and construction of digital elevation models and data structures that best depict topography

linear: stream channel plan

• stream channels are generally mapped as lines even though they have width; their length is infinitely greater than their width
• the standard classes are straight, meandering and braided the difference between first two classes is form while the distinction between last two is number of channels
• number of channels should be the main criteria; single channels just vary in degree of meandering
• the traditional approach is to quantifying degree of sinuosity is the length of stream versus a straight line distance
• there are several limitations to use of sinuosity measures:
  
  
  • operational definition of the straight line distance: valley length, length of meander axis belt, wavelength of a curve
  • the sinuosity value is sensitive to the scale of map from which the measurements are derived
  • the limits of straight, sinuous and meandering behaviour are arbitrary and thus have no theoretical basis
  • sinuosity measures don't capture the shape or symmetry of meanders
  
  
• alternatives:
  
  
  • total sinuosity: length of all active channels to valley length, encompasses both single channel and multiple channel streams
  • modelling meanders as sine generated curves embraces the concept of symmetry and is more theoretically based, because a sine curve has fewest changes in direction and thus represent least work and the most probable statistical (energy) distribution; however it does not work for acute meander bends
  
  
• a deductive (deterministic) approach to fluvial geomorphology is constrained by the lack of physical theory dealing with two-phase (solid-liquid) flow and also factors not encompassed by hydrologic and hydraulic theory
  
  
  • long timescales (e.g., underfit streams)
  • spatial interaction (e.g., with valley sides)
  • also stream channels can adjust in several ways (plan form, longitudinal profile, cross-sectional geometry) and the same form results from different initial conditions (equifinality; e.g., the meandering of meltwater on glaciers, and currents in oceans and the atmosphere)
  
  
• thus much research in fluvial geomorphology is empirical and probabilistic; about the only theory to derive from work on the form of meanders is a relationship with stream discharge

areal: drainage basins

• hydrologists and geomorphologists have had a historic interest in the two-dimensional shape of drainage basins, the fundamental hydrologic and geomorphic spatial units hydrologists have explored relationships between basin morphometry and discharge at the mouth
• geomorphologists have examined basins as landforms, in term of evolution of basin shape and spatial variations with climate, geology and vegetation
• most morphometric indices are dimensionless ratios, enabling scale linkage (scale as a variable is controlled)
  
  
  • various permutations of compactness or circularity (ratios of perimeters, diameters, areas, perimeters of inscribed and circumscribed circles) have a theoretical basis because a circle encloses the maximum area for a given perimeter and thus is envisaged as the lowest free-energy form
  • however, a circle is unlikely to evolve from erosion by a linear form (stream)
  • thus the mathematical properties of the lemniscate loop (tear or petal shaped) have been applied to the morphometry of drainage basins
  • an alternative to a single form factor if the analysis of the distribution of radii lengths (amplitude) at various intervals (phase) that extend from the centre of gravity of the perimeter of the shape
  • this approach can be based on mathematical functions relating phase and amplitude (Fourier or harmonic analysis) or simplified by using a constant angle interval
  • a hydrological equivalent of this approach has the radii connecting the basin mouth with the headward end of streams
  • in fact, single measures are unlikely to reflect process since basins are landscapes involving slope and channel processes which are often not well integrated especially where a floodplain buffers slopes from streams
  
  
• the use of most morphometric measures is based on correlation (usually with some measure of stream flow) rather than theory
• thus most of the studies of basin morphology are good examples of measuring form and then trying to relate it to process rather than hypothesizing form based on understanding of process