SPACE IN GEOMORPHOLOGY

General themes

• there are no natural measures of space
• unlike time where we use days, seasons and years according to the rotation and orbit of the earth
• that is, other than the space within which we conduct our daily affairs and the increasing larger spaces with which we are increasingly less familiar
• the arbitrary spatial measures are linear (m, km) or areal (acre, ha)
• thus there are no natural measures or standard scales for the study of the dimensions and distribution of landforms
• the obvious spatial units, the slope profile (linear) and drainage basin (areal) have large size variation
  
  
• spatial patterns often reflect past events
  
  
  • the generally slow rates of landscape change represent a constraint on the study of process and form
  • inherited patterns are the response to processes not currently operating (paleoprocess)
  • thus just as time scale depends on the spatial perspective (scale), time intrudes on any consideration of space in geomorphology
  • landscapes that bear the imprint of both former and current geomorphic processes have been described as a palimpsest
  
  

  palimpsest

  a piece of parchment that had been written upon more than once

  
  
  • models of landscape evolution vary in the extent to which they describe these residual effects (inherited forms)
  
  
• in addition to the historical tension in landscape studies, there is dimensional tension, i.e., interaction between point, line and areal features (e.g., rock outcrop, stream and drainage basin)

Fundamental Spatial Properties

1. orientation
   
   
   • direction or aspect of linear and areal features
   • in geomorphology, this property is particularly significant relative to the direction of winds, insolation and geologic structures
     
     examples
     • north- versus south-facing slopes with respect to the solar energy balance
     • east- versus west-facing slopes with respect to prevailing winds and latent heat flux: valley asymmetry and maximum geomorphic activity on north- to east-facing mountain rockwalls
     • orientation of shorelines with respect to wave fetch, winds, longshore processes
     • direction and distance from a point source: glacial erratics, tephra thickness and texture
     • orientation of linear features (e.g., valleys) relative to geologic structures
     
     
   • these are all examples of orientation in the horizontal plane
   • orientation in the vertical plane is measured as dip of bedded rocks and sediments(strata), imbrication of clasts (fabric) in alluvium and till, and the gradient of slope profiles
   • orientation can be a strong and complex characteristic of active landscapes with short reaction and relaxation times (e.g., aeolian and coastal landscapes).
   • orientation is measured on a circular scale and thus most summary statistics are inappropriate (the arithmetic mean of 1o and 359o is 180o); there is a separate set of statistical techniques for analyzing circular data (e.g., using sines and cosines which range from -1 to +1).
   • the location of any feature can be determined from orientation (horizontal and/or vertical) and distance
   
   
2. distance
   
   
   • the shortest path between two objects measured in time or length units
   • often asymmetrical (scalar versus vector) because paths represents a flux (e.g., flow in a stream channel) or cause at one location results in an effect at the other
   • distance is an important variable in most relationships among geomorphic parameters
     
     examples
     1. decay with increasing distance
        
        
        • changes in the thickness and texture (sorting) of deposits in aeolian, fluvial, coastal and lacustrine environments, and even with mass wasting (i.e., fall sorting)
        • however, sediments are easily reworked (redistributed) such that original relationships between distance, thickness and texture are quickly masked
        
        
     2. constant up to a boundary
        
        
        • spatial uniformity never exists, but is assumed or portrayed as a common means of storing, processing and presenting geographic information
        • all thematic mapping (stratification) and spatial correlation of areal features is based on identification of uniform areas or consistent patterns with respect to specific criteria and scale
        
        
     3. no effect except at a certain distance
        
        
        • best examples are coastal where waves that develop in open sea represent the transfer of energy that eventually causes geomorphic work on a distant shoreline
        • the extreme example is a tsunami, energy derived from the tectonic disturbance of an ocean basin is transferred as waves with low amplitude and very long wavelength
        
        
   • distances in the vertical plane tend to be much shorter but just as important
     
     
     • exponential decay of rates of weathering and soil creep
     • concentration of saltation load near the ground
     • depth to water table and permafrost as a control on many earth surface processes
     
     
   
   
3. connectiveness
   
   
   • relative location, contiguity, adjacency
   • well developed concept in human geography: nearest neighbour analysis, central place theory
   • most easily understood with respect to distribution of point features (everything at a small enough scale): clustered, random and regular distributions
   • three basic and independent characteristics of connectiveness:
     
     

     pattern

     areal or geometric arrangement irrespective of the size of a study area
     
     

     density

     frequency of occurrence expressed as number of occurrences per unit area (i.e., relative to the size of the study area)
     
     

     dispersion

     spread of phenomena relative to the size of the study area; a clustered distribution has the least dispersion

     
     
   
   These concepts provide an objective theoretical basis for the measurement and comparisons of spatial distributions, but this type of analysis is of little value without some reason to suspect (hypothesize) that a particular process would produce a definite distribution.
   
   
   • linear patterns
     
     
     • e.g., stream networks
     • original work by Horton and Strahler and subsequent stochastic modelling as random networks
     
     
   • areal patterns
     
     
     • two-dimensional shape of landforms (morphology)
     • the distribution of groups of areas usually corresponding to groups of landforms
     • the most compact (least work) shape that provides total coverage of areas is the hexagon; this geometric principle is a theoretical basis for the study of the arrangement and genesis of drainage basins, patterned ground, desiccation cracks, and columnar joint blocks
     
     
   • boundaries
     
     
     • abstract, a concept to satisfy the "intellectual need for simplification that mandates division of the indivisible"
     • thus there will never be a truly satisfactory theoretical basis for boundary delimitation
       
       
     • regional boundaries
       • various criteria, not formally defined, vague
       • e.g. physiographic regions
     • drainage divide
       • topographic boundary and thus easily approximated
       • assumes no transfer of water across boundary, but this does not necessarily imply that geomorphic systems are integrated within a basin
       • there is often little interaction between major valleys and interfluve landscapes; much of the sediment transported by streams is reworked floodplain alluvium of derived from valley sides
     • boundary delimiting a discrete landform
       • these boundaries require definition of landforms according to mappable criteria, which is problematic for incomplete and gradational forms (polygenesis)
     
     

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Scale issues

1. sampling (spatial resolution)
   
   
   • usually purposive, especially when a limited number of occurrences are under investigation
   • use of inferential statistical methods to estimate population parameters and establish relationships is constrained by lack of random sampling and by spatial autocorrelation, that is, neighbouring observations often influence one another, although the degree of later can be used to characterize landscapes
   • stratification is usually a necessity since there are large spatial variations in resistance and stability of surface materials (e.g., vegetation cover) and thus effectiveness of geomorphic processes
   
   
2. linkages between scales
   
   
   • scale itself is a significant variable and the results of research at one scale do not necessarily apply to other scales
   • for practical reasons, research is often done at a different scale than the scale of the phenomenon (process or feature) under study
   • three strategies developed to overcome this problem are:
     
     
     1. using ratio data or dimensionless numbers
        • e.g., bifurcation ratio, standardized data (relative to the mean), relative relief
        • eliminates scale as a variable, size is not implied by the units used
        
        
     2. smoothing local observations
        • to extract the dominate trends over an area and detect significant deviations (residuals)
        • e.g., splines and trend surface analysis
        
        
     3. synthetic landscapes
        • placing isolated observations in a sequence (e.g., Caine, 1979) to depict variation along a transect or over an area
        • enables extrapolation from detailed observations to a broader scale while retaining statistical treatment and a physical model
   
   
3. standardization
   
   
   • standard scale for studies of a similar nature has not been recognized in geomorphology
   • thus, for example, there is no standard size of research plots for the study soil erosion or standard length of slope facet for the study of hillslopes
   • although there has been little conscious attempt to adopt standard scales, and particularly to investigate the impact of scale variation on research results, some standardization is a function of confining research to specific landforms or to drainage basins of a specific order
   • there are also logistical constraints on the size of area that can be studied in detail in the field or on the scale of a laboratory experiment
   • the apparent disparity among the results of individual studies can be an artefact of scale divergence