TIME AND SPACE IN GEOMORPHOLOGY

• time and space are the two fundamental perspectives of all human enquiry and experience
• the disciplines of history and geography are characterized not by subject matter but by the study of temporal and spatial relations, respectively
• geomorphology has strong ties to geology historically and topically, so there is a strong theme of earth history, especially since we focus on retrodiction rather than prediction and landforms evolve at geological time scales
• however given the affiliation with geography and relation to climate, hydrology, biogeography and soils, there is also a significant spatial element to the study of landforms

Fundamental concepts of landscape evolution

uniformitarianism

• introduced by James Hutton (1788), champoined by John Playfair and named by Charles Lyell (1830) in "Principles of Geology"
• usually defined by the phrase "the present is the key to the past" but also encompasses the notions that
  
  
  • physical and chemical laws are invariant with time,
  • geomorphic processes are of the same kind and rate as in the past, and thus
  • the history of the earth can be explained from current observations and relationships (causes)
• uniformitarianism was such a profound departure from the prevailing view of nature that it developed a broad scope in terms of its implications and application
• originally Hutton was seeking an alternative to supernatural cataclysmic origin of a young earth, but through the work of proselytes like Playfair and Lyell it evolved into a complex idea with two components

  substantive uniformitarianism

  • the underlying hypothesis which postulates the uniformity of material conditions and rates of processes; the notion of temporal uniformity of material conditions and process rates (gradualism) can be dismissed;
  • "The picture that physics gives us of the universe is of relative macrocosmic stability overlying violent and discontinuous microcosmic activity...Uniformitarianism of this sort defies the findings and whole tenor of modern science." (Goodman, 1967)

  methodological uniformitarianism

  • all historical enquiry assumes that natural laws are constant in time and space and that "no hypothetical and unknown process can be invoked if observed historical results can be explained by presently observable processes"
  • however, earth physics may change over earth history with changes in the composition of the atmosphere or position of the earth in the universe; but natural laws have a restricted domain beyond which they don't apply nor can they be applied since these are "highly inaccessible" domains
  • a more significant objection to methodological uniformitarianism as a formal concept is that it lacks any contemporary usefulness because the assumption of constancy of nature is so fundamental to all modern scientific enquiry that it does not require a formal statement; there is no alternative mode of thinking as in Hutton's day nor does anyone even consider an alternative
  • science demands generalizations, the simpler the better; even if there is no pattern to the frequency and magnitude of natural events, at the very least we have to seek approximations of constancy in "the rate of change of rate of change" so that are laws describe the behaviour of nature; thus "the principle of uniformity dissolves into a principle of simplicity that is not peculiar to geology but pervades all science and even everyday life" (Goodman, 1967)

neocatastrophism

• the contemporary alternative to substantive uniformitarianism:
• neocatastrophism is the modern version of the notion that rare, high-magnitude events have played an important role in landscape evolution
• it is devoid of the original constraints of a short geological record and appeal to supernatural powers, i.e., it is scientifically-based whereas the original catastrophism that uniformitarianism overcame was biblically based
• ironically, to suggest neocatastrophism in the hay day of uniformitarianism was almost as heretical as the views of Steno and Hutton
• Lyell efforts to popularize uniformitarianism, plus the concept of evolution advocated by his close friend Charles Darwin, served to entrench the concept of slow change in the earth and natural sciences, defeating the notions of a short earth and supernatural powers
• in geomorphology, catastrophism was replaced by gradualism, the idea that landscape change is slow, occurs in small increments, and involves weak forces; the dismissal of rare, high-magnitude events was as much emotional as scientific and accounts for the initial response to Bretz's (1923) explanation of the Channeled Scablands of eastern Washington State during the 1920s and 30s
• acceptance of the importance of large events occurred as paleontologists supplied evidence of mass extinctions and other geologists described rocks that show evidence of large, individual geomorphic events in sedimentary rocks
• for most geomorphologists, neocatastrophism represents only reappraisal of the importance of geomorphic processes in the terms of magnitude and frequency if there is room for the interpretation of unique events, however , then geology and geomorphology become a form of history rather than science

erodicity (ergodic theorem, hypothesis, assumption)

• because most landscapechange occurs over longer than human timescales, geomorphologists infer the nature of landscape evolution by comparing similar landforms of different age, that is at different stages of evolution
• that is, a temporal sequences (landform evolution) cannot generally be observed and thus must be reconstructed from a theoretical basis (i.e. by invoking ergodicity)
• this practice is so common that we are not always conscious of the underlying assumption, that is, that we can substitute observation in space for observations in time
• despite its significance, the ergodic assumption receives little attention in the geomorphic literature
• the concept of ergodicity developed in physics because molecules move so rapidly compared to the duration of observation that their spatial distribution cannot be easily established; therefore physicists hypothesized that "the mean observations of an individual made over time is equal to the mean observations of many individuals made of may individuals at a single moment in time over an area"
• thus the ergodic assumption in physics was formulated so that observations at different times could be used as a surrogate for the spatial distribution at a single moment, but in geomorphology
  
  
  • this hypothesis has never been tested (i.e. studied quantitatively), rather ergodicity is assumed
  • space is used as a surrogate for time,
  • ergodicity is not applied in the original sense of time and space 'averages', and
  • but is used to translate spatial distribution into temporal sequences, which was not intended by the original concept
  
  
• since the use of ergodicity in geomorphology is conceptual rather than mathematical and departs from the formal concept, phrases like "location-for-time" or "space-for-time" substitution are used to describe the assumption in geomorphology
• although there are a few examples of truly ergodic modelling in fluvial geomorphology; use of space-for-time substitution has been applied most often to studies of scarp evolution; scarps tend to form quickly (e.g. tectonism, mass wasting) or undercutting of erosional scarps ceases as streams shift or relative sea level drops
• a special case of ergodicity is allometry, the study of proportional changes correlated with variations in size
  
  
  • dynamic allometry describes changes in relationships between parts of an individual through time; static allometry describes changes in relationships between variously-sized members of a group at a moment in time; both kinds of relationships are usually expressed as power functions
  • allometry has been used to describe the evolution of cirques and alluvial fans
  • comparisons of the dynamic and static allometry of the same landform reveal that the relationships differ (analogous to differences in hydraulic geometry along a river at the same time versus at a station at different times); a statistically significant difference would violate the ergodic assumption
  
  In summary, there must be some theoretical foundation for the widespread assumption that the spatial distribution of landforms reveals something about the evolution of individual landforms or, that is, that present landscapes can reveal something about their paleo-equivalents (methodological uniformitarianism). Ergodicity would seem to be this framework, however it has applied to geomorphology without rigour or formal definition.