The role and nature of time in geomorphology

• time is a fundamental concept given the traditional preoccupation with landscape change over time
• until recently geomorphologists have deferred the study of material properties and process mechanics to engineers
• there is no geomorphic time scale, that is, there are standard time periods besides the divisions of the geologic time scale, which are based on the age of rocks and sediments (i.e., mostly fossil evidence)
• thus geomorphologists have tended to treat time in a relative way as discussed below
• there is a broad positive correlation between the size of a landscape unit and the duration of change
  
  
  • e.g. ripples change quickly, dunes less quickly; or rills vs. gullies vs. stream channels
  • thus the relevant time period can vary with nature of a study (e.g. process versus climatic geomorphology)
  
  
• all models of landscape change are of two types

1. time-dependent (developmental or relaxation-time models)
   
   
   • landforms change in response to an initial disturbance or change in input (climatic change, tectonism), and then gradual progressive sequential change is characterized by the association of morphology with stage of development
   • e.g. the Davisian cycle of erosion that dominated geomorphological thinking for decades
   • it was a time-decay model because no further inputs were envisioned after the initial uplift of the landscape
   • just gradual, inevitable landscape evolution at an increasingly slower rate as the initial energy is dissipated
   
   
2. time-independent (characteristic-form models)
   
   
   • the alternative and subsequent view of landscape evolution
   • rather than subject to ever-decreasing energy, landscapes are open systems, constantly adjusting to changing inputs and levels of internal energy
   • geomorphic systems adjust to approach an equilibrium with the inputs acting on them
   • because the inputs constantly vary, equilibrium can probably never be attained and thus characteristic is preferred to equilibrium to describe forms which reflect the landscape after a period of adjustment (relaxation) to a disturbance or major change in inputs
   
   

1. Classification and sampling of time

The subdivision of time according to whether variables of landscape evolution are independent, semi-dependent or dependent:

• cyclic (geologic, 106 yrs)
  
  
  • longest timespans of landscape evolution
  • time is an independent variable and the most important one, because there are no specific or constant temporal relationships between independent and dependent variables (cause and effect)
  • climate, initial relief and geology are the other independent variables, all others are dependent
  
  
• graded (modern, 102 yrs)
  
  
  • a short segment of cyclic time during which a graded condition or dynamic equilibrium exists, that is, fluctuations about (approaches to) a steady state and tendency for negative feedback
  • applies to some but not all components of a geomorphic system because relief is still being reduced throughout the entire system
  • time and initial relief are irrelevant because parts of a geomorphic system are adjusted to prevailing inputs
  • the only dependent variables are responses (i.e. morphology and output from the system)
  
  
• steady (present, 10-2 yrs or 3-4 days)
  
  
  • a brief period during which some part of a system is unchanging and thus truly time-independent
  • once again time and initial relief are irrelevant
  • the only dependent variable is outputs of energy and mass since morphology is constant
  • more recently referred to as engineering time
  
  

sampling of time

• according to technique
  
  
  1. direct observation and measurement (< 10 yrs)
  2. historical (archival) data, usually generated for other purposes, e.g., stream flow records
  3. absolute dating of materials and surfaces, limit of conventional 14c dating is about 50,000 yrs
  4. stratigraphic methods employing both absolute and relative dating techniques, in particular, the age correlation of surfaces and strata
  
  
• according to duration of observation
  
  
  1. continuous: these observations are rarely reported rather nearly always reduced before analysis, that is
  2. quantized: division of continuous time into useful or familiar segments (e.g. hour, day, month, year), when data are summarized by segment some are always lost depending on the duration of the segment and the manner of summarization (weekly means from daily means or from average of max and min); e.g. weather data
  3. discrete: one observation per interval (day, month, etc.); also a means of expressing frequency
  4. sampled: a continuous process observed intermittently (e.g. one day per month)

2. Magnitude and frequency

• how often an event of a certain magnitude occurs expressed as
  
  
  • the number of occurrences relative to a period of time or number of observations
  • the probability of such an event, or
  • the recurrence interval (return period)
  
  
• magnitude and frequency are inversely related
• lognormal frequency distributions are common, because the lowest magnitude is fixed at just above zero but the upper magnitude (rare events) is limited only by earth and atmospheric physics
• which magnitude is most important geomorphologically?

Wolman and Miller determined that at least 50% of sediment transport was by flows of a magnitude that occurred at least once per year, that is, that events of intermediate magnitude and frequency generally dominate fluvial sediment transport. This benchmark analysis sparked much further consideration of magnitude and frequency including elaboration of the concepts and recognition of its limitations and complexities:

1. the common calculation of recurrence intervals for meteorological and hydrological events is useful but the geomorphic significance of these events also depends on other controls (i.e. vegetation, soil, morphology and rock)
2. frequency and magnitude assume stationarity of the series, that the mean and variance do not vary over time (basically equivalent to substantive uniformitarianism), however trend, persistence and intermittency in the behaviour of geomorphic systems makes the frequency distribution an incomplete description of a sequence of geomorphic events
   
   
   • trend, the direction of change, can include cyclic patterns
   • persistence (autocorrelation) occurs when a value influences an adjoining value in a series (e.g. tree ring widths) and implies that the true variability of a series may not be evident in a short record
   • intermittency, the nonperiodic clustering of similar values over long periods, is perhaps the most problematic because cumulative effects can have large geomorphic impact
   
   
3. extremely rare events (e.g., once in half a million years or an annual probability of 10^-5) may have tremendous geomorphic consequences as postulated by neocatastrophists (e.g. draining of glacial Lake Missoula creating the eastern Washington scablands)
4. there is a fundamental difference between the processes of quasi-continuous sediment transport and the processes that create landforms in terms of magnitude/ frequency characteristics
   
   
   • therefore the effectiveness of geomorphic events can be expressed in terms of timing and magnitude relative to other events and the recovery (relaxation) of the geomorphic system
   • if two low frequency events occur in consecutive years, they will differ in effectiveness as the landscape will be rendered more (e.g., lag deposit) or less resistant (e.g., lack of vegetation) by the first event
   
   
5. just as magnitude and frequency relationships differ between transport and formative processes, they also differ for various parts of a landscape, particularly between stream channels and interfluves, and over larger areas between regional climates (note: the original magnitude/ frequency work was based in humid temperate climates)
6. for the above reasons, comparisons of the effectiveness of various geomorphic processes are increasingly based, not on magnitude and frequency, but on more uniform measures of erosion such as mass of sediment moved or amounts of geomorphic work

3. Change through time

• disturbances or changes in controls, that exceed geomorphic thresholds, can be classified as either
  
  
  • pulsed: short duration compared to time period under consideration (e.g., tectonism), or
  • ramped: sustained at a new level once initiated (e.g., climatic change)
  
  
• the response of a landscape in quasi-equilibrium is to absorb the input without changes
• adjustment with or without perceptible change are described by the following concepts:

reaction and relaxation

• absorbing and adjusting to change or disturbance, respectively
• the response of landscapes and geomorphic systems often occurs over longer time periods than the duration of the disturbance or change in controls (inputs)
  
  

  reaction time

  the interval between a disturbance or change in controls and observable morphological change
  

  relaxation time

  the ensuing period of adjustment up to a new equilibrium or another geomorphic threshold adjust

hysteresis

• incomplete reversibility (Gr. a deficiency, same root as hysteria)
• when a condition changes from A to B and back to A, the pathways may differ and thus condition a may not be regained
• e.g., soil moisture or suspended sediment load before and after a storm
• this usually results from a change in boundary conditions caused by the process (e.g., residual stress from loading and unloading of clay)

4. Entropy and equilibrium

• the concept of entropy, the degree of disorder in an isolated system, and the second law of thermodynamics dictate that, irrespective of the initial level of energy, energy becomes more evenly distributed over time (i.e., energy gradients are reduced) and processes proceed at an ever decreasing rate
• ultimately, energy is evenly distributed, entropy is a maximum and free energy (available for conversion to work) is zero, this is, the state of equilibrium where the most probable energy distribution is uniform with least work (least landscape change)
• these concepts explain characteristic (least-work, graded) landforms like longitudinal stream profiles, stream channel meanders, dendritic drainage networks, and concave-conves slope profiles
• entropy is maximized when all possible energy states have equal probability (i.e., random distribution)
• thus there is rapid change away from any highly abnormal configuration of a system, corresponding to the notion of initially rapid change in response to an input or disturbance and then a decreasing rate of change over time

1. static
   
   
   • some system properties are unchanging, absolutely and relatively, over a period of time
   
   
2. stable
   
   
   • tendency to revert to a previous condition after a limited disturbance
   
   
3. unstable
   
   
   • a small disturbance results in continuous movement away from an old equilibrium and towards a new stable one
   
   
4. metastable
   
   
   • an incremental change (trigger mechanism) pushes a system across a threshold from stable equilibrium to a new equilibrium
   
   
5. steady state
   
   
   • numerous small-scale about a mean that has no trend
   
   
6. thermodynamic
   
   
   • a tendency towards maximum equilibrium, second law of thermodynamics
   
   
7. dynamic
   
   
   • balanced fluctuations about a trending, nonrepetative mean value; often called quasi-equilibrium because of the tendency towards a steady state with a trending mean (i.e., equilibrium is never attained)
   
   
8. dynamic metastable
   
   
   • both dynamic and metastable, fluctuations about a trending mean interspersed by large jumps as thresholds are crossed; used by many geomorphologists to explain landscape behaviour
   
   

related equilibrium concepts

1. feedback
   
   
   • accounts for movement away from (positive) and back to negative)a mean value
   • that is, the effect of a disturbance or change in controls is either magnified or dampened, respectively
   
   
2. threshold
   
   
   • a transition in behaviour, operation or state
   • a large response to a small or incremental change
   • extrinsic and intrinsic, i.e., response to change in an external (e.g., climate) or internal (e.g., shear strength) variable, respectively
   
   
3. "a tendency toward equilibrium"
   
   
   • favoured by a variety of reaction and relaxation times, and a constant stream of inputs which all but preclude equilibrium
   • landform change is precluded only by static equilibrium, which is highly unlikely in the natural world
   • equilibrium is relative to the timescale of interest, since
   • a landform can be in equilibrium with respect to one timescale (graded or steady) and in disequilibrium with respect to another (cyclic)
   
   
4. complex response
   
   
   • parts of a geomorphic system approach equilibrium at different rates and a single part will exhibit different tendencies at different times
   • e.g. lack of correlation between cross-sections in the response of Douglas Creek, Colorado to overgrazing in the "cowboy era"
   • difficult to recognize from short term process studies
   • serious implications for interpretations of earth history, by precluding the interpretation of single causes for geomorphic responses identified in the quaternary record
   • e.g., the incision of One Tree Creek, Alberta, and formation of terraces, was the response to both base level change as the Red Deer River shifted across its floodplain and to Holocene climatic changes; the first factor is imposed from the mouth of stream the second controls the supply of water and sediment to the channel from upstream
   • thus, geomorphologists need to be much more rigorous and precise in defining their temporal and spatial scales