Page 41 - Fundamentals of Geomorphology

24 INTRODUCING LANDFORMS AND LANDSCAPES

to study geomorphic systems is to discover expressions timescales, well beyond the span of an individual human’s
with explanatory and predictive powers. These powers experience – centuries, millennia, millions and hundreds
set mathematical models apart from conceptual models. of millions of years. Such considerations go well beyond
An unquantified conceptual model is not susceptible of the short-term predictions of the process modellers.They
formal proof; it is simply a body of ideas. A mathematical bring in the historical dimension of the subject with all
model, on the other hand, is testable by matching predic- its attendant assumptions and methods. Historical geo-
tions against the yardstick of observation. By a continual morphology relies mainly on the form of the land surface
process of mathematical model building, model testing, and on the sedimentary record for its databases.
and model redesign, the understanding of the form and
function of geomorphic systems should advance. Reconstructing geomorphic history
Three chief classes of mathematical model assist the
study of geomorphic systems: stochastic models, statis- The problem with measuring geomorphic processes is
tical models, and deterministic models. The first two that, although it establishes current operative processes
classes are both probabilistic models. Stochastic mod- and their rates, it does not provide a dependable guide
els have a random component built into them that to processes that were in action a million years ago,
describes a system, or some facet of it, based on prob- ten thousand years ago, or even a hundred years ago.
ability. Statistical models, like stochastic models, have Some landform features may be inherited from the past
random components. In statistical models, the random and are not currently forming. In upland Britain, for
components represent unpredictable fluctuations in lab- instance, hillslopes sometimes bear ridges and channels
oratory or field data that may arise from measurement that were fashioned by ice and meltwater during the
error, equation error, or the inherent variability of the last ice age. In trying to work out the long-term evolu-
objects being measured. A body of inferential statistical tion of landforms and landscapes, geomorphologists have
theory exists that determines the manner in which the three options open to them – modelling, chronosequence
data should be collected and how relationships between studies, and stratigraphic reconstruction.
the data should be managed. Statistical models are, in Mathematical models of the hillslopes predict what
a sense, second best to deductive models: they can be happens if a particular combination of slope processes
applied only under strictly controlled conditions, suffer is allowed to run on a hillslope for millions of years,
fromanumberofdeficiencies, andareperhapsmostprof- given assumptions about the initial shape of the hillslope,
itably employed only when the ‘laws’ determining system tectonic uplift, tectonic subsidence, and conditions at the
form and process are poorly understood. Deterministic slope base (the presence or absence of a river, lake, or sea).
models are conceptual models expressed mathemati- Some geomorphologists would argue that these models
cally and containing no random components. They are are of limited worth because environmental conditions
derivable from physical and chemical principles without will not stay constant, or even approximately constant,
recourse to experiment. It is sound practice, therefore, for that long. Nonetheless, the models do show the
to test the validity of a deterministic model by compar- broad patterns of hillslope and land-surface change that
ing its predictions with independent observations made occur under particular process regimes. Some examples
in the field or the laboratory. Hillslope models based on of long-term hillslope models will be given in Chapter 7.
the conservation of mass are examples of deterministic
models (p. 175).
Stratigraphic and environmental
reconstruction
HISTORY Fortunately for researchers into past landscapes, sev-
eral archives of past environmental conditions exist:
Historical geomorphologists study landform evolu- tree rings, lake sediments, polar ice cores, mid-latitude
tion or changes in landforms over medium and long ice cores, coral deposits, loess, ocean cores, pollen,