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