Modelling and Model Building - Environmental Modelling: Finding Simplicity in Complexity - page 20

more pore space for water to flow through, so we have
significantly altered what we intended to observe). Even
if we were foolish enough to want to use this approach at
the landscape scale, it is clearly not feasible (or legal!), so
we might use a spatial sample of auger holes. However,
the auger might hit a stone and thus have difficulty
penetrating to the soil base - in stony soils, we usually
only reach into the upper part of the C horizon. We
might therefore try a non-invasive technique such as
ground-penetrating radar (GPR). GPR uses the measured
reflections of transmitted radio-frequency waves (usually
in the 25-1,200 MHz range) to provide 'observations'
of the changes in dielectric constant in engineering
structures such as building and bridges or in the ground.
Dielectric constant is determined by changes in material
density and water content. Where transmitted waves
encounter a change in dielectric constant some energy
passes through the interface and some is reflected. The
reflected energy from a GPR transmitter is recorded on
a nearby receiver with the time delay (in nanoseconds)
between the transmission of the pulse and its receipt
indicating the distance of the reflecting object from the
transmitter-receiver array. In this way GPR can image
the subsurface and has found application in archaeology
(Imai et al ., 1987), hydrology (van Overmeeren et al .,
1997), glaciology (Nicolin and Koffman, 1994) and geol-
ogy (Mellett, 1995). The difficulty with electromagnetic
non-invasive techniques is that whilst dielectric discon-
tinuities can be fairly obviously seen, the techniques
provide little information on what these discontinuities
are (rocks, roots or moisture for example). Thus,
non-invasive techniques are also subject to significant
potential error. The implication is that all measurements
should have their associated error cited so that the
implications can be considered and due care be taken in
interpreting results. Care is particularly necessary in the
use of secondary data, where one may have very little idea
about how the data were collected and quality controlled.
Field measurements are often particularly prone to
error, because of the difficulty of collecting data. We
may choose to use techniques that provide rapid results
but which perhaps provide less precise measurements,
because of the high costs involved in obtaining field
data. Note the difference between error and precision
(sometimes called the tolerance of a measurement) - the
latter relates only to the exactness with which a mea-
surement is taken. A lack of precision may give very
specific problems when measuring features with fractal
characteristics, or when dealing with systems that are sen-
sitive to initial conditions. Thus, a consideration of the

modelling requirements is often important when deciding
the precision of a measurement.
Specification errors can arise when what is being
measured does not correspond to the conceptualization
of a parameter in the model. This problem may arise
if a number of processes are incorporated into a single
parameter. For example, if erosion is being considered as
a diffusion process in a particular model, diffusion may
occur by a number of processes, including rainsplash,
ploughing, animal activity and soil creep. The first two
might be relatively easy to measure, albeit with their
own inherent problems (e.g. Torri and Poesen, 1988;
Wainwright et al ., 2008), while the latter may be more
difficult to quantify either because of inherent variability
in the case of bioturbation or because of the slow rate of
the process in the case of creep. Interactions between the
different processes may make the measurement of a com-
pound diffusion parameter unreliable. It is also possible
that different ways of measurement, apparently of the
same process, can give very different results. Wainwright
et al . (2000) illustrate how a number of measurements
in rainfall-runoff modelling can be problematic, includ-
ing how apparent differences in infiltration rate can be
generated in very similar rainfall-simulation experiments.
Using pumps to remove water from the surface of the plot
led to significant overestimation of saturated infiltration
because of incomplete recovery of ponded water, when
compared to direct measurement of runoff from the base
of the plot (which itself incorporates ponding into the
amount of infiltration and thus also overestimates the
real rate). The pumping technique also introduces a sig-
nificant time delay to measurements, so that unsaturated
infiltration is very poorly represented by this method.
Differences between infiltration measured using rainfall
simulation, cylinder infiltration and the falling-head tech-
nique from soil cores for the same location can be orders
of magnitude (e.g. Wainwright, 1996) because each are
representing infiltration in different ways. Different infil-
tration models may be better able to use measurements
using one technique rather than another. Such specifica-
tion errors can be very difficult to quantify, and may in fact
only become apparent when problems arise during the
modelling process. It should always be borne in mind that
errors in model output may be due to incorrect parameter
specification. When errors occur, it is an important part
of the modelling process to return to the parameters and
evaluate whether the errors could be caused in this way.
Environmental models operate in a defined space
in the real world. However, the representation of that
space will always be some form of simplification. At the