Modelling and Model Building - Environmental Modelling: Finding Simplicity in Complexity - page 19

Sensitivity analysis is a very powerful tool for interact-
ing with simple or complex models. Sensitivity analysis is
used to:

may repeat the measurement at a number of positions
across the cross section and provide an average discharge
(usually weighting by the width of flow represented by
each measurement). But this average will only be as good
as the choice of positions taken to represent the flow.
Sampling theory suggests that a greater number of mea-
surements will provide a better representation, with the
standard error decreasing with the square root of the
number of measurements made. However, a larger num-
ber of samples will take a longer time to make, and thus
we have possible temporal changes to contend with in
giving added error. Clearly, this approach is impractical
when flows are rapidly changing. If we require continuous
measurements, we may build a structure into the flow,
such as a flume or weir (e.g. French, 1986) which again
perturbs the system being measured (possibly with major
effects if the local gradient is modified significantly, or if
sediment is removed from the system). Furthermore the
devices used to measure flow through these structures
will have their own uncertainties of measurement, even if
they are state-of-the-art electronic devices. In the flume
case, the measurement is usually of a depth, which is then
calibrated to a discharge by use of a rating curve. The
rating curve itself will have an uncertainty element, and
is usually proportional to depth to a power greater than
one. Any error in measurement of depth will therefore
be amplified in the estimation of discharge. Although it
might be possible to measure flow depth non-invasively
(e.g. using an ultrasonic detector), unless the channel
section is well controlled (by invasive means), there is
likely to be an even larger error in the rating curve used
(e.g. because the channel cross-section changes as the
flow gets deeper due to erosion or deposition of sedi-
ment). Such measurements also tend to be costly, and the
cost and disturbance therefore prevents a large number
of measurements being taken in a specific area, which
is problematic if we are interested in spatial variability
or if we wish to simulate at larger (more policy and
management relevant) scales.
Other environmental modelling questions might
require even further perturbation of the system. For
example, soil depth is a critical control of water flow
into and through the soil and thus has an impact on
other systems too, such as vegetation growth or mass
movement. In a single setting, we might dig a soil pit.
Even if we try to replace the soil as closely as possible
in the order in which we removed it, there will clearly
be a major modification to the local conditions (most
notably through bulk-density changes, which often mean
a mound is left after refilling; a lower bulk density means

(a) better understand the behaviour of the model, par-
ticularly in terms of the ways in which parameters
interact;
(b) verify (in the computer-science sense) multicompo-
nent models;
(c) ensure model parsimony by the rejection of parame-
ters or processes to which the model is not sensitive;
(d) targeting field parameterization and validation pro-
grammes for optimal data collection focusing on the
most sensitive inputs; and
(e) provide a means of better understanding parts of or
the whole of the system being modelled.

Another form of sensitivity analysis is changing the
model instead of changing the parameter values. A
modeller might 'play' with different models or model con-
figurations and thereby better understand the dynamics
of the system before committing to a more sophisticated
model-building adventure. This approach tends to be
most effective with very simple (sometimes called 'toy')
models or model components. An excellent example is
described in detail in Chapter 16.

2.5 Errors and uncertainty

2.5.1 Error
No measurement can be made without error. (If you
doubt this statement, get ten different people to write
down the dimensions in mm of this page, without telling
each other their measurements, and compare the results.)
Although Heisenberg's uncertainty principle properly
deals with phenomena at the quantum scale, there is
always an element of interference when making an obser-
vation. Thus, the act of observation perturbs what we are
measuring. Some systems may be particularly sensitive
to these perturbations, for example when we introduce
devices into a river to measure patterns of turbulence.
The very act of placing a flow meter into the flow causes
the local structure of flow to change. If we were inter-
ested in the river section discharge rather than the local
changes in velocity, our single measuring device would
have less significant impacts of perturbation, but the
point measurement would be a very poor measurement
of the cross-section flow. To counter this problem, we