Page 285 - Soil and water contamination, 2nd edition

272 Soil and Water Contamination

Internal functions
-1
-3
F = resuspension rate [M.L .T ]
r
-3
-1
F = settling rate [M.L .T ]
s
-3
O sat = dissolved oxygen saturation concentration [M.L ]
2
-1
U = mean flow velocity [L.T ]
x
z = water depth [L]
Figure 15.2b (continued) Nomenclature for Figure 15.2a (Van der Perk, 1998)
complex at first glance, they always remain simplified mathematical representations of the
real world.
The construction of complex environmental models usually proceeds in stages . The
first step is to propose a mathematical model, based on a combination of theoretical and
empirical considerations and heuristics. The next step is to determine and check whether
the mathematical model is a faithful representation of the conceptual model. If applicable,
this step also involves a test to check if the numerical implementation of the mathematical
model is a faithful representation of the mathematical model. This procedure is called model
verification , which denotes the establishment of truth. Model verification is only possible
for the mathematical steps in the model construction.
In Section 10.2 we saw that besides the set of mathematical equations, it is also necessary
to input variables and parameters in the model, to perform mathematical modelling . The
values of the model input variables, for instance time series of mass discharge inputs and
water temperature, or digital maps of aquifer properties, are usually based on field data but
may also be hypothetical. The values of the model parameters, such as for example rate
constant or equilibrium coefficients, are usually chosen initially from laboratory studies or
the literature. Often, these values of the model parameters must be adjusted to improve the
model results to a satisfactory level. To evaluate whether the model results are satisfactory,
a data set of experimental or field observations of the model’s state variables is needed. In
addition, some criteria are needed against which the model’s performance can be evaluated.
If the model results correspond favourably with the observations, then the model is accepted;
if they do not, the model parameters should be further adjusted to fit the observations better.
This procedure of tuning the model parameters is called model calibration .
If the model has been calibrated, i.e. the errors are within an acceptable range, the model
is often tested using a second, independent, data set of experimental or field observations:
for example, observations from another year or a different site. At this stage, the model
parameters are not adjusted any more. This procedure, called model validation , provides
reassurance that the model is performing adequately and fulfils the purpose for which it
was constructed. In this case too, prescribed criteria are needed so it can be decided whether
to accept or reject the model. If the model fails to reproduce the observed values within
acceptable limits, the model must be redesigned and the procedure of model calibration
described above should be repeated.
A verified, calibrated, and validated model does not necessarily imply that the model
includes all major processes and that that the processes are formulated correctly. Real-world
systems are intractable and the processes governing the transport and fate of chemicals
in the environment usually depend on more factors than the models account for, but the
degree of influence of those factors is often obscure. For example, most models used in river
water quality management that account for the sinks and sources of dissolved oxygen and
the nitrogen and phosphorus cycles, do not take account of the adverse effects of accidental
toxin discharges on biochemical transformation rates. These models may perform well under
regular conditions but are not intended to predict water quality after accidents. In other
words, these models have not been validated for circumstances in which accidental toxin

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