MODELING OF WATER QUALITY - Water Quality Engineering in Natural Systems - page 387

Additional sources of uncertainty in model predictions
that are commonly overlooked include uncertainty in
model boundary and initial conditions, and uncertainty
in the model numerical formulation (gourley and
Vieux, 2006).
In engineering practice, the use of computer models
is commonplace. In formulating these models, there are
usually a variety of codes to choose from for a particular
application, but in doing work to be reviewed by regula-
tory agencies, codes developed and maintained by agen-
cies of the U.S. government have the greatest credibility,
and, perhaps more important, are almost universally
acceptable in supporting permit applications and
defending design protocols. These are also several
widely accepted commercial codes used in water-quality
engineering, and it is relatively rare to develop new
codes for specific applications.

and transport models at the field and watershed scales
(Mayer et al., 1999). As a general guide, the best-
performing model in likely to be the one which has
approximately the same spatial and temporal resolution
as the available data that is most highly correlated with
the model output of interest (Das et al., 2008).
The development or selection of a computer code is
based on the following criteria:

• The code must be verified that it is free from errors.
• The code must represent the key processes expected
to occur at the scale for which the model is applied.
• The assumptions associated with the conceptual
models embedded in the code must be reasonable
for the particular application being considered.
• The input data required must be readily available.
• The code must provide the output that is of interest
to the user.

11.2 CODE SELECTION

For most applications, several computer codes can be
found that solve the tasks at hand with varying levels of
complexity. In these cases, model selection requires a
number of considerations, specifically (Ford, 2006):

Computer codes are typically based on conceptual
models of how the systems behaves (e.g., flow is
described by Darcy's law), and each conceptual model
is represented by an algorithm consisting of mathemati-
cal expressions of variables and parameters. After a
code is developed, it is typically verified by comparing
the solutions produced by the code to those of analytical
models of simplified systems in which the solutions are
known. Code verification is intended to make sure that
the computer code accurately incorporates the concep-
tual model; most reputable codes have been verified by
their developers.
It is imperative that the process equations used in a
model correspond to the scale of the model. The appro-
priate process equations for the same phenomena can
be significantly dependent on the scale of the process,
with mechanistic formulations (using fundamental
equations of mechanics) frequently used in fine-scale
models and functional formulations using empirical
equations and continuity relationships frequently used
in coarse-scale models. Sampling and measurement
(spatial and temporal) resolution for both input param-
eters and observations to evaluate model performance
must be consistent with the model resolution, and
models developed for a specific spatial scale must be
calibrated with data from the same scale, otherwise,
model parameters will have little physical significance
and the modeling approach is questionable (Corwin et
al., 1999b). The sensitivity of model output to scale is
typically different for different output variables. Certain
applications require that processes be represented a
certain scales. For example, nonpoint source pollution
assessments in the vadose zone require chemical fate

• Objectives of the application
• Access to expertise for developing and using the
model
• Data availability
• Time and money resources

Less complex models are typically used for planning-
level analyses, and, in most cases, availability of data is
the binding constraint in model selection.
In water-resources engineering, the most widely used
computer codes focus on either surface water or ground-
water, with relatively few models comprehensively inte-
grating both surface water and groundwater hydrology
(e.g., Jones et al., 2008). In selecting an appropriate code,
the importance of feedback between surface water and
groundwater must be an important consideration.
Once a verified computer code is developed or
selected, the steps to be followed in developing a com-
puter model are: calibration, validation, and application
of the model. The essentials of these steps are described
in the following sections.

11.3 CALIBRATION

Calibration is the process of adjusting model parame-
ters and comparing the model output to measured data
until an acceptable level of agreement is achieved.
Approaches for selecting model parameters can be