MODELING OF WATER QUALITY - Water Quality Engineering in Natural Systems - page 386

11

MODELING OF WATER QUALITY

11.1 INTRODUCTION bounds are essential considerations in taking any sub-

stantive actions based on model output. In the United
States, the issue of uncertainty is particularly relevant in
estimating total maximum daily loads (TMDLs) that
must be determined for impaired waters. Sustainable
decisions in hydrologic risk management require
detailed information on the probability density function
(pdf) of model output. Only then can probabilities for
the failure of a specific management option or the
exceedance of critical thresholds (e.g., pollutants) be
derived. If uncertainties in model predictions are over-
looked in the context of water-quality modeling, it is
entirely possible that deterministic models could predict
safe water conditions, even if there is significant risk that
water-quality standards will be violated.
Uncertainties in model predictions arise from three
principal sources of uncertainty: (1) uncertainty in the
representation of the physical, chemical, and biological
processes, called structural uncertainty or model uncer-
tainty ; (2) uncertainty in the model parameters, called
parameter uncertainty ; and (3) uncertainty in the input
and output data used to calibrate the model, called data
uncertainty or observational uncertainty . Structural
uncertainty arises from incomplete understanding of
the system being modeled and/or the inability to accu-
rately reproduce the processes with mathematical equa-
tions. Parameter uncertainty results from incomplete
knowledge of parameter values, ranges, physical
meaning, and temporal and spatial variability. Data
uncertainty results primarily from measurement errors.
Data uncertainty can be further split into uncertainty in
forcing inputs and uncertainty in output responses.

The term computer model or numerical model is often
confused with the term computer code . A computer
code is a generic source code for a computer, typically
written in C++ or FORTRAN, that provides instructions
to solve a set of process equations corresponding to
certain conceptual models. The process equations
embedded in a computer code involve parameters that
must be specified by the user of the code. For example,
MODFLOW (Harbaugh and McDonald, 1996) is a
computer code that provides a simultaneous solution to
the Darcy and continuity equations, with required user
input of parameters, such as the hydraulic conductivity
and specific storage in each cell of the specified grid.
When a computer code is used along with site-specific
parameters, then the combination of the site-specific
input data with the generic computer code yields a
model of a particular phenomena at the site. For
example, if the hydrogeologic properties corresponding
to subsurface conditions in the Biscayne aquifer (in
south Florida) are input into the MODFLOW code, this
would yield a MODFLOW model of groundwater heads
in the Biscayne aquifer.
In developing and testing hydrological models, split-
sample testing, involving calibration of a model based
on a period in which data are available, followed by
validation using another period of similar length, is nor-
mally done. In presenting results derived from model
simulations, an accompanying uncertainly analysis is
widely regarded as being essential. Uncertainty analyses
provide error bounds to the model output, and such