MODELING OF WATER QUALITY - Water Quality Engineering in Natural Systems - page 401

Validation must be regarded as an ongoing dynamic
process continually dependent on new and more reli-
able data. A growing body of scientific research has
clearly demonstrated that site-specific models that
provide good representations of processes that are
capable of historically matching data still do not render
accurate predictions at future times. A good calibration
match does not prove validity, nor should it be sufficient
for acceptability. To be scientifically valid or even accept-
able, not only must a model it the observed data, but it
must do so for the right reasons. In other words, a
model's robustness is also a prime consideration. Valida-
tion must consider both accuracy and robustness. Vogel
and Sankarasuramanian (2003) have suggested that an
important component of the validation process is that
the model output also demonstrate similar covariance
structure as the actual processes, and demonstration of
agreement in this regard should be done prior to param-
eter estimation.
For any modeling approach to be valid and useful in
terms of calibration and prediction, it must be closely
related to what can be determined experimentally
(Wagenet and Hutson, 1996).

• State Uncertainty. The actual state of the catch-
ment (e.g., moisture conditions and snow cover) is
usually not directly observed but calculated using
model equations.
• Process Uncertainty. The main hydrological pro-
cesses are described using equations that can only
capture parts of the complex natural processes.
• Model Structure Uncertainty. The model structure
itself leads to uncertainty due to the inherent sim-
plification of the more complex real system.
• Output Uncertainty. Observed discharge, ground-
water level, soil moisture, conductivity, and other
observations are also based on rating curves, point
measurements, or remote sensing and can be cor-
rupted by measurement errors and neglected
spatial variability.

Among these different sources of errors, process defi-
nition and model structure errors are generally the most
poorly understood and the most difficult to cope with,
and their impacts on hydrologic predictions can be far
more detrimental than those of parameter errors and
data errors (Abramowitz et al., 2006; Liu and gupta,
2007). Most approaches to uncertainty analysis either
address individual components of uncertainty or lump
all uncertainty into a single model prediction error term;
a few approaches have been suggested for disaggregat-
ing the model uncertainty into its various sources (e.g.,
götzinger and Bárdossy, 2008).
Uncertainty in the predictions of hydrologic models
are typically characterized by either probability distri-
butions of output variables or by upper and lower per-
centiles (typically the 5- and 95-percentile) expressed as
a function of time.

11.5 SIMULATION

The final step in the modeling process is simulation.
Whether for the purpose of understanding or predic-
tion, a simulation is not simply a matter of running the
model for a set of agreed-upon inputs and conditions. A
knowledge of the level of uncertainty associated with
each simulation is crucial. A map of simulated results is
only of value when accompanied with an associated
map of uncertainty (Loague et al., 1999).

11.6.1 Bayesian and GLUE Analyses

11.6 UNCERTAINTY ANALYSIS

Bayesian uncertainty analyses are based on the
relation Quantification of the uncertainty associated with hydro-

logical predictions is required for the proper application
and interpretation of model results (e.g., Ma et al., 2007;
Matott et al., 2009). Uncertainty in model predictions
can be traced to five areas: inputs, state specification,
process definition, model structure, and output. These
error sources are particulary significant in hydrologic
models and can be illustrated as follows (götzinger and
Bárdossy, 2008),

= ∫

f y x Y X ( | , , ) f y x ( | , θ ) ( g Y X d θ | , ) θ

(11.51) p p n n p p n n

Θ

where y p is the (observable) predictand of interest, x p is
the corresponding value of the covariate, Y n is the set
of historical predictand observations (e.g., water levels
and discharges), X n is the set of historical covariates
(e.g., rainfall, upstream inflows), f ( y p | x p , Y n , X n ) is the
probability density of the predictand conditional upon
the historical observations and the covariate after mar-
ginalizing the uncertainty due to the parameters, Θ is
the ensemble of all possible parameter realizations,
f ( y p | x p , θ ) is the probability density of the predictand
value of interest conditional upon the covariate and a

• Input Uncertainty. The meteorological input is
based on point observations that are themselves
uncertain and sometimes combined with indirect
measurements,

such as radar or satellite

information.