Applied numerical modeling of saturated / unsaturated flow and ...

The conceptual model used is a rigorous
simplification of the processes observed in
natural aquifer systems, as K varies in space
and contaminant degradation usually follows
more complicated laws, depends on
microorganism growth and may be limited
or inhibited by other substances. The
simplifications assumed here are however
necessary to study the sole effects of measurement
error on rate constant estimation
under otherwise ideal conditions for the
application of the center line method and
the analytical models of Tab. 1.
In this synthesis only results for method 1
of Tab. 1 are presented. The degradation
rate estimated from evaluation of measured
heads and concentrations is divided by the
true rate constant used in the numerical
model yielding normalized overestimation
factors. To assess the range of uncertainty
resulting from the random measurement
error a Monte Carlo analysis is conducted
for five increasing values of ��h, each with
a sample size of 100. Fig. 7 presents the
rate constants thus estimated versus ��h.
Without measurement error the correct rate
constant is obtained. However, already for
very small ��h < 1 cm, a significant
overestimation can be observed. This has
two main reasons: Firstly, an erroneous
head yields an incorrect transport velocity
and thus results in rate constant
overestimation for too high velocities and in
underestimation for too low velocities.
Secondly, erroneous heads result in an incorrect
derivation of the flow direction
using the hydrogeologic triangle. Thus the
observation wells installed downgradient of
the source may be placed off the true center
line position (compare Fig. 6). Hence, concentrations
measured in off center line wells
are too low, indicating an overly high rate
of degradation. Overestimation of the
degradation rate increases with the maximum
head error and reaches factors of more
than 20 in the worst cases.
In Bauer et al. (2007 [EP 4]) also the
influence of concentration measurement
errors was studied. It was found that also
12
this type of error results in overestimation
of the rate constant on average. Erroneous
heads, however, were found to have a larger
impact on the rate constant estimates. For
real field applications therefore much care
has to be taken when measuring hydraulic
heads for the derivation of the plume center
line position.
Fig. 7: Influence of head measurement
error on rate constant estimates (Bauer et
al., 2007 [EP 4]). The reference rate
constant is indicated by the horizontal line,
small symbols represent single estimates,
big symbols are ensemble averages with
standard deviation as error bars.
Influence of aquifer heterogeneity
The second aspect studied using the VA
concept is the influence of spatially heterogeneous
hydraulic conductivity distributions
on the accuracy of rate constant
estimation methods 1 – 4 of Tab. 1. For this
end the conceptual model used so far is
modified by assuming all head, concentration
and K measurements to be free of
measurement error and regarding K as a
spatial random variable. This is done to
study the sole influence of heterogeneous
conductivity. Multiple realizations of heterogeneous
K fields for four degrees of
aquifer heterogeneity characterized by the
ln-conductivity variance 2
� Y were generated,
using a Monte Carlo approach to study
the range of investigation result uncertainty.
� at least 100 different reali-
For each 2
Y