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

samples taken at all eight wells do not allow for an estimation of lYand σY 2 , which would be required
to derive αL and αT. A detailed study on the effects of dispersivity parameterization on the
performance of methods 2 and 3 is presented in Bauer et al. (2006).
The information obtained by the site investigation allows the application of the five methods for
estimation of the degradation kinetic parameters and the subsequent calculation of contaminant
plume lengths as presented in Sections 4.1 and 4.2. The investigation setup is designed to resemble
ideal conditions for this purpose. All measurements are assumed to be exact, i.e. without measurement
error, and are obtained by reading the model output at the respective well positions. The
only uncertainty and variability is introduced by the heterogeneity of the hydraulic conductivity.
6. Results and discussion
C. Beyer et al. / Journal of Contaminant Hydrology 87 (2006) 73–95
As outlined in Section 3, three different cases A, B and C are investigated here (see Table 1). The
next three Sections 6.1, 6.2 and 6.3 present detailed results and discussions for each case studied. A
detailed comparison and discussion of the performance of the different approaches is given in
Section 6.4.
6.1. Case A: estimation of first order degradation rate constants and plume lengths for plumes
following a first order degradation kinetics
6.1.1. Estimation of rate constants
In case A methods 1–4 are tested and compared based on their ability to estimate the first order
degradation rate constant λ and the contaminant plume length in heterogeneous aquifers.
Therefore, plumes following first order degradation kinetics are investigated here. The four
estimated rate constants λi are divided by the true rate constant to yield corresponding normalized
Λi, which can be interpreted as an over- or underestimation factor. Fig. 3 presents ensemble means
with corresponding standard deviations as error bars, medians, coefficients of variation and the
single realization results for methods 1–4 against the aquifer heterogeneity σY 2 .
Results for method 1 (Fig. 3 (a)) show that Λ1=1 in the homogeneous case (σY 2 =0), thus in this case
the true rate is obtained. However, already for the lowest degree of heterogeneity (σY 2 =0.38), about
77% of the rate constants estimated fall above the reference line which indicates the true rate constant,
overestimating λ up to factors of 4.79 in the worst case. In the remaining realizations λ is
underestimated. The spread of the ensemble of 100 realizations covers about one order of magnitude.
When σY 2 is further increased, spread and standard deviation also increase. For σY 2 =4.5 the Λ1 cover
almost two orders of magnitude with single realizations showing overestimation factors N10. Mean Λ1
is 3.3 with standard deviation and coefficient of variation of 3.65 and 1.11, respectively. Increasing the
heterogeneity of the aquifer thus results in a higher uncertainty of λ and increases the probability of a
significant overestimation. For method 2 normalized rate constants Λ2 are shown in Fig. 3 (b). As seen
for method 1 a systematic overestimation of λ can be observed, increasing with σ Y 2 . However, the Λ2
are significantly larger than the corresponding Λ 1. In the homogeneous case method 2 yields Λ 2=1.7,
increasing to 9.38 for σY 2 =4.50. In extreme cases, overestimation of λ is larger than a factor of 50. Also
spread and standard deviations are larger than for Λ1. Estimated rate constants Λ3 obtained by method
3(Fig. 3 (c)) are only slightly lower than those of method 2, ranging from 1.17 in the homogeneous
case to 7.39 for σY 2 =4.5. Method 4 (Fig. 3(d)) yields the true rate for homogeneous conditions, i.e.
Λ4=1. As for the other methods, spread and uncertainty increase with σY 2 . Compared to methods 1–3
the spread is smaller and balanced around the true rate constant. For σY 2 ≤2.7 the ensemble averages
and medians match the true rate constant well. For σ Y 2 =4.50 the average Λ4 reaches 1.73.
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