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

86 C. Beyer et al. / Journal of Contaminant Hydrology 87 (2006) 73–95
As shown before, degradation rate constants λ4 in general are significantly better estimated
than those obtained by the other three approaches. This is also reflected in plume lengths L4 (Fig.
4 (c)). For all σY 2 the ensemble means almost perfectly match the true L. Of all four approaches the
L4 consistently show the lowest coefficients of variation, indicating the lowest spread and thus the
lowest uncertainty.
The plume length results presented for case A demonstrate that the determination of
degradation rate constants using the center line method as well as the subsequent calculation of
contaminant plume lengths both are subject to uncertainty induced by the heterogeneity of the
medium. However, the uncertainty observed for the rate constants is only partially transferred to
the calculated plume lengths. For all approaches the observed spread of the ensembles of estimated
plume lengths is smaller than for the corresponding rate constants. This is most obvious for the L4,
which also show the best agreement with the true plume lengths. Moreover, the L4 are unbiased,
showing equal amounts of under- as well as overestimation. However, both types of error are
undesirable. Underestimation of the contaminant plume length, i.e. a “non-conservative” result,
may pose a threat to down gradient receptors. On the other hand, a “conservative” result, i.e. an
overestimation of plume dimensions, might result in wrong decisions regarding the necessity and
dimensioning of engineered remediation measures with unnecessary financial expenses. In
Fig. 4. Plume lengths Li calculated with degradation rate constants λ1 through λ4. The Li are normalized by the true plume
length L (indicated by the horizontal line) for case A.