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

Table 4: Normalized degradation rate
constants estimated with method B.
WS = 4 m WS = 16 m
mean 4.51 1.92
median 1.96 1.14
stdv. 8.34 2.97
cv 1.85 1.55
N 41 33
norm. degradation rate constant [-]
100
10
1
0.1
WS = 4 m WS = 16 m
Figure 6: Normalized degradation rate constants estimated with method B for source widths of 4 m and 16 m.
10
single realization result
ensemble mean
Variability of estimated rate constants for a single site
For each source width, one single plume was repeatedly investigated 13 times by different investigators. For this subset
of plumes the variability of estimated rate constants for a single site, resulting from different notions on “sufficient
accuracy” of the plume investigation, is studied. As the incorporation of conductivity measurements from all observation
wells of the monitoring network significantly improves rate constant estimation with methods A1, A2 and A3, this
approach is used in this comparison. Results for strategies A and B are summarized in Table 5 and Figure 7.
For source width WS = 4 m a slightly stronger overestimation of λ can be observed for strategy A (methods A1 - A3) in
comparison to the results for the complete data set. Here, the mean ΛA1 resulting from 13 investigations of the single site
is 5.26, while ΛA1 for the complete data set is 4.75. For methods A2 and A3 the same tendency of increased
overestimation is found. The variability among the sets of 13 estimated ΛA1, ΛA2 and ΛA3, however, is much smaller. The
cv here are only 0.3, 0.34 and 0.68, respectively. With strategy B, i.e. method B, a slightly smaller mean ΛB = 4.26 is
found than for the complete data set and the cv of 0.78 here also is reduced. For a source width of 16 m, all four methods
show a much lower mean value of normalized rate constants than for the complete data set. On average, method A1 and
A3 yield the correct result for the single investigated site, while method A2 and B show a slight overestimation.
Variability of the estimated rate constants in terms of cv is lower than for the complete data set of WS = 16 m. For
strategy B no clear dependence between the precision of the rate constant estimate and the absolute number of wells in
the monitoring network nor the number of respective wells showing considerable contaminant concentrations (e.g.
C/C0 > 0.001) could be observed. The absence of such an obvious relationship may be due to the low sample size of only
13 investigations of both plume realizations. As described before, it seems, however, that the spread of estimated rate
constants decreases slightly with increasing numbers of wells (not shown here).
The stronger overestimation observed for WS = 4 m as well as the more precise estimation of λ for WS = 16 m do not
allow for any general conclusions regarding the absolute magnitude of errors, as this might probably be an effect of the
two individual realizations investigated and their respective plume geometry. The variability observed among the 13
results for each of the two single plumes however shows, that for a single realization of a contaminant plume,
substantially different investigation results, in this case degradation rate constants, may be obtained, when investigated
by individual persons. For both, the narrow plume with a comparatively small source zone of 4 m width as well as for the
wider plume with WS = 16 m, the variability of investigation results here has a magnitude of 25 % up to 69 % of the
variability observed among different realizations of the plume, depending on the method used for rate constant
estimation. This clearly shows, that a substantial part of rate constant estimation uncertainty is due to the individual
configuration of the monitoring network.