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

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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.
C. Beyer et al. / Journal of Contaminant Hydrology 87 (2006) 73–95 contrast to L4, plume lengths L1, L2 and L3 show a clear tendency of underestimation, demonstrating the non-conservativeness of too large rate constants. Comparing methods 1, 2 and 3, differences in calculated plume lengths are not as pronounced as for the rate constants. Thus it can be concluded, that the same underlying equation should be used for rate constant and plume length estimation. However, if e.g. a rate constant estimated with method 2 is used in a two- or threedimensional (numerical) transport model, results are susceptible to the bias in method 2, resulting in a significantly stronger underestimation of the plume length. 6.2. Case B: estimation of first order degradation rate constants and plume lengths for plumes following Michaelis–Menten degradation kinetics In case B the additional error is studied, that arises when the four methods for the estimation of first order degradation rate constants (Table 2, equations (1)–(4)) and the respective equations for plume lengths (Table 3, equations (7)–(9)) are used for plumes with a degradation kinetics deviating from first order but following MM degradation kinetics instead (see Table 1). Since a direct comparison of estimated rate constants λ 1 through λ 4 with the MM parameters k max and MC used in the numerical simulations is not possible, the evaluation here is based on calculated Fig. 5. Normalized plume lengths Li calculated with degradation rate constants λ1 through λ4 for the contaminant plumes following Michaelis–Menten degradation kinetics. 87
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Applied numerical modeling of satur
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Abstract Applied numerical modeling
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Vorwort Die zurückliegenden drei J
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List of abbreviations and mathemati
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for the application studies outline
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path lengths of water molecules tha
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where vmax [s -1 ] is a maximum gro
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domain is discretized along advecti
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conceptional model error: wrong pro
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The conceptual model used is a rigo
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equires therefore a higher degradat
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studied for heterogeneous sites wit
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Fig. 13: Plume length overestimatio
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Page 46 and 47: Assessing measurements of first-ord
Page 55 and 56: WATER RESOURCES RESEARCH, VOL. 42,
Page 57 and 58: W01420 BAUER ET AL.: ASSESSING FIRS
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Page 98 and 99: Einführung In dieser Arbeit wird e
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Grundlage des Korngrößenspektrums
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Dies ist als konservative Abschätz
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Randbedingungen abhängig ist. Aus
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keinen Einfluss auf die abgebaute M
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Carsell, R. F., Parish, R. S.: Deve
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van Genuchten, M.T.: A closed form
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