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Robust Estimation of the Generalized Solute Transfer Function Parameters

M. Javaux* and M. Vanclooster

Dep. of Environmental Sciences and Land Use Planning, Université catholique de Louvain (UCL), Croix du Sud, 2 Bte 2, B-1348 Louvain-la-Neuve, Belgium



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Fig. 1. Influence of {lambda}1 - {lambda}2 on the apparent dispersivity in function of the depth. Values in the graph represent the {lambda}a calculated from Eq. [19] with reference depth l = 1 m, {sigma}l = 0.2, and µl = 10.

 


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Fig. 2. Error contaminated data simulated with Eq. [11] at four different depths (0.1, 0.4, 0.7, and 0.85 m, l = 1 m) and a realistic noise of standard deviation of 8 x 10-4 [-].

 


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Fig. 3. Numerical simulation of a CDE and a CLT process at the 0.3-, 0.6-, and 1-m depth fitted by the GTF solution (Eq. [11]). The CDE parameters: D = 5 cm h-2 and v = 1 cm h-1, fitted parameters are {lambda}1 = 1, {lambda}2 = 0.49, µl = 3.81, and {sigma}l = 0.435. The CLT parameters: µl = 3.73, {sigma}l = 0.480, fitted GTF parameters are exactly the same with {lambda}1 and {lambda}2 equal to 1.

 


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Fig. 4. Surface plots of the objective function related to the error-contaminated Crt* at 0.1- and 0.4-m depth. The cross indicates the actual parameters ({lambda}1 = 0.7, {lambda}2 = 0.7, µl = 3.6, and {sigma}l = 0.32).

 


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Fig. 5. Objective function of error-contaminated Crt* from the six BTCs couples with actual parameters: {lambda}1 = 0.7, {lambda}2 = 0.7, µl = 3.6, and {sigma}l = 0.32. Comparison of response surfaces of parameters {lambda}1 and {lambda}2 in function of the dataset used. The two figures labeling each subplot give the position of the two BTC used. Figure 1, 2, 3, and 4 correspond respectively to 0.1-, 0.4-, 0.7-, and 0.85-m depths.

 


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Fig. 6. Comparison of experimental BTCs at the 0.15- and 0.3-m depth in an undisturbed sandy subsoil and fitted results of the CD, CLT, and GTF models.

 


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Fig. 7. Comparison of experimental BTC at the 0.45-m depth in an undisturbed sandy subsoil and predictions of the CD, CLT and GTF models.

 





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