A data-driven approach for simplifying the estimation of time for contaminant plumes to reach their maximum extent

Globally there exist a very large number of contaminated or possibly contaminated sites where a basic preliminary assessment has not been completed. This is largely, among others, due to limited simple methods/models available for estimating key site quantities such as the maximum plume length, further denoted as L_max and the corresponding time T=T_Lmax, at which the plume reaches its maximum extent L=L_max. An approach to easily obtain an estimate of T_Lmax in particular is presented in this work. Limited availability of high-quality field data, particularly of T_Lmax, necessitates the use of synthetic data, which constrains the overall model development works. Taking BIOSCREEN-AT (transient 3D model) as a base model, this work proposes second-order polynomial models, with only two parameters, for estimating L_max and T_Lmax. This reformulation of the well established solution significantly reduces data requirement and workload for initial site assessment purposes. A global sensitivity analysis (Morris, 1991), using a large number of random synthetic data, identifies the first-order decay rate constants in the plume λ_EFF and at the source γ as dominantly most influential for T_Lmax. For L_max, the first-order decay rate constant λ_EFF and groundwater velocity v are the two important parameters. The sensitivity analysis also identifies that these parameters non-linearly impact T_Lmax or L_max. With this information, the proposed polynomial models (each for L_max and T_Lmax) were trained to obtain model coefficients, using a large amount of synthetic data. For verification, the developed models were tested using four datasets comprising over 100 sample sets against the results obtained from BIOSCREEN-AT and the developed BIOSCREEN-AT-based steady-state model. Additionally, the developed models were evaluated against two well documented field sites. The proposed models largely simplify estimation, particularly, of T_Lmax, for which only very limited field or literature information is available.