CMG Collaborative Research: Tempered Stable Models for Preasymptotic Pollutant Transport in Natural Media

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Contaminant transport through natural aquifers typically exhibits pre-asymptotic or transient anomalous behavior on the space and time scale critical to most environmental concerns. Complex and usually unpredictable medium heterogeneity at all relevant scales motivates the application of non-local transport theories. The proposed work will develop tempered stable models, which generalize standard non-local transport theories by adjusting fractal power-laws, to simulate pre-asymptotic transport and reveal the nature of real-world dispersion missed previously. There will be three major outcomes, including (1) a novel non-local transport theory and model based on tempered power laws that can efficiently simulate transient anomalous diffusion, (2) a quantitative linkage between the observable statistics of natural heterogeneous media and the model parameters built by a systematic Monte Carlo study, and (3) a convenient software suite with open source codes that solve and apply the model. This collaborative research will also test the model, the solver and the model predictability, by using historical tracer data and well-studied aquifer information. A careful consideration of the physical meaning of model components, and connections to statistical aquifer properties, will ensure that the resulting model is not limited to curve fitting applications.Accurate prediction of contaminant migration in real-world aquifers is critical to groundwater protection and cleanup. The proposed work will develop appropriate transport theory and build effective modeling components to address this problem. Hence this research is both highly theoretical and applied. In particular, the proposed work more accurately represents the underlying link between fractional calculus and power-law statistics in real aquifer material. The PI team includes mathematicians and hydrologists, forming interdisciplinary cooperation in cutting edge research.