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When pollutants are found in the environment (such as indoor air, land surface, rivers, and aquifers), one of the major challenges is to identify the source position(s) or the release history of the pollutants. This issue can be most efficiently addressed by the inverse modelling approach, which can direct ly back track the pollutant’s previous location(s) given the current location and travel time, o r calculate the pollutant’s release history given the current and initial positions. It is, however, not trivial to develop the inverse model. Most importantly, both normal and anomalous transport can occur for pollutants in different systems, and how to build inverse models to efficiently back track these quite different transport dynamics using a unified, physically reasonable approach remains a historical challenge. This study develops inverse models for pollutants undergoing either normal transport or super-diffusive, anomalous transport using the well-known and universal mass conservation law. Results show that the combination of the mass balance law with reversing time and the standard Tayler series expansion leads to the inverse model for normal transport, while the mass balance law combined with the Grünwald approximation of fractional derivative builds the inverse model for anomalous transport. Numerical solvers are also developed to approximate the forward and inverse models, so that this study provides convenient tools to identify environmental po llutants with a wide range of intrinsic heterogeneity.

Develop Inverse Models to Track Environmental Pollutants Using Mass Conservation Law for Both Normal and Anomalous Transport