This $198,334 National Science Foundation (NSF) Project Grant, awarded under the Geosciences program (CFDA 47.050) on February 1, 2025, will develop innovative models to enhance the ability to trace the origins of reactive pollutants in aquifers. The key activities include:
Advancing a new theory for backward tracking that incorporates non-Fickian diffusion and reaction models, which addresses limitations of traditional methods that assume linear, or "Fickian," diffusion. The project will propose the adjoint of the tempered stable law to create new backward tracking models for reactive pollutants experiencing super- and sub-diffusion. Numerical simulations and machine learning techniques will be used to approximate key parameters of these models, improving their accuracy and applicability. The models will be validated through real-world applications, such as calculating groundwater ages and assessing aquifer vulnerability.
The expected outcomes are a robust backward probability theory with corresponding physical models, a comprehensive set of predictive parameters, and an upgraded and validated software suite for practical applications. These advancements are expected to improve the resolution of inverse problems in hydrology, environmental science, and engineering, contributing to better environmental management and policymaking.
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