Premium
Backward fractional advection dispersion model for contaminant source prediction
Author(s) -
Zhang Yong,
Meerschaert Mark M.,
Neupauer Roseanna M.
Publication year - 2016
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2015wr018515
Subject(s) - fade , dispersion (optics) , advection , atmospheric dispersion modeling , skewness , diffusion , mathematics , fractional calculus , point source , environmental science , statistical physics , statistics , physics , air pollution , chemistry , organic chemistry , acoustics , optics , thermodynamics
The forward Fractional Advection Dispersion Equation (FADE) provides a useful model for non‐Fickian transport in heterogeneous porous media. The space FADE captures the long leading tail, skewness, and fast spreading typically seen in concentration profiles from field data. This paper develops the corresponding backward FADE model, to identify source location and release time. The backward method is developed from the theory of inverse problems, and then explained from a stochastic point of view. The resultant backward FADE differs significantly from the traditional backward Advection Dispersion Equation (ADE) because the fractional derivative is not self‐adjoint and the probability density function for backward locations is highly skewed. Finally, the method is validated using tracer data from a well‐known field experiment, where the peak of the backward FADE curve predicts source release time, while the median or a range of percentiles can be used to determine the most likely source location for the observed plume. The backward ADE cannot reliably identify the source in this application, since the forward ADE does not provide an adequate fit to the concentration data.