The frequency domain approach to analyse field-scale miscible flow transport experiments in the soils

Abstract

A new approach to the estimate of the parameters u (advective velocity) and λ (dispersivity) characterizing solute transport in soils is presented. The pair (u, λ) is estimated by matching in the frequency domain (FD) the theoretical expression of moments pertaining to the breakthrough curve (BTC) against to the one evaluated by means of the experimental data. In particular, we demonstrate that to reduce the impact of the random measurement-errors upon such an estimate, it is worth retaining in the Fourier's expansion of the moments only the harmonics associated to the smaller frequencies. This is due to the fact that the Fourier transform moves most of the measurement-errors affecting moments in the high-frequency range. As a consequence, by adopting a relatively small number of harmonics to compute the Fourier transform of the experimental moments, one may filter out most of the noise. It is also shown that the number of harmonics to retain (cut-off) depends upon the soil's water content as well as the magnitude of the characteristic length l E of the error relative to the dispersivity λ. The proposed methodology has been applied to a recently conducted plot-scale transport experiment. For comparison purposes, we have also estimated the pair (u, λ) by the classical method of moments (MM). Both the methods lead to the same value of the advective velocity u. This is explained by recalling that u depends upon the first-order moment, a quantity that is scarcely influenced by the measurement-errors. Instead, the estimate of the dispersivity λ (which is related to the second-order moment) is largely different (with the value achieved by the MM larger than the one obtained by the FD approach). Such a difference is addressed to the fact that in the MM the distortion-effect due to the measurement-errors amplifies with the increasing order of the moments, a phenomenon which is completely avoided in the FD approach by adopting the above mentioned cut-off.