Solute Concentration Statistics in Heterogeneous Aquifers for Finite Péclet Values

By V. Fiorotto, E. Caroni. 2002

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Best unbiased ensemble linearization and the quasi‐linear Kalman ensemble generator (2009, background): “[95] Theoretically, concentration follows the beta distribution [ Fiorotto and Caroni, 2002; Caroni and Fiorotto, 2005] if measured in small support volumes, and approaches normality for larger support volumes [Schwede et al., 2008].”
First‐order based cumulative distribution function for solute concentration in heterogeneous aquifers: Theoretical analysis and implications for human health risk assessment (2014, methodology): “This approach has been used in the literature for r2Y 1 [Fiori, 2001; Fiorotto and Caroni, 2002; Bellin and Tonina, 2007; Cirpka et al., 2008; Bellin et al., 2011] and has been numerically verified [e.g., Schwede et al., 2008; Meyer et al., 2010].”
The lamellar description of mixing in porous media (2015, methodology): “A common approach used is to assume an ad-hoc distribution, which is parametrized from analytical derivation of concentration moments obtained under diﬀerent approximations (e.g., Fiorotto & Caroni 2002; Bellin & Tonina 2007; Tonina & Bellin 2008; Cirpka et al. 2008).”
Impact of sampling volume on the probability density function of steady state concentration (2008, methodology): “ Fiorotto and Caroni [2002] and Caroni and Fiorotto [2005] had already shown that point-like concentration measurements exhibit a bimodal pdf at short travel distance.”