Impact of sampling volume on the probability density function of steady state concentration

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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].”
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].”
Bayesian geostatistical design: Task‐driven optimal site investigation when the geostatistical model is uncertain (2010, background): “[40] Structural uncertainty also affects the standard deviation of concentration, compare Figures 2 and 3 and analytical expressions [e.g., Fiorotto and Caroni, 2002; Caroni and Fiorotto, 2005; Schwede et al., 2008].”