Propagation of Uncertainty in Aqueous Equilibrium Calculations:  Non-Gaussian Output Distributions

The effects of database parameter uncertainty on uranium(VI) equilibrium calculations

“…This type of behaviour has been observed before, for example simulations of base titration's of simple acids performed by Cabaniss (1997) produced large uncertainties in the pH output distributions near to the equivalence points, the distributions being bimodal with minima at or close to the equivalence points. …”

“…The use of a low discrepancy sequence and also Latin Hypercube sampling (McKay et al, 1979), results not presented, did not reduce the error of the parameter estimates compared to the Monte Carlo method, however these different sampling strategies may be more successful when applied to different scenarios. If the modelled system is suitable then the derivative method of estimating the uncertainty proposed by Cabaniss (1997) would be preferred due to the greatly reduced processing requirements. Large ranges of input conditions used together with the randomised parameter values can lead to convergence problems in the modified Newton-Raphson algorithm of CHESS.…”

“…Ideally, each thermodynamic value may be characterised by its expectation value and an assigned uncertainty depending on the extent and quality of the available data. The propagation of these input uncertainty distributions can lead to very different species concentration output distributions (Cabaniss, 1997). Consideration of this uncertainty propagation should be integral to the application of speciation modelling to environmental studies, including both the interpretation of acquired data and the predictive modelling for transport, bioavailability or toxicity studies for the studied element.…”

“…The calculations were performed using Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods, assuming mutually independent gaussian distributions for the parameter uncertainty. Although derivative methods of predicting uncertainty exist (Cabaniss, 1997) and are considerably faster than Monte Carlo methods, the requirement of linear combination of the parameter uncertainties was not satisfied for the speciation of uranium, and so this method was not applied. The number of runs required to provide acceptably small parameter estimate errors was investigated for a number of descriptive parameters.…”

Assessment of parametric uncertainty for groundwater reactive transport modeling

“…For such objective function surfaces, gradient‐based parameter estimation algorithms (e.g., the Gauss‐Levenberg‐Marquardt method implemented in UCODE_2005 [ Poeter et al ., ] and PEST [ Doherty , ]) may perform poorly, for example, by terminating at a local minimum. In addition, due to the nonlinearities, the probability distributions of model parameters and outputs may be non‐Gaussian with multiple modes and/or long tails [ Cabaniss , ; Denison and Carnier‐Laplace , ; Leavitt et al ., ]. This puts question in the accuracy of uncertainty quantification methods that either explicitly [ Srinivasan et al ., ; Liu et al ., ; Tartakovsky et al ., ] or implicitly [ Dai and Samper , ] assume Gaussian parameters of groundwater reactive transport models.…”