(Un)certainty of overall binding constants of Al with dissolved organic matter determined by the Scatchard approach

One of the best approaches to date to obtain overall binding constants (K_o) for Al and dissolved organic matter (DOM) from acidic soil solutions is to collect 'free' Al data with diffusive gradients in thin films (DGT) and to infer the K_o values by fitting a continuous distribution model based on Scatchard plots. Although there is clear established literature demonstrating the usefulness of the Scatchard approach, relatively little attention has been given to a realistic assessment of the uncertainties associated with the final fitted K_o values. In this study we present an uncertainty analysis of the fitted K_o values using a synthetic dataset with different levels of random noise and a real data set using DGT data from an acidic soil solution. The parameters in the continuous distribution model and their corresponding upper and lower 95% uncertainty bounds were determined using the Shuffled Complex Evolution Metropolis (SCEM) algorithm. Although reasonable fits of the distribution model to the experimental data were obtained in all cases, an appreciable uncertainty in the resulting K_o values was found due to three main reasons. Firstly, obtaining 'free' Al data even with the DGT method is relatively difficult, leading to uncertainty in the data. Secondly, before Scatchard plots can be constructed, the maximum binding capacity (MBC) must be estimated. Any uncertainty in this MBC propagates into uncertainty associated with the final plots. Thirdly, as the final fitted K_o values are largely based on extrapolation, a small uncertainty in the fit of the binding data results in an appreciable uncertainty in the obtained K_o. Therefore, while trends in K_o for Al and DOM could easily be discerned and compared, the uncertainty in the K_o values hinders the application in quantitative speciation calculation. More comprehensive speciation models that avoid the use of K_o seem to fit better for this purpose.