Assessment of Modeling Uncertainties Using a Multistart Optimization Tool for Surface Complexation Equilibrium Parameters (MUSE)

The MUlti-start optimization algorithm for Surface complexation Equilibrium (MUSE) algorithm has been developed to optimize the fitting of thermodynamic constants for surface complexation modeling (SCM). Although there is a plethora of software to perform data fitting and determine intrinsic equilibrium constants, the algorithms used are highly dependent on initial values and choice of parameters. This limits their transferability to model other systems, for example, reactive transport processes. With this in mind, a hybridized optimization approach, based on a multistart algorithm combined with a local optimizer, has been developed to allow the simultaneous optimization of SCM parameters and to assess the sensitivity of these parameters to changes in the model assumptions. In this study, the CD-MUSIC formalism with a Basic Stern electrostatic model is utilized to model chromate adsorption on ferrihydrite, although the MUSE algorithm can be applied to any adsorption data set and be implemented in any model formulation. This study offers two innovative components to the inverse SCM modeling approach: (a) determination of the true global optimum by performing multiple minimizations of the mean squared error between the simulated and observed data using a large number of initial starting points and (b) quantitative simulation of spectroscopic pH-dependent profiles for two chromate surface complexes. We demonstrate that when MUSE is implemented to determine chromate log Ks, their dependence on other adjustable parameters such as specific surface area (SSA) and capacitance is relatively small (i.e., less than one unit difference for chromate log Ks on ferrihydrite) and can be accounted by mathematical functions determined through the MUSE algorithm. The robustness of the algorithm is demonstrated in the absence of the spectroscopy data as well, with traditional batch tests yielding similar thermodynamic constants as the spectroscopic profiles.