Pareto optimal calibration of highly nonlinear reactive transport groundwater models using particle swarm optimization

Abstract:

Groundwater management and remediation requires the implementation of numerical models in order to evaluate the potential anthropogenic impacts on aquifer systems. In many situations, the numerical model must, not only be able to simulate groundwater flow and transport, but also geochemical and biological processes. Each process being simulated carries with it a set of parameters that must be identified, along with differing potential sources of model-structure error. Various data types are often collected in the field and then used to calibrate the numerical model; however, these data types can represent very different processes and can subsequently be sensitive to the model parameters in extremely complex ways. Therefore, developing an appropriate weighting strategy to address the contributions of each data type to the overall least-squares objective function is not straightforward. This is further compounded by the presence of potential sources of model-structure errors that manifest themselves differently for each observation data type. Finally, reactive transport models are highly nonlinear, which can lead to convergence failure for algorithms operating on the assumption of local linearity. In this study, we propose a variation of the popular, particle swarm optimization algorithm to address trade-offs associated with the calibration of one data type over another. This method removes the need to specify weights between observation groups and instead, produces a multi-dimensional Pareto front that illustrates the trade-offs between data types. We use the PEST++ run manager, along with the standard PEST input/output structure, to implement parallel programming across multiple desktop computers using TCP/IP communications. This allows for very large swarms of particles without the need of a supercomputing facility. The method was applied to a case study in which modeling was used to gain insight into the mobilization of arsenic at a deepwell injection site. Multiple data types (e.g., hydrochemical, geophysical, tracer, temperature, etc.) were collected prior to, and during an injection trial. Visualizing the trade-off between the calibration of each data type has provided the means of identifying some model-structure deficiencies.