MODFLOW-style parameters in underdetermined parameter estimation

In this article, we discuss the use of MODFLOW-Style parameters in the numerical codes MODFLOW_2005 and MODFLOW_2005-Adjoint for the definition of variables in the Layer Property Flow package. Parameters are a useful tool to represent aquifer properties in both codes and are the only option available in the adjoint version. Moreover, for overdetermined parameter estimation problems, the parameter approach for model input can make data input easier. We found that if each estimable parameter is defined by one parameter, the codes require a large computational effort and substantial gains in efficiency are achieved by removing logical comparison of character strings that represent the names and types of the parameters. An alternative formulation already available in the current implementation of the code can also alleviate the efficiency degradation due to character comparisons in the special case of distributed parameters defined through multiplication matrices. The authors also hope that lessons learned in analyzing the performance of the MODFLOW family codes will be enlightening to developers of other Fortran implementations of numerical codes.