Inverse modeling and parameter estimation
have become valuable tools for calibration of water resources and environmental
models as well as for quantifying uncertainties associated with the use of these
models in planning and operation. Due to the nonlinearity of these models, estimates
of derivatives are essential for such application. In addition, other applications
such as solution of nonlinear systems using Newton-Raphson requires estimate
of derivatives. The traditional approach of using numerical derivatives requires
running the models repeatedly. For complex problems routinely facing environmental
engineers, the cost of obtaining numerical derivatives limits the usefulness
of automatic calibration. As an alternative, analytical derivatives can be obtained
with limited overhead for complex models. However, considerable effort from
the code developer is required to build the derivatives into the modeling code.
In this paper, we introduce automatic differentiation as an approach for building
analytical derivatives into MODFLOW for a wide range of applications. A new
MODFLOW code is developed where analytical derivatives are calculated as part
of the solution for a wide range of parameters. We discus a test problem where
the cost saving and the improved accuracy obtained by analytical derivatives
are clearly
demonstrated. The analytical derivatives results and run times are compared
to numerical derivatives obtained by PEST and the analytical derivatives are
used in PEST for uncertainty analysis. The test problem involves a large complex
MODFLOW model simulating surface/subsurface interaction between groundwater,
wetlands, and canals in South Florida.