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INTERA Develops Breakthrough Adjoint Sensitivity Code for Coupled Surface Water-Groundwater Models

In the assessment of sustainable groundwater development, capture functions, graphically displayed by capture maps over the modeled domain, are used to optimize the location of pumping wells, timing of pumping and other well field design features. Capture functions denote the fraction of the pumped water drawn from a selected source of supply (groundwater storage, ET, enhanced recharge, boundary flux such as streams, etc.)

Dr. Ramarao Banda and Dr. Tom Clemo at INTERA Incorporated have advanced the adjoint sensitivity technique by developing a new subroutine to MODFLOW-2005 that allows efficient calculation of capture function. Recognized experts in the development and application of adjoint techniques, their most recent contribution to the advancement of the adjoint sensitivity technique focuses on the development of exact sensitivities when computing sensitivities of groundwater capture from streams. This important development overcomes a limitation that arises when the stream package is simplified to a river package. This is achieved by developing the adjoint formulation for a fully coupled surface water groundwater system.

MODFLOW offers RIV and STR packages (among others) to implement river or stream boundary conditions. The RIV model maintains a constant stage in the river; while the STR model implements a fully coupled groundwater and surface water formulation. While the overall verification of the adjoint capture solution in 2011 [using the river approximation] was good, errors in a few grid blocks were revealed due to the river approximation of the STR package. To correct these errors, they developed an exact adjoint formulation for the STR package in December, 2012. The adjoint formulation was verified with the USGS San Pedro model capture results obtained via perturbation techniques [Leake et al., 2010: Groundwater (September/October 2010. 48(5). pp. 690-700)]. This development involved substantial developments in the derivation of algebraic formulas and in code modifications. Since that time, the new adjoint code has been applied to the USGS Northern Arizona Regional Groundwater Flow Model (NARGFM).

This most recent development enables the computation of sensitivities of stream stage to groundwater pumping throughout the stream network in one direct MODFLOW simulation resulting in significant computational savings.