Optimal groundwater management models are based on the hydraulic equations of the aquifer system. These equations relate the state variables of the groundwater system, the head, and the decision variables that control the magnitude, location, and timing of pumping, or artificial recharge. For the unconfined aquifer these management models are large‐scale, nonlinear programming problems. A differential dynamic programming (DDP) algorithm is used for unsteady, nonlinear, groundwater management problems. Due to the stagewise decomposition of DDP, the dimensionality problems associated with embedding the hydraulic equations as constraints in the management model are significantly reduced. In addition, DDP shows a linear growth in computing effort with respect to the number of stages or planning periods, and quadratic convergence. Several example problems illustrate the application of DDP to the optimal control of nonlinear groundwater hydraulics.
Glacial till overlies many bedrock aquifers in Iowa, and a number of landfills and leaking underground storage tank sites are located in weathered and unweathered till. To investigate the potential for significant lateral ground‐water flow in Wisconsin age weathered loam till in Iowa, two 24‐hour pumping tests were performed in the shallow unconfined ground water present in the weathered till, a constant flowrate pumping test and a constant drawdown pumping test. The saturated thickness in the weathered till at the research site is less than 3 m, and choosing a constant flowrate sufficient for significant drawdown in the monitoring wells without dewatering the pumping well was difficult. In a low conductivity medium with a thin saturated thickness, the constant drawdown pumping test was found to be a more practical field technique. In the constant drawdown test, a chosen level of constant drawdown is maintained in the pumping well for the duration of pumping, and the flowrate decreases with time. The changing flowrate of the constant drawdown pumping test was approximated as a series of step decreases, and superposition of the Theis solution was used for simulation. Both types of pumping tests yielded similar parameter estimates for the weathered loam till region in Iowa, with an average bulk horizontal hydraulic conductivity of around 5×10‐4 cm/s and an average specific yield of about 0.032. Single well response (bail) tests produced comparable estimates for hydraulic conductivity, with a mean of 3×10‐4 cm/s. The results imply significant lateral ground‐water flow is possible, and the weathered till should not be considered a significant barrier to the lateral spread of shallow ground‐water contamination.
The low conductivity of glacial till is usually thought to preclude pumping tests, which has led to the predominate use of laboratory permeameter and single well response (slug) tests for estimating hydraulic conductivity. Slug tests only sample a small region around the well and may be more representative of the disturbance of well installation or development than in situ conductivity. To provide a larger scale comparison to slug test estimates of hydraulic conductivity for unweathered Wisconsin age till in Iowa, a pumping test was performed, with both the pumping and monitoring wells placed in unweathered till. Maintaining a constant drawdown of 439 cm in the pumping well for over five days yielded an average flowrate of only 26.3 ml/min, but produced a maximum drawdown of 104 cm at a radial distance of 178 cm. Assuming radial and vertical flow, least‐squares parameter estimation yielded a hydraulic conductivity estimate of 7.5 · 10‐7 cm/s and a specific storage estimate of 6.6 · 10‐6 cm‐1. Slug test results compared favorably, with geometric mean hydraulic conductivity estimates of 4.9 · 10‐7 cm/s from a Cooper et al. (1967) analysis and 7.1 · 10‐7 cm/s from a Hvorslev (1951) analysis. For this relatively low clay till (20% clay fraction), borehole smearing does not appear to have a significant impact on slug tests. The results indicate pumping tests can be performed, on an appropriate scale, in some unweathered tills.
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