MODELING UNCERTAINTY FOR WELL-HEAD PROTECTION

"Hugo" and "Oneka" are the code names for two simple Analytic Element models used to help identify well-head protection zones around public water supply wells. The models are based upon steady flow in a single, homogeneous, isotropic, flat-lying aquifer. The aquifer properties (hydraulic conductivity and porosity) are treated as uncertain parameters. They are specified by ranges of values in "Hugo", and by inferred statistical distributions in "Oneka".

The models include the following features: uniform infiltration, regional uniform flow, and a general set of discharge-specified wells. The strength of the uniform infiltration, as well as the magnitude and direction of the uniform flow, are determined by analyzing the modelling errors at a set of specified piezometers. A linear programming formulation underlies "Hugo", while "Oneka" employs stochastic simulations.

The output from "Hugo" is a capture zone envelope. A capture zone envelope is the union of possible capture zones taken over a range of comparably likely parameter values. The shape of an envelope is a direct reflection of the model misfit and the specified ranges of the aquifer parameters. The output from "Oneka" is a capture zone probability map. The combination of these two representations of uncertainty offers quantitative and qualitative insights well beyond those found in the output of more common deterministic models.

"Hugo" and "Oneka" are being used as initial screening tools in the extensive well-head protection campaign currently underway in the State of Minnesota.