USGS Water-Resources Investigations Report 00-4172

Simulation of the Recharge Area for Frederick Springs, Dane County, Wisconsin

By R.J. Hunt and J.J. Steuer

This report is also available in PDF format here (826 k file)

Abstract

The Pheasant Branch watershed in Dane County is expected to undergo development. There are concerns that this development will adversely affect water resources, including Frederick Springs, a large spring complex in the watershed. The spring's recharge area was delineated using a telescopic mesh refinement (TMR) model constructed from an existing regional-scale ground-water flow model, and further refined by adding nearby surface-water features, a refined recharge array based on a surface-water model, and increasing the vertical leakage between the deep aquifers. This TMR model was formally optimized using the parameter estimation code UCODE. The results of optimization demonstrated that the best fit to measured heads and fluxes was obtained by using a horizontal hydraulic conductivity two times that of the original regional model for layer 2 and 80 percent smaller for layer 3. This range of parameter values was formally considered using a stochastic Monte Carlo approach.

Two-hundred model runs used uniformly distributed, randomly sampled, horizontal hydraulic conductivity values within the range given by the TMR optimized values and the previously constructed regional model. A probability distribution of particles captured by the spring, or a "probabilistic capture zone" was calculated from the realistic Monte Carlo results (136 runs of 200). In addition to portions of the local surface watershed, the capture zone encompassed distant areas in the North Fork of the Pheasant Branch watershed and areas entirely outside of the Pheasant Branch - demonstrating that the ground-watershed and surface watershed do not coincide. Analysis of samples from the springs and a nearby municipal well identified large contrasts in chemistry, even for springs within 50 feet of one another. The differences were stable over time, were present in both ion and isotope analyses, and showed a distinct gradation from high nitrate, high calcium, Ordovician-carbonate dominated water in western spring vents to low nitrate, lower calcium, Cambrian-sandstone influenced water in eastern spring vents. The difference in chemistry was attributed to distinctive bedrock geology as demonstrated by overlaying the 50 percent probability capture zone over a bedrock geology map for the area. This finding gives additional confidence to the capture zone calculated by the ground-water flow model.