A Darcian Model for the Flow of Big Spring and the hydraulic head in the Ozark aquifer, Missouri, USA

Abstract

The complex discharge hydrographfor Big Spring, Missouri, can be described as the sum of two terms governed by Darcy’s Law. The dominant, long-term component is proportional to the regional hydraulic gradient, and constitutes about 80% of the average flow of 12.6 m3/s. Superimposed on this is a tran­sient component witha time-constant of about 1.5 days that represents the Darcian response to sharp, rainfall-driven pulses on the head of the shallow groundwater system. This tran­sient component delivers about 20% of the average total flow, but over short intervals can exceed the long-term component. However, the long-term component is so large that the ratio of record highflows to the average flow is only about 4x for Big Spring, and 1.5 to 4.5x for most other large Ozark springs; for comparison, this ratio is 10 to 3000x for most surface streams in Missouri. The strong correlation between the discharge of the large springs and the head in the Ozark aquifer permits the extension of the Darcian rainfall-runoff model to predict groundwater levels in wells.