A theory of groundwater motion in small drainage basins in central Alberta, Canada

Abstract

On the basis of the parallel pattern of the water divides and the valleys in parts of central Alberta and the inferred difference in permeability between the Paskapoo and Edmonton formations, basins are considered to be separate units of flow in the groundwater regime. For the cross-sectional distribution of the fluid potential in a basin of homogeneous lithology an equation is found that relates the fluid potential to the acceleration of gravity, topographic gradient of the valley flank, horizontal distance between water divide and valley bottom, elevation of the water table at the valley bottom above the horizontal impermeable boundary, elevation above the horizontal impermeable boundary, and horizontal distance from the valley bottom. The validity of the assumption that groundwater runoff is discharged mainly at the valley bottoms is disputed. A boundary between areas of recharge and discharge is proved mathematically. A theory is advanced to explain the systematic deviation of the theoretical value of the fluid potential from the observed values. Local anomalies of the piezometric surface are accounted for by the presence of lenticular bodies of relatively high permeability. Mathematical formulas are used to express the relation between those anomalies and the permeability ratios and the size and shape of the lenses. A schematic cross section of possible potential distribution and flow pattern across a watershed is presented.