glover function

Streamflow depletion with fully-penetrating stream and no streambed.

glover(t, d, S, Tr)

Arguments

• t: times you want output for [T]
• d: distance from well to stream [L]
• S: aquifer storage coefficient (specific yield if unconfined; storativity if confined)
• Tr: aquifer transmissivity [L2/T]

Returns

A numeric of Qf, streamflow depletion as fraction of pumping rate [-]. If the pumping rate of the well (Qw; [L3/T]) is known, you can calculate volumetric streamflow depletion [L3/T] as Qf*Qw

Details

This function is described in Glover & Balmer (1954) based on work by Theis (1941). It contains numerous assumptions:

• Horizontal flow >> vertical flow (Dupuit assumptions hold)
• Homogeneous, isotropic aquifer
• Constant Tr: Aquifer is confined, or if unconfined change in head is small relative to aquifer thickness
• Stream is straight, infinitely long, and remains in hydraulic connection to aquifer
• Constant stream stage
• No changes in recharge due to pumping
• No streambank storage
• Constant pumping rate
• Aquifer extends to infinity
• Stream fully penetrates through aquifer (see hunt or hantush for partially penetrating stream)
• No streambed resistance to flow (see hunt or hantush for streambed resistance)

Examples

glover(t = 1.5777e8, d = 1000, S = 0.2, Tr = 0.1)   # Glover & Balmer (1954) Table 1, Well 1
glover(t = 1.5777e8, d = 5000, S = 0.2, Tr = 0.1)   # Glover & Balmer (1954) Table 1, Well 2
glover(t = 1.5777e8, d = 10000, S = 0.2, Tr = 0.1)  # Glover & Balmer (1954) Table 1, Well 3

References

Glover, RE, and GG Balmer (1954).River Depletion Resulting from Pumping a Well near a River. Eos, Transactions American Geophysical Union 35(3): 468-70. doi:10.1029/TR035i003p00468.

Theis, CV (1941). The Effect of a Well on the Flow of a Nearby Stream. Eos, Transactions American Geophysical Union 22(3): 734-38. https://doi.org/10.1029/TR022i003p00734.