induce_infiltration_time {streamDepletr}

Calculate the critical time at which stream transitions from gaining to losing.

Description

Calculate the critical time at which stream transitions from gaining to losing.

Usage

induce_infiltration_time(d, S, Tr, Qa, Qw)

Arguments

d

distance from well to stream [L]

S

aquifer storage coefficient (specific yield if unconfined; storativity if confined)

Tr

aquifer transmissivity [L2/T]

Qa

ambient groundwater inflow rate per unit length of stream [L2/T]

Qw

well pumping rate [L3/T]

Details

This calculates the critical time at which induced infiltration due to groundwater pumping begins, based on the glover model of streamflow depletion. Derived in Chen (2003) Eq. 4.

Assumptions:

• Groundwater flow is perpendicular to stream

• 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

• No streambed resistance to flow (see hunt or hantush for streambed resistance)

Value

A numeric of tc, the critical time at which induced infiltration begins [T].

References

Chen, X (2003). Analysis of Pumping-Induced Stream-Aquifer Interactions for Gaining Streams. Journal of Hydrology 275(1): 1-11. doi:10.1016/S0022-1694(02)00320-7

Examples

# recreate Figure 2 in Chen (2003)
Qa <- c(0.0001, 0.0003, 0.0005, 0.0008, 0.001)
tc <- induce_infiltration_time(d = 575, S = 0.2, Tr = 100*15, Qa = Qa, Qw = 2727)
plot(x = (pi * Qa * 100 * 15 * 575 / 2727), y = tc, log = "y")