induce_infiltration_time: Calculate the critical time at which stream transitions from...

In streamDepletr: Estimate Streamflow Depletion Due to Groundwater Pumping

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")

streamDepletr documentation built on July 26, 2023, 5:42 p.m.