streamDepletr (version 0.2.0)

hunt: Streamflow depletion in partially penetrating stream with semipervious streambed.

Description

Streamflow depletion in partially penetrating stream with semipervious streambed.

Usage

hunt(t, d, S, Tr, lmda, lmda_max = Inf, prec = 80)

Value

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

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]

lmda

streambed conductance term, lambda [L/T]. Can be estimated with streambed_conductance.

lmda_max

maximum allowed `lmda` [L/T]. If `lmda` is too high, exp and erfc calculations in Hunt solution are not computationally possible, so you may need to artifically reduce `lmda` using this term.

prec

precision for Rmpfr package for storing huge numbers; 80 seems to generally work but tweak this if you get weird results. Reducing this value will reduce accuracy but speed up computation time. If set to `NULL`, the `mpfr` function is not used which can address an occasional issue on Mac computers but lead to problems under some combinations of `Tr` and `lmda`.

Details

This function is described in Hunt (1999). When lmda term gets very large, this is equivalent to glover. 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

References

Hunt, B (1999). Unsteady Stream Depletion from Ground Water Pumping. Ground Water 37 (1): 98-102. doi:10.1111/j.1745-6584.1999.tb00962.x.

Examples

hunt(t = 1826, d = 1000, S = 0.2, Tr = 8640, lmda = 864)    # ~equal to glover because lmda=Tr
hunt(t = 1826, d = 1000, S = 0.2, Tr = 8640, lmda = 0.864)  # less depletion due to lower lmda

lmda <- streambed_conductance(w = 10, Kriv = 0.0864, briv = 1) # estimate lmda
hunt(t = 1826, d = 1000, S = 0.2, Tr = 8640, lmda = lmda)

Qf <- hunt(t = seq(1, 1826), d = 1000, S = 0.2, Tr = 8640, lmda = 0.864)
plot(x = seq(1, 1826), y = Qf, type = "l")