hunt {streamDepletr}

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)

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

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

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")