Green-Ampt flow time

This function models the Green-Ampt equation, with a saturated surface flowing vertically downward into a soil profile. The assumptions are:

1. Homogeneous soil with initial water content (theta_0) 2. Constant pressure head (h_0) at the wetting front 3. Saturated soil above above wetting front 4. Continuous supply of water with constant head (h_b) at the soil surface boundary

With these assumptions, the amount of time for a particular infiltration depth (Fcum) can be calculated using Darcy's law as:

$$t = \frac{1}{K_{sat}}\Big[F - \Delta \theta (h_b - h_0) \ln (1 + \frac{F}{\Delta \theta (h_b - h_0)}) \Big]$$

Usage

get_greenampt_time(theta_0, theta_s, Fcum, Ksat, h_b, h_0)

Arguments

theta_0

Soil volumetric water content prior to event

theta_s

Soil porosity

Fcum

cumulative infiltration in mm water equivalent

Ksat

Saturated hydraulic conductivity

h_b

Hydraulic head at soil surface boundary

h_0

Hydraulic head in soil prior to event

Value

Returns the time at which a cumulative amount of infiltration occurs.

Examples

library(units)
theta_0 <- 0.2 # unitless
theta_s <- 0.35 # unitless
Fcum <- set_units(1:20, "mm") # depth
Ksat <- set_units(0.2, "cm/h") # length / time
h_b <- set_units(6, "ft") # hydraulic head (length)
h_0 <- set_units(-10, "cm") # hydraulic head (length)
get_greenampt_time(theta_0, theta_s, Fcum, Ksat, h_b, h_0)
#> Units: [h]
#>  [1] 0.0008621092 0.0034405339 0.0077235112 0.0136993988 0.0213566732
#>  [6] 0.0306839281 0.0416698731 0.0543033317 0.0685732399 0.0844686452
#> [11] 0.1019787042 0.1210926820 0.1417999501 0.1640899855 0.1879523692
#> [16] 0.2133767845 0.2403530159 0.2688709481 0.2989205640 0.3304919441