Compute unsaturated hydraulic conductivity (Mualem-Van Genuchten) — hydraulic

Calculates unsaturated hydraulic conductivity at given matric potential values using the Mualem (1976) - Van Genuchten (1980) model.

Usage

hydraulic_conductivity(data, ks, alpha, n, m, h, tau = 0.5)

Arguments

data: A data frame or tibble. Passed as the first argument so the function is compatible with |> and %>% pipes.
ks: Saturated hydraulic conductivity (any consistent unit, e.g. cm/day). Either a bare column name from data or a scalar numeric value. Must be strictly positive.
alpha: Van Genuchten shape parameter (1/cm or 1/m). Either a bare column name or a scalar numeric value. Must be strictly positive.
n: Van Genuchten shape parameter (dimensionless). Either a bare column name or a scalar numeric value. Must be strictly positive.
m: Van Genuchten shape parameter (dimensionless). Typically set to 1 - 1/n, but can be specified independently. Must satisfy 0 < m < 1. Either a bare column name or a scalar numeric value.
h: Matric potential / pressure head. Either a bare column name or a scalar numeric value. Sign convention: absolute value is used internally.
tau: Tortuosity/connectivity parameter (dimensionless). Defaults to 0.5 (Mualem 1976). Must satisfy tau > -2. Either a bare column name or a scalar numeric value.

Value

The input data as a tibble with an additional column .K containing the computed hydraulic conductivity in the same units as ks.

Details

The effective saturation is first computed as: $$S_e(h) = \frac{1}{(1 + (\alpha |h|)^n)^m}$$

Then hydraulic conductivity is given by: $$K(h) = K_s \cdot S_e^{\tau} \cdot \left(1 - \left(1 - S_e^{1/m}\right)^m\right)^2$$

The tortuosity/connectivity parameter tau (τ) defaults to 0.5, which is the value proposed by Mualem (1976). Soilhypfit and other tools treat it as a free parameter; values between −2 and 2 are physically plausible.

References

Mualem, Y. (1976). A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research, 12(3), 513–522. https://doi.org/10.1029/WR012i003p00513

Van Genuchten, M. Th. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44(5), 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x

Examples

library(tibble)

soil <- tibble(h = c(0, 10, 100, 1000, 15000))

# Default tau = 0.5 (Mualem)
hydraulic_conductivity(
  soil,
  ks    = 10,
  alpha = 0.02,
  n     = 1.5,
  m     = 1 - 1/1.5,
  h     = h
)
#> # A tibble: 5 × 2
#>       h      .K
#>   <dbl>   <dbl>
#> 1     0 1   e+1
#> 2    10 3.15e+0
#> 3   100 7.37e-2
#> 4  1000 6.46e-5
#> 5 15000 9.89e-9

# Custom tortuosity parameter
hydraulic_conductivity(
  soil,
  ks    = 10,
  alpha = 0.02,
  n     = 1.5,
  m     = 1 - 1/1.5,
  h     = h,
  tau   = 1.0
)
#> # A tibble: 5 × 2
#>       h      .K
#>   <dbl>   <dbl>
#> 1     0 1   e+1
#> 2    10 3.11e+0
#> 3   100 5.89e-2
#> 4  1000 3.05e-5
#> 5 15000 2.38e-9