hc_model {soilhypfit}R Documentation

Models for Soil Hydraulic Conductivity Functions

Description

The functions hc_model and hcrel_model compute, for given capillary pressure head hh, the hydraulic conductivity K(h)K(h) and the relative hydraulic conductivity k(h)k(h) respectively, of a soil by parametrical models.

Usage

hcrel_model(h, nlp, precBits = NULL, hcc_model = "vgm")

hc_model(h, nlp, lp, precBits = NULL, hcc_model = "vgm")

Arguments

h

a mandatory numeric vector with values of capillary pressure head for which to compute the hydraulic conductivity. For consistency with other quantities, the unit of head should be meter [m].

nlp

a mandatory named numeric vector, currently with elements named "alpha", "n" and "tau", which are the nonlinear parameters νT=(α,n,τ)\boldsymbol{\nu}^\mathrm{T} = (\alpha, n, \tau), where α\alpha, nn and τ\tau are the inverse air entry pressure, the shape and the tortuosity parameters, see Details. For consistency with other quantities, the unit of α\alpha should be 1/meter [m1\mathrm{m}^{-1}].

lp

a mandatory named numeric vector, currently with a single element named "k0", which is the saturated hydraulic conductivity K0K_0, the only linear parameter of the model, see Details. For consistency with other quantities, the unit of K0K_0 should be meter/day [md1\mathrm{m}\,\mathrm{d}^{-1}].

precBits

an optional integer scalar defining the maximal precision (in bits) to be used in high-precision computations by mpfr. If equal to NULL (default) then mpfr is not used and the result of the function call is of storage mode double, see soilhypfitIntro.

hcc_model

a keyword denoting the parametrical model for the hydraulic conductivity function. Currently, only the Van Genuchten-Mualem model (wrc_model = "vgm") is implemented, see Details.

Details

The functions hcrel_model and hc_model currently model soil hydraulic conductivity functions only by the simplified form of the Van Genuchten-Mualem model (Van Genuchten, 1980) with the restriction m=11nm = 1 - \frac{1}{n}, i.e. by

kVGM(h;ν)=SVG(h;ν)τ[1(1SVG(h;ν)nn1)n1n]2, k_\mathrm{VGM}(h; \boldsymbol{\nu}) = S_\mathrm{VG}(h; \boldsymbol{\nu})^\tau \, \left[ 1 - \left( 1 - S_\mathrm{VG}(h; \boldsymbol{\nu})^\frac{n}{n-1} \right)^\frac{n-1}{n} \right]^2,

K_\mathrm{VGM}(h; \mbox{$\mu$}, \boldsymbol{\nu}) = K_0 \, k_\mathrm{VGM}(h; \boldsymbol{\nu}),

where μ=K0\mu = K_0 is the saturated hydraulic conductivity (K0>0K_0 > 0), νT=(α,n,τ)\boldsymbol{\nu}^\mathrm{T} = (\alpha, n, \tau) are the inverse air entry pressure (α>0\alpha > 0), the shape (n>1n > 1) and tortuosity parameter (τ>2\tau > -2), and SVG(h;ν)S_\mathrm{VG}(h; \boldsymbol{\nu}) is the the volumetric water saturation, see sat_model for an expression.

Note that μ\mu and ν\boldsymbol{\nu}^\mathrm{} are passed to the functions by the arguments lp and nlp, respectively.

Value

A numeric vector with values of (relative) hydraulic conductivity.

Author(s)

Andreas Papritz papritz@retired.ethz.ch.

References

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

See Also

soilhypfitIntro for a description of the models and a brief summary of the parameter estimation approach;

fit_wrc_hcc for (constrained) estimation of parameters of models for soil water retention and hydraulic conductivity data;

control_fit_wrc_hcc for options to control fit_wrc_hcc;

soilhypfitmethods for common S3 methods for class fit_wrc_hcc;

vcov for computing (co-)variances of the estimated nonlinear parameters;

evaporative-length for physically constraining parameter estimates of soil hydraulic material functions.

Examples

## define capillary pressure head (unit meters)
h <- c(0.01, 0.1, 0.2, 0.3, 0.5, 1., 2., 5.,10.)

## compute (relative) hydraulic conductivity
hcrel <- hcrel_model(h, nlp = c(alpha = 1.5, n = 2, tau = 0.5))
hc <- hc_model(h, nlp = c(alpha = 1.5, n = 2, tau = 0.5), lp = c(k0 = 5))

## display hydraulic conductivity function
op <- par(mfrow = c(1, 2))
plot(hcrel ~ h, log = "xy", type = "l")
plot(hc ~ h, log = "xy", type = "l")
on.exit(par(op))

[Package soilhypfit version 0.1-7 Index]