soilphysics (version 5.0)

llwr: Least Limiting Water Range (LLWR)

Description

Graphical solution for the Least Limiting Water Range and parameter estimation of the related water retention and penetration resistance curves. A summary containing standard errors and statistical significance of the parameters is also given.

Usage

llwr(theta, h, Bd, Pr, 
    particle.density, air, 
    critical.PR, h.FC, h.WP, 
    water.model = c("Silva", "Ross"), 
    Pr.model = c("Busscher", "noBd"),
    pars.water = NULL, pars.Pr = NULL, 
    graph = TRUE, graph2 = TRUE, 
    xlab = expression(Bulk~Density~(Mg~m^{-3})), 
    ylab = expression(theta~(m^{3}~m^{-3})), 
    main = "Least Limiting Water Range", ...)

Arguments

theta

a numeric vector containing values of volumetric water content (\(m^3~m^{-3}\)).

h

a numeric vector containing values of matric head (cm, Psi, MPa, kPa, ...).

Bd

a numeric vector containing values of dry bulk density (\(Mg~m^{-3}\)). Note that Bd can also be a vector of length 1. See details.

Pr

a numeric vector containing values of penetration resistance (MPa, kPa, ...).

particle.density

the value of the soil particle density (\(Mg~m^{-3}\)).

air

the value of the limiting volumetric air content (\(m^3~m^{-3}\)).

critical.PR

the value of the critical soil penetration resistance.

h.FC

the value of matric head at the field capacity (cm, MPa, kPa, hPa, ...).

h.WP

the value of matric head at the wilting point (cm, MPa, kPa, hPa, ...).

water.model

a character; the model to be used for calculating the soil water content. It must be one of the two: "Silva" (default) or "Ross". See details.

Pr.model

a character; the model to be used to predict soil penetration resistance. It must be one of the two: "Busscher" (default) or "noBd". See details.

pars.water

optional; a numeric vector containing the estimates of the three parameters of the soil water retention model employed. If NULL (default), llwr() estimates them using a Newton-Raphson algorithm. See details.

pars.Pr

optional; a numeric vector containing estimates of the three parameters of the model proposed by Busscher (1990) for the functional relationship among Pr, theta and Bd. If NULL (default), llwr() estimates them using a Newton-Raphson algorithm. Moreover, if Pr.model = "noBd", then the third value is considered to be null.

graph

logical; if TRUE (default) a graphical solution for the Least Limiting Water Range is plotted.

graph2

logical; if TRUE (default) a line of the Least Limiting Water Range as a function of bulk density is plotted. If graph = FALSE, then llwr() will automatically consider graph2 = FALSE too.

xlab

a title for the x axis; the default is \(Bulk~Density~(Mg~m^{-3})\).

ylab

a title for the y axis; the default is \(\theta~(m^{3}~m^{-3})\).

main

a main title for the graphic; the default is "Least Limiting Water Range"

…

further graphical arguments.

Value

A list of

limiting.theta

a \(n x 4\) matrix containing the limiting values of water content for each input value of bulk density at the volumetric air content (thetaA), penetration resistance (thetaPR), field capacity (thetaFC) and wilting point (thetaWP).

pars.water

a "nls" object or a numeric vector containing estimates of the three parameters of the model employed by Silva et al. (1994) for the functional relationship among theta, Bd and h.

r.squared.water

a "Rsq" object containing the pseudo and the adjusted R-squared for the water model.

pars.Pr

a "nls" object or a numeric vector containing estimates of the three parameters of the penetration resistance model.

r.squared.Pr

a "Rsq" object containing the pseudo and the adjusted R-squared for the penetration resistance model.

area

numeric; the value of the shaded (LLWR) area. Calculated only when Bd is a vector of length > 1.

LLWR

numeric; the value of LLWR (\(m^3~m^{-3}\)) corresponding to Bd. Calculated only when Bd is a single value.

Details

The numeric vectors theta, h, Bd and Pr are supposed to have the same length, and their values should have appropriate unit of measurement. For fitting purposes, it is not advisable to use vectors with less than five values. It is possible to calculate the LLWR for a especific (unique) value of bulk density. In This case, Bd should be a vector of length 1 and, therfore, it is not possible to fit the models "Silva" and "Busscher", for water content and penetration resistance, respectively.

The model employed by Silva et al. (1994) for the soil water content (\(\theta\)) as a function of the soil bulk density (\(\rho\)) and the matric head (h) is:

$$\theta = exp(a + b \rho)h^c$$

The model proposed by Ross et al. (1991) for the soil water content (\(\theta\)) as a function of the matric head (h) is:

$$\theta = a h^c$$

The penetration resistance model, as presented by Busscher (1990), is given by

$$Pr = b0 * (\theta^{b1}) * (\rho^{b2})$$

If the agrument Bd receives a single value of bulk density, then llwr() fits the following simplified model (option noBd):

$$Pr = b0 * \theta^{b1}$$

References

Busscher, W. J. (1990). Adjustment of flat-tipped penetrometer resistance data to common water content. Transactions of the ASAE, 3:519-524.

Leao et al. (2005). An Algorithm for Calculating the Least Limiting Water Range of Soils. Agronomy Journal, 97:1210-1215.

Leao et al. (2006). Least limiting water range: A potential indicator of changes in near-surface soil physical quality after the conversion of Brazilian Savanna into pasture. Soil & Tillage Research, 88:279-285.

Ross et al. (1991). Equation for extending water-retention curves to dryness. Soil Science Society of America Journal, 55:923-927.

Silva et al. (1994). Characterization of the least limiting water range of soils. Soil Science Society of America Journal, 58:1775-1781.

See Also

fitbusscher

Examples

# NOT RUN {
# Example 1 - part of the data set used by Leao et al. (2005)
data(skp1994)
ex1 <- with(skp1994,
	llwr(theta = W, h = h, Bd = BD, Pr = PR,
		particle.density = 2.65, air = 0.1,
		critical.PR = 2, h.FC = 100, h.WP = 15000))
ex1

# Example 2 - specifying the parameters (Leao et al., 2005)
a <- c(-0.9175, -0.3027, -0.0835) # Silva et al. model of water content
b <- c(0.0827, -1.6087, 3.0570)   # Busscher's model
ex2 <- with(skp1994,
	llwr(theta = W, h = h, Bd = BD, Pr = PR,
		particle.density = 2.65, air = 0.1,
		critical.PR = 2, h.FC = 0.1, h.WP = 1.5,
		pars.water = a, pars.Pr = b))
ex2

# Example 3 - specifying a single value for Bd
ex3 <- with(skp1994,
	llwr(theta = W, h = h, Bd = 1.45, Pr = PR,
		particle.density = 2.65, air = 0.1,
		critical.PR = 2, h.FC = 100, h.WP = 15000))
ex3

# End (not run)
# }