VanGenuchtenMualem Class Reference

Provides the use of the Van Genuchten - Mualem retention curve (Van Genuchten 1980) More...

Inheritance diagram for VanGenuchtenMualem:

Collaboration diagram for VanGenuchtenMualem:

Detailed Description

Provides the use of the Van Genuchten - Mualem retention curve (Van Genuchten 1980)

Head - moisture relationship:

\begin{eqnarray*} W(\theta) &=& \frac{\theta - \theta_r}{\theta_s - \theta_r} \\ K(W) &=& K_{sat} \sqrt{W} \left(1-\left(1-W^{1/m}\right)^m\right)^2 \\ m &=& 1-\frac 1 n \\ \Psi(W) &=& 0.01 \frac{m}{cm} \frac{{\left(1-{W}^{\frac{1}{m}}\right) }^{\frac{1}{n}}}{\alpha\,{W}^{\frac{1}{m\,n}}} \\ W(\Psi) &=& \left(1+\left(\alpha\,100\frac{cm}{m}\Psi\right)^n\right)^{-m} \end{eqnarray*}

where:

• \(K\) is the conductivity in \(\frac m {day}\)
• \(W\) is the wetness (Volume of soil water per volume of pores)
• \(n\) is a shape parameter of the retention curve
• \(\alpha\) is inverse of the air entry potential in \(cm^{-1}\)
• \(\Psi(W)\) is the matric potential in \(m H_2O\) at wetness W

Public Member Functions
	VanGenuchtenMualem (real Ksat=15, real phi=0.5, real alpha=0.2178, real n=1.211, real m=-1, real theta_r=0.0, real w0=0.99)
	Creates a van Genuchten-Mualem retention curve.
virtual real	Diffusivity (real wetness) const
	Returns the diffusivity of the soil according to its wetness as given by VanGenuchten 1980.
virtual real	dPsiM_dW (real wetness) const
	returns \(\tfrac{d\Psi_M}{dW}\)
virtual real	FillHeight (real lowerDepth, real Area, real Volume) const
	Returns the thickness of a soil column with a certain pore volume.
real	fit_w0 (real w1=1.01, real Psi_p=1.0, real tolerance=0.05)
	Fits the break point wetness w0, to ensure a specific oversaturation at a given hydrostatic potential.
virtual real	K (real wetness) const
	returns the conductivity of the soil at a given saturation
virtual real	MatricPotential (real wetness) const
	returns the matrix potential at a given saturation
virtual real	Porosity (real depth) const
	Returns the porosity at a certain depth.
virtual real	theta (real wetness) const
	returns the water content \(theta\) for a given wetness
virtual real	VoidVolume (real upperDepth, real lowerDepth, real Area) const
	Returns the void volume of a soil column.
virtual real	Wetness (real suction) const
	returns the saturation at a given suction (matrix potential).
virtual real	Wetness_eff (real wetness, real pF_r=4.2) const
	Returns the effective wetness, using a residual pF value.
real	Wetness_pF (real pF) const
	returns the volumetric water content at a given pF value

Public Attributes
real	alpha
	Inverse of water entry potential in 1/cm.
real	Ksat
	Saturated conductivity in m/day.
real	l
	VanGenuchten - Mualem tortoisivity, defined in Van Genuchten 1980 as 0.5 (default here)
real	m
	VanGenuchten m (if negative, 1-1/n is used)
real	n
	Pore size distribution parameter [-].
real	Phi
	Porosity in m3/m3.
real	theta_r
	residual water content in m3 Water/ m3 soil (default=0.0)
real	w0
	Breakpoint wetness. If W>w0, a parabolic extrapolation is used.

Constructor & Destructor Documentation

VanGenuchtenMualem()

VanGenuchtenMualem	(	real	Ksat = 15,
		real	phi = 0.5,
		real	alpha = 0.2178,
		real	n = 1.211,
		real	m = -1,
		real	theta_r = 0.0,
		real	w0 = 0.99 )

Creates a van Genuchten-Mualem retention curve.

Parameters

Ksat	Saturated conductivity in \(\frac m{day}\)
phi	Porosity in \(\frac{m^3 Pores}{m^3 Soil}\)
alpha	Van Genuchten \(\alpha\) in \(\frac 1{cm}\)
n	Van Genuchten n
m	Van Genuchten m parameter, if negative m is calculated as \( 1-\frac 1 n\)
theta_r	Water content for \(\lim\limits_{\Psi_M \rightarrow -\infty}{\theta(\Psi_M)}\)
w0	Wetness above the parabolic extrapolation is used instead of the Van Genuchten curve (usually calculated with fit_w0)

Member Function Documentation

Diffusivity()

virtual real Diffusivity ( real wetness ) const

virtual

Returns the diffusivity of the soil according to its wetness as given by VanGenuchten 1980.

Deprecated

The current implementation goes to infinity at saturation, as noted by VanGenuchten. Diffusivity is therefore currently not usable in any model.

\[D(W) = K(W)\left|\frac{d\Psi}{d\theta}\right|\ eq. 10\]

where:

• \(D(W)\) Diffusivity in \(m^2/day\)
• \(K(W)\) Conductivity as a function of saturation W in m/day
• \(\Psi\) Pressure head
• \(\theta\) water content of the soil

Applying Van Genuchten theory (Van Genuchten 1980) yields to:

\[D(W) = \frac{(1-m)K_{sat}}{\alpha m \Phi} W^{l-1/m}\left(\left(1-W^{1/m}\right)^{-m} + \left(1-W^{1/m}\right)^{m} -2\right)\]

where:

• \(m = 1 - \frac 1 n\) acc. Mualem theory
• \(K_{sat}\) saturated conductivity in m/day
• \(\alpha\) inverse water entry potential in 1/m. Note \(\alpha\) is given in cmf in 1/cm
• \(\Phi\) porosity
• \(W = \frac{\theta - \theta_r}{\Phi - \theta_r}\) saturation of the soil

Reimplemented from RetentionCurve.

dPsiM_dW()

virtual real dPsiM_dW ( real wetness ) const

virtual

returns \(\tfrac{d\Psi_M}{dW}\)

\[\frac{0.01 w^{\frac{1}{m}} w^{- \frac{1}{m n}} \left(- w^{\frac{1}{m}} + 1\right)^{\frac{1}{n}}}{\alpha m n w \left(- w^{\frac{1}{m}} + 1\right)} + \frac{0.01 w^{- \frac{1}{m n}} \left(- w^{\frac{1}{m}} + 1\right)^{\frac{1}{n}}}{\alpha m n w}\]

Reimplemented from RetentionCurve.

fit_w0()

real fit_w0	(	real	w1 = 1.01,
		real	Psi_p = 1.0,
		real	tolerance = 0.05 )

Fits the break point wetness w0, to ensure a specific oversaturation at a given hydrostatic potential.

Parameters

w1	The oversaturation wetness to archieve (>1), default = 1.01
Psi_p	the hydrostatic potential for w1, default = +1.0 m
tolerance

K()

virtual real K ( real wetness ) const

virtual

returns the conductivity of the soil at a given saturation

\[K(W) = K_{sat} \sqrt{W} \left(1-\left(1-W^{1/m}\right)^m\right)^2 \]

Reimplemented from RetentionCurve.

MatricPotential()

virtual real MatricPotential ( real wetness ) const

virtual

returns the matrix potential at a given saturation

\[\Psi(W) = 0.01 \frac{m}{cm} \frac{{\left(1-{W}^{\frac{1}{m}}\right) }^{\frac{1}{n}}}{\alpha\,{W}^{\frac{1}{m\,n}}} \]

Reimplemented from RetentionCurve.

Wetness()

virtual real Wetness ( real suction ) const

virtual

returns the saturation at a given suction (matrix potential).

\[ W(\Psi) = \left(1+\left(\alpha\,100\frac{cm}{m}\Psi\right)^n\right)^{-m} \]

Reimplemented from RetentionCurve.

Wetness_eff()

virtual real Wetness_eff ( real wetness, real pF_r = 4.2 ) const

virtualinherited

Returns the effective wetness, using a residual pF value.

\[w_{eff} = \frac{w_{act}-w\left(pF_r\right)}{1-w\left(pF_r\right)}\]