fronts.D.van_genuchten¶

fronts.D.van_genuchten(n=None, m=None, l=0.5, alpha=1.0, Ks=1.0, S_range=(0.0, 1.0))

Return a Van Genuchten moisture diffusivity function.

Given the parameters $$K_s$$, $$\alpha$$, m, l, $$S_r$$ and $$S_s$$, the Van Genuchten moisture diffusivity function D is defined as:

$D(S)=\frac{(1-m)K_s}{\alpha m (S_s-S_r)} S_e^{(l-\frac{1}{m})}\left((1-S_e^\frac{1}{m})^{-m} + (1-S_e^\frac{1}{m})^m - 2 \right)$

where:

$S_e = \frac{S-S_r}{S_s-S_r}$

and S is the saturation (or moisture content).

In common usage, the m parameter is replaced with an n parameter so that $$m=1-\tfrac{1}{n}$$. This function supports either parameter.

Parameters
• n (float, optional) – n parameter in the Van Genuchten model. Must be >1. You must pass either n or m (but not both).

• m (float, optional) – m parameter in the Van Genucthen model. Must be strictly between 0 and 1. You must pass either n or m (but not both).

• l (float, optional) – Pore connectivity parameter. The default is 0.5. Must be strictly between 0 and 1.

• alpha (float, optional) – $$\alpha$$ parameter of the Van Genucthen model. The default is 1. Must be positive.

• Ks (float, optional) – $$K_s$$, the hydraulic conductivity when saturated. The default is 1. Must be positive.

• S_range ((float, float), optional) – the tuple ($$S_r$$, $$S_s$$), where $$S_r$$ is the minimum (or residual) saturation and $$S_s$$ the maximum saturation. The default is (0, 1). $$S_s$$ must be greater than $$S_r$$.

Returns

D – Twice-differentiable function that maps values of S in the open interval ($$S_r$$, $$S_s$$) to positive values. It can be called as D(S) to evaluate it at S. It can also be called as D(S, n) with n equal to 1 or 2, in which case the first n derivatives of the function evaluated at the same S are included (in order) as additional return values. While mathematically a scalar function, D operates in a vectorized fashion with the same semantics when S is a numpy.ndarray.

Return type

callable

Notes

The expression used is the one found in Van Genuchten’s original paper [1], but with the addition of the optional l parameter.

References

[1] VAN GENUCHTEN, M. Th. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil science society of America journal, 1980, vol. 44, no 5, p. 892-898.