Unit in SWRC Fit

In SWRC Fit, any unit can be used as the input data, and the unit of the calculated parameters depend on the unit of the input data.

Unit of h

Unit of pressure head (matric head, matric suction) is cm H₂O in the sample data of UNSODA. Other unit such as kPa for matric potential can also be used for h. Conversion of matric potential ψ in kPa to matric head h in cm H₂O: Let ρ_w (density of water) = 10³ kg m^-3 and g = 9.8 m s^-2. Then as 10³ψ = 10^-2hgρ_w = 98h, ψ = 0.098 h.

Following parameters has the unit as same as h; h_b in BC model, h_m in KO model, a in FX model, and corresponding parameters in bimodal models, hb₁, hb₂, hm₁, hm₂, and H. If h is in cm, unit of these parameters are also in cm.

α in VG model has the unit inverse to h. If h is in cm, unit of α is 1/cm or cm^-1. Same to corresponding parameters in bimodal models, α₁ and α₂.

Unit of θ

Unit of θ is dimensionless or expressed cm³ cm^-3. θ_s and θ_r has the same unit with θ.

When you have gravimetric water content w, θ is obtained with the relationship \(\theta = w\frac{\rho_b}{\rho_w}\) where ρ_b is bulk density and ρ_w is the density of water. Therefore if you have data of bulk density you can convert your data to volumentric water content. You can also directly use (h, w) relationship. In this case θ_s becomes w_s, gravimetric saturated water content, and θ_r becomes w_r, gravimetric residual water content.

Similarly, when you have degree of saturation S_r, θ is obtained by \(\theta = \frac{e}{1+e} S_r\) where e is porosity.

Definitions in these terms are summarized.

• θ (Volumetric water content) = V_w / V
• w (Gravimetric water content) = M_w / M_s
• ρ_b (Bulk density) = M_s / V
• ρ_w (Density of water) = M_w / V_w
• S_r (Degree of saturation) = V_w / (V_a + V_w)
• e (Porosity) = (V_a + V_w) / V_s

• M_w = Water mass
• M_s = Dry soil mass
• V_w = Volume of water
• V_a = Volume of air
• V = Total volume

Units of other parameters

Units of other parameters used in SWRC Fit are dimensionless; λ in BC model, n in VG model, σ in KO model, m, n in FX model, λ₁, λ₂, n₁, n₂, σ₁ and σ₂ in bimodal models.

Persistent URL of this page is http://purl.org/net/swrc/unit.html.

Author: Katsutoshi Seki