Model name Abbreviation Equation Fitting parameters Five parameter models Van Genuchten VG1 $\theta \left(h\right)={\theta }_{r}+\left({\theta }_{s}-{\theta }_{r}\right)/{\left[1+{\left(\alpha h\right)}^{n}\right]}^{m}$ θr, θs, α, n, m Fredlund-Xing FX $\theta \left(h\right)={\theta }_{r}+{\left({\theta }_{s}-{\theta }_{r}\right)/\left[\mathrm{ln}\left[2.7183+{\left(\alpha h\right)}^{n}\right]\right]}^{m}$ θr, θs, α, n, m Omuto Omuto $\theta \left(h\right)={\theta }_{r}+{\theta }_{s1}\ast \mathrm{exp}\left(-{\alpha }_{1}h\right)+{\theta }_{s2}\ast \mathrm{exp}\left(-{\alpha }_{2}h\right)$ θr, θs1, θs2, α1, α2 Four-parameter models Gardner Gard $\theta \left(h\right)={\theta }_{r}+\left({\theta }_{s}-{\theta }_{r}\right)/\left[1+\alpha {h}^{n}\right]$ θr, θs, α, n Brooks-Corey BC $\theta \left(h\right)={\theta }_{r}+\left({\theta }_{s}-{\theta }_{r}\right)/{\left(\alpha h\right)}^{n}$ θr, θs, α, n Kosugi Kosugi $\theta \left(h\right)={\theta }_{r}+\left({\theta }_{s}-{\theta }_{r}\right)Q\left[\mathrm{ln}\left(\alpha h\right)/n\right]$ , Q is complimentary normal distribution function define as $Q\left(h\right)=1-\underset{h}{\overset{\infty }{\int }}\left(\left(\mathrm{exp}\left(-0.5{h}^{2}\right)\right)/\sqrt{2\pi }\right)\text{d}h$ θr, θs, α, n Double exponential Dexpo $\theta \left(h\right)={\theta }_{s1}\ast \mathrm{exp}\left(-{\alpha }_{1}h\right)+{\theta }_{s2}\ast \mathrm{exp}\left(-{\alpha }_{2}h\right)$ θs1, θs2, α1, α2 Van Genuchten VG2 $\theta \left(h\right)={\theta }_{r}+\left({\theta }_{s}-{\theta }_{r}\right)/{\left[1+{\left(\alpha h\right)}^{n}\right]}^{1-1/n}$ θr, θs, α, n Russo Ruso $\theta \left(h\right)={\theta }_{r}+\left({\theta }_{s}-{\theta }_{r}\right)/{\left[\left(1+0.5\ast {\left(\alpha h\right)}^{n}\right)\ast \mathrm{exp}\left(-0.5\ast \left(\alpha h\right)\right)\right]}^{2/\left(n+2\right)}$ θr, θs, α, n Three-parameter models McKee-Bumb MB $\theta \left(h\right)={\theta }_{r}+\left({\theta }_{s}-{\theta }_{r}\right)\ast \mathrm{exp}\left(-\alpha h\right)$ θr, θs, α Campbell Camp $\theta \left(h\right)={\theta }_{s}\ast {\left(\alpha h\right)}^{n}$ θs, α, n Tani Tani $\theta \left(h\right)={\theta }_{r}+\left({\theta }_{s}-{\theta }_{r}\right)\ast \left[1+\left(\alpha h\right)\right]\ast \mathrm{exp}\left(-\alpha h\right)$ θr, θs, α