2nd Generation Row Column Node Appendix references Concept Depends on/ Related to Contribution 2 1 ASTM2,1 [5] Intrinsic Permeability PP1,1 Hydraulic conductivity (K) depends on intrinsic permeability (kintr), according to the implicit function: $\begin{array}{l}K=\left({v}_{z}\right)\ast f\left(\left(\frac{{v}_{z}}{q}\right),\left(\frac{\rho \ast {v}_{z}^{2}}{\psi }\right),\left(\frac{1}{Ri}\right),\left(\frac{1}{Re}\right),\left(\frac{{H}^{2}}{{A}_{inf}}\right),\left(\frac{\rho }{{\rho }_{s}}\right),\left(\frac{{H}^{2}}{{k}_{intr}}\right),\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\text{ }\left(\frac{H}{{v}_{z}\ast t}\right),\left(\frac{{v}_{z}\ast H}{D}\right),\left(\frac{\rho \ast {v}_{z}^{2}\ast H}{\sigma }\right),\Phi ,\theta ,{S}_{e},n,i\right)\end{array}$ The terms, definitions and dimensions of $\left(K,{v}_{z},q,\rho ,\psi ,Ri,Re,H,{A}_{inf},{\rho }_{s},{k}_{intr},t,D,\sigma ,\Phi ,\theta ,{S}_{e},n,i\right)$ are presented in detail in the below terminology (Table A8) of the Appendix. For clarification purposes, (q) refers to infiltration rate, (Φ) is the total porosity, (θ) is the liquid content/soil-water content, (n) is pore size distribution index. Rayleigh’s method of indices was deployed along with the echelon matrix procedure as an additional confirmation method. 2 2 ASTM2,2 [8] Hydraulic conductivity PP1,2 Soil sorptivity (S) depends on hydraulic conductivity (K), according to the implicit function: $\begin{array}{l}S=\left(\frac{z}{{t}^{0.5}}\right)\ast f\left(\left(\frac{z}{q\ast t}\right),\left(Sh\right),\left(Re\right),\left(\frac{\gamma }{\psi \ast z}\right),\left(Ri\right),\left(\frac{t\ast \gamma }{\mu \ast z}\right),\left(\frac{z}{{v}_{z}\ast t}\right),\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\left(\frac{{t}^{2}\ast \gamma }{{\rho }_{s}\ast {z}^{3}}\right),\left(\frac{{z}^{2}}{{k}_{intr}}\right),\left(Sc\right),\left(\frac{z}{H}\right),\left(\frac{z}{{h}_{c}}\right),\Phi ,\theta ,n\right)\end{array}$ Where the terms, definitions and dimensions of $\left(S,z,t,q,Sh,Re,\gamma ,\psi ,Ri,\mu ,{v}_{z},{\rho }_{s},{k}_{intr},Sc,H,{h}_{c},\Phi ,\theta ,n\right)$ are presented in detail in the below terminology (Table A8) of the Appendix. For clarification purposes, (q) refers to infiltration rate, (Φ) is the total porosity, (θ) is the liquid content/soil-water content, (n) is pore size distribution index. Rayleigh’s method of indices was deployed along with the echelon matrix procedure as an additional confirmation method. 2 3 ASTM2,3 [3] Hydraulic Diffusivity ASTM1,3 Soil sorptivity (S) depends on hydraulic diffusivity (D), according to the implicit function: $\begin{array}{l}S=\left(\frac{z}{{t}^{0.5}}\right)\ast f\left(\left(Sh\right),\left(\frac{M}{\rho \ast {z}^{3}}\right),\left(\frac{M}{\psi \ast {t}^{2}\ast z}\right),\left(\frac{z}{g\ast {t}^{2}}\right),\left(\frac{\mu \ast t\ast z}{M}\right),\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\left(\frac{M}{{\rho }_{s}\ast {z}^{3}}\right),\left(\frac{{z}^{2}}{{k}_{intr}}\right),\left(Sc\right),\left(\frac{M}{{t}^{2}\ast \gamma }\right)\right)\end{array}$ Where the terms, definitions and dimensions of $\left(S,z,t,Sh,M,\rho ,\psi ,g,\mu ,{\rho }_{s},{k}_{intr},Sc,\gamma \right)$ are presented in detail in the terminology (Table A8) of the Appendix. For clarification purposes, (M) refers to the initial liquid mass. Rayleigh’s method of indices was deployed along with the echelon matrix procedure as an additional confirmation method. 2 4 PP2,4 [20] Effective liquid saturation ASTM1,4 Hydraulic conductivity (Κ) depends on effective saturation or degree of saturation (Se), according to Van Genuchten-Mualem model [20], (equation 15c, page 23) initially introduced by van Genuchten, 1980 and Mualem, 1976: $K\left(\theta \right)={K}_{s}\ast {S}_{e}^{l}\ast {\left[1-{\left(1-{S}_{e}^{\left(\frac{1}{m}\right)}\right)}^{m}\right]}^{2}$ where the terms, definitions and dimensions of $\left(K\left(\theta \right),{K}_{s},{S}_{e},m\right)$ are presented in detail in the terminology (Table A8) of the Appendix (where $m=1-\frac{1}{n}$ ).