(k_th), (k_th(s)), (k_th(w))

Heat transfer coefficient/coefficient of convection the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat (i.e., the temperature difference, ΔT). (_s) denotes the coefficient of the bulk soil and (_w) denotes “as regards the water”

[M∙T^−2.5∙Θ⁻¹]

(l)

Pore connectivity empirical parameter of Mualem’s equation with the value 0.5 commonly used defined ad hoc by Di Prima, 2016 as given in [20] and by (Oh et al., 2015) as given in [34]

[1]

(LE)

Latent heat defined as the flux of heat from the Earth’s surface to the atmosphere and is associated with evaporation or transpiration

[M∙T⁻³]

(M)

Initial liquid mass defined as the mass of our interest before the progress of a physical phenomenon

[M]

(M_s)

Soil mass/Mass of the bulk soil of our interest (control mass)

[M]

(m)

Parameter defined ad hoc by (Liu, et al., 2014) as given in [30]

[1]

(m)

Calculated value defined ad hoc by Di Prima, 2016 as the equal of the numerical quantity 1-(1/n) as given in [20], (eq. 15b)

[1]

(𝓃)

Shape parameter defined ad hoc by Xu et al., 2012 as given in [46]

[1]

(n)

Pore size distribution index defined ad hoc by Mualem, 1976 & Van Genuchten, 1980 as given in [32] & [42]

[1]

(n)

Parameter defined ad hoc by Liu, et al., 2014 as given in [30]

[M⁻¹∙L∙T²]

(p)

Matric suction defined ad hoc by Oh et al., 2015 as the pressure difference between the air and the water in soil pores [34]

[L]

(P_c)

Capillary pressure defined as the difference in pressure across the interface between two immiscible fluid phases jointly occupying the interstices of a porous medium caused by interfacial tension between the two phases American Geosciences Institute—AGI, Glossary of Geology, as given in [48]

[M∙L⁻¹∙T⁻²]

q(t), (q)

Infiltration rate defined as the volume flux of water entering through a unit soil surface area. Alternative symbols (f), i(t)

[L∙T⁻¹]

(q_H)

Heat flux/heat transfer rate defined ad hoc by Wang & Bou-Zeid, 2012, as given in [45]

[Μ∙L²∙Τ⁻³]

(r)

Average pore space defined as the average space diameter among soil particles

[L]

(r)

Radius of natural pores defined as the radius of, for simplicity purposes, spherical shaped pores

[L]

(Re)

Reynolds number, where $Re=\frac{{\rho }_w\ast v_z\ast z}{\mu }$ introduced by Sommerfeld, 1909, as given in [40]

[1]

(Ri)

Richardson number, where $Ri=\frac{g\ast z}{v_z^2}$ dimensionless quantity in fluid mechanics

[1]

(R_n)

Net radiation see Heat flux/heat transfer rate/defined as the radiative flux transported towards the earth’s surface

[M∙T⁻³]

(s)

Liquid saturation defined as the volume of the liquid phase per unit void volume in the packed column

[1]

(S)

Sorptivity/soil sorptivity defined ad hoc by Philips, 1957 as the measure of the capacity of the medium to absorb or desorb liquid by capillarity, as given in [36]

[L∙T^−0.5]

(Sc)

Schmidt number, where $Sc=\frac{\mu }{\rho \ast D}$ dimensionless quantity in fluids mechanics

[1]

(S_e)

Effective saturation/Degree of saturation/Percent saturation/Normalize water content terms used equally, defined as the ratio expressed as a percentage of the volume of water to the total volume of intergranular space (voids) in a given porous medium regarding Van Genuchten, 1980, as given in [42]. Alternative symbol (Θ)

[1]

(S_o)

Sorptivity in state (_o) as regards Haverkamp, 1994 equation, as given in [24]

[L∙T^−0.5]

(Sh)

Sherwood number, where $Sh=\frac{K\ast z}{D}$ dimensionless quantity in diffusion mass transport

[1]

(S_max)

Maximum Sorptivity defined as the maximum capacity of a medium (dry state) to absorb or desorb liquid by capillarity

[L∙T^−0.5]