Table 5.

Different wetting pattern models for sub-surface drip irrigation.

S. No.	Model(s)	Model equation	Parameters used
1.	Philip [70]	$R_s=\left[\frac{2Q}{8\pi {\mathrm{\Phi }}_0+\alpha Q}\right]$	Emitter flow rate, saturated hydraulic conductivity, and soil matric potential.
2.	Warrick [55])	$R_0=\frac{4}{\alpha }\exp \left[-\left(\frac{2\pi K_s}{\alpha .q}\right)-\gamma \right]$	Saturated bulb under steady-state conditions from a quasi-Emitter flow rate and saturated hydraulic conductivity.
3.	Shani and Or [71]	$R_e=\left[\frac{2Q\alpha }{8\pi K_s\left(\alpha P+1\right)+{\alpha }^{2}Q}\right]$	Saturated bulb under steady-state conditions from a quasi-Emitter flow rate, saturated hydraulic conductivity, and Soil water pressure head at the source.
4.	Singh et al. [36]	$\mathrm{W}={3.27\mathrm{V}}^{0.44}{\left(\frac{\mathrm{K}}{\mathrm{q}.\mathrm{z}}\right)}^{-0.06}$ $\mathrm{Z}={3.86\mathrm{V}}^{0.31}{\left(\frac{\mathrm{K}}{\mathrm{q}.\mathrm{z}}\right)}^{-0.19}$	Emitter flow rate, the total volume of water applied, and hydraulic conductivity of soil and emitter installation depth.
5.	Aldhfees et al. [72]	$\mathrm{Z}={11.7\mathrm{V}}^{0.63}{\left(\frac{\mathrm{K}}{\mathrm{q}}\right)}^{0.45}$	Emitter flow rate, the total volume of water applied, and Saturated hydraulic conductivity
6.	Kandelous et al. [73]	$\mathrm{W}={4.244\mathrm{V}}^{0.526}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}.\mathrm{z}}\right)}^{-0.026}$ ${\mathrm{Z}}_{+}={0.72\mathrm{V}}^{0.344}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}.\mathrm{z}}\right)}^{-0.156}$ ${\mathrm{Z}}_{-}={0.66\mathrm{V}}^{0.333}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}.\mathrm{z}}\right)}^{-0.167}$	Emitter flow rate, the total volume of water applied, Saturated hydraulic conductivity, and emitter installation depth.
7.	Phull and Babar [32]	$\mathrm{W}=3.245\left(\frac{{\mathrm{q}}^{0.5}{\mathrm{z}}^{0.065}{\mathrm{t}}^{0.435}}{{\mathrm{K}}_{\mathrm{s}}^{0.065}}\right)$ $\mathrm{Z}=3.572\left(\frac{{\mathrm{q}}^{0.5}{\mathrm{z}}^{0.177}{\mathrm{t}}^{0.323}}{{\mathrm{K}}_{\mathrm{s}}^{0.177}}\right)$	Emitter flow rate, time duration of irrigation, Saturated hydraulic conductivity, and emitter installation depth.
8.	Liu et al. [74]	a. For the bulk density of 0.15 $\mathrm{W}={0.379\mathrm{V}}^{0.616}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}{\mathrm{\theta }}_{\mathrm{i}}}{\mathrm{q}.\mathrm{z}}\right)}^{0.283}$ $\mathrm{Z}={2.726\mathrm{V}}^{0.216}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}{\mathrm{\theta }}_{\mathrm{i}}}{\mathrm{q}.\mathrm{z}}\right)}^{-0.117}$ b. For the bulk density of 0.184 $\mathrm{W}={0.151\mathrm{V}}^{1.012}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}{\mathrm{\theta }}_{\mathrm{i}}}{\mathrm{q}.\mathrm{z}}\right)}^{0679}$ $\mathrm{Z}={2.957\mathrm{V}}^{0.277}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}{\mathrm{\theta }}_{\mathrm{i}}}{\mathrm{q}.\mathrm{z}}\right)}^{-0.056}$	Emitter flow rate, Total volume of applied water, initial soil moisture content, Saturated hydraulic conductivity, and emitter installation depth.
9.	Rasheed and Abid [75]	a. For sandy soil $W=7.599t^{0.471}{K_{se}}^{0.433}{L}^{0.354}{h}^{0.335}{\theta }^{0.099}$ $Z=16.891t^{0.396}{K_{se}}^{0.275}{L}^{0.521}{h}^{0.208}{\theta }^{0.108}$ b. For sandy Loam $W=6.301t^{0.481}{K_{se}}^{0.290}{L}^{0.314}{h}^{0.341}{\theta }^{0.137}$ $Z=13.493t^{0.229}{K_{se}}^{0.126}{L}^{0.470}{h}^{0.123}{\theta }^{0.086}$	Pressure head, saturated hydraulic conductivity, time duration of irrigation, soil moisture content, and length of ceramic pipe.
10.	Abid and Abid [76]	a. For 14.59 lph $W=22.4256t^{0.4551}{q}^{0.3318}{{\theta }_i}^{0.1284}{z}^{0.02}$ $Z=22.1315t^{0.4635}{q}^{0.3628}{{\theta }_i}^{0.1323}{z}^{0.0666}$ b. For 4.42 lph $W=22.2614t^{0.4722}{q}^{0.3515}{{\theta }_i}^{0.1644}{z}^{-0.0023}$ $Z=22.1775t^{0.4377}{q}^{0.3443}{{\theta }_i}^{0.1445}{z}^{0.0078}$ c. For 4.42 lph $W=10.8094t^{0.4552}{q}^{0.1404}{{\theta }_i}^{0.3479}{z}^{-0.2377}$ $Z=10.1302t^{0.4143}{q}^{0.1359}{{\theta }_i}^{0.2819}{z}^{0.2309}$	Emitter flow rate, time duration of irrigation, initial soil moisture content, and emitter installation depth.
11.	Zandi et al. [77]	a. Silty clay loam $w=2.9158v^{0.4366}{z}^{0.4366}{\left(\frac{k}{q}\right)}^{0.3732}$ $Z_{+}=1.358V^{0.5033}{z}^{0.5033}{\left(\frac{k}{q}\right)}^{0.5066}$ $Z_{-}=3.358V^{0.7063}{z}^{0.7063}{\left(\frac{k}{q}\right)}^{0.9126}$ b. Sand $w=1.596v^{0.3006}{z}^{0.3006}{\left(\frac{k}{q}\right)}^{0.1012}$ $Z_{+}=1.358V^{0.2179}{z}^{0.2179}{\left(\frac{k}{q}\right)}^{-0.0642}$ $Z_{-}=2.1596V^{0.47923}{z}^{0.47923}{\left(\frac{k}{q}\right)}^{0.4584}$ c. Loam $w=1.751v^{0.322}{z}^{0.322}{\left(\frac{k}{q}\right)}^{0.164}$ $Z_{+}=0.8879V^{0.3083}{z}^{0.3083}{\left(\frac{k}{q}\right)}^{0.1166}$ $Z_{-}=1.482V^{0.4247}{z}^{0.4247}{\left(\frac{k}{q}\right)}^{0.3546}$	Emitter flow rate, the total volume of water applied, and hydraulic conductivity of soil and emitter installation depth.