Table 4.

Different wetting pattern models for surface drip irrigation.

S. No.	Model(s)	Model equation	Parameters used
1.	Ben-Asher et al. [54]	$\mathrm{R}={\left(\frac{3\mathrm{q}\mathrm{t}}{\Delta \mathrm{\theta }}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.},\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\Delta \mathrm{\theta }=\frac{{\mathrm{\theta }}_{\mathrm{s}}}{2}$	Emitter flow rate, time duration of irrigation, and average change of soil moisture content.
2.	Schwartzman and Zur [52]	$\mathrm{W}={1.28\mathrm{V}}^{0.22}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}}\right)}^{-0.17}$ $\mathrm{Z}={2.54\mathrm{V}}^{0.63}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}}\right)}^{0.45}$	Emitter flow rate, the total volume of water applied, and Saturated hydraulic conductivity.
3.	Warrick [55]	${\mathrm{V}}_{\mathrm{s}}=7.83{\mathrm{V}}^{0.994}$ $\mathrm{W}=2.9{\mathrm{Z}}^{0.652}$	Total added water volume and wetted soil volume.
4.	Zur [53]	${\mathrm{V}}_{\mathrm{S}}=\frac{\mathrm{\pi }}{12}{\mathrm{W}}^2\left[2\mathrm{Z}+\mathrm{h}-\frac{{\mathrm{h}}^3}{{\left(\mathrm{Z}-\mathrm{h}\right)}^2}\right]$	Wetted soil width, depth, and depth between maximal lateral front advance and soil surface level.
5.	Li et al. [56]	$\mathrm{R}=13.85{\left(\mathrm{q}.\mathrm{t}\right)}^{0.29}$ $\mathrm{Z}=8.69{\left(\mathrm{q}.\mathrm{t}\right)}^{0.53}$	The total volume of applied water.
6.	Li et al. [57]	a. Sandy Soil $\mathrm{R}=13.40{\left(\mathrm{q}.\mathrm{t}\right)}^{0.33}\text{,}$ $\mathrm{Z}=12.10{\left(\mathrm{q}.\mathrm{t}\right)}^{0.46}$ b. Loamy Soil $\mathrm{R}=13.60{\left(\mathrm{q}.\mathrm{t}\right)}^{0.29}\text{,}$ $\mathrm{Z}=10.10{\left(\mathrm{q}.\mathrm{t}\right)}^{0.44}$	The total volume of applied water.
7.	Ekhmaj et al. [27]	a. For 3 l h−1, $\mathrm{R}=0.89{\mathrm{V}}^{0.29}$ b. For 5.616 l h−1, $\mathrm{R}=0.91{\mathrm{V}}^{0.28}$ c. For 6.984 l h−1, $\mathrm{R}=0.88{\mathrm{V}}^{0.29}$ d. For any rate (l h−1), $\mathrm{R}=0.90{\mathrm{V}}^{0.28}$	Flow rate and total volume of applied water.
8.	Amin and Ekhmaj [58]	$\mathrm{R}={\Delta \mathrm{\theta }}^{-0.5626}{\mathrm{V}}^{0.2686}{\mathrm{q}}^{-0.0028}{{\mathrm{K}}_{\mathrm{s}}}^{-0.0344}$ $\mathrm{Z}={\Delta \mathrm{\theta }}^{-0.383}{\mathrm{V}}^{0.365}{\mathrm{q}}^{-0.101}{{\mathrm{K}}_{\mathrm{s}}}^{0.195}$	The average change in volumetric water content within the wetted zone, the total volume of applied water, emitter flow rate, and saturated soil hydraulic conductivity.
9.	Acar et al. [59]	$\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\left(\mathrm{z}+\mathrm{h}\right)}^2}{{\mathrm{b}}^2}=1$ $\mathrm{x}=\pm \frac{\mathrm{a}}{\mathrm{b}}\sqrt{{\mathrm{b}}^2-{\left(\mathrm{z}+\mathrm{h}\right)}^2}$ ${\mathrm{V}}_{\mathrm{o}\mathrm{z}}=\frac{{\mathrm{a}}^2\mathrm{\pi }}{{3\mathrm{b}}^2}\left(\mathrm{b}+\mathrm{h}\right)\left({2\mathrm{b}}^2-{\mathrm{h}}^2+\mathrm{h}\mathrm{b}\right)$	Wetted soil volume, maximal lateral wetting front advance, depth between maximal lateral wetting front advance and vertical wetting front advance, and depth between maximal lateral front advance and soil surface level.
10.	Ainechee et al. [22]	a. Sandy soil $\mathrm{W}=5.32{\mathrm{V}}^{0.21}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}}\right)}^{0.185}$ $Z=8.04{\mathrm{V}}^{0.59}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}}\right)}^{0.385}$ b. Loam soil $\mathrm{W}=2.21{\mathrm{V}}^{0.75}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}}\right)}^{0.625}$ $Z=2.23{\mathrm{V}}^{0.52}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}}\right)}^{0.28}$ c. Silty clay loam soil $\mathrm{W}=3.25{\mathrm{V}}^{0.48}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}}\right)}^{0.22}$ $Z=4.06{\mathrm{V}}^{0.74}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}}\right)}^{0.61}$	Emitter flow rate, the total volume of water applied, and Saturated hydraulic conductivity.
11.	Malek and Peters [60]	$\mathrm{R}={\mathrm{q}}^{0.543}{{\mathrm{K}}_{\mathrm{s}}}^{0.772}{\mathrm{t}}^{0.419}{\Delta \mathrm{\theta }}^{-0.687}{{\mathrm{\rho }}_{\mathrm{b}}}^{0.305}$ $\mathrm{Z}={\mathrm{q}}^{0.398}{{\mathrm{K}}_{\mathrm{s}}}^{0.208}{\mathrm{t}}^{0.476}{\Delta \mathrm{\theta }}^{-1.253}{{\mathrm{\rho }}_{\mathrm{b}}}^{0.445}$	Emitter flow rate, saturated hydraulic conductivity, time duration of irrigation, the average change in volumetric water content within the wetted zone, and bulk density of soil.
12.	Molavi et al. [30]	a. For 2 l h−1 $\mathrm{W}=4.5327{{\mathrm{K}}_{\mathrm{s}}}^{0.03765}{\mathrm{t}}^{0.5187}$ b. For 4 l h−1 $\mathrm{W}=1.9038{{\mathrm{K}}_{\mathrm{s}}}^{–0.1282,}{\mathrm{t}}^{0.58248}$	Saturated hydraulic conductivity and time duration of irrigation.
13.	Samadianfard et al. [61]	$\mathrm{R}=20.6+\left[\left(29.4{\mathrm{\theta }}_{\mathrm{r}}\right)-\left(15.7{\mathrm{\theta }}_{\mathrm{s}}\right)-\left(15.7{\mathrm{\theta }}_{\mathrm{i}}\right)-\left(206\mathrm{\alpha }\right)-\left(0.28\mathrm{n}\right)+\left(0.00605{\mathrm{K}}_{\mathrm{s}}\right)+\left(5.4\mathrm{q}\right)+\left(3.36\mathrm{t}\right)\right]$ $\mathrm{Z}=19.2+\left[\left(8.8{\mathrm{\theta }}_{\mathrm{r}}\right)-\left(61.3{\mathrm{\theta }}_{\mathrm{s}}\right)+\left(74.3{\mathrm{\theta }}_{\mathrm{i}}\right)-\left(105\mathrm{\alpha }\right)-\left(6.15\mathrm{n}\right)+\left(0.0744{\mathrm{K}}_{\mathrm{s}}\right)+\left(8.52\mathrm{q}\right)+\left(5.96\mathrm{t}\right)\right]$	Physical properties of soil, emitter flow rate, and duration of irrigation.
14.	Zhang et al. [62]	$\mathrm{W}=14.69{\left(\mathrm{q}.\mathrm{t}\right)}^{0.35}$ $\mathrm{Z}=7.9{\left(\mathrm{q}.\mathrm{t}\right)}^{0.56}$	Emitter flow rate and time duration of irrigation.
15.	Krada and Munjapara [33]	$\mathrm{W}=28.9308{\mathrm{q}}^{0.1283}{\mathrm{t}}^{0.8137}$ $\mathrm{Z}=18.3943{\mathrm{q}}^{0.4996}{\mathrm{t}}^{0.1954}$	Emitter flow rate and time duration of irrigation.
16.	Ismail et al. [63]	a. Continuous flow $\mathrm{W}=0.769{\mathrm{K}}_{\mathrm{s}}^{0.1945}{\mathrm{t}}^{0.463}{\mathrm{q}}^{0.2685}$ $\mathrm{Z}=0.887{\mathrm{K}}_{\mathrm{s}}^{0.6325}{\mathrm{t}}^{0.755}{\mathrm{q}}^{0.1225}$ b. Intermittent flow $\mathrm{W}=1.202{\mathrm{K}}_{\mathrm{s}}^{-0.2}{\mathrm{t}}^{0.2}{\mathrm{q}}^{0.4}{\mathrm{C}\mathrm{R}}^{0.369}$ $\mathrm{Z}=1.183{\mathrm{K}}_{\mathrm{s}}^{0.196}{\mathrm{t}}^{0.465}{\mathrm{q}}^{0.267}{\mathrm{C}\mathrm{R}}^{0.295}$	Saturated hydraulic conductivity, emitter flow rate, and time duration of irrigation.
17.	Naglič et al. [64]	$\mathrm{W}={1.56\mathrm{V}}^{0.29}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}}\right)}^{-0.057}$ $\mathrm{Z}={1.71\mathrm{V}}^{0.41}{\left(\frac{{\mathrm{K}}_{\mathrm{s}}}{\mathrm{q}}\right)}^{0.11}$	Emitter flow rate, the total volume of water applied, and Saturated hydraulic conductivity.
18.	Al-Ogaidi et al. [65]	$\mathrm{R}={7.0916{\mathrm{q}}^{0.2562}\mathrm{t}}^{0.2717}{{\mathrm{K}}_{\mathrm{s}}}^{2.0770}{{\mathrm{\theta }}_{\mathrm{i}}}^{0.1122}{{\mathrm{\rho }}_{\mathrm{b}}}^{-0.2435}{\mathrm{S}}^{-0.1082}{{\mathrm{S}}_{\mathrm{i}}}^{0.0852}{\mathrm{C}}^{-0.1540}$ $\mathrm{Z}={0.4586{\mathrm{q}}^{0.3902}\mathrm{t}}^{0.3249}{{\mathrm{K}}_{\mathrm{s}}}^{6.1919}{{\mathrm{\theta }}_{\mathrm{i}}}^{0.0520}{{\mathrm{\rho }}_{\mathrm{b}}}^{0.0010}{\mathrm{S}}^{-0.0928}{{\mathrm{S}}_{\mathrm{i}}}^{0.2574}{\mathrm{C}}^{-0.2162}$	Emitter flow rate, duration of irrigation, soil bulk density, initial soil moisture content, saturated soil hydraulic conductivity, percentage of sand silt and clay.
19.	Al-Ogaidi et al. [66]	$\mathrm{R}=0.0625{\mathrm{t}}^{0.2562}{\mathrm{q}}^{0.2716}{\mathrm{\rho }}_{\mathrm{b}}^{-0.0255}{\mathrm{\theta }}_{\mathrm{i}}^{0.1112}{\mathrm{K}}_{\mathrm{s}}^{0.335}{\mathrm{S}}^{0.6303}{\mathrm{S}\mathrm{i}}^{0.1222}{\mathrm{C}}^{0.6028}$ $\mathrm{Z}=6.3555{\mathrm{t}}^{0.3903}{\mathrm{q}}^{0.324}{\mathrm{\rho }}_{\mathrm{b}}^{1.8315}{\mathrm{\theta }}_{\mathrm{i}}^{0.0198}{\mathrm{K}}_{\mathrm{s}}^{-0.084}{\mathrm{S}}^{-0.1917}{\mathrm{S}}_{\mathrm{i}}^{0.1105}{\mathrm{C}}^{-0.4265}$	Emitter flow rate, duration of irrigation, soil bulk density, initial soil moisture content, saturated soil hydraulic conductivity, percentage of sand silt and clay.
20.	Al-Ogaidi et al. [67]	a. Homogeneous profiles: $\mathrm{W}\mathrm{P}={{\mathrm{a}}_1\mathrm{t}}^{\mathrm{a}1}{\mathrm{q}}^{\mathrm{a}2}{{\mathrm{\rho }}_{\mathrm{b}}}^{\mathrm{a}3}{{\mathrm{\theta }}_{\mathrm{i}}}^{\mathrm{a}4}{{\mathrm{K}}_{\mathrm{s}}}^{\mathrm{a}5}{\mathrm{S}}^{\mathrm{a}6}{{\mathrm{S}}_{\mathrm{i}}}^{\mathrm{a}7}{\mathrm{C}}^{\mathrm{a}8}$ b. Layered profiles $\mathrm{W}\mathrm{P}={{\mathrm{b}}_1\mathrm{t}}^{\mathrm{b}1}{\mathrm{q}}^{\mathrm{a}2}{\left(\frac{{\mathrm{\rho }}_{\mathrm{b}1}}{{\mathrm{\rho }}_{\mathrm{b}}2}\right)}^{\mathrm{b}3}{\left(\frac{{\mathrm{\theta }}_{\mathrm{i}1}}{{\mathrm{\theta }}_{\mathrm{i}}2}\right)}^{\mathrm{b}4}{\left(\frac{{\mathrm{K}}_{\mathrm{s}1}}{{\mathrm{K}}_{\mathrm{s}2}}\right)}^{\mathrm{b}5}{\left(\frac{{\mathrm{S}}_1}{{\mathrm{S}}_2}\right)}^{\mathrm{b}6}{\left(\frac{{\mathrm{S}}_{\mathrm{i}1}}{{\mathrm{S}}_{\mathrm{i}2}}\right)}^{\mathrm{b}7}{\left(\frac{{\mathrm{C}}_1}{{\mathrm{C}}_2}\right)}^{\mathrm{b}8}$Refer to the original paper for the empirical coefficient.	Emitter flow rate, duration of irrigation, soil bulk density, initial soil moisture content, saturated soil hydraulic conductivity, percentage of sand silt and clay.
21.	Shan et al. [68]	${\mathrm{X}}_{\mathrm{i}\mathrm{f}}=1.77{\mathrm{t}}^{0.6358}\left({\mathrm{t}}_1\le \mathrm{t}\le {\mathrm{t}}_2\right)$ ${\mathrm{X}}_{\mathrm{i}\mathrm{f}}=1.06{\mathrm{Z}}_{\mathrm{i}\mathrm{f}}$	Intersection time of wetting front and final time of wetting front.
22.	Abu-Awwad et al. [69]	$\mathrm{W}\mathrm{A}=\frac{\mathrm{Q}}{\mathrm{I}}$	Emitter flow and infiltration rates at the time soil surface wetted area became almost constant.