Experimental procedure
To observe the soil moisture flow in DI system under different conditions, experiments were carried out in the Water Resources Engineering Laboratory of Civil Engineering Department at NIT Patna, India, during January 2022. Experimental setup presented in Fig 1 consists of a rectangular box with length, width and height 1, 0.6 and 0.75 m, respectively. The front side of the box consists of a transparent glass. To prevent the preferential flow, the glass surface was roughened by applying glue and spraying a coarse sand over it by preserving the transparency of glass (
Kandelous and Simunek, 2010). Water was supplied from the storage tank and pumped with the help of a motor through the low-density polyethylene pipes. Constant pressure was maintained in the laterals throughout the irrigation supply. Valves were used to regulate the discharge to the experimental setup and additional water was diverted back to the tank. Emitter was placed at the center of the length and near to the transparent face of box.
The soil was collected from the field of NIT Patna and dried for 48 hrs to attain uniform moisture content. It was sieved through 2 mm size sieve to avoid lumps, stones and gravels. Soil texture was sandy loam and characteristics of soil are presented in Table 1. Fig 2 presents soil water retention curve, which was obtained using pressure plate apparatus in the above lab for the pressures between 0.1 to 15 bar. Parameters of van Genuchten characteristic curve (α, n) were computed using MATLAB and values are presented in Table 1. Soil was placed in the experimental setup with known bulk density. The initial moisture content was noted.
Three sets of experiment were conducted with different discharge rates 0.5, 0.85 and 2 lph for 20, 12, 5 hrs irrigation period, respectively to supply total 10 litres of irrigation in all sets. Wetting pattern of the soil was marked at regular intervals of time for 48 hrs.
Numerical procedure
The essential aspect in the design of DI is soil wetting pattern, which depends on the discharge rate, frequency, soil characteristics, plant characteristics, spacing of laterals and emitters
(Prajapat et al., 2020).
Governing equations
The soil moisture movement in the unsaturated zone is assumed as 1-D transient flow in vertical direction assuming incompressible fluid and isotropic incompressible porous medium,
i.e., the mixed form of 1-D RE,
Where,
θ = Moisture content (cm
3/cm
3).
Ψ = Pressure/suction head (cm).
K(Ψ) = Unsaturated hydraulic conductivity (cm/sec).
z = Vertical distance.
t = Time (sec).
Soil moisture characteristic equations of
Haverkamp et al. (1977) and
Van Genuchten, (1980) equations have been used.
Haverkamp equation:
Van Genuchten equation:
![](data:image/png;base64,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)
Where,
K
s = Saturated hydraulic conductivity (cm/sec).
Ψ = Suction head (cm).
θ(Ψ) = Moisture content depends on the pressure head (cm
3/cm
3).
θ
s = Saturated moisture content (cm
3/cm
3).
θ
r = Residual moisture content (cm
3/cm
3).
A, B, a, b = Haverkamp parameters.
α, m, n,
l = Van Genuchten parameters.
S
e = Effective water content.
Numerical solution
Governing equation is a non-linear partial differential equation and solved using fully implicit finite-difference scheme with appropriate initial and boundary conditions (BC). The subsurface flow domain is divided into a soil column of rectangular blocks with node size, Dz in vertical direction and specifying moisture content, q and pressure head, y at the centre of the block (node). In contrast, the flow velocity is defined at the interblock faces, as shown in Fig 3.
The finite-difference form of Eq. (1) is
Where,
superscripts ‘n’ = Known time level.
‘n+1’ = Unknown time level.
subscript ‘j’ = Block number in the z-direction.
V = The time-averaged value of the velocity.
Δt and Δz = Time spacing and nodal spacing in z-direction, respectively.
The time-averaged velocity is given as:
![](data:image/png;base64,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)
Where,
w = Time weighting factor.
w = 1.0 for a fully implicit scheme.
Velocity at any interblock was computed using the pressure heads at the adjoining nodes
Where,
K
II= Unsaturated hydraulic conductivity at interblock face II.
K
IV= Unsaturated hydraulic conductivity at interblock face IV.
The unsaturated hydraulic conductivity at the interblock face was computed using weighted arithmetic mean of unsaturated hydraulic conductivity at the adjoining nodes
i.e.,
![](data:image/png;base64,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)
By substituting Eqs. (9) to (13) in Eq. (8)
![](data:image/png;base64,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)
The residual equation [
i.e., Eq. (14)] is represented as
![](data:image/png;base64,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)
, which was written for all the nodes in the flow domain that results in a set of highly non-linear simultaneous algebraic equations in the unknown
![](data:image/png;base64,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)
. These equations were solved using an iteration method, Newton-Raphson technique, which was written for all the nodes by considering upper and lower boundary conditions. These equations form a tridiagonal matrix, which was solved using successive over Relaxation (SOR) method. At each iteration, new hydraulic parameters are simulated and solved to obtain the soil suction head and moisture content at all the nodes in flow domain. The iterative process will continue until all nodes reach a reasonable convergence (0.001). This process is repeated for all the time steps upto simulation time. Flow chart of the numerical solution is presented in Fig 4.
Initial condition
Initial moisture content, θ
ini was specified at all the nodes and corresponding values of Ψ and K(Ψ) were computed using soil moisture characteristic equations.
θ = θ
ini for 0<z<zmax
Boundary conditions
No flow was considered in lateral directions. The upper BC and lower BC have been applied at the top face of the first block and last block’s lower face, respectively. Upper BC was considered as the constant flux during irrigation period and no flux during no irrigation period. Lower BC was considered as free drainage.
Upper BC during irrigation
![](data:image/png;base64,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)
Where
q = Constant flux (cm/hr).
Q = Emitter discharge (cm
3/hr).
A = Surface area (cm
2).
Upper BC during no irrigation
Lower BC
Statistical evaluation
Statistical indices - root mean square error (RMSE), coefficient of determination (R
2) and Percentage Bias (PBIAS) between the depths of wetting fronts of experiments and present model at different times have been computed. Better model should have lower RMSE values, R
2 values near to 1 and smaller PBIAS values (
Ranjan and Singh, 2022).
Where,
X = Observed value of the present model.
Y = Observed value from experimental models.
n = Total number of observations.
i = 1, 2, 3,…n.