Modeling of Irrigation and
Related Processes with
HYDRUS

Naftali Lazarovitch
Ben-Gurion University of the Negev

Share of freshwater withdrawals by sector

https://www.globalagriculture.org/

Questions to be asked:

Why ?
How ?
How much ?
When ?

Questions to be asked:

Why ?
How ?
How much ?
When ?

DripSprinkler

SurfaceQuestions to be asked:
58
L/Kg

142
L/Kg

Why ?
How ?
How much ?
When ?
Trifonov et al., 2017

“Irrigation” + “HYDRUS” =αn
θsθr

0.06
3.44
131.174.62

van Genuchten, (1980)(θ=(θ s − θ r ) 1 + (αVG h )) +θn −mrαnθsθr

0.036
4.009914
7.61

The objective of this manuscript is to further expand ontheses older reviews and to examine HYDRUS current
modeling abilities to evaluate various irrigation methods
and related processes

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•
•
•
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Water flow: Drip, Sprinkler, Furrow
Solute transport: Fertigation ,Salinity and sodicity, Chemigation
Spatial variability
Optimization
Special irrigation methods

Drip irrigation• Give water (and nutrients) to plants
where they need it and when they need it• Initial cost is high• Salt accumulation

Drip irrigation simulation with HYDRUS

Prescribed boundary fluxes

Surface Drip With Dynamic Wetting

Subsurface Drip Characteristic Functionq (L/T)

Drip irrigation simulation with HYDRUS

Prescribed boundary fluxes

Surface Drip With Dynamic Wetting

Subsurface Drip Characteristic Function

Q (L3/T)Drip irrigation simulation with HYDRUS
q (L/T)
Prescribed boundary fluxes

Q = Q0 ( hin - hs )Surface Drip With Dynamic Wetting

Subsurface Drip Characteristic FunctioncThe radius of the saturated zone as a function of time in various soils

Relative root water uptake as a function of the critical stress index and two rooting depths

0.121 0.124 0.130 0.137 0.143 0.149 0.156 0.163 0.169 0.176 0.182 0.191

Water Content - th[-], Min=0.121, Max=0.191

The spatial distribution of water contents in a three-dimensional
domain (A), an axisymmetric domain (B), and at threeobservation points (5, 15, and 25 cm away from the dripper) as afunction of time (C)-100.000-88.000-82.500-77.000-71.500-66.000-60.500-55.000

Pressure Head - h[cm], Min=-100.000, Max=-37.457-49.500-44.000-38.500-37.457

Sprinkler irrigation

Tobias Oker

Isaya Kisekka• Irrigating crops where the plant population
per unit area is very high• Capital cost is high with greater operationalcosts• Not suitable for soils with low infiltrability

Sprinkler irrigation simulation with HYDRUS

qPrescribed boundary fluxes

RunoffPondingiR

Sprinkler irrigation simulation with HYDRUS

qPrescribed boundary fluxes

RunoffPondinghiRApplication rates of a LEPA bubbler (a) and sprinkler (b), both located 80 mfrom the center of a pivot and applying an irrigation depth of 25.4 mm, withcorresponding infiltration rates for loamy sand and silt loam soils

Cumulative surface runoff of loamy sand, loam, and silty clay loam for irrigation
using a sprinkler and a LEPA bubbler.

(a) Initial and (b) final (t = 24 h) water contents in loamy sand and silt loam soils in theHYDRUS-2D simulation of soil water redistribution following sprinkler irrigation

Loamy sandSilt loam

The soil water content at t = 24 h at distances of 0, 19.1, 38.1, and 76.2 cm
from the edge of the HYDRUS-2D model domain for loamy sand (a) and silt
loam (b) following irrigation with a LEPA bubbler.

Furrow irrigation

Giuseppe Brunetti

Low investment required to buy
equipment
Not suitable for soils with highinfiltrability
Very low efficiency

Furrow irrigation simulation with HYDRUS

Constant / variable pressure head

Reservoir boundary condition

Furrow module (Brunetti et al., 2019)

Furrow irrigation simulation with HYDRUS

Constant / variable pressure head

Reservoir boundary condition

Furrow module (Brunetti et al., 2019)

Furrow irrigation simulation with HYDRUS

Constant / variable pressure head

Reservoir boundary condition

Furrow module (Brunetti et al., 2019)A schematic of the boundary conditions for different soil
surface management scenarios

Simulated distributions of soil water contents at time t=1.5 h at different
locations along the furrow (horizontal direction) for the original (S0), compacted(Sc), and plastic (Sp) scenarios.

Simulated distributions of solute concentration at time t=1.5 h at different locations along thefurrow (horizontal direction) for the original (S0), compacted (Sc), and plastic (Sp) scenarios

Fertigation

Li Yong

Li Xianyue

Salinity and Sodicity

Chemigation

Todd H. Skaggs

Alex Furman∂ ( ρb s + θ c + ag ) ∂  w ∂c  ∂  g ∂g  ∂ ( qi c )=−φ θ Dij
 + aDij −∂t∂xi ∂x j  ∂xi ∂x j ∂xi

Modeling Salinity Using the UnsatChem
Module of HYDRUS-1DHYDRUS, no salinity
HYDRUS, ECiw = 3 dS/m

UNSATCHEM, ECiw ≈ 3 dS/m, chloride
UNSATCHEM, ECiw ≈ 3 dS/m, sulfate

Root uptake density distribution

Rootzone salinity profiles at the midpoint of the growing season for two irrigationlevels (Irr = 0.9 Tp and 1.1 Tp) and three modeling scenarios (the standard
HYDRUS and the UNSATCHEM model with chloride- and sulfate-dominatedwater).

Computed seasonal relative yields (RY) and leaching fractions (LF)
ModelTa/Tp (%)

LF (%)-------- Irr = 0.9 Tp -------HYDRUS, no salinity900

HYDRUS, ECiw = 3 dS/m7714UNSATCHEM, ECiw ≈ 3 dS/m, chloride

79

12

UNSATCHEM, ECiw ≈ 3 dS/m, sulfate

82

8-------- Irr = 1.1 Tp -------HYDRUS, no salinity

100

9

HYDRUS, ECiw = 3 dS/m

88

20

UNSATCHEM, ECiw ≈ 3 dS/m, chloride

90

19

UNSATCHEM, ECiw ≈ 3 dS/m, sulfate

9315

ECiw = irrigation water salinity; Irr = seasonal irrigation; Tp = seasonal potential transpiration

Spatial Variability

Iael Raij-Hoffman Salini SasidharanWater contents (A, B) and water content coefficient of variation (CV) (C, D) in the threeobservation nodes (F) (x = 4.3, y = 6.3 cm; x = 8.5, y = 13.5 cm; x = 13.9, y = 23.7 cm)
during four irrigation events in a loam soil (A and C) and a sandy loam soil (B and D) for
three levels (CV = 2%, 4.4%, and 9%) of irrigation uniformity (E). Irrigation fluxes for threelevels of heterogeneity (E) and the simulation domain with three observation nodes (F).

The flow domain of two-layered systems (the left panel; A:loam with a sandy loamlayer, B: sandy loam with a loam layer) and corresponding soil water content
distributions with time (0–5 days).

Drip lateral
Volcanic ash
SandCloth
GravelIntroduced capillary barrier profile to increase watercontent in the root zone and reduce soil spatial variability

Numerical simulation of water flow0hCapillarybarrier‫מחסום קפילרי‬Control‫ביקורת‬0100cm
0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Numerical simulation of water flow

1h
Capillarybarrier‫מחסום קפילרי‬

0.00

0.05

0.100.15

Control‫ביקורת‬

0.20

0.25

0.300.35

0.400.45

Numerical simulation of water flow

48 hCapillarybarrier‫מחסום קפילרי‬

0.00

0.05

0.10

0.15

Control‫ביקורת‬

0.20

0.25

0.30

0.35

0.400.45

Numerical simulation of water flow

72 hCapillarybarrier‫מחסום קפילרי‬

0.00

0.05

0.10

0.15

Control‫ביקורת‬

0.20

0.25

0.30

0.35

0.40

0.45

Numerical simulation of water flow

120 hCapillarybarrier‫מחסום קפילרי‬

0.00

0.05

0.10

0.15

Control‫ביקורת‬

0.20

0.25

0.30

0.35

0.40

0.45

Numerical simulation of water flow

160 hCapillarybarrier‫מחסום קפילרי‬

0.00

0.05

0.10

0.15Control‫ביקורת‬

0.20

0.25

0.30

0.35

0.40

0.45

Average and 95% confidence intervals for 187 simulations with varying Ks values for loam andsandy loam soils. Water contents at observation points located at depths of 20 cm (vertical) (dripperdepth) and 5 cm (A), 15 cm (B), and 25 cm (C) away (horizontal) from the dripper. Time-dependent
water fluxes at the bottom boundary (D)Model Calibration
Uncertainty Assessment
Sensitivity Analysis
Irrigation Optimization

Giuseppe Brunetti Thomas WohlingModel Calibration

Relative positions and depths of the neutronprobe access tubes and tensiometers

Domínguez-Niño et al. 2020

flow domain and boundary conditions
used in the HYDRUS-3D simulations

Triggered irrigation

Ta / Tp

256 soils with different hydraulic properties
Uniform irrigation for all columns triggered
from average of n sensors

Irrigation

123

Number of sensors

Number of sensors

ANN as an approximator of flow and transport system
Same properties in all simulations:
Processes: Water flow, Solute transport, Root water uptake
Soil Depth: 200 cm
Simulation duration: 7 days
Observation point depth: 15 cm
Sandy loam soil: θr=0.065, θs=0.41, α=0.075 cm-1, n=1.89, KS=4.421 cm h-1
Root water uptake parameters (Feddes, 1978): P0=0, Popt=-40 cm, P2=-300 cm, P3=-1000 cm
Solute stress (van Genuchten, 1987): EC50=4 dSm-1, P=3
Field capacity initial condition: h=-73 cm
Root Distribution (Vrugt et al., 2001): Zmax =80 cm, Z*=20 cm, Pz =2

2080 unique simulations:
5 Potential transpiration: 1.4, 2.8, 4.2, 5.8, 7 cm
13 hcrit=-1000, -769, -591, -455, -350, -269, -207, -159, -122, -94, -72, -55, -42 cm
8 Irrigation EC = 0.2, 1, 2, 3, 4, 5, 6, 7 dS m-1
4 Irrigation Rate (cm h-1), Irrigation duration (h), Lag (h)= 2,1,1; 1.333,1.5,1; 0.625,3.2,1;
0.4,5,1]

Network Architecture Options
Number of Inputs (5): Potential transpiration, hcrit, Irrigation EC, Irrigation Rate, Irrigation
duration
Number of Outputs (one each time): Irrigation, Transpiration
Number of Hidden Layers: 2Hidden Layer sizes (20): Hidden 1 (15) Hidden 2 (15)Training Options
Total #rows in your data: 2000
No. of Training cycles: 150
Validation set: Randomly select, 15% of data as Validation setETp
Ctop
Irrigation flux
Irrigation duration
Desired relative irrigation

Irrigation
Transpiration
Relative transpiration
Relative irrigation
hcrit

θcrit

Input
cm

2dSm
-1
cmhh-

2
12
1

Outputcm
cmcm
cm3 cm-3

1.52
1.52
0.76
1.00
-136.45-1

0.108

3Trigger irrigation of 2 cm when soil water content is lower than: 0.108 cm cm

Solve!

-3

ETp
Ctop
Irrigation flux
Irrigation duration
Desired relative irrigation

Irrigation
Transpiration
Relative transpiration
Relative irrigation
hcritθcrit

Input
cmdSm-1
cmh-1
h-Output
cmcm
cm
cm3 cm-3

7
2

Trigger irrigation of 2 cm when soil water content is lower than: 0.125 cm3 cm-3

1
2
1

5.19
5.19
0.74
1.00
-93.050.125

Solve!

Special Irrigation Methods

Pitcher irrigation and the axisymmetric finite
element mesh diagram to simulate water
infiltration from a buried pitcher

Pitcher irrigationSimulated wetting of initially dry loam soil under pitcher irrigation
for differing pitcher wall saturated hydraulic conductivities

Summary and Outlook• HYDRUS can help design irrigation systems and determine theoptimal irrigation and fertilization regimes• Computational power• Using emulators to perform computationally intensive tasks• HYDRUS ability to simulate crop growth is still relatively limited• Dynamic soil hydraulic and solute transport parameters• The progress in sensing the agricultural field is limited

Summary and Outlook• HYDRUS can help design irrigation systems and determine theoptimal irrigation and fertilization regimes• Computational power• Using emulators to perform computationally intensive tasks• HYDRUS ability to simulate crop growth is still relatively limited• Dynamic soil hydraulic and solute transport parameters• The progress in sensing the agricultural field is limited

Summary and Outlook• HYDRUS can help design irrigation systems and determine theoptimal irrigation and fertilization regimes• Computational power• Using emulators to perform computationally intensive tasks• HYDRUS ability to simulate crop growth is still relatively limited• Dynamic soil hydraulic and solute transport parameters• The progress in sensing the agricultural field is limited

Summary and Outlook• HYDRUS can help design irrigation systems and determine theoptimal irrigation and fertilization regimes• Computational power• Using emulators to perform computationally intensive tasks• HYDRUS ability to simulate crop growth is still relatively limited• Dynamic soil hydraulic and solute transport parameters• The progress in sensing the agricultural field is limited

Summary and Outlook• HYDRUS can help design irrigation systems and determine theoptimal irrigation and fertilization regimes• Computational power• Using emulators to perform computationally intensive tasks• HYDRUS ability to simulate crop growth is still relatively limited• Dynamic soil hydraulic and solute transport parameters• The progress in sensing the agricultural field is limited

Summary and Outlook• HYDRUS can help design irrigation systems and determine theoptimal irrigation and fertilization regimes• Computational power• Using emulators to perform computationally intensive tasks• HYDRUS ability to simulate crop growth is still relatively limited• Dynamic soil hydraulic and solute transport parameters• The progress in sensing the agricultural field is limited

Thank you!