Agronomic irrigation design and scheduling

Shmulik FriedmanDepartment of Environmental Physics and Irrigation, Institute of Soil, Water and Environmental

Sciences (ARO), The Volcani Center, Rishon LeZion 7505101, Israel, vwsfried@agri.gov.il

Workshop on “The future of water for irrigation in California and Israel”Davis CA, July 16th, 2018

http:/app.agri.gov.il/didas

General design of drip irrigation

Dripper configurationDripper depths

Irrigation scheduling

Daily irrigation dose

Dripper discharge rate

profit = income – total costs

Daily irrigation dose

Yield

income

system costenergy cost

water costenergy cost

total costs

waterother factors

plantsoil

climate

plantsoil

climate

plant climate salinity

system costenergy costadditional costs

plantsoil

control

Brief introduction to agronomic irrigation design and scheduling Main principles of the DIDAS approachCoupled source-sink model for water uptake evaluation

Steady-state water flow and uptake module (for system design):Single emitter-root zone pairArrays of emitters and root zonesSubsurface drip irrigation(Yield – Plant Population Density relationship in sprinkler irrigation)

(Quasi steady-state water flow and uptake module)

Unsteady water flow and uptake module (for irrigation scheduling)Morning and all-day-long daily irrigationsEvery-few-days irrigations

Soil salinity module (for salinity management)

The DIDAS program – will be demonstrated briefly in the poster session

In this lecture:

Design and Scheduling of Drip Irrigation Systems•Distance between emitters along a drip line •Distance between drip lines•Depth of subsurface emitters•Emitter discharge rate•Irrigation frequency•Starting hour•Duration of irrigation •Daily irrigation dose

Drip (Trickle) Irrigation

on-surface sub-surface

annual crops

trees high pressure

low pressure

DIDAS- A New Approach and User-Friendly Software Package for

Assisting Drip Irrigation Design And Scheduling

Gregory Communar, Alon Gamliel and Shmulik FriedmanDepartment of Environmental Physics and Irrigation, Institute of Soil, Water and Environmental

Sciences (ARO), The Volcani Center, Rishon LeZion 7505101, Israel

http://app.agri.gov.il/didas

Previous suggestions based on analytical solutions to the water flow problem

Bresler (1978) recommended on using Wooding's (1968) solution for steady infiltration from a circular disk, describing the ponding zone around the emitter, and to determine the combination of emitter discharge and distance between emitters along the dripline according to a criterion of a threshold value

for the capillary pressure at mid-distance between emitters in the soil surface. Limitations of the approach: ignores water uptake; refers to an irrelevant location.

According to another, more realistic approach of Amoozegar-Fard et al. (1984)one should solve the problem of steady water flow from a source assuming a prescribed, constant and a priori known water uptake rate within a rooting zone of simple geometry (e.g. vertical cylinder or 1-D variation with depth), the design criterion being again threshold value for the capillary pressure at any depth within the active root zone midway between emitters. Limitations of the approach: water uptake is assumed to be knownrefers to an irrelevant location.

Previous suggestions based on analytical solutions to the water flow problem

A new approach• The new, proposed approach for the design of a drip

irrigation system is based on a different principle of evaluating the water use efficiency (RWUR ≡ water uptake rate relative to water supply rate) in a source (emitter) – sink (rooting zone) system, so the potential water uptake is not given (/prescribed) but computed.

• The potential (maximum possible) water uptake is evaluated assuming no local soil-plant resistance to uptake. Namely, the plant roots apply maximum possible suction and the water uptake is determined just by the soil’s ability to conduct water from the sources (emitters) to the sinks (rooting zones).

Coupled source-sink model

r0

d0

water source

point sink, qsi

actual sink

potential sink

reference suction point: ϕf = ϕso - qsiϕsi = 0

(uzθ) = -mαϕ(r,0)/2 evaporation:

r

z soil sorptive number: α

( )( )botsi

botsosi ,0

,0ΖΦΖΦ

=q

The RWUR is evaluated from:

α−1 – soil’s capillary lengthr0 – radius of the rooting zonem – potential evaporation

Model assumptionsThe relative water uptake rate will be evaluated with an analytical solution under the following assumptions:• Steady flow (resulting in maximum uptake rate)• A homogenous, isotropic and exponential (Gardner, 1958) soil: K = Ksat e-αh

• Linearization of the flow problem with Kirchoff transformation: • The solution for the water uptake and for the spatial distribution of water contents is a superposition of the fundamental solutions for water infiltration from point or line sources: positive sources representing the emitters and negative sinks representing the root systems• The maximum possible water uptake will be evaluated assuming maximum suction in a volume of rooting zone with a simple geometry (sphere, horizontal cylinder) and given depth and size, the point (/line) sink located in its center.• Evaporation from the soil surface will be assumed proportional to the matrix flux potential, ϕ: (uzθ) = -mαϕ(r,0)/2 (following Lomen and Warrick, 1978)

∫ ∞−=

hKdhϕ

Coupled source-sink model: loam, 2 l/h dripperstream lines, saturation degrees stream lines, hydraulic heads

qsi = 0.62

actual sink

dividing stream line

uptakedeep percolation

α = 0.04 cm-1

0 25 50

75

50

25

0Sf = 1

0.49

0.590.76Hf = -60

z, cm

r, cm0 25 50

-199

-156

-129

-179

-91

Soil 3

r, cmConceived root zone: r0 = 25 cm

Effect of soil typecoarse sand (α = 0.4 cm-1) loam (α = 0.04 cm-1)

75

50

25

0

0.04

0.060.10.17

z, cm

a

Sf = 0.33

So

0 25 50

75

50

25

0Sf = 1

0.49

0.590.76

z, cm

r, cm

So

qsi = 0.62qsi = 0.52

02 =∂∂

−∇zϕαϕ

0 25 50

75

50

25

0

0.37

0.49

Sf = 1

0.67

z, cm

r, cm

Soil

Effect of evaporation from soil surfacewith evaporation (m=2) without evaporation

qsi = 0.62qsi = 0.40;qE = 0.43

uptake deep percolation

evaporation

0 25 50

75

50

25

0Sf = 1

0.49

0.590.76

z, cm

r, cm

So

uzθ = -mαϕ(r,0)/2 qE = m/(m+2)

Determining the values of the 3 parameters: α,r0,m •α−1 – “capillary length” characterizes the soil texture ( K = Ksat e-αh)α- influence of gravitational vs capillary forcesCharacteristic values:

coarse sand: 0.4 cm-1

loamy sand: 0.13 cm-1

loam: 0.04 cm-1

clay: 0.004 cm-1

• r0 – characterizes the extent of the rooting zonecarrot, radish: 10cm, pepper: 15cm, tomato: 25cm; cotton, corn: 50cm

•m – characterizes the potential evaporation (uzθ) = -mαϕ(r,0)/2• a crop that cover the soil surface: m = 0• Overall relative evaporation from on-surface emitters: qE = m/(m+2)

0 1 2 3 4 50.00

0.03

0.06

0.09 cyclical tests

α (c

m-1)

Ks (cm h-1)

Besor experimental station

α(cm) = 0.04035 Ks(cm/h)1/2

Sample Scenarios for drip irrigation

yso = 2 ysi

ysi

xso

xsi = 2xso

f

0.5

0.6

0.7

0.8

0.9

1.0

Coupled line source/sink

YSI=0.5

Coupled point source/sink

1

5432

q si/q

so

a

Plants-emitters along a dripline: emitter near each plant

ysi – distance between emitters, Ysi = αysi/2

Sample computation:pepper: r0 = 15 cmsand: α = 0.1 cm-1

distance between emitters:ysi = 40 cmR0 = αr0/2 = 0.75Ysi = αysi/2 = 2Relative water uptake:⇒ qsi/qso = 0.69

ysi = yso

R0 = αr0/2; D0 = αd0/2 = 0

[ ] [ ]

[ ] [ ]∑

∑Ν

=

Ν

=

ΥΦ+Φ

ΖΥΦ+ΖΦ

=

−

si

si1

10sisi0si

1botsisobotso

si

R,,02R,0,0

,,02,0,0

j

j

j

j

q

ββ

1siso ==ΥΥ β

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5.

Ro

m = 0 (no evaporation)

r0 small (cm) r0 large (cm)clay sand

Additional emitter in between plants

yso

ysi = 2yso

[ ] [ ]

[ ] [ ]∑

∑Ν

=

Ν

=

ΥΦ+Φ

ΖΥΦ+ΖΦ

=

−

si

si1

10sisi0si

1botsisobotso

si

R,,02R,0,0

,,02,0,0

j

j

j

j

q

ββ

5.0siso ==ΥΥ β

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Ro

0.30.40.50.60.70.80.9

1

5432

Ysi = 0.5a

0.5(q

si/qso)

5.0siso ==ΥΥ β

0.00.10.20.30.40.50.60.70.80.91.0

41

(qsi/qso)cent+(qsi/qso)intr

32Ysi = 0.5

43 (qsi/qso)intr

(qsi/qso)cent

a

q si/qso

Additional plant in between emitter

close

distant

closeclose distant

overall

yso = 2 ysi

ysi

=+

=+•

•

2sisi

1sisi

dqaqb

dqbqao

o

( ) [ ]∑Ν

=ΥΦ+Φ=

si

10sisi0si R,2,02R,0,0

jja

( )[ ]∑Ν

=Υ+Φ=

si

00sisi R,12,02

jjb

( ) ( )∑−Ν

=ΖΥΦ+ΖΦ=

1si

1botsisobotso1 ,,02,0,0

ββ

jjd

( )( )∑−Ν

=ΖΥ+Φ=

1si

0botsiso2 ,12,02

β

jjd

2siso ==ΥΥ β

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.50.0

Ro

Watering a plant row with one or two drip lines at different distances(Bell pepper, sandy soil, Besor experimental station, Meiri et al., 2011)

Photographed soil cross sections (perpendicular to the plant row) showing the root distribution in one-sided (top right) and two-sided (top left) irrigation at 0 distance

and one-sided at disatnce of 60 cm (bottom)

Comparison of measured plant growth and predicted RWUR

Measured plant growthEvaluated Relative Water Uptake Rate

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 10 20 30 40 50 60

Pot

entia

l rel

ativ

e w

ater

upt

ake

rate

Driplines distance from plant (cm)

two-side

one-side

a

60

70

80

90

100

110

120

130

140

150

160

0 10 20 30 40 50 60

Pla

nt d

ry w

eigh

t (g/

plan

t)

Driplines distance from plant (cm)

two-side

one-side

b

Sources and sinks offset from the center of a confined rectangular domain

An alternative for using superposition to represent beds with few plant rows and driplines

Y Y

Y Y

-Y -Y

-Y -Y

X X

X X

A A A A

A A A A

B

B

B

B

B B

B

B

B B

B

B

a) 1 source – 1 sink b) 1 source – 2 sinks

c) 2 sources – 1 sink d) 2 sources – 2 sinks

One or Two drip lines per plant rowBell pepper, Besor Experimental Station, 2010

2DL 1DL 2DL 1DL June September

RWUR as a function of root system size for the various scenarios

B = 0.25 ; A/B = 2 B = 0.25 ; A/B = 4

Y Y

Y Y

-Y -Y

-Y -Y

X X

X X

A A A A

A A A A

B

B

B

B

B B

B

B

B B

B

B

a) 1 source – 1 sink b) 1 source – 2 sinks

c) 2 sources – 1 sink d) 2 sources – 2 sinks

1DL

1DL

2DL

2DL

Markers:B = 0.25 ; A/B = ∞

Two extreme scenarios forsub-surface drip irrigation

Early season:rooting zoneabove emitter

Mature stage: rooting zonebellow emitter

r0

zso water source

point sink, qsi

actual sink

potential

reference suction point: ϕf = ϕso - qsiϕsi = 0

soil surface

a

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0 0.1 0.2 0.3 0.4 0.5

q Si/q

so

zso

b) R0 = 2; Ysi = 2

0.00.51.01.52.0

0.70

0.75

0.80

0.85

0.90

0.95

0 0.1 0.2 0.3 0.4 0.5

q Si/q

so

zso

a) R0 = 0.1; Ysi = 0.1

RWUR as function of emitter burial depth (Zso)and potential evaporation (m)

no evaporation m:

Zsi = Zso + R0

no evaporation

strong evaporationstrong evaporation

Plants of small root systems (clayey soil)at small spacing along the drip line

Plants of large root systems (sandy soil)at large spacing along the drip line

Effect of changes in hydraulic conductivityon conduction in the soil profile and local resistance

Relative water uptake rates (qsi/qso) for a rectangular array (120 x 30 cm) and conceived radius ofr0 = 15 cm, in a loam of Ks

0 = 1 cm h-1 (α = 0.04035 cm-1).

ζ = (Ks0/Ks -1)

Φsi/Φso(α)

RWUR = Φsi/Φso∙(1/(1+ζ))

0 1 2 3 4 50.00

0.03

0.06

0.09 cyclical tests

α (c

m-1)

Ks (cm h-1)

water conduction in the soil profile

local resistancewater uptake

α(cm) = 0.04035 Ks(cm/h)1/2

Unsteady (transient) water flow and uptake

0 24 48 72

q so

0 24 48 72

ζ,W

UR

r0

water source, qso

point sink, qsi

actual sink

conceived rooting zone

reference suction point:

ϕf = Σϕso(t) – (qsi/qso)(ϕsi+ξ(t)) = 0 zbot

z∗

tst tst+ttr

W0

t0

soil coefficients: α, β

Daily Irrigation Scenarios

Single morning irrigationContinuous, all day irrigationMultiple pulse irrigations

Transient model predictions of daily water uptake patterns from one-hour and continuous (12h) irrigation in a fine sand

0 6 12 18 240

20

40

60

80

100β = 0

c

1h 12h

WUR

(cm3 h-1

)

Time (h)0 6 12 18 24

β = -0.75 1h 12h

d

Time (h)

α = 0.04 cm-1, Ks = 10 cm h-1, r0= 15 cm, rc= 30 cm, m = 0 (no evaporation)

homogeneous Ks decreasing with depth soilsKs(z) = Ks (0)e-βz

0 6 12 18 240.0

0.2

0.4

0.6

0.8

1.0 one pulse per day ten pulses per day

q si/qso

time (h)Assouline et al. 2006

steady flowRelative Water

Uptake Rate

weatherpotential evaporation

soilsorptive length

plantdiameter of root zone

(distance between plants)

distance between

emitters & driplines

aSoil

sat. hydraulic conductivity,

sorptive length, porosity

unsteady flowRelative WaterUptake Volume b

irrigation frequency

water consumption

durationof

irrigation

c

starting hour of irrigation

d

Irrigationdoze

Plant-Weatherdiurnal transpiration

resistance pattern

emitter discharge

rate

f

e

f

e

Quasi-steady flowRelative WaterUptake Volume

Weather: diurnal pattern of potential evaporation

g

g

A New Approach for the Design and Scheduling

DIDAS main window for choosing among the steady, quasi-steady and unsteady

modeling for the design and scheduling

http://app.agri.gov.il/didas

DIDAS window for choosing between theCoupled Source-Sink Systems

with On-surface or Sub-surface emitters

An example of DIDAS Scenarios for Drip Irrigation

The water flow and uptake problem can be formulated in two, equivalent modes:1.Superposition of neighboring

sources and sinks2.Flow in a laterally-confined,

equivalent domain

An example of DIDAS steady modeling output:RWUR as function of the radius of the root zone for various

distances of plants and emitters along the driplines

DIDAS window defining the irrigation scheduling scenario:Daily, 2h-irrigation at 6:00

Sample of DIDAS unsteady model output:Diurnal patterns of the RWUR

Conclusion (1) •The proposed coupled source/sink model allows evaluating:

the RWU rate when using steady-state solutions and the RWU volume when using time-dependent solutions

•When the plant roots create maximum possible suction and there is no local soil-plant resistance the water uptake is determined just by the capability of the soil to conduct water from the sources to the sinks.•We suggest that this RWUR is maximal for the given source/sink geometry and propose to use it as a criterion for the design of drip irrigation systems. •The computations of the RWUR requires only a minimum number of 3 parameters describing the soil texture, the size of the root zoneand the potential evaporation, in the few cases when it is important to account for also evaporation form the soil surface.

Conclusion (2) •The design of drip irrigation systems can be made by superposing the solutions for water infiltration from sources to sinks: positive sourcesrepresenting the emitters and negative sinks representing the root systems.•The water flow and uptake problem can be formulated in two, equivalent modes: 1.Superposition of neighboring sources and sinks; 2. Flow in a laterally-confined, equivalent domain.

•The irrigation scheduling optimizing tool is based on a RWUV (ratio between daily water uptake volume and daily irrigation volume) criterion. •The computations of the diurnal patterns of the water uptake rates and the daily RWUV for a given irrigation scenario require additional information on the diurnal pattern of the plant resistance to water uptake and on the hydraulic conductivity of the soil. •The simulated scenario of irrigation scheduling should include a sufficient number of irrigation cycles (larger for clayey as compared to sandy soils) for approaching a quasi-steady periodic pattern.

Conclusion (3) •DIDAS includes also a module of quasi-steady flow for evaluating the diurnal water uptake patterns that accounts for the diurnal patterns of the plant resistance and evaporation and serves for fine-tuning of the design and preliminary evaluation of scheduling scenarios. •DIDAS was programmed in DELPHI and it runs on any Windows operating system-PC, with no further software requirements. The construction of the drip irrigation scenario is performed via few GUI windows, which contain also a library of the required input parameters, and several best-fitting procedures. •The computed RWURs and RWUVs are displayed graphically and the tabulated output results can be exported to e.g. Windows Excel for further processing.•DIDAS depicts the steady flow patterns (potentials and streamlines) for various geometrical and plant resistance scenarios and also the temporal patterns of the water potential at specified locations.