CROP COEFFICIENT

This lecture is mainly based on

Benoit Duchemin – IRRIMED 1st Training Workshop – Evapotranspirationand Crop Water Requirements, 8-12 February 2004, Palmyria (Syria)

SOWAMED WORKSHOP

Michel Le Page, June 2008, Amman (Jordania)

1. Reminder of the FAO water budget

Remind : FAO simplified water balance equation

DE[d+1] = DE[d] + ET - R - I + DP

Rain R

ET evapoTranspiration

Irrigat° I

DE ("Depletion") = soil water‘ déficit ’ = amount of waterlost regarding the Total Available Water (TAW) thatthe soil contains for evapotranspiration.

0 ≤ D ≤ TAW0 < D < TAWD = 0 when there is no water left

D = TAW after large water supply

D = TAW - CAW [ mm ]

CAW = Current Available Water

Deep Percolation DP

Effective Rainfall : Amount of water thatreach the soil during a rain event.

-> if R < 0.2 ET0 mm are supposed to beevaporated because of interception by vegetation (important in arid area !!!)

RunOff : believed null (generally lowslopes & occur when D=0) or equal to a fraction of rainfall in case of high slopes.

Deep Percolation : believed null except in case of important water supply. Once the soil fullfilled, DP = additional rain or irrigation (no delay)

The capillary rises are neglected. This assumption is reasonable if the watertable is deep enough (1 meter from the effective rooting zone ?)

Effec-tiverain R

EvapoTranspiration

Irrigat° RunOff

RO

Deep Percolation DP

Remind : FAO simplified water balance equation

Readily Available Water (RAW) Total Available Water (TAW)

Soil = water for evapotranspiration

TAW = 1000 ( θFC - θWP ) . Zr (mm)RAW = p x TAW (mm)

- Zr is the Root Depth- p is the « DepletionFraction » (percentage of water easily transpirable)

Soil = water for evapotranspiration

Irrigation Monitoring (Standard Condition)

When to irrigate (*) Before depletion reaches RAW = p . TAW

(one neccessary to be a crop in Standard Condition

+ disease-free + no N stress + infinite extent… )

How much water ? Depletion losses by evapotranspiration

(*) There is other possible answers, according to the level of water stress (and loss of production) that we accept

Standard condition ( ETC ) for a specific crop= reference condition for the grasses

(well-watered, no disease, completely shading the ground…)

2. Single Crop Coefficient

( Reference = Well - Watered Grass )

( Standard Condition for Other Crops )

FAO-24 (1973, 1977) & FAO-56 (1998)

1 Cultural Coef. (Kc) such as

ETC = Kc. ET0

2 calculation Steps

• ET0

• ETC

ET0

ETC

ET0 x

FAO method : ‘Dual Step/Single Coefficient’ (1)

The cultural coefficient group the difference betweengrass and other crops in terms of evapotranspiration

Basic Equation : ETC = Kc. ET0

for well-watered grass : Kc = 1. (ETC = ET0)

for other crops, Kc account for all the differences with ET of

well-watered grass as expressed in the PM equation

FAO method : ‘Dual Step/Single Coefficient’ (2)

( ) ( )( )

⎟⎟⎠

⎞⎜⎜⎝

⎛++Δ

−+−Δ=

1rr

eTerc

GRnE

a

s

aasata

p

γ

ρ

λ

what is changing in PM ( Rn, ra, rs, fraction cover… ) ?

TRANSPIRATION (ra, rs) :

Crop phenological status

Crop Type

EVAPORATION

Fraction cover

Soil Type

These differences depend of climate !!!

Crop coefficient will changebecause of differences in:

Kc = fn(Phenological stages) (1)

Crop calendar is described with

- 4 phases (Initial, Growth, Maturity, Senescence) linked to

- 3 ‘ key ’ Crop Coefficients :. KcINI --> KcMID --> KcEND .

Init. Growth Maturity Senescence

For annual plant, crop calendar in 4 phases :

• Initial Stage. From sowing to vegetation fraction cover of 10%. Kc = KcINI : constant, generally low, but highly variable with rain and irrigation frequency (evaporat° dominates !).

• Growth (or development stage).Until effective cover (flowering, LAI ≈ 3 ?). KcINI < Kc < KcMID : evaporat°/transpirat° partitioning

• Maturity (or mid-stage). Until start of leave yellowing (?). Kc = KcMID (maximum and constant, generally > 1)

• Senescence (or late-stage). Until total yellowing or yield. KcMID < Kc < KcEND : evaporat°/transpirat° partitioning

(and date of yield !!!)

Kc = fn(Phenological stages) (2)

Phenological stages duration (1)

Forage crop (alfalfa)

FAO Irrigation & Drainage Paper No. 24 provides general lengths for the four stages & the total growing period for various types of climates & locations. This information has been supplemented from other sources and is summarized in Table 11.

In ‘Crop evapotranspiration - Guidelines for computing crop water requirements’ by Allen R.G., Pereira L.S., Raes D. and Smith M. as FAO – I&D Paper No. 56 (1998).

Phenological stages duration (2)

Kc = fn(Crop Type) (1)

2 physical processes :

1) Aerodynamical (height, roughness, structure)Transfer of water is facilitated with more roughness

=> Kc > 1 by a factor 5 – 20 %,

2) Physiological (nature)Because the density and the functioning of stomata

differs from one specie to another=> Dominant group type

annual ~ grassspecific species (citrus, ananas)

It also depends on cultural practices…

TABLE 12. Single (time-averaged) crop coefficients, Kc, and mean maximum plant heights for non stressed, well-managed crops in subhumid climates(RHmin ≈ 45%, u2 ≈ 2 m/s) for use with the FAO Penman-Monteith ETo.

Kc = fn(Crop type) (2)

In ‘Crop evapotranspiration - Guidelines for computing crop water requirements’ by Allen R.G., Pereira L.S., Raes D. and Smith M. as FAO – I&D Paper No. 56 (1998).

Kc_mid & Kc_end variation

Difference in evaporation => Kc_INI variation

coarsetextured soils

Kc ini related to the level of ETo and the interval between irrigations and/or significant rain

When the cover is full-developped, aerodynamical differenceswill be more or less large depending on climatic condition, but coefficients reported in FAO table correspond to a particularclimate (RHmin ≈ 45%, u2 ≈ 2 m/s).

KcMID & KcEND = fn(Climate) !

Kc at mid-season (KcMID)

Humide

Vent Faible

Sec

Vent Fort

For other climaticconditions, Kc are different

Correction formula

In summary…

Calculation steps for FAO ‘ Single Coefficient ’

6 steps :

1. Calculation of reference evapotranspiration ( ETo )

2. Determination of crop calendar

3. Selection of crop coefficients for the 3 key-stages of crop calendar : KcINI , KcMID, KcEND

4. Calculation of climatic condition during maturity andsenescence stages. Correction of KcMID, KcEND

5. Numerical determination of crop coefficients curve

6. Estimation of ETc as ETo x Kc

3. Dual Crop Coefficient

Need for a more complex approachFAO dual coefficient method

Method FAO ‘Dual Crop Coefficient’

FAO-56 (1998) : crop coefficient is explained as thesum of two coefficients that are believed to account

for soil evaporation and plant transpiration

ETC = ( Kcb + Ke ) ET0

Transpiration

Evaporation

(Dual Step : ET0 then ETC)

Basal Crop Coefficient

Assumption = no evaporation (dry soil top layer )

Plant is in standard condition (humid deep soil layer) .

Advantage = constrained value

DEJ = DEJ-1 - RJ - IJ / fw + ETsolJ / few + RPJ

RI

RP

fw = Wetted Fraction --> Irrigation

System

few = Exposed andWetted Fraction

--> Evaporation

(root Zone Percolation term)

Soil top layer water balance

DE

Evaporation phases

Soil capacity to diffuse water

ET0

time

Soil evaporation

phase 1

phase 2

ETsol = Ke ET0 ?

Evaporation Coefficient (Ke)

Ke = min ( Kr . (Kcmax- Kcb) , few . Kcmax )

Kr = 1 during phase 1

Phase 2 : evaporation is limited by water availability in the soil top layer Kr : Ke = Kr . (Kcmax- Kcb)

+ Evaporation comes from the wetted and exposed fraction of soil : Ke ≤ few . Kcmax

Phase 1 : evapotranspiration is limited (by available energy), Kcb + Ke cannot be large than one value ( Kcmax )

( Ke ≤ Kcmax – Kcb )

Evaporation Coefficient Ke (2)

Sol = Readily & Total Evaporable Water = REW & TEW

Ze = top soil layer ( 10 - 15 cm )

(m)

Evaporation Coefficient Ke (3)

DEJ = DEJ-1 - RJ - IJ / fw + ETsolJ / few + DPJ

Phase 1 ( DEJ ≤ REW ) Kr =1

Phase 2 ( DEJ ≥ REW )

Kr = ( TEW - DEj )

/ (TEW -REW)

Ke = min ( Kr . (Kcmax- Kcb) , few . Kcmax )

Three steps :1. Kcmax -> 2. Kr -> 3. Fw & Fc

Ex

Heavy Rain, depletion isempty, and Kr=1

At stage 2 (De>REW), Krbegins to drop

Initial values fromFAO tables andformulas

Wetted soil fraction

fw still constant between watersupply event

Fraction de Sol ExposéExposed and wetted soil fraction

Comparison of single and approaches…

More accurate estimation of ET but the calculation and theformulation is much more complex (and not so clear)

4. Water Stress condition

Water-stressed Condition

similar approach than for evaporation reduction factorneed to consider two buckets (top & root soil layer)

( Pb de la gestion de deux réservoirs )

Mono-Coefficient : ETc_adj = Ks. Kc ET0

Water-stressed Condition

Dual-Coefficient : ETc_adj = ( Kcb.Ks + Ke ) ET0

Conclusion

Many processes are no taken into account (Interception, RunOff, transfer between different soil layer…)

…BUT IT IS OPERATIONAL

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Mar-03 Apr-03 Jun-03 Aug-03 Oct-03Date

Irrig

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n (m

m)

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Applied Irrigations

Total water use 800mm

Ks

stressFAO

Irrigations

Total use 630mm Ks

FAO Method : Example of benefits

Olive trees (Agdal site)

2nd MEDA Water Regional Event on Local Water Management – Marrakech 28-30 April 2008

Crop evapotranspiration - Guidelines forcomputing crop water requirements -FAO Irrigation and drainage paper 56

Richard G. AllenLuis S. PereiraDirk RaesMartin Smith

http://www.fao.org/docrep/X0490E/X0490E00.htm