PRINCIPLES OF CROP GROWTH SIMULATION MODELLING

Potential production

The Rice System and boundaries – Potential Production Situation

Radiation, CO2, O2

Temperature

A. GROWTH

Photosynthesis (CO2 assimilation)

CO2 + H2O + solar energy => CH2O + O2

Respiration (maintenance, growth)

CH2O + O2 => CO2 + H2O + chemical energy

Assimilation respiration = net growth rate

B. DEVELOPMENT

Development rate = f(temperature)=> growth period=> partitioning

C. BIOMASS PRODUCTION = growth rate x growth period

PROCESSES OF CROP GROWTH

A. CROP GROWTH RATE

Daily gross crop assimilation rate (kg CH2O ha1 d1)

CO2 assimilation

I. CO2 assimilation of a single leaf

• Individual leaf light response curve

II. Canopy CO2 assimilation

• Integration over leaves in canopy (depth, z)• Integration over leaves in time (day, t)

III. Leaf area growth in time

I. CO2 assimilation of a single leaf

Cross section of a leaf through a stoma (a), indicating components of resistances to CO2 diffusion (b).

radiation(Wm-2)per mm

PAR

50%

1.0

.5

500 1000 1500ultra violet visible infra-red wavelength (nm)

Spectral composition of global radiation, discriminating between direct radiation (clear area) and diffuse (i.e. indirect) radiation scattered by clouds (hatched area). PAR = photosynthetically active radiation.(Source: Monteith and Unsworth, 1990. Principles of environmental physics. Edward Arnold, London, 291 p.)

Schematic representation of a leaf chamber for the measurement of CO2 assimilation.

80

60

40

20

00 100 200 300 400

Fg C3

Fg C4

APAR (J/m2/s)

Fm C3 crop

Fm C4 crop

Fg (kg CO2/ha leaf/hr)

Leaf light response curve:

Fg = gross rate of CO2 assimilationFm = maximum rate of CO2 assim. at high light intensity = initial light use efficiencyAPAR = Absorbed Photosynthetic Active Radiation

Fg = Fm (1e(APAR / Fm))

C3 crops C4 crops

Potato, sugar beet, wheat, rye, barley, rice, rape, soy bean, broad beans, almost all trees

Sorghum, maize, millet, sugarcane, rhodes grass, sisal, mangrove

Characteristic values of Fm and

Fm

C3 crops 40 (15 - 50) 0.45

C4 crops 70 (30 - 90) 0.45

Fm : kg CO2 ha leaf1 d1

: (kg CO2 ha leaf1 h1)(J m2 s1)1

0 200 400 600 0 200 400 600 0 20 3010 40 50

0

25

50

75

100

0 0

25

50

75

100

1

2

0

25

50

75

100

0

1

2

0

1

2

net assimilation rate net assimilation rate net assimilation rate

[kg (CO2) ha-1 h-1] [mg (CO2) m-2 s-1] [kg (CO2) ha-1 h-1] [mg (CO2) m-2 s-1] [kg (CO2) ha-1 h-1] [mg (CO2) m-2 s-1]

C3C4

C3C4

C3C4

A B C

PAR [J m-2 s-1] internal CO2 [ppm] temperature [oC]

The effect of light (a) CO2 concentration (b) and temperature (c) on net assimilation rate of a C3 (solid line) and a C4 (dashed line) species. Assimilation rates in (b) and (c) refer to light saturated values. In (b) CO2 concentration in the stomatal cavity is used to avoid confounding stomatal to changes in external CO2 concentration.

Effect of N in leaf on photosynthesis

Van Keulen and Seligman, 1987

II. Canopy CO2 assimilation

Direct light

Diffuse light

Canopy reflection (5%)

Atmospheric scattering

Weather station: radiometerIncident radiation

diffuse radiation

direct radiation

II.1 Integration over leaves in canopy (depth, z)

Light and single leaf

Light and multiple leaves

0

5

10

15

20

25

30

35

40

45

50

55

60

0.0 0.2 0.4 0.6 0.0 0.2 0.4 0.6 0.8 1.0

depth [cm]

A

LAI rel. light intensity

The distribution of leaf area over the depth (I.e. LAI per layer of 5 cm) and of the light intensity in the crop, relative to the light intensity above the (sugar beet) crop (a). The relation between relative light intensity and cumulative LAI calculated from the top downwards (b). LAI = leaf are index [in m2 (leaf surface) m-2 (ground surface)].

Extinction of radiation in the canopy

PARd = PAR0 e( LAId)

PARd = PAR at depth d in canopy

PAR0 = PAR above crop canopy

LAId = Leaf Area Index above d

= extinction coeff. (0.5 - 0.7)

Canopy (leaves) architecture

II.2 Integration over leaves in time (day, t)

Time course of PAR and crop CO2 assimilation rate on an average (left) and a clear and overcast day (right) in June in the Netherlands.

0

100

200

300

400

PAR

[J m-2 s-1]

Agross

[kg (CO2) ha-1 h-1]

0

100

200

300

400

0

20

40

60

80

0

20

40

60

80

2 6 10 14 18 22 2 6 10 14 18 22

time [h] time [h]

AgrossPAR

Average dayClear day

Overcast day

Summary calculation of daily canopy gross CO2 assimilation rate:

• At any depth in the canopy, at any time of the day (and latitude, season), calculate gross leaf CO2 assimilation rate from ‘leaf light response curve’ and PARd.

• Integrate over depth (LAId) of the canopy

• Integrate over day length (time of day)

Canopy assimilation = t z (leaf assimilation)

So far, gross CO2 assimilation rate was expressed in kg CO2 ha1 d1

Since:

CO2 + H2O + solar energy => CH2O + O2

Molecular weight of CO2 is 30

Molecular weight of CH2O is 44

To calculate daily gross accumulation rate of assimilates:

1 kg CO2 ha1 d1 CO2 assimilation rate

= 30/44 kg CH2O ha1 d1

Month f Aclear Aovercast Aaverage Agross

J 0.47 616 252 445 303

F 0.34 674 281 540 368

M 0.37 734 311 577 394

A 0.28 781 334 656 447

M 0.42 800 342 608 414

J 0.52 804 342 564 384

J 0.59 803 343 532 362

A 0.62 791 339 511 348

S 0.58 757 323 505 345

O 0.54 698 293 479 327

N 0.54 633 261 432 295

D 0.54 600 244 408 278

------ kg CO2 ha1 d1 ------ kg CH2O ha1 d1

Rice canopy assimilation rate, Los Baños, Philippines

III. Leaf area growth in time

0

1

2

3

4

5

6

7

0 10 20 30 40 50 60 70 80 90 100 110 120

TIME

Exponentialphase

Linear phase

Leaf death

Seedbed

Leaf Area Index (ha leaf ha-1 soil)

Exponential phase: leaf area growth determined by temperature

LAIt = LAI0 e(RGRL Tsum)

RGRL = Relative Growth Rate Leaves (°Cd)-1

Tsum = Temperature sum since emergence (°Cd)

Linear phase: leaf area growth determined by assimilates available, as expressed in weight of leaves

LAIt = SLA Wlvg,t

SLA = Specific Leaf Area (ha leaf kg-1 leaf)

Wlvg = Weight of green leaves (kg ha-1 soil surface)

NET CROP GROWTH RATE

Crop respiration

10

14

18

22

0.2

0.4

0.6

0.8

1.0

16 20 24 4 8 12 16 20 24 4 8 12 16

Growth respiration

Maintenance respiration

26 April 27 April 28 April

Figure 2.24 CO2 efflux of an enclosed sward of perenial ryegrass, at ambient temperature during two days of darkness.

(a) ______ : continuous record of CO2 efflux; --------- : maintenance respiration, calculated as the mean rate of CO2 efflux after 40-46 hours of darkness, adjusted for the effect of temperature.

(b) continuous record of air temperature in closure.

Source : Jones, Leafe, Sites & Collett, 1978. Ann. Bot. (42):693-703.

Maintenance respiration

• Resynthesis components (enzyme turnover: 10% d1)• Concentration gradients• Metabolic activity

Maintenance respiration rate: Rm = f(composition, weight)

Rm = 0.02 Wleaf + 0.015 Wstem + 0.01 Wroot + 0.03 Wstorage

(in kg CH2O (kg CH2O)1 d1 )

Rm,t = Rm Q10 [ (T Tref) /10 ]

with Q10 = 2, and Tref = 25 ºC

and at any temperature:

For lowland rice (IR72):

Growth respiration

Sugars ( CH2O) => structural matter

Conversion efficiency:

Eg = f(chemical composition)

in (kg dry matter) (kg CH2O)1

• Uptake nitrogen and minerals

• Transport of sugars

• Synthesis end-product

Carbohydrates 0.826

N-compound from NO3 0.404

N-compound from NH+4 0.616

Organic acids 1.104

Lignin 0.465

Lipids (fats) 0.330

Conversion efficiency for chemical compounds

Growth respiration

Composition (%) and conversion efficiency for rice:

Leaf Stem Root Panicle

Carboh. 52 62 56 76

Protein 25 10 10 12

Fats 5 2 20 2

Lignin 5 20 20 6

Org. ac 5 2 2 2

Mineral 8 4 10 2

Eg 0.75 0.75 0.75 0.68

Net crop growth rate

Daily rate of increase in structural dry weight of a crop (dW):

dW = Eg (Agross Rm W) in: kg dry matter ha1 d1

where:• Eg = conversion efficiency (kg dry matter (kg CH2O)1)

• Agross = gross CO2 assimilation rate (kg CH2O ha1 d1)

• Rm = maintenance respiration (kg CH2O) (kg CH2O)1 d1

• W = dry weight of the crop (kg ha1)

Net crop growth rate

Mean values of Rm and Eg, at 20 °C

Rm Eg

Root/tuber crops 0.010 0.75

Cereals (rice) 0.015 0.70

Protein-rich seed crop 0.025 0.65

Oil-rich seed crop 0.030 0.50

For rice in Los Baños, Philippines

dW = Eg (Agross Rm W)

Dry season – April:

dW = 0.70 (447 0.015 5000) = 261 (kg dry matter) ha1 d1

Wet season – October:

dW = 0.70 (327 0.015 5000) = 176 (kg dry matter) ha1 d1

0

5000

10000

15000

20000

25000

0 50 100 150 200 250 300 350

266 kg DM ha-1 d-1

177 kg DM ha-1 d-1

Dry season

Wet season

kg DM

Day of year

Rice IR72, IRRI farm 1991-1993, Los Baños

Month f Aclear Aovercast Aaverage Agros Anet

J 0.47 333 120 233 159 59

F 0.34 445 169 351 239 115

M 0.37 586 233 455 310 165

A 0.28 737 304 616 420 241

M 0.42 843 354 638 435 252

J 0.52 892 377 624 426 245

J 0.59 873 368 575 392 222

A 0.62 788 329 503 343 188

S 0.58 652 264 427 291 151

O 0.54 497 193 333 227 106

N 0.54 364 133 239 163 62

D 0.54 304 107 198 135 42

------ kg CO2 ha1 d1 ------- kg CH2O ha1 d1

Rice canopy assimilation rate, Beijing, China

Rice, Changle (Beijing), 2001, China

0

5000

10000

15000

20000

25000

0 50 100 150 200 250 300 350

232 kg DM ha-1 d-1

kg DM

JD305

HD502

HD297

Day of year

B. CROP DEVELOPMENT

Development rate and assimilate partitioning

Thermal Unit (or temperature sum):

anthesis maturity

(T - T0) dt and (T - T0) dt

emergence anthesis

Expressed in day degrees (°C d)

where T = average daily temperature

T0 = base temperature (0 - 10 °C)

Per crop (and cultivar), there is constant TU between emergence-anthesis, and anthesis-maturity

Rice variety IR72

0

500

1000

1500

2000

2500

0 0.5 1 1.5 2

Development stage

Temperature sum (°C)

Flowering Maturity

Development rate is inverse of number of degree days between development stages (°Cd 1)

Period DVS IR72 HD502

Juvenile 0.0-0.4 0.001161 0.000506

Photoperiod-sensitive

0.4-0.65 0.000064 0.000758

Panicle formation

0.65-1.0 0.001152 0.000769

Grain filling 1.0-2.0 0.000504 0.001417

Partitioning of assimilates

Assimilate partitioning is function of development stage (DVS) of crop.

Example for fraction of assimilates (growth) partitioned to the shoot (FSH), for rice:

DVS FSH

0.00 0.50

0.43 0.75

1.00 1.00

2.00 1.00

E.g. at development stage of 0.43 => 75% of daily growth goes to the shoot, and 25% to the roots.

Partitioning of assimilates; Rice IR72

Fraction daily dry matter increase

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2

SHOOT

ROOT

Development stage

ROOT

SHOOT

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2

STORAGE ORGAN

STEM

LEAF

Development stage

Fraction daily dry matter increase

Partitioning of assimilates; Rice IR72

C. BIOMASS PRODUCTION

Total crop growth simulation

Photosynthesis

Assimilatepool Biomass

Leaves

Stems

Panicles

Roots

LAI

Developmentstage

Maintenancerespiration

Growthrespiration

Partitioning

Developmentrate

N leaves

Light

Temperature

Crop model Potential Production

Reduced grain yield through spikelet sterility; effect of temperature

Horie (1993)

Input

1. Weather data: daily temperature, radiation => Weather data file

2. Management: emergence date, density, etc => Experiment data file

3. Crop characteristics: Fm, partitioning, etc => Crop data file

Output

• Time course of leaf area index, biomass

of various crop organs

• Yield, yield components

0

1

2

3

4

5

6

7

0 10 20 30 40 50 60 70 80 90 100 110 120

TIME

Run 3, LAIRun 3, LAI_OBS

IR72; Los Baños; DS 1992; 225 kg N ha1

LAI simulated

LAI measured

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 10 20 30 40 50 60 70 80 90 100 110 120

TIME

Run 3, WAGTRun 3, WAGT_OBSRun 3, WLVGRun 3, WLVG_OBSRun 3, WSORun 3, WSO_OBS

Total biomass

Panicle biomass

Green leaf biomass

kg dry matter ha-1.