2.1 Physiologicalprinciples
H.D.J.vanHeemst
In agriculture, solar energy is conserved for future use via its fixation in
biomass bytheprocessof photosynthesis. Inthisprocess C0 2 from theairis
convertedintocarbohydrates(CH20)naccordingtotheoverallreaction:
C0 2+H 2 0+solarenergy->CH20+0 2
(1)
This process is also called C0 2 assimilation. Part of the carbohydrates
producedisusedasbuildingmaterial forstructuralplantdrymatter,as cellulose, proteins, ligninandfats andpartisusedasasourceof energyforplant
processes. The release of energy from carbohydrates produced during the
assimilationprocessisdescribedbytheequation:
CH20 + 0 2 -*C0 2 + H 2 0 + chemicalenergy
(2j
Thisprocessiscalledrespiration.About40%oftheweightofthecarbohydrates formed during the assimilation process is lost byrespiration. Subtraction
oftherateofrespirationfromtheassimilationrategivestherateofincreasein
plant dryweight, i.e. thegrowth rate. InFigure4, thetimecourse of growth
rateandtotal drymatter accumulation isinaschematic waypresented fora
summerwheatcrop.Thegrowthratesareobtained fromthedrymatteraccumulationcurvebydeterminingateachpointtheslopeofthecurve.
With respect to the growth ratethree phases may bedistinguished: (i)during the first phase, the crop consists of individual plants that do not shade
each other and the growth rate increases; (ii) in the second phase the crop
covers the soil completely and the growth rate is constant; (iii) in the third
phasethecropismaturingandthegrowthrateisdecreasing..
Inthefirstphasethemajorpartoftheassimilatesisinvestedinleafgrowth.
Thisincreaseinleaf areaisaccompanied byaproportional increaseinenergy
interception, because neighbouring plants are so small that mutual shading
hardlyplaysarole.Individualplantweightincreasesbyaconstantproportion
perday, thus leading to exponential growth. After aclosed cropsurface has
beenformed, moreleafgrowthdoesnotleadtomorelightinterception,hence
thegrowth rateremainsconstant andtotal plant weight increases linearly. In
thelastphaseleafsenescenceleadstoadecreaseinthegrowthrate.
Themajorpartof thetotal drymatteraccumulationisachievedduringthe
secondphase.Totaldrymatterproductionofthecropisthuslargelydetermined by the magnitude of the growth rate during the linear phase and the
durationofthatphase.
13
growth rate (kg h a ^ d " 1 )
total dry weight ( kg ha" 1 )
200
200 0 0 -
100
1000
April
individual
plants
yiay
June
'
J u
closed crop canopy
leaves
dying
May
June
I
exponential • linear g r o w t h
growth
.
Apri
July
jdecreasing
, growth
Figure 4. Schematized course of growth rate and total dry weight of summer wheat in time.
Theduration of theperiod of lineargrowth isspecies andcultivar specific
and, moreover, isinfluenced byenvironmental conditions (Section 2.2).The
actual growth rateispredominantly influenced byenvironmental conditions,
such as solar radiation and temperature, the supply of nutrients and water,
andtheoccurrenceofweeds,pestsanddiseases.
Withanoptimalsupplyof waterandnutrientsandintheabsenceofweeds,
pestsanddiseases,thegrowthrateisdeterminedbysolarradiationandtemperature and is referred to as the potential growth rate. Such conditions are
supposed to prevail when discussing the basic processes of plant growth. A
simple model for the calculation of potential dry matter production will be
presentedthatmaybeappliedtovariouscropsatdifferentlocations.
2.1.1 CO2assimilationofasingleleaf
Intheleaves of aplant thephotosynthetically activeradiation isabsorbed
bygreenchlorophyl andotherpigmentsandisusedforthereductionof C0 2 .
Not all radiation of the sunis photosynthetically active, but only thevisible
radiationinthewavelengthrangefrom400to700nm,whichrepresentsabout
50%ofthetotalglobalradiation(Figure5).
TherateofC0 2assimilationotaleafcanbemeasuredbyenclosingaleafin
a so called leaf-chamber and analysing the C0 2 concentration of theincomingandtheoutgoingair,thatpassestheleafataknownflowrate.Whenthe
assimilationrateisdeterminedatvariousradiationintensities,alightresponse
curvecanbeconstructed asillustrated inFigure 6 for leaves of plant species
referred to as C3 and C4 types. The main parameters characterizing these
14
radiation
(WITT2)
per nm
1.0h
ultra violet
500
' visible
•
1000
1500
I infra-red
wavelength(nm)
Figure 5. Spectral distribution of total solar radiation (upper curve) and direct solar
radiation (lower curve). Solar elevation is 30° and precipitable water in the atmosphere is
21mm. (Source: Monteith, 1973)
kg ha'V 1
60-
30-
Figure 6. Characteristic net C0 2 assimilation functions for individual leaves of C3 and C4
plant species.
15
curvesaretheinitiallightuseefficiency, 8,therespirationrateinthedark,Rd,
andthemaximumrateof netC0 2 assimilationathighlightintensity, Fm.The
latter ranges from 30-90 kg ha"1 (leaf) h"1 for C4 type plants and from
15-50 kg ha"1 (leaf) h"1 for C3 type plants, depending on environmental
conditions. Thegross rateof C0 2 assimilation, Fg, isthesum of the netrate
andtheconcurrentdarkrespiration.Thedarkrespirationisatnormaltemperaturesroughlyone- ninthofthemaximumnetassimilationrate.
Themaximum netassimilation rateandthedarkrespiration ratearemuch
moreaffected bytemperaturethantheinitiallightuseefficiency. Theeffect of
temperature onthemaximumassimilation rateisillustrated inFigure7fora
C3andaC4type plant. However, thesetemperature responses wereobtained
with plants grown under controlled conditions at atemperature close tothe
optimumfoundinFigure7.Underfieldconditionswhereplantsaresubjected
to fluctuating temperature conditions, there appears to beadaptation of the
photosyntheticapparatus.Itwasfoundthatforsuchplantsthemaximumleaf
assimilation ratewas practically independent of temperature above about 13
°CforC4speciesandabove8°CforC3species.
Thedifference ininitial light useefficiency betweentheC3andC4typesof
photosynthesis issmall, buttheassimilation rateatlight saturation is forthe
C4typeplantsgenerallyhigher.ThenamesC3andC4refertothelengthofthe
C skeleton of the first stable product in the photosynthetic process. Several
characteristics of thesetwoplant typesaredifferent (Gifford, 1974),suchas:
(i) the main carboxylating enzyme in the C4 photosynthetic pathway hasan
affinity to C0 2 that is about twice as high as that in the C3 photosynthetic
pathway;(ii)intheC3typeplantsarespiratoryprocesstakesplaceinthelight
assimilation
(pi cm'V 1 )
assimilation
(pi cm'V 1 )
100r
(a)
30*
50 - / ^ £ ^ i ^ 2 v ? 2 0 o
0.1 0.2 03 0.U05
radiation
(cal cm"2 min" 1 )
*' 0.1 02 03 0.4 0.5
radiation
-2
(cal cm min"1)
Figure 7. The relation between temperature and the maximum rate of C 0 2 assimilation for
a C3 (a) and a C4 (b) crop species.
16
whichresultsinadependenceofassimilationrateontheoxygenconcentration
in the ambient air, whereas that process is absent in C4 species; (iii) under
conditions wheretheC0 2 concentration intheintercellular spaceisregulated
overawiderangeofexternal C0 2 concentrations andlightintensities through
adaptation ofstomatal aperture,thelevelatwhichtheinternal concentration
is maintained in C4 types is about half of that in C3 types (Raschke,1975;
Goudriaan &van Laar, 1978b). This last characteristic will be discussed in
detailinSection3.3.
ExamplesofspecieshavingtheC3typeofassimilation, which prevailinthe
temperate zones, aresmall grains, including rice. Species that areof theG4
type,whicharemoreabundant insubtropical andtropical regions,aremaize,
sorghum, millet, sugar cane and most tropical grasses. Extensive lists of C4
species have been compiled by Downton (1975) and Raghavendra &Das
(1978).
2.1.2 CanopyC02assimilation
The rate of C0 2 assimilation of acrop depends onincoming visible radiation inthesame wayasthat of an individual leaf. Suppose for simplicity a
crop with a horizontal layer of large leaves, forming a closed surface. This
layer acts as onebigleaf, and knowing the light intensity, the rate of C0 2
assimilation canberead from Figure 6,taking into account that 10%ofthe
incomingvisibleradiation isreflected, 10%istransmitted through the leaves,
10% is absorbed by pigments not contributing to photosynthesis, and that
only the remaining 70% is absorbed by the chloroplasts. At an incoming
visible radiation intensity of 300J m"2s"1 this crop, if it wasa C3species,
wouldhaveaC0 2 assimilation rateofabout 25kgha - 1 h"1. Suchacrophasa
leaf area index (LAI)of one, because there is 1 m2of leaf area perm2ofsoil
surface area. When another layer ofsuch bigleavesissituated under thefirst
one, thecrop hasaLAIof2,becausethereis2m2ofleaf area perm2 ofsoil
surface area. Theincoming radiation intensity inthesecond layer isequalto
thelighttransmitted throughthefirst layer, thus 10%of300,or30Jm"2s"1,
resulting inanadditional assimilation rateofabout 3kgha"1 h"1. The result
•
is a small increase in assimilation rate for thetwolayer crop. Adding more
layersunderthesecondonewillnotsubstantiallyincreasetheassimilation rate
ofsuchacropwithlayersoflargehorizontalleaves.
Inreality,acropdoesnotconsistofhorizontal layersoflargeclosely fitting
leaves, buttheleaves of a crop arespread inevery direction andthelightis
therefore more evenly distributed over the leaves. Thelight extinction ina
canopy canbeexperimentally determined bymeasuring thelight intensityat
different levels inthecrop, whileatthesame time measuring thecumulative
leaf area at thesame levels.Theresult of such anexperiment ispresentedin
Figure8,whichdepictstherelation betweentherelativelight intensityandthe
cumulative LAI,counting the leaf area from the top of the canopy down17
LAI(m2m-2)
0
50
100
radiation intensity %
Figure 8. Extinction of radiation in a crop canopy.
wards.Theextinction of thelightisexponential for anincreasing numberof
leaf layers. For any LAI the proportion of absorbed radiation can beread
from Figure 8. In combination with Figure 6 this yields an estimate of the
assimilationrateofthecrop.ForanLAIof four, theC0 2 assimilationrateis
about 39 kg ha"1 h"1, or about one and a half times that of the crop with
layersof largehorizontal leaves.Thereason for this isthatinarealcropthe
light intensity distribution over the leaves is more even and therefore more
leaves are exposed to light intensities in the linear part of the light response
curve.
Theprocedurejust outlined isaschematized wayof calculatingtherateof
C0 2 assimilation of acrop. Reality is more complicated, as the influence of
direct and diffuse light, total leaf area, leaf angle distribution, leaf optical
propertiesandsolarheightonthelightdistributionwithinthecanopyhaveto
betaken into account. The problem hasbeen tackled with computer models
(de Wit 1965; Duncan et al., 1967; Goudriaan, 1977) which calculate the
assimilation rate of a canopy at any moment of a day in response to the
incoming photosynthetically active radiation, which is dependent on solar
heightandthedegreeofcloudinessofthesky.
In a schematized set up, two situations areconsidered: acompletely clear
skyandacompletelycloudysky. Integrationof theinstantaneousratesyields
the daily total amount of C0 2 fixed. InTables 1and2these dailytotalsare
presentedasafunction ofgeographicallatitudeforbothcompletelyclearand
completely overcast days, under the assumption of zero respiration and an
LAIof five, fortwomaximumratesofgrossC0 2 assimilationof asingleleaf
athighlightintensity,Fg :40kgha -1 (leaf)h _1 ,typicalforaC3typeofplant,
18
Table1.CalculatedgrossC02assimilationrate(kgha"1d"1)ofaclosedcanopywitha
sphericalleafangledistribution,forclear(Fcl)andovercast(Fov)days,andamaximum
leafC02assimilationrate,Fg,of40kgha"1d"1.
Date
15 15 15 15 15 15 15 15 15 15 15 15
Northern Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec.
Hemisph.
Southern July Aug. Sep. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June
Hemisph.
Latitude
0°
F„
F
*•ov
10° Fc,
F
*ov
20° Fc,
F
*•ov
30° FcI
F
*•ov
40° Fc,
Fx
50° Fovc,
FA
ov
60° Fc,
F
*ov
70° Fc,
Fx
ov
728
306
652
270
562
226
454
175
333
120
202
63
68
15
0
0
753
320
701
295
634
261
549
219
445
169
324
114
191
57
46
10
768
328
748
319
713
300
659
271
586
233
491
187
375
132
240
73
761
324
779
334
783
334
768
324
737
304
686
275
615
236
527
189
737
311
786
336
820
351
839
357
843"
354
833
343
813
323
798
302
720
302
784
333
834
356
869
371
892
377
904
375
915
368
967
369
727
306
785
335
829
355
858
366
873
368
877
363
875
351
896
341
752
319
784
336
802
343
804
341
788
329
757
307
7Q8
277
649
240
768
328
765
327
745
316
708
295
652
264
574
224
474
175
353
118
760
324
720
305
665
276
591
239
497
193
384
140
255
83
114
27
736
311
667
277
583
236
481
187
364
133
234
77
102
25
0
0
720
302
638
262
542
216
429
163
304
107
172
52
39
8
0
0
(Source:Goudriaan&VanLaar,1978a)
and 70 kgha"1 (leaf) h"1, typical for aC4type oi plant. Onthebasis of such
tables, which for various maximum rates of C0 2 assimilation at high light
intensity can be found in Goudriaan & Van Laar (1978a), potential crop,
assimilation can becalculated for anydate, given thetypeof crop (C3 orC4),
thelatitudeofthelocationandthefraction ofthetimetheskyisclouded.
Crop type determines which table is used; given the latitude and the date,
the assimilation rate of a closed canopy for a clear and an overcast day is
obtained byinterpolation. The assimilation rate for partially overcast daysis
obtained formthe formula:
F
gc = f0•Fov + (1- f0) •Fcl
(3)
where
Fgc istnegrosscanopyC0 2 assimilationrate(kgha -1d"1)
f0 istriefraction of thedaythe skyisovercast (f0is0 for completely clear
days,f0is 1 forcompletelyovercastdays)
19
Table2.CalculatedgrossC0 2assimilationrate(kgha"1d"1)of aclosedcanopywitha
sphericalleafangledistribution,forclear(Fcl)andovercast(Fov)days,andamaximum
leafC0 2assimilationrate,Fg,of 70 kgha"1 d"1.
Date
15 15 15 15 15 15 15 15 15 15 15 15
Northern Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec.
Hemisph.
Southern July Aug. Sep. Oct.Nov.Dec. Jan.Feb.Mar. Apr. M a y June
Hemisph.
Latitude
0°F d
Fov
10°Fcl
Fov
20°Fc,
Fov
'30°Fcl
Fov
40°FcI
Fov
50°Fcl
Fov
60°Fcl
Fov
70°Fc,
ov
Fov
959 99510171007 973 947 958 99310181007 971 947
326 341 350 346 331 321 325 340 351 346 331 321
852 922 989103210391035103710381012 949 873 832
285 313 340 357 358 356 357 359 349 324 294 277
726 827 93710351086110310971062 983 870 755 698
237 276 319 356 375 381 379 366 336 292 248 226
577 707 86010111109114911341060 927 765 613 542
182 229 287 345 381 396 391 363 313 251 195 170
410 562 755 9621108117511501033 845 633 452 372
123 176 245 322 377 402 392 349 278 201 138 110
236 397 620 885108611831145 982 733 477 278 198
65 117 194 289 362 398 384 324 234 145 78 53
71 220 460 779104611821129 905 591 301 109 40
15 58 136 246 340 388 369 290 181 85 25 8
0 47 277 649100612221132 810 421 121 0
0
0 10 74 195 314 385 356 249 120 28 0
0
(Source:Goudriaan&Van Laar,1978a)
Fov
is the gross C0 2 assimilation rate on completely overcast days (kg ha
Fc,
isthegrossC0 2 assimilation rateon aperfectly clearday(kgha l d *)
-l
The fraction of the day the sky is overcast is obtained from the measured
actual daily global irradiation and the daily global irradiation on a perfectly'
clearday, which istabulated inTable3.
Dailyglobal irradiation on acompletely overcast daymaybeapproximated by
multiplying thevalue for aperfectly cleardaywith0.2. Thus:
f0 = (Hg - H a )/(H g - 0.2 • Hg)
where
Hg
Ha
20
istotal global irradiation on aperfectly clearday(Jm"2d"1)
ismeasured total global irradiation (Jm" 2 d _1 )
(4)
If thecanopy doesnot form aclosed cover, asat thebeginning and theend
of thegrowthcycle,not allincomingradiation isintercepted, and C0 2assimilationisreduced relativetothat ofaclosedcanopy.Thereductionisestimated
from thefraction oftheincomingradiation intercepted bythecrop,asdiscussedearlier:
fh = ( l - e - k e - L A I )
(5)
where
fh
ke
isthefraction oflightintercepted bythecrop
istheextinction coefficient for visiblelight, thevaluebeingbetween 0.5
and0.8,dependingoncropgeometry
Exercise1
CalculatethedailygrossC0 2 assimilation for themiddleofeachmonth of the
year for a completely clear and for a completely overcast sky at your own
location,assumingaclosedcanopy, for bothaC3andaC4typeofcrop.
Exercise2
RepeatExercise 1 assumingLAI= 1.5
The rate of C0 2 assimilation has been expressed sofar in amounts of C0 2 .
Theabsorbed C0 2 isreduced inthecropto carbohydrates orsugars (CH20)n.
Togetanassimilation rateexpressed inCH 2 0, therateinC0 2 ismultiplied by
30/44(theratiooftheirmolecularweights).
2.1.3 Respiration
The sugars produced in the assimilation process may be converted into
structural dry matter, they may be accumulated and temporarily stored as
reserves,ortheymaybeusedasasourceofenergy.Theplant needsenergy for
twoprocesses.Ontheonehand for maintenanceof ionicgradientsand resynthesis of degrading structural proteins; on the other hand for the conversion
of primary photosynthetic products into structural plant material. In these
processesC0 2 isproduced, thustheyarerespiratory processes:the first oneis
21
o
2Q
o
vq
C
3
q o*—* 8
o\
•
CO
•
•
o o g o o o
•
•
•
•
•
•
00»r>^vo*-<VO<SOOO
CN n <N ~-«i—i
0 0 T t O < N r t O Q Q
ONtOOOONOOfSOO
00
ONr-Tt^vo^vocs oo
N (S (N ( S »H ^
oo
f-4
2o
•
©d
ON T t ©
voootTf
>
88
vo
<
T f O O V O ^ - O O ^ t O O T f O O
cO
• • • • • • • • •
•
OOOOVOfOON^ONTfO
w m ( s (S N ^ ^
CO
in <u
VO<NOOOOVOOOVO<SVO
n o v o N o o < n m < o v o ^
O N ^ ^ ^ O N t ^ " * © ^ ^
00
«n 3
^
<
co
ONOOf-r^t'-OQCSt^TtON
•
• • • • • • • • •
o
co
h O N n m N H 0 \ O O
co
c
co
co
a>
TfOOMtOONVOOOTfW
o
•
•
•
•
•
•
•
•
•
cN ro ro f^> co co t o co co co
*-*
•
i
•
c«
o
«o ON ^ o s rn oo so ^ h; O
oddc4c4c4©ao*v6«nvd
<Ncococococo<NfN<N<N
•
•
O v o v o c N o o o o o o r a t S
OsoohvoTtTfinONmt^
2
>
I
o
60
c
o
.2
o
«o
o
<
•
•
•
•
•
•
•
•
•
CO
•
ONOOONr^Ttov->^ON
00
ON
•
(NTfSOrjTtrtVOVOVO
n m m T f v o » H ^ o s N
•
co
•
0
0
\
•
h t
•
O
•
^
•
H
•
i
•
n
•
n
•
O
88
•
CO
<
cO
•
CO
CO
HJ
C
^•OOVOOOOOOV©
Tfoorrcovovovor^
ON vo r s ONTf
ON ^f O O O
M M N <-<«-H
CO
>
85C O0 ©w* - r« »i - *NC NS < oS ©g ©o©
# e0
c
cO
"co
a
»n as
*
C » T | - 0 « O O « O ^ O O O
N (S (S ^
o
H
en
a h a
2 S* S - (A
T3
H
22
V a B <D
£c4 S^O fiJ-i
CO»-U
o o o o o o o o o o
O O O O O O O O O O
^HCJcoTfmvor-ooON
i C »^* _ c •—<
co
^
CO
"C
o
a
••
O
»-.
O
CO
called maintenance respiration, thesecond growth respiration.
Maintenance respiration
The proteins in the plant, especially in the leaves, consist mainly of enzymes, which have only alimited life span. They deteriorate at a relative rate of
about 0.1 per day at a temperature of 20 °C, and have to be resynthesized.
The rate of protein turnover is temperature dependent with a Q10 of about 2
(Penning de Vries et al., 1979). This means that the rate of protein turnover
doubles for temperature increases of 10°C.
The concentration of ions in the vacuoles of plant cells is higher than in the
surrounding tissue, which causes leakage of ions from the vacuoles. To maintain the desired internal concentration, the ions have to be taken up against a
concentration gradient. That requires an active transport through cell membranes, which demands energy.
Although accurate data on maintenance requirements are scarce, reasonable estimates of the relative maintenance respiration rate can be made on the
basis of the composition of the biomass present. Such estimates are given in
Table 4 for four groups of crops, each group having approximately the same
chemical composition.
Growth respiration
(/"»iv()'<)
The conversion of primary photosynthates into structural plant material as
cellulose, proteins, lignin and fats requires substrate for building materials
and energy for synthesis of the end product, the transport of sugars and the
uptake of nitrogen and minerals. Therefore, part of the sugars assimilated is
respired to provide energy for the synthesis of new plant components. Another part is lost as refuse in the process of synthesis. The magnitude of
growth respiration is determined by the composition of the end product for-, ,r
med. Thus the weight efficiency of conversion of primary photosynthates into "
structural plant material varies with the composition of that material./Fats
and lignin are produced at high costs; structural carbohydrates and organic
acids are relatively cheap. Proteins and nucleic acids form an intermediate
group (Table 5).
/
1
Table4. Relative maintenance
respiration
rate,
R
m,at 20 °C (kg kg'd ), andconver- /
sionefficiency, Eg,(kgkg"1).
Cropgroup
Root/tuber crops
cereals
protein-richseedcrops
oil-richseedcrops
Rm
0.010
0.015
0.025
0.030
Eg
0.75
0J0
0.65
0.50
23
Table5.Efficiency ofconversion,Eg,ofsubstrate(sugars)intoplantconstituents(kg
kg"1).
Compound
Eg
Carbohydrates
Nitrogenouscompounds(normalmixofamino-acids,
proteinsandnucleicacids)fromNO"
0.826
0.404
fromNH+
0.616
4
Organicacids
Lignin
Lipids
1.104
0.465
0.330
(Source:PenningdeVries,1975)
For the same groups ofxrops distinguished above, theconversion efficienciesaretabulatedinTable4.Athighertemperatures,therateof conversionof
primary photosynthates into structural plant material changes, but the conversion efficiency remains constant, because the biochemical pathway is riot
affected byterriperature.VConversionof primary photosynthates into structural plant material occurs to a large extent at night. Low night temperatures
may hamper this conversion to such an extent that not all the assimilates
formed during the daycan beconverted into structural material. As aresult,
carbohydrates and starch accumulate in the plant and eventually this may
affect theassimilationrate,eitherthroughabiochemical feedback orthrough
physical damage to the chloroplasts. Under such conditions the assimilation
rateisvirtuallydeterminedbythecapacityof theplanttoconverttheassimilationproducts.
2.1.4 Dry matteraccumulation
On the basis of the processes presented in this section, the daily rate of
increaseinstructuraldryweightof acropsurfacemaybeapproximatedbythe
formula
AW=E g - ( F g s - R m - W )
where
AW istherateof increaseinstructuraldryweight(kgha"1 d"l)
Eg is the conversion efficiency of carbohydrate into dry matter (kgkg"1);
seeTable4
Fgs isthegrossrateofcropassimilationexpressedincarbohydrates(kgha"l
d"1)
24•
(6)
Rm istherelativemaintenancerespirationrate(kgkg ld ! );Table4
W isthetotaldryweightofthelivepartsofthecrop(kg ha"l)
Inatemperate, humid climatee.g. intheNetherlands,thepotential growth
rate, ascalculated byEquation 6,appears tobeabout 200kgha"1d"1during
the growing season (Table 6). Experimental evidence confirming these estimatesisgivenbySibma(1968),whocalculated growthcurvesfor anumberof
field crops growing under near-optimal conditions, as shown in Figure 9.
The main agricultural crops in the Netherlands all appear to have practically
thesameslope.ThattheC4typecropmaizeshowsthesameslopeisbecausein
theNetherlandsitisgrownatthelimitofitstemperaturerange.
accumulated dry matter (kgha -1 )
22.000
20000
18000
16.000f14.000
12.000
10.000
8.000
6000
4.000
=000
0 LA
^Wf
rr^-r:
x-*t*?
April May
L-
June
July
August
Sep.
Oct.
time
Figure 9. Growth rates of the main agricultural crops in the Netherlands under (near)optimal growth conditions compared to growth rates of 200, 175 and 150kg ha -1 d",
respectively. 1. grass 2. wheat 3. oats + barley 3a. oats + peas 4. oats 5. peas 6. barley 7.
potatoes 8. sugar beets 9. maize. (Source: Sibma, 1968)
25
Exercise 3
Calculate the potential growth rate per month of a C3 crop for your own
location, following thescheme presented inTable 6.
Estimate the fraction overcast from your own experience, if no data on radiationareavailable (heavyclouds:f0 = 1;clearskiesprevailing:f0 = 0).
Table 6. Example of calculation scheme for thepotential growth rateat De Bilt,the
Netherlands(52°N)assumingtheoveralllossbyrespirationtobe40%.
Month
May
June
July
August
Ha
Hg
fo
Fd
F
16.92
18.60
16.45
14.57
30.43
33.78
32.50
26.86
0.55
0.56
0.62
0.57
829
906
877
747
339
374
361
301
A
OV
F
x
F
560
608
557
493
382
414
380
336
gc
* gs
Ha = longtermaverageactualglobalradiation(106Jm^d*1)
Hg = total global radiation on a clear day at 52° N.L. (106Jm"2d*1)(obtained by
linearinterpolationinTable3)
f0 = fractionofthedaytheskyisovercast(Equation4)
Ed = grossC0 2 assimilationrateoncompletelycleardays(kgha*1 d*1) (interpolation
inTable1 or2)
Fov = grossC0 2 assimilationrateoncompletelyovercastdays(kgha*1 d'1) (interpolationinTable1 or2)
Fgc = actualgrosscanopyC0 2assimilationrate(kgha*1d*1)(Equation3)
Fgs = grosscanopyassimilationrateincarbohydrates(30/44xFgc)
AW= thepotentialgrowthrate(kgha*1d*1)(0.60xFgs)
26
AW
229
249
228
202