Simulation of the maximum yield of sugar cane at different altitudes: Effect of temperature on the conversion of radiation into biomass

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Simulation of the maximum yield of sugar cane at

different altitudes: Effect of temperature on the

conversion of radiation into biomass

J.F. Martiné, P. Siband, Raymond Bonhomme

To cite this version:

J.F. Martiné, P. Siband, Raymond Bonhomme. Simulation of the maximum yield of sugar cane at

different altitudes: Effect of temperature on the conversion of radiation into biomass. Agronomie,

EDP Sciences, 1999, 19 (1), pp.3-12. �hal-02687088�

Original

article

Simulation

of the maximum

_yield

of

_sugar

cane

at

different altitudes: effect of

_temperature

on

the conversion of radiation into biomass

Jean-François

Martiné

a

Pierre

Siband

b

_Raymond

Bonhomme

c

a

CIRAD-CA Station de la _Bretagne, BP 20, 97408 Saint-Denis cedex 9, France b

CIRAD-CA 2477, avenue du Val de _Montferrand, BP 5035, 34032 Montpellier cedex 1, France

c

Unité de recherche en _{bioclimatologie,} Inra, 78850 _{Thiverval-Grignon,} France

(Received 15 March 1998; accepted 8 December ₁₉₉₈₎

Abstract - To minimize the

_production

costs _{of sugar} cane, for the diverse sites of

production

found in La Réunion, an

improved understanding

of the influence of temperature on the

_dry

matter radiation

_quotient

is

_required.

_Existing

mod-els simulate

_poorly

the

_{temperature-radiation}

interaction. A model _{of sugar} cane

_growth

has been fitted to the results

from two

_contrasting

sites _{(mean temperatures:} 14-30 _°C; total radiation: 10-25

_MJ·m

_-2

_·d

_-1

_),

on a ratoon _{crop of} cv

R570, under conditions of

_non-limiting

resources. Radiation

_{interception,}

aerial biomass, the fraction of millable stems,

and their moisture content, were measured. The time-courses of the

_efficiency

of radiation

_interception

differed between sites. As a function of the sum of

_day-degrees,

_they

were similar. The

_dry

matter radiation

_quotient

was related to

tem-perature. The moisture content of millable stems

_depended

on the

_day-degree

sum. On the other hand, the leaf/stem ratio

was

_independent

of _temperature. The

_{relationships}

established enabled the construction of a

_simple

model of

_yield

poten-tial.

_Applied

to a set of sites

_representing

the _sugar cane

_growing

area of La Réunion, it gave a

_good

_prediction

of

max-imum

_yields.

_{(© Inra/Elsevier, Paris.)}

sugar cane /

_{plant growth}

_{model / dry}

matter radiation

_quotient

/ _temperature

Résumé - Simulation du rendement maximal de la canne à sucre à différentes altitudes : effet de la

_température

sur la conversion du _rayonnement en biomasse.

_Optimiser

les coûts de

_production

de la canne à sucre, dans la

diver-sité des situations de la _Réunion, nécessite une meilleure

_{compréhension}

de l’influence de la

_température

sur le facteur de conversion du _rayonnement

_intercepté

en biomasse. Les modèles existants simulent mal l’interaction

température-rayonnement.

On a

_ajusté

un modèle de croissance de la canne à sucre sur les résultats de deux sites

contras-tés

_{(températures}

_{moyennes : 14-30°C; rayonnement}

_global:

10-25

_),

_-1

_.j

_-2

_MJ.m

sur une _{repousse du} cv _R570, en

condi-Communicated by John E. _{Sheehy (Manila, Philippines)}

*

Correspondence and _reprints E-mail: martine@cirad.fr

tions de ressources non limitantes.

_{L’interception}

du _rayonnement, la biomasse aérienne, la _part de

_tiges

_usinables, et leur humidité ont été mesurées. Les

_progressions

dans le _temps de l’efficience

_{d’interception}

du _rayonnement diffèrent entre

sites. En fonction de la somme des

_degré-jour

elles sont similaires. Le facteur de conversion du _rayonnement

_intercepté

en biomasse

_dépend

de la

_{température.}

L’humidité des

_tiges

usinables est déterminée _{par la} somme des

_degré-jour.

En

revanche, le _rapport

_{feuilles/tiges}

est

_indépendant

de la

_{température.}

Les relations établies _permettent de construire un

modèle de

_potentiel

_{simple. Appliqué}

à un

_jeu

de situations

_{qui représentent}

la zone de culture de canne de la Réunion,

il

_prédit

bien les rendements maximaux. _{(© Inra/Elsevier, Paris.)}

canne à sucre / modèle de croissance / facteur de conversion du _rayonnement /

_température

1. INTRODUCTION

The

_production

costs _{of sugar from} cane are

high,

and very sensitive both to

_management

deci-sions and the duration of the

_{harvesting period.}

This

emphasises

the

_importance

of farm

_inputs

and of the

_factory

infrastructures needed for a

given

pro-duction. Their

_optimisation

is an

_important

factor.

In La

Réunion,

cane

_yield

varies from 30 to 180

_t·ha

_-1

_·year

_-1

_.

_Harvesting

lasts 4-5 months. The

diversity

of

_agricultural

sites offers

_great

_{scope for}

improvements,

but makes the

_optimization

_of pro-duction difficult. A

_{strictly experimental approach}

to _{this crop is}

_{particularly expensive,}

slow and unsuitable for

_dealing

with climatic variation. Recourse to simulation reduces the need for exper-imentation and

_helps

with the formulation of local-ized solutions.

_Development

of a model should be facilitated

_by

the

_simplicity

of the

_plant

and the wide range of accessible sites.

The literature contains various models of _sugar

cane

_growth,

such as Auscane

_[8]

and

_Canegro

[7].

These models seem well

_adapted

to the conditions under which

_they

were

_developed.

Their

_application

to the

_contrasting

sites of La Réunion

_{has, however,}

proved

to be

difficult,

calibration

_parameters

differ-ing

from site to site

_{[2, 12].}

The main differences between sites

_{being largely}

attributable to

_temperature

and

_radiation,

one is led

to _{suppose that these models fail} to treat the inter-action between these two climatic

_parameters

satis-factorily.

Thus,

in the

_majority

_{of studies where the range} of variation in

_temperature

is

limited,

or does not

involve low

_{temperatures,}

the conversion factor of radiation into biomass is assumed constant. This is indeed observed for

_sorghum

_[15],

millet

_[22],

maize and other cereals

_[9],

_{and sugar} cane

[6,

_16,

19].

However,

in colder

climates,

similar studies

performed

on maize

_[1]

and

_sorghum

_[4]

have shown a fall in conversion factor below a certain

temperature.

Robertson et al.

_[18]

and Liu and

Kingston

[10]

introduced into their models a func-tion for the response of

photosynthesis

to

tempera-ture.

To take account of such climatic variations in the conditions of La

_Réunion,

we set out to redefine a

simple

model,

notably formalizing

the effect of low temperatures on the

_dynamics

of radiation

intercep-tion,

on the conversion of

_intercepted

radiation into biomass and on the

_partition

of the aerial biomass.

Sugar

cane is a

_perennial

_{crop which is}

periodi-cally replanted,

after which it is cut and

successive-ly

ratooned

_annually

in La Réunion. The area of

planted

cane

_being

four times less than that of the

ratoon _crop, we will be

_mainly

concerned with the

latter,

and with the main

_variety

on the

island,

namely

R570.

2. MATERIALS AND METHODS

2.1. Model

Incident

_{photosynthetically}

active radiation PAR is

The model

_comprises

three

_major

_{physiological}

processes:

- the

interception

of incident

_{photosynthetically}

active radiation _PAR, a function of the

_interception

effi-ciency

ϵi, defined

_by

Varlet-Grancher et al. [24] as the

ratio of the radiation

_{intercepted by}

the _crop, PARi, and the PAR;

- the conversion of PARi into

dry weight

of aerial

biomass AB; a function of the

_dry

matter radiation quo-tient

_(DMRQ,

defined

_by

Russel _[20] and often

incor-rectly

called radiation use

_efficiency,

_RUE);

- the

partition

of this aerial biomass AB into

_dry

weight

of millable cane _(MMC), a function of the

Harvest Index HI; HI

_depends

on the variable fraction of

dry weight

of stem _(SM) in AB; SM =

f(AB),

and on the

variable fraction of MMC in SM: MMC =

_g(SM).

It will be assumed that the fraction of assimilates

allo-cated to roots is constant [23, 5].

Every

day

(d):

Every day,

to

_computation

of the useful

_yield

Y, at the actual moisture content, from the

_{dry weight}

of millable

cane MMC is obtained

by taking

account of the moisture

content

_(%

_H

₂

_O)

on fresh

_weight

basis:

Thus, we need to determine ϵi, DMRQ, HI and %

H

2

O.

2.2.

_Experiments

Three

_experiments

served to define the

_{relationships}

which make _{up the} model. A set of

_independent

results

was available to test the model.

The

_experiments,

each

_consisting

of two

_plots

of 195-225 m2 with the same

_cropping

_system, were

car-ried out at two sites:

_Ligne

Paradis

₍₁₅₀

m in altitude on a _stony brown

_soil)

and

_Colimaçons

₍₇₈₀

m in altitude on

a

non-perhydrated

andosol), situated at 21.3 and 21.1°S

latitude, 55.5 and 55.3°E

_longitude,

_{respectively.}

The

experiments

of

_Ligne

Paradis _(LP1 and _LP2) and

Colimaçons

(CO) are described in table I.

The crop was a first ratoon of cv _R570; the rows were

1.5 m _apart. The fertilizer

applied

was 210

_kg

N, 70

_kg

P

2

O

5

and

270

_kg

_K

₂

_O

_{per hectare.} The

_nitrogen

was

applied

as four

_dressings,

the

potassium

as three and the

phosphorus

as one,

_during

the first 6 months. Soil mois-ture content was maintained at a level above 2/3 of the

available water content AWC

_by

trickle

_irrigation.

To test the model, we used the cane

_yields

₍₁₈

obser-vations) from

_plots

of tests of

_potential

_yields.

The

experimental

sites were at Trois Bassins _(TB, altitude 990 _m), Piton St. Leu _(PSL 565 _m),

_Leroy

_(LR 500 _m),

Ligne

Paradis _(LP 150 m) and Tirano (TIR 150 _m). The

plots

were

_optimally

trickle

irrigated

and

liberally

fertil-ized. We used the results from the first and second

ratoons of the

_variety

R570.

2.3. Procedure and measurements

2.3.1. Radiation measurements

The

_daily

incident total radiation _(Rt) was measured

every

day

with a

Kipp

& Zonen CM5 radiation

pyra-nometer. The

_daily

minimum _(Tn) and maximum _(Tx)

temperatures were measured with a Cimel

_Electronique

platinum

resistance _temperature

_probe.

The data were

recorded

_using

Cimel 407 data

_logger.

The

_daily

incident

photosynthetically

active radiation _(PAR) was measured

with a Li-Cor cell _type 190SB50

_placed

above the

canopy.

The

_daily

transmitted

_{photosynthetically}

active

radia-tion _(PARt) was measured

_using

a 30-cell

_amorphous

These Solem cells were fixed on six rails _(five cells _per

rail)

such that each rail covered half an inter-row _space

(75 cm). The six rails were

_arranged

on each side of the

observation line _[11]. The PAR and PARt were mea-sured over a

_{complete day.ϵi}

and PARi were

_finally

cal-culated

_by:

2.3.2. Biomass measurements

In order to follow the evolution of biomass over the same _group of

_{plants throughout}

the whole

_experiment,

at each measurement date

_(table

_I) and on each

_plot:

- the

height

of every stem was measured on two 9-m2

quadrats;

- outside these

quadrats,

a destructive

_sample

was

taken of 30-50 stems.

This

_sample

was

_separated

into five lots of different

heights,

treated

_separately.

On each lot, the fraction

which had

_completed

its

_growth

was

_separated

_(hard

mil-lable

_stems);

also the non-millable stem _fraction,

_living

leaves, and dead leaves. For all these fractions, fresh and

dry weight

were measured. Statistical

_{relationships}

were

established between

_height

and total mean

_dry

mass _per

stem _{(AB) per lot,} and between the

_{dry weights}

of the various _fractions;

- the biomasses

corresponding

to each 9-m2

_quadrat

were then estimated

_using

these

_{relationships}

_[11]. The cane

_yield

used to test the model was measured on

_plots

of 200-300 m2.

2.4. Treatment of data

2.4.1. Determination

_{of ϵi}

The

_relationship

was established between the

temper-ature

_(day-degree

_sum) and the observed

_efficiency

of radiation

_interception

ϵi. It was fitted

_using

non-linear

regression.

2.4.2. Determination

_{of DMRQ}

The values of _{DMRQ (ΔAB/PARi)} were calculated between two dates of biomass measurement; their

varia-tion over time was related to the mean

_{meteorological}

variables for the same time intervals: in

_particular

with

the mean air _temperature Tm calculated as (Tn +

_Tm)/2.

The methods and statistical _parameters used were: the correlation coefficient _(r) and

_analysis

of variance

(Fisher’s

test:

_probability

_P) for

_calibrating

the _model; a

threshold of

_{acceptability}

_(boundary

line of

_adequacy)

for validation of the model _[14].

3. EXPERIMENTAL RESULTS

AND PARAMETERIZATION OF THE MODEL

3.1. Climatic conditions

Figures

1 and 2 show the main climatic variables

applicable

to the

_{experiments, expressed}

as

_10-day

means. Over the whole

_experiment,

the mean

daily

temperature

varied from 14 to

_{30 °C,}

and the mean

daily

radiation from 10 to 25

MJ.m

-2

.

_{These ranges}

of variation define the limits of

_{applicability}

of the

study.

3.2. Radiation

_interception

The

_dynamics

of the trend of ϵi as a function of

duration of

_{growth (figure}

₃₎

are of similar

_shape,

but

_quite

distinct for the three

_experiments.

A value of 0.7

_corresponds

to the

_beginning

_{of canopy}

clo-sure, and the start of senescence on the

_youngest

tillers. It is reached from the fourth month at low altitudes

_(LP1),

and

_probably

even a month earlier

on

_LP2,

whilst it takes

_nearly

6 months at

_high

alti-tude

_(CO).

The

_interception

efficiencies still differ after 8 months’

_growth.

Since ϵi is

_{directly dependent}

on the leaf area

index

_(LAI),

whose time-course is often related to the

_day-degree

sum

_(SDD

₁₂

_),

we have converted the time into these units. The best fit is obtained with a base

_temperature

_(Tbase)

of 12 °C. This

tem-perature

is similar to that which we find from

analy-ses of the rates of leaf _appearance

_{(phyllochrone)}

and stem

_elongation.

The literature does not contain values for the base

_temperature

for LAI

develop-ment. _{The tbase values for the sugar} cane

phyl-lochrone vary from 10 to 12 °C

_{[6, 17, 25].}

When the data are

_{plotted against}

accumulated

day-degrees

(figure

4),

the

_{points representing}

ϵi fall on a

_single

_line,

which fits a

simple Gompertz

curve with a coefficient of correlation of 0.999

(P

<

0.001).

3.3. Conversion of

_intercepted

radiation into biomass

_(DMRQ)

The

_{DMRQ (&Delta;AB/PARi),}

established between

two measurement dates seem to decrease with the age of the crop

(figure

5a),

although

the

relationship

is not

_significant

_(r

=

0.61,

P =

_0.06).

However,

these variations are

essentially

due to the difference in rate of

_development

between the

measurements at LP

_(high

_{temperatures,}

_figure

2)

As well as this

_temperature

difference between

sites,

there was a fall in

_temperature

towards the end of the

_growing

_period.

These two variations result-ed in a

_{significant relationship}

between

_DMRQ

and

the mean _temperatures over the

_{corresponding}

peri-ods as shown

_{in figure}

5b. This

_relationship

has the

equation:

and thus leads in our _{range of} measurements to

values between 2.38

_g·MJ

_-1

(PARi)

at 15 °C and 3.55

_g·MJ

_-1

_(PARi)

at 26 °C.

This variation in

_DMRQ

with

_temperature

has

already

been observed for maize

_{[1] and}

_sorghum

[15]

but not _{for sugar} cane.

_However,

the low

val-ues of

_DMRQ

seen

_{in figure 4}

in Muchow et al.

_{[ 16]}

correspond

to lower

_temperatures

at the

_beginning

and end of

_growth.

A

_{rigorous comparison}

with the results of Muchow et al.

_[16]

and Robertson et al.

[19]

is thus not

_possible,

since these authors used a

questionable

procedure

which relates cumulative

biomass with cumulative total

_intercepted

radiation.

But the orders of

_magnitude

of

_DMRQ

obtained in

our conditions are

_comparable

to the values obtained

_by

these authors

_(from

1.59 to 1.75

_g·MJ

_-1

(Rt

intercepted))

which must be

_multiplied

_by

a

value

_slightly

inferior to 2.

The

_comparison

between the observed values of

shows that a

_fairly

constant difference exists between observed and simulated AB

_(figure

6).

The

mean difference between observed and simulated

AB is 700 ± 80

_g·m

_-2

_.

This bias is due to the basal

part

(stem

and

_leaf),

_underground

and not

mea-sured,

of the cane formed

_especially

at the

begin-ning

of

_growth.

The measurable aerial

_dry

matter AB can thus be found from the

_equation:

3.4. Partition of the aerial biomass

_(HI)

3.4.1. Growth

_{of stems}

Figure

7 shows the variation of &Delta;SM/&Delta;AB as a

function of AB. The values which come from two sites fall on the same line. The fraction allocated to stem increases

_linearly

_up to 1.8

_kg·m

_-2

_{of AB,}

after which it tends to _{fall very}

_slightly.

For the sake of

_simplicity

of the

model,

and

con-sidering

the

_imprecision

attached to _{the small}

gra-dient of the second

_part

of the

_relation,

we will

adopt

the

_{following equations:}

with &Delta;SM/&Delta;AB = 0.75 if AB _> 1 800

g·m

-2

.

The error in

_calculating

SM never exceeds 5 %.

3.4.2. Millable stems

The linear relation between the observed values of MMC and SM is

_highly

_significant

_{(MMC =}

1.0

x SM -

_140,

r =

0.999,

P _<

0.001).

The

equation

which can be used to calculate the millable cane

_dry

matter is the

_following:

3.5. Trend of actual stem moisture content

The _percent of water fell over

the

course of time.

The best fit

_(figure

₈₎

was obtained

_by

_using

the

sum

_(ST)

of mean

_temperatures

Tm since the

fol-lowing equation:

One

_might

think that the r obtained is

_good

enough

for

_prediction.

It is

_probable

that %

_H

₂

_O

would

_depend

on the moisture state _{of the crop,} which

_superimposes

_rapid

variations on this trend.

This

_{variation, however,}

_appears to be too small to

be attributed to water stress in our

experiments.

One

would

_hope

to

_improve

the

_prediction

of the

agri-cultural

_{yield by}

the introduction of the water

bal-ance into the model.

4. TESTING THE MODEL

The

_improved

model can be

applied

to the set of sites reserved for its

_{testing, by}

_calculating

the

expected agricultural

yield.

To evaluate the

_performance

of the model we

have used Mitchell’s method

_[14]

and have studied the deviations between observed and simulated

yields

with a threshold of

acceptability

of

± 10

T·ha

-1

.

_Figure

9,

which shows the relation between the simulated

_yields

and the

deviations,

shows that no deviation exceeds this

threshold,

and that there is no relation between the simulated

yields

and the deviations.

It _{appears that the model}

_predicts

well the

maxi-mum

_yields

obtained over a _{range of altitudes}

which

_largely

_applies

to the

_cane-growing

area of

La Réunion.

5. DISCUSSION

On the basis of a dataset from

fairly contrasting

sites,

it has been

_possible

to establish the different

relationships

needed to construct a

_simple

model of the

_yield

of a _sugar cane _{crop with}

_satisfactory

pre-cision.

All that was needed was the correction of the

DMRQ

by

a

_temperature

factor. This has lead to a

para-meter. This

_improvement

makes

_possible

predic-tions of

_yield

close to those measured.

Inman-Bamber

_{[5, 7]}

broke down the

_expression

for the energy conversion term

_by

_{distinguishing}

gross

photosynthesis

and

growth

and maintenance

respiration.

These

_respiration

terms are also

tem-perature

dependent. Having only

measured the net

result of these processes, it seemed

inopportune

to

us to

_attempt

to calculate these

_parameters.

However,

the absence of a

_significant

relation

between

_DMRQ

_{and age}

_(increasing

_AB)

shows that if the maintenance

_respiration

has a

_bearing

on

this

relation,

it is not

_proportional

to the elaborated

biomass;

also its distinction here does not _appear as

useful.

The

_{interception efficiency}

&epsiv;i,

being

fitted to the

day-degree

sum, is also

temperature

dependent,

and contributes to the

_explanation

of the site effect. The

same

_applies

to the moisture content of the millable

stems. On the other

_hand,

the

_partition

of aerial

bio-mass _appears to be

_independent

of

_temperature.

The decision to

_regard

the

_production

of root

bio-mass as a constant

_proportion

of aerial biomass appears to be

_acceptable.

The aerial biomass situat-ed below the soil

(the

stump),

which was not

mea-sured and cannot be

_harvested,

is considered to be

constant in the model. Its value

₍₇₀₀

_g·m

_-2

₎

is sim-ilar to values found in the literature

_[23].

The moisture content of the stems remains one of

the least well fitted term in the model. This does not affect its

_capacity

to

_predict,

as the

_testing

_shows,

inasmuch as it is a model for

_{potential yield.}

This

implies

that the moisture content of the tissues is

not

_greatly

affected

_by

the

_growing

conditions. This term could be formulated with

_greater

_precision

once the water stress is taken into account.

This

_model,

which takes into account the interac-tion between radiation and

_temperature

_during

_yield

formation,

has allowed

_growth

to be

_analysed,

together

with the

_{yield potential}

in different climat-ic zones of La Réunion and for various cultural

sit-uations with different

_cutting

_{dates and ages} at har-vest

_[13].

_Depending

on the climate and

cutting

date,

the results enable the recommendation of dif-ferent scenarios for weed control and

_irrigation,

to

identify

the

_periods

most sensitive to water and

nutrient stress, to estimate

_{possible yield}

increases and thus to assess the

_advisability

of investments.

ABREVIATIONS

Symbol

Unit Definition

%

_H

₂

_O

% moisture content of millable

cane

_(fresh

_weight

_basis)

AB

_g·m

_-2

aerial biomass

_dry

matter

AWC mm available water content of soil

DMRQ

g·MJ

-1

dry

matter radiation

_(PARi)

quotient

&Delta;AB

_g·m

_-2

_·d

_-1

_daily

increase of AB &Delta;MMC

_g·m

_-2

_·d

_-1

_daily

increase of MMC &Delta;SM

_g·m

_-2

_·d

_-1

_daily

increase of SM &epsiv;i fraction

_{daily interception efficiency}

HI fraction harvest index

LAI fraction leaf area index

MMC

_g·m

_-2

millable cane

_dry

matter

PAR

MJ·m

-2

·d

-1

_daily

incident

photosynthetically

active radiation

PARi

M·Jm

-2

·d

-1

_{daily intercepted}

photosynthetically

active radiation

PARt

MJ·m

-2

·d

-1

_daily

transmitted

photosynthetically

active radiation

Rt

MJ·m

-2

·d

-1

_daily

total incident radiation RUE

_g·MJ

_-1

radiation use

efficiency

(of

intercepted

radiation)

SDD

12

°C sum of

_day-degrees

(tbase 12)

since

_{previous cutting}

SM

_g.m

_-2

stem

_dry

matter

ST °C sum of

_daily

mean air

temperatures

since

_previous

cutting

Tbase °C base

_temperature

Tm °C

_daily

mean air

_temperature

Tn °C

_daily

minimum air

temperature

Tx °C

_daily

maximum air

temperature

Y

T·ha

-1

_yield

_(millable

cane

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