Rice clock model—a computer model to simulate rice development

Agrtcultural and Forest Meteorology, 60 (1992) 1-16

1

Elsewer Science Pubhshers B V , Amsterdam

Rice clock model a computer model to simulate rice development Dangzhl Gao, Zhlqlng Jln, Yao Huang and Dzhong Zhang Sectton of Agrometeorologv, Jtangsu Academy of Agricultural Sctences, Nan)mg210014 People's Repubhc of China (Received 30 September 1991, accepted 27 February 1992)

ABSTRACT Gao, L , Jin, Z , Huang, Y and Zhang, L , 1992 Rice clock model--a computer model to simulate rice development Agnc For Meteorol, 60 1-16 This paper describes a simulation model ofnce development It consists of four submodels dealing with (l) phenology, (2) leaf age, (3) total leaf number, (4) organ development After combining the first two submodels, the submodel of (3) was obtained, which could be used to predict the total number of leaves on the mare culm With the synchronous relationship between development of leaves and organs, the morphological appearance and organ development for a given rice variety can be predicted Model parameters were determined using rice data from 15 locations In the Yangtze River Valley, China for 1985-1986 The model was vahdated with a separate data set collected from Jlangsu province during 1988-1989 The average error in heading date for that test was 3 5 days with a correlation coefhclent of 0 88

INTRODUCTION

The concept of crop development mainly involves the processes of crop phenology, leaf age increment and appearances of various morphological organs such as leaf blades, leaf sheaths, tdlers, roots, stem mternodes and panicles It is of great importance to simulate and predict the processes of crop development in crop management A computer simulation model of nce development presented in this paper Is called the Rice Clock Model, since it can mdacate the processes of rice development day by day, as if a clock indicates the time processes exactly Many scientists (Nuttonson, 1943, Brown and Chapman, 1960, Robertson, 1973, Gao et al, 1987, Rltchle et al, 1987, Penning de Vrles et al, 1989) have been making efforts to estabhsh and improve crop phenology models The Rice Clock Model is a new advance with regards to the same purpose Its Correspondence to L Gao, Section ofAgrometeorology, Jlangsu Academy ofAgncultural Sctences, Nanjmg 210014, People's Repubhc of China 0168-1923/92/$05 00 © 1992 Elsevier Soence Pubhshers B V All nghts reserved

2

L GAOETAL

characteristic is to combine submodels of rice phenology, leaf age increment and morphogenetlc processes It has been found to be suitable for computer simulation of rice development DESCRIPTION OF THE MODEL

The Rice Clock Model has four submodels The first one was developed to stmulate the effects of mean daily temperature and day length day by day on rice phenologlcal development The second was developed to describe the day-by-day dependence of rice leaf age upon time and mean daily temperature The third submodel is obtained by combining the above two submodels to predict the total leaf number on the mam culm for a given rice variety And the last submodel can predict the appearance of various morphological organs, based on the synchronous relationship between development of leaves and development of organs A general diagram showing the

l I

Pro9rams to Compute daily Daylength

1

1

I I Weather Data Files I I I ( gean, Max.and Nin. I I I Daily Temp.) I J

I

f

t

Programs to I I Parameters I Input II of the I Crop Data I I Submodels I

J

"r

J

I

[. . . . .

i

L

f

I t

f

Leaf A9e Submodel

L_

t

i

l

1 r I l l l I l

L

J

T

I

Submodel of Total Leaf Number

L

r T

t J

1

Rice Calendar

t

Fig 1 Diagramof the Rice Clock Model Components

I I l J

I

1

Or9an Development Subsodel

[

i

J

i

r l Synchronous Relatlonshlps [ Between Developments I of Leaves & Or9ans

t

E~----I I

]

~=. -J.-.=.~

I

I

I

I I

Phenolo91eal Subsodel

l

1

I

F

l

f

i J

3

A C O M P U T E R M O D E L T O S I M U L A T E RICE D E V E L O P M E N T

structures, processes, and fluxes of the Rice Clock Model with its major variables is presented in Fig 1

Phenologtcal submodel Basw form The basic form of rice phenologlcal submodel is gwen by

dM dt

-

' _ exp(k)('T- TL)e(Tu- T ~

N

.

.

~_ J T Tuo

To

exp[G(/) - O')]

(1)

It was assumed that in eqn (1) TL for 7~ < TL 7-=

Tu for 7~ > TU

z3 =

D' f o r / 5 < D'

and _

\a

_

O

where M is the development process for a gwen phase, 0 ~< M ~< 1, N is the number of days covering the phase, dM/dt is the development rate within the phase, 7~ is the mean temperature during the phase, TU is the upper temperature limit for rice development, taking TU = 40°C, TL is the lower temperature limit for rice development, taking the value of 10°C for japonica, 12°C and 13°C for lndlca and hybrid (Gao et al, 1987), respectively, TO is the optimum temperature for rice development, with the values of 28°C and 30°C for japonica and lndlca (Gao et al, 1987), respectwely,/5 is the average day length In hours within the development phase, D' is the critical day length In hours, taking D' = 13 h, k, P, Q, and G are inmal values of the submodel's parameters To determine the values of the initial parameters which might be necessary when the range of the values for a varietal type are not known, eqn (1) should be converted into a linear form, by taking logarithms to the base e, then solving by using the least squares method Note that k, P, Q and G should be modified when the submodel IS converted from its basic form (eqn (1)) to the simulation form (eqn (4)) Equation (1) has the following advantages in comparison with the rice phenologlcal models and model components from the hterature (1) Both the genetic characteristics and environmental factors which determine the length of growth duration (or development rate) are considered (2) On the genetic characteristics, the submodel of eqn (1) reflects the basic duration (k value), thermal sensmvlty (P and Q values) and photoperlod

4

L GAO ET AL

sensitivity (G value) for a given rice variety Under the optimum condition (T = To a n d / ) ~< D'), eqn (1) becomes 1 --

No

=

exp(k)

orNo

=

exp(-k)

(2)

Therefore, No represents the minimum duration and k is its coefficient (3) With respect to the environment, the effects of both temperature and day length on development rate can be considered (4) Equation (1) has the flexibahty to produce various kinds of reponse curve by changing the values of parameters P, Q and G When P = 1, Q = 0 and G = 0, eqn (1) is similar to the representation of degree-day method Therefore, the latter IS a special case of eqn (1) (5) Temperature and day length factors in eqn (1) are expressed in a product form which has a better explanatory ability than that of the sum form as in a multiple regression model Phasic development in the Rice Clock Model was divided Into three growth stages, l e (1) sowing-emergence, (2) emergence-heading, (3) headingmaturity During stages (1) and (3), G = 0 was assumed, because day length has almost no effect on development rate (Chang and Oka, 1976, Gao et al, 1987)

Stmulatton form Equation (1) can be rewritten as

It can be easily integrated or expressed approximately in summation form to generate a simulation submodel on a daily basis, but with T replaced by the mean dally temperature T, (~ = 1, 2, , N) a n d / ) replaced by the dally day length D, This is

f~,S~dM = M =

~ exp(k') t~l

x exp [G'(D, - D')] =

-

To,

1

(4)

where Sl and $2 represent the beginning and end of the given phase, and k', P', Q' and G' are, respectively, the final values of parameters k, P, Q and G When the development rate in a given phase is simulated day by day on a computer according to eqn (4), the accumulated total of M is used as a criterion for the developmental phase, if M reaches 1, then p n n t N which is the simulated number of days required to complete the phasic development The procedure to determine k', P', Q' and G' was executed on a computer

A (OMPUTER MODEL TO SIMULATE RICE DEVELOPMENT

5

by using the step search method (LI et al, 1982), in which the submodel was run with the initial values of the parameters for the variety in question, and then N was compared with the actual number of days required to cover the phase, adjusting the parameters' values and repeating until acceptable fits were obtained

Phystologtcal day of development If the thermal-day-length condition in a given day was optimum (T, = To, D, ~< D'), we defined it as a physiological day of development (DPD, = l) In fact, the thermal-day-length condition cannot always be optimal, so DPD, of an actual day is often less than unity The calculation of the/th physiological day (t = 1, 2, , N) and the sum from the first day up to Nth day (E DPD,) are then taken in the following form

t7 ~,

--

DPD,

=

-

(5)

To,/

No

where N O is the number of physiological days required to complete a given phase F r o m eqns (2) and (5), we can see that the number of physiological days which a crop requires to complete a given phasic development is constant, although other factors such as soil-moisture content, soil fertlhty, diseases and pests might have minor influences on it, which could be Ignored This principle is the theoretical foundation of the Race Clock Model, which is more reasonable than the concept used in the degree-day method where the

TABLE 1 Physiological days o f development (DPD,) and their sums (Z DPD,) from emergence to heading under optimum and natural conditions, Nanjing, 1985 Condalon Item

Day/month 4/5

5/5

6/5

7/5

8/5

Optimum

Temp (°C) Day length(h) DPD, (d) Z DPD, (d)

Natural

Temp (°C) 237 237 166 180 18 1 Day length(h) 135 135 135 135 136 DPD,(d) 071 071 029 038 038 DPD,(d) 071 142 171 209 247

30 30 30 30 30 <13 <13 <13 <13 <13 1 1 1 1 1 1 2 3 4 5

11/7

18/8

19/8

20/8

21/8

30 <13 1 69

30 30 30 30 <13 <13 <13 <13 1 1 1 1

301 141 067 36 71

264 273 282 280 132 13 1 131 13 1 090 095 097 099 66 52 67 47 68 44 69 41

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L GAO ET AL

summation of degree-days that a crop requires to complete a given phase is assumed to be constant In fact, the effect of day lehgth on crop development is not considered, and only a simple linear relationship between development rate and temperature is assumed in the degree-day method, which does not accord with the biological laws Table 1 gives an example for comparison of the physiological days (DPD,) and their sum (Z DPD,) from emergence to heading under different conditions It shows that 109 days from 4 May to 21 August is equivalent to 69 physiological days for development in Nanjlng, 1985

Leaf age submodel Dynamics of plant age, expressed as number of leaves, is of importance in rice development, because the morphogenetic process can be determined by the number of leaves on the main culm (De Datta, 1981, Yoshlda, 1981) In this paper we defined the number of leaves on the main culm as plant age in leaves, abbreviated to leaf age For example, the leaf age was j when the jth leaf was fully developed on the main culm

Basic form

Lj =

exp(-c)

Njb T =

To for T~> To

(6)

when T = To, and after arrangement, we have Njo = [exp (e) Lj] '/b

(7)

In eqns (6) and (7) Lj is thejth leaf. o r j t h leafage, Tis the mean temperature from emergence to jth leaf, To is the optimum temperature for leaf development, taking To = 30°C for indlca, and To = 28°C for japonica, TL is the lower limit of temperature for leaf development, taking TL = 10°C for japonica, and 12°C and 13°C for indlca and hybrid, respectively, Nj is the number of days actually reqmred from emergence t o j t h leaf, Njo is the number of days required from emergence to jth leaf under optimum temperature conditions, defined as the number of physiological days ofjth leafage, c, a and b are initial values of the parameters To evaluate the values of c, a and b, a simple linear regression procedure can be directly applied, after llneanzatlon by taking logarithms to the base e on the two sides of eqn (6) Equation (7) illustrates that the number of physiological days required to reach a certain leaf age for a given rice variety as constant, and ItS variation with different leaf ages reflects the biological rhythm of leaf development

A ( O M P U T E R M O D E L TO S I M U L A T E RICE D E V E L O P M E N T

7

Stmulatlon form In order to simulate the dynamics of leaf age on a computer, a simulation submodel on a daily base can be derived by making the m e a n daily temperature T, = T of eqn (6) and replacing the initial values of the parameters c, a and b with their final values, c', a' and b', which can be obtained using the same m e t h o d mentioned In the section on the Phenologlcal submodel After rearrangement, eqns (6) and (7) can be combined to give

NJ° -

(T----'Y/b I T '

Nj

\To/

=

_T, =

0

for T, < T L

To for T, > To

(8)

The ratios of the two sides of eqn (8) are usually less than or equal to 1 (since T~ ~< To), which exhibits a fraction of 1 physiological day of leaf age under temperature 7], for 1 day In order to obtain the sum of the dally value in eqn (8), we have

,Y,X

-

(LY Y\ro:

=

(9)

Up to now, we can calculate Njo, the n u m b e r of physiological days required from emergence to t h e j t h leaf according to eqn (7), then input the mean dally temperature, T,, day-by-day into eqn (9), and count the sum on a c o m p u t e r W h e n the accumulated total reaches Njo, print Nj and finally obtain t h e j t h leaf age on the Nth day, L;, by substituting Nj into eqn (6)

Total leaf number submodel The phenologlcal and leaf age submodels can be combined because they follow a c o m m o n principle, 1 e the n u m b e r of physiological days (both for phenologlcal development and leaf age) is constant, and both have similar expressions The combined submodel could be used to estimate the total n u m b e r of leaves The procedures linking these two submodels are as follows Step 1 Calculating the actual n u m b e r of days required from emergence to heading, N, according to eqn (4) F o r a given rice variety, N differs in year, latitude and sowing date Step 2 Replacing Ns in eqn (6) by N, in principle, we can calculate the total n u m b e r of leaves under the given condition (year, location and sowing date etc ), if rice leaves could develop continuously until heading In fact. rice plants cannot bear any more leaf after flag leaf appearance Step 3 It is, therefore, assumed that the elongation of panicle is equivalent to an additional leaf of the plant, so we define the heading date as when the plant reaches its whole leaf age ( L . ) On the other hand, we also define the actual total n u m b e r of leaves on the main culm, Lt, as the total leaf age being

8

L GAO ET AL

equal to the L wminus an empirical constant m which indicates how many leaf ages the time interval would be equal to, from flag leaf appearance to heading, le

Lt

~-

Lw - m

(10)

The procedure mentioned above illustrates why a given rice variety has a different total number of leaves on the main culm when grown at various latitudes, or at different sowing dates For example, when a rice variety which has a strong sensitivity to photoperlod IS grown at higher latitude or its sowing date is earlier, more total leaves will result from the delayed growth duration

Submodel for organ development The synchronous relationships between emerged leaves and development of rice organs (such as tillers, culms, sheath, roots and panicles etc ) have been widely studied by many scientists (Dlng, 1969, De Datta, 198 l, Yoshlda, 1981, Lln et al, 1983, Matsushlma, 1984) The main points related to this field are stated as follows (1) simultaneous with the emergence of the nth leaf, the (n - 1)th leaf elongates, (2) in parallel with the emergence of the nth leaf, the nth leaf sheath elongates, (3) when the nth leaf emerges, a tiller starts emerging from the (n - 3)th node, (4) the number of nodes on the main culm corresponds to the number of leaves developed on the culm minus two, (5) there exists a synchronous growth between the nth leaf and the (n - 3)th roots, (6) synchronlzaton between leaf age (counted from the top of plant) and panicle development 3 5th l e a f - - initial stage of panicle differentiation, 3rd l e a f - primary branch differentiation stage, 2nd l e a f - panicle prlmordla dIfferentlatxon, 1st l e a f - - end of splkelet number increase, 0 5th l e a f - - initial stage of reduction division, 0th l e a f - - ripe pollen stage Based on the synchronization mentioned above, the submodel of organ development was constructed by using the leaf age and the total leaf number submodels DATA USED

Crop data were taken from the Chmatlc-Ecologlcal Joint Experiments for different rice varieties in the Yangtze River Valley, China The experiments were conducted at 15 locations (Fig 2) over ten provinces/municipalities

82.5

b

90 0

- ~

97 5

105. 0

10,

6

112. 5

.

f 15 L-~

/

_

120. 0

15/

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127.5

j

Fig 2 The locations for the chmatlc-ecologlcal joint experiments m the Yangtze valley, China (1985-1986)

75 0

15

20

25

30

35

4,5,

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135.0

Xuancneng Snanghaz Kunshan

7

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Cnangsha

Nanenang

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10

L GAO ET AL

TABLE 2 P a r a m e t e r s of the p h e n o l o g l c a l s u b m o d e l for four representative rice varleues Development phase

Sowingemergence Emergenceheading

Headingmaturity

Parameter

k' P' k' P' Q' G' k' P'

Varieties S U 63 Hybrid i

D T W X Medmm i

7038 Medmm j

10175 Late j

- 0 60 0 40 - 4 387 1 265 0 777 00 - 3 560 0 226

- 0 83 0 45 - 4 372 1 117 0 421 00 - 3 498 0 269

- 0 70 0 56 - 4 080 2 761 1 628 -0291 - 3 327 0 875

- 0 65 0 80 - 4 235 1 711 1 000 -0359 - 3 575 0 335

l, Or~ z a mdt¢ a, J, Or~ z a j a p o n u a

(Slchuan, Shaanxl, Hubel, Hunan, Jlangxl, Anhul, Jlangsu, Zhejiang, Fujian and Shanghai), during 1985-1986 A separate crop data set for vahdatlng the model was collected from six locations In Jlangsu province during 1988-1989 The mean dally temperature data for the same period were supplied by the local meteorological stations The daffy day-length data were generated by a harmonic function (Jones, 1983) PARAMETERS

IN THE SUBMODELS

Phenologlcal submodel Following the procedures described in the section on Description of the model, the phenologlcal submodel was fitted to both the crop data and environmental data, then the relevant parameters were obtained which are shown in Table 2 Taking into account that the developmental phase from emergence to heading varies greatly and largely determines the overall growth duration (Gao et al, 1987), Table 3 gives some statistical tests for the phase from emergence to heading only According to the parameters listed In Table 2, it is easy to distinguish the basic duration (1 e I/exp (k')), thermal and p h o t o p e n o d sensitivities for different rice varieties For example, during the phase from emergence to heading, the late japomca w~th early maturity is the most strongly sensmtve to the p h o t o p e n o d ( G ' = - 0 359), followed by the medium japonica (G' = - 0 291), and the medium mdlca and hybrid are essentially referred to

A COMPUTER MODEL TO SIMULATE RICE DEVELOPMENT

11

TABLE 3

Statistical test of the phenologlcal submodel for four representative rice varieties for the emergence to heading phase Statistics

Varieties S U 63 Hybrid i

D T W X Medium i

7038 Medium j

10175 Late j

0 841"* 4 01 5 41 16

0 869** 3 23 4 44 41

0 924** 3 24 6 41 16

0 955** 3 39 7 32 38

R22 ~ SE b SE "~ nd

'Coefficient of deterrnmatlon of the submodel bStandard error in days of the submodel ~Standard error m days of the degree-day method d Sample size l, Orvza mdwa, j On, za japontca **Significant at 1% statistical level

the msensmve-photoperlod type (G' = 0) The thermal sensitivity (represented by P', Q') of japonica (especially medium japonica) is usually greater than that of lndlca From Table 3 we can see that the coeffioents of determination are above 0 84 and the phenologlcal submodel reduced errors over the tradmonal degree-day method by about 1-4 days for lndlca and 3-4 days for japonica

Leaf age submodel In Table 4, the statistical test shows that the coeffioents of determination R22) for the two representative varieties are greater than 0 90 The standard errors (SE) in leaf age are less than 1

TABLE 4

Parameters of the leaf age submodel and its statlsUcal tests for two rice varieties Variety

D T W X N J 10175

Parameter

StatlsUcs

c'

a'

b'

RZ2

n

SE

- 0 20 0 05

0 25 0 48

0 68 0 67

0 960** 0 903**

90 90

0 63 0 72

**Significant at 1% statistical level

12

L GAO ET AL

TABLE 5 C o r n b m a t t o n o f the p h e n o l o g t c a l a n d l e a f a g e s u b m o d e l s a n d t h e i r statistical test (variety D T W X ) Number of physiological days of development No

Mean growth duration simulated (in days) N

Mean whole leaf age simulated Lw

Mean actual total leaf age Lt

R

Mean difference between actual and simulated leaf ages m

Standard error m leaf ages

Sample size n

79 2

94 7

17 7

16 3

0 638***

14

10

34

***Sigmfit.ant at 1% statistical level

Submodel of total leaf number Table 5 illustrates how the phenologlcal and leaf age submodels can be combined, with an example of the D T W X variety The development phase concerned is from emergence to heading According to the phenologlcal submodel (eqn (4)), we first calculated N, the number of actual days covering the phase, then used N and the mean daily temperature data within the phase with the leaf age submodel (eqn (6)) to calculate the whole leaf age (Lw) Finally, we compared Lw with the actual total leaf age (Lt) There exists a significant correlation coefficient between L w and L t, with a SE of 1 0 leaf Their difference m is equal to 1 4 (in leaf age), showing that the time interval from the fully developed flag leaf to heading is equwalent to 1 4 leaf age PHYSIOLOGICAL

AGE AND

RICE

CALENDAR

In this paper, the concept of development index (DVI) was used to identify quantitatively the development processes between emergence and heading for rice crop The DVI is defined as

DVI

= (U o)

\No/

where DVIj 1s the plant's physiological age corresponding to j t h leaf age Njo and No are. respectively, the numbers of physiological days o f j t h leaf and the whole duration in days from emergence to heading under optimum condltlOnS For a given variety grown at a certain location with a certain sowing date, constant DVI values are often required for bearing a certain leaf number and for the appearance of various organs Therefore, DVI serves as a good criterion for simulation of the development processes

2

2

I

1

1

0

-

-

Leaf age

Elongation of leaf sheaths

Elongation of leaf blade

Emergence of primary tdlers

Root's growth

-

aTotal leaf age bWhole leaf age ~Pamcle ax~s dlmtml stage of pamcle ePrlmary branch dlfferentlatmn CPanlcle pnmordla dlfferentlaUon gEnd of splkelet number increase hActwe stage of reduction dwlslon 'Pollen formation stage 'Heading

Pamcle development

Elongation of mternodes

37

13

Number of physiological days

-

004

001

0

0

2

3

3

66

007

1

1

3

4

4

I01

011

Development index (DVI)

2

2

4

5

5

140

015

3

3

5

6

6

183

020

4

4

6

7

7

229

024

5

5

7

8

8

278

030

6

6

8

9

9

331

035

Schematic of rice calendar (variety D T W X , sowing date 30 April, Nan ling)

TABLE 6

7

9

I0

10

386

041

8

10

11

11

443

047

9

d

1

12

13

12 11

13

566

060

12

503

054

~

2

13

14

14

630

067

f

3

14

15

15

697

074

g

4

15

16

16

766

082

h

5

16

17

17 a

837

089

940 18 4b

18

100 910

097

~r P~ z .q

?

,< m

¢7

m

-.] m

K

.-1 O o~

©

14

L GAO ET AL

Using the local chmatlc data, a rice calendar for a given variety at a certain location could be constructed, which is o f considerable importance in rice cultural management Table 6 shows an example

VALIDATION OF THE MODEL

Model predictions o f heading date were tested with the Rice Clock Model Table 7 and Fig 3 make comparisons between the measured and simulated dates for the S U 63 variety, obtained from an independent study conducted at six locations in Jlangsu province, during 1988-1989 An average error in heading date with a SD of about 3 5 days and a correlation coefficient as high as 0 88 indicate that the model behaves satisfactorily

TABLE 7 Comparison between pre&cted and measured durations m days from emergence to heading for the model vahdatlon, using a hybrid indlca rice of S U 63, at six locaUons m Jlangsu Province, 1988-1989 Location

Year

Nanjlng

32°00'N 118°48'E

Baoymg

33 °14'N 119°18'E 31°46'N 119°56'E 32°5 I ' N 120°18'E

Wujln Dongtal

Hualymg

33°36'N 119°02'E

Suqlan

33°57'N 118°14'E

1988a b 1989a b 1988a b 1988a 1989a 1988a b 1989a b 1988a b 1988a b 1989a b

Mean Standard deviation a, the first sowing date b, the second sowing date

Growth duration m days Pre&cted

Measured

Difference

99 90 98 93 100 91 90 92 106 95 107 97 96 91 93 90 105 97

102 90 98 95 107 94 87 90 109 93 102 93 93 89 98 90 105 97

- 3 0 0 - 2 - 7 - 3 - 3 2 - 3 2 5 4 3 - 2 - 5 0 0 0

95 7

95 7 -

0 35

A COMPUTER

MODEL TO SIMULATE RICE DEVELOPMENT

15

115 110 105 lO0 95

90 85

80 |

75

80

85

|

90

95

,

•

100

105

110

115

Measured (d) Fig 3 Relationship between predicted and measured duration in days from emergence to heading for the S U 63 variety at six locations m Jmngsu Province, China

REFERENCES Brown, D M and Chapman, L, 1960 Soybean ecology Development-temperature-moisture relationship from field studies Agron J, 52 496-499 Chang, T T and Oka, I , 1976 GeneUc reformation in the chmatlc adaptablhty of rice cultlvars In Proceedings of the Symposium on Climate and Rice, International Rice Research Institute, Los Banos, Phdlpplnes, pp 87-111 De Datta, K , 1981 Principles and PracUces of Rice Production John Wiley, New York, pp 25-40 Dlng, Y (Ed), 1961 Cultivation of Chinese Paddy Rice Agnc Pubhshlng House, Beljmg, pp 101-113 (in Chinese) Gao, L Z , Jm, Z Q and LI, L, 1987 Photo-thermal models of rice growth duration for various varietal types m China Agrlc For Meteorol, 39 205-213 Jones, H G , 1983 Plant and Microchmate Cambridge Umverslty Press, London pp 281-283 Lx, W Z , et al, 1982 Operation Analysis Qlnhua Umverslty, Beljmg, pp 185-186 (in Chinese) Lm, Q H , (Ed), 1991 LeafAge Pattern for Rice and Its Apphcations Jlangsu Science and Techmcal Publishing House, Nanjlng, pp 4-17 (in Chinese) Matsushlma, S, 1984 Crop Soence m Rice Nippon Koel, Tokyo, pp 89-109 Nuttonson, M Y, 1948 Some prehmlnary observations of phenological data as a tool m the study of photoperlod and thermal requirements of various plant materml Vernahzatlon and photoperlodlsm A symposmm, Waltham, Mass, Chronlca Botamca, pp 129-143 Penning de Vrles F W T , Jasen, D M , Ten Berge, H F M and Bakema, A , 1989 Simulation of Ecophyslologlcal Processes of Growth m Several Annual Crops IRRI-PUDOC, Wagenlngen, Netherlands, pp 73-81

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L GAO ET AL

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