全 文 ： ACTA AGRONOMICA SINICA 2008, 34(2): 311−317 http://www.chinacrops.org/zwxb/
ISSN 0496-3490; CODEN TSHPA9 E-mail: xbzw@chinajournal.net.cn
:  (863) (2003AA209030) (BG2004320)
 : (1976–), , , ,  !#$%&%()*
* +,#-(Corresponding author): ./(1976–), , 0+, , 123, 456789:)Tel;025-84396565
E-mail: yanzhu@njau.edu.cn
Received(<=>?): 2007-03-23; Accepted(@A>?B: 2007-08-11.
DOI: 10.3724/SP.J.1006.2008.00311
 
       *
(/  ,   210095)
 :   ,    !#$%
&()*+ 4 ,-./0 1234567, 8945:;<45=>?-.@ :A
BCDEFGHI, JK9LMNOPQRSTD UV=> WXY, DZ[\M
   0 0]$ Logistic^ _`Mabc9dSef(GDD) g ; h$
ijkl_`MAS GDD W ; 9m$nopqij^ _`MP(-.r A) 
W ; st, +;<9uv9m_`M-.;wP\x yz{|.}h$~
€45‚7ƒ\ 0DEMI4„5, ab9dW:A …^†‡(RMSE)9m3 3.6 cm:
3.96 cm+c 3.15 cm:3.56 cmˆ( 0 g ‰Š ‹IŒŽŒ
: ; ; A; 0; ;  0
A Simulation Model of Leaf Elongation Process in Rice
CHANG Li-Ying, GU Dong-Xiang, ZHANG Wen-Yu, YANG Jie, CAO Wei-Xing, and ZHU Yan*
(Nanjing Agricultural University/ Hi-Tech Key Laboratory of Information Agriculture of Jiangsu Province, Nanjing 210095, Jiangsu, China)
Abstract: Modeling leaf growth dynamics in rice is of significant importance for realizing virtual and digital plant growth. Based
on time-course observations on leaf morphological properties (leaf length and leaf width) on main stems and tillers under different
nitrogen rates and water regimes with four rice cultivars, the change patterns of leaf morphology with growth progress and envi-
ronmental factors were characterized, and a dynamic model was developed to simulate time-course growth characters of different
leaves on rice plant. The growth dynamics of leaf length on stem and tiller could be described with a logistic model, leaf width
with conic equation, and leaf shape with exponential function and quadratic equation. The effects of nitrogen and water conditions
on leaf growth were quantified by the effective values of leaf nitrogen concentration and water content. The model was validated
with independent field experiment data of different nitrogen rates, and the mean RMSEs of dynamic leaf length were 3.60 cm and
3.96 cm, those of leaf width were 3.15 cm and 3.56 cm on main stem and tillers, respectively. The results indicated that the present
model had a good performance in predicting morphological growth of leaf on stem and tiller in rice plant.
Keywords: Rice; Leaf length; Leaf width; Leaf shape; Dynamic; Simulation model
  , 
 [1] !#$
%&()*+,-. /0
1234[2-6]56 7 834
9: , ;34<=>?@ , ABCD
EFG<H>IJ, KLMN2O;=>
IJPQRFS0RTFSQRUVWJ
X<YZ[\T]^_7`G
34ab$c , def#$ghij , 5
6 k7el/mnopq%r, LMNs
tl/uvmwxyz{|7ghij<
}~[7-9]%& €uT, 
312      34
‚\ƒ„…†{…N0‡ˆM‰Š
…, K‹ŒhŽef‘{|’
c\“”•T–M—‹, ˜™N
QRšv%&l/›œž, ŸI ¡¢£d
ef#QR%m¤¥¦§yz¨ ©mªQ
RU>«.‡ˆ{|¬
­ , 4®%&=><ccv , N¯
%&=>°±®²³´µ¶·¸¹º
1 
1.1 
˜cv4®m»œ¼½¾¢¿ÀžÁ 3 –
QR›œ
›œ 1¤Ã›œ2005Ä;ÅÆÇțœÉ
abÊË() , ÌÍÎÌ , Ï\ÐÑ
1.61%Ò¤ 0.14%Ӕ¤ 74.70 mg kg−1ÔÕÖ
10.36 mg kg−1ÔÕ× 82.60 mg kg−1´ ›l/Ø
ÙÚ 14Û 4 –¤¥¦§%r, N1N2N3N4
Ü 082.50164.70247.00 kg N hm-2, ÉÃ 
à  Ý-ÃÞ-à 5  1  2  2ߦ§¼¾Ö
×ÃàÜ 82.50 kg hm−2 P2O5m 164.70 kg hm−2
K2O, ÉÃTáâ¾5 ã 20 äå/, æWç, 6
ã 20äèp, bšé 16.6 cm × 20.0 cmêë
¿›ìíî, ïðèp(ñ@ò 3 m × 4 m, EÐ
ñÛó, ƒ 3 áß(ñôõNöž÷øùú,
û²üýþpq
âRô
›œ 2%›œ2005Ä;ÅÆ6!
›œ% ñab ,  Ûâ , ¨F
ú , Q¨FÌÍÍ , Ï\ÐÑ
1.10%Ò¤ 0.11%Ӕ¤ 95.50 mg kg−1ÔÕÖ
35.90 mg kg−1ÔÕ× 108.80 mg kg−1´›l/
ØÙÚ 14Û 4 –%¦§, ¿eÌÍôG
º%f, dôGº%f 70%80%90%ý%
fN0%§(3~5 cm) W1W2W3W4, 7
ÌÍabý%, N 2~3 d Šß%  20
cmÌÍ¿eÏ%f, d¦§  !ÌÍÏ%
f%¦§ë#$%&%5ã 20äå
/, æWç, 6ã 20äèp, bšé 16.6 cm × 20
cmê뿛ìíî, ïðèp, (ñ@ò 1 m ×
1 m, ƒ 3 á, EÐñÛó¤Ã§R›œ 1
P N3, Ö×Ãmþ§àR›œ 1
›œ 3l/›œ2005Ä;ÅÆ6!
›œ% ñab&¾ 4 –QRšv%
&l/´›ž, A(²Ú&l/Ø
ÙÚ 14 mä˜), *+,&l/ÅÆ 16 m
-& 6./%§R›œ 10, 1R›œ 2
1.2 
¦§ƒ¿f 3š((ñ 1š), eš¿f
2>m« ¡¢£<IJ, T3
 2 4¿ 1 á, =>A56N0 =>{|A7
F¯4¿ 1á(Œ89¯)>:$É
é;, «;:$É< 2 cm>¦
¿T–j
¢£%&šQRU%m¤¥Ïf
<{|IJ, =èp>%, < 4~5 dŠTá
?, &Š>@ATAšáŠ? 3 š((ñ 1
š), UBÔCŠ©DE¼\, ¾ÂFöž
GFHIJKœLMŠN, OPQR 105S
# 30 min, _ 80Q$T, MŠU, NóV
Ï%f, d¾WXYZfe¤[¿eϤf
=%&èp$\]ª¯G, (ñ&Š 30š
‚\^9…š, ab_=0ªªUˆ
í, N`ªa=áb ©í M, Tcªí
 PT, dcªí ST, í L
;%&e–=W¯ , ¾fÇ6!=
ZDR-11 vgXíhiÂ<íhß(ñ4gX
{|, íhFGG< 0.5 hã¨îTágX
j
1.3  
›œ 2 m 3 ¢¿Àž ¾ë4®%&
=><cv, ›œ 1 ¢¿Àž ¾ëcv
¿›m»œ, ¼‰›œjàŠ 3 ჿfr
àjklj§±ó#?[, ®²‘%&
=>IJ{|¬­0ìwxKmµ°j!9:
n, RF½¾o(dp[m›q[.ŽecvÉ
˜ij½¾rsEt¾à?Y RMSE(Root
Mean Square Error), 7cj좿juXa
b±ó#RMSEjv(, 9wcj좿j
TA…vx, cvc3yvŽ†zRMSE
óV{nŒ¨, P OBSi¢¿j, SIMic
j, n?˜|f
2
1
( )
n
i i
i
OBS SIM
RMSE
n
=
−
=
∑
 2 :    313
2 
2.1 
2.1.1 %& ©H>IJE
GDD {|T–}~>7>~IJ, u S
v€ Logistic ?J, ‚Tcªìdcª
ì ©ƒ„R?{|cn(… 1)
K‹, 7%&H>IJ†¾?J(1)Áe
f‘
n ( ) /( ) 1 e n n
n
Lb GDD IGDD GDD
LL
LL GDD
La − × − Δ
=
+ ×
(1)
nP, GDD †ä‡ˆ=>Xä, e‰Te
F¯ëɗgXäràgXìVWɗg
XYj‡òj , ïUd, óVŠ?J (2);
LLn(GDD)‹ n;Œ GDDF>; LLn‹
n e>X, óVŠiC™[10]; LaLb
?J°j, ŸI7›œ 2 m 3 j#܊
j 8.656.26( ©), 6.156.86(Tcª), 6.65
6.12(dcª); IGDDn‹ n=>Ž GDD
j; GDDn‹ n=>¼ GDDj
( )i bGDD T T= −∑ (2)
?J(2)P, Ti‹ i4ràgX; Tb%&V
WɗgX, T3Ú& 10‘, ,& 12‘
 1  14(A) 6 (B)  14    GDD
Fig. 1 Changes of leaf length of L14 on main stem and synchronous leaves of primary tillers, secondary tillers with cumulated GDD
after leaf emergence in Wuxiangjing 14 (A) and Yangdao 6 (B)
™[11]0˜’“, %&ß (
”9G&•)=H>$e>H>–¯— 1.5
–˜˜E GDD{|™š›jµ°, K‹
˜ì GDD µ°†N‘ LA(˜) = aœ
GDDb, P ab?J°j, ŸI7›œ 2m 3
j#܊j 0.0154 m 0.998%&
RHµ°, ‹ n UOF, ‹ n1 ”ì
‹ n29GH>, ¼N‹ nU IGDDn
ìGDDnóV܊?J(3)m(4)P, kl
ž°j, Kl/LZ, T3 0.1
1/
n
b
n
nIGDD kl GDD
a
⎛ ⎞⎟⎜= − ×Δ⎟⎜ ⎟⎜⎝ ⎠
(3)
1/ 1/
n
1.5 b bn nGDD
a a
⎛ ⎞ ⎛ ⎞+ ⎟ ⎟⎜ ⎜Δ = −⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜⎝ ⎠ ⎝ ⎠
(4)
Ò¤ÏfŸt†š¤¥%rT–
=§‡ˆ˜9w, %&>XEŸ¤Ïf
 ˆL ˆ , ¡Tµ°udခ?J , =L
Že¤¥}~Km F(N)óVŒ?J(5)
21 ( )( )
1
Nla ANCL MNCLF N
⎧⎪ − × −⎪=⎨
⎪
⎪⎩
0 ANCL MNCL
MNCL ANCL
< <

(5)
P Nlaj 0.0028, ?J°j; ANCL
Ks¤Ïf(%), }›œ¿f‰¢; MNCL %
&on¤Ïf£T¤#9w, QRl/
=¥a>%on¤ÏfQ¦{|, ™O†
§¨¨©@ , ¡Tµ°†N¾‡j?JÁ‘ ,
Œ?J(6)
MNCL = NLbœe NleI (6)
?JP, i¥a GDD; NlbNlc?
J°j, ŸI7›œ 2 m 3 j#܊j
 1.12−0.15
%ÏfŸtsªš%«¬=
§‡ˆ , ›œ9w , EŸÏ%f 6 , ­ª
>X†§ >, 5ëonÏ%f®
¯†§{(, =LŽe F(W)óVŒ?J(7)
314      34
21 ( )( )
1
wp
wp
AWCL LW
Wla
MWCL LWF W
⎧ −⎪
⎪ − ×⎪⎪ −=⎨
⎪
⎪
⎪
⎪⎩
0 AWCL MWCL
MWCL AWCL
< <

(7)
F(W)%}~Km; Wla j0.016, ?
J°j; AWCLKsÏ%f, †}›œ¿f
¢>; LWwpMWCLÜ°±—Ï%fì
onÏ%f, QRl/Šràj 30%70%
2.1.2  ™9w, %&H>
F, «X²³´É˜µŽe[12]˜3y
¶’“, EŸ¥a, «{|YZQ’·5
eo6«EQRUL{|, ‚™O
dခ{|¬­(… 2)‹0, o6«;QR
l/G\¸’·YZ(?Y# Fj 89.29, F0.01
j 4.29), Œ… 2¼“
›œ3y¹’“ , QR¤¥m%¦§¨ , ­
RUo6«É˜TA(… 3)RF?Y
#3y9w , QR¤¥m%¦§ F jÜ
2.16m 2.59, º(ë F0.05j 2.80m 2.79}‹†»,
¤¥ì%7«}~Q’·, KL%&QR
Uo6«{|¬­†¾?J(8)Áef‘
 2   
Fig. 2 Changes of the maximum leaf width with leaf positions
on main stem in different cultivars
 3 (A)(B) 14  
Fig. 3 Changes in maximum leaf width with leaf positions on main stem under different nitrogen rates (A: kg N hm−2) and soil water
regimes (B: field water capacity %) in Wuxiangjing 14
2
n nLW GDD LW Wa n Wb n Wc= = × + × +  (8)
nP, LWn‹ nUo6«; n9“U;
WaWbWc?J°j, ܊j0.0042
0.21940.0341
[0 , ˜›œ¢£9w , %&ª«ì ©
RH«É˜­R
2.1.3  =:$ÉQ
R>¦«{|%&e<=
>IJ(… 4-A)9O>{|6ë«{|cn
=… 4-B P†N¼a, ½QRU>m
«QT?, 5QRU«E>{|¬
­TA
… 5 9w, ;¥aIJP, «E>{
|àuT¾dá?JK‹, QRU¿
>?À«{|†¾?J(9)Áef‘
2(n n nLWid LL GDD WPa LL GDD= × +  
nWPb LL GDD WPc× +  (9)
?J(9)P, LWidn (LLnGDD)‹ nU; LLn
(GDD)>¦«; LLn (GDD)‹ n;Œ GDD
F>, óVŠ?J(1); WPaWPbWPc?J
°j, ܊j0.00030.04170.0761
… 6 Á“a 4 –´›%&l/ ©QRU
e>ìo6«<µ°†N¼a ,
o6«EŸ> ˆL ˆ,  >ÔXEŸ
b ˆLÂ(LÃìþ{|¬­Ä\Y
ZK;ë89a=ÜÃ, 
 2 :    315
 4  14 14  (A)(B)
Fig. 4 Growth dynamics of L14 shape (A) and change patterns of final leaf shape (B) in Wuxiangjing 14
 5  6 14   
Fig. 5 Changes of L14 leaf width with leaf length growth on
main stem in Yangdao 6
 6 !#$%&()*+ ! ,
  (-./0; 1./23)
Fig. 6 Changes of leaf width with leaf length from leaf apex to
basal part on main stem in different rice cultivars (Solid line:
flag leaf; Dotted line: other leaves)
>’·{Å, L«’\ ˆ©@½ ©
>mo6«;QRl/GÆ;w’ÉKvY
Z, 5QRl/ ©e>ìo6«
­7µ°Ç†¾š‡j?J(‹TìÃ)md
ခ?J(þ)Ax9:, Œ?J(10)
WLR
2
( )n
P LLen
LWid LLen
WPd LLen WPe LLen
⎧⎪ ×⎪
=⎨
⎪ × + ×⎪⎪⎩
1 or
2 1
n LN
n LN
=
− 
(10)
LWidn(LLen)‹ n U; LLen >¦«;
LLen ¿>?À>X; ŠjÈÉ 0~LLn,
LLn‹ nÒÁ>X; P?J°j, Ê n
= 1 F , Šj 0.28, WLR ‹To6«
(FLWidn)ìo6«¼7ª>(FLn)Ëj, }
?J(11)¢, T3 0.38 FLnÌo6>XË
Í, ;QRl/GYZQ’·, Ίràj; Ê n
= LNF, PŠj 0.27, WLRŠj 0.46
1n
n
FLWid
WLR n
FL
= = (11)
WPdWPe?J°j, Ü}?J(12)m?
J(13)a
max
20.22
n
n
Width
WPd
LL
−
=
− ×
(12)
max
0.215
n
n
Width
WPe
LL
−
=
×
(13)
nP, Widthmax-n‹ n2o6«X, †}
?J(8)a
316      34
2.2 
Ͼ›œ 1 ¢¿Àž7¼®%&>«
cvab$»œ, dÐacj좿j 1Ñ1µ
°…(… 7~… 8), 3y’“;=><c
jmK¿jG‚\AxTA…muX=…
7 †N¼a, ˜cv7QR¤¥%r¨%& ©(…
7-A)mª(… 7-B)QRU;QRGDDF
>‚\AxÒ¿…RF=… 8†N¼a, ˜cv
7%& ©(… 8-A)mª(… 8-B)QRU0R
TQR>¦«{|¶‚\AÓÒ¿Ô³
±ó#9w, cv7 ©mª<>«
Ò¿à?YÜ 3.603.963.153.56 cm
 7    GDD
Fig. 7 Comparison between simulated and observed values for leaf length of different leaf positions on main stem (A) and tillers (B)
at varied GDD under different nitrogen rates
 8    
Fig. 8 Comparison between simulated and observed values for leaf width at varied leaf length on different leaf positions on main
stem (A) and tillers (B) under different nitrogen rates
3 
µë®cv´\ÕÖ, Hanan
.[13]$,-®cv, Fournier .[14]$
*+×Ø34=>IJ, ÙÚ.[15]7*+Ûab
$‘m×Ø34®, Pommel.[16]c$*+×Ø
ÛIJ5}ë€u†{
…ƒ„…N0‡ˆ<jjM‰Š…, T3ºs܅8cvÝeyz¨
cv, LÞB³aÔÒ¿®IJßn…<
ccv˜ŸIàP¢¿m°±#%&
r@RT>ì«Gµ°N0
©ìªRH>XGµ°, %&
®IJ, ®²$†á‘%&QRU=
><ìghijIJccv
%&=>âl/uvmwxyz’·}
~[17-18]5;NãP, cvT3}nopq
%rme=wx¨ôG›œ¢>, K‹cv¬
B7QRpq
âm=wxnª…[19-20]Lä
%&=><ccvQå Ôæef‘%&
=>=!IJ, ¹ †zÒ¿%&=>IJ
7l/…mwxyz{|<~ª‹, ˜
 2  :   317
½¾Â}¤Ïf°±—Ï%fìo
nÏ%f.l/ijÁef‘QRuv%&
l/;=>IJPYZ, dç᪾Ï
¤fmÏ%f7QR¤¥m%yz}~¨
=><ab$°±#mefc, Ax
2O$QRl/mQRpqyz¨%&
{|, KLècv‚\Ax”é…mÒ¿…
Ê_, ˜k7%&=>‚2…
L¢> , åêë$%&ghij , Lìí
eî‰E%&=>, ¹ï3%&šðñ
34<{| `G.|, ¡]º
\“ëaT¤mVÁ˜cvòŸIQR
¤%ó¬KmÁstÃ%yz7=>IJ}
~, L%&=>IJ¹¯â>þwxyz
!—, ŒÖ×%rmôõö.K‹, ÷
aT¤ðÁcv;QRyz¨n¾… , RF , 
cvì=>cvøÐ!ì?[, K
O34cì=§IJc [21]ùúì±T ,
aT¤Ó|%&=><‘Ч…mßn
…, d³c°±á…m†z…
4 
4®$%&=>IJ<ccvcv
½¾ Logistic ?J‘$%& ©0ªE=>
Xä(GDD)<H>IJ; Ͼdခ‘$
«E GDD <{|IJ; ܾš›jmT¾d
á?J‘$(QR>¦«)<{|I
J; ¹N¤¥m%Kmܐ‘$QR%¤%
r7®IJef}~˜cv7%&
<H>IJ‚\AxÒ¿…m”é…
References
[1] Guo Y(), Li B-G(). Research of review virtual
plant. Chin Sci Bull ( ), 2001, 46(4): 273−280(in
Chinese with English abstract)
[2] Zhao C J, Wang J H, Wu H R, Huang W J, Zheng W G.
Simulation models and deduction system for interspace de-
scription of wheat leaf shape. Trans CSAE (  ),
2002, 18(5): 221−225
[3] Song Y-H(), Guo Y(), Li B-G(), de Reffye
P. Virtual maize model I. biomass partitioning based on plant
topological structure. Acta Ecol Sin ( ), 2003, 23(11):
2333−2341 (in Chinese with English abstract)
[4] Zhang J-E(), Huang R(), Liu C-S(), Yao
W-M(), Liu Z-F(). Preliminary study on the
visualization modeling of maize leaf structure. J South China
Agric Univ ( ! ), 2001, 22(4): 5−7(in Chi-
nese with English abstract)
[5] Andrieu B, Ivanov N, Boissard P. Simulation of light inter-
ception from a maize canopy model constructed by stereo
plotting. Agric For Meteorol, 1995, 75: 103−119
[6] Mi X-C(#$%), Ao H-J(&(), Zou Y-B()*+). Appli-
cation of visualization technology, model-document-view ar-
chitecture in crop simulation. Trans CSAE (  ),
2003, 19(4): 164−167 (in Chinese with English abstract)
[7] Lawless C, Semenov M A, Jamieson P D. A wheat canopy
model linking leaf area and phenology. Eur J Agron, 2005, 22:
19–32
[8] Watanabe T, Room P M, Hanan J S. Virtual rice: simulating
the development of plant architecture. Int Rice Res Notes,
2001, 26: 60−62
[9] Hanan J S. Virtual plants—integrating architectural and
physiological models. Environ Model Software, 1997, 12(1):
35−42
[10] Shi C-L(,-.), Zhu Y(/0), Cao W-X(12). A simula-
tion analysis on geometrical parameters of rice leaf blade. Sci
Agric Sin (3), 2006, 39(5): 910−915(in Chinese
with English abstract)
[11] Jiang M-N(456), Lin Y-Z(.7), Piao Y-Z(89:).
Corresponding relations between leafing stage of rice and
elongation stage of rice organs. J Northeast Agric Univ (;<
 ), 1998, 29(4): 345−351 (in Chinese with Eng-
lish abstract)
[12] Ling Q-H(=>?), Zhang H-C(@), Su Z-F(ABC),
Ling L(=D). The New Theoretical Study of Rice Cultivation
EModel of Rice Leaf Age (FGHIJEEKFLMNO).
Beijing: Science Press, 1994. pp 27−28 (in Chinese)
[13] Hanan J S, Hearn A B. Linking physiological and architec-
tural models of cotton. Agric Syst, 2003, 75: 47−77
[14] Fournier C, Andrieu B. A 3D architectural and process-based
model of maize development. Ann Bot, 1998, 81: 233−250
[15] Guo Y(), Li B-G(). Mathematical description and
three dimensions reconstruction of maize canopy. Chin J Appl
Ecol (*P ), 1999, 10(1): 39−41 (in Chinese with
English abstract)
[16] Pommel B, Sohbi Y, Andrieu B. Use of virtual 3D maize
canopies to assess the effect of plotheterogeneity on radiation
interception. Agric For Meteorol, 2001, 110: 55−67
[17] Zou J-S)Q,, Yao K-MRST,Lü C-GUVW, Hu
X-QXYZ).Study on individual plant type character of
Liangyoupeijiu rice.Acta Agron Sin (G[ ),2003, 29:
652−657 (in Chinese with English abstract)
[18] Wu W-G(\]^), Chen Z-Q(_`a), Wang S-H(bcd),
Wu S(\e). Effects of rice cultivation under different irri-
gating conditions on the plant type of Hua’an 3. Hybrid Rice
(fgKF), 2001, (1): 30−32(in Chinese with English ab-
stract)
[19] Watanabe T, Hanan J S, Room P M, Hasegawa T, Nakagawa H,
Takahashi W. Rice morphogenesis and plant architecture:
measurement, specification and the reconstruction of
structural development by 3D architectural modelling. Ann
Bot, 2005, 95: 1131−1143
[20] Jonathan H, David M, Bruno A. Maximum likelihood infer-
ence and bootstrap methods for plant organ growth via
multi-phase kinetic models and their application to maize.
Ann Bot, 2005, 96: 137−148
[21] Li W-G( ), Dai T-B(hij ), Zhu Y(/0 ), Cao
W-X(12). An ecological model for predicting protein
content in rice grains. Acta Phytoecol Sin (k[ ),
2005, 29(4): 630−635 (in Chinese with English abstract)