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Analysis of phenological observations on barley (Hordeum vulgare) using the feekes scale
Agricultural and Forest Meteorology, 39 (1987) 37-48 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
37
ANALYSIS OF PHENOLOGICAL OBSERVATIONS ON BARLEY (HORDEUM VULGARE) USING THE FEEKES SCALE
D.W. STEWART and L.M. DWYER
Agrometeorology Section, Land Resource Research Centre, Research Branch, Agriculture Canada, Ottawa, Ontario KIA 0C6 (Canada) (Received March 5, 1986; revision accepted June 1, 1986)
ABSTRACT Stewart, D.W. and Dwyer, L.M., 1987. Analysis of phenological observations on barley (Hordeum vulgare) using the Feekes scale. Agric. For. Meteorol., 39: 37-48. Phenological observations on cereals using the Feekes scale are made in many crop growth studies, although this data collection is very time consuming and labour intensive. Despite the investment in time and labour, quantitative comparison of crop development rates among environments with different thermal, photoperiod, or moisture stress conditions is often difficult because of the non-linearity of the Feekes scale with time. Furthermore, as a result of this non-linearity, it is common for some phenological stages to be missed, even when frequent (e.g., three times weekly) observations are made. In this study, several approaches were taken to quantifying phenological development rates of barley under different growth conditions. First, all stages were expressed as a function of growing degree days (GDD) with a base temperature of 5°C. Missing phenological observations were then interpolated using a linear technique and an iterative procedure that included information from development rates of replicate plants to calculate the GDD associated with missing stages. Finally, a non-linear least squares algorithm was used to fit phenological observations to a function of GDD modified by photoperiod. Statistical analysis of function coefficients provided a quantitative basis for comparison of phenological development rates among different environments. In addition, the non-linear function could be used to predict phenological stage according to the Feekes scale as a function of GDD and photoperiod. INTRODUCTION P h e n o l o g i c a l o b s e r v a t i o n s a r e a n i n t e g r a l p a r t of m a n y c e r e a l c r o p g r o w t h and development studies. These observations are usually recorded using the F e e k e s s c a l e ( L a r g e , 1954). H o w e v e r , o f t e n o n l y a few o f t h e m a j o r s t a g e c h a n g e s , e.g., e m e r g e n c e , t i l l e r i n g , j o i n t i n g , h e a d i n g , a n t h e s i s , soft d o u g h o r r i p e n i n g , a r e n o t e d . I n a d d i t i o n , b e c a u s e of t h e n o n - l i n e a r i t y of t h e s c a l e w i t h time, t r a n s i t i o n s a m o n g these states m a y be t r e a t e d separately, r a t h e r t h a n c o n t i n u o u s l y , w i t h a c o r r e s p o n d i n g i n c r e a s e i n t h e c o m p l e x i t y a n d n u m b e r of c o e f f i c i e n t s r e q u i r e d for a n a l y s i s of p h e n o l o g i c a l o b s e r v a t i o n s f r o m e m e r g e n c e to r i p e n i n g ( R o b e r t s o n , 1968; W i l l i a m s , 1974; D o r a i s w a m y a n d T h o m p s o n , 1982). T h e r e f o r e , d e s p i t e a l a r g e n u m b e r o f s t u d i e s w i t h t h e a i m of d e f i n i n g a L.R.R.I. Contribution No. 86-10.
0168-1923/87/$03.50
© 1987 Elsevier Science Publishers B.V.
38 phenological index to predict cereal crop development as a function of meteorological or edaphic parameters (Robertson, 1968; Williams, 1974; Gallagher et al., 1976; Idso et al., 1978; Doraiswamy and Thompson, 1982; Davidson and Campbell, 1983) a simple method based on recognized procedures has not been developed to analyze phenological observations on cereals as a function of both meteorological and edaphic parameters. This paper describes several approaches to the analysis of phenological observations, based on the Feekes scale, made three times weekly on barley (Hordeum vulgare) grown in a greenhouse under three photoperiod treatments. Suggestions are made for analyzing data sets with missing observations and a technique to quantitatively compare phenological development rates in cereals is presented. METHODS
Experimental details One hundred and ninety-two barley plants were grown in a greenhouse in 15.2-cm diameter pots of sandy loam soil. An automated canopy system controlled three photoperiods (8, 12 and 16 h), and 64 pots were maintained under each photoperiod. On cloudy days, when the daytime quantum radiation (Q) was < 100pEm 2 s-l, natural light in the greenhouse was augmented with fluorescent lights to bring Q to a minimum 200pEm-2 s 1. Mean daily temperatures averaged -~ 25°C, but thermocouples monitored air temperature 60 times per hour and average hourly temperatures were recorded on a datalogger. Pots were weighed daily and watered to maintain a soil water content between 80% available water (defined as water held between - 0 . 0 3 and 1.5MPa) and field capacity ( - 0.03MPa or 0.165cm 3 cm 3). Phenological observations were made three times weekly on each plant and stages were recorded according to the Feekes scale (Large, 1954). Observations from 96 plants were analyzed originally. The remaining 96 plants formed an independent data set. -
Theoretical considerations The influence of temperature on phenological development is well documented from the early work of de R~aumur (1735) and Boussengault (1837) to the more recent studies of Brown (1960), Robertson (1968), De Wit et al. (1970), Williams (1974) and Arkin et al. (1976). The degree day or heat unit hypothesis has been widely used to describe crop development (e.g., Pirasteh and Welsh, 1980; Keitzar and Singh, 1981; Hammer et al., 1982; Neild et al., 1983; Davidson and Campbell, 1983). Briefly, a sum, S(°C), is accumulated for a development period beginning at emergence (day 0) and ending at day m from the following expression:
39
2
w h e r e Tmax is m a x i m u m daily air t e m p e r a t u r e (°C), Tmi n is m i n i m u m daily air t e m p e r a t u r e (°C) and Tb is a basal or t h r e s h o l d t e m p e r a t u r e (°C) below w h i c h d e v e l o p m e n t ceases. In this study, t h e r e f o r e , the n u m b e r of growing degree days ( G D D ) a c c u m u l a t e d to each F e e k e s d e v e l o p m e n t stage of b a r l e y was c a l c u l a t e d based on a Tb of 5°C for g e n e r a l p l a n t g r o w t h (Edey, 1977). F o l l o w i n g the F e e k e s scale (Large, 1954) 22 p h e n o l o g i c a l stages in b a r l e y were observed (stage 10.5.1 was omitted) on 64 r e p l i c a t e plants for e a c h p h o t o p e r i o d t r e a t m e n t . A subset of 32 r e p l i c a t e plants from e a c h p h o t o p e r i o d was r a n d o m l y selected for the original analysis. The d a t a for e a c h t r e a t m e n t were t h e n s u m m a r i z e d in two m a t r i c e s Ai, j and aij w h e r e i = 1, u (u is the n u m b e r of plants = 32) and j = 1, v (v is the n u m b e r of stages observed = 22). Ai, j is the a c c u m u l a t e d G D D from p l a n t i n g date to the jth stage of the ith p l a n t and a~j is the difference b e t w e e n A~,~and A~j 1. F o r the first c o l u m n Ai,1 = ai,1; for all o t h e r columns: Ai,j -
Ai,: 1 =
(2)
aij
F o r a complete set of o b s e r v a t i o n s (i = 32, j = 22), m e a n s for a given stage are c a l c u l a t e d as: 32
,7ir =
~ Aij/32
(3)
i=l
and 32
(4)
aiJ32 i=l
If o b s e r v a t i o n s are missir.g, m e a n s can be c a l c u l a t e d using the o b s e r v a t i o n s w h i c h are available, or the following t e c h n i q u e can be used to fill in missing d a t a to o b t a i n a s m o o t h e d s e q u e n c e of means. F o r n missing o b s e r v a t i o n s in sequence: Ai,j+n -
Aij
1 = aij + aij+l + ...
+ aij+n
(5)
F o r a first a p p r o x i m a t i o n we assume: aij
=
aij+l
=
...
=
aij+n
(6)
w h i c h allows us to estimate missing v a l u e s and to o b t a i n a n estimate of ~i and 5i from eqs. 3 and 4. We t h e n made the more realistic a s s u m p t i o n of: aij
_
aij+l
aij+n -
(~j
aj + 1
. . .
-
(7)
aj + n
Combining eqs. 5 and 7 and r e a r r a n g i n g results in:
40
a~j =
( Aij., - Aij i)/(1.0 + ~t~+llgtj + ~j+21Etj + . . .
+ aj+nlaj)
(8)
Similarly, aij+l
=
(Ai,j+n -
Aij_l)/(ctj/ctj+l
a~,s+n
=
(A~u+n -
A,j
-4- 1 + aj+2/aj+l
,)/(~1lgtj+n + aj+llaj+n Jr- . . .
+ ...
-~- 1)
~- a j + n / a j + l )
(9)
(10)
From these new estimates ofaij, we can recalculate Aij and then A]j and ~j. The process is repeated in an iterative cycle until values of A i j converge to constant values. This procedure requires observed data in each column. However, t h r o u g h trial and error we found t h a t the procedure converges when up to 65% of the data are missing for a given column, although this percentage is also a function of the total number of observations per matrix. The above analysis is useful for smoothing accumulated G D D averaged over a number of plants since it takes advantage of the fact t hat stages occur c o n c u r r e n t l y for a given t r e a t m e n t and both the rows and columns of the matrices can be used for averaging. However, if accumulated G D D could be related to development stage by a continuous function, then it would be possible to fit G D D directly to raw phenological data. Visual observation of the data suggested the following function: H
=
(11)
ax + b(x/Xc) n
where H is accumulated G D D at any stage x on the Feekes scale (°C). H is equivalent to ~i except t h a t it is not restricted to the discrete stages of the Feekes scale; a value of H can be calculated for any value of x between 1 and 11.4. Also note t h a t the flowering stages (e.g., 10.5.2) are converted to real numbers (i.e., 10.52). The values of the empirical coefficients a(°C), b(°C) and n were obtained by fitting eq. 11 to observations of each photoperiod using Marquardt's algorithm (Marquardt, 1963). When xc was included as an unknown, the algorithm had difficulty converging to a unique set of values. This means t h a t more t han one combination of b, Xc and n produce the same curve. Thus, Xc was set as the value of x at which eq. 11 departed from linearity. When x becomes greater t h a n Xc, the power term in eq. 11 becomes significantly large. The value of xc was estimated graphically as 9.8. No furt her difficulty with convergence was encountered. Note t h a t a, b and n vary with photoperiod. Equation 11 can be expanded to include a photoperiod effect by dividing by a response function t aken from the CERES model (Ritchie and Otter, 1984). This results in: H
=
( a ' x + b'(x/Xc)n')/(1
-
d(20 - p ) 2 )
(12)
where p is photoperiod (h) and d is an empirical coefficient (h-2). The coefficients a', b" and n ' have the same units as their counterparts in eq. 11. The
I
of accumulated
are
estimated
2
76.0 76.0
458.0 379.0
76.0 76.0
455.0 379.0
76.0 76.0
455.0 379.0
76.0 76.0
455.0 379.0
76.0 76.0
455.0 379.0
76.0 76.0
455.9 379.0
76.0 76.0
455.0 379.0
76.0 76.0
455.0 379.0
~j fij
76.0 76.0
455.0 379.0
8-5 photoperiod
~j ~j
12-h photoperiod
~; (i/
16-h photoperiod
(c)
~/ al
~h photoperiod
~j 5j
12-h photoperiod
~j fij
16-h photoperiod
Co)
~j 51
H-h photoperiod
,~j ~ij
12-h photoperiod
"~1 fij
(a) l f h photoperiod
1
590.0 135.0
534.4 79 4
534.4 79.4
590.0 135.0
534.4 79.4
534.4 79.4
590.0 135.0
534.4 79.4
634.4 79.4
3
Feekes scale stage
technique
values
663.0 73.0
590.0 55.6
590.0 55.6
663.0 73.0
590.0 55.6
590.0 55.6
666.3 73.0
590.0 55.6
590.0 55.6
4
using
8539 190.9
666.3 76.3
666.3 76.3
853.9 190.9
666.3 76.3
663.3 76.3
853.9 190.9
666.3 76.3
666.3 76.3
5
10308 176.9
928.0 261.7
918.4 2521
1030.8 176.9
928.0 261.7
918.4 252.1
1030.8 176.9
928.0 261.7
918.4 252.1
6
1242.9 14.1
9
1161.7 90.2
1359.2 156.5
1219.2 53.4
1468.0 108.8
~227.2 1304.9 161.0 77.7
1228.8 161.8
8
1455.3 ll4.1
1495.8 40.4
1217.5 1278.2 1489 60.7
14929 311
1341.4 63.1
1161.7 1213.3 1296.0 90.1 51.7 82.7
1341.3 142.0
1199.6 1343.4 1461.8 1 6 8 . 9 1 4 3 . 7 118.5
1068.7 140.6
1071.6 153.1
1199.3 168.5
1342.5 65.3
1295.4 81.3
1489.0 21.0
1339.8 34.9
1301.3 58.5
l0
(c) c a l c u l a t e d
10.2
1576.9 84.0
1417.2 - 4.3
1397.8 17.1
1638.5 61.6
1428.2 28.3
1393.6 25.6
1648.6 71.7
1688.9 40.2
1448.2 20.0
1416.8 19.0
1688.9 50.3
1448.2 20.0
1416.3 19.2
1678.1 1920.8 17.7 242.7
1421.5 7.2
1420.2 1428.2 78.8 8.0
1380.7 84.6
1576.9 81.2
1399.9 57.4
1362.4 76.8
1660.4 171.4
1414.3 74.4
1413.3 13.8
10.3
1456.0 19.2
1695.2 48.0
1454.9 48.7
1418.4 40.5
10.5
1490.6 25.7
1454.5 19.3
1876.2 114.2
1588.7 68.2
1547.0 64.1
1874.4 112.4
1598.3 49.8
1662.8 158.2
10.53
1516.0 25.4
1876.2 114.2
1586.3 70.3
1483.1 1547.0 28.5 63.9
1762.0 27.3
1520.5 28.6
1486.0 28.4
1762.0 66.9
1548.5 93.6
1504.6 86.2
1 7 1 1 . 1 1734.7 1762.0 22.2 23.6 27.3
1464.9 16.7
14352 18.5
1 7 1 1 . 1 1734.7 22.2 23.6
succssive
1990.8 114.6
1648.6 62.3
1574.2 27.2
1990.8 114.6
1657.3 68.6
1993.2 35.6
2017.5 143.1
1574.8 - 23.5
1538.7 124.2
10.54
2100A 109.6
]729.5 80.9
1636.7 62.5
2099.8 109.0
1733.8 76.5
1658.4 59.9
2121.1 103.6
1715.8 141.0
1611.9 73.2
11.1
are estimated
2299.2 - 80.4
2480.5 181.3
2424.0 412.1
2193.5 268.0
2480.5 181.3
2424.0 412.1
2011.8 124.9
2480.5 181.3
2424.0 412.1
1925.5 2193.5 1 2 9 . 0 268.0
2299.2 95.5
2203.7 2299.2 103.2 95 5
1886.9 157.3
1796.5 159.8
2203.7 103.9
1881.9 2011.8 1 4 8 . 1 129.9
1797.3 1925.5 1 5 2 . 3 130.7
2379.6 258.5
11.4
1925.5 2193.5 1 3 4 . 1 268.0
11.3
the iterative
1879.7 2011.8 1 6 3 . 9 132.2
1791.4 179.5
11.2
using
data when missing
s t a g e s (fij) f o r p h o t o p e r i o d s
from phenological
values
10.52
missing
1 4 6 7 . 7 1491.9 19.5 24.2
1435.2 17.3
1647.2 273.7
1406.2 11.0
1377,9 35.4
10.4
when
v a l u e s , (b) c a l c u l a t e d
data
missing
phenological
1411.1 1399.6 109.8 11.6
1O.l
from
estimating
s t a g e (,~j) a n d m e a n d i f f e r e n c e i n G D D b e t w e e n
data without
1068.7 1212.8 1277.2 1 4 0 . 7 144.1 64.4
1069.8 153.0
1202.7 172.0
1066.2 138.2
1067.0 148.6
7
interpolation,
from raw phenological
G D D (°C) to each phenological linear
o f 16, 1 2 a n d 8 h: ( a ) c a l c u l a t e d
Mean number
TABLE
42 v a l u e s a, b a n d n a r e e q u a l to a', b' a n d n', r e s p e c t i v e l y , w h e n p equals 20. N o t e t h a t eq. 12 is r e s t r i c t e d to v a l u e s of p ~< 20. V a l u e s of a', b', n' a n d d w e r e o b t a i n e d by fitting eq. 12 to t h e t h r e e sets of o b s e r v a t i o n s . O n c e coefficient v a l u e s w e r e c a l c u l a t e d f r o m o u r e x p e r i m e n t a l d a t a , eq. 12 w a s t e s t e d on i n d e p e n d e n t p h e n o l o g i c a l o b s e r v a t i o n s m a d e on a t o t a l of 96 b a r l e y p l a n t s g r o w n in a g r e e n h o u s e u n d e r 16-, 12- a n d 8-h p h o t o p e r i o d s . RESULTS AND DISCUSSION T a b l e I s h o w s c a l c u l a t e d m e a n a c c u m u l a t e d GDD to e a c h p h e n o l o g i c a l s t a g e (~j) a n d m e a n d i f f e r e n c e s in G D D b e t w e e n s u c c e s s i v e s t a g e s (~i) for t h e t h r e e p h o t o p e r i o d s a n d using: (a) o n l y t h e r a w d a t a , (b) s m o o t h e d d a t a u s i n g l i n e a r i n t e r p o l a t i o n a n d (c) s m o o t h e d d a t a u s i n g t h e i t e r a t i v e t e c h n i q u e . D e s p i t e t h e r e l a t i v e l y l a r g e n u m b e r of o b s e r v a t i o n s (32 p l a n t s per p h o t o p e r i o d o b s e r v e d t h r e e t i m e s p e r week), s c a t t e r in t h e r a w d a t a is obvious, p a r t i c u l a r l y since t h e r e a r e n e g a t i v e v a l u e s of ~i. T h e i t e r a t i v e s m o o t h i n g t e c h n i q u e elimin a t e t h e s e n e g a t i v e v a l u e s a n d p r e s e n t s a m o r e credible a c c o u n t of phenological d e v e l o p m e n t . T h i s t e c h n i q u e w o u l d be m o s t useful to s c i e n t i s t s w h o wish to p r e s e n t p h e n o l o g i c a l d e v e l o p m e n t in t a b u l a r form. F o r s c i e n t i s t s m o r e c o m f o r t a b l e w i t h e q u a t i o n s , t h e r a w d a t a is b e s t u s e d d i r e c t l y w i t h t h e fitting t e c h n i q u e . W h e n m e a n s f r o m T a b l e Ib a n d c for e a c h p h o t o p e r i o d w e r e fit to eq. 11 u s i n g a n o n - l i n e a r l e a s t s q u a r e s a l g o r i t h m ( M a r q u a r d t , 1963; S t e w a r t , 1984), coefficients w e r e a l m o s t identical, t h e i r s t a n d a r d e r r o r s of e s t i m a t e o v e r l a p p e d , a n d c o r r e l a t i o n coefficients w e r e all 0.99. W e t h e r e f o r e c o n c l u d e d t h a t e i t h e r e s t i m a t i o n t e c h n i q u e w a s s u i t a b l e w h e n m o s t s t a g e s of the F e e k e s s c a l e w e r e observed. H o w e v e r , if o b s e r v a t i o n s of s e v e r a l s t a g e s w e r e m i s s i n g in s o m e plants, a n d e s p e c i a l l y if t h e y w e r e m i s s i n g in t h e n o n - l i n e a r p h a s e f r o m h e a d i n g to ripening, t h e i t e r a t i v e techn i q u e w o u l d p r o v i d e m o r e r e a l i s t i c e s t i m a t e s of h e a t u n i t r e q u i r e m e n t s of the m i s s i n g stages. T a b l e I I c o m p a r e s t h e m e a n s a n d s t a n d a r d e r r o r s of a c c u m u l a t e d G D D s TABLE II Mean accumulated GDD (4i) followed by bracketed standard error of the mean (°C) to beginning of tillering (stage 2), beginning of stem extension (stage 6), completion of heading (stage 10.5), and completion of ripening (stage 11.4) under photoperiods of 16, 12 and 8h Photoperiod (h) 16 12 8
Stage 2
6
10.5
11.4
455.0 (0.0) 455.0 (0.0) 455.0 (0.0)
918.4 (12.0)~ 928.0 (8.1) 1030.8 (11.9)a
1454.5 (16.8)a 1490.6 (16.8)a 1734.7 (118.7)~
2193.5 (30.9)~ 2424.0 (31.4) 2480.5 (18.7)a
Denotes significant difference (P < 0.05) to the next largest or smallest photoperiod.
43 H (°C)
J
/
,°
./j
./ ///"
,~
I
,
,
i
i
,
k
i
L
I~herto|~ical Stogo (Fookee scale)
Fig. 1. Rate of phenological development expressed in GDD (H, °C) under 16-, 12- and 8-h photoperiods.
(using the iterative technique to estimate missing values) to several major growth stages, i.e., beginning of tillering (stage 2), beginning of stem extension (stage 6), completion of heading (stage 10.5) and completion of ripening (stage 11.4), for three photoperiods. Even this relatively simple statistical approach indicates the signficant influence of a photoperiod change from 16 to 8h (P < 0.05) on development rates at the heading and ripening stages. Although the development rate of the 12-h photoperiod was intermediate between those of 16 and 8 h, all differences between 16- and 12-h and 12- and 8-h photoperiods are not statistically significant using this approach (P > 0.05). To utilize data collected at all phenological stages and to simplify comparison of many stages throughout development, observations were fit to a power equation. Figure 1 plots the curves fit to eq. 11 using phenological
44 TABLE III Coefficients, standard errors of estimate and correlation coefficients from a non-linear fitting procedure on: (a) expression to calculate G D D ( H ) for phenological stages (x) and (b) expression to calculate modified G D D (H~) for phenological stages (x) under photoperiod (p) (a) H - ax + b(x/xo)" a 16-h photoperiod 12-h photoperiod 8-h photoperiod
S.e2 (°c)
141.6 144.6 164.9
0.7622 0.7323 1.396
b
0.01938 0.01325 6.277
(b) H m = a'x + b'(x/x¢)"'/(1 - d(20 -p)2) a' s.e2 b' s.e.a n' (°C) (°C) 136.1
S.e2 (°c)
n
0.01576 68.19 0.008660 72.52 3.823 30.19
s.e.a
d
S.e2
rh
S.e.e.°
5.404 4.339 4.043
0.98 0.99 0.98
105.8 108.0 152.2
s.e. (h 2)
0.6881 0.1582 0.06810 54.26 2.871 0.001217
0.00003739
rb
see
0.98
127.9
c
aS.e. denotes standard error of estimate of a coefficient br denotes correlation coefficient of model fit. cS.e.e. denotes standard error of estimate of a fit. o b s e r v a t i o n s for p h o t o p e r i o d s of 16, 12 and 8 h. It is a p p a r e n t t h a t a decrease in p h o t o p e r i o d from 16 to 12 h h a d a small effect on d e v e l o p m e n t rate, but t h a t w h e n p h o t o p e r i o d d r o p p e d to 8 h, d e v e l o p m e n t r a t e slowed markedly. Table I I I a lists coefficient v a l u e s a n d t h e i r s t a n d a r d errors of estimate for the t h r e e p h o t o p e r i o d s fit to eq. 11. Since coefficient a d e t e r m i n e s the slope of the linear p o r t i o n of the curve, it is this coefficient t h a t most clearly differentiates the influence of p h o t o p e r i o d . S t a n d a r d errors of estimate for coefficient a are small and c u r v e s r e p r e s e n t i n g all t h r e e p h o t o p e r i o d s are significantly different (P < 0.05). Thus, eq. 11 a c c u r a t e l y describes the m e a s u r e d p h e n o l o g i c a l response of b a r l e y ( a c c o r d i n g to the Feekes scale) as a f u n c t i o n of t e m p e r a t u r e , and a n a l y s i s of the s t a n d a r d errors of the coefficients differentiates the effect of p h o t o p e r i o d . However, in o r d e r to eliminate the influence of p h o t o p e r i o d to s t u d y the effect of o t h e r f a c t o r s (e.g., w a t e r stress or n u t r i e n t availability) on d e v e l o p m e n t rate, we also fit all p h e n o l o g i c a l o b s e r v a t i o n s to eq. 12 w h i c h i n c o r p o r a t e d a p h o t o p e r i o d effect. F i g u r e 2 shows the close c o r r e s p o n d e n c e b e t w e e n o b s e r v e d a n d e s t i m a t e d G D D ( H ) u s i n g eq. 12. The p h o t o p e r i o d term a c c o u n t s for the n o n - l i n e a r effect of p h o t o p e r i o d on d e v e l o p m e n t r a t e (Major, 1980). The v a l u e s of coefficients a ' , b ' , n" a n d d and t h e i r s t a n d a r d e r r o r s are s h o w n in Table IIIb. T h r e e c u r v e s identical to those in Fig. 1 are g e n e r a t e d from this one set of coefficients a n d p v a l u e s of 8, 12 a n d 16. N o t e t h a t in this fitting process, only a c t u a l m e a s u r e m e n t s were used, e l i m i n a t i n g the need to estimate missing data. E q u a t i o n s 11 and 12 h a v e p r o v e d useful in q u a n t i f y i n g p h o t o p e r i o d a n d w a t e r stress effects in a g r e e n h o u s e e x p e r i m e n t u s i n g a relatively small n u m b e r of coefficients. We tested eq. 12 on an i n d e p e n d e n t b a r l e y d a t a set for the same 8-, 12- and 16-h photoperiods. Again, good a g r e e m e n t was o b t a i n e d (Fig. 3). The c o r r e l a t i o n coefficient b e t w e e n o b s e r v a t i o n s a n d model
45
~(.¢ /
2400
[] /o
°rj o
i
//o
°
~o~ /
o~/
o~
o/ ~ /
oo(~// ////// /
cD i
i
l
L
2400
E~lm~ld H
28~
(°C)
Fig. 2. Regression of observed to estimated GDD (H, °C) accumulated to each phenological stage for photoperiods of 16h (O), 12h (O) and 8h (z~)(r = 0.99). Note that observed values are means of those used to develop model coefficients. e s t i m a t e s w a s 0.99, a l t h o u g h this s e e m i n g l y near perfect c o r r e l a t i o n is misleading b e c a u s e of t h e c o r r e l a t i o n of b o t h H and x w i t h time., W e h a v e n o t tested t h e e q u a t i o n u n d e r field c o n d i t i o n s w h e r e p h o t o p e r i o d w o u l d c h a n g e c o n t i n u o u s l y w i t h time. P r e l i m i n a r y r e s u l t s of a field barley e x p e r i m e n t at o n e l o c a t i o n ( O t t a w a , C a n a d a ) i n d i c a t e that eq. 12 c a n be used w i t h different n u m e r i c a l v a l u e s of t h e coefficients, but a r i g o r o u s test of t h e p h o t o p e r i o d f u n c t i o n h a s n o t b e e n made. It is clear t h a t w h e n p h o t o p e r i o d varies w i t h time a m o d i f i c a t i o n of eq. 12 is n e c e s s a r y . Therefore, a modified g r o w i n g degree ( M G D D ) day c a n be defined as: MGDD
=
GDD/(1
-
d(p
20) 2)
-
(13)
Then k
Hm=
~, G D D / ( 1
-
d(p
-
20) 2
(14)
i=l
w h e r e H~. is c u m u l a t i v e M G D D Also: Hm
=
a ' x + b'(x/Xc) n"
and k is the n u m b e r o f days from e m e r g e n c e .
(15)
T h u s eq. 14 is used to c a l c u l a t e Hm o n a daily basis o v e r a g r o w i n g period and
46 /
/
/
2111~
/
/4) / c~
-
D
1600
~Z ° /
J ~cp
/
/
/
// i
I
i
/
i
i 1200
i
Eltlmltld
, I~0 X
i
, 2O00
l 24OO
i
= Z800
(°(3)
Fig. 3. Regression of observed to estimated G D D (H, °C) accumulated to each phenological stage for photoperiods of 16h (O), 12h (O) and 8h (t~) (r = 0.99). Note that observed values are means of independent data collected at each stage. eq. 15 is used to c a l c u l a t e v a l u e s of rim at each p h e n o l o g i c a l stage. For in a g r o w t h model, we could use eqs. 14 and 15 to calculate the time h e a d i n g began, providing v a l u e s of a ' , b ' , x c , n" and d were k n o w n . H o w e v e r , if a data set where p varies with time was to be used to these coefficients, x w o u l d h a v e to be treated as the dependent Therefore, we w o u l d first define F as: F
=
Hm
-
a'x
-
b ' ( x / x c ) n"
example, at w h i c h evaluate variable. (16)
where Hm is c a l c u l a t e d from eq. 14. N o t e that for any non-linear fitting process initial e s t i m a t e s of the u n k n o w n coefficients are needed. U s i n g N e w t o n ' s m e t h o d (Conte, 1965) of s o l v i n g a non-linear equation: Xi+ 1
X i --
~-
F/F"
(17)
where xi is the old estimate of x used to c a l c u l a t e F and F ' and xi+l is the new estimate. F ' is the derivative of F with respect to x or: F"
=
-
a'
-
b'n'(X/Xc)'-i/Xc
W h e n xi+l is c a l c u l a t e d it is set equal to x~ in the n e x t iteration Iterations c o n t i n u e until the difference b e t w e e n xi+ ~ and xi b e c o m e s This a l l o w s us to express x as a f u n c t i o n of Hm, w h i c h in turn can Marquardt's a l g o r i t h m to s o l v e for the u n k n o w n coefficients. Once ficients are k n o w n , we can revert b a c k to eqs. 14 and 15.
(18) sequence. negligible. be used in these coef-
47 I n s u m m a r y , a l t h o u g h p h e n o l o g i c a l o b s e r v a t i o n s of c e r e a l s b a s e d o n t h e F e e k e s scale are n o n - l i n e a r w i t h respect to time a n d h e a t units, the a p p r o a c h e s p r e s e n t e d h e r e s i m p l i f y a n a l y s i s of t h e s e o b s e r v a t i o n s a n d f a c i l i t a t e q u a n titative comparisons among varieties and treatments. Although these approaches have been developed and tested only on greenhouse data, they are t h e o r e t i c a l l y t r a n s f e r r a b l e t o t h e field. R e s e a r c h is c o n t i n u i n g o n u s i n g t h e s e t y p e s of a n a l y s i s o n field d a t a .
REFERENCES Arkin, G.F., Vanderlip, R.L. and Ritchie, J.T., 1976. A dynamic grain sorghum growth model. Trans. ASAE, 19: 622-630. Boussengault, J.J., 1837. Economie rurale consideree dans ses rapports avec la chimie, la physique et al meteorologie. 1~ ed., 8° Paris, (cited by Abbe (1905), p. 73). Brown, D.M., 1960. Soybean ecology: I. Development-temperature relationships from controlled environment studies. Agron. J., 52: 493-496. Conte, S.D., 1965. Elementary Numerical Analysis. McGraw-Hill, New York. Davidson, H.R. and Campbell, C.A., 1983. The effect of temperature, moisture and nitrogen on the rate of development of spring wheat as measured by degree days. Can. J. Plant Sci., 63: 833-846. De R~aumur, R.A.F., 1735. Observations du thermom~tre, faites ~ Paris pendant l'ann~e 1735, compar~es avec celles qui ont ~t~ faites sous la ligne, ~ L'Ile de France, ~ Alger et en quelquesunes de nos iles de l'Am~rique. Paris Memoires, Acad. Sci. (cited in Meteorological Monographs; Recent Studies in Bioclimatology, Vol. 2, pp. 1-3, Am. Meteorol. Soc.). De Wit, C.T., Brouwer, R.B. and Penning de Vries, F.W.T., 1970. Proc. IBP/PP Tech. Meeting, Trebon, Pudoc, Wageningen, pp. 47-70. Doraiswamy, P.C. and Thompson, D,R., 1982. A crop moisture stress index for large areas and its application in the prediction of spring wheat phenology. Agric. Meteorol., 27: 1-15. Edey, S.N., 1977. Growing degree-days and crop production in Canada. Agriculture Canada Publication 1635, 63 pp. Gallagher, J.N., Biscoe, P.V. and Scott, R.K., 1976. Barley and its environment. VI Growth and development in relation to yield. J. Appl. Ecol,, 13: 563-583. Hammer, G.L., Goyne, P.J. and Woodruff, D.R., 1982. Phenology of sunflower cultivars. III. Models for prediction in field environments. Aust. J. Agric. Res., 33: 263-274. Idso, S.B., Jackson, R.D. and Reginato, R.J., 1978. Extending the "degree-day" concept of plant phenological development to include water stress effects. Ecology, 59: 431-433. Keitzar, S.R. and Singh, C.M., 1981. Influence of temperature on emergence of maize seeds and degree day requirement for various growth stages. Agric. Sci. Digest, 1: 1-4. Large, E.C., 1954. Growth stages in cereals - - illustration of the Feekes scale. Plant Pathol., 3: 128-129. Major, D.J., 1980. Photoperiod response characteristics controlling flowering of nine crop species. Can. J. Plant Sci., 60: 777-784. Marquardt, D.W., 1963. An algorithm for least-squares estimation of non-linear parameters. J. Soc. Ind. Appl. Math., 11: 431-441. Neild, R.E., Logan, J. and Cardenas A., 1983. Growing season and phenological response of sorghum as determined from simple climatic data. Agric. Meteorol., 30: 34-48. Pirasteh, B. and Welsh, J.R., 1980. Effect of temperature on the heading date of wheat cultivars under a lengthening photoperiod. Crop Sci., 20: 453-456. Ritchie, J.T. and Otter, S., 1984. CERES-Wheat: a user-oriented wheat yield model. Preliminary documentation, AgRISTARS Publication No. YM-U3-04442-JSC-18892.
48 Robertson, G.W., 1968. A biometeorological time scale for a cereal crop involving day and night temperatures and photoperiod. Int. J. Biometeorol., 12: 191-223. Stewart, D.W., 1984. Fitting crop growth data using Marquardt's algorithm. Agric. For. Meteorol., 32: 71-77. Williams, G.D.V., 1974. Deriving a biophotothermal time scale for barley. Int. J. Biometerol., 18: 57~9.
37
ANALYSIS OF PHENOLOGICAL OBSERVATIONS ON BARLEY (HORDEUM VULGARE) USING THE FEEKES SCALE
D.W. STEWART and L.M. DWYER
Agrometeorology Section, Land Resource Research Centre, Research Branch, Agriculture Canada, Ottawa, Ontario KIA 0C6 (Canada) (Received March 5, 1986; revision accepted June 1, 1986)
ABSTRACT Stewart, D.W. and Dwyer, L.M., 1987. Analysis of phenological observations on barley (Hordeum vulgare) using the Feekes scale. Agric. For. Meteorol., 39: 37-48. Phenological observations on cereals using the Feekes scale are made in many crop growth studies, although this data collection is very time consuming and labour intensive. Despite the investment in time and labour, quantitative comparison of crop development rates among environments with different thermal, photoperiod, or moisture stress conditions is often difficult because of the non-linearity of the Feekes scale with time. Furthermore, as a result of this non-linearity, it is common for some phenological stages to be missed, even when frequent (e.g., three times weekly) observations are made. In this study, several approaches were taken to quantifying phenological development rates of barley under different growth conditions. First, all stages were expressed as a function of growing degree days (GDD) with a base temperature of 5°C. Missing phenological observations were then interpolated using a linear technique and an iterative procedure that included information from development rates of replicate plants to calculate the GDD associated with missing stages. Finally, a non-linear least squares algorithm was used to fit phenological observations to a function of GDD modified by photoperiod. Statistical analysis of function coefficients provided a quantitative basis for comparison of phenological development rates among different environments. In addition, the non-linear function could be used to predict phenological stage according to the Feekes scale as a function of GDD and photoperiod. INTRODUCTION P h e n o l o g i c a l o b s e r v a t i o n s a r e a n i n t e g r a l p a r t of m a n y c e r e a l c r o p g r o w t h and development studies. These observations are usually recorded using the F e e k e s s c a l e ( L a r g e , 1954). H o w e v e r , o f t e n o n l y a few o f t h e m a j o r s t a g e c h a n g e s , e.g., e m e r g e n c e , t i l l e r i n g , j o i n t i n g , h e a d i n g , a n t h e s i s , soft d o u g h o r r i p e n i n g , a r e n o t e d . I n a d d i t i o n , b e c a u s e of t h e n o n - l i n e a r i t y of t h e s c a l e w i t h time, t r a n s i t i o n s a m o n g these states m a y be t r e a t e d separately, r a t h e r t h a n c o n t i n u o u s l y , w i t h a c o r r e s p o n d i n g i n c r e a s e i n t h e c o m p l e x i t y a n d n u m b e r of c o e f f i c i e n t s r e q u i r e d for a n a l y s i s of p h e n o l o g i c a l o b s e r v a t i o n s f r o m e m e r g e n c e to r i p e n i n g ( R o b e r t s o n , 1968; W i l l i a m s , 1974; D o r a i s w a m y a n d T h o m p s o n , 1982). T h e r e f o r e , d e s p i t e a l a r g e n u m b e r o f s t u d i e s w i t h t h e a i m of d e f i n i n g a L.R.R.I. Contribution No. 86-10.
0168-1923/87/$03.50
© 1987 Elsevier Science Publishers B.V.
38 phenological index to predict cereal crop development as a function of meteorological or edaphic parameters (Robertson, 1968; Williams, 1974; Gallagher et al., 1976; Idso et al., 1978; Doraiswamy and Thompson, 1982; Davidson and Campbell, 1983) a simple method based on recognized procedures has not been developed to analyze phenological observations on cereals as a function of both meteorological and edaphic parameters. This paper describes several approaches to the analysis of phenological observations, based on the Feekes scale, made three times weekly on barley (Hordeum vulgare) grown in a greenhouse under three photoperiod treatments. Suggestions are made for analyzing data sets with missing observations and a technique to quantitatively compare phenological development rates in cereals is presented. METHODS
Experimental details One hundred and ninety-two barley plants were grown in a greenhouse in 15.2-cm diameter pots of sandy loam soil. An automated canopy system controlled three photoperiods (8, 12 and 16 h), and 64 pots were maintained under each photoperiod. On cloudy days, when the daytime quantum radiation (Q) was < 100pEm 2 s-l, natural light in the greenhouse was augmented with fluorescent lights to bring Q to a minimum 200pEm-2 s 1. Mean daily temperatures averaged -~ 25°C, but thermocouples monitored air temperature 60 times per hour and average hourly temperatures were recorded on a datalogger. Pots were weighed daily and watered to maintain a soil water content between 80% available water (defined as water held between - 0 . 0 3 and 1.5MPa) and field capacity ( - 0.03MPa or 0.165cm 3 cm 3). Phenological observations were made three times weekly on each plant and stages were recorded according to the Feekes scale (Large, 1954). Observations from 96 plants were analyzed originally. The remaining 96 plants formed an independent data set. -
Theoretical considerations The influence of temperature on phenological development is well documented from the early work of de R~aumur (1735) and Boussengault (1837) to the more recent studies of Brown (1960), Robertson (1968), De Wit et al. (1970), Williams (1974) and Arkin et al. (1976). The degree day or heat unit hypothesis has been widely used to describe crop development (e.g., Pirasteh and Welsh, 1980; Keitzar and Singh, 1981; Hammer et al., 1982; Neild et al., 1983; Davidson and Campbell, 1983). Briefly, a sum, S(°C), is accumulated for a development period beginning at emergence (day 0) and ending at day m from the following expression:
39
2
w h e r e Tmax is m a x i m u m daily air t e m p e r a t u r e (°C), Tmi n is m i n i m u m daily air t e m p e r a t u r e (°C) and Tb is a basal or t h r e s h o l d t e m p e r a t u r e (°C) below w h i c h d e v e l o p m e n t ceases. In this study, t h e r e f o r e , the n u m b e r of growing degree days ( G D D ) a c c u m u l a t e d to each F e e k e s d e v e l o p m e n t stage of b a r l e y was c a l c u l a t e d based on a Tb of 5°C for g e n e r a l p l a n t g r o w t h (Edey, 1977). F o l l o w i n g the F e e k e s scale (Large, 1954) 22 p h e n o l o g i c a l stages in b a r l e y were observed (stage 10.5.1 was omitted) on 64 r e p l i c a t e plants for e a c h p h o t o p e r i o d t r e a t m e n t . A subset of 32 r e p l i c a t e plants from e a c h p h o t o p e r i o d was r a n d o m l y selected for the original analysis. The d a t a for e a c h t r e a t m e n t were t h e n s u m m a r i z e d in two m a t r i c e s Ai, j and aij w h e r e i = 1, u (u is the n u m b e r of plants = 32) and j = 1, v (v is the n u m b e r of stages observed = 22). Ai, j is the a c c u m u l a t e d G D D from p l a n t i n g date to the jth stage of the ith p l a n t and a~j is the difference b e t w e e n A~,~and A~j 1. F o r the first c o l u m n Ai,1 = ai,1; for all o t h e r columns: Ai,j -
Ai,: 1 =
(2)
aij
F o r a complete set of o b s e r v a t i o n s (i = 32, j = 22), m e a n s for a given stage are c a l c u l a t e d as: 32
,7ir =
~ Aij/32
(3)
i=l
and 32
(4)
aiJ32 i=l
If o b s e r v a t i o n s are missir.g, m e a n s can be c a l c u l a t e d using the o b s e r v a t i o n s w h i c h are available, or the following t e c h n i q u e can be used to fill in missing d a t a to o b t a i n a s m o o t h e d s e q u e n c e of means. F o r n missing o b s e r v a t i o n s in sequence: Ai,j+n -
Aij
1 = aij + aij+l + ...
+ aij+n
(5)
F o r a first a p p r o x i m a t i o n we assume: aij
=
aij+l
=
...
=
aij+n
(6)
w h i c h allows us to estimate missing v a l u e s and to o b t a i n a n estimate of ~i and 5i from eqs. 3 and 4. We t h e n made the more realistic a s s u m p t i o n of: aij
_
aij+l
aij+n -
(~j
aj + 1
. . .
-
(7)
aj + n
Combining eqs. 5 and 7 and r e a r r a n g i n g results in:
40
a~j =
( Aij., - Aij i)/(1.0 + ~t~+llgtj + ~j+21Etj + . . .
+ aj+nlaj)
(8)
Similarly, aij+l
=
(Ai,j+n -
Aij_l)/(ctj/ctj+l
a~,s+n
=
(A~u+n -
A,j
-4- 1 + aj+2/aj+l
,)/(~1lgtj+n + aj+llaj+n Jr- . . .
+ ...
-~- 1)
~- a j + n / a j + l )
(9)
(10)
From these new estimates ofaij, we can recalculate Aij and then A]j and ~j. The process is repeated in an iterative cycle until values of A i j converge to constant values. This procedure requires observed data in each column. However, t h r o u g h trial and error we found t h a t the procedure converges when up to 65% of the data are missing for a given column, although this percentage is also a function of the total number of observations per matrix. The above analysis is useful for smoothing accumulated G D D averaged over a number of plants since it takes advantage of the fact t hat stages occur c o n c u r r e n t l y for a given t r e a t m e n t and both the rows and columns of the matrices can be used for averaging. However, if accumulated G D D could be related to development stage by a continuous function, then it would be possible to fit G D D directly to raw phenological data. Visual observation of the data suggested the following function: H
=
(11)
ax + b(x/Xc) n
where H is accumulated G D D at any stage x on the Feekes scale (°C). H is equivalent to ~i except t h a t it is not restricted to the discrete stages of the Feekes scale; a value of H can be calculated for any value of x between 1 and 11.4. Also note t h a t the flowering stages (e.g., 10.5.2) are converted to real numbers (i.e., 10.52). The values of the empirical coefficients a(°C), b(°C) and n were obtained by fitting eq. 11 to observations of each photoperiod using Marquardt's algorithm (Marquardt, 1963). When xc was included as an unknown, the algorithm had difficulty converging to a unique set of values. This means t h a t more t han one combination of b, Xc and n produce the same curve. Thus, Xc was set as the value of x at which eq. 11 departed from linearity. When x becomes greater t h a n Xc, the power term in eq. 11 becomes significantly large. The value of xc was estimated graphically as 9.8. No furt her difficulty with convergence was encountered. Note t h a t a, b and n vary with photoperiod. Equation 11 can be expanded to include a photoperiod effect by dividing by a response function t aken from the CERES model (Ritchie and Otter, 1984). This results in: H
=
( a ' x + b'(x/Xc)n')/(1
-
d(20 - p ) 2 )
(12)
where p is photoperiod (h) and d is an empirical coefficient (h-2). The coefficients a', b" and n ' have the same units as their counterparts in eq. 11. The
I
of accumulated
are
estimated
2
76.0 76.0
458.0 379.0
76.0 76.0
455.0 379.0
76.0 76.0
455.0 379.0
76.0 76.0
455.0 379.0
76.0 76.0
455.0 379.0
76.0 76.0
455.9 379.0
76.0 76.0
455.0 379.0
76.0 76.0
455.0 379.0
~j fij
76.0 76.0
455.0 379.0
8-5 photoperiod
~j ~j
12-h photoperiod
~; (i/
16-h photoperiod
(c)
~/ al
~h photoperiod
~j 5j
12-h photoperiod
~j fij
16-h photoperiod
Co)
~j 51
H-h photoperiod
,~j ~ij
12-h photoperiod
"~1 fij
(a) l f h photoperiod
1
590.0 135.0
534.4 79 4
534.4 79.4
590.0 135.0
534.4 79.4
534.4 79.4
590.0 135.0
534.4 79.4
634.4 79.4
3
Feekes scale stage
technique
values
663.0 73.0
590.0 55.6
590.0 55.6
663.0 73.0
590.0 55.6
590.0 55.6
666.3 73.0
590.0 55.6
590.0 55.6
4
using
8539 190.9
666.3 76.3
666.3 76.3
853.9 190.9
666.3 76.3
663.3 76.3
853.9 190.9
666.3 76.3
666.3 76.3
5
10308 176.9
928.0 261.7
918.4 2521
1030.8 176.9
928.0 261.7
918.4 252.1
1030.8 176.9
928.0 261.7
918.4 252.1
6
1242.9 14.1
9
1161.7 90.2
1359.2 156.5
1219.2 53.4
1468.0 108.8
~227.2 1304.9 161.0 77.7
1228.8 161.8
8
1455.3 ll4.1
1495.8 40.4
1217.5 1278.2 1489 60.7
14929 311
1341.4 63.1
1161.7 1213.3 1296.0 90.1 51.7 82.7
1341.3 142.0
1199.6 1343.4 1461.8 1 6 8 . 9 1 4 3 . 7 118.5
1068.7 140.6
1071.6 153.1
1199.3 168.5
1342.5 65.3
1295.4 81.3
1489.0 21.0
1339.8 34.9
1301.3 58.5
l0
(c) c a l c u l a t e d
10.2
1576.9 84.0
1417.2 - 4.3
1397.8 17.1
1638.5 61.6
1428.2 28.3
1393.6 25.6
1648.6 71.7
1688.9 40.2
1448.2 20.0
1416.8 19.0
1688.9 50.3
1448.2 20.0
1416.3 19.2
1678.1 1920.8 17.7 242.7
1421.5 7.2
1420.2 1428.2 78.8 8.0
1380.7 84.6
1576.9 81.2
1399.9 57.4
1362.4 76.8
1660.4 171.4
1414.3 74.4
1413.3 13.8
10.3
1456.0 19.2
1695.2 48.0
1454.9 48.7
1418.4 40.5
10.5
1490.6 25.7
1454.5 19.3
1876.2 114.2
1588.7 68.2
1547.0 64.1
1874.4 112.4
1598.3 49.8
1662.8 158.2
10.53
1516.0 25.4
1876.2 114.2
1586.3 70.3
1483.1 1547.0 28.5 63.9
1762.0 27.3
1520.5 28.6
1486.0 28.4
1762.0 66.9
1548.5 93.6
1504.6 86.2
1 7 1 1 . 1 1734.7 1762.0 22.2 23.6 27.3
1464.9 16.7
14352 18.5
1 7 1 1 . 1 1734.7 22.2 23.6
succssive
1990.8 114.6
1648.6 62.3
1574.2 27.2
1990.8 114.6
1657.3 68.6
1993.2 35.6
2017.5 143.1
1574.8 - 23.5
1538.7 124.2
10.54
2100A 109.6
]729.5 80.9
1636.7 62.5
2099.8 109.0
1733.8 76.5
1658.4 59.9
2121.1 103.6
1715.8 141.0
1611.9 73.2
11.1
are estimated
2299.2 - 80.4
2480.5 181.3
2424.0 412.1
2193.5 268.0
2480.5 181.3
2424.0 412.1
2011.8 124.9
2480.5 181.3
2424.0 412.1
1925.5 2193.5 1 2 9 . 0 268.0
2299.2 95.5
2203.7 2299.2 103.2 95 5
1886.9 157.3
1796.5 159.8
2203.7 103.9
1881.9 2011.8 1 4 8 . 1 129.9
1797.3 1925.5 1 5 2 . 3 130.7
2379.6 258.5
11.4
1925.5 2193.5 1 3 4 . 1 268.0
11.3
the iterative
1879.7 2011.8 1 6 3 . 9 132.2
1791.4 179.5
11.2
using
data when missing
s t a g e s (fij) f o r p h o t o p e r i o d s
from phenological
values
10.52
missing
1 4 6 7 . 7 1491.9 19.5 24.2
1435.2 17.3
1647.2 273.7
1406.2 11.0
1377,9 35.4
10.4
when
v a l u e s , (b) c a l c u l a t e d
data
missing
phenological
1411.1 1399.6 109.8 11.6
1O.l
from
estimating
s t a g e (,~j) a n d m e a n d i f f e r e n c e i n G D D b e t w e e n
data without
1068.7 1212.8 1277.2 1 4 0 . 7 144.1 64.4
1069.8 153.0
1202.7 172.0
1066.2 138.2
1067.0 148.6
7
interpolation,
from raw phenological
G D D (°C) to each phenological linear
o f 16, 1 2 a n d 8 h: ( a ) c a l c u l a t e d
Mean number
TABLE
42 v a l u e s a, b a n d n a r e e q u a l to a', b' a n d n', r e s p e c t i v e l y , w h e n p equals 20. N o t e t h a t eq. 12 is r e s t r i c t e d to v a l u e s of p ~< 20. V a l u e s of a', b', n' a n d d w e r e o b t a i n e d by fitting eq. 12 to t h e t h r e e sets of o b s e r v a t i o n s . O n c e coefficient v a l u e s w e r e c a l c u l a t e d f r o m o u r e x p e r i m e n t a l d a t a , eq. 12 w a s t e s t e d on i n d e p e n d e n t p h e n o l o g i c a l o b s e r v a t i o n s m a d e on a t o t a l of 96 b a r l e y p l a n t s g r o w n in a g r e e n h o u s e u n d e r 16-, 12- a n d 8-h p h o t o p e r i o d s . RESULTS AND DISCUSSION T a b l e I s h o w s c a l c u l a t e d m e a n a c c u m u l a t e d GDD to e a c h p h e n o l o g i c a l s t a g e (~j) a n d m e a n d i f f e r e n c e s in G D D b e t w e e n s u c c e s s i v e s t a g e s (~i) for t h e t h r e e p h o t o p e r i o d s a n d using: (a) o n l y t h e r a w d a t a , (b) s m o o t h e d d a t a u s i n g l i n e a r i n t e r p o l a t i o n a n d (c) s m o o t h e d d a t a u s i n g t h e i t e r a t i v e t e c h n i q u e . D e s p i t e t h e r e l a t i v e l y l a r g e n u m b e r of o b s e r v a t i o n s (32 p l a n t s per p h o t o p e r i o d o b s e r v e d t h r e e t i m e s p e r week), s c a t t e r in t h e r a w d a t a is obvious, p a r t i c u l a r l y since t h e r e a r e n e g a t i v e v a l u e s of ~i. T h e i t e r a t i v e s m o o t h i n g t e c h n i q u e elimin a t e t h e s e n e g a t i v e v a l u e s a n d p r e s e n t s a m o r e credible a c c o u n t of phenological d e v e l o p m e n t . T h i s t e c h n i q u e w o u l d be m o s t useful to s c i e n t i s t s w h o wish to p r e s e n t p h e n o l o g i c a l d e v e l o p m e n t in t a b u l a r form. F o r s c i e n t i s t s m o r e c o m f o r t a b l e w i t h e q u a t i o n s , t h e r a w d a t a is b e s t u s e d d i r e c t l y w i t h t h e fitting t e c h n i q u e . W h e n m e a n s f r o m T a b l e Ib a n d c for e a c h p h o t o p e r i o d w e r e fit to eq. 11 u s i n g a n o n - l i n e a r l e a s t s q u a r e s a l g o r i t h m ( M a r q u a r d t , 1963; S t e w a r t , 1984), coefficients w e r e a l m o s t identical, t h e i r s t a n d a r d e r r o r s of e s t i m a t e o v e r l a p p e d , a n d c o r r e l a t i o n coefficients w e r e all 0.99. W e t h e r e f o r e c o n c l u d e d t h a t e i t h e r e s t i m a t i o n t e c h n i q u e w a s s u i t a b l e w h e n m o s t s t a g e s of the F e e k e s s c a l e w e r e observed. H o w e v e r , if o b s e r v a t i o n s of s e v e r a l s t a g e s w e r e m i s s i n g in s o m e plants, a n d e s p e c i a l l y if t h e y w e r e m i s s i n g in t h e n o n - l i n e a r p h a s e f r o m h e a d i n g to ripening, t h e i t e r a t i v e techn i q u e w o u l d p r o v i d e m o r e r e a l i s t i c e s t i m a t e s of h e a t u n i t r e q u i r e m e n t s of the m i s s i n g stages. T a b l e I I c o m p a r e s t h e m e a n s a n d s t a n d a r d e r r o r s of a c c u m u l a t e d G D D s TABLE II Mean accumulated GDD (4i) followed by bracketed standard error of the mean (°C) to beginning of tillering (stage 2), beginning of stem extension (stage 6), completion of heading (stage 10.5), and completion of ripening (stage 11.4) under photoperiods of 16, 12 and 8h Photoperiod (h) 16 12 8
Stage 2
6
10.5
11.4
455.0 (0.0) 455.0 (0.0) 455.0 (0.0)
918.4 (12.0)~ 928.0 (8.1) 1030.8 (11.9)a
1454.5 (16.8)a 1490.6 (16.8)a 1734.7 (118.7)~
2193.5 (30.9)~ 2424.0 (31.4) 2480.5 (18.7)a
Denotes significant difference (P < 0.05) to the next largest or smallest photoperiod.
43 H (°C)
J
/
,°
./j
./ ///"
,~
I
,
,
i
i
,
k
i
L
I~herto|~ical Stogo (Fookee scale)
Fig. 1. Rate of phenological development expressed in GDD (H, °C) under 16-, 12- and 8-h photoperiods.
(using the iterative technique to estimate missing values) to several major growth stages, i.e., beginning of tillering (stage 2), beginning of stem extension (stage 6), completion of heading (stage 10.5) and completion of ripening (stage 11.4), for three photoperiods. Even this relatively simple statistical approach indicates the signficant influence of a photoperiod change from 16 to 8h (P < 0.05) on development rates at the heading and ripening stages. Although the development rate of the 12-h photoperiod was intermediate between those of 16 and 8 h, all differences between 16- and 12-h and 12- and 8-h photoperiods are not statistically significant using this approach (P > 0.05). To utilize data collected at all phenological stages and to simplify comparison of many stages throughout development, observations were fit to a power equation. Figure 1 plots the curves fit to eq. 11 using phenological
44 TABLE III Coefficients, standard errors of estimate and correlation coefficients from a non-linear fitting procedure on: (a) expression to calculate G D D ( H ) for phenological stages (x) and (b) expression to calculate modified G D D (H~) for phenological stages (x) under photoperiod (p) (a) H - ax + b(x/xo)" a 16-h photoperiod 12-h photoperiod 8-h photoperiod
S.e2 (°c)
141.6 144.6 164.9
0.7622 0.7323 1.396
b
0.01938 0.01325 6.277
(b) H m = a'x + b'(x/x¢)"'/(1 - d(20 -p)2) a' s.e2 b' s.e.a n' (°C) (°C) 136.1
S.e2 (°c)
n
0.01576 68.19 0.008660 72.52 3.823 30.19
s.e.a
d
S.e2
rh
S.e.e.°
5.404 4.339 4.043
0.98 0.99 0.98
105.8 108.0 152.2
s.e. (h 2)
0.6881 0.1582 0.06810 54.26 2.871 0.001217
0.00003739
rb
see
0.98
127.9
c
aS.e. denotes standard error of estimate of a coefficient br denotes correlation coefficient of model fit. cS.e.e. denotes standard error of estimate of a fit. o b s e r v a t i o n s for p h o t o p e r i o d s of 16, 12 and 8 h. It is a p p a r e n t t h a t a decrease in p h o t o p e r i o d from 16 to 12 h h a d a small effect on d e v e l o p m e n t rate, but t h a t w h e n p h o t o p e r i o d d r o p p e d to 8 h, d e v e l o p m e n t r a t e slowed markedly. Table I I I a lists coefficient v a l u e s a n d t h e i r s t a n d a r d errors of estimate for the t h r e e p h o t o p e r i o d s fit to eq. 11. Since coefficient a d e t e r m i n e s the slope of the linear p o r t i o n of the curve, it is this coefficient t h a t most clearly differentiates the influence of p h o t o p e r i o d . S t a n d a r d errors of estimate for coefficient a are small and c u r v e s r e p r e s e n t i n g all t h r e e p h o t o p e r i o d s are significantly different (P < 0.05). Thus, eq. 11 a c c u r a t e l y describes the m e a s u r e d p h e n o l o g i c a l response of b a r l e y ( a c c o r d i n g to the Feekes scale) as a f u n c t i o n of t e m p e r a t u r e , and a n a l y s i s of the s t a n d a r d errors of the coefficients differentiates the effect of p h o t o p e r i o d . However, in o r d e r to eliminate the influence of p h o t o p e r i o d to s t u d y the effect of o t h e r f a c t o r s (e.g., w a t e r stress or n u t r i e n t availability) on d e v e l o p m e n t rate, we also fit all p h e n o l o g i c a l o b s e r v a t i o n s to eq. 12 w h i c h i n c o r p o r a t e d a p h o t o p e r i o d effect. F i g u r e 2 shows the close c o r r e s p o n d e n c e b e t w e e n o b s e r v e d a n d e s t i m a t e d G D D ( H ) u s i n g eq. 12. The p h o t o p e r i o d term a c c o u n t s for the n o n - l i n e a r effect of p h o t o p e r i o d on d e v e l o p m e n t r a t e (Major, 1980). The v a l u e s of coefficients a ' , b ' , n" a n d d and t h e i r s t a n d a r d e r r o r s are s h o w n in Table IIIb. T h r e e c u r v e s identical to those in Fig. 1 are g e n e r a t e d from this one set of coefficients a n d p v a l u e s of 8, 12 a n d 16. N o t e t h a t in this fitting process, only a c t u a l m e a s u r e m e n t s were used, e l i m i n a t i n g the need to estimate missing data. E q u a t i o n s 11 and 12 h a v e p r o v e d useful in q u a n t i f y i n g p h o t o p e r i o d a n d w a t e r stress effects in a g r e e n h o u s e e x p e r i m e n t u s i n g a relatively small n u m b e r of coefficients. We tested eq. 12 on an i n d e p e n d e n t b a r l e y d a t a set for the same 8-, 12- and 16-h photoperiods. Again, good a g r e e m e n t was o b t a i n e d (Fig. 3). The c o r r e l a t i o n coefficient b e t w e e n o b s e r v a t i o n s a n d model
45
~(.¢ /
2400
[] /o
°rj o
i
//o
°
~o~ /
o~/
o~
o/ ~ /
oo(~// ////// /
cD i
i
l
L
2400
E~lm~ld H
28~
(°C)
Fig. 2. Regression of observed to estimated GDD (H, °C) accumulated to each phenological stage for photoperiods of 16h (O), 12h (O) and 8h (z~)(r = 0.99). Note that observed values are means of those used to develop model coefficients. e s t i m a t e s w a s 0.99, a l t h o u g h this s e e m i n g l y near perfect c o r r e l a t i o n is misleading b e c a u s e of t h e c o r r e l a t i o n of b o t h H and x w i t h time., W e h a v e n o t tested t h e e q u a t i o n u n d e r field c o n d i t i o n s w h e r e p h o t o p e r i o d w o u l d c h a n g e c o n t i n u o u s l y w i t h time. P r e l i m i n a r y r e s u l t s of a field barley e x p e r i m e n t at o n e l o c a t i o n ( O t t a w a , C a n a d a ) i n d i c a t e that eq. 12 c a n be used w i t h different n u m e r i c a l v a l u e s of t h e coefficients, but a r i g o r o u s test of t h e p h o t o p e r i o d f u n c t i o n h a s n o t b e e n made. It is clear t h a t w h e n p h o t o p e r i o d varies w i t h time a m o d i f i c a t i o n of eq. 12 is n e c e s s a r y . Therefore, a modified g r o w i n g degree ( M G D D ) day c a n be defined as: MGDD
=
GDD/(1
-
d(p
20) 2)
-
(13)
Then k
Hm=
~, G D D / ( 1
-
d(p
-
20) 2
(14)
i=l
w h e r e H~. is c u m u l a t i v e M G D D Also: Hm
=
a ' x + b'(x/Xc) n"
and k is the n u m b e r o f days from e m e r g e n c e .
(15)
T h u s eq. 14 is used to c a l c u l a t e Hm o n a daily basis o v e r a g r o w i n g period and
46 /
/
/
2111~
/
/4) / c~
-
D
1600
~Z ° /
J ~cp
/
/
/
// i
I
i
/
i
i 1200
i
Eltlmltld
, I~0 X
i
, 2O00
l 24OO
i
= Z800
(°(3)
Fig. 3. Regression of observed to estimated G D D (H, °C) accumulated to each phenological stage for photoperiods of 16h (O), 12h (O) and 8h (t~) (r = 0.99). Note that observed values are means of independent data collected at each stage. eq. 15 is used to c a l c u l a t e v a l u e s of rim at each p h e n o l o g i c a l stage. For in a g r o w t h model, we could use eqs. 14 and 15 to calculate the time h e a d i n g began, providing v a l u e s of a ' , b ' , x c , n" and d were k n o w n . H o w e v e r , if a data set where p varies with time was to be used to these coefficients, x w o u l d h a v e to be treated as the dependent Therefore, we w o u l d first define F as: F
=
Hm
-
a'x
-
b ' ( x / x c ) n"
example, at w h i c h evaluate variable. (16)
where Hm is c a l c u l a t e d from eq. 14. N o t e that for any non-linear fitting process initial e s t i m a t e s of the u n k n o w n coefficients are needed. U s i n g N e w t o n ' s m e t h o d (Conte, 1965) of s o l v i n g a non-linear equation: Xi+ 1
X i --
~-
F/F"
(17)
where xi is the old estimate of x used to c a l c u l a t e F and F ' and xi+l is the new estimate. F ' is the derivative of F with respect to x or: F"
=
-
a'
-
b'n'(X/Xc)'-i/Xc
W h e n xi+l is c a l c u l a t e d it is set equal to x~ in the n e x t iteration Iterations c o n t i n u e until the difference b e t w e e n xi+ ~ and xi b e c o m e s This a l l o w s us to express x as a f u n c t i o n of Hm, w h i c h in turn can Marquardt's a l g o r i t h m to s o l v e for the u n k n o w n coefficients. Once ficients are k n o w n , we can revert b a c k to eqs. 14 and 15.
(18) sequence. negligible. be used in these coef-
47 I n s u m m a r y , a l t h o u g h p h e n o l o g i c a l o b s e r v a t i o n s of c e r e a l s b a s e d o n t h e F e e k e s scale are n o n - l i n e a r w i t h respect to time a n d h e a t units, the a p p r o a c h e s p r e s e n t e d h e r e s i m p l i f y a n a l y s i s of t h e s e o b s e r v a t i o n s a n d f a c i l i t a t e q u a n titative comparisons among varieties and treatments. Although these approaches have been developed and tested only on greenhouse data, they are t h e o r e t i c a l l y t r a n s f e r r a b l e t o t h e field. R e s e a r c h is c o n t i n u i n g o n u s i n g t h e s e t y p e s of a n a l y s i s o n field d a t a .
REFERENCES Arkin, G.F., Vanderlip, R.L. and Ritchie, J.T., 1976. A dynamic grain sorghum growth model. Trans. ASAE, 19: 622-630. Boussengault, J.J., 1837. Economie rurale consideree dans ses rapports avec la chimie, la physique et al meteorologie. 1~ ed., 8° Paris, (cited by Abbe (1905), p. 73). Brown, D.M., 1960. Soybean ecology: I. Development-temperature relationships from controlled environment studies. Agron. J., 52: 493-496. Conte, S.D., 1965. Elementary Numerical Analysis. McGraw-Hill, New York. Davidson, H.R. and Campbell, C.A., 1983. The effect of temperature, moisture and nitrogen on the rate of development of spring wheat as measured by degree days. Can. J. Plant Sci., 63: 833-846. De R~aumur, R.A.F., 1735. Observations du thermom~tre, faites ~ Paris pendant l'ann~e 1735, compar~es avec celles qui ont ~t~ faites sous la ligne, ~ L'Ile de France, ~ Alger et en quelquesunes de nos iles de l'Am~rique. Paris Memoires, Acad. Sci. (cited in Meteorological Monographs; Recent Studies in Bioclimatology, Vol. 2, pp. 1-3, Am. Meteorol. Soc.). De Wit, C.T., Brouwer, R.B. and Penning de Vries, F.W.T., 1970. Proc. IBP/PP Tech. Meeting, Trebon, Pudoc, Wageningen, pp. 47-70. Doraiswamy, P.C. and Thompson, D,R., 1982. A crop moisture stress index for large areas and its application in the prediction of spring wheat phenology. Agric. Meteorol., 27: 1-15. Edey, S.N., 1977. Growing degree-days and crop production in Canada. Agriculture Canada Publication 1635, 63 pp. Gallagher, J.N., Biscoe, P.V. and Scott, R.K., 1976. Barley and its environment. VI Growth and development in relation to yield. J. Appl. Ecol,, 13: 563-583. Hammer, G.L., Goyne, P.J. and Woodruff, D.R., 1982. Phenology of sunflower cultivars. III. Models for prediction in field environments. Aust. J. Agric. Res., 33: 263-274. Idso, S.B., Jackson, R.D. and Reginato, R.J., 1978. Extending the "degree-day" concept of plant phenological development to include water stress effects. Ecology, 59: 431-433. Keitzar, S.R. and Singh, C.M., 1981. Influence of temperature on emergence of maize seeds and degree day requirement for various growth stages. Agric. Sci. Digest, 1: 1-4. Large, E.C., 1954. Growth stages in cereals - - illustration of the Feekes scale. Plant Pathol., 3: 128-129. Major, D.J., 1980. Photoperiod response characteristics controlling flowering of nine crop species. Can. J. Plant Sci., 60: 777-784. Marquardt, D.W., 1963. An algorithm for least-squares estimation of non-linear parameters. J. Soc. Ind. Appl. Math., 11: 431-441. Neild, R.E., Logan, J. and Cardenas A., 1983. Growing season and phenological response of sorghum as determined from simple climatic data. Agric. Meteorol., 30: 34-48. Pirasteh, B. and Welsh, J.R., 1980. Effect of temperature on the heading date of wheat cultivars under a lengthening photoperiod. Crop Sci., 20: 453-456. Ritchie, J.T. and Otter, S., 1984. CERES-Wheat: a user-oriented wheat yield model. Preliminary documentation, AgRISTARS Publication No. YM-U3-04442-JSC-18892.
48 Robertson, G.W., 1968. A biometeorological time scale for a cereal crop involving day and night temperatures and photoperiod. Int. J. Biometeorol., 12: 191-223. Stewart, D.W., 1984. Fitting crop growth data using Marquardt's algorithm. Agric. For. Meteorol., 32: 71-77. Williams, G.D.V., 1974. Deriving a biophotothermal time scale for barley. Int. J. Biometerol., 18: 57~9.