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Comparison of models to simulate leaf appearance in wheat
Eur. J. Agron .. 1995, 4(1), 15-25
Comparison of models to simulate leaf appearance in wheat M. Bindi*
1,
J. R. Porter 2 and F. Miglietta 3
Centro di Studio per l'Applicazione dell'lnformatica in Agricoltura, Accademia dei Georgofili, Piazzale delle Cascine 18, 50144 Firenze, Italy. 2 Department of Agricultural Sciences, University of Bristol, AFRC Institute of Arable Crops Research, Long Ashton Research Station, Bristol, BSI8 9AF, UK. New address,' Department of Agricultural Sciences, the Royal Agricultural and Veterinary University, Agrovej 10, 2630 Taastrup, Denmark Istituto per l'Agrometeorologia e l'Analisi Ambientale applicata all'Agricoltura, Consiglio Nazionale delle Ricerche, Piazzale delle Cascine 18, 50144 Firenze, Italy. 1
3
Accepted 6 June 1994.
* to whom correspondence should be addressed. Abstract
Prediction on of leaf appearance in cereals is important for modelling canopy development and timing crop management practices. Four models which aim to predict leaf emergence on the basis of temperature and, in three cases, photoperiod are compared against independent data from a wide range of sites, sowing dates and cultivars of spring and winter wheat. Three of the models behaved bery similarly and had root mean square errors of the order of one leaf in their prediction of leaf appearance. The fourth model performed better in predicting differences in leaf appearance for different sowing dates than it did for latitudes. The prediction of the day of emergence of leaf number seven followed a similar response to that of leaf appearance. These results are discussed in terms of the hypothesised relationships between temperature, photoperiod and ontogeny within the models. Key-words: wheat, leaf appearance, models
INTRODUCTION The importance of leaf area for growth, development, and yield of cereals has been recognised by crop physiologists and agronomists for a long time (Watson, 1958; Friend et aI., 1962; Gallagher and Biscoe, 1978). Hence, crop simulation models of cereals need to incorporate the development of the leaf canopy (Horie et al., 1979). To achieve this goal it is necessary to simulate the rate of appearance of successive leaves on a shoot (Porter, 1984; 1985). There are also practical reasons to anticipate leaf appearance since the control of plant disease epidemics is often linked to a specific developmental stage. Leaf appearance is the result of the initiation of leaf primordia and their extension to form leaves (Dale and Milthorpe, 1983). Under optimal conditions both processes are controlled by temperature (Gallagher, 1979; Baker and Gallagher, 1983; Warrington and Kanemasu, 1983a,b ; Hay and Brown, 1988; Kirby, 1992). The concept of thermal time, heat units or growing degree-days measured as °C d, has been used to predict the rate of leaf appearance (Hay and Kirby, 1991). Heat units are useful predictors of leaf appearance and many investigators have found ISSN I161 -0301195101/$ 4.001 © Gauthier-Villars - ESAg
significant linear relationships between leaf number and the number of degree-days accumulated from emergence (Baker et aI., 1980; Delecolle et aI., 1985; Kirby et aI., 1985). However, the thermal time between successive leaves varies with cultivar, planting date and latitude. Broadly, two methodologies have been proposed to predict the rate of leaf appearance in cereals. The first is based on empirically derived effects of photoperiod and temperature on the rate of leaf emergence. Examples of this approach are : the rate of leaf emergence in thermal time in relation to the rate of change of daylength (Baker et aI., 1980) ; the leaf emergence rate in thermal time in relation to the ratio of daily mean temperature to photoperiod (Cao and Moss, 1989a,b) and the leaf emergence rate in relation to the accumulation of thermal time during daylight only (Mas Ie et aI., 1989). The second broad approach attempts to be more mechanistic and describes the ontogenetic processes of leaf primordia initiation and lamina extension (Miglietta, 1989; 1991a,b; 1992).
This study compares the ability of the different approaches to calculate rates of leaf appearance in wheat for a range of locations in the UK, Italy, the
M. Bindi et al.
16
Netherlands and the USA, and for different sowing dates and cultivars. We compared models for their ability to predict number of leaves on the main shoot during growth as well as the date of emergence of leaf seven. In wheat, seven is, for developmental reasons, about the minimum leaf number that a wheat plant can produce, in cultivars that have no vernalis ation requirement and are also insensitive to daylength beyond a given value (Kirby, 1990; Brooking et aI., unpublished). Also, leaf sheaths, through which later leaves have to grow to emergence, do not appear until after the sixth leaf (Gallagher, 1979). Prediction of the time of emergence of the seventh leaf examines the ability of a model to predict the strictly ontogenetic events associated with leaf production and to exclude confounding growth effects. Finally, intermodel comparison is an important, although rarely performed, part of the development of models (de Willigen, 1991 ; Porter et aI., 1993).
dl/dTt = 1/( a
+ b TtIP)
(2).
On the basis of previous studies (Kirby, pers. comm.), values of intercept and slope were calculated from the upper series of points (for cv. Stephens winter wheat) from Figure 3 of Cao and Moss (1991) giving: a = 71.3 and b = 19.9.
Masle et al. (1989) - Model PT. Mas1e et al. (1989) proposed the use of photo-thermal, rather than thermal time, to predict leaf appearance. In this case, photo-thermal time (Tip, equivalent to ~ in Mas1e et aI., 1989) was calculated as the thermal time accumulated during daylight. Leaf number (L) was calculated in relation to photo-thermal time by the equation L = 0.0245 Ttp
(3).
The coefficient in equation (3) was calculated from data presented in Figure 7 of Masle et al. (1989). Ttp was calculated as described by Mas1e et al. (1989).
MODELS AND METHODS The models
The four models were written as FORTRAN computer programs.
Baker et al. (1980) - Model RC This model predicts leaf emergence on the basis of an empirical linear relationship between the rate of leaf appearance per unit thermal time (dUdTt) and the rate of change of daylength at crop emergence (de Idt). Rate of leaf emergence was calculated to be lower when day length is decreasing and vice versa. The model simulates the rate of emergence of leaves for different sowing dates at the same site and for different latitudes since daylength is a (non-linear) function of latitude. The equation of their regression was dLldTt = 0.010 + 0.025* (d e Idt)
appearance in thermal time. Therefore, the equation of their relationship, expressed in term of dUdTt is
(1).
Values of the intercept and slope of the above equation were recalculated from the data presented for cv. Huntsman by Baker et al. (1980) since their published value for the slope of the regression line (0.062 ; Figure 3 therein) was misprinted.
Cao and Moss (1989a,b; 1991) - Model TtlP These workers proposed that the thermal phyllochron (dTtldL) is linearly correlated with a thermalphoto quotient, calculated as the ratio between the mean daily thermal time (Tt) accumulated from 3 d before until 7 dafter 50 per cent seedling emergence and the daylength at emergence (P). The thermal phyllochron is the reciprocal of the rate of leaf
Miglietta (1989; 1991a,b) - Model O. This model proposes that differences in rate of leaf appearance for crops sown at different dates can be explained via a decline, during ontogeny, in the rate of leaf appearance (dUdt) caused by an increase in the time taken by each leaf primordium to extend from the apex to visible emergence. The daily rate of leaf appearance was calculated as dLidt = dPldt ( 1 - 0.03 L)
(4)
where, dPldt is the rate of production of vegetative primordia and L is the leaf number. In addition, dPldt = - 0.038 + 0.0149 T for T > 2.55 °C (5) where T is the mean daily temperature (0C). dPldt was set to zero for temperatures below 2.55 °C. For the RC and TtIP models thermal time (Tt) was calculated, above a base temperature (Tb)' from the maximum (T maJ and minimum (Tmin) daily screen temperatures (0C) as
Tt = (Tmax - Tmin)!2 - Tb
(6).
We used 0 °C as the base temperature (Gallagher, 1979; Baker et aI., 1980; Cao and Moss, 1989a,b) except for model 0, where 2.55 °C was used (Miglietta, 1991). Whenever the mean daily temperature was less than the base, Tt was zero for the day. For the PT model, photo-thermal time was calculated (Masle et aI., 1989) as (7)
where, I is the daylight period (h) as a proportion of 24 h. T[ was obtained from Tmax and T min as T, = T min + 0.065 (Tmax - T min )
(8). Eur. 1. Agron.
Comparison of leaf appearance models for wheat
Source of data The models were tested for their ability to predict leaf number and the day number of appearance of leaf seven from 55 field experiments with wheat (Triticum aestivum L.) in the northern hemisphere with a latitudinal range from 39.2° N to 57.2° N (Table 1). The models were run using the daily screen temperature data available from the meteorological station closest to the experiment. Estimated leaf production was ended on the same day number as the last recording date for the observed crop. The leaf number on this day was considered the final value. When day of seedling emergence was required for model calculations but was not recorded in an experiment, it was estimated to occur at 130°C d, accumulated above 0 °C, after sowing (Willington and Biscoe, 1984). To identify the combination of sowing dates and latitude for which the models diverge in their predictions, an analysis was made of their sensitivity to coincidental changes in these variables. Goodness of fit In order to assess the goodness-of-fit of the models to observed data, observed data (Table 1) were split, by site, variety and sowing date, into three sub-sets. For each, goodness-of-fit assessed from the positive or negative mean bias error (MBE) calculated as N
:2 (Xsim. -
t = 1
l
Xobs.) 1
MBE=------~N~----
where, t = the sample number, N = the number of observations throughout the season, Xsim i and Xobs i = the simulated and observed leaf number or the time of the seventh leaf appearance of the i th cultivar. A positive value of MBE indicates that, on average, a model over-estimated a value with respect to that observed and vice versa. To measure the absolute error of a model the root mean square error (RMSEO) was calculated as
RMSE=
N :2 (Xsim. =
t
{
1
1
Xobs.)2
}In
I
N
RESULTS Leaf appearance Of the four models tested, the largest MBE (Table 2a) for different latitudes was for the PT model which, in all except one case, overestimated leaf number. In general, the other models overestimated VoL 4, n° 1 - 1995
17
leaf appearance for latitudes from 40° N to 50° N but underestimated it for higher latitudes. For the RC, TtIP and 0 models MBE was about one leaf. RMSEs (Table 2a) for the RC, TtIP and 0 models showed very similar patterns (Figure Ia,b and d) whereas little pattern was seen for the PT model (Figure Ie). MBEs and RMSEs (Table 2b) for different months of sowing pointed to a generally similar and good ability of the models to predict leaf number for the main sowing periods (October to December) of winter wheat cultivars in the northern hemisphere. September sowings gave a high MBE for the PT model (Table 2b). Spring sowings were handled much less well by all except the PT model. The general tendency was to underestimate leaf appearance (Figure 2a,b,c, and d). Errors of prediction for different cultivars showed that, as for latitude, three of the models mostly underestimated leaf appearance (Table 2c), whereas the PT model overestimated leaf appearance for all cultivars (Table 2c). RMSEs (Table 2c) were consistently higher for the PT model when compared with the others which had values of about one leaf. There were no consistent differences between spring as opposed to winter cultivars in any model's prediction of leaf appearance. Taken over all variables the average RMSE for the RC, TtIP and 0 models was about one leaf and their standard deviations overlapped substantially (Table 3a). Mean RMSE for the PT model varied between about two leaves (month of sowing) to over three leaves for sites at different latitudes. A Student t test failed to detect significant difference between all pair-wise combinations of the models for month of sowing. For the other two variables, significant differences in RMSE (p < 0.001) were found between the PT model and the other three. Day of emergence of leaf seven Three models (RC, TtIP and 0) performed Slmllarly in predicting the day of appearance of leaf seven as with their estimates of leaf number. Systematic differences existed in the behaviour of the RC and PT models with respect to site latitude (Table 4a). The RC model generally simulated the appearance of leaf seven early at lower latitudes but late at latitudes above about 50° N. The PT model, except in one case, simulated the appearance of leaf seven early. Errors in the other two models were not so clearly related to changes in site latitude (Table 4a). The RMSE of the PT model increased with latitude (Figure 3c), a result not seen with any of the other models (Figure 3a,b and d). MBEs for the RC and TtiP models (Table 4b) changed similarly with month of sowing, with the
M. Bindi et al.
18
Table 1. Site, latitude, cultivar and the sowing and emergence dates (day number * emergence estimated as occurring 130°C d after sowing) of experiments used for the inter-model comparison of leaf emergence. (W), cultivar with vernalisation requirement; (S) cultivar without vernalisation requirement. Sources of the data are 1, Porter et al., 1987 and unpublished data from this experiment; 2 Willington and Biscoe, 1982; 3 Willington and Biscoe, 1983; 4 Willington and Biscoe, 1984; 5 Willington and Biscoe, 1985; 6, Kirby et aI., 1985; 7, Miglietta et aI., 1987; 8, Miglietta, 1989; 9, Miglietta, 1992; 10 Groot 1987; ", Bauer et ai., 1988. Country (code)
Location (code)
Cultivar
Sowing date
1983
Sept. 13 (256) 1 Oct. 11 (284)1 Nov. 15 (319)1 Sept. 14 (257) 1 Oct. 12 (285)1 Nov. 15 (319)1 Sept. 23 (266)1 Oct. 13 (286) 1 Nov. 18 (322)1 Sept. 26 (270)2 Nov. 3 (308)2 Feb. 2 (3W Sept. 16 (25W Nov. 10 (314)3 Sept. 13 (256)4 Sept. 13 (256)1 Sept. 19 (262)5 Oct. 12 (285)1 Nov. 16 (320)1 Nov. 16 (32W Sept. 25 (269)2 Nov. 3 (308)2 Dec. 12 (347)2 Oct. 24 (298)6 Dec. 4 (339/ Feb. 25 (56)6 Sept. 10 (253)6 Oct. 14 (288)6 Nov. 18 (323)6 Mar. 8 (67)6 Sept. 13 (257) 1 Oct. 11 (284) 1 Nov. 15 (319)1 Sept. 15 (258) 1 Oct. 11 (284)1 Nov. 16 (320)1 Sept. 14 (257)1 Oct. 11 (284)1 Nov. 16 (320)1 Sept. 14 (256)1 Oct. 11 (284) 1 Nov. 14 (31W Sept. 14 (257) 1 Oct. 11 (284)1 Nov. 15 (319)1
Sept. 27 (270) Nov. 4 (308) Dec. 23 (357) Sept. 29 (272) Oct. 28 (301) Dec. 8 (342) Oct. 2 (276) Nov. 3 (307) Dec. 24 (358) Oct. 6 (280)* Nov. 22 (327)* Mar. 8 (67)* Sept. 24 (267)* Nov. 27 (331)* Sept. 20 (263)* Sept. 23 (266) Sept. 27 (270)* Oct. 28 (301) Dec. 28 (362) Dec. 27 (361)* Oct. 6 (280) Nov. 23 (328) Jan. 3 (3) Nov. 17 (322)* Jan. 15 (15)* Mar. 29 (88)* Sept. 18 (261)* Nov. 1 (305)* Dec. 31 (365)* Mar. 29 (88)* Sept. 24 (267) Oct. 27 (301) Dec. 26 (360) Sept. 28 (271) Oct. 29 (302) Dec. 23 (257) Oct. 3 (276) Oct. 30 (303) Dec. 17 (351) Sept. 25 (268) Oct. 27 (300) Dec. 17 (351) Sept. 23 (266) Oct. 27 (300) Dec. 14 (348)
UK Aberdeen (Ab)
57.2
Auchn've (Au)
55.5
H. Mowth'pe (Hi)
54.1
Brooms Bam (Br)
52.3
Ropsley (Ro)
52.3
Cambridge (Ca)
52.2
Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Norman (W) Norman (W) Norman (W) Avalon (W) Norman (W) Avalon (W) Avalon (W) Norman (W) Avalon (W) Avalon (W)
1983
1983
1980 1981
1982 1983
1980
a
1980
a
1981
a Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon
(W) (W) (W) (W) (W) (W) (W) (W) (W) (W) (W) (W) (W) (W) (W)
Emergence date
Year
1982 1983
Rothamsted (Rt)
51.8
Oxford (Ox)
51.8
Long Ashton (Lo)
51.4
Seale Hayne (Se)
50.6
Rutigliano (Ru) Firenze (Fi) Ostellato (Os)
40.2
Creso (W)
1983
Nov. 30 (334)"
Dec. 14 (348)*
43.9
b b Pandas (W)
1986 1987 1988
Nov. 12 (316)8 Feb. 5 (36)8 Oct. 31 (305)9
Nov. 23 (328)* Feb. 23 (54)* Nov. 30 (335)*
1983
1983
1983
1983
ITALY
44.5
a) Av, Avalon (W) ; No, Nonnan (W); Aq, Aquila (W); Fe, Fenman (S) ; Hi, Highbury (S); Hu, Maris Huntsman (W); We, Wembley (S) ; Ta, Talent (W) ; Dg, 1772/8 (W). b) Cr, Creso (W) ; Ma, Maris Huntsman, Italy (W).
Eur. J. Agron.
Comparison of leaf appearance models for wheat
19
Table 1 (cont.). Site, latitude, cultivar and the sowing and emergence dates (day number * emergence estimated as occurring 130°C d after sowing) of experiments used for the inter-model comparison of leaf emergence. (W), cultivar with vemalisation requirement; (S) culrivar without vemalisation requirement. Sources of the data are " Porter et at., 1987 and unpublished data from this experiment; 2, Willington and Biscoe, 1982; 3, Willington and Biscoe, 1983; 4, Willington and Biscoe, 1984; 5, Willington and Biscoe, 1985; 6, Kirby et al., 1985; 7, Miglietta et ai., 1987; 8, Miglietta, 1989; 9, Miglietta, 1992; 10, Groot 1987; II Bauer et ai., 1988.
Country (code)
Latitude e N)
Location (code) Stuard (St) Martorano (Ma)
Cultivar
Year
Sowing date
Emergence date
44.5
Pandas (W)
1988
Oct. 31 (305)9
Dec. 1(336)*
44.5
Pandas (W)
1988
Oct. 31 (305)9
Nov. 20 (324)*
51.9
Arrninda (W)
1982
Oct. 21 (294)10
Nov. 2 (307)*
52.5
Arrninda (W)
1983
Oct. 21 (294)10
Nov. 7 (312)*
46.8
Colt (S)
1984
Sept. 19 (263)"
Oct. 15 (289)
39.2
Colt (S)
1985
Sept. 20 (263) "
Nov. 5 (309)
THE NETHERLANDS Randwijk (Ra) Lelystad (Le)
USA Mandan ND (Mn) Manhattan KS (Mh)
") Av, Avalon (W) ; No, Norman (W) ; Aq, Aquila (W); Fe, Fenman (S) ; Hi, Highbury (S); Hu, Maris Huntsman (W); We, Wembley (S) ; Ta, Talent (W) ; Dg. 1772/8 (W). b) Cr. Creso (W) ; Ma, Maris Huntsman, Italy (W).
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Figure 1. Root mean square error (RMSE, a-d) between estimated (Est) and observed (Obs) values of leaf number for four models of leaf appearance (a - model RC; b - model TtIP; c - model PT; d - model 0: see text for further details) at sites with different latitudes (see Table 1). Vol. 4, n° 1 - 1995
20
M. Bindi et aL
Table 2. Mean bias error (MBE) and root mean square error (RMSE) between estimated (Est) and observed (Obs) values of leaf number for f our models of leaf appearance (see text and Table 1 for further details). MBE between Est-Obs Leaf no. RC a)
b)
c)
RMSE between Est-Obs leaf no.
PT
0
RC
TtJP
PT
0
0.58 0.46 0.25 0.64 0.24 0.38 0.58 0.\ 9 0.52 0.03 1.69 0.26 0.45 2.07 \ .03 0.43 0.65 0. \3 0.32
4.06 -0.33 1.34 2.41 1.04 1.33 4.06 3.9 \ 2.80 2.80 1.39 2.43 1.4\ 4.9 \ 1.09 4.20 1.38 2.78 2.07
0.77 0.17 0.03 0. 30 - 0.38 -0.70 0.77 0.37 - 0.36 0.1 1 - 1.84 -0.59 -0.62 1.34 - 1.56 0.42 -0.97 0.01 -0.54
1.05 0.66 1.1 5 0.72 0.44 0.37 1.05 0.67 0.8 1 1.01 2.06 0.34 1.05 2.48 1.02 0.99 1.19 1.22 0.74
0.96 0.58 1.11 0.68 0.44 0.44 0.96 0.66 0.84 1.0 1 2. \0 0.37 0.98 2.39 1.06 0.95 1.22 1.23 0.76
4.30 0.51 2.14 2.59 1.66 1.47 4.30 5.\3 3.51 3.46 2.79 2.67 2.76 5.81 1.5 \ 5.27 2.07 3.72 3.1 2
1.13 0.42 0.98 0.36 0.60 0.72 1.13 0.74 0.82 0.66 2.30 0.64 1.03 1.73 1.59 1.1 7 1.66 1.30 1.1 5
TtJP
Latitude CON) Mh (39.2) Ru (40.2) Fi (43.9) Ma (44.5) St (44.5) Os (44.5) Mn (46.8) Se (50.6) Lo (5 1.4) Ox (5 1.8) Rt (5 1.8) Ra (5 1.9) Ca (52.2) Ro (52.3) Le (52.5) Br (52.3) Hi (54. 1) A u (55.5) Ab (57.2)
0.69 0.56 0.33 0.70 - 0.17 - 0.30 0.69 0.25 - 0.46 0.08 -1.64 - 0.20 -0.74 2.16 - 0.98 0.50 - 0.6 1 - 0.08 -0.28
Sowing Sept. Oct. Nov. Dec. Feb. Mar.
- 0.71 - 0.41 0.06 - 0.06 - 0.64 - 2.00
- 0.26 0. \8 0.26 0.02 - 0.92 - 2.38
3.92 1.53 0.55 0. \0 0.4\ - 0.47
- 0.09 - 0.4 \ - 0.53 -0.70 -1.10 - 2.43
1.\ 6 0.80 0.89 0.52 1.03 2.06
1.1 1 0.82 1.01 0.56 1.24 2.47
4 9. 6 2.\3 1.50 0.76 1.20 1.29
0.89 0.88 1.1 6 0.90 1.45 2.54
Cu\tivar Av No Aq Fe Hi Hu Ss Ta Dg Cr Ma Pa Ar Co
- 0.34 - 0.51 - 0.77 - 0.75 - 0.38 -1. \0 - 0.74 - 0.79 - 1.32 0. 11 0.56 0.07 - 0.59 0.43
- 0.40 - 0.58 - 0.84 -0.82 - 0.45 - 1.1 7 - 0.81 - 0.86 - 1.40 0.04 0.46
2.50 2.21 1.46 1.47 1.7 1 1.1 2 1.40 1.38 0.49 0.61 1.75 1.59 1.76 4.17
- 0.41 -0. 37 -0.63 - 0.60 -0.24 - 0.96 -0.60 -0.64 -1.27 -0.1 3 0. 19 -0.26 -1.08 0.67
1.27 0.90 1.08 1.00 0.94 1.35 1.06 1.06 1.52 0.54 1.45 0.5 1 0.76 0.76
1.29 0.96 1.14 1.07 0.98 1.41 1.12 1.1 2 1.59 0.52 1.40 0.52 0.80 0.70
3.66 3.82 3.01 3.09 3.30 2.81 3.06 2.85 1.84 1.02 2.66 1.90 2.17 4.42
1.33 1.06 1.04 1.04 1.05 1.27 1.11 1.02 1.50 0.49 1.22 0.56 1.2 1 0.97
-
-
om
- 0.64 0.3 1
lowest values occurring for sowings from October to December and higher values for more extreme sowings (Table 4b) . MBE's for the PT and 0 models generally rose as sowing was delayed (Figure 4c,d) . Winter sowings were simulated m ore accurately by the RC and TtIP model (Figure 4a,b). RMSE values (Table 4b) were most consistent for the 0 m odelwith respect t o month of sowing. The pattern for the other
models w as for afall in RMSE fro m sowings made in September through t o February, followed b y a rise in March (Table 4b). The RC, TtIP and 0 models distinguished between spring and winter cultivars i n a similar way (Table 4c), also reflected in the RMSE values (Table 4c). The PT model simulated early the appearance of leaf seven for all cultivars. Eur. J. Agron.
Comparison of leaf appearance models for wheat
ci c
(ij
91
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(ij
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Sept
Oct
Jan Nov Dec Month of Sowing
Feb
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(a)
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-3
Sept
Oct
Jan Nov Dec Month of Sowing
Feb
-3
Mar
(e)
Sept
Oct
Dec Jan Nov Month of Sowing
Feb
Mar
(d)
Figure 2_ Mean bias error (MBE, a-d) between estimated (Est) and observed (Obs) values of leaf number for four models of leaf appearance (a - model RC ; b - model TtIP; c - model PT; d - model 0 : see text for further details) for sowing dates in different months (see Table 1).
Table 3. Average root m ean square error (RMSE± s. d.) bet· ween (a) estimated and observed leaf number and (b) estimated and observed day number of the appearance of leaf number seven with respect to site, cultivars and month of sowing. The models of leaf appearance are described in the text. Model of leaf appearance
Variable
(a) RC TtIP PT 0 0.97 (.124) 0.96 (. 122) 3.11 (.329) 1.04 (. ll5) Site (n 19) Cultivar (n = 14) 1.02 (.083) 1.04 (.087) 2.83 (.236) 1.06 (.072)
=
Month (n '" 6)
1.08 (.217) 1.20 (.272) 1.98 (.626) 1.31 (.647)
(b) Site (n= 19) 12.2 (2.15) 15.6 (2.52) 34.5 (4.25) 13.6 (2.20) Cultivar (n 14) 20.2 (3.1 3) 17.6 (2.13) 22.2 (3.50) 14.4 (1.77)
=
Month (n '" 6)
16.4 (4.68) 16.4 (3.33) 20.7 (6.6) 17.3 (0.55)
Taken over all variables, the average RMSE for the RC, TtiP and 0 models was about 15 days (Table 3b). Whereas RMSE for the PT model varied between about 20 days (month of sowing) to 30 days for sites at different latitudes, but a pair-wise Student's t test failed to detect Significant differences between the models in their RMSE values. Vol. 4, n° 1 - 1995
DISCUSSION The four models of leaf appearance were compared using field data recorded from a wide range of sites and sowing dates and cultivars. The data are independent of those used to develop the models and provide a stringent test of their ability to simulate the behaviour of field-grown crops. It was not possible statistically to distinguish between three of them (RC, TtIP and 0) in terms of their ability to predict either leaf number or the day of emergence of leaf seven ; whereas the predictions with the fourth model (PT) were substantially different from those of the others. The main reason for this discrepacy between the models is that the PT model assumes a particular and fixed site-based relationship between maximum, minimum and mean daily temperature and photoperiod. The RC and TtIP models modify the phyllochron on the basis of either the rate and direction in which daylength is changing at emergence (RC model) or the ratio of thermal time to photoperiod around emergence (TtiP model) and the 0 model deals with differences in sowing date by increasing the phyllochron interval for later leaves.
22
M. Bindi et al.
Table 4. Mean bias error (MBE) and root mean square error (RMSE) between estimated (Est) and observed (Obs) values of leaf seven for four models of leaf appearance (see text and Table 1 for further details). MBE between Est-Obs day no.
a)
b)
c)
Latitude eN) Mh (39.2) Ru (40.2) Fi (43.9) Ma (44.5) St (44.5) Os (44.5) Mn (46.8) Se (50.6) Lo (51.4) Ox (51.8) Rt (51.8) Ra (51.9) Ca (52.2) Ro (52.3) Le (52.5) Br (52.3) Hi (54.1) Au (55.5) Ab (57.2) Sowing Sept. Oct. Nov. Dec. Feb. Mar.
RMSE between Est-Obs day no.
RC
TtIP
PT
o
RC
TtIP
PT
o
0.0 -1.0 -5.0 -4.0 5.0 -2.0 -16.0 -6.6 7.0 2.3 19.0 0.1 17.6 -6.0 -29.3 20.3 0.6 10.3 10.0
-6.0 -2.0 -17.0 -6.0 -3.0 -11.0 -17.0 -16.3 - 3.0 -6.0 10.0 -10.0 12.4 -16.5 -46.0 6.0 -15.3 -5.3 -5.0
- 33.0 -12.0 - 25.0 6.0 -8.0 -17.0 -44.0 - 36.6 -29.6 - 33.0 -26.6 -38.0 -7.7 -46.5 -60.0 -27.3 -38.0 -37.6 -16.0
-4.0 3.2 -3.0 1.0 7.0 -1.0 -16.0 -11.6 1.3 1.6 20.6 5.0 13.1 -8.4 -23.6 33.0 0.1 17.6 18.0
0.0 4.8 5.0 4.0 5.0 2.0 16.0 10.3 9.8 19.4 21.2 0.0 27.5 10.3 32.0 22.2 20.3 12.2 10.0
6.0 5.2 17.0 6.0 3.0 11.0 17.0 18.7 12.4 22.8 14.3 10.0 20.4 23.2 48.7 7.2 30.6 17.0 5.0
33.0 15.2 25.0 6.0 8.0 17.0 44.0 39.3 34.3 41.8 33.2 38.0 15.2 57.1 69.1 45.9 54.5 61.7 16.0
4.0 6.5 3.0 1.0 7.0 1.0 16.0 16.6 7.4 9.6 22.0 5.0 15.9 21.8 28.5 33.6 19.8 22.1 18.0
25.2 7.0 1.1 3.1 5.7 14.8
11.3 -4.7 -2.0 -0.9 9.3 17.9
- 37.9 - 23.6 -2.4 -1.3 1.3
-1.4 9.6 11.4 13.3 13.4 16.7
39.0 14.5 11.5 7.9 9.6 15.9
31.3 15.3 13.3 7.8 11.9 18.4
47.1 32.6 15.7 8.6 8.5 10.4
18.8 16.4 17.9 15.4 16.3 18.4
4.4 2.7 19.2 17.1 11.0 25.7 17.5 17.5 28.5 0.6 -5.0 -0.6 5.0 - 8.0
-6.9 -6.0 14.0 11.8 5.7 20.5 12.2 12.2 20.5 -1.0 -5.5 -10.3 -7.5 -11.5
- 33.6 - 30.2 -7.3 -9.5 -15.6 -0.8 -9.1 -9.1 -4.2 -2.3 -17.5 -16.6 -27.0 -38.5
5.0 -0.8 14.7 12.6 6.5 21.2 13.0 13.0 19.5 4.6 0.1 1.0 11.5 -10.0
21.9 24.0 28.4 26.2 22.7 35.5 26.0 27.0 38.9 4.1 5.3 4.2 7.0 11.3
25.5 26.5 20.6 19.2 16.5 27.4 18.9 19.8 28.5 3.8 7.1 11.8 7.9 12.7
47.1 44.7 12.2 17.0 23.7 9.6 18.6 14.5 9.3 8.2 19.4 18.0 29.1 38.8
20.8 20.9 15.8 15.8 15.6 23.1 17.8 14.6 19.7 7.5 0.1 4.4 13.2 11.6
3.2
Cultivar
Av No Aq Fe Hi Hu Ss Ta Dg Cr Ma Pa Ar Co
It is evident from the analysis presented in this paper that three of the models can be used satisfactorily to simulate leaf appearance under a range of conditions. Predictions were generally accurate for latitudes and sowing dates appropriate to common agricultural practices. Nevertheless, the problem of a correct interpretation of the mechanisms of leaf appearance remains largely unresolved. Two of the
three models (Re and TtIP) require that plants have a "memory" of their photoperiodic environment into which they emerge and for this to set a rate of leaf production for the rest of the plant's growth. The third one (0) assumes that the morphology of the plant determines the decrease in the rate of leaf appearance of subsequent leaves. Experiments in which the rate of change in day length was manipuEur. J. Agron.
Comparison of leaf appearance models for wheat
23
g 70,---------------------------------, ~
"0
o13
60 50
g ~
"0
o13
40
70,---------------------------------, 60 50 40
, 30
"Ii; 30
!:!:!. 20 w
~ 10 0 35
a:
40
--
45
Jtw
20
~ 10
50
Latitude (deg. N)
55
60
(a)
a:
0 35
40
45
55
50
Latitude (deg. N)
60
(b)
o
70.---------------------~--------~
c 60 ~
"0
13 o ~-
w
d 70,----------------------------------, c 60 ~
50 40
"0
13 o
30
~~ -
20
w
~ 10 a: 0 35
40
45
50
60
55
50 40
30 20
D
~ 10 a: 0 35
40
50
60
55
Latitude (deg. N)
Latitude (deg. N)
(c)
45
D
(d)
Figure 3. Root mean square error (RMSE, a-d) between estimated (Est) and observed (Obs) values of the day of appearance of leaf seven on the main shoot for four models of leaf appearance (a - model RC ; b - model TtlP ; c - model PT; d - model 0 : see text for further details) at sites with different latitudes (see Table 1).
g
30,--------------------------------, 20
~
10
13
0
"0
o
-
-10
g
~ 10
13 o
~ -20
w -30
[D
~
-50l-~--~~--~--~~--~~--~--~~~
Sept
Oct
Nov Dec Jan Month of Sowing
Feb
~
13 o
-40 -50~~--~~~~--~----~--~~--~~
Mar
(a)
"0
O+-------------~----~------------------~
-10
~ -20
w -30 [D ~ -40
g
~.-------------------------------,
20
Sept
Oct
Nov Dec Jan Month of Sowing
Feb
Mar
(b)
30.-------------------------------, 20
g
10
~
"0
13
0
o
-10
30.-------------------------------, 20 10
0
-10
"lii -20
~ -20 w -30
!:!:!. w -30 [D ~ -40
~ -40
-50~~~~~~~--~--~--~~--~~
-50~~--~~~~~~--~--~~--~~
Sept
(c)
Oct
Nov Dec Jan Month of Sowing
Feb
Sept
Mar
Oct
Nov Dec Jan Month of Sowing
Feb
Mar
(d)
Figure 4. Mean bias error (MBE, a-d) between estimated (Est) and observed (Obs) values of the day number of appearance of leaf seven on the main shoot for four models of leaf appearance (a - model RC; b - model TtIP; c - model PT; d - model 0: see text for further details) for sowing dates in different months (see Table 1). Vol. 4, n° 1 - 1995
24
lated artificially in the laboratory have not solved this problem. Although, in such cases, changes in dcJJldt were never observed to affect the rate of leaf appearance (van Dobben, 1960; J. T. Ritchie, pers. comm.) it might be argued that changes in light quality and intensity affected leaf extension. Although the models led to comparable predictions of leaf number, any difference becomes important for a further description of the effect of the environment on leaf growth and morphology in wheat. In fact, provided there is a strict coordination between leaf appearance and cell division rate (Horie et al., 1979) the two above hypotheses (RC, Tt/P versus 0) would lead to different predictions of the final cell number of successive leaves and, with this, of final leaf size. Models RC and Tt/P assume that, for a constant temperature, the time elapsing between leaf initiation and the appearance of the lamina tip is a constant for every leaf, while model 0 assumes that this time increases linearly with leaf number. Since the division of epidermal cells occurs largely during this time and the relative rate of cell division declines in successive main stem leaves (Castellani and Miglietta, 1993), model 0 explains how the final number of epidermal cells along the leaf lamina and final leaf length increase with leaf number. New ideas are emerging to describe the mechanism of leaf appearance. One of these considers that soil rather than air temperature drives apical development rates in the first stages of vegetative growth before stem extension. Since the difference between soil and air temperature varies seasonally, this could account for differences in the rate of leaf appearance between crops sown on different dates (Brooking and Ritchie, 1993). Since differences between models are expected to be largest when dcJJldt is constant throughout the year, we suggest that a series of sowing date experiments at the equator would provide a critical test of the rate of change of day length and ontogenetic hypotheses. Provided that soillair temperature differences are near constant throughout the year in this environment, such an experiment would be and excellent test of the recent hypothesis of mechanisms governing leaf appearance mentioned above.
ACKNOWLEDGEMENTS We thank Dr. Michael Kirby for useful discussions during the early part of this work. This research was supported by the National Research Council of Italy, Special Project RAISA, sub-project 2, Paper No. 1917 and the Commission of the European Communities Environment Programme CROPCHANGE (Contract Number EV5V-CT92-0169).
M. Bindi et al.
REFERENCES Baker C. K. and Gallagher J. N. (1983). The development of winter wheat in the field. II. The control of primordium initiation rate by temperature and photoperiod. J. agric. Sci., Camb., 101, 337-344. Baker C. K., Gallagher J. N. and Monteith J. L. (1980). Daylength change and leaf appearance in winter wheat. Plant Cell Environ., 3, 285-287. Bauer A., Garcia R., Kanemasu E. T., Blad B. L., Hatfield J. L., Major D. J., Reginato R. J. and Hubbard K. G. (1988). Effect of latitude on phenology of "Colt" winter wheat; Agric. For. Met., 44, 131-140. Brooking I. R. and Ritchie J. T. (1993). Leaf appearance and the phyllochron in wheat. In : Agronomy Abstract. Madison: American Society of Agronomy, 109 pp. Cao W. and Moss D. N. (1989a). Temperature and daylength interaction on phyllochron in wheat and barley. Crop Sci., 29, 1046-1048. Cao W. and Moss D. N. (I 989b). Temperature and daylength interaction on phyllochron in wheat and barley. Crop Sci., 29, 1046-1048. Cao W. and Moss D. N. (1991). Phyllochron change in winter wheat with planting date and environmental changes. Agron. J., 83, 396-401. Castellani M. and Miglietta F. (1993). Relationship between leaf appearance and leaf extension rates in wheat. In: Agronomy Abstract. Madison: American Society of Agronomy, 11 pp. Dale J. E. and Milthorpe F. L. (1983). General features of the production and growth of leaves. In: Dale J. E. and Milthorpe F. L. (Eds.) The Growth and Functioning of Leaves. Cambridge: Cambridge University Press, pp. 151-178. Delecolle R., Couvreur F., Pluchard P. and VarletGrancher C. (1985). About the leaf-daylength model under French conditions. In : Day W. and Atkin R. K. (Eds.) Wheat Growth and Modelling. New York: Plenum Press, pp. 25-31. Dobben W. H. van (1960). De invloed van de daglengte op overwinterende gewassen. Medeling van I.B.S., no. 113. Wageningen, 85-96. Friend D. J. c., Helson V. A. and Fisher J. E. (1962). Leaf growth in Marquis wheat, as regulated by temperature, light intensity and daylength. Can. J. Bot., 40, 1299-1311. Gallagher J. N. (1979). Field studies of cereal leaf growth. I. Initiation and expansion in relation to temperature and ontogeny. J. expo Bot., 30, 625-636. Gallagher J. N. and Biscoe P. V. (1978). Radiation, absorption, growth and yield of cereals. J. agric. Sci., Camb., 91,47-60. Groot J. J. R. (1987). Simulation of nitrogen balance in a system of winter wheat and soil. Simulation Reports CABO-IT no. 13. Wageningen: Pudoc. Hay R. K. M. and Brown J. R. (1988). Fields studies of leaf development and expansion in the leek (Allium porrum). Ann. appl. BioI., 113, 6l7-625. Eur. J. Agron.
Comparison of leaf appearance models for wheat
Hay R K. M. and Kirby E. J. M. (1991). Convergence and synchrony: a review of the coordination of development in wheat. Aust 1. agric. Res., 42,661-700. Horie T, de Wit C. T, Goudriaan J. and Bensink J. (1979). A formal template for the development of cucumber in its vegetative stage. In : Proc. Koninklijke Nederlandse Akademie van Wetenschappen. , 82, 433479. Kirby E. J. M. (1990). Co-ordination of leaf appearance and leaf spikelet primordium initiation in wheat. Field Crops Res., 25, 253-264. Kirby E. J. M. (1992) . A field study of the number of main shoot leaves in wheat in relation to vernalization and photoperiod. 1. agric. Sci., Camb., 118, 271278. Kirby E. J. M. Appleyard M. and Fellowes G. (1985). Effect of sowing date and variety on main shoot leaf appearance and number of leaves of barley and wheat. Agronomie, 5, 117-126. Masle J., Doussinault G. , Farquhar G. D. and Sun B. (1989) . Foliar stage in wheat correlates better to photothermaltime than to thermal time. Plant Cell Environ., 12, 235-247. Miglietta F, Vazzana c., LoSavio N., Mastrorilli M. and Raschi A. (1987). Calibrazione di un modello di simulazione della crescita del frumento in due ambienti italiani. Riv. Agron., 21, 240-245. Miglietta F (1989). The effect of photoperiod and temperature on leaf initiation rates in wheat (Triticum spp.). Field Crop Res., 21, 121-131. Miglietta F (1991a). Simulation of wheat ontogenesis. I. Appearance of main stem leaves in the field. Clim. Res., 1, 145-450. Miglietta F (1991 b). Simulation of wheat ontogenesis. II. Predicting dates of ear emergence and main stem final leaf number. Clim. Res., 1, 151-160. Miglietta F (1992). Simulation of wheat ontogenesis. III. Effect of variety, nitrogen feltilisation and water stress on leaf appearance and final leaf number in the field . Clim. Res., 2, 233-242. Porter 1. R (1984) . A model of canopy development in winter wheat. 1. agric. Sci., Comb. , 103, 383-392.
Vol. 4. n° 1 - 1995
25
Porter J. R (1985). Approaches to modelling canopy development in wheat. In: Day W. and Atkin R K. (Eds.) Wheat Growth and Modelling. New York: Plenum Press, pp. 69-81. Porter 1. R Jamieson P D . and Wilson D. W (1993). Comparison of the wheat simulation models AFRCWHEATI, CERES-Wheat and SWHEAT for non-limiting conditions of crop growth. Field Crops Res., 33, 131-157. Porter J. R, Kirby EJ.M., Day W, Adam J. S., Appleyard M., Ayling S ., Baker C. K., Beale P , Belford R. K., Biscoe P. v., Chapman A., Fuller M. P, Hampson J., Hay R K. M., Hough M., Matthews S., Thomson W. J., Weir A. H., Willington V. B. A. and Wood D. W (1987). An analysis of morphological development stages in Avalon winter wheat crops with different sowing dates at ten sites in England and Scotland. 1. agric. Sci, Camb., 109, 107121. Warrington I. J. and Kanemasu E. T (1983a). Com growth response to temperature and photoperiod. II . Leaf initiation and leaf appearance rates. Agron. 1., 75, 755-761. Warrington I. J. and Kanemasu E. T. (1983b). Com growth response to temperature and photoperiod. III. Leaf number. Agron. 1., 75, 762-766. Watson D. 1. (1958). The dependence of net assimilation rate on leaf area index. Ann. Bot., 22, 37-54. Willigen P. de (1991) . Nitrogen turnover in the soil-crop system; comparison of fourteen simulation models. Fert. Res., 27, 141-149. Willington V. B. A. and Biscoe P V. (1982). Growth and development of winter wheat. Annual Report No. 1. Higham (UK) : Brooms Bam Experimental Station. Willington V. B. A. and Biscoe P. V. (1983). Growth and Development of Winter Wheat. annual Report No.2. Higham (UK) : Brooms Bam Experimental Station. Willington V. B. A. and Biscoe P V. (1984). Growth and Development of Winter Wheat Annual Report No.3. Higham (UK) : Brooms Bam Experimental Station. Willington V. B. A. and Biscoe P. V. (1985). Growth and Development of Winter Wheat. Annual Report No. 4. Higham (UK) : Brooms Barn Experimental Station.
Comparison of models to simulate leaf appearance in wheat M. Bindi*
1,
J. R. Porter 2 and F. Miglietta 3
Centro di Studio per l'Applicazione dell'lnformatica in Agricoltura, Accademia dei Georgofili, Piazzale delle Cascine 18, 50144 Firenze, Italy. 2 Department of Agricultural Sciences, University of Bristol, AFRC Institute of Arable Crops Research, Long Ashton Research Station, Bristol, BSI8 9AF, UK. New address,' Department of Agricultural Sciences, the Royal Agricultural and Veterinary University, Agrovej 10, 2630 Taastrup, Denmark Istituto per l'Agrometeorologia e l'Analisi Ambientale applicata all'Agricoltura, Consiglio Nazionale delle Ricerche, Piazzale delle Cascine 18, 50144 Firenze, Italy. 1
3
Accepted 6 June 1994.
* to whom correspondence should be addressed. Abstract
Prediction on of leaf appearance in cereals is important for modelling canopy development and timing crop management practices. Four models which aim to predict leaf emergence on the basis of temperature and, in three cases, photoperiod are compared against independent data from a wide range of sites, sowing dates and cultivars of spring and winter wheat. Three of the models behaved bery similarly and had root mean square errors of the order of one leaf in their prediction of leaf appearance. The fourth model performed better in predicting differences in leaf appearance for different sowing dates than it did for latitudes. The prediction of the day of emergence of leaf number seven followed a similar response to that of leaf appearance. These results are discussed in terms of the hypothesised relationships between temperature, photoperiod and ontogeny within the models. Key-words: wheat, leaf appearance, models
INTRODUCTION The importance of leaf area for growth, development, and yield of cereals has been recognised by crop physiologists and agronomists for a long time (Watson, 1958; Friend et aI., 1962; Gallagher and Biscoe, 1978). Hence, crop simulation models of cereals need to incorporate the development of the leaf canopy (Horie et al., 1979). To achieve this goal it is necessary to simulate the rate of appearance of successive leaves on a shoot (Porter, 1984; 1985). There are also practical reasons to anticipate leaf appearance since the control of plant disease epidemics is often linked to a specific developmental stage. Leaf appearance is the result of the initiation of leaf primordia and their extension to form leaves (Dale and Milthorpe, 1983). Under optimal conditions both processes are controlled by temperature (Gallagher, 1979; Baker and Gallagher, 1983; Warrington and Kanemasu, 1983a,b ; Hay and Brown, 1988; Kirby, 1992). The concept of thermal time, heat units or growing degree-days measured as °C d, has been used to predict the rate of leaf appearance (Hay and Kirby, 1991). Heat units are useful predictors of leaf appearance and many investigators have found ISSN I161 -0301195101/$ 4.001 © Gauthier-Villars - ESAg
significant linear relationships between leaf number and the number of degree-days accumulated from emergence (Baker et aI., 1980; Delecolle et aI., 1985; Kirby et aI., 1985). However, the thermal time between successive leaves varies with cultivar, planting date and latitude. Broadly, two methodologies have been proposed to predict the rate of leaf appearance in cereals. The first is based on empirically derived effects of photoperiod and temperature on the rate of leaf emergence. Examples of this approach are : the rate of leaf emergence in thermal time in relation to the rate of change of daylength (Baker et aI., 1980) ; the leaf emergence rate in thermal time in relation to the ratio of daily mean temperature to photoperiod (Cao and Moss, 1989a,b) and the leaf emergence rate in relation to the accumulation of thermal time during daylight only (Mas Ie et aI., 1989). The second broad approach attempts to be more mechanistic and describes the ontogenetic processes of leaf primordia initiation and lamina extension (Miglietta, 1989; 1991a,b; 1992).
This study compares the ability of the different approaches to calculate rates of leaf appearance in wheat for a range of locations in the UK, Italy, the
M. Bindi et al.
16
Netherlands and the USA, and for different sowing dates and cultivars. We compared models for their ability to predict number of leaves on the main shoot during growth as well as the date of emergence of leaf seven. In wheat, seven is, for developmental reasons, about the minimum leaf number that a wheat plant can produce, in cultivars that have no vernalis ation requirement and are also insensitive to daylength beyond a given value (Kirby, 1990; Brooking et aI., unpublished). Also, leaf sheaths, through which later leaves have to grow to emergence, do not appear until after the sixth leaf (Gallagher, 1979). Prediction of the time of emergence of the seventh leaf examines the ability of a model to predict the strictly ontogenetic events associated with leaf production and to exclude confounding growth effects. Finally, intermodel comparison is an important, although rarely performed, part of the development of models (de Willigen, 1991 ; Porter et aI., 1993).
dl/dTt = 1/( a
+ b TtIP)
(2).
On the basis of previous studies (Kirby, pers. comm.), values of intercept and slope were calculated from the upper series of points (for cv. Stephens winter wheat) from Figure 3 of Cao and Moss (1991) giving: a = 71.3 and b = 19.9.
Masle et al. (1989) - Model PT. Mas1e et al. (1989) proposed the use of photo-thermal, rather than thermal time, to predict leaf appearance. In this case, photo-thermal time (Tip, equivalent to ~ in Mas1e et aI., 1989) was calculated as the thermal time accumulated during daylight. Leaf number (L) was calculated in relation to photo-thermal time by the equation L = 0.0245 Ttp
(3).
The coefficient in equation (3) was calculated from data presented in Figure 7 of Masle et al. (1989). Ttp was calculated as described by Mas1e et al. (1989).
MODELS AND METHODS The models
The four models were written as FORTRAN computer programs.
Baker et al. (1980) - Model RC This model predicts leaf emergence on the basis of an empirical linear relationship between the rate of leaf appearance per unit thermal time (dUdTt) and the rate of change of daylength at crop emergence (d
appearance in thermal time. Therefore, the equation of their relationship, expressed in term of dUdTt is
(1).
Values of the intercept and slope of the above equation were recalculated from the data presented for cv. Huntsman by Baker et al. (1980) since their published value for the slope of the regression line (0.062 ; Figure 3 therein) was misprinted.
Cao and Moss (1989a,b; 1991) - Model TtlP These workers proposed that the thermal phyllochron (dTtldL) is linearly correlated with a thermalphoto quotient, calculated as the ratio between the mean daily thermal time (Tt) accumulated from 3 d before until 7 dafter 50 per cent seedling emergence and the daylength at emergence (P). The thermal phyllochron is the reciprocal of the rate of leaf
Miglietta (1989; 1991a,b) - Model O. This model proposes that differences in rate of leaf appearance for crops sown at different dates can be explained via a decline, during ontogeny, in the rate of leaf appearance (dUdt) caused by an increase in the time taken by each leaf primordium to extend from the apex to visible emergence. The daily rate of leaf appearance was calculated as dLidt = dPldt ( 1 - 0.03 L)
(4)
where, dPldt is the rate of production of vegetative primordia and L is the leaf number. In addition, dPldt = - 0.038 + 0.0149 T for T > 2.55 °C (5) where T is the mean daily temperature (0C). dPldt was set to zero for temperatures below 2.55 °C. For the RC and TtIP models thermal time (Tt) was calculated, above a base temperature (Tb)' from the maximum (T maJ and minimum (Tmin) daily screen temperatures (0C) as
Tt = (Tmax - Tmin)!2 - Tb
(6).
We used 0 °C as the base temperature (Gallagher, 1979; Baker et aI., 1980; Cao and Moss, 1989a,b) except for model 0, where 2.55 °C was used (Miglietta, 1991). Whenever the mean daily temperature was less than the base, Tt was zero for the day. For the PT model, photo-thermal time was calculated (Masle et aI., 1989) as (7)
where, I is the daylight period (h) as a proportion of 24 h. T[ was obtained from Tmax and T min as T, = T min + 0.065 (Tmax - T min )
(8). Eur. 1. Agron.
Comparison of leaf appearance models for wheat
Source of data The models were tested for their ability to predict leaf number and the day number of appearance of leaf seven from 55 field experiments with wheat (Triticum aestivum L.) in the northern hemisphere with a latitudinal range from 39.2° N to 57.2° N (Table 1). The models were run using the daily screen temperature data available from the meteorological station closest to the experiment. Estimated leaf production was ended on the same day number as the last recording date for the observed crop. The leaf number on this day was considered the final value. When day of seedling emergence was required for model calculations but was not recorded in an experiment, it was estimated to occur at 130°C d, accumulated above 0 °C, after sowing (Willington and Biscoe, 1984). To identify the combination of sowing dates and latitude for which the models diverge in their predictions, an analysis was made of their sensitivity to coincidental changes in these variables. Goodness of fit In order to assess the goodness-of-fit of the models to observed data, observed data (Table 1) were split, by site, variety and sowing date, into three sub-sets. For each, goodness-of-fit assessed from the positive or negative mean bias error (MBE) calculated as N
:2 (Xsim. -
t = 1
l
Xobs.) 1
MBE=------~N~----
where, t = the sample number, N = the number of observations throughout the season, Xsim i and Xobs i = the simulated and observed leaf number or the time of the seventh leaf appearance of the i th cultivar. A positive value of MBE indicates that, on average, a model over-estimated a value with respect to that observed and vice versa. To measure the absolute error of a model the root mean square error (RMSEO) was calculated as
RMSE=
N :2 (Xsim. =
t
{
1
1
Xobs.)2
}In
I
N
RESULTS Leaf appearance Of the four models tested, the largest MBE (Table 2a) for different latitudes was for the PT model which, in all except one case, overestimated leaf number. In general, the other models overestimated VoL 4, n° 1 - 1995
17
leaf appearance for latitudes from 40° N to 50° N but underestimated it for higher latitudes. For the RC, TtIP and 0 models MBE was about one leaf. RMSEs (Table 2a) for the RC, TtIP and 0 models showed very similar patterns (Figure Ia,b and d) whereas little pattern was seen for the PT model (Figure Ie). MBEs and RMSEs (Table 2b) for different months of sowing pointed to a generally similar and good ability of the models to predict leaf number for the main sowing periods (October to December) of winter wheat cultivars in the northern hemisphere. September sowings gave a high MBE for the PT model (Table 2b). Spring sowings were handled much less well by all except the PT model. The general tendency was to underestimate leaf appearance (Figure 2a,b,c, and d). Errors of prediction for different cultivars showed that, as for latitude, three of the models mostly underestimated leaf appearance (Table 2c), whereas the PT model overestimated leaf appearance for all cultivars (Table 2c). RMSEs (Table 2c) were consistently higher for the PT model when compared with the others which had values of about one leaf. There were no consistent differences between spring as opposed to winter cultivars in any model's prediction of leaf appearance. Taken over all variables the average RMSE for the RC, TtIP and 0 models was about one leaf and their standard deviations overlapped substantially (Table 3a). Mean RMSE for the PT model varied between about two leaves (month of sowing) to over three leaves for sites at different latitudes. A Student t test failed to detect significant difference between all pair-wise combinations of the models for month of sowing. For the other two variables, significant differences in RMSE (p < 0.001) were found between the PT model and the other three. Day of emergence of leaf seven Three models (RC, TtIP and 0) performed Slmllarly in predicting the day of appearance of leaf seven as with their estimates of leaf number. Systematic differences existed in the behaviour of the RC and PT models with respect to site latitude (Table 4a). The RC model generally simulated the appearance of leaf seven early at lower latitudes but late at latitudes above about 50° N. The PT model, except in one case, simulated the appearance of leaf seven early. Errors in the other two models were not so clearly related to changes in site latitude (Table 4a). The RMSE of the PT model increased with latitude (Figure 3c), a result not seen with any of the other models (Figure 3a,b and d). MBEs for the RC and TtiP models (Table 4b) changed similarly with month of sowing, with the
M. Bindi et al.
18
Table 1. Site, latitude, cultivar and the sowing and emergence dates (day number * emergence estimated as occurring 130°C d after sowing) of experiments used for the inter-model comparison of leaf emergence. (W), cultivar with vernalisation requirement; (S) cultivar without vernalisation requirement. Sources of the data are 1, Porter et al., 1987 and unpublished data from this experiment; 2 Willington and Biscoe, 1982; 3 Willington and Biscoe, 1983; 4 Willington and Biscoe, 1984; 5 Willington and Biscoe, 1985; 6, Kirby et aI., 1985; 7, Miglietta et aI., 1987; 8, Miglietta, 1989; 9, Miglietta, 1992; 10 Groot 1987; ", Bauer et ai., 1988. Country (code)
Location (code)
Cultivar
Sowing date
1983
Sept. 13 (256) 1 Oct. 11 (284)1 Nov. 15 (319)1 Sept. 14 (257) 1 Oct. 12 (285)1 Nov. 15 (319)1 Sept. 23 (266)1 Oct. 13 (286) 1 Nov. 18 (322)1 Sept. 26 (270)2 Nov. 3 (308)2 Feb. 2 (3W Sept. 16 (25W Nov. 10 (314)3 Sept. 13 (256)4 Sept. 13 (256)1 Sept. 19 (262)5 Oct. 12 (285)1 Nov. 16 (320)1 Nov. 16 (32W Sept. 25 (269)2 Nov. 3 (308)2 Dec. 12 (347)2 Oct. 24 (298)6 Dec. 4 (339/ Feb. 25 (56)6 Sept. 10 (253)6 Oct. 14 (288)6 Nov. 18 (323)6 Mar. 8 (67)6 Sept. 13 (257) 1 Oct. 11 (284) 1 Nov. 15 (319)1 Sept. 15 (258) 1 Oct. 11 (284)1 Nov. 16 (320)1 Sept. 14 (257)1 Oct. 11 (284)1 Nov. 16 (320)1 Sept. 14 (256)1 Oct. 11 (284) 1 Nov. 14 (31W Sept. 14 (257) 1 Oct. 11 (284)1 Nov. 15 (319)1
Sept. 27 (270) Nov. 4 (308) Dec. 23 (357) Sept. 29 (272) Oct. 28 (301) Dec. 8 (342) Oct. 2 (276) Nov. 3 (307) Dec. 24 (358) Oct. 6 (280)* Nov. 22 (327)* Mar. 8 (67)* Sept. 24 (267)* Nov. 27 (331)* Sept. 20 (263)* Sept. 23 (266) Sept. 27 (270)* Oct. 28 (301) Dec. 28 (362) Dec. 27 (361)* Oct. 6 (280) Nov. 23 (328) Jan. 3 (3) Nov. 17 (322)* Jan. 15 (15)* Mar. 29 (88)* Sept. 18 (261)* Nov. 1 (305)* Dec. 31 (365)* Mar. 29 (88)* Sept. 24 (267) Oct. 27 (301) Dec. 26 (360) Sept. 28 (271) Oct. 29 (302) Dec. 23 (257) Oct. 3 (276) Oct. 30 (303) Dec. 17 (351) Sept. 25 (268) Oct. 27 (300) Dec. 17 (351) Sept. 23 (266) Oct. 27 (300) Dec. 14 (348)
UK Aberdeen (Ab)
57.2
Auchn've (Au)
55.5
H. Mowth'pe (Hi)
54.1
Brooms Bam (Br)
52.3
Ropsley (Ro)
52.3
Cambridge (Ca)
52.2
Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Avalon (W) Norman (W) Norman (W) Norman (W) Avalon (W) Norman (W) Avalon (W) Avalon (W) Norman (W) Avalon (W) Avalon (W)
1983
1983
1980 1981
1982 1983
1980
a
1980
a
1981
a Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon Avalon
(W) (W) (W) (W) (W) (W) (W) (W) (W) (W) (W) (W) (W) (W) (W)
Emergence date
Year
1982 1983
Rothamsted (Rt)
51.8
Oxford (Ox)
51.8
Long Ashton (Lo)
51.4
Seale Hayne (Se)
50.6
Rutigliano (Ru) Firenze (Fi) Ostellato (Os)
40.2
Creso (W)
1983
Nov. 30 (334)"
Dec. 14 (348)*
43.9
b b Pandas (W)
1986 1987 1988
Nov. 12 (316)8 Feb. 5 (36)8 Oct. 31 (305)9
Nov. 23 (328)* Feb. 23 (54)* Nov. 30 (335)*
1983
1983
1983
1983
ITALY
44.5
a) Av, Avalon (W) ; No, Nonnan (W); Aq, Aquila (W); Fe, Fenman (S) ; Hi, Highbury (S); Hu, Maris Huntsman (W); We, Wembley (S) ; Ta, Talent (W) ; Dg, 1772/8 (W). b) Cr, Creso (W) ; Ma, Maris Huntsman, Italy (W).
Eur. J. Agron.
Comparison of leaf appearance models for wheat
19
Table 1 (cont.). Site, latitude, cultivar and the sowing and emergence dates (day number * emergence estimated as occurring 130°C d after sowing) of experiments used for the inter-model comparison of leaf emergence. (W), cultivar with vemalisation requirement; (S) culrivar without vemalisation requirement. Sources of the data are " Porter et at., 1987 and unpublished data from this experiment; 2, Willington and Biscoe, 1982; 3, Willington and Biscoe, 1983; 4, Willington and Biscoe, 1984; 5, Willington and Biscoe, 1985; 6, Kirby et al., 1985; 7, Miglietta et ai., 1987; 8, Miglietta, 1989; 9, Miglietta, 1992; 10, Groot 1987; II Bauer et ai., 1988.
Country (code)
Latitude e N)
Location (code) Stuard (St) Martorano (Ma)
Cultivar
Year
Sowing date
Emergence date
44.5
Pandas (W)
1988
Oct. 31 (305)9
Dec. 1(336)*
44.5
Pandas (W)
1988
Oct. 31 (305)9
Nov. 20 (324)*
51.9
Arrninda (W)
1982
Oct. 21 (294)10
Nov. 2 (307)*
52.5
Arrninda (W)
1983
Oct. 21 (294)10
Nov. 7 (312)*
46.8
Colt (S)
1984
Sept. 19 (263)"
Oct. 15 (289)
39.2
Colt (S)
1985
Sept. 20 (263) "
Nov. 5 (309)
THE NETHERLANDS Randwijk (Ra) Lelystad (Le)
USA Mandan ND (Mn) Manhattan KS (Mh)
") Av, Avalon (W) ; No, Norman (W) ; Aq, Aquila (W); Fe, Fenman (S) ; Hi, Highbury (S); Hu, Maris Huntsman (W); We, Wembley (S) ; Ta, Talent (W) ; Dg. 1772/8 (W). b) Cr. Creso (W) ; Ma, Maris Huntsman, Italy (W).
ci
6.-------------------------------------,
c:
ci
6.------------------------------------,
c:
:m
5
o
3
:m
5
o
4 3
E4
E
1ii !:!:!,.2
1ii !:!:!,. 2
-.
w
en
•
::E
cr:
40
.-
45 50 Latitude (deg N)
w
en
::E
55
60
(a)
cr:
0 35
40
60
55
45 50 Latitude (deg N)
(b)
ci 6
ci 6.--------------------------------,
:m
5
:m
5
o
3
o
3
c:
c:
E4
E4 ~2 w
C)::::J
~ 1
cr:
0 35
(c)
ao
40
45 50 Latitude (deg N)
55
60
40
45 50 Latitude (deg N)
'0 B
0 Cl
55
0
60
(d)
Figure 1. Root mean square error (RMSE, a-d) between estimated (Est) and observed (Obs) values of leaf number for four models of leaf appearance (a - model RC; b - model TtIP; c - model PT; d - model 0: see text for further details) at sites with different latitudes (see Table 1). Vol. 4, n° 1 - 1995
20
M. Bindi et aL
Table 2. Mean bias error (MBE) and root mean square error (RMSE) between estimated (Est) and observed (Obs) values of leaf number for f our models of leaf appearance (see text and Table 1 for further details). MBE between Est-Obs Leaf no. RC a)
b)
c)
RMSE between Est-Obs leaf no.
PT
0
RC
TtJP
PT
0
0.58 0.46 0.25 0.64 0.24 0.38 0.58 0.\ 9 0.52 0.03 1.69 0.26 0.45 2.07 \ .03 0.43 0.65 0. \3 0.32
4.06 -0.33 1.34 2.41 1.04 1.33 4.06 3.9 \ 2.80 2.80 1.39 2.43 1.4\ 4.9 \ 1.09 4.20 1.38 2.78 2.07
0.77 0.17 0.03 0. 30 - 0.38 -0.70 0.77 0.37 - 0.36 0.1 1 - 1.84 -0.59 -0.62 1.34 - 1.56 0.42 -0.97 0.01 -0.54
1.05 0.66 1.1 5 0.72 0.44 0.37 1.05 0.67 0.8 1 1.01 2.06 0.34 1.05 2.48 1.02 0.99 1.19 1.22 0.74
0.96 0.58 1.11 0.68 0.44 0.44 0.96 0.66 0.84 1.0 1 2. \0 0.37 0.98 2.39 1.06 0.95 1.22 1.23 0.76
4.30 0.51 2.14 2.59 1.66 1.47 4.30 5.\3 3.51 3.46 2.79 2.67 2.76 5.81 1.5 \ 5.27 2.07 3.72 3.1 2
1.13 0.42 0.98 0.36 0.60 0.72 1.13 0.74 0.82 0.66 2.30 0.64 1.03 1.73 1.59 1.1 7 1.66 1.30 1.1 5
TtJP
Latitude CON) Mh (39.2) Ru (40.2) Fi (43.9) Ma (44.5) St (44.5) Os (44.5) Mn (46.8) Se (50.6) Lo (5 1.4) Ox (5 1.8) Rt (5 1.8) Ra (5 1.9) Ca (52.2) Ro (52.3) Le (52.5) Br (52.3) Hi (54. 1) A u (55.5) Ab (57.2)
0.69 0.56 0.33 0.70 - 0.17 - 0.30 0.69 0.25 - 0.46 0.08 -1.64 - 0.20 -0.74 2.16 - 0.98 0.50 - 0.6 1 - 0.08 -0.28
Sowing Sept. Oct. Nov. Dec. Feb. Mar.
- 0.71 - 0.41 0.06 - 0.06 - 0.64 - 2.00
- 0.26 0. \8 0.26 0.02 - 0.92 - 2.38
3.92 1.53 0.55 0. \0 0.4\ - 0.47
- 0.09 - 0.4 \ - 0.53 -0.70 -1.10 - 2.43
1.\ 6 0.80 0.89 0.52 1.03 2.06
1.1 1 0.82 1.01 0.56 1.24 2.47
4 9. 6 2.\3 1.50 0.76 1.20 1.29
0.89 0.88 1.1 6 0.90 1.45 2.54
Cu\tivar Av No Aq Fe Hi Hu Ss Ta Dg Cr Ma Pa Ar Co
- 0.34 - 0.51 - 0.77 - 0.75 - 0.38 -1. \0 - 0.74 - 0.79 - 1.32 0. 11 0.56 0.07 - 0.59 0.43
- 0.40 - 0.58 - 0.84 -0.82 - 0.45 - 1.1 7 - 0.81 - 0.86 - 1.40 0.04 0.46
2.50 2.21 1.46 1.47 1.7 1 1.1 2 1.40 1.38 0.49 0.61 1.75 1.59 1.76 4.17
- 0.41 -0. 37 -0.63 - 0.60 -0.24 - 0.96 -0.60 -0.64 -1.27 -0.1 3 0. 19 -0.26 -1.08 0.67
1.27 0.90 1.08 1.00 0.94 1.35 1.06 1.06 1.52 0.54 1.45 0.5 1 0.76 0.76
1.29 0.96 1.14 1.07 0.98 1.41 1.12 1.1 2 1.59 0.52 1.40 0.52 0.80 0.70
3.66 3.82 3.01 3.09 3.30 2.81 3.06 2.85 1.84 1.02 2.66 1.90 2.17 4.42
1.33 1.06 1.04 1.04 1.05 1.27 1.11 1.02 1.50 0.49 1.22 0.56 1.2 1 0.97
-
-
om
- 0.64 0.3 1
lowest values occurring for sowings from October to December and higher values for more extreme sowings (Table 4b) . MBE's for the PT and 0 models generally rose as sowing was delayed (Figure 4c,d) . Winter sowings were simulated m ore accurately by the RC and TtIP model (Figure 4a,b). RMSE values (Table 4b) were most consistent for the 0 m odelwith respect t o month of sowing. The pattern for the other
models w as for afall in RMSE fro m sowings made in September through t o February, followed b y a rise in March (Table 4b). The RC, TtIP and 0 models distinguished between spring and winter cultivars i n a similar way (Table 4c), also reflected in the RMSE values (Table 4c). The PT model simulated early the appearance of leaf seven for all cultivars. Eur. J. Agron.
Comparison of leaf appearance models for wheat
ci c
(ij
91
en .c
0
U;
21
6 5 4
ci c
(ij
91
3
en
.c
2
0
1
w
-3
Sept
Oct
Jan Nov Dec Month of Sowing
Feb
c
~
0
1
-3
Mar
(a)
91
3
2
w -1 co :!: -2
-1 :!: -2
co
(ij
4
in !:!:!. 0
!:!:!. 0
ci
6 5
Sept
Oct
Dec Jan Nov Month of Sowing
Feb
Mar
(b)
6 5 4
ci c
(ij
91
3
en .D
2
0
U;
6 5 4 3
2 1
in !:!:!. 0
!:!:!. 0
w co -1 :!: -2
LJJ -1 co :!: -2
-3
Sept
Oct
Jan Nov Dec Month of Sowing
Feb
-3
Mar
(e)
Sept
Oct
Dec Jan Nov Month of Sowing
Feb
Mar
(d)
Figure 2_ Mean bias error (MBE, a-d) between estimated (Est) and observed (Obs) values of leaf number for four models of leaf appearance (a - model RC ; b - model TtIP; c - model PT; d - model 0 : see text for further details) for sowing dates in different months (see Table 1).
Table 3. Average root m ean square error (RMSE± s. d.) bet· ween (a) estimated and observed leaf number and (b) estimated and observed day number of the appearance of leaf number seven with respect to site, cultivars and month of sowing. The models of leaf appearance are described in the text. Model of leaf appearance
Variable
(a) RC TtIP PT 0 0.97 (.124) 0.96 (. 122) 3.11 (.329) 1.04 (. ll5) Site (n 19) Cultivar (n = 14) 1.02 (.083) 1.04 (.087) 2.83 (.236) 1.06 (.072)
=
Month (n '" 6)
1.08 (.217) 1.20 (.272) 1.98 (.626) 1.31 (.647)
(b) Site (n= 19) 12.2 (2.15) 15.6 (2.52) 34.5 (4.25) 13.6 (2.20) Cultivar (n 14) 20.2 (3.1 3) 17.6 (2.13) 22.2 (3.50) 14.4 (1.77)
=
Month (n '" 6)
16.4 (4.68) 16.4 (3.33) 20.7 (6.6) 17.3 (0.55)
Taken over all variables, the average RMSE for the RC, TtiP and 0 models was about 15 days (Table 3b). Whereas RMSE for the PT model varied between about 20 days (month of sowing) to 30 days for sites at different latitudes, but a pair-wise Student's t test failed to detect Significant differences between the models in their RMSE values. Vol. 4, n° 1 - 1995
DISCUSSION The four models of leaf appearance were compared using field data recorded from a wide range of sites and sowing dates and cultivars. The data are independent of those used to develop the models and provide a stringent test of their ability to simulate the behaviour of field-grown crops. It was not possible statistically to distinguish between three of them (RC, TtIP and 0) in terms of their ability to predict either leaf number or the day of emergence of leaf seven ; whereas the predictions with the fourth model (PT) were substantially different from those of the others. The main reason for this discrepacy between the models is that the PT model assumes a particular and fixed site-based relationship between maximum, minimum and mean daily temperature and photoperiod. The RC and TtIP models modify the phyllochron on the basis of either the rate and direction in which daylength is changing at emergence (RC model) or the ratio of thermal time to photoperiod around emergence (TtiP model) and the 0 model deals with differences in sowing date by increasing the phyllochron interval for later leaves.
22
M. Bindi et al.
Table 4. Mean bias error (MBE) and root mean square error (RMSE) between estimated (Est) and observed (Obs) values of leaf seven for four models of leaf appearance (see text and Table 1 for further details). MBE between Est-Obs day no.
a)
b)
c)
Latitude eN) Mh (39.2) Ru (40.2) Fi (43.9) Ma (44.5) St (44.5) Os (44.5) Mn (46.8) Se (50.6) Lo (51.4) Ox (51.8) Rt (51.8) Ra (51.9) Ca (52.2) Ro (52.3) Le (52.5) Br (52.3) Hi (54.1) Au (55.5) Ab (57.2) Sowing Sept. Oct. Nov. Dec. Feb. Mar.
RMSE between Est-Obs day no.
RC
TtIP
PT
o
RC
TtIP
PT
o
0.0 -1.0 -5.0 -4.0 5.0 -2.0 -16.0 -6.6 7.0 2.3 19.0 0.1 17.6 -6.0 -29.3 20.3 0.6 10.3 10.0
-6.0 -2.0 -17.0 -6.0 -3.0 -11.0 -17.0 -16.3 - 3.0 -6.0 10.0 -10.0 12.4 -16.5 -46.0 6.0 -15.3 -5.3 -5.0
- 33.0 -12.0 - 25.0 6.0 -8.0 -17.0 -44.0 - 36.6 -29.6 - 33.0 -26.6 -38.0 -7.7 -46.5 -60.0 -27.3 -38.0 -37.6 -16.0
-4.0 3.2 -3.0 1.0 7.0 -1.0 -16.0 -11.6 1.3 1.6 20.6 5.0 13.1 -8.4 -23.6 33.0 0.1 17.6 18.0
0.0 4.8 5.0 4.0 5.0 2.0 16.0 10.3 9.8 19.4 21.2 0.0 27.5 10.3 32.0 22.2 20.3 12.2 10.0
6.0 5.2 17.0 6.0 3.0 11.0 17.0 18.7 12.4 22.8 14.3 10.0 20.4 23.2 48.7 7.2 30.6 17.0 5.0
33.0 15.2 25.0 6.0 8.0 17.0 44.0 39.3 34.3 41.8 33.2 38.0 15.2 57.1 69.1 45.9 54.5 61.7 16.0
4.0 6.5 3.0 1.0 7.0 1.0 16.0 16.6 7.4 9.6 22.0 5.0 15.9 21.8 28.5 33.6 19.8 22.1 18.0
25.2 7.0 1.1 3.1 5.7 14.8
11.3 -4.7 -2.0 -0.9 9.3 17.9
- 37.9 - 23.6 -2.4 -1.3 1.3
-1.4 9.6 11.4 13.3 13.4 16.7
39.0 14.5 11.5 7.9 9.6 15.9
31.3 15.3 13.3 7.8 11.9 18.4
47.1 32.6 15.7 8.6 8.5 10.4
18.8 16.4 17.9 15.4 16.3 18.4
4.4 2.7 19.2 17.1 11.0 25.7 17.5 17.5 28.5 0.6 -5.0 -0.6 5.0 - 8.0
-6.9 -6.0 14.0 11.8 5.7 20.5 12.2 12.2 20.5 -1.0 -5.5 -10.3 -7.5 -11.5
- 33.6 - 30.2 -7.3 -9.5 -15.6 -0.8 -9.1 -9.1 -4.2 -2.3 -17.5 -16.6 -27.0 -38.5
5.0 -0.8 14.7 12.6 6.5 21.2 13.0 13.0 19.5 4.6 0.1 1.0 11.5 -10.0
21.9 24.0 28.4 26.2 22.7 35.5 26.0 27.0 38.9 4.1 5.3 4.2 7.0 11.3
25.5 26.5 20.6 19.2 16.5 27.4 18.9 19.8 28.5 3.8 7.1 11.8 7.9 12.7
47.1 44.7 12.2 17.0 23.7 9.6 18.6 14.5 9.3 8.2 19.4 18.0 29.1 38.8
20.8 20.9 15.8 15.8 15.6 23.1 17.8 14.6 19.7 7.5 0.1 4.4 13.2 11.6
3.2
Cultivar
Av No Aq Fe Hi Hu Ss Ta Dg Cr Ma Pa Ar Co
It is evident from the analysis presented in this paper that three of the models can be used satisfactorily to simulate leaf appearance under a range of conditions. Predictions were generally accurate for latitudes and sowing dates appropriate to common agricultural practices. Nevertheless, the problem of a correct interpretation of the mechanisms of leaf appearance remains largely unresolved. Two of the
three models (Re and TtIP) require that plants have a "memory" of their photoperiodic environment into which they emerge and for this to set a rate of leaf production for the rest of the plant's growth. The third one (0) assumes that the morphology of the plant determines the decrease in the rate of leaf appearance of subsequent leaves. Experiments in which the rate of change in day length was manipuEur. J. Agron.
Comparison of leaf appearance models for wheat
23
g 70,---------------------------------, ~
"0
o13
60 50
g ~
"0
o13
40
70,---------------------------------, 60 50 40
, 30
"Ii; 30
!:!:!. 20 w
~ 10 0 35
a:
40
--
45
Jtw
20
~ 10
50
Latitude (deg. N)
55
60
(a)
a:
0 35
40
45
55
50
Latitude (deg. N)
60
(b)
o
70.---------------------~--------~
c 60 ~
"0
13 o ~-
w
d 70,----------------------------------, c 60 ~
50 40
"0
13 o
30
~~ -
20
w
~ 10 a: 0 35
40
45
50
60
55
50 40
30 20
D
~ 10 a: 0 35
40
50
60
55
Latitude (deg. N)
Latitude (deg. N)
(c)
45
D
(d)
Figure 3. Root mean square error (RMSE, a-d) between estimated (Est) and observed (Obs) values of the day of appearance of leaf seven on the main shoot for four models of leaf appearance (a - model RC ; b - model TtlP ; c - model PT; d - model 0 : see text for further details) at sites with different latitudes (see Table 1).
g
30,--------------------------------, 20
~
10
13
0
"0
o
-
-10
g
~ 10
13 o
~ -20
w -30
[D
~
-50l-~--~~--~--~~--~~--~--~~~
Sept
Oct
Nov Dec Jan Month of Sowing
Feb
~
13 o
-40 -50~~--~~~~--~----~--~~--~~
Mar
(a)
"0
O+-------------~----~------------------~
-10
~ -20
w -30 [D ~ -40
g
~.-------------------------------,
20
Sept
Oct
Nov Dec Jan Month of Sowing
Feb
Mar
(b)
30.-------------------------------, 20
g
10
~
"0
13
0
o
-10
30.-------------------------------, 20 10
0
-10
"lii -20
~ -20 w -30
!:!:!. w -30 [D ~ -40
~ -40
-50~~~~~~~--~--~--~~--~~
-50~~--~~~~~~--~--~~--~~
Sept
(c)
Oct
Nov Dec Jan Month of Sowing
Feb
Sept
Mar
Oct
Nov Dec Jan Month of Sowing
Feb
Mar
(d)
Figure 4. Mean bias error (MBE, a-d) between estimated (Est) and observed (Obs) values of the day number of appearance of leaf seven on the main shoot for four models of leaf appearance (a - model RC; b - model TtIP; c - model PT; d - model 0: see text for further details) for sowing dates in different months (see Table 1). Vol. 4, n° 1 - 1995
24
lated artificially in the laboratory have not solved this problem. Although, in such cases, changes in dcJJldt were never observed to affect the rate of leaf appearance (van Dobben, 1960; J. T. Ritchie, pers. comm.) it might be argued that changes in light quality and intensity affected leaf extension. Although the models led to comparable predictions of leaf number, any difference becomes important for a further description of the effect of the environment on leaf growth and morphology in wheat. In fact, provided there is a strict coordination between leaf appearance and cell division rate (Horie et al., 1979) the two above hypotheses (RC, Tt/P versus 0) would lead to different predictions of the final cell number of successive leaves and, with this, of final leaf size. Models RC and Tt/P assume that, for a constant temperature, the time elapsing between leaf initiation and the appearance of the lamina tip is a constant for every leaf, while model 0 assumes that this time increases linearly with leaf number. Since the division of epidermal cells occurs largely during this time and the relative rate of cell division declines in successive main stem leaves (Castellani and Miglietta, 1993), model 0 explains how the final number of epidermal cells along the leaf lamina and final leaf length increase with leaf number. New ideas are emerging to describe the mechanism of leaf appearance. One of these considers that soil rather than air temperature drives apical development rates in the first stages of vegetative growth before stem extension. Since the difference between soil and air temperature varies seasonally, this could account for differences in the rate of leaf appearance between crops sown on different dates (Brooking and Ritchie, 1993). Since differences between models are expected to be largest when dcJJldt is constant throughout the year, we suggest that a series of sowing date experiments at the equator would provide a critical test of the rate of change of day length and ontogenetic hypotheses. Provided that soillair temperature differences are near constant throughout the year in this environment, such an experiment would be and excellent test of the recent hypothesis of mechanisms governing leaf appearance mentioned above.
ACKNOWLEDGEMENTS We thank Dr. Michael Kirby for useful discussions during the early part of this work. This research was supported by the National Research Council of Italy, Special Project RAISA, sub-project 2, Paper No. 1917 and the Commission of the European Communities Environment Programme CROPCHANGE (Contract Number EV5V-CT92-0169).
M. Bindi et al.
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