Published in Agron J 100:490-501 (2008)
DOI: 10.2134/agronj2007.0156
© 2008 American Society of Agronomy
677 S. Segoe Rd., Madison, WI 53711 USA
MODELING
Simulating Leaf Appearance in Rice
Nereu Augusto Strecka,*,
Leosane Cristina Boscob and
Isabel Lagob
a Dep. de Fitotecnia, Centro de Ciências Rurais, Univ. Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil
b Programa de Pós-graduação em Agronomia, Univ. Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil
* Corresponding author (nstreck2{at}yahoo.com.br).
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ABSTRACT
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Most rice (Oryza sativa L.) simulation models assume that only temperature affects leaf appearance rate (LAR). This assumption ignores results from controlled environment studies that show that LAR in rice is not constant with time (calendar days) under constant temperature. The Streck model, which takes into account age effects on LAR, improved the prediction of leaf appearance in winter wheat (Triticum aestivum L.) cultivars compared with the Wang and Engel (WE) model and the phyllochron model but has not been evaluated in rice. The objective of this study was to adapt and evaluate the Streck model to simulate main stem LAR and leaf number in rice. A 4-yr experiment with several sowing dates from 2003–2004 to 2006–2007 was performed at Santa Maria, RS, Brazil. Seven rice cultivars were used: IRGA 421, IRGA 420, IRGA 417, IRGA 416, BRS 7 (TAIM), BR-IRGA 409, and EPAGRI 109. Plants were grown in 12-L pots during the 4 yr, and in a paddy rice field during the 2006–2007 growing season. Coefficients necessary to run the Streck model, the WE model, and the phyllochron model were estimated with data from five sowing dates of the 2003–2004 growing season and the models were evaluated with independent data from the other three growing seasons. Predictions of the main stem leaf number, represented by the Haun Stage (HS), were better with the Streck model. The RMSE was 0.7, 1.0, and 1.8 leaves, for the Streck model, the WE model, and the phyllochron model, respectively.
Abbreviations: NL, number of leaves • LAR, leaf appearance rate • WE, Wang and Engel (model) • HS, Haun Stage • TT, thermal time • ATT, accumulated thermal time
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NOTES
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All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Received for publication May 8, 2007.
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INTRODUCTION
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THE CALCULATION OF LAR is an important part of many crop simulation models (Hodges, 1991), including those computing development and growth of rice (Gao et al., 1992; Lee et al., 2001). The integration of LAR over time gives the number of accumulated or emerged leaves (NL) on a stem. Vegetative development of plants, especially in small grains, is defined by main stem NL (Haun, 1973). The main stem NL in rice is related to the timing of several plant development stages such as tillering (Tivet et al., 2001; Jaffuel and Dauzat, 2005; Watanabe et al., 2005), panicle initiation (Ellis et al., 1993; Lee et al., 2001; Watanabe et al., 2005), booting and anthesis (Counce et al., 2000; Watanabe et al., 2005). Leaf area that intercepts and absorbs photosynthetically active radiation for canopy photosynthesis, which impacts dry matter production and crop yield, is also related to the main stem NL (Amir and Sinclair, 1991; McMaster et al., 1991; Tivet et al., 2001). In small grains, NL if often represented by the HS, which is the number of fully expanded leaves plus a ratio of the length of the expanding leaf to the penultimate leaf (Haun, 1973).
Temperature is a major factor that drives leaf appearance in rice (Gao et al., 1992; Ellis et al., 1993; Sié et al., 1998). One approach to predict the appearance of individual leaves is to use the phyllochron concept, defined as the time interval between the appearance of successive leaf tips (Klepper et al., 1982; Kirby, 1995; Wilhelm and McMaster, 1995). The time needed for the appearance of one leaf can be expressed in thermal time (TT), with units of °C day. In this case, the phyllochron has units of °C day leaf–1. However, the TT approach may be subject to criticism because there are different ways to calculate TT, which can cause different results from the same data (McMaster and Wilhelm, 1997), and because of the assumption of a linear response of development to temperature, which is not biologically sound (Shaykewich, 1995; Xue et al., 2004).
One way to overcome some of the disadvantages of the TT approach is to use nonlinear temperature response functions and multiplicative models. An example of the latter is the WE model (Wang and Engel, 1998). Xue et al. (2004) demonstrated that the predictions of leaf appearance in several winter wheat cultivars were improved with the WE model compared to the phyllochron concept.
Although temperature is the major factor that drives LAR in rice, results from growth chamber experiments showed that LAR is not constant with time when rice plants are grown at constant temperature and light (Yin and Kropff, 1996). These results suggest age effects on LAR in rice. Streck et al. (2003a) modified the WE model for simulating LAR in wheat, a species similar to rice in morphology and growth habit, by incorporating age effects through a chronology response function that takes into account the effect of seed reserves for the first two leaves and a decrease in LAR with increase in leaf number. Hereafter this model will be referenced as the Streck model.
The chronology response function in the Streck model has two stages. The first stage is when HS < 2, and the assumption during this stage is that seed reserves represent a plentiful source of carbohydrates and nutrients for growth and therefore the first two leaves have the highest LAR. This assumption was based on results from wheat, but in rice the main source of energy and nutrients up to the time the first two leaves are fully expanded also comes from seed reserves (Stansel, 1975; Hoshikawa, 1993). The second stage of the chronology response function in the Streck model is when HS 
2, and the assumption during this stage is a decrease in LAR with time following a power law due to the fact that higher leaves take more time to appear because the distance that each leaf tip has to traverse from the apical meristem to the whorl increases for each subsequent leaf. The Streck model improved the prediction of leaf appearance in several winter wheat genotypes compared with the WE model. Similarities in plant morphology and growth habit between rice and wheat and the fact that the Streck model has not been evaluated in rice constituted the rationale for this research effort. In this study we hypothesized that the chronology response function is appropriated for LAR in rice and that the Streck model is better than other approaches to simulate the main stem LN in rice. The objective of this study was to adapt and evaluate the Streck model (Streck et al., 2003a) for simulating main stem LAR and LN in rice.
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MATERIALS AND METHODS
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Streck Model
The Streck model (Streck et al., 2003a), adapted for simulating leaf appearance in rice, combines nonlinear temperature and age effects on LAR in a multiplicative fashion, and has the general form
 | [1] |
where LAR is measured in leaves d–1, LARmax12 is the maximum daily leaf appearance rate (leaves d–1) of the first two leaves under optimum temperature, f(T) and f(C) are dimensionless temperature and chronology response functions (varying from 0–1) for LAR, respectively. The f(T) is a beta function:
 | [2] |
 | [3] |
where Tmin, Topt, and Tmax are the cardinal (minimum, optimum, and maximum) temperatures for LAR and T is the mean daily air temperature calculated from the average of minimum and maximum air temperatures. The cardinal temperatures for LAR in rice are 11°C (Ellis et al., 1993; Infeld et al., 1998), 26°C (Ellis et al., 1993) and 40°C (Gao et al., 1992). The curve generated by Eq. [2, 3] with these cardinal temperatures for LAR is shown in Fig. 1a
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Fig. 1. (a) The temperature response function (Eq. [2, 3]) in the Wang and Engel (WE) and Streck leaf appearance models with cardinal temperatures for rice of 11, 26, and 40°C; (b) the chronology response function (Eq. [4, 5]) used in the Streck leaf appearance model; (c) method of calculating daily values of thermal time (TT; Eq. [7, 8]) for leaf appearance in rice with cardinal temperatures of 11, 26, and 40°C.
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The f(C) is given as
 | [4] |
 | [5] |
where b is a sensitivity coefficient and has a value of –0.3 (Streck et al., 2003a). The curve generated by Eq. [4, 5] is shown in Fig. 1b.
The main stem number of emerged leaves, represented by the HS, is calculated by accumulating daily LAR values (i.e., at a daily time step) starting at emergence, that is, HS = 
LAR.
Wang and Engel Model
The WE model (Wang and Engel, 1998), which uses a nonlinear temperature response function combined in a multiplicative fashion, was also used in the simulation of LAR and HS. The WE model for rice has the general form:
 | [6] |
where LARmax is the maximum daily leaf appearance rate (leaves d–1) under optimum temperature (26°C). Cardinal temperatures for rice in the f(T) of the WE model are the same as in Eq. [2, 3]. The HS is also calculated by accumulating daily LAR values (i.e., at a 1 d time step) starting at emergence, that is, HS = LAR.
Phyllochron Model
A third model evaluated in this study was the phyllochron model (Klepper et al., 1982; Kirby, 1995; Wilhelm and McMaster, 1995) using the TT approach. This model was also evaluated because it is a simple and widely used model to simulate leaf appearance is small grains (McMaster et al., 1991; Amir and Sinclair, 1991; McMaster, 2005). Daily values of TT (°C day) were calculated as Matthews and Hunt (1994) and Streck et al. (2007):
 | [7] |
 | [8] |
where Tmin, Topt, Tmax, and T have been defined in Eq. [2, 3]. Values of Tmin, Topt, and Tmax have also been previously defined. The schematic representation of this TT approach is in Fig. 1c. The accumulated thermal time (ATT) from emergence was calculated by accumulating TT, that is, ATT = TT. The main stem HS is calculated by HS = ATT/phyllochron.
Field Experiments
Data used in this study are from a 4-yr experiment conducted in the field research area, Plant Science Department, Federal University of Santa Maria (UFSM), Santa Maria, Rio Grande do Sul (RS) State, Brazil (29°43' S, 53°43' W, altitude = 95 m) during the 2003–2004, 2004–2005, 2005–2006, and 2006–2007 growing seasons to evaluate the influence of varying planting time on leaf appearance of several rice cultivars. There were five sowing dates in the 2003–2004 and 2004–2005 seasons, three sowing dates in 2005–2006, and two sowing dates in 2006–2007 (Table 1
). The wide range of sowing dates each year, except 2006–2007, correspond with sowing dates before, during, and after the recommended sowing time for this location, which is from 1 October to 10 December, and was chosen to have plants growing and developing under different temperatures, which is important for model parameterization and testing. Seven rice cultivars widely grown commercially in Southern Brazil were used: IRGA 421, IRGA 420, IRGA 417, IRGA 416, BRS 7 (TAIM), BR-IRGA 409, and EPAGRI 109. These rice cultivars were chosen because they have a broad range of rate of development, varying from very early (IRGA 421) to late (EPAGRI 109) maturation (Table 2
). In the 2006–2007 growing season, only the cultivars IRGA 421 and EPAGRI 109 were used.
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Table 2. Characteristics of the seven rice cultivars used in this study at Santa Maria, RS, Brazil, and estimates of LARmax12 (maximum daily leaf appearance rate of the first two leaves under optimum temperature), LARmax [maximum daily leaf appearance rate under optimum temperature (26°C)], and the phyllochron from data collected during the 2003–2004 growing season.
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The rice plants were sown in 12-L pots (30-cm diam. and 26-cm height) buried in the soil, leaving a 5-cm rim of the pot above soil surface. We assumed that growing rice plants in pots is representative of growing rice plants in a paddy rice field because previous studies with wheat, a species similar to rice, showed that LAR was not affected by restricted rooting volume and pot size (Peterson et al., 1984). Pots were buried in the soil to maintain soil temperature similar to the soil temperature of the surrounding area. Pot spacing was 1.5 m x 0.8 m. Pots were spaced to reduce shading, which would be a major factor affecting plant growth by suppressing tillering (Peterson et al., 1984). Soil type at the experimental site was a Rhodic Paleudalf (USDA Taxonomy) and pots were filled with this soil. Soil tests in the 0–30 cm layer used to fill pots indicated 2.2% organic matter, 3.2 mg L–1 P, and 46.0 mg L–1 K. A completely randomized experimental design was used with four replications (replication = experimental unit = pot), totaling 28 pots per sowing date (7 cultivars x 4 replications within each sowing date). Thirty seeds were sown in each pot and at least 20 plants emerged in each pot. During the 2006–2007 growing season, we also grew rice plants of the two cultivars with the largest difference in developmental cycle (IRGA 421 and EPAGRI 109) in a 10-ha paddy rice field located about 600 m from the pots, and with similar soil used to fill the pots, in two sowing dates (13 Dec. 2006 and 16 Jan. 2007). In the paddy field, there were four plots with four rows of 1 m and 17 cm between rows in a complete randomized block design.
Emergence was measured in each pot and field plot by counting the number of emerged plants on a daily basis. Date of emergence was considered when 50% of the plants were emerged from the soil surface. Fertilization followed local recommendation for field flood-irrigated rice. In the pots, a 20 g pot–1 of a 7–11–9 N–P–K fertilizer was used at sowing. Additional nitrogen was added as a side-dress application at beginning of tillering (V4 stage; Counce et al., 2000) and at panicle differentiation (R1 stage; Counce et al., 2000) with urea at a rate of 8.5 g of urea pot–1. The same fertilizer rates at sowing and side-dressings were used in the field plots, corresponding to 300 kg ha–1 of 7–11–9 N–P–K fertilizer and 222 kg ha–1 of urea. At the V3 stage (three fully expanded leaves) of the Counce et al. (2000) scale, plants were thinned to 15 plants per pot, resulting in a plant density of about 200 plant m–2, which is a plant density commonly found in commercial rice fields in southern Brazil. The same plant density was used in the field plots. Irrigation in both pots and field plots was performed to keep a continuous 5- to 7-cm water layer above the soil surface (flooded soil) from V3 to R9 (physiological maturity) Counce stages.
Five plants per pot and five plants in the central row of the field plots were tagged with colored wires 1 wk after emergence. In the pots, plants located in the central part of the pot were tagged. In doing so, a red–far red balance similar to the one found in a rice field was attempted to achieve, as such balance is affected by the proximity of nearest neighbor and it is known to affect development in small grains (Wilhelm and McMaster, 1995). Tagged plants were used to measure the NL on the main stem. A leaf was counted when the tip had visibly emerged from the whorl, independent of ligule formation. The NL, the blade length of the expanding leaf (Ln), and the penultimate leaf (Ln–1) on the main stem were measured once a week throughout the experiment. The Haun Stage (leaves) was calculated as follows (Haun, 1973; Wilhelm and McMaster, 1995):
 | [9] |
Daily minimum and maximum air temperatures were measured by a standard meteorological station located at about 200 m from the pots and about 500 m from the field plots. Mean daily air temperature (T) used in the temperature response functions (Eq. [2, 3, 7, 8]) was calculated as the average of daily minimum and maximum temperatures.
Estimates of Coefficients of the Models
Coefficients LARmax12 (Eq. [1]), LARmax (Eq. [6]), and the phyllochron are genotype dependent. These coefficients were estimated for each cultivar using HS data collected from the five sowing dates of the 2003–2004 growing season. Coefficients LARmax12 and LARmax were estimated by changing (increasing and decreasing) an initial value (0.3 leaves d–1) by a 1% step until obtaining the best fit between observed and estimated HS values by minimizing the RMSE, calculated as (Janssen and Heuberger, 1995):
 | [10] |
where p = predicted HS values, o = observed HS values, and N = number of observations. The unit of RMSE is the same as p and o, that is, leaves.
The phyllochron was estimated by the inverse of the slope of the linear regression of HS against ATT (Klepper et al., 1982; Kirby, 1995; Xue et al., 2004). The estimates of LARmax12, LARmax, and phyllochron for each cultivar were the average of the five sowing dates (Table 2). We averaged the estimates over the five sowing dates because an ANOVA analysis revealed no significant interaction between sowing date and genotypes for the variable phyllochron (inverse of leaf appearance) during the 2003–2004 growing season and because of the low values of the standard deviations of the mean values (Table 2).
Evaluation of Models
The values of main stem HS predicted by the Streck model, the WE model, and the phyllochron model were compared with the observed HS values for each cultivar during the sowing dates of the 2004–2005, 2005–2006, and 2006–2007 growing seasons, which were all independent data sets. Models performance was evaluated with the RMSE statistic (Eq. [10]). Better predictions result in smaller RMSE. Systematic and unsystematic errors of models predictions was calculated for each model by the MSE, that is, RMSE2, and decomposing the MSE into systematic and unsystematic (random) components (systematic + unsystematic = 100%) according to Willmott (1981). A good model has low systematic and high unsystematic error.
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RESULTS
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There was variation in meteorological conditions during the period of leaf appearance of the four growing seasons (Table 3
). The 2004–2005 growing season was the warmest, with the highest average monthly mean (26.6°C) and maximum (33.4°C) air temperatures, which occurred in January 2005. The lowest average monthly minimum air temperature was in May 2006 (9.4°C). On the other hand, sunshine duration was greater in the 2003–2004 and in the 2005–2006 growing seasons, with the highest average monthly values in February 2004 (9.5 h d–1) and December 2005 (9.4 h d–1). The distinct meteorological conditions in the different sowing dates during each year provide a rich data set to calibrate and evaluate the different LAR models.
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Table 3. Monthly average of minimum, mean, and maximum air temperature, and sunshine duration during the period of leaf appearance in the four growing seasons at Santa Maria, RS, Brazil.
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An analysis of the HS data of cultivars IRGA 421 and EPAGRI 109 grown in the 2006–2007 growing season showed HS difference between plants grown in the pots and plants grown in the paddy rice field less than 0.6 leaves. These small differences in HS indicate that results from the potted plants can be extrapolated to a rice field. In addition, they are consistent with the results presented in Peterson et al. (1984) with wheat that LAR is not affected by restricted rooting volume and pot size.
Predicted vs. observed values for main stem HS for the independent data (pooling data for different cultivars, sowing dates and years) are presented in Fig. 2
(plants grown in pots) and Fig. 3
(plants grown in the paddy rice field). We pooled cultivar, sowing date, and year data, and separated results from pots (Fig. 2) and from the paddy rice field (Fig. 3) in our first data analysis to present an overall RMSE, and for better visualizing data, making results interpretation easier. In panels a, b, and c of Fig. 2 and 3, models were run from emergence, whereas panels d, e, and f show the results when models were run starting at the day of first HS measurement. The predicted HS at this day was set equal to the observed HS. We also started the simulation at the day of first HS measurement because on closer inspection of Fig. 2c and 3c, it is clear that the phyllochron approach misses the first and two leaves. In doing so, we removed this initial error and all three models started running from the same initial condition, which from a modeling perspective can be interpreted as a fairer comparison amongst them.
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Fig. 2. Predicted vs. observed values of main stem Haun Stage in rice using the three leaf appearance rate (LAR) models [Streck; Wang and Engel (WE); phyllochron]. Data are pooled for seven rice cultivars [IRGA 421, IRGA 420, IRGA 416, IRGA 417, BRS 7 (TAIM), BR-IRGA 409, and EPAGRI 109] sown on 10 dates in pots at Santa Maria, RS, Brazil, during three growing seasons (2004–2005, 2005–2006, and 2006–2007). Panels a, b, and c are data when the simulation started at emergence. Panels d, e, and f are data when the simulation started at the day of the first observed Haun Stage. The solid line is the 1:1 line.
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Fig. 3. Predicted vs. observed values of main stem Haun Stage in rice using the three leaf appearance rate (LAR) models [Streck; Wang and Engel (WE); phyllochron]. Data are pooled for two rice cultivars (IRGA 421 and EPAGRI 109) sown on two dates in a paddy rice field at Santa Maria, RS, Brazil, during the 2006–2007 growing season. Panels a, b, and c are data when the simulation started at emergence. Panels d, e, and f are data when the simulation started at the day of first observed Haun Stage. The solid line is the 1:1 line.
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From Fig. 2 and 3, the accuracy of the HS predictions decreased in the sequence Streck model > WE model > phyllochron model when the simulation started at emergence and Streck model > phyllochron model > WE model when the simulation started at the day of first observed HS. For the pot experiment, the overall RMSE was 0.7 leaves, 1.0 leaves, and 1.8 leaves when the simulation started at emergence and 0.6 leaves, 1.1 leaves, and 0.8 leaves when the simulation started at the day of first observed HS with the Streck model, WE model, and phyllochron model, respectively. For the paddy rice field experiment, RMSE was 0.8 leaves, 1.3 leaves, and 1.4 leaves when the simulation started at emergency, and 0.8 leaves, 1.4 leaves, and 1.2 leaves when the simulation started at the day of first HS measurement.
Values of RMSE with the three LAR models when simulation started at emergence and at the day of first observed HS for the different sowing dates within each year and for each cultivar are presented in Tables 4 to 9
. Analyzing RMSE averages across sowing dates and across cultivars within each year, predictions of HS followed the same trend as the overall RMSE when all data were polled, both in pots and in the paddy rice field (i.e., when simulation started at emergence, the Streck model was the best model followed by the WE model and the phyllochron model, and when simulation started at the day of first observed HS, the Streck model was also the best model, but followed by the phyllochron model and the WE model).
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Table 4. Values of RMSE (leaves) for the prediction of the Haun Stage of seven rice cultivars with the Streck model, Wang and Engel (WE) model, and phyllochron model at Santa Maria, RS, Brazil, when the simulation started at emergence during the 2004–2005 growing season.
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Table 5. Values of RMSE (leaves) for the prediction of the Haun Stage of seven rice cultivars with the Streck model, Wang and Engel (WE) model, and phyllochron model at Santa Maria, RS, Brazil, when the simulation started at the day of first observed Haun Stage during the 2004–2005 growing season.
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Table 6. Values of RMSE (leaves) for the prediction of the Haun Stage of seven rice cultivars with the Streck model, Wang and Engel (WE) model, and phyllochron model at Santa Maria, RS, Brazil, when the simulation started at emergence during the 2005–2006 growing season.
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Table 7. Values of RMSE (leaves) for the prediction of the Haun Stage of seven rice cultivars with the Streck model, Wang and Engel (WE) model, and phyllochron model at Santa Maria, RS, Brazil, when the simulation started at the day of first observed Haun Stage during the 2005–2006 growing season.
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Table 8. Values of RMSE (leaves) for the prediction of the Haun Stage of seven rice cultivars with the Streck model, Wang and Engel (WE) model, and phyllochron model at Santa Maria, RS, Brazil, when the simulation started at emergence during the 2006–2007 growing season.
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Table 9. Values of RMSE (leaves) for the prediction of the Haun Stage of seven rice cultivars with the Streck model, Wang and Engel (WE) model, and phyllochron model at Santa Maria, RS, Brazil, when the simulation started at the day of first observed Haun Stage during the 2006–2007 growing season.
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Comparing years, average RMSE over years varied 0.1 leaves, 0.2 leaves, and 0.5 leaves among years when the simulation started at emergence, and 0.3 leaves, 0.4 leaves, and 0.2 leaves among years when the simulation started at the day of first observed HS with the Streck model, WE model, and phyllochron model, respectively. These results indicate high stability of the models across years, especially the Streck model run from emergence.
Among sowing dates, RMSE averages over cultivars indicate, in general, better predictions in the earliest sowing date and worst predictions in the latest sowing dates with the Streck model and the WE model, except for the WE model prediction when the simulation started at emergence in the 2006–2007 season (Table 8). For the phyllochron model, predictions were better in the latest sowing date and worst in the earliest sowing date when simulations started at emergence (Tables 4, 6, 8). When simulation started at the first observed HS, the phyllochron model performed better in the intermediate sowing dates of the 2004–2005 growing season (Table 5), in the latest sowing date of the 2005–2006 growing season (Table 7), and in the earliest sowing date of the 2006–2007 growing season (Table 9). These results indicate greater stability of the Streck model and lower stability of the phyllochron model among sowing dates.
Among cultivars, no clear trend could be detected from the RMSE data presented in Tables 4 to 9
in terms of HS prediction (i.e., models performed better for some cultivars in some sowing dates and years and for the same cultivars models performed not as good in other sowing dates and years). In the 2004–2005 and 2005–2006 growing seasons, which included all seven cultivars, and considering simulations starting both at emergence and at the day of first observed HS, the difference between the cultivars with the lowest RMSE and the cultivars with the highest RMSE (average over sowing dates, Tables 4–7) varied from 0.2 to 0.5 leaves with the Streck model, 0.1 to 0.7 leaves with the WE model, and the 0.2 to 0.8 leaves with the phyllochron model. These results again favor the Streck model, which had greater stability of the predictions across cultivars.
When the simulation started at emergence, the WE model had systematic errors, with underpredictions at low HS (HS < 4) and overpredictions at high HS (HS > 10) (Fig. 2b, 3b). The phyllochron model had even greater systematic errors, and most of the HS values were underpredicted (Fig. 2c, 3c). Systematic errors were smallest with the Streck model, with data scattered around the 1:1 line (Fig. 2a, 3a), with somewhat wider scatter above the 1:1 line than below. As expected, scattering decreased when the simulation started at the day of first observed HS for all models, but systematic errors still appear more evident with WE and the phyllochron models (Fig. 2d, 2e, 2f, 3d, 3e, 3f). Predictive accuracy of all models declined as the crop aged. The systematic and unsystematic (random) components of the MSE with the three LAR models for each cultivar (average of sowing dates) within each year are presented in Table 10
(simulation starting at emergence) and in Table 11
(simulation starting at the day of first observed HS). We pooled the data of different sowing dates presented in Tables 10 and 11 to reduce the number of tables and because of similar results among sowing dates. When the simulation started at emergence, the lowest systematic and the highest unsystematic values were obtained with the Streck model, whereas the highest systematic and the lowest unsystematic values were obtained with the phyllochron model both across cultivars and years. Overall, the systematic component varied from 1.0 to 76.3%, from 18.3 to 74.8%, and from 28.8 to 96.3% for the Streck, WE, and phyllochron models, respectively (Table 10). When the simulation started at the day of the first observed HS, the lowest and the highest values of the systematic and unsystematic components of the MSE with the three LAR models varied among cultivars and years, whereas the systematic component decreased drastically with the phyllochron model. Overall, the systematic component varied from 0.1 to 84.3%, from 3.4 to 75.4%, and from 4.2 to 65.8% for the Streck, WE, and phyllochron models, respectively (Table 11).
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Table 10. Values of systematic (SYS) and unsystematic (UNSYS) components of MSE for the prediction of the Haun Stage of seven rice cultivars with the Streck model, Wang and Engel (WE) model, and phyllochron model at Santa Maria, RS, Brazil, when the simulation started at emergence during the 2004–2007 growing season.
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Table 11. Values of systematic (SYS) and unsystematic (UNSYS) components of MSE for the prediction of the Haun Stage of seven rice cultivars with the Streck model, WE model, and phyllochron model at Santa Maria RS, Brazil, when the simulation started at the day of first observed Haun Stage during the 2004–2007 growing season.
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The performance of the Streck model in selected sowing dates is presented in Fig. 4. Figure 4a
presents the prediction of HS for the cultivar BR-IRGA 409 grown in pots in the five sowing dates of the 2004–2005 growing season. Plants on these sowing dates grew under extreme temperature conditions for rice. Plants on the first sowing date (2 Sept. 2004, DOY = 245) were subjected to minimum daily air temperature as low as 4.6°C in September 2004, whereas plants on the fourth sowing date (3 Dec. 2004, DOY = 337) where exposed to maximum daily air temperature as high as 38.2°C in January 2005. The third sowing date (4 Nov. 2004, DOY = 308) represents a normal sowing date for local conditions. On the fifth sowing date (2 Mar. 2005, DOY = 61) plants died by middle June 2005 due to low temperatures and cloudy days before the flag leaf emerged from the whorl. The Streck model captured the HS variation quite well in the five sowing dates, except an overprediction of the last two observed data of the fifth sowing date collected in end of May and early June, when conditions were not favorable for rice (low temperature and cloudy days). Figure 4b and 4c present predictions with the Streck model for cultivars IRGA 421 and EPAGRI 109, respectively, grown in the paddy rice field in the two sowing dates. Here again the Streck model captured the HS variation in the two sowing dates for both cultivars, excepted an overprediction of the four last points for cultivar EPAGRI 109 on the latest sowing date (16 Jan. 2007, DOY = 16) (Fig. 4c), when, again, low temperature and cloudy days were frequent.
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Fig. 4. Observed main stem Haun Stage and values predicted by the Streck model for (a) ‘BR-IRGA 409’ rice grown in pots in five sowing dates [2 Sept. 2004 (DOY = 245), 7 Oct. 2004 (DOY = 280), 4 Nov. 2004 (DOY = 308), 3 Dec. 2004 (DOY = 337) and 2 Mar. 2005 (DOY = 61)] and for (b) ‘IRGA 421’ and (c) ‘EPAGRI 109’ rice grown in the paddy rice field in two sowing dates [13 Dec. 2006 (DOY = 347), and 16 Jan. 2007 (DOY = 16)]. Santa Maria, RS, Brazil, 2004–2007.
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DISCUSSION
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The low overall RMSE of 0.7 leaves obtained with the Streck model for plants grown in pots and when the simulation started at emergence (Fig. 2a, 2b, 2c) represented a reduction of 44 and 61% of the RMSE obtained with the WE and with the phyllochron models, respectively. Similarly, for the plants grown in the paddy rice, the RMSE of 0.8 leaves with the Streck model is a reduction of 38 and 43% of the RMSE obtained with the WE and phyllochron models, respectively (Fig. 3a, 3b, 3c). The RMSE for the WE and the phyllocron models was often greater than one leaf for all cultivars (Tables 4, 6, 8). If the prediction of leaf number is off by one leaf, this difference can have a considerable impact on the predictions of other processes based on the number of emerged leaves. For example, tiller appearance and number can be predicted based on NL (Nemoto et al., 1995; Tivet et al., 2001; Jaffuel and Dauzat, 2005; Watanabe et al., 2005). We observed in the 2005–2006 growing season that the first tiller of rice cultivars used in the study appeared when there were about five leaves on the main stem, and the appearance of further tillers was synchronized with the main stem NL. Therefore, when there are less than six leaves on the main stem, the number of tillers is small (1 or 2) and errors in the prediction of HS have a small impact on predicted number of tillers. However, at higher main stem leaf numbers (HS > 6), an error of one leaf can cause considerable errors in the prediction of tiller appearance, because a rice plant with 7, 8, and 9 fully expanded main stem leaves has 3, 4, and 5 first-order tillers, respectively (Nemoto et al., 1995) and when Leaf 10 emerges on the main stem, second-order tillers are visible (Jaffuel and Dauzat, 2005). Errors in the predictions of tiller appearance will have further impacts on the predictions of appearance of leaves and growth of leaf area on culms, and, consequently, on the whole plant leaf area. Panicle initiation, booting, and heading are also related to main stem leaf number (Yin et al., 1997; Counce et al., 2000; Lee et al., 2001). In the 2005–2006 and 2006–2007 growing seasons, we observed that panicle initiation occurred when HS was from 7 to 11, depending on the cultivar, and booting and heading occurred when the flag leaf was just visible at the whorl and when the flag leaf was almost expanded, respectively. Therefore, an error of one leaf may lead to errors of several days in prediction of the date of these developmental stages.
The phyllochron model gave the poorest predictions of HS when the simulation started at the day of first observed HS, with predictions often being off by at least 1.5 leaves (Tables 4, 6, 8), and with high values of systematic component of MSE (Table 10). This model uses the TT approach as a measure of time. The TT approach has the assumption of a linear relationship between temperature and development, which is not completely realistic from a biological viewpoint. Biological processes, including plant development, respond to temperature in a nonlinear fashion (Yin et al., 1995; Granier and Tardieu, 1998; Bonhomme, 2000), with only a small portion of the response being linear (Wang and Engel, 1998; Streck et al., 2003b; Streck et al., 2007). The predictions of HS with the WE model were better than with the phyllochron model (Table 4, 6, 8), confirming previous results that LAR response to temperature in rice is nonlinear (Gao et al., 1992; Ellis et al., 1993; Sie et al., 1998). Similar results with the WE model gave better predictions of main stem HS than the phyllochron model, as reported by Xue et al. (2004) in winter wheat.
It is evident that the phyllochron model misses the first and second leaves, but the scattering of points around the 1:1 is less than for the other two models at higher HS (Fig. 2c, 3c). Considering the simplicity and wide use of the phyllochron model, we tested the removal of this initial error by setting the first estimated HS value equal to the observed HS value. If the predictions were improved by removing the initial error, then a reason for the large error in predicting the time of appearance of the first and second leaves with the phyllochron model could be found. The results of these simulations showed a considerable reduction in the RMSE with the phyllochron model and little or no change in the RMSE with the Streck and the WE models, resulting in a lower RMSE with the phyllochron model compared with the WE model, but still greater RMSE than the Streck model, both in the pot experiment (Fig. 2d, 2e, 2f) and the paddy rice experiment (Fig. 3d, 3e, 3f).
The predictive accuracy for HS declined for all models as plants aged (Fig. 2, 3), with the Streck model showing the smallest decline in the predictions. Small errors from the beginning of the simulations added up throughout the period of leaf appearance contributed to the decline in the predictions late in the growing season. However, decline in the predictions with the Streck model were found due to overpredictions at the end of the latest sowing date with cultivars BR-IRGA 409 and EPAGRI 109, mainly the latter (Fig. 2a, 2d, 3a, 3d). Two aspects are important here. First, in all 3 yr used as independent data sets to evaluate the models, the last sowing dates (2 Mar. 2005, 2 Feb. 2006, and 16 Jan. 2007) were late and out of the recommended sowing date for this location. Second, these two cultivars are mid late and late cultivars, respectively, and had the lowest LARmax12 and LARmax (Table 2). The combination of late sowing date and low LAR resulted in plants of these two cultivars growing leaves in May and early June, when temperatures and solar radiation were low as a result of the Fall in the Southern Hemisphere, and did not flower because of low temperatures in the weeks after (winter). For this location, paddy rice is harvested in late February and March, so the overpredictions of HS observed for these two cultivars in the latest sowing dates (Fig. 2a, 2d, 3a, 3d) do not represent a significant problem from a practical field perspective.
Most rice simulation models assume that only temperature affects LAR (Alocilja and Ritchie, 1991; Gao et al., 1992; Horie, 1994; Sié et al., 1998). If this assumption is correct, then the NL (at HS) should increase linearly as a function of time (calendar days) under constant temperature or as a function of TT in the field (Streck et al., 2003a). Results from growth chamber experiments with rice at constant temperature show that this assumption is not correct—as time progresses, LAR in rice decreases (Baker et al., 1990; Yin and Kropff, 1996). Results presented in Fig. 2b, 2c, 2e, 2f, 3b, 3c, 3e, 3f also show that this assumption is not correct and support the hypothesis that LAR in rice decreases as a plant ages. Predictions with the WE model (Fig. 2b, 2c, 3b, 3c) and with the phyllochron model (Fig. 2e, 2f, 3e, 3f) were curvilinear upward because of a constant LARmax and phyllochron assumed in the models, respectively, and because of a decreasing observed LAR as time progresses, resulting in underprediction early in the growing season and overprediction late in the growing season. The under- and overpredictions with the WE and phyllochron models increased the systematic errors of the predictions with these two models (Table 10). In the Streck model, LAR is assumed affected by seed reserves and plant age, represented by accumulated leaf number, through a chronology response function [f(C)]. The first two leaves have the highest LAR due to seed reserves. As the number of emerged leaves increases, LAR decreases because the distance that each leaf primordium must extend to appear at the whorl increases for each subsequent leaf. This assumption was proposed for wheat (Streck et al., 2003a) and predictions with the Streck model (Fig. 2a, 2d, 3a, 3d) showing no curvilinear response, at least for HS < 10, demonstrating that this assumption is also valid for rice.
The decrease in LAR as a plant ages results from an increasing time required for leaf tips to grow from the apical meristem to the whorl for each successive leaf; it is accounted for by the decreasing f(C) in the Streck model (Fig. 1b). This approach is biologically and mathematically sound. Biologically, as more leaves are produced and successive leaves have longer sheaths, each additional leaf must grow longer and takes more time before the tip is visible at the whorl, which decreases LAR with time. Mathematically, this decrease in LAR is represented by a decreasing time response function [f(C)] that multiplies LARmax12. The scatter of points curving upward from the 1:1 line in Fig. 2b, 2c, 2e, and 2f, with underpredictions at lower HS and overpredictions at higher HS, can be attributed to the absence of an age factor decreasing LAR in the WE model and phyllchron model. If the very few points at the highest HS values in Fig. 2a and 2d are excluded (as discussed above, these points probably are off due to low temperature and cloudy days as results of plants growing late in Fall), then no upward or downward trend in the points is evident in the simulations with the Streck model.
The strength of a crop simulation model is how well it works under a wide range of different environmental conditions and different genotypes. The greatest stability of the Streck model, characterized by the lowest RMSE across cultivars, sowing dates, and years (Tables 4–9) and the lowest systematic component of MSE (Tables 10 and 11) both when simulations started at emergence and at the day of first observed HS, compared with the other two LAR models, indicates high robustness of this model. The predictions with the phyllochron model were greatly improved when the simulations started at the day of first observed HS, but were the worst when the simulation started at plant emergence. We seek a model that performs well with simulations starting as early as possible, so we can predict events as soon as the plant emerges. If we are interested in tracking leaf area from leaf number, predictions of the first leaves impacts greatly on leaf area. These results highlight some limitations of the phyllochron model.
In this application of the Streck model, there was only one coefficient that is genotype dependent: LARmax12. The temperature [f(T)] and the chronology [f(C)] response functions were assumed genotype independent. These assumptions worked well for the seven genotypes used in this study, with no additional input being necessary to run the Streck model compared with the WE and the phyllochron models. These results and the fact that the chronology response function has worked with wheat and rice indicate two important features of the Streck model that are sought for any crop simulation model—generality and robustness—while maintaining accurate predictions.
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ACKNOWLEDGMENTS
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To the Instituto Rio Grandense do Arroz (IRGA) for providing the seeds, and to Dr. Albert Weiss at the University of Nebraska-Lincoln (USA) and anonymous peer reviewers for valuable comments on early versions of the manuscript. The authors gratefully thank the students Simone Michelon, Lidiane Cristine Walter, Hamilton Telles Rosa, Cátia Camera, Gizelli Moiano de Paula, and Flávia Kaufmann Samboranha for their assistance in collecting data and technical support during the four years of experiments, and Dr. Luis Antonio de Avila for the facilities of the paddy rice field experiment. Funding to N.A. Streck through Conselho Nacional de Desenvolvimento Científico e Tecnológico- CNPq (Bolsa de Produtividade em Pesquisa) at the Ministry of Science and Technology of Brazil and to L.C. Bosco and I. Lago through Fundação CAPES (Bolsa de Mestrado) at the Ministry of Education of Brazil are greatly acknowledged.
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TOP
ABSTRACT
INTRODUCTION
