Number of leaves and phenology of rice hybrids simulated by the SimulArroz model

Número de folhas e fenologia de híbridos de arroz simulado pelo modelo SimulArroz R E S U M O Modelos matemáticos baseado em processos podem prever o desenvolvimento folhar e reprodutivo de cultivos agrícolas. Objetivou-se, com este trabalho, calibrar e avaliar o modelo SimulArroz em simular o número de folhas e a fenologia de três cultivares de arroz híbrido no Rio Grande do Sul. Foram conduzidos experimentos de campo em Santa Maria, Cachoeirinha, Uruguaiana e Santa Vitória do Palmar, no Rio Grande do Sul, em dois anos agrícolas. Foram realizadas observações para determinar o número de folhas do colmo principal através da escala da Haun e a fenologia de três cultivares híbridas (PRIME CL, INOV CL e QM 1010 CL) e uma convencional de arroz usada como testemunha (IRGA 424). A calibração do modelo SimulArroz utilizada foi eficiente em simular o número de folhas e a fenologia em função da época de semeadura e do grupo de maturação de três cultivares híbridas de arroz irrigado no Rio Grande do Sul.


Introduction
Brazil is the ninth largest rice producer in the world (USDA, 2016).The Brazilian production is approximately 12 Mt and the South region is responsible for 76%, while the state of Rio Grande do Sul (RS) is the largest producer, with 70% of the national production (CONAB, 2016).Annually, the RS state cultivates 1.1 million ha with irrigated rice; thus, it is one of the crops that represent a significant part of the gross national product, generated by the agricultural sector (CONAB, 2016).Hybrid cultivars are the most productive, for producing more per unit of area, due to the heterosis (Cantrell, 2003), which allows to reach yields 20 to 30% higher than those of conventional cultivars (Li & Yuan 2000;Coimbra et al., 2006).
In the agricultural sector, for reliability and applicability, there is the necessity to develop models adapted and tested in different environments (Streck et al., 2008;2011).After tested, the agricultural models have multiple applications, because they can predict growth, development and yield of the crop as a function of the meteorological conditions during the growth season (Shin et al., 2006;2010).The SimulArroz model is a dynamic ecophysiological process-based model that simulates growth, development and yield of irrigated rice.This model differs from the others for having been adapted for cultivars in the flood irrigation system in RS (Streck et al., 2011;Walter et al., 2012).The SimulArroz model contains a "biological clock" that controls growth and development by calculating the production of leaves and the phenology of the crop (Streck et al., 2008;2011).In the current version of the SimulArroz (version 1.0), there is no option for hybrids, which is a limitation, as hybrid rice has been cultivated in RS since 2002 and currently has an area of approximately 68 thousand ha (IRGA, 2015).This study aimed to calibrate and evaluate the SimulArroz model in simulating the number of leaves and phenology of three hybrid rice cultivars in Rio Grande do Sul.The sowing dates of the experiments encompassed the period recommended for the crop in RS (early September until mid December) (Table 1).The density was 40 kg ha -1 for the hybrids PRIME CL and QM 1010 CL, and 50 kg ha -1 for INOV CL, due to the genetic characteristic of lower tillering (Peske et al., 2004).Besides the hybrids, a conventional cultivar was also used at the density of 100 kg ha -1 as a control (Table 1).The conventional cultivar IRGA 424 (medium maturity group) was selected because it is recommended for all rice-growing regions of RS and also for showing higher yield among the conventional cultivars, because its productive potential is close to that of hybrid cultivars (SOSBAI, 2014).

Experiments
The spacing between rows was 0.17 m in all locations.The size of the plot for each cultivar was 17 x 17 m in Santa Maria, 1.57 x 47 m in Cachoeirinha, 1.53 x 5 m in Santa Vitória do Palmar and in Uruguaiana.The experimental design in Santa Vitória do Palmar and in Uruguaiana was randomized blocks with 4 replicates.In Santa Maria and Cachoerinha, there was no experimental design and samplings were performed according to the methodology described by Gabriel et al. (2014).
Leaf production and phenology were weekly evaluated (in Santa Maria and Cachoeirinha) and biweekly evaluated in the other locations in plants that were identified in the V2/V3 stage of the scale of Counce et al. (2000).These plants were evaluated for number of leaves in the main culm through the Haun scale, HS (Haun, 1973), which is calculated as follows: where: HS -number of leaves in the main culm; NL -number of expanded leaves in the main culm; L last -length of the last leaf (without the formed collar); and, L pnult -length of the penultimate leaf (last one with formed collar), both in centimeters (cm).
Panicle differentiation (R1) was determined through the destructive sampling of 10 plants and the R1 date occurred when 50% of the plants were in this development stage.Marked plants were observed to identify the dates in which 50% of the plants were in anthesis (R4) and physiological maturity (R9) (Counce et al., 2000).
The daily rate of leaf production in the main culm in the SimlArroz model was calculated according to Streck et al. (2003): LAR -leaf appearance rate (leaves d -1 ); LAR max1,2 -maximum rate of appearance of the first and second leaves (leaves d -1 ); f(T) -LAR response function with respect to air temperature, with cardinal temperatures for leaf production equal to 11 °C (Ellis et al., 1993;Infeld et al., 1998), 26 °C (Ellis et al., 1993) and 40 °C (Gao et al., 1992), respectively; and, (2) f(C) -chronology function that causes LAR to decrease, from the third leaf on.
The cumulative number of leaves, represented by the Haun scale, is calculated as: where: HS -Haun stage (leaves in the main culm).
For the calculation of the progress of the phenology in SimulArroz, the development stage of the crop (DVS) was daily calculated as: where: DTT -daily thermal time ( o C day); and, TT -total thermal time ( o C day) to complete the stage.
The calibration of both submodels consisted in estimating the values of LAR max1,2 (Eq.2) and TTS (Eq.10) for each hybrid, with data of experiments in Table 1.Both submodels were evaluated with independent data (Table 1).
Simulations were performed with the SimulArroz model for the cultivar IRGA 424, already available in the version 1.0, in order to compare the performance of the model in the The performance of both submodels in the SimulArroz model was evaluated using the following statistics: Root-meansquare error (RMSE), BIAS index, agreement index (dw) and Pearson's correlation coefficient (r).

Results and Discussion
The maximum appearance rate of the first and second leaves (LAR max1,2 ) is higher in the hybrid with medium cycle (QM 1010 CL) and lower in that of early cycle (PRIME CL), indicating lower speed of leaf production in PRIME CL in comparison to the other two hybrids.The total thermal sum necessary to complete the Sowing-Emergence stage is similar in the three hybrids.The duration of the Emergence-Panicle Differentiation stage is shorter in the early hybrids, especially PRIME CL.For the hybrid cultivars, the vegetative stage is the one with highest influence on the duration of the total cycle (Table 2), regardless of the maturity group.
The simulation of the HS of the hybrids in the different locations showed RMSE from 0.5 to 1.9 leaves in the main  Table 2. Parameters of the submodels of leaf production and phenology in the SimulArroz model calibrated for three rice hybrids stem, close to the values found for maize (0.8 leaves) (Streck et al., 2010) and lower than that found for cassava (3.2 leaves) (Samboranha et al., 2013) using the model of Wang and Engel.The BIAS index varied from -0.03 to 0.45, indicating a slight underestimation of the model.The dw index and the correlation coefficient were high for all hybrids (above 0.89).Considering all locations, the RMSE of the hybrids varied from 0.6 to 1.4 leaves (Figure 1A).Comparing the statistics of the hybrids with those of the IRGA 424 (Table 3 and Figure 1A), it is noticed that the SimulArroz model simulates well the number of leaves, represented by the HS, in the three hybrids.The final leaf number (FLN) in the main culm, which is intrinsically solved (Streck et al., 2003), showed a RMSE of 1.1 leaves, being slightly higher than that reported for wheat (0.55 leaves) (He et al., 2012), using a nonlinear model, thus emphasizing to continue the efforts to improve the simulation of FNL.The other statistics (Figure 1B) indicate a very good performance in the model for this variable.
The RMSE of the cultivar IRGA 424 was close to those of the hybrids for the phenology, and the simulation of R1, R4 and R9 varied from 3.6 to 8.1 days between both locations.Considering all locations, the RMSE was equal to 4.2, 4.7 and 5.9 d (Table 4).
These values (Table 4) are lower than those described for wheat (12.6 days) and barley (11.5 days) using nine simulation models (APES-ACE, CROPSYST, DAISY, DSSAT-CERES, FASSETT, HERMES, MONICA, STICKS and WOFOST) (Rotter et al., 2012), confirming the better performance of the model used in the present study.
The hypothesis for the delay of the simulated emergence can be related to three factors, which are not considered in the model: (i) sowing depth, (ii) soil temperature (the model uses air temperature to estimate emergence) and (iii) rainfall from sowing to emergence, which can alter soil temperature and create an anoxic environment, which decreases the germination speed.Running the model from the observed emergence date, the RMSE is equal to 7.2, 4.8 and 4.6 days for R1, R4 and R9, respectively.
Figure 2 shows an application of the SimulArroz model to describe the Genotype x Environment interaction on the duration of the development cycle (Sowing to R9), of the three rice hybrid cultivars, on four sowing dates, in four locations of RS.The shortest duration of the development cycle occurred for the sowings in the months of November and December, due to the higher air temperature, which caused the thermal accumulation for each development stage to be faster, except in Uruguaiana, where QM 1010 CL showed the longest duration of the cycle for the sowing on December 25 (Figure 2).Among the locations, the duration of the cycle was longer in Santa Vitória do Palmar (sowing on September 25) and in Uruguaiana (sowing on December 25).In these two locations, due to the geographic position, the lower temperature in the spring (Santa Vitória do Palmar) and in the autumn (Uruguaiana) determined the lower daily rate of development and, consequently, prolongation of the cycle.Considering all locations and sowing dates, the cycle varied from 121 to 96 days for PRIME CL, 127 to 102 days for INOV CL and 134

Conclusions
1.The calibration approach of the SimulArroz model is efficient to simulate the number of leaves in the main culm and phenology of three hybrid cultivars of irrigated rice in Rio Grande do Sul.
2. The SimulArroz model captures the effect of sowing period on the hybrid cultivars and the stage from sowing to panicle differentiation has the highest influence on the duration of the total cycle.
3. The SimulArroz model is sensitive to the maximum leaf appearance rate, which varies with the maturity group, being higher in all cultivars of medium cycle.
lower base temperature; T opt -optimum temperature; T B -upper base temperature; and, T mean -mean daily air temperature.The T b , T opt , and T B vary according to the developmental phase, being T b = 11 °C, T opt = 30 °C and T B = 40 °C for the Sowing-Emergence and Emergence-Panicle Differentiation Phases, T b = 15 °C, T opt = 25 °C and T B = 35 °C for the Panicle Differentiation-Anthesis phase, and T b = 15 °C, T opt = 23 °C e T B = 35 °C for the Anthesis-Physiological Maturity phase simulation of the hybrids with the conventional cultivar.The parameters of both submodels for the cultivar IRGA 424 in the SimulArroz model are: LAR max1,2 = 0.347 leaves d -1 , TTEM = 50.0o C day, TTVG = 644.3o C day, TTRP = 153.0o C day, TTEG = 112.78o C day.

Figure 1 .
Figure 1.Number of leaves per plant on the main culm -HS (A), final leaf number in the main culm -FLN (B) and days after sowing (DAS) of the stages of emergence-EM (C), panicle differentiation (R1), anthesis (R4) and physiological maturity (R9) obseved and simulated with the SimulArroz model for three hybrids (PRIME CL, INOV CL and QM 1010 CL) and one conventional cultivar (IRGA 424) of irrigated rice in Rio Grande do Sul in the 2014/2015 growing season RMSE -Root-mean-square error, BIAS -BIAS index; DW -Agreement index; R -Pearson's correlation coefficient (r); The hybrid cultivars PRIME CL and INOV CL were not evaluated in these locations; In Santa Vitória do Palmar, dw and r were not determined because of the lower number of observed data

Figure 2 .
Figure 2. Development cycle duration (Sowing to R9) for three hybrid cultivars of irrigated rice, INOV CL, PRIME CL and QM 1010 CL, on four sowing dates, in Santa Maria (A), Cachoeirinha (B), Uruguaiana (C) and Santa Vitória do Palmar (D), RS, simulated with the SimulArroz model

Table 1 .
Rice hybrids, locations and sowing dates of the experiments of flood-irrigated rice used for the calibration and evaluation (independent data) of the submodels of leaf appearance and phenology in SimulArroz model

Table 3 .
Performance of the SimulArroz model in simulating the Haun stage on the main culm of three hybrids and one cultivar (IRGA 424) of irrigated rice in four locations of Rio Grande do Sul, during the 2014/2015 crop season RMSE -Root-mean-square error; BIAS -BIAS index; dw -Agreement index; r -Pearson's correlation coefficient; The hybrid cultivars PRIME CL and INOV CL were not evaluated in these locations

Table 4 .
Performance of the SimulArroz model in simulating the date of emergence, panicle differentiation (R1), anthesis (R4) and physiological maturity (R9) of three hybrids and one cultivar (IRGA 424) of irrigated rice in four locations of Rio Grande do Sul, during the 2014/2015 crop season