Calibration and Simulation of the CERES-Sorghum and CERES-Maize Models for Crops in the Central-West Region of Paraná State

Simulation models have been widely used to generate yield data by forecasting climate variables and changes in growing seasons. The aim of this study was to calibrate genetic coefficients and simulate growth, development and yield in maize and sorghum crops based on historical meteorological data for the municipality of Juranda (2007 to 2013), in the central-west region of Paraná State, Brazil. Treatments were established based on three planting dates in two growing seasons for a group of super early maturity maize hybrids (DKB 330 Pro), and two groups of sorghum hybrids, the first a super early variety (ADV 123) and the second with a normal cycle (1G282). The variables assessed were number of days from planting to flowering, leaf area index (LAI), and 1000 seed weight and yield. Statistical coefficients were used to evaluate calibration accuracy. The results demonstrated that the models were highly efficient at simulating crop cycles, yield and leaf area index, with agreement indices and modeling efficiency values above 0.90. The results indicated that the CERES-Maize and CERES-Sorghum models generated satisfactory and comparative simulations of maize and sorghum yield for the study area on different planting dates.


Introduction
The economic viability and agronomic benefits associated with crop rotation are major incentives for growing maize as a succession crop. In different regions, water availability is one of the primary factors considered when establishing preferred growing periods to obtain optimal yields, as well as in agricultural zoning and its applications (Wagner, Jadoski, Maggi, Saito, & Lima, 2013).
Dynamic mechanistic models describe daily changes in the plant variables assessed considering the main morphophysiological processes that occur during the simulation period. These simulations are then used to plan optimal management strategies such as planting dates and irrigation practices (Dallacort et al., 2011).
In this respect, a number of authors have used simulation models in different regions around the world to evaluate water availability and its use by plants, either inserting historical climate data into the models or simulating future data, with results indicating similar estimated and actual values (Grossi et al., 2013;Wagner et al., 2013;Kadiyala, Jones, Mylavarapuc, Lic, & Reddy, 2015;Vivan et al., 2015;Dokoohaki et al., 2016). Lopez et al. (2017) successfully modified the CERES-Sorghum model in order to better assess root growth and development. The authors highlighted the importance of growing deeper-rooted sorghum cultivars and optimizing planting dates to obtain higher yields.
With a view to providing an alternative for succession crops in Paraná State, this study aimed to assess sorghum and maize crop simulation models based on different planting dates and their effect on crop development.

Method
Experiments were conducted with maize and sorghum succession crops under dry conditions, using three planting dates in 2014 and 2015, to calibrate the CERES-Maize and CERES-Sorghum models. The study area was located on a farm (Sitio Nossa Senhora Aparecida) in the municipality of Juranda (PR) (24°23′10″ S, 52°49′30″ W), at an altitude of 570 m. The soil in the area is predominantly distroferric red latosol (oxisol) (EMBRAPA, 2013), with a humid subtropical climate (Cfa) according to Köppen's classification, average annual temperature of 22.2 °C and annual rainfall of around 2,100 mm.
Meteorological data were obtained by installing a weather station (Davis Vantage Pro 2) in the study area to determine minimum and maximum temperatures, relativity humidity, solar radiation, rainfall and wind speed.
A database bank of climatological data prior to the study was compiled using information provided by INMET (National Institute of Meteorology), obtained from the automated weather station in Goioerê (PR), the closest city to Juranda (PR), as well as rainfall data collected by the COAMO agribusiness cooperative.
For the maize crop, three planting dates and four blocks were used in both growing seasons (02/20, 03/02 and 03/12 in 2014, and 02/09, 02/19 and 03/01 in 2015); however, harvesting was not possible for the last two dates of 2014 and the last date in 2015 due to wind lodging.
All the plots (maize and sorghum) contained six 6-meter-long rows spaced 0.70 m apart and the study area of each plot consisted of the two central rows disregarding two meters on either end. Maize was planted using approximately 4.3 seeds per meter, producing a final population of about 56,000 plants per hectare, and sorghum with around 22 seeds per meter, totaling approximately 280,000 plants per hectare.
The following variables were analyzed to calibrate the models: Number of days from planting and flowering: The plots were visited every three days and the date on which 50% of plants were releasing pollen was considered the flowering date.
Leaf area index (LAI): the area of each leaf was calculated by adding the maximum length and width and multiplying the amount obtained by a correction factor of 0.75, as described by Francis et al. (1969). The area occupied per plant was determined based on the ratio between the number of plants and the study area of the respective experimental unit. IAF measurements were obtained using the average of two plants per plot.
Yield (kg ha -1 ): at the end of the experiment, the two 4 m-long center rows (5.6 m 2 ) of each plot were harvested, the panicles threshed and the kernels weighed and then dried in an oven at 65 °C until constant weight; 1000 seed weight (1000SW-g): Of the kernels used for yield assessment, 1000 from each plot were weighed after oven drying; Grain filling rate (g): The grain filling rate was calculated for both growing seasons and crops, whereby two panicles were randomly collected and 1000 kernels removed from their center every seven days in 2014 and every ten days in 2015. Total weight was measured (dry weight plus water) and the kernels were then dried in an oven at 65 °C until constant weight.
LAI during development: In 2015, LAI was calculated every ten days as the crops developed, using the same method as that applied for the final IAF.  There were three 12 to 15-day periods without rain in 2015. Despite accumulated rainfall of 227 mm from late March to late May, rain only fell over two short periods, resulting in poor distribution during a critical time for the crops. Total accumulated rainfall in 2015 was 1,209 mm.
After obtaining the climate data for the study period and measurements for the variables assessed, we began adjusting the process of the values recorded and those simulated by the program. However, a comparison of these values indicated the need to adjust coefficients. This was achieved by increasing or decreasing coefficient values until the simulated amounts were closer to those measured within each treatment.
First, data on the phenological growth stages of sorghum and maize were fit to the flowering and physiological maturity dates, and the coefficients of LAI and yield were then adjusted. According to Jones et al. (2003), growth and development parameters are interdependent, which corroborates the calibration sequence followed.
Simulation planning considered two scenarios, one for potential production (without drought stress) and another for actual production governed by rainfall during the simulated period.
In potential production simulations, the model assumed that water was not a limiting factor, that is, yield was largely dependent on other climate elements, such as solar radiation and temperature. This makes it possible to analyze the influence of these climate factors on the yield of sorghum and maize succession crops as a function of planting date.
For the actual production scenario, simulation was based on the climate data input into the software, whereby crop water needs were only met by rainfall recorded in the climatological database. This enabled us to evaluate the effect of water availability on the crop at different growth stages, which, depending on the planting date, influenced establishment, phenology and yield. Bao, Hoogenboom, McClendon, and Vellidis (2017) calibrated the genetic coefficients of the CERES-Maize model for different maize cultivars using only variables related to yield and harvest dates and found a difference of only 3% for calibration and 8% for validation in relation to actual data, in a 54-year study at six different locations. Singh et al. (2014) reported that sorghum crops are better able to adapt to drought than an increase in the average temperature. Grossi, Justino, Rodrigues, and Andrade (2015) concluded that sorghum yield is less affected by wind and relative humidity and more sensitive to water availability and solar radiation.
Sutka, Manzur, Vitali, Micheletto, and Amodeo (2016) studied the physiological response of two sorghum genotypes to drought based on different morphological and physiological root and shoot traits and observed a differential response between the two, indicating plasticity in water management under drought conditions during the seedling stage, with particularly noteworthy responses by whole plants to soil moisture deficits. Different drought tolerance strategies have also been reported in sorghum hybrids by Yi et al. (2014) and Fracasso, Trindade, and Amaducci (2016).
Calibrating the coefficients between the actual and simulated crop development values generated the genetic coefficients representing the crops in the DSSAT program (Tables 1 and 2). Note. P1: duration of the vegetative stage, based on the thermal sum from emergence to the end of the juvenile phase (base temperature of 8 ºC); P2: sensitivity to the photoperiod, based on the delay in days until the onset of male flowering for every one hour increase in the photoperiod after 12.5 hours; P5: duration of the reproductive stage, based on the thermal sum from stigma emergence to physiological maturity (base temperature of 8 ºC); G2: number of kernels per plant; G3: grain filling rate under optimal growth conditions; PHINT: phyllocron interval corresponding to the time between the emergence of successive leaves. Note. P1: Thermal time during which plants did not respond to photoperiod changes, with duration from seedling emergence to the end of the juvenile phase; P2: thermal time from the end of the juvenile phase to panicle initiation, under short days; P2O: photoperiod limit above which the thermal time for panicle initiation is affected by the photoperiod; P2R: rate at which the thermal time for panicle initiation increases for every hour added to the photoperiod above P2O; PANTH: thermal time from the end of panicle initiation to flowering; P3: thermal time from the end of flag leaf expansion to flowering; P4: thermal time from flowering to the onset of grain filling; P5: thermal time from the onset of grain filling to physiological maturity; PHINT: phyllocron interval corresponding to the time between the emergence of successive leaves; G1: coefficient expressing the relative leaf size; G2: fraction of photoassimilates distributed to the panicle.
Calibration of the genetic coefficients was followed by the simulation of crop growth, development and yield. Table 3 shows the calibration results for the CERES-Maize model for 2014 and 2015. Considering the results obtained for the variables studied in terms of the relationship between actual and simulated values, positive percent deviations (PD) indicate overestimation and negative PD underestimation.
Based on an analysis of the data (Table 3), the CERES-Maize model shows a good fit to the data, suggesting good accuracy in simulating maize growth and development. This is supported by the agreement indices and MEF values obtained in calibration for 2014 and validation in 2015, with yield values greater than 0.9. The model exhibited low efficiency in simulating the flowering period since cultivation over a two-year period increased crop cycle variation. The variables with the best fit for maize were flowering date and yield, whereas Kadiyala et al. (2015) reported the best agreement indices and MEF statistics for physiological maturity date and shoot dry weight. Leaf area index (LAI) was underestimated in simulations, with values up to 20% lower than those observed in the field (Table 3), and 1000 seed weight displayed the worst fit, with over 60% variation. Pereira, Von Pinho, Paglis, Pereira and Altoé (2010) studied maize crops with three different planting dates in Lavras, Minas Gerais state, Brazil, using the CERES-Maize model and also obtained low statistical indices for number of seeds and 1000 seed weight, with a better fit for flowering and physiological maturity dates, yield components and yield.
Analysis of the goodness of fit of the CERES-Sorghum model for the two sorghum hybrids shows agreement index values greater than 0.90 for almost all the variables except 1000SW, which, despite an MEF of 0.72, indicates good model efficiency (Table 4). The PF for these treatments was very high, particularly for yield. The results suggest that factors other than those analyzed and simulated influenced yield on the last planting date. A high incidence of disease in some cultivars is assumed to be the main indicator, even with protective management practices, corroborating the findings of Grossi et al. (2013). Simulation data for 2015 are presented in Table 5. Chimonyo, Modi and Mabhaudhy (2016) also found that actual data were influenced by uncontrolled environmental factors, with hail affecting the number of leaves and LAI in an experiment with sorghum and cowpea.
In 2015, PD for flowering date (  Maximum temperatures from planting until flowering declined by an average of 2.0 °C every ten days between planting dates for the two-year study period (Figures 2A and 2B). These high initial temperatures meant the accumulated thermal sum needed for flowering was reached more quickly. Akinseye et al. (2017) compared three sorghum growth simulation models and concluded that SAMARA was better able to predict LAI than APSIM and DSSAT, although the last two models showed greater accuracy for grain yield and biomass production, which may explain the values found here and in the two aforementioned studies.
Yield exhibited a low PD, with simulated values within the standard deviation of actual data. Similarly, Singh et al. (2014) obtained Willmott agreement indices (d) above 0.95 for the yield of three sorghum hybrids grown in two regions of India, with r 2 greater than or equal to 0.85.
The difficulty in fitting the model to experimental data can be attributed to experimental error resulting from sampling problems and the frequency needed to obtain realistic values, as well as difficulty keeping the kernels collected before physiological maturation intact and dry weight loss during oven drying.
Genetic coefficients are interconnected in model calibration, making it impossible to change an individual variable since one may be a better fit than another. In the present study, 1000SW was considered a secondary variable. Leaf area index showed a better fit than 1000SW, as shown in Figure 3.
jas.ccsenet.     Figure 6 or 2007 to 201 However, the op e to the low rai e probably lim avior was also Vol. 11,No.     Based on the yield reduction by planting date methodology, potential and actual yield values were calculated to determine the optimal planting date for maize and sorghum (Table 6). Assessment of the optimal planting date based on potential yield showed that both the sorghum hybrids and maize performed better when planted early, with a smaller difference between the first and last planting dates for sorghum. Based on the results obtained, we believe that the sooner sorghum and maize succession crops are planted (from January onwards or after the summer crop), the better their yields will be, since the results indicate February 20 as the optimal planting date.
In Goiás state, Grossi et al. (2013) observed the smallest sorghum yield reduction for planting dates in January, with losses increasing at later dates. These findings corroborate those of Cardoso, Faria, and Folegatti (2004)

Conclusions
The CERES-Maize and CERES-Sorghum models were efficient at simulating flowering and physiological maturity dates as well as the actual and potential yield in sorghum and maize crops from 2007 to 2015, in Central-West Paraná State.
Leaf area index was satisfactorily simulated for the two sorghum hybrids, but underestimated for the maize hybrid. Both models were limited in simulating the grain filling rate.
Sorghum exhibited greater potential and actual yield stability for the different planting dates, whereas maize yield decreased with later dates.
Sorghum has the same agronomic potential as maize when grown as a succession crop in Central-West Paraná State, depending only on market conditions and farmers' crop management practices.
Farmers could opt to plant sorghum as a succession crop when droughts are forecast for this period since maize is more sensitive to dry weather, whereas sorghum may not be the best alternative when frost is forecast.