MODELING APPLIED TO SOWING DATE OF IRRIGATED MAIZE

In Brazil, the rainfed maize crop may undergo yield breaks due to uncertainties in the rainfall distribution. Irrigation can be a management alternative that, however, requires evaluation and planning to be helpful. The objective of this work was to analyze the simulated yield data of irrigated maize in counties of Minas Gerais state, Brazil. The CSM-CERES-Maize model was used to simulated weekly sowings of maize considering optimum agronomic conditions. A sprinkler irrigation scheme with 80% efficiency was used with automatic applications when the crop withdrew 50% of the soil available water. The harvest was scheduled to happen automatically when the crop had reached physiological maturity. The results were statistically analyzed for each county, based on goodness of fit test, ANOVA, Tukey’s test and risk analysis (stochastic dominance). The most promising sowing period was from January 16 to March 27 for all locations, except for Janaúba, for which the best sowing window was from November 14 to January 2. The treatments of highest average simulated maize yield stochastically dominated the other treatments evaluated. The CSM-CERES-Maize model proved to be a useful tool to help making decision in irrigated maize crop systems.

Brazil is the third world largest maize producer.
In some regions, the sowing season takes place twice a year.In the first growing season, at the traditional producing regions, the rainfall amounts can supply the crop water requirement, however, dry spells can occur.Currently, Minas Gerais is the leading state in maize production during this first growing period.It is expected to represent 19% of all national production for the 2016-2017 season (Acompanhamento da Safra Brasileira [de] Grãos, 2017).In a same sowing date, simulated maize yield for Janaúba, MG, Brazil, was sometimes above and sometimes below average due to water deficit (Alves et al., 2011).For the central region of Paraná state, Brazil, Wagner et al. (2013) concluded that maize yield is affected by the soilwater availability throughout the crop season and that the average probability of yield reduction due to water deficit is about 50%.
For the year of 2017, it was estimated that 61.3% of the national maize production will come from the off-season growing period (Acompanhamento da Safra Brasileira [de] Grãos, 2017), which is subjected to uncertainties due to climate elements' variability (Soler et al., 2010).In a study using computer modeling, Cardoso et al. (2004) found that rainfed maize sowed off-season in northern Paraná state, Brazil, suffers yield breaks and cycle interruption due to lack of rainfall and low temperatures.
The use of irrigation eliminates the risk of maize yield loss due to water stress.Another simple management strategy is setting sowing periods for which high yields are more likely.This can be facilitated using computational models applicable to agricultural systems.These computer-implemented models, representing mathematically the soil-plantatmosphere system, have been developed and applied in various countries (Katerji et al., 2013;Singh et al., 2014;Negm et al., 2014;Kadiyala et al., 2015;Li et al., 2015).Calibrated crop models have the potential to be used as tools in studies of agricultural zoning and to establish sowing dates (Andrioli & Sentelhas, 2009).More recently, computer models have also been utilized in studies related to the impact of climate change on agricultural crops (Islam et al., 2012;Singh et al., 2014;Moradi et al., 2014).
It was employed to evaluate the off-season yield of four maize hybrids in Piracicaba, SP, Brazil, under rainfed and irrigated conditions, confirming the model accuracy to simulate crop cycle and yield (Soler et al., 2007).
The rainfed maize crop zoning was established in Minas Gerais state, Brazil, due to climate risk using the CSM-CERES-Maize model, which provided the advantage of obtaining yield estimates in addition to the sowing periods (Paixão et al., 2014).The DSSAT model was applied to simulate long-term trends in maize and wheat yield and the soil carbon and nitrogen dynamics using 14 years of weather data of northwestern China (Li et al., 2015).The authors found that the model could contribute to the definition of optimal management practices.
The objective of this work was to analyze, through the application of CSM-CERES-Maize model, the variation of irrigated maize yield in six counties of Minas Gerais state, Brazil, for different sowing dates throughout the year.Table 1.Coordinates, average minimum temperature, average maximum temperature, average annual precipitation and number of years considered in the analysis.
(1) Average minimum temperature; (2) average maximum temperature; (3) average annual precipitation; (4) number of years considered in the analysis; equivalent to the number of replicates per treatment; (5) Meteorological station of Patos de Minas.

Material and Methods
The CSM-CERES-Maize model of DSSAT, version 4.5.1.023,previously parameterized for the single-cross hybrid DKB390YG (Amaral et al., 2011), was used in the study.Weather data from six counties of Minas Gerais state, Brazil (Janaúba, Lavras, Presidente Olegário, Sete Lagoas, Uberaba and Viçosa), were downloaded from the database of the National Institute of Meteorology (INMET) and were used as input in the model.For each county, 48 years  of observed daily data of maximum and minimum temperatures (°C), precipitation (mm) and solar radiation (MJ m -2 day -1 ) were used.Discarding some of the years of this period was necessary due to missing information and some anomalies in the dataset (Boggione, 2014).Information on elevation, latitude, longitude and number of years used in the simulations for each county, are presented in Table 1.
Samples were taken in the mid portion of five soil profile layers: 0 to 0.05 m 0.05 to 0.20 m, 0.20 0.40 m, 0.40 to 0.70 m and from 0.70 to 1.00 m.Data on soil particle size, bulk density, porosity, saturated hydraulic conductivity and soil upper and lower limits of available water, required by the model, were obtained using standard methods of analysis (Boggione, 2014).To adequately represent the natural drainage conditions of tropical soils, data on total soil porosity estimated from the data of soil density and soil particle size were reduced by 5%.As the upper limit of available water (field capacity), it was used the soil-water content in equilibrium with -2 and -30 kPa, depending on the soil particle size (Table 2).
We used the seasonal analysis tool of DSSAT to simulate the weekly maize sowing dates, repeated every year for which meteorological data was available.The crop management files were prepared considering a high-yield maize cultivar, grown without water, nutrient and pest stresses.The simulations considered a no-tillage system, having dry beans as the previous crop, which left at the soil surface to the subsequent maize crop about 3,600 kg ha -1 of straw with 20% of nitrogen and 1.8% of phosphorus.Sowing was performed at depth of 0.05 m, row spacing of 0.70 m and a population of 68,000 plants per hectare, as established in previous work (Tigges et al., 2016).As there was no data on initial soil-water content and soil nitrate and ammonium

Locality
Latitude Longitude Altitude T mmin (1) It was considered a sprinkler irrigation system, with 80% application efficiency, set to automatically irrigate the maize crop.The irrigation was triggered when the simulated soil-water content at the 0 to 0.20 m soil layer corresponded to 50% of the total soilwater availability.It was also assumed a nitrogen fertilization rate that allowed the cultivar to express its genetic yield potential without nitrogen stress.
The harvest was scheduled to happen automatically when the crop had reached physiological maturity.
As for the output data, grain yield, expressed as dry matter, was corrected to 13% moisture.In order to analyze the impact of solar radiation on yield, three phases along the maize cycle were selected: Phase 1 (vegetative phase, from emergence to anthesis); Phase 2 (reproductive phase, from anthesis to 15 days after that event); and Phase 3 (grain filling phase, 15 days after anthesis to physiological maturity).To extract the solar radiation values accumulated for each period, the meteorological data were post-processed using macros in a spreadsheet.
The statistical analysis consisted of goodness of  using the Excel spreadsheet (Microsoft Corporation), developing specific macros for the latter.
The @RISK program was used to verify the stochastic dominance on the risk analysis of three selected treatments for each county.It was selected the treatment with the highest average yield, the first for which the yield was statistically different by Tukey's test, and the one that required the lowest irrigation depth (Boggione, 2014).

Results and Discussion
Analyzing the average simulated crop yield  during the crop cycle and phases.
(1) Treatment and corresponding year; (2) vegetative phase; (3) reproductive phase; (4) grain filling phase.Bert et al. (2007), in a study conducted in the Argentine Pampas, found that the CSM-CERES-Maize showed greater sensitivity to solar radiation input data as compared to soil input data (N content at harvest time, organic matter content, soil's capacity to retain water, etc.).
As expected, the simulations did not show risk of crop loss in irrigated systems, which may occur as a consequence of unfavorable distribution of temperature or solar radiation during the cycle, even if there is no water deficit.However, it is noteworthy that there is uncertainty in estimates of crop yield         Through the use of risk analysis software, it is possible to verify the stochastic dominance, which is a necessary tool to decision-makers for determining the most promising sowing window of irrigated maize.
Priestley-Taylor and FAO-56 Penman-Monteith methods are the only options in DSSAT to estimate potential evapotranspiration.The Priestley-Taylor method is a simplified version of combined equations (e.g.Penman-Monteith) having a dimensionless empirical coefficient which can be locally adjusted to reduce inaccuracies due to non-consideration of the aerodynamic component.Since no wind speed and relative humidity data were available the Priestley- fit test, ANOVA, Tukey's test and risk analysis.It was considered 52 treatments in a completely randomized design.The treatments were weekly sowing dates sequentially numbered over the year.The first treatment (T1) and the last treatment (T52) refer to the August 1 and July 24 sowing dates, respectively.Each year was considered a replication.The goodness of fit test aimed to verify the adequacy of the analysis of variance and support the risk analysis.The crop yield output data for each treatment was checked for normal distribution, by using the @RISK program, version 6 (Palisade Corporation).The goodness of fit test used was the Kolmogorov-Smirnov at a significance level of 5% as used in the F and Tukey tests.The analysis of variance by F test and Tukey's test was performed

(Figure 1 .
Figure 1.Average simulated crop yield obtained for the different treatments (T1 refers to the sowing on August 1 and T52 to the sowing on July 24) for the six counties.

Figure 4 .
Figure 4. Notched box plot for Presidente Olegário (treatments 1 and 52 refer to the August 1 and July 24 sowing dates, respectively).

Figure 5 .
Figure 5. Notched box plot for Sete Lagoas (treatments 1 and 52 refer to the August 1 and July 24 sowing dates, respectively).

Figure 6 .
Figure 6.Notched box plot for Uberaba (treatments 1 and 52 refer to the August 1 and July 24 sowing dates, respectively).

Figure 7 .
Figure 7. Notched box plot for Viçosa (treatments 1 and 52 refer to the August 1 and July 24 sowing dates, respectively).

Figure 8 .
Figure 8. Cumulative probability versus simulated grain yield for the treatment with the highest average crop yield, for the first to differ statistically from the best evaluated for average crop yield and to treatment with lowest irrigation requirement.

( 1 )
Treatment with highest simulated average crop yield.(2)First treatment statistically different, in relation to simulated crop yield, to the treatment with highest simulated average crop yield.(3)Treatment with lowest simulated irrigation depth.17 T13-10/24 T13-10/24 T12-10/17 T16-11/14 T11-10/10ConclusionsThe CSM-CERES-Maize model proved to be a useful tool in providing information regarding the variability of irrigated maize yield in the selected counties, allowing the sowing window establishing and the temporal synchrony analysis of the intraannual crop yield variation among the counties.

Table 2 .
Water content at wilting point (θ PM ) and at field capacity (θ CC ) in the layer from 0.05 to 0.20 m for the

Table 3 .
Highest and lowest values of simulated average crop yield and respective sowing dates obtained with

Table 4 .
Simulated maximum and minimum crop yield by county and average daily solar radiation(Rad.)

Table 1 )
, respectively.IQR is also showed in box plots, as upper and lower whiskers and outliers (open circles).There is strong evidence to differences in two medians if respective notches do not overlap.
Liu et al. (2011)S-Maize arising from factors not considered in the model, such as weather short-term events (high intensity rains, high wind speeds, hail, etc.), as reported byLiu et al. (2011).In critical instances, such factors could cause significant crop yield losses.

Table 5 .
Treatments and selected sowing dates for risk analysis.