Optimizing the amount and splitting of nitrogen fertilizer in corn using response surface modeling

Introduction
Corn is one of the most widely consumed cereals in the world, which is highly compatible with many climates. For this reason, corn has been cultivated in most regions of the world since ancient times. Therefore, it is also considered a part of people's food all over the world. The effect of nitrogen fertilizer, as an agricultural solution, on the growth and yield of corn has caused it to be split to increase the plant's access time to this nitrogen source. In fact, due to the leaching of nitrogen fertilizer, it is usually not applied in one step. For this reason, based on the prevailing conditions of the field, the operators divide it into two or more divisions and perform nitrogen fertilization during the growth period. In each division, it is necessary to determine and apply the optimal amount of nitrogen fertilizer in order to minimize environmental pollution in addition to being economical. It requires many field experiments, which require a lot of time and money. To solve this problem, the use of simulation and optimization models, such as response-surface modeling, is suggested. The response-surface method is one of the suitable optimization tools that has been considered in various sciences for many years. The statistical basis of this method is very complex and uses a multi-objective nonlinear model for optimization and modeling. The response-surface method first provides a suitable combination of treatments, and by considering them, a statistical model is created that has the best fit compared to other models. Next, the most optimal value is determined for the independent variables so that the value of the dependent variables reached their maximum or minimum.
 
Materials and Methods
For this purpose, the data collected from a research project, which was carried out in the 500-hectare farm of the Seedling and Seed Research Institute in two years (2011-2012), were used. Two factors consisted of fertilizer in three levels (N1: 100 and N2: 60% and N3: 50% of fertilizer requirement) and the time of splitting into three methods (T1: the farmer's application with two splittings; T2: three equal divisions and T3: four equal divisions) was considered. The response surface method was used to optimize yield and yield components. In the response-surface method, the code of -1, 0, and +1 for nitrogen indicates 50, 60, and 100 kg/ha of nitrogen fertilizer, respectively. The code of -1, 0, and +1 for fertilizer splitting indicates the number of 2, 3, and 4 nitrogen fertilizer splitting during the growing season, respectively. In this method, to fit the data, multivariate regression was used by adding linear terms, quadratic, and interaction between factors. Then, regression was evaluated based on the analysis of variance. The statistical criteria used included root mean square error (RMSE), normalized root mean square error (NRMSE), mean bias error (MBE), model efficiency (EF), index of agreement (d), and coefficient of explanation (R²).
 
Results and Discussion
The results of ANOVA showed that the linear and quadratic regression model for seed yield and the linear regression model for fertilizer efficiency was significant at the 5 % probability level (P-value ≤ 0.05). For water productivity, the splitting factor had a greater effect on the regression than the amount of fertilizer, although both factors did not show a significant effect. The regression model had a significant effect on the 1000 seed weight, number of seeds in a row, number of rows in a cob, cob length, and seed size. The regression of other variables was not statistically significant. Therefore, the response-surface method can be used to predict and optimize variables with significant regression. The results showed that the regression model was capable of predicting variables including 1000 seed weight, number of seeds in a row, number of rows in a cob, corn length, and seed zinc content. But this model had an underestimation error (MBE ≤ 0.0) for all variables. The accuracy of the regression model for grain zinc content was in a good category (0.1 < NRMSE < 0.2) and for other variables in the excellent category (0.0 <NRMSE< 0.1). By increasing the amount of fertilizer (changing from code -1 to + 1), the yield initially decreased and then increased. With the increase of fertilizer splitting, corn yield decreased first and then increased. The effect of the amount and splitting of fertilizer on changes in the 1000 seed weight was linear and with the increase of these two factors, the 1000 seed weight also increased. This result was also observed for the number of seeds in the cob. In terms of cob length and grain zinc percentage, the two factors of fertilizer amount and splitting had similar effects on the increase of these two variables, but at low values of both factors, the mentioned variables decreased slightly. Increasing the amount and distribution of fertilizer caused an increase in the number of rows in the cob, but high amounts of these two factors had no effect on the increase in the number of rows in the cob. Except for the number of rows, other variables increased along with increasing the amount of fertilizer and its splitting. Providing 100% fertilizer requirement and increasing the number of divisions to 5 times, can increase maize yield by up to 1.5 tons per hectare. This was about 28% of the average yield and 6 % of the maximum corn yield in this study. The weight of the thousand seeds increased to 3.5 grams under optimal conditions, which increased by 32 and 9 % compared to the average and maximum values in this study, respectively. The variable of the row was not much of a change in the average variable (1.5 cm) and increased by only 1 %. The optimal length increased to 3.5 cm and the optimal rate increased to 62%.
 
Conclusion
In general, the optimization results of all variables showed that if the fertilizer requirement is applied as N1 and in five splittings; the amount of yield, 1000 seed weight, the number of seeds in a row, the length of the cob and the amount of seed will increase by 6, 9, 12, 18.5, and 19.6% respectively compared to the maximum values of these variables. Therefore, it is suggested to apply this scenario in the field to improve yield and yield criteria such as zinc concentration in corn seeds.