Optimization of irrigation intervals and amount of super absorbent in peppermint cultivation using response-surface modeling

Introduction
The water shortage in the agricultural sector in recent years and its continuation in the future is an undeniable reality in Iran. Super absorbent materials can be used to cope with the effects of drought and water stress on plants. As a result of absorbing and storing water, these materials can change the amount or frequency of irrigation water. To ensure the optimal development of the root structure of medicinal plants, aerial parts, and essential oil percentage, it is necessary to create optimal conditions for providing moisture. It is time-consuming and costly to conduct multiple tests to achieve this objective. Thus, simulation and optimization models have been suggested to solve this problem. The researcher must first prepare the required data for each combination of treatments mentioned in this model, then build a statistical model based on it. The next step is to determine the optimal conditions for the independent variables so that the dependent variables approach their maximum, minimum, or target value. According to the literature review, response-surface methodology (RSM) has been effective in determining the optimal values of factors in the agricultural sector. As a result, it can be also used to optimize the application of super absorbent in peppermint cultivation. So, this study was designed to optimize the use of super absorbent in different irrigation rounds to maximize quantitative and qualitative traits of peppermint (Mentha piperita).
 
Materials and Methods
The present research was conducted in the research greenhouse of the Agricultural Engineering Research Institute (AERI) in Karaj in 2018-2019. Specifically, three irrigation intervals (two, four, and six days) and three weight percent of Aquasource superabsorbent (zero, one, and two %W of superabsorbent/soil) were tested. Before irrigation, the moisture content in each pot was measured using a Lutron Professional Soil Moisture Meter (PMS-714), and the amount of irrigation in each round was determined based on the amount of moisture deficiency up to the field capacity (FC). The central square design is one type of response surface method. In this method, independent variables are determined to determine the predicted dependent variable through an experimental design. This design considers the average levels of the factors as the central point. Using this method, the experimental treatments are displayed as +1, zero, and ‒1, which represent the highest, average, and lowest levels of the independent variable, respectively. Using regression analysis of variance, linear terms, quadratic terms, and interactions between factors were added to the multivariate regression model to evaluate the model-data fit. Finally, the significance of the model and its accuracy in fitting the data were determined. To compare the obtained model results with observed values, the root mean square error (RMSE), normalized root mean square error (NRMSE), mean bias error (MBE), efficiency factor (EF), agreement index (d), and the coefficient of determination (R²), were used.
 
Results and Discussion
Variance analysis showed that the regression model for water productivity was statistically significant at the five percent probability level (P-value≤0.05) and for the other traits studied at the one percent probability level (P-value≤0.01). In contrast, quadratic regression was statistically significant only for root weight, root length, shoot weight, essential oil percentage, and water productivity traits. The regression of other traits was not statistically significant. Therefore, the RSM cannot be used to predict and optimize these traits. Based on the lack of significance of the lack of fit test, the results of regression analysis are reliable compared to variance analysis. The RSM was also confirmed to be effective in optimizing the traits studied. The overlapping map of the investigated parameters was prepared to determine the optimal limit and common surface. In the upper range of this map, which includes the most irrigation intervals and super absorbent consumption; parameters such as water productivity do not change much. This parameter reaches its maximum value in the center of the map. Generally, other parameters tend to reach the optimal limit within the range of the bottom right part of the map, so, to optimize the parameters of root weight, root length, shoot weight, essential oil percentage, and water productivity, their target values were determined as 1.1 kg m^-2, 3 cm, 2 kg m^-2, 3 %, and 4 kg m^-3.
 
Conclusion
The effects of different irrigation intervals (three levels of two, four, and six days) and Aquasource super absorbent (three levels of zero, one, and two %W of super absorbent/soil) were examined on some peppermint plant traits. Results showed that the response-surface model did not significantly differ from statistical methods. As a result, it is possible to trust the results obtained. The traits of root weight and length, shoot weight, essential oil percentage, and water productivity were used in the RSM, and all other traits were found to increase with an increase in irrigation water, except for essential oil percentage and water productivity. In terms of essential oil percentage and water productivity, the reduction in irrigation intervals to +0.8 levels had an upward trend and then it declined afterward. Increasing the amount of super absorbent negatively affected the characteristics of root weight and length, shoot weight, and essential oil percentage. As the amount of super absorbent was increased to a range of -0.3, water productivity increased, and then the value of this parameter also decreased. As a result of these conditions, the RSM was effectively used to optimize the irrigation interval and super absorbent amount, and it was determined that the best conditions were obtained by utilizing a three-day irrigation interval with a super absorbent concentration of 0.3%. Therefore, compliance with these conditions is recommended for peppermint cultivation.