Evaluation of Grade 3, Logarithmic and Exponential Production Functions in Different Irrigation Scenarios for Winter Wheat and Barley

Water-crop production functions indicate an increase or a decrease in harvest for the plant’s consumed water (evaporation-respiration). To assess production functions of wheat and barley products, linear and second-order methods are used in numerous researches. On the other hand, since the mentioned relationships for some products may not have an acceptable correlation, third-order, logarithmic, and polynomial functions are used in various deficit irrigation treatments of 50, 60, 70, 80, and 90 percent.

Farm data were evaluated and validated with resulted data from discussed equations. In order to study the proposed functions, statistical indices such as root mean square error (RMSE), normalized root mean square error (NRMSE), mean absolute error (MAE), Wilmott index (d), and F-test were used via measurement data in every scenario.

All statistic values of both winter wheat and barley were in permissible range, indicating properness and acceptance of the equations. All functions were acceptable at a significance level of 5 percent for both products. According to the results of studying irrigation depth in terms of winter wheat and barley yield, it can be argued that third-order functions provide more accurate prediction in comparison with logarithmic and polynomial functions in both winter wheat and barley crops, and therefore, third-order function is prioritized over other functions