Crop yield and water productivity modeling using nonlinear growth functions

Growth curve modeling plays a crucial role in precision agriculture by enabling rapid analysis of plant growth dynamics. Understanding the complex mechanisms of crop growth is essential for optimizing agricultural productivity. In this study, nonlinear Logistic and Gompertz models were employed to predict biological yield and water productivity of silage maize in arid and semi-arid regions, using growing degree days (GDD) as a key predictor. The experiment included two primary irrigation regimes: deficit irrigation (W₂ and W₃, providing 60% and 80% of crop water requirements, respectively) and full irrigation (W₁, providing 100%). A sigmoid model was also introduced for its ease of biological interpretation. To evaluate model performance, coefficient of determination (R²), normalized root mean square error (NRMSE), and mean absolute percentage error (MAPE) were used. Results indicated that Logistic and Gompertz models achieved high accuracy, with R² exceeding 99% under pulse irrigation and 80% under continuous irrigation. These models revealed that the maximum biological yield rate occurred at GDD equal 1014 °C (50 days after planting). Furthermore, the absolute growth rate followed a bell-shaped pattern in the Logistic model and a right-skewed distribution in the Gompertz model. The findings confirm that Logistic and Gompertz models effectively simulate the dynamic growth of silage maize under varying irrigation and temperature conditions. These models not only facilitate quantitative crop growth predictions but also provide a decision-support tool for irrigation planning and precision crop management in arid and semi-arid regions. The integration of such models into smart agricultural systems can significantly enhance resource optimization and sustainable farming practices.