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 p...

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Bibliographic Details
Published in:Scientific reports Vol. 15; no. 1; pp. 30087 - 19
Main Authors: Hajirad, Iman, Ahmadaali, Khaled, Liaghat, Abdolmajid
Format: Journal Article
Language:English
Published: London Nature Publishing Group UK 17.08.2025
Nature Publishing Group
Nature Portfolio
Subjects:
631/449/2653
639/705
Agricultural Irrigation
Agricultural practices
Agricultural production
Agriculture
Arid zones
Calibration
Corn
Crop management
Crop modelling
Crop yield
Crops, Agricultural - growth & development
Deficit irrigation
Efficiency
Environmental conditions
Farming systems
Gompertz
Growth models
Humanities and Social Sciences
Irrigation
Irrigation management
Logistic
Models, Biological
multidisciplinary
Nonlinear Dynamics
Plant growth
Precision agriculture
Productivity
Science
Science (multidisciplinary)
Semiarid zones
Silage
Sustainable agriculture
Sustainable practices
Water
Water - metabolism
Water requirements
Zea mays - growth & development
Irrigation management
Deficit irrigation
Crop modelling
Logistic
Gompertz
ISSN:2045-2322, 2045-2322
Online Access:Get full text
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Summary: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 (W 2 and W 3 , providing 60% and 80% of crop water requirements, respectively) and full irrigation (W 1 , 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.
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ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-025-16096-0