Shirazi et al. (2025) Predicting sugar beet leaf area index: evaluating performance of double sigmoid functions under different irrigation and plant density scenarios

Identification

• Journal: Scientific Reports
• Year: 2025
• Date: 2025-12-29
• Authors: Saba Hashempour Motlagh Shirazi, Fatemeh Razzaghi, Ali Shabani, Ali Shabani, Maryam Khozaei
• DOI: 10.1038/s41598-025-28713-z

Research Groups

• Water Engineering Department and Drought Research Center, School of Agriculture, Shiraz University, Shiraz, Iran
• Irrigation Department, Fasa University, Fasa, Iran

Short Summary

This study evaluated the performance of 15 double sigmoid functions to model sugar beet leaf area index (LAI) under various irrigation and plant density scenarios, identifying the Logistic-Richards and Hill-Hill functions as the most accurate for predicting LAI dynamics based on growing degree days and days after planting.

Objective

• To estimate the leaf area index (LAI) of sugar beet using 15 different double sigmoid functions under varying irrigation treatments and crop densities, for both direct sowing and transplant cultivation.
• To assess sugar beet LAI dynamics based on days after planting (DAP) and growing degree days (GDD).
• To select the best-performing double sigmoid functions for sugar beet LAI prediction.

Study Configuration

• Spatial Scale: Field experiments conducted at the Research Station, School of Agricultural, Shiraz University, Iran (16 km north of Shiraz).
• Temporal Scale: Two growing seasons (2017 for calibration, 2018 for validation).

Methodology and Data

• Models used: 15 double sigmoid functions, constructed from combinations of 7 singular sigmoid functions: Logistic, Gompertz, Richards, Weibull, Beta, Hill, and Von Bertalanffy.
• Data sources:
  • Leaf Area Index (LAI) measurements.
  • Depth of irrigation water.
  • Rainfall amount.
  • Mean daily air temperature for Growing Degree Days (GDD) calculation (base temperature = 2.6 °C).
  • Data obtained from previous studies by Khozaei et al. (2020, 2021).
• Experimental Design: Split-split plot experimental design in a complete randomized block framework with three replications.
  • Main plots: Three irrigation levels (100%, 75%, and 50% of full irrigation).
  • Subplots: Two planting methods (direct sowing and transplant cultivation).
  • Sub-subplots: Four plant density treatments (180,000, 135,000, 90,000, and 45,000 plants per hectare).
• Parameter Estimation: Coefficients of functions determined using Excel Solver (Generalized Reduced Gradient method) by minimizing the sum of square error (SSE).
• Statistical Evaluation: Normalized Root Mean Square Error (NRMSE), index of agreement (d), and Mean Residual Error (MRE).

Main Results

• The Logistic-Richards (LR) and Hill-Hill (HH) functions consistently demonstrated the best performance in modeling sugar beet LAI dynamics across various irrigation and plant density scenarios, for both direct sowing and transplant cultivation, using both GDD and DAP.
• For direct sowing calibration based on GDD, the Logistic-Richards function achieved the best performance (NRMSE = 0.04, d = 0.99, MRE = -0.006).
• For transplant cultivation calibration based on GDD, the Logistic-Hill function performed best (NRMSE = 0.06, d = 0.99, MRE = -0.004).
• In the validation phase (2018 data, GDD-based), the Logistic-Richards function was superior for direct sowing (R² = 0.98, NRMSE = 0.147, d = 0.98), while the Hill-Hill model was best for transplant cultivation (R² = 0.99, NRMSE = 0.127, d = 0.99, MRE = -0.05).
• Functions incorporating Von Bertalanffy, Weibull, or Beta components, especially as the initial stage of the double sigmoid, were generally not suitable for describing sugar beet LAI dynamics.
• Adjusting function coefficients to account for environmental factors (seasonal applied water, rainfall, plant density) generally led to a decrease in predictive accuracy during both calibration and validation phases.
• The Logistic-Richards model maintained robust fits under water stress conditions (NRMSE ranging from 0.03 to 0.09) and showed highest accuracy under full irrigation and high planting density (NRMSE = 0.008 at 180,000 plants per hectare).

Contributions

• This study provides a comprehensive evaluation of 15 double sigmoid functions for modeling sugar beet LAI, identifying the most robust and accurate empirical models (Logistic-Richards and Hill-Hill) for different cultivation methods and environmental conditions.
• It highlights the effectiveness of GDD as a time scale for LAI modeling, making the results more broadly applicable across different climates.
• The research demonstrates that simpler, transparent double sigmoid models can achieve high accuracy comparable to or exceeding complex process-based models, offering a computationally efficient alternative for precision agriculture in data-limited regions.
• The findings offer a reliable tool for estimating sugar beet LAI throughout the growing season, supporting optimized irrigation scheduling and planting density adjustments.

Funding

• Shiraz University (Grant #2GCB1M222407)
• Shiraz University Research Council
• Drought Research Center
• Center of Excellent for On-Farm Water Management
• Iran National Science Foundation (INSF)

Citation

@article{Shirazi2025Predicting,
  author = {Shirazi, Saba Hashempour Motlagh and Razzaghi, Fatemeh and Shabani, Ali and Shabani, Ali and Khozaei, Maryam},
  title = {Predicting sugar beet leaf area index: evaluating performance of double sigmoid functions under different irrigation and plant density scenarios},
  journal = {Scientific Reports},
  year = {2025},
  doi = {10.1038/s41598-025-28713-z},
  url = {https://doi.org/10.1038/s41598-025-28713-z}
}