Sensitivity Analysis of Rainfed Wheat Yield to Climatic Indices Using The Interpretable Xgboost–SHAP Model Under Climate Change Conditions: Zanjan Province Case Study

Document Type : Research Paper

Authors

• sajjad Asgary ¹
• Zahra Aghashariatmadari ²

¹ irrigation and reclamation engineering, agricultural and forest meteorology, University of tehran

² Associate Prof., Irrigation & Reclamation Engrg. Dept. University of Tehran Karaj, Iran.

Abstract

Keywords

• Length of Growing Period
• Effective Rainfall
• Rainfall Distribution Pattern
• Trend Analysis
• Machine Learning

Main Subjects

• ...

Introduction

Rainfed wheat (Triticum aestivum L.) in semiarid regions is highly sensitive to climate variability, and extreme temperatures along with changing precipitation patterns threaten its yield. Accurate analysis of the climate–yield relationship, identification of key influencing indices, and determination of optimal and limiting ranges for rainfed wheat yield are essential. Many previous studies relied on annual or fixed-season climate averages, which overlooked actual crop exposure during the true growing period (GP). To address these limitations, this study calculated all climatic indices exclusively for the real GP of rainfed wheat across three major production districts in Zanjan Province, Iran (Zanjan, Khodabandeh, and Khorramdarreh). The objectives were to: (i) identify key climatic factors driving yield variability, (ii) determine their location-specific optimal and limiting ranges, and (iii) provide actionable insights for targeted adaptation strategies.

Materials and Methods

This study aimed to assess the sensitivity of rainfed wheat yield to climatic indices over the period 1990–2023 across three representative stations in Zanjan Province, Iran — Zanjan, Khodabandeh, and Khorramdarreh. The Extreme Gradient Boosting (XGBoost) algorithm, interpreted via SHapley Additive exPlanations (SHAP) values, was employed to identify the most influential climatic variables and to determine their optimal and yield-limiting thresholds. The relationship between key climatic indices and dryland wheat yield was evaluated using this advanced machine‑learning model. The research methodology comprised four main steps: (i) estimation of the length of the growing period (LGP) based on the updated FAO guidelines, (ii) aligning all datasets with the actual plant growing period, (iii) analyzing the temporal distribution of climatic indices, and (iv) performing an interactive and interpretable climatic index analysis. This approach enabled the identification of location‑specific key variables, quantification of their optimal ranges, and improved understanding of regional yield variability.

Results and Discussion

In this analysis, the influential variables for each region were identified, and their optimal and limiting ranges—as well as thresholds—were quantified, providing clearer insight into the drivers of yield variability at the regional scale. Across all three study regions, both rainfed wheat yield and the length of the growing period (LGP) showed increasing trends; however, the trend in Zanjan was not statistically significant (p > 0.1). At the regional scale, correlation analysis between yield and agro‑climatic indices during the growing period indicated that moisture‑related indices were more strongly associated with yield than thermal indices. This pattern was consistent with the XGBoost–SHAP results, which also highlighted the predominance of moisture variables in explaining yield variability.In all stations, the number of precipitation days () exhibited the highest positive correlation with yield. Neither thermal indices nor LGP were significantly correlated with yield in Zanjan or Khodabandeh. By contrast, in Khorramdarreh, mean minimum temperature(T ̅_min^GP, r = 0.52, p < 0.01) and mean growing period temperature  (, r = 0.37, p < 0.1) were both significantly and positively correlated with yield. The XGBoost–SHAP modeling outcomes broadly agreed with the linear correlation analysis, although differences arose in the ranking of dominant moisture related indices.This integrated approach identified effective rainfall (ER_GP  = 1.8–2.9 mm day⁻¹; mean daily rainfall during the growing period; threshold: 1.8 mm day⁻¹) in Khodabandeh, the number of precipitation days ( = 32–42 days; threshold: 32 days) in Zanjan, and the uneven rainfall index (UR_GP  ≥ 9.0 mm; hreshold: 9.0 mm) in Khorramdarreh as the primary determinants of yield. Moreover, ER_GP= 1.8–2.9 mm day⁻¹ in Khodabandeh, optimal rainfall distribution (UR/ER(GP) = 10.3–12.4), and optimal mean temperature ( = 9.0–9.2 °C) in Khorramdarreh emerged as the most influential factors enhancing yield. Conversely, shorter growing periods (LGP = 50–68 days) in Khodabandeh, uneven rainfall distribution (UR_GP  = 1.1–8.7 mm) in Khorramdarreh, and low  = 4–31 days in Zanjan were the main limiting factors.

Conclusion

This study demonstrated that rainfed wheat yield variability across the three regions is driven by a limited set of agro‑climatic indices, each with distinct optimal and limiting ranges. The identified thresholds — such as ER_GP, , and UR_GP — revealed that yield responses are inherently non‑linear and threshold‑dependent, which is a pattern clearly captured through the machine learning framework enhanced by SHAP interpretation. These findings highlight the necessity of region‑specific management strategies that align planting and water resource practices with the identified optimal climatic windows, thereby improving resilience and yield stability under variable climatic conditions.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Authors’ contributions

1. Asgary: Gathering the experimental data, Data curation, Software; Methodology; Investigation, Conceptualization, Methodology, Writing-Reviewing and Editing, Formal analysis, Analyzing the experimental data, *Z. Aghashariatmadari: Supervision, Investigation, Conceptualization, Methodology, Analyzing the experimental data, Validation, Visualization, Writing-Original draft preparation, Writing-Reviewing and Editing. All authors have read and agreed to the published version of the manuscript.All authors contributed equally to the conceptualization of the article and writing of the original and subsequent drafts.

Data Availability Statement

Data available on request from the author.

Acknowledgements

The research was supported by the University of Tehran. The authors would like to express their special thanks to the vice chancellor for research affairs.

Ethical considerations

The author avoided data fabrication, falsification, plagiarism, and misconduct.

Conflict of interest

All authors declare that they have no conflict of interest.