<p>Rainfed agriculture in semi-arid regions like East Azerbaijan Province, Iran, faces significant challenges due to climatic variability, necessitating robust risk assessment frameworks to inform sustainable management. This study employs a copula-based approach to model the multivariate dependence between rainfed wheat yield and key climatic variables (precipitation, temperature, and relative humidity) across East Azerbaijan Province. Using the Growing Degree Days (GDD) method, growing periods ranged from 250–296 days, with reference evapotranspiration (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({ET}_{0}\)</EquationSource> </InlineEquation>) estimated at 3.11–4.53 mm/day via Penman–Monteith-FAO56, crop evapotranspiration (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({ET}_{c}\)</EquationSource> </InlineEquation>) at 432–709 mm/growing period, and effective rainfall (FAO method) at 41–73 mm/growing period, highlighting substantial spatial variability in water availability. Best marginal distributions (Normal, Weibull, Cauchy) and multivariate copulas (Clayton for most stations, Gaussian for Tabriz) were selected based on AIC, BIC, and RMSE. From 27 scenarios derived from the 25th, 50th, and 100th percentiles of climatic variables, probabilities of below-average yields ranged from 0.92–29.99%, with return periods of 2–109 years. Low risks were observed under Scenario 1 (0.92% in Ahar, 109-year return period), while high risks occurred in scenarios with elevated temperature (Scenarios 18, 24, 26: up to 29.99% probability in Mianeh, 19.2-year return period). Spatial mapping revealed Ahar’s resilience and Mianeh’s vulnerability. Model robustness was confirmed through leave-one-out cross-validation (LOOCV; mean predictive log-likelihood: -2.51 to -4.22, highest in Mianeh) and bootstrap 95% confidence intervals for return periods, quantifying uncertainty from the limited record. These findings provide a framework for targeted interventions, emphasizing drought-tolerant cultivars and water-conservation practices to enhance rainfed wheat resilience.</p> Graphical Abstract <p>This research was conducted to quantify the multivariate dependence structure between rainfed wheat yield and key climatic variables (precipitation, temperature, and relative humidity) and to develop a probabilistic risk-assessment framework for rainfed wheat production in the East Azerbaijan Province, Iran. The work explicitly addresses the complex non-linear and tail dependencies that traditional correlation-based methods fail to capture in agro-climatic systems dominated by climatic extremes. Long-term historical records of wheat yield and growing-season climatic data from five representative meteorological stations (Ahar, Maragheh, Mianeh, Sarab, and Tabriz) were used. Kendall’s tau rank correlation was first applied to identify the direction and strength of monotonic associations between yield and each climatic driver. Best-fit marginal distributions (Normal, Weibull, and Cauchy) were then selected for yield and climatic variables. Multivariate dependence structures were modelled using Archimedean and elliptical copulas, with final copula choice determined by Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Root Mean Square Error (RMSE). The Clayton copula proved superior for most stations due to its ability to capture lower-tail dependence—critical for reproducing concurrent occurrences of low precipitation/high temperature and yield failure. Twenty-seven realistic climatic scenarios were constructed from combinations of the 25th, 50th, and 100th percentiles of the three climatic variables, enabling estimation of conditional and joint probabilities of below-average yield and corresponding return periods. Spatial mapping revealed strong regional contrasts: Ahar exhibited remarkable resilience, whereas Mianeh emerged as highly vulnerable under adverse climatic combinations. The proposed copula-based framework provides a flexible, statistically robust, and spatially explicit tool for probabilistic yield-risk forecasting in rainfed wheat systems. The findings offer actionable insights for policymakers and agricultural planners in prioritizing drought-tolerant cultivars, optimizing sowing dates, and implementing targeted water-conservation measures in semi-arid regions under increasing climatic uncertainty.</p>

Copula-Based Mapping of Compound Climate Risks to Rainfed Wheat Yield in Semi-Arid Iran

期刊论文
发表日期：

2026年3月3日

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Pouya Allahverdipour,
Ahmad Fakheri-Fard

摘要

Rainfed agriculture in semi-arid regions like East Azerbaijan Province, Iran, faces significant challenges due to climatic variability, necessitating robust risk assessment frameworks to inform sustainable management. This study employs a copula-based approach to model the multivariate dependence between rainfed wheat yield and key climatic variables (precipitation, temperature, and relative humidity) across East Azerbaijan Province. Using the Growing Degree Days (GDD) method, growing periods ranged from 250–296 days, with reference evapotranspiration ( \({ET}_{0}\) ) estimated at 3.11–4.53 mm/day via Penman–Monteith-FAO56, crop evapotranspiration ( \({ET}_{c}\) ) at 432–709 mm/growing period, and effective rainfall (FAO method) at 41–73 mm/growing period, highlighting substantial spatial variability in water availability. Best marginal distributions (Normal, Weibull, Cauchy) and multivariate copulas (Clayton for most stations, Gaussian for Tabriz) were selected based on AIC, BIC, and RMSE. From 27 scenarios derived from the 25th, 50th, and 100th percentiles of climatic variables, probabilities of below-average yields ranged from 0.92–29.99%, with return periods of 2–109 years. Low risks were observed under Scenario 1 (0.92% in Ahar, 109-year return period), while high risks occurred in scenarios with elevated temperature (Scenarios 18, 24, 26: up to 29.99% probability in Mianeh, 19.2-year return period). Spatial mapping revealed Ahar’s resilience and Mianeh’s vulnerability. Model robustness was confirmed through leave-one-out cross-validation (LOOCV; mean predictive log-likelihood: -2.51 to -4.22, highest in Mianeh) and bootstrap 95% confidence intervals for return periods, quantifying uncertainty from the limited record. These findings provide a framework for targeted interventions, emphasizing drought-tolerant cultivars and water-conservation practices to enhance rainfed wheat resilience.

Graphical Abstract

This research was conducted to quantify the multivariate dependence structure between rainfed wheat yield and key climatic variables (precipitation, temperature, and relative humidity) and to develop a probabilistic risk-assessment framework for rainfed wheat production in the East Azerbaijan Province, Iran. The work explicitly addresses the complex non-linear and tail dependencies that traditional correlation-based methods fail to capture in agro-climatic systems dominated by climatic extremes. Long-term historical records of wheat yield and growing-season climatic data from five representative meteorological stations (Ahar, Maragheh, Mianeh, Sarab, and Tabriz) were used. Kendall’s tau rank correlation was first applied to identify the direction and strength of monotonic associations between yield and each climatic driver. Best-fit marginal distributions (Normal, Weibull, and Cauchy) were then selected for yield and climatic variables. Multivariate dependence structures were modelled using Archimedean and elliptical copulas, with final copula choice determined by Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Root Mean Square Error (RMSE). The Clayton copula proved superior for most stations due to its ability to capture lower-tail dependence—critical for reproducing concurrent occurrences of low precipitation/high temperature and yield failure. Twenty-seven realistic climatic scenarios were constructed from combinations of the 25th, 50th, and 100th percentiles of the three climatic variables, enabling estimation of conditional and joint probabilities of below-average yield and corresponding return periods. Spatial mapping revealed strong regional contrasts: Ahar exhibited remarkable resilience, whereas Mianeh emerged as highly vulnerable under adverse climatic combinations. The proposed copula-based framework provides a flexible, statistically robust, and spatially explicit tool for probabilistic yield-risk forecasting in rainfed wheat systems. The findings offer actionable insights for policymakers and agricultural planners in prioritizing drought-tolerant cultivars, optimizing sowing dates, and implementing targeted water-conservation measures in semi-arid regions under increasing climatic uncertainty.