Document Type : English paper for special issue on "climate change & insurance industry"

Authors

• Mohammad Amin Natanzi ¹
• hassan jabari ²

¹ IT Managment, Management and Accounting, Allameh Tabataba'i University, Tehran, Iran.

² Eco insurance managment, Eco insurance managment, Allameh Tabataba'i University, Tehran, Iran.

Abstract

SPEI Drought is one of the most critical climate-related hazards affecting Iran, with substantial consequences for agricultural production, water resources, and socio-economic stability. The predominance of arid and semi-arid climatic conditions, coupled with high interannual variability in precipitation and a sustained increase in temperature, has intensified both the frequency and severity of drought events across the country. Traditional drought assessments in Iran have largely relied on single drought indices and linear correlation measures, which are often inadequate for capturing the compound nature of drought processes driven by the simultaneous effects of precipitation deficits and increased atmospheric water demand.
In recent decades, temperature-driven evapotranspiration has emerged as a key driver of drought severity under climate change, highlighting the limitations of precipitation-only indicators such as the Standardized Precipitation Index (SPI). In this context, the Standardized Precipitation Evapotranspiration Index (SPEI), which explicitly incorporates potential evapotranspiration, provides a more comprehensive representation of drought conditions. However, understanding drought risk requires not only the analysis of individual indices but also the characterization of their joint behavior and dependence structure.
The primary objective of this study is to provide a probabilistic and multivariate assessment of drought risk across major climatic regions of Iran by jointly analyzing SPI and SPEI using copula theory. By modeling the dependence structure between these indices, the study aims to capture nonlinear and asymmetric relationships, particularly tail dependence associated with extreme drought events. In addition to advancing methodological understanding, the study seeks to demonstrate the relevance of copula-based drought modeling for practical applications in drought risk management, climate adaptation planning, and the conceptual development of index-based insurance schemes.
METHODS: This study is based on long-term climatic observations from synoptic meteorological stations distributed across Iran, covering the period 1981–2020. Monthly precipitation and temperature data were used to compute SPI and SPEI at multiple accumulation time scales, enabling the assessment of both short-term and long-term drought conditions. The calculation of SPEI incorporated potential evapotranspiration to account for the influence of rising temperatures on drought intensity.
Marginal probability distributions of SPI and SPEI were fitted using the Maximum Likelihood Estimation (MLE) method. Several copula families—including Gaussian, Student-t, Clayton, and Gumbel—were evaluated to model the dependence structure between the two indices. These copulas were selected to represent a wide range of dependence behaviors, including symmetric dependence, tail dependence, and asymmetric lower- or upper-tail dependence. Model selection was conducted using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and goodness-of-fit tests.
Lower- and upper-tail dependence coefficients were estimated to quantify the likelihood of concurrent extreme drought conditions. Joint probabilities and return periods of severe and extreme drought events were derived from the fitted copula models for different climatic regions of Iran. These probabilistic measures were further examined in relation to historical drought occurrences to ensure consistency with observed drought behavior
FINDINGS: The results reveal pronounced spatial heterogeneity in drought characteristics and dependence structures across Iran. Arid and semi-arid regions, particularly the Central Plateau and eastern parts of the country, exhibit strong lower-tail dependence between SPI and SPEI, indicating a high likelihood of concurrent extreme drought conditions driven by both precipitation deficits and elevated evaporative demand. In these regions, the Clayton copula consistently provided the best fit, reflecting its ability to capture asymmetric lower-tail dependence relevant to severe drought events.
In contrast, humid regions along the Caspian coast display weaker dependence structures and longer drought return periods, with limited evidence of strong tail dependence. Transitional climatic zones were better represented by the Student-t copula, which captures symmetric tail dependence and intermediate drought behavior. Estimated joint probabilities and return periods indicate that severe compound droughts recur approximately every 14–20 years in arid regions, while recurrence intervals exceed 50 years in northern humid areas. These findings are consistent with documented historical drought events in Iran, including major drought episodes in the early 1970s, late 1990s, and late 2010
CONCLUSION: The findings contribute to a probabilistic characterization of drought risk in Iran and provide a quantitative basis for understanding compound drought behavior. While this study does not develop a full actuarial pricing framework, the results may support future applications in drought risk management and the conceptual design of index-based insurance and climate adaptation strategies
By integrating multivariate drought indices with copula-based dependence modeling, this study demonstrates the importance of moving beyond univariate and correlation-based approaches in drought risk assessment. The results highlight the increasing role of temperature-driven evapotranspiration under climate change and underscore the value of SPEI-based analyses in warming environments. Overall, the proposed framework offers a robust, flexible, and policy-relevant tool for assessing drought risk in Iran and provides a scientific foundation for future efforts aimed at enhancing climate resilience, improving agricultural risk management, and supporting the development of innovative risk transfer mechanisms

Keywords

• Drought Risk
• - Iran
• - Copula Models
• -SPI-
• SPEI
• -Copula Models