Analyzing precipitation variability in major cities of Iran using continuous wavelet transform

Introduction
In recent years, the impacts of climate change on water security have been extensively investigated. Evidence suggests that climate change alters precipitation and temperature patterns, thereby affecting access to water resources (Ahmed and Akter, 2024). These changes influence not only the quantity but also the quality of water (Van Vliet et al, 2023). Particularly in urban areas, variability in monthly precipitation and climatic fluctuations is considered one of the key challenges of the 21st century. In Iran, due to its arid and semi-arid climate, water resource management and precipitation pattern analysis hold special importance (Modarres and Sarhadi, 2009). International studies have shown that water accessibility indicators are most sensitive to precipitation variability (Barbosa et al, 2023). Moreover, changes in evapotranspiration can reduce net primary production, thereby influencing water security (Gao et al, 2023). The resilience of water systems has also gained attention; increasing resource diversity and managing demand can enhance resilience against climate change (Kharrazi et al, 2024; Srinivasan et al, 2024). In terms of scenario analysis, recent studies using machine learning reveal that even minor climate variations can significantly impact water security indices (Chen et al, 2024). In Iran, numerous studies have examined precipitation trends. Talaei and Tabari (2011) analyzed annual and seasonal precipitation at 41 stations between 1966 and 2005, reporting a decreasing trend in about 60% of them. Similarly, Modarres et al. (2009), based on 145 rain gauge stations, identified decreasing annual precipitation in more than half of the stations and increasing 24-hour maximum precipitation in others. These findings indicate early manifestations of climate change in Iran. Theoretically, water security is a multidimensional concept encompassing access, quality, and resilience of water resources, requiring interdisciplinary and integrated analyses. Advanced statistical and computational methods such as hydrological modeling, machine learning, and wavelet transforms provide deeper insights into climate variability and precipitation patterns. However, the application of wavelet transform in climate data analysis in Iran, especially in urban areas, remains limited. The aim of this study is to investigate the variability of monthly precipitation in urban areas of Iran using continuous wavelet transform (CWT). Adopting a multiscale approach, the study analyzes temporal-spatial precipitation trends, identifies hidden patterns, and explores periodic variations across different time scales. The novelty of the research lies in employing wavelet analysis for detailed examination of precipitation data, thereby offering deeper insights into the impacts of climate change on precipitation behavior in Iran.
Materials and Methods
 
This study analyzes the variability of monthly precipitation in Iran with a focus on nine synoptic stations located in Tehran, Mashhad, Isfahan, Tabriz, Karaj, Kermanshah, Arak and Ahvaz. The selection of these stations was based on the availability of long-term and continuous data, appropriate geographical distribution, and representation of the country’s diverse climatic conditions. The study period from 1980 to 2020 was considered in order to cover extreme climatic fluctuations, including both dry and wet years, and to enable the assessment of long-term precipitation trends. The stations represent different climatic regimes: Tehran, Karaj, Kermanshah, and Arak are situated in a semi-arid climate with annual precipitation ranging from 250 to 500 mm, with rainfall occurring mainly in winter and spring. Mashhad and Tabriz, characterized by mountainous and semi-arid climates, experience higher winter precipitation, and precipitation variability in these regions is greater due to elevation and geographical factors. Isfahan has an arid and low-rainfall climate, while Ahvaz, located in a relatively dry and lowland region, further enriches the climatic diversity and allows for examining the influence of different climates on precipitation patterns. Monthly precipitation data were obtained from the Iran Meteorological Organization and underwent preprocessing, including the identification and replacement of missing data, removal of outliers, assessment of inhomogeneities, and normalization. Data validation was performed using statistical tests such as Pettitt, Mann-Kendall, and SNHT to ensure quality and continuity. Data analysis was carried out using Continuous Wavelet Transform (CWT) with the Morlet wavelet to explore simultaneous variations in the time–frequency domain. Wavelet power spectra were generated to identify periods with high precipitation energy, and the Cone of Influence (COI) was used to minimize boundary effects. The wavelet analysis results were validated against independent datasets and previous studies to ensure the reliability of the identified patterns. By applying the wavelet approach, this study provides a detailed temporal–spatial analysis of precipitation trends in urban areas of Iran and offers practical insights for water resources management under climate change conditions. Furthermore, the results can support decision-making in drought and flood risk management across different regions of the country. Identifying precipitation cycles at medium- and long-term scales can also play a crucial role in agricultural planning, dam management, and water resources development projects. Ultimately, the wavelet-based methodology presented here can serve as a model for similar studies in other regions of Iran and countries with comparable climatic conditions.
 
Results and Discussion
Wavelet analysis of precipitation data at the Isfahan, Ahvaz, Arak, Tehran, Mashhad, Karaj, Tabriz and Kermanshah stations showed that seasonal and multi-year precipitation patterns are accompanied by distinct fluctuations. At the Isfahan station, short-term seasonal patterns of about one year exhibited strong fluctuations; the minimum variability occurred in summer, while the maximum seasonal variability was observed in winter and autumn. In the multi-year cycles, the highest fluctuations occurred in the 3–4 year and 8–10 year periods. The intensity of the wavelet coefficients fluctuated across different scales from 1980 to 2005, and from 2008 to 2020 greater intensity and strength were observed at both short (seasonal) and long (multi-year) scales, indicating climate change in recent decades. At the Ahvaz station, the seasonal and multi-year precipitation patterns were irregular, but the amplitude of the fluctuations was smaller compared to high-altitude stations. The temporal analysis over the period 1980–2020 showed that the intensity of the wavelet coefficients increased in the second half of the study period, and fluctuations in seasonal, annual, and multi-year cycles continued, which is not a direct reflection of climate change but is consistent with precipitation patterns at other stations. At the Arak station, seasonal patterns exhibited strong periodicity with frequent short-term fluctuations. Multi-year cycles occurred with high intensity and were influenced by large-scale atmospheric patterns. The analysis of the period from 1980 to the first decade of the 21st century showed that the wavelet coefficients at different scales were significantly associated with precipitation variability, and short-term and multi-year variations became more pronounced under climatic transformations in the second decade of the century. At the Tehran station, one-year seasonal patterns coexisted with multi-year cycles, and the yellow and light green areas on the wavelet spectrum indicated seasonal fluctuations. Multi-year cycles of 2–4 years and 5–10 years were observed with high power, likely associated with large-scale climatic phenomena such as ENSO. Decadal changes from the early 1980s to 2010 reflected stronger or weaker variability in the intensity of the wavelet coefficients, and after 2010 a marked increase in the strength of both short- and long-term scales was observed. At the Mashhad station, seasonal and annual precipitation patterns showed distinct fluctuations during autumn and winter. Multi-year cycles of 2–5 years and 6–10 years also exhibited significant variability. The intensity of the wavelet coefficients increased from 1980 to 2010, reflecting the influence of multiple climatic factors and climate change on precipitation behavior. The Karaj station, with its arid and semi-arid climate, showed minimum 
seasonal variability in summer and maximum in autumn and winter. Longer multi-year cycles, especially those of 2–3 years and 5–10 years, occurred with high intensity. From 2010 to 2020, however, the intensity of fluctuations decreased. At the Tabriz station, precipitation was more intense and frequent in winter and autumn, while summer showed weaker variability. Multi-year cycles of 2–4 and 6–10 years displayed considerable fluctuations, and the intensity of the wavelet coefficients increased from 1980 to 2020. The Kermanshah station had strong fluctuations in winter and autumn and weaker ones in summer and spring. Multi-year cycles between 2–5 and 6–10 years were observed, and the intensity of the wavelet coefficients increased after 2010. Comparison with previous studies indicated that this research, by applying wavelet analysis, examined precipitation cycles with greater accuracy and analyzed seasonal and multi-year fluctuations in several major Iranian cities. In addition to ENSO, the NAO and MO climate indices were also investigated. The results are consistent with similar international studies in Europe, China, and the Indian subcontinent, but the focus on Iran’s arid climate and the spatial diversity of large cities provides an innovative perspective. Overall, wavelet analysis showed that short- and long-term precipitation fluctuations with varying intensities are evident in most stations. Stations such as Kermanshah, Tabriz, and Mashhad exhibited high-intensity wavelet coefficients in 2–10 year cycles and were influenced by large-scale climatic indices, while stations such as Ahvaz and Karaj displayed relatively uniform behavior. The increase in wavelet coefficient intensity during 2008–2020 indicates the impact of recent climate changes on precipitation patterns. Furthermore, the results of this study revealed that the intensity and extent of precipitation variability in recent decades have been accompanied by greater fluctuations. Comparative analysis among stations demonstrated that geographical location and elevation play a decisive role in the strength of seasonal and multi-year cycles. In addition, the observed trends can be applied in the management of urban and rural water resources and in the development of climate adaptation strategies. The findings also showed that integrating wavelet analysis with large-scale climate indices increases the accuracy of identifying precipitation cycles. In conclusion, this study provides a comprehensive picture of precipitation behavior in Iran and establishes a valuable foundation for future research on climate change.
 
Conclusion
This study applied continuous wavelet transform (CWT) to analyze temporal variability of monthly precipitation in Iranian metropolitan areas from 1980 to 2020, identifying both seasonal and multi-annual cycles. Results showed precipitation patterns were influenced by annual cycles (~1 year) and multi-annual cycles (3–10 years). Strong oscillations were particularly evident in Tehran, Kermanshah, and Mashhad, coinciding with large-scale climate indices such as ENSO and NAO. In contrast, stations like Ahvaz, characterized by lower altitude and warmer conditions, showed weaker intensities and less regular oscillations, underscoring the importance of geographic factors such as elevation, temperature, and latitude in precipitation variability. The analysis further indicated that after 2010, precipitation variability intensified at both seasonal and multi-annual scales across most stations, serving as evidence of the increasing impacts of climate change. The findings are practically valuable for water resource management, drought and flood preparedness, as well as urban and agricultural planning. Furthermore, linking results to large-scale climate indices enhances the potential for predictive modeling and early warning systems.