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Estimation of return levels and associated uncertainties of extreme temperatures using a time-varying framework: a case study in Iran

  • Research Article - Atmospheric & Space Sciences
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Abstract

In recent decades, Iran has seen unprecedented extreme temperatures (ETs) in different climatic zones, resulting in significant shifts and inconsistencies in their distributions. So, estimating ETs and associated uncertainties within a non-stationary (NS) context becomes a crucial step in modeling of hydro-climatic events like floods, droughts etc. This study examines the time-varying evaluation of extreme hot and cold temperatures (EHTs and ECTs) at 12 weather stations in Kerman province, Iran. Moreover, two recently proposed methodologies are investigated: conditional and integrated (unconditional), for estimating return levels (RLs) and their corresponding confidence intervals (CIs) within a NS framework. Analyses were conducted using Generalized Extreme Value (GEV) distribution under two assumptions: stationary (S-GEV) and non-stationary (NS-GEV). The EHTs and ECTs time series from 1979 to 2019 underwent testing for trends, homogeneity, and stationarity. The maximum likelihood estimator (MLE) was adopted to estimate the distribution parameters. The NS impacts of EHTs and ECTs were quantified by calculating the difference between stationary and non-stationary RLs, denoted as SRL and NSRL, respectively. Analysis of trends and stationarity indicated that the EHTs and ECTs time series were non-stationary. The Akaike information criterion (AIC) favored the NS-GEV model over the S-GEV model. Our results demonstrated that NS-GEV frequency analyses have a growing impact on the RL for both EHTs and ECTs. One finding was that the visualization of conditional RL plots turned out to be a valuable approach to assess uncertainties in future scenarios; another that climatology (e.g. arid and excessive arid areas across Kerman) seems to influence shapes and features of RL in future outcomes. Our findings can significantly contribute to policy-making and strategic planning in water resource management, particularly in areas such as infrastructure development and risk assessment.

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Data availability

The station-based meteorological data have been prepared from the Iran Meteorological Organization(IMO) and after validation have been used. The CRU Tmax datasets were extracted from https://crudata.uea.ac.uk/cru/data.

Notes

  1. https://climateknowledgeportal.worldbank.org/country/iran-islamic-rep/climate-data-historical.

  2. https://www.climatestotravel.com/temperatures/iran

References

  • Akaike H (1974) A new look at the statistical model identification. EEE T Automat Contr 19(6):716–723

    Article  Google Scholar 

  • Aksu H (2021) Nonstationary analysis of the extreme temperatures in Turkey. Dynam Atmos Oceans 95:101238

    Article  Google Scholar 

  • Alizadeh-Choobari O, Najafi MS (2018) Extreme weather events in Iran under a changing climate. Clim Dyn 50(1):249–260

    Article  Google Scholar 

  • Anvari S, Moghaddasi M (2023a) Historical changes of extreme temperature in relation to soil moisture over different climatic zones of Iran. Stoch Env Res Risk Assess 38(1):157–173

    Article  Google Scholar 

  • Anvari S, Moghaddasi M (2023b) Exploring the effects of nonstationary and diverse covariates on extreme hot events. ECOPERSIA 11(4):275–289

    Google Scholar 

  • Anvari S, Moghaddasi M, Bagheri MH (2023) Drought mitigation through a hedging-based model of reservoir-farm systems considering climate and streamflow variations. Theoret Appl Climatol 152(1):723–737

    Article  Google Scholar 

  • Aziz R, Yucel I, Yozgatligil C (2020) Nonstationarity impacts on frequency analysis of yearly and seasonal extreme temperature in Turkey. Atmos Res 238:104875

    Article  Google Scholar 

  • Babaeian I, Karimian M, Modirian R, Mirzaei E (2019) Future climate change projection over Iran using CMIP5 data during 2020–2100. NIVAR 43(104–105):62–71

    Google Scholar 

  • Banerjee A, Dolado JJ, Galbraith JW, Hendry D (1993) Co-integration, error correction, and the econometric analysis of non-stationary data. Oxford University Press

    Book  Google Scholar 

  • Behzadi F, Javadi S, Hafezi S, Farahani E V, Golmohammadi G (2024) Flood risk projection in Iran using CMIP6 models and frequency analysis of precipitation. Stochast Environ Res Risk Assess 38(12):4843–4861. https://doi.org/10.1007/s00477-024-02835-8

    Article  Google Scholar 

  • Belzile LR, Dutang C, Northrop PJ, Opitz T (2023) A modeler’s guide to extreme value software. Extremes 26(4):595–638

    Article  Google Scholar 

  • Cannon AJ (2011) GEVcdn: An R package for nonstationary extreme value analysis by generalized extreme value conditional density estimation network. Comput Geosci 37(9):1532–1533

    Article  Google Scholar 

  • Cheng L, AghaKouchak A, Gilleland E, Katz RW (2014) Non-stationary extreme value analysis in a changing climate. Clim Change 127:353–369

    Article  Google Scholar 

  • Coles S (2001) An introduction to statistical modeling of extreme values. Springer-Verlag

    Book  Google Scholar 

  • Coles SG, Dixon MJ (1999) Likelihood-based inference for extreme value models. Extremes 2:5–23

    Article  Google Scholar 

  • Cooley, D. (2013). Return periods and return levels under climate change. In: Extremes in a Changing Climate, Ed. AghaKouchak A et al. Springer-Verlag.

  • Darand M (2020) Future changes in temperature extremes in climate variability over Iran. Meteorol Appl 27(6):e1968

    Article  Google Scholar 

  • De Martonne E (1926) Une nouvelle function climatologique: L’indice d’aridité [A New Climatological Function: The Aridity Index]. La Meteorologie 2:449–458

    Google Scholar 

  • Deville, Y. (2022). R package NSGEV. https://github.com/IRSN/NSGEV.

  • Dey, D., Roy, D., & Yan, J. (2016). Univariate extreme value analysis. In Extreme Value Modeling and Risk Analysis. Methods and Applications. CRC Press, Chapman & Hall

  • Doulabian S, Golian S, Toosi AS, Murphy C (2021) Evaluating the effects of climate change on precipitation and temperature for Iran using RCP scenarios. J Water Climate Change 12(1):166–184

    Article  Google Scholar 

  • Ebi KL, Vanos J, Baldwin JW, Bell JE, Hondula DM, Errett NA, Hayes K, Reid CE, Saha S, Spector J, Berry P (2021) Extreme weather and climate change: population health and health system implications. Ann Rev Public Health 42(1):293–315. https://doi.org/10.1146/annurev-publhealth-012420-105026

    Article  Google Scholar 

  • Ferreira A, De Haan L (2015) On the block maxima method in extreme value theory: PWM estimators. Ann Stat 43(1):276–298

    Article  Google Scholar 

  • Ganeshi NG, Mujumdar M, Krishnan R, Goswami M (2020) Understanding the linkage between soil moisture variability and temperature extremes over the Indian region. J Hydrol 589:125183

    Article  Google Scholar 

  • Gilleland E, Katz RW (2016) extRemes 2.0: an extreme value analysis package in R. J Stat Softw 72:1–39

    Article  Google Scholar 

  • Guannan H, Franzke CLE (2020) Evaluation of daily precipitation extremes in reanalysis and gridded observation‐based data sets over germany. Geophys Res Lett. https://doi.org/10.1029/2020GL089624

    Article  Google Scholar 

  • Hamdi Y, Duluc C-M, Rebour V (2018) Temperature extremes: estimation of non-stationary return levels and associated uncertainties. Atmosphere 9:129

    Article  Google Scholar 

  • Heffernan JE, Stephenson., A.G. (2018) ismev: An introduction to statistical modeling of extreme values. R Package Version 1:42

    Google Scholar 

  • Hesarkazzazi S, Arabzadeh R, Hajibabaei M, Rauch W, Kjeldsen TR, Prosdocimi I, Castellarin A, Sitzenfrei R (2021) Stationary vs non-stationary modelling of flood frequency distribution across northwest England. Hydrol Sci J 66(4):729–744. https://doi.org/10.1080/02626667.2021.1884685

    Article  Google Scholar 

  • Hosking JR (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc Ser B Stat Methodol 52(1):105–124

    Article  Google Scholar 

  • Hosking JRM, Wallis JR, Wood EF (1985) Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. Technometrics 27(3):251–261

    Article  Google Scholar 

  • Karpa O, Naess A (2013) Extreme value statistics of wind speed data by the ACER method. J Wind Eng Ind Aerodyn 112:1–10

    Article  Google Scholar 

  • Kendall MG (1975) Rank Correlation Methods. Oxford University Press, New York

    Google Scholar 

  • Kwiatkowski D, Phillips PC, Schmidt P, Shin Y (1992) Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? J Econometrics 54(1–3):159–178

    Article  Google Scholar 

  • Mansouri Daneshvar MR, Ebrahimi M, Nejadsoleymani H (2019) An overview of climate change in Iran: facts and statistics. Environ Syst Res 8(1):1–10

    Article  Google Scholar 

  • Mitchell TD, Jones PD (2005) An improved method of constructing a database of monthly climate observations and associated high-resolution grids. Int J Climatol A J Royal Meteorol Soc. 25(6):693–712

    Google Scholar 

  • Modarres R, Sarhadi A, Burn DH (2016) Changes of extreme drought and flood events in Iran. Global Planet Change 144:67–81

    Article  Google Scholar 

  • Moghaddasi M, Anvari S, Mohammadi T (2022a) Comparison of extreme value theory approaches in temperature frequency analysis (case study: Arak plain in Iran). Arab J Geosci 15(12):1–13

    Article  Google Scholar 

  • Moghaddasi M, Anvari S, Akhondi N (2022b) A trade-off analysis of adaptive and non-adaptive future optimized rule curves based on simulation algorithm and hedging rules. Theoret Appl Climatol 148(1):65–78

    Article  Google Scholar 

  • Mohamadi S, Mianabadi A, Anvari S (2024) Investigating the vegetation’s temporal–spatial response to meteorological and hydrogeological drought in drylands. Geoscience Data J 11(2):197–215

    Article  Google Scholar 

  • Mohammadi T, Moghaddasi M, Anvari S, Aziz R (2024) Estimation of non-stationary return levels of extreme temperature by CMIP6 models. Water Practice Technol 19(2):594–610

    Article  Google Scholar 

  • Nabavi E (2017) (Ground) Water governance and legal development in Iran, 1906–2016. Middle East Law and Governance 9(1):43–70

    Article  Google Scholar 

  • New M, Hulme M, Jones P (1999) Representing twentieth-century space–time climate variability. Part I: Development of a 1961–90 mean monthly terrestrial climatology. J Climate. 12(3):829–56

    Article  Google Scholar 

  • Parey S, Hoang TTH, Dacunha-Castelle D (2010) Different ways to compute temperature return levels in the climate change context. Environmetrics 21(7–8):698–718

    Article  Google Scholar 

  • Park JS (2005) A simulation-based hyperparameter selection for quantile estimation of the generalized extreme value distribution. Math Comput Simul 70(4):227–234

    Article  Google Scholar 

  • Pettitt AN (1979) A non-parametric approach to the change point problem. J R Stat Soc: Ser c: Appl Stat 28:126–135

    Google Scholar 

  • Raggad B (2018) Stationary and non-stationary extreme value approaches for modelling extreme temperature: the Case of Riyadh City. Saudi Arabia Environ Model Assess 23(1):99–116

    Article  Google Scholar 

  • Rashki A, Middleton NJ, Goudie AS (2021) Dust storms in Iran-Distribution, causes, frequencies and impacts. Aeol Res 48:100655

    Article  Google Scholar 

  • Raziei T (2022) Climate of Iran according to Köppen-Geiger, Feddema, and UNEP climate classifications. Theoret Appl Climatol 148(3):1395–1416

    Article  Google Scholar 

  • Rydén J (2011) Statistical analysis of temperature extremes in long-time series from Uppsala. Theoret Appl Climatol 105:193–197

    Article  Google Scholar 

  • Rydén J (2019) A note on analysis of extreme minimum temperatures with the GAMLSS framework. Acta Geophys 67:1599–1604

    Article  Google Scholar 

  • Rydén J (2024) Estimation of return levels with long return periods for extreme sea levels in a time-varying framework. Environ Syst Decisions 44:1019–1028

    Article  Google Scholar 

  • Sen PK (1968) Estimates of the regression coefficient based on Kendall’s Tau. J Am Stat Assoc 63(324):1379–1389

    Article  Google Scholar 

  • Slater LJ, Anderson B, Buechel M, Dadson S, Han S, Harrigan S, Kelder T, Kowal K, Lees T, Matthews T, Murphy C, Wilby RL (2021) Nonstationary weather and water extremes: a review of methods for their detection, attribution and management. Hydrol Earth Syst Sci 25(7):3897–3935

    Article  Google Scholar 

  • Stephenson AG (2002) Evd: extreme value distributions. R News. 2(2):31–2

    Google Scholar 

  • Stephenson A, Tawn J (2004) Bayesian inference for extremes: accounting for the three extremal types. Extremes 7:291–307

    Article  Google Scholar 

  • Thompson P, Cai Y, Reeve D, Stander J (2009) Automated threshold selection methods for extreme wave analysis. Coast Eng 56(10):1013–1021

    Article  Google Scholar 

  • Trenberth KE, Paolino DA (1980) The Northern Hemisphere sea-level pressure data set: trends, errors and discontinuities. Mon Wea Rev 108(7):856–872

    Article  Google Scholar 

  • Tu K, Yan Z (2021) Non-stationary climate changes in summer high-temperature extremes in Shanghai since the late 19th century. Int J Climatol 41:E718–E733

    Article  Google Scholar 

  • Vaghefi SA, Keykhai M, Jahanbakhshi F, Sheikholeslami J, Ahmadi A, Yang H, Abbaspour KC (2019) The future of extreme climate in Iran. Sci Rep 9(1):1464

    Article  Google Scholar 

  • Wang XL, Trewin B, Feng Y, Jones D (2013) Historical changes in Australian temperature extremes as inferred from extreme value distribution analysis. Geophys Res Lett 40(3):573–578

    Article  Google Scholar 

  • Whan K, Zscheischler J, Orth R, Shongwe M, Rahimi M, Asare EO, Seneviratne SI (2015) Impact of soil moisture on extreme maximum temperatures in Europe. Weather Climate Extremes 9:57–67

    Article  Google Scholar 

  • Wijngaard JB, Klein Tank AMG, Können GP (2003) Homogeneity of 20th century European daily temperatature and precipitation series. Int J Climatol 23:679–692

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge the Graduate University of Advanced Technology and support from the Swedish University of Agricultural Sciences; Faculty of Natural Resources and Agricultural Sciences.

Funding

Funding for JR: Swedish University of Agricultural Sciences; Faculty of Natural Resources and Agricultural Sciences.

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Authors and Affiliations

  1. Department of Ecology, Institute of Science and High Technology and Environmental Science, Graduate University of Advanced Technology, Kerman, Iran

    Sedigheh Anvari

  2. Unit of Applied Statistics and Mathematics, Department of Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden

    Jesper Rydén

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The material preparation and analysis were conducted by [Sedigheh Anvari] and [Jesper Rydén]. [Sedigheh Anvari] collected the data. Both authors contributed to the writing and final approval of the manuscript.

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Correspondence to Sedigheh Anvari.

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Edited by Dr. Ahmad Sharafati (ASSOCIATE EDITOR) / Prof. Theodore Karacostas (CO-EDITOR-IN-CHIEF).

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Anvari, S., Rydén, J. Estimation of return levels and associated uncertainties of extreme temperatures using a time-varying framework: a case study in Iran. Acta Geophys. (2025). https://doi.org/10.1007/s11600-025-01544-2

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