Analysis of Drought Dynamics Using the SPEI Index and the Markov Chain Model (Case Study: Mashhad Synoptic Weather Station)

Document Type : Applied Article

Authors

Hosein Jahangiri ¹

Mehdi Jabbari Nooghabi ²

Nafise Seyednejad Gol Khatmi ³

¹ Department of Water Science and Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.

² Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

³ Graduate in Water Science and Engineering, Agricultural Meteorology, Faculty of Agriculture, University of Tehran, Karaj, Iran.

https://doi.org/10.22067/jwsd.v12i4.2509-1459

Abstract

Drought, as a natural and creeping phenomenon, is considered one of the most important climate challenges in arid and semi-arid regions, including Iran. Given the context of climate change and the increased severity of drought events, a dynamical analysis is crucial for effective water resource management. This study aimed to investigate the probabilistic behavior and drought dynamics within the Mashhad Plain. To achieve this, the Markov Chain model was applied to a 127-year time series of precipitation and mean temperature data. The core innovation lies in employing the Twelve-Fold Hydrologic Time Series method. By analyzing the data across twelve annual time scales, this approach facilitated a more comprehensive and precise characterization of drought features, effectively revealing long-duration events often masked in conventional annual analyses. The results derived from the transition probability matrix indicated that extreme climatic states (severe drought and extreme wet periods) exhibit significant persistence, whereas intermediate states (moderate drought and moderate wet periods) are inherently more transient. Furthermore, the calculation of the steady-state distribution provided a clear perspective on the long-term behavior of the climatic system. The findings reveal that, in the long run, the combined probability of residing in drought states (severe and moderate), totaling 42%, is higher than the probability of residing in wet states (38%). These results yield invaluable insights for strategic, long-term planning in water resource management and facilitate effective adaptation strategies against future climatic conditions in arid and semi-arid regions.

Keywords

Drought

Stationary Distribution

Transition Probability Matrix

SPEI Index

Markov Chain

Subjects

• Surface and Groundwater Resources

---

References

بذرافشان، ام‌البنین، محمودزاده، فوزیه، عسگری‌نژاد، امین، و بذرافشان، جواد. (1398). مقایسه تطبیقی شاخص‌های SPI، RDI  و SPEI در تحلیل روند شدت، مدت و فراوانی خشک‌سالی در مناطق خشک و نیمه خشک ایران. علوم مهندسی و آبیاری، 42(3)، 131-117. https://doi.org/10.22055/jise.2017.22113.1585

سلاجقه، علی، نجفی حاجی‌ور، منصور، و فتح‌آبادی، ابوالحسن. (1388). تحلیل خشکسالی با استفاده از شاخص SPI و زنجیره مارکف (مطالعه موردی: استان چهار محال و بختیاری). همایش ملی علوم و مهندسی آبخیزداری ایران (مدیریت پایدار بلایای طبیعی). دانشگاه علوم کشاورزی و منابع طبیعی گرگان، گرگان، ایران. https://sid.ir/paper/817138/fa

فرزندی، محبوبه، ثنایی‌نژاد، سیدحسین، قهرمان، بیژن، و سرمد، مجید. (1398). ترمیم داده‌های مفقود هواشناسی با روش‌های تکاملی و یادگیری ماشین مطالعه موردی: بارش و دمای ماهانه درازمدت مشهد. آب و خاک (علوم و صنایع کشاورزی)، 33(2)، 377-361. https://doi.org/10.22067/jsw.v33i2.74125

فرزندی، محبوبه، و رضایی‌پژند، حجت. (1400). معرفی روش MICE در ترمیم داده‌های گمشده هواشناسی و مقایسه با رگرسیون؛ مطالعه موردی: 130 سال دمای ماهانه مشهد، جاسک و بوشهر. آب و توسعه پایدار، 8(3)، 42-31. https://doi.org/10.22067/jwsd.v8i3.2104.1038

قربانی، خلیل، ولی‌زاده، اسماعیل، و برارخان‌پور، صدیقه. (1397). بررسی روند تغییرات مکانی-زمانی شاخص دومتغیره خشکسالی هواشناسی SPEI در ایران. مدیریت بیابان، 6(11)، 38-25. https://doi.org/10.30488/ccr.2023.375498.1107

مقیمی، محمدمهدی.، کوهی، امیر، و زارعی، عبدالرسول. (1397). پایش و پیش‌بینی وضعیت خشکسالی در استان فارس با استفاده از شاخص RDI و مدل ریاضی زنجیره مارکف. فصلنامه علمی و پژوهشی مهندسی آبیاری و آب ایران، 8(3)، 165-153.

مصطفی‌زاده، رئوف، و ذبیحی، محسن. (1395). تحلیل و مقایسه شاخص‌های SPI و SPEI در ارزیابی خشک‌سالی هواشناسی با استفاده از نرم‌افزار R (بررسی موردی: استان کردستان). مجله فیزیک زمین و فضا، 42(3)، 633-643. https://doi.org/10.22059/jesphys.2016.57881

Alam, N. M., Sharma, G. C., Moreira, E., Jana, C., Mishra, P. K., Sharma, N. K., & Mandal, D. (2017). Evaluation of drought using SPEI drought class transitions and log-linear models for different agro-ecological regions of India. Physics and Chemistry of the Earth, Parts a/b/c, 100, 31-43. https://doi.org/10.1016/j.pce.2017.02.008

Ansori, A., Sulistiyono, H., & Yasa, I. W. (2024). Study of drought using the theory of run and hydrological drought index and its relationship to reservoir storage at the Batujai Dam and Pengga Dam. RESEARCH REVIEW International Journal of Multidisciplinary, 9(7), 116-127. https://doi.org/10.31305/rrijm.2024.v09.n07.016

Avilés, A., Célleri, R., Solera, A., & Paredes, J. (2016). Probabilistic forecasting of drought events using Markov chain-and Bayesian network-based models: A case study of an Andean regulated river basin. Water, 8(2), 37. https://doi.org/10.3390/w8020037

Azimi, S., Hassannayebi, E., Boroun, M., & Tahmoures, M. (2020). Probabilistic analysis of long-term climate drought using steady-state Markov chain approach. Water Resources Management, 34(15), 4703-4724. https://doi.org/10.1007/s11269-020-02683-5

Grimmett, G., & Stirzaker, D. (2020). Probability and random processes. Oxford university press, NewYork, USA.

Levin, D. A., & Peres, Y. (2017). Markov chains and mixing times (Vol. 107). USA. https://doi.org/10.1090/mbk/107

Mondal, A., Kundu, S., & Mukhopadhyay, A. (2012). Rainfall trend analysis by Mann-Kendall test: A case study of north-eastern part of Cuttack district, Orissa. International Journal of Geology, Earth and Environmental Sciences, 2(1), 70-78. 13USGS.

Norris, J. R. (1998). Markov chains (No. 2). Cambridge university press. https://doi.org/10.1017/CBO9780511810633

Sheffield, J., & Wood, E. F. (2008). Projected changes in drought occurrence under future global warming from multi-model, multi-scenario, IPCC AR4 simulations. Climate dynamics, 31(1), 79-105.

Spinoni, J., Naumann, G., & Vogt, J. V. (2017). Pan-European seasonal trends and recent changes of drought frequency and severity. Global and Planetary Change, 148, 113-130. https://doi.org/10.1016/j.gloplacha.2016.11.013

Trenberth, K. E., Dai, A., Van Der Schrier, G., Jones, P. D., Barichivich, J., Briffa, K. R., & Sheffield, J. (2014). Global warming and changes in drought. Nature Climate Change, 4(1), 17-22.https://doi.org/10.1038/nclimate2067

Vicente-Serrano, S. M., Beguería, S., & López-Moreno, J. I. (2010). A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index. Journal of climate, 23(7), 1696-1718. https://doi.org/10.1175/2009JCLI2909.1

Vivekanandan, N. (2024). Trend analysis of rainfall data using mann-kendall test and sen's slope estimator. i-Manager's Journal on Civil Engineering, 14(2), 18. https://doi.org/10.26634/jce.14.2.21074

Wald, A., & Wolfowitz, J. (1940). On a test whether two samples are from the same population. The Annals of Mathematical Statistics, 11(2), 147-162.

Wang, L., Zhang, X., Wang, S., Salahou, M. K., & Fang, Y. (2020). Analysis and application of drought characteristics based on theory of runs and copulas in Yunnan, Southwest China International Journal of Environmental Research and Public Health, 17(13), 4654. https://doi.org/10.3390/ijerph17134654

Yan-Jun, L. I., Xiao-dong, Z. H. E. N. G., Fan, L. U., & Jing, M. A. (2012). Analysis of drought evolvement characteristics based on standardized precipitation index in the Huaihe River basin. Procedia Engineering, 28, 434-437. https://doi.org/10.1016/j.proeng.2012.01.746

Zarei, A. R. (2018). Evaluation of drought condition in arid and semi-arid regions, using RDI index. Water Resources Management, 32(5), 1689-1711. https://doi.org/10.1007/s11269-017