Irrigation and Water Engineering

Irrigation and Water Engineering

A Hybrid Marcos Chain–Based Approach Integrating Shannon Entropy and Evidential Belief Function (EBF) Models for Analyzing Flood Hazard Dynamics: A Case Study of the Kela rud Watershed, Babol

Document Type : Original Article

Authors
Seyed Asadullah Hejazi 1
Masumeh Rajabi 2
Sabikeh Rohanizadeh 3
1 Associate Professor, Department of Geomorphology, Faculty of Planning and Environmental Sciences, University of Tabriz, Tabriz. Iran.
2 Professor of Geomorphology, Department of Geomorphology, Faculty of Planning and Environmental Sciences, University of Tabriz, Tabriz, Iran.
3 PhD Student in Geomorphology, Faculty of Planning and Environmental Sciences, University of Tabriz, Tabriz.Iran.
10.22125/iwe.2026.559343.1908
Abstract
The present study aimed to map and analyze the spatiotemporal dynamics of flood hazard in the Kalarud watershed, Babol (northern Iran), covering an area of 216 km². This basin, with an elevation range of 45–2272 m and an average slope of 19.46%, is among the flood-prone zones of the Central Alborz Mountains. To achieve a comprehensive assessment, a hybrid approach combining Shannon Entropy (SE), Evidential Belief Function (EBF), and Markov Chain (MC) models was applied to evaluate both spatial and temporal aspects of flood risk.

Nine conditioning factors—elevation, slope, slope aspect, drainage density, distance from rivers and roads, land use, soil, and Topographic Wetness Index (TWI)—were analyzed in a GIS environment. Results of the SE model indicated that elevation (0.1983), slope aspect (0.1517), and slope (0.1423) were the most influential factors. The EBF model confirmed the 48% cumulative weight of these variables, while the Markov Chain model was employed to forecast spatial changes in flood hazard from 2013 to 2030.

Model performance evaluation showed that EBF (AUC = 0.83, RMSE = 0.219) outperformed the Shannon model (AUC = 0.71, RMSE = 0.293), whereas the Markov model (AUC = 0.79) exhibited stable temporal behavior. Overall, 26.4% of the basin area falls within high and very high hazard classes, mainly encompassing the central and southern sectors, including the villages of Shiyadeh, Anjilek, and Lamsukola. The integrated EBF–Markov–SE framework effectively addresses spatial uncertainty and temporal dynamics, providing a reliable tool for flood risk management, watershed planning, and sustainable development in northern Iran.
Keywords
Flood Hazard Zoning
Shannon Entropy
Evidential Belief Function (EBF)
Marcos Chain
Hybrid Modeling
Subjects
    تقوایی سلیمی، س و باغی‌زاده، ا. (۱۴۰۲). ارزیابی خطر سیلاب با مدل‌های هیبریدی داده‌محور (EBF–SE–FR) در شمال ایران. مجله زمین‌شناسی مهندسی و محیط‌زیست ایران، ۱۲(۱)، ۵۴–۷۳.
    رحمتی، ا، زینی‌وند، ه و نادری، ن. (۱۴۰۱). مقایسه مدل‌های داده‌محور در پیش‌بینی پهنه‌های خطر سیلاب با استفاده از GIS. فصلنامه منابع آب ایران، ۱۸(۲)، ۱۴۲–۱۵۶.
     صالحی، م و عنایتی، ز. (۱۴۰۲). پهنه‌بندی خطرپذیری سیلاب با استفاده از مدل‌های آماری و GIS در حوضه نکا، مازندران. مجله جغرافیا و مخاطرات محیطی، ۱۱(۲)، ۹۱–۱۰۹.
       عابدی، ف.، حسینی، ر.، و رجبی، م. (۱۴۰۱). ارزیابی تغییرات زمانی خطر سیلاب با استفاده از مدل زنجیره مارکوس و منطق فازی، فصلنامه جغرافیای مخاطرات طبیعی، 12(3): 45–67.
   عرب‌عامری، ع ر، رضایی، ک، و پورقاسمی، ح ر. (۱۳۹۹). پهنه‌بندی خطر سیلاب با استفاده از مدل آنتروپی شانون و نسبت فراوانی در شمال ایران. مجله علوم زمین، ۲۹(۴)، ۲۳۵–۲۵۰.
کاظمی، ع و بغدادی، ر. (۱۴۰۰). تحلیل پویایی خطر سیلاب با مدل زنجیره مارکوس در حوضه طالقان. مجله اکوهیدرولوژی، ۷(۳)، ۶۴–۷۸.
    کاظمی، س.، شیرمحمدی، ع.، جعفری، س. (۱۳۹۷). مدل‌سازی تغییرات زمانی پوشش اراضی با استفاده از زنجیره مارکوس و مدل آنتروپی شانون، مجله محیط‌شناسی ایران، 41(4): 189–204.
     یزدانی، م.، احمدی، ح.، و خلیلی، م. (۱۳۹۸). تحلیل تغییرات زمانی کاربری اراضی با استفاده از زنجیره مارکوس و مدل سلول خودکار (CA–Marcos) در محیط GIS، فصلنامه پژوهش‌های جغرافیا و برنامه‌ریزی، 23(2): 115–134.
     Ahmed, B., & Dewan, A. (2018). Application of Marcos chain and cellular automata models in predicting future land use changes in Dhaka, Bangladesh. Environmental Monitoring and Assessment, 190(10), 565.
       Arabameri, A., Rezaei, K., Pourghasemi, H. R., et al. (2020). GIS-based flood susceptibility mapping using Shannon Entropy and Frequency Ratio models: A case study of northern Iran. Journal of Environmental Management, 267, 110–116.                                                                                                                                   
   Bui, D. T., Shirzadi, A., Shahabi, H., Chapi, K., Hoang, N. D., & Pham, B. T. (2021). A novel integrated approach using multivariate statistical models and machine learning for flood susceptibility assessment. Science of the Total Environment, 765, 142760. https://doi.org/10.1016/j.scitotenv.2020.142760.
     Eastman, J. R. (2012). IDRISI TerrSet manual: The Marcos and Cellular Automata Model of Land Cover Change Prediction. Clark University, Worcester, MA.
     Halmy, M. W. A., Gessler, P. E., Hicke, J. A., & Salem, B. B. (2015). Land use/cover change detection and prediction in the north-western coastal desert of Egypt using the Marcos–CA model. Applied Geography, 63, 101–112.
    Hajizadeh, M., Pourghasemi, H. R., & Rahmati, O. (2021).Flood susceptibility mapping using a combination of Evidential Belief Function and fuzzy logic models in northern Iran.Environmental Earth Sciences, 78(5), 169–182.
      Khaledian, Y., Enayati, Z., & Taghvayi Salimi, S. (2022). Hydrological hazard zoning and watershed sustainability in Mazandaran Province, Iran. Environmental Earth Sciences, 81(4), 77–91.                                    
                                 
     Khosravi, K., et al. (2020). Flood susceptibility mapping using entropy and Marcos chain                      models. Journal of Hydrology, 590, 125475.                                                                                                 
                                                                                                    
     Moayedi, H., & Bui, D. T. (2020). Predicting flood hazard area by hybrid Shannon Entropy–EBF models. Environmental Earth Sciences, 79(11), 280–293.
      Pontius, R. G., & Malanson, J. (2005). Comparison of the structure and accuracy of two land change models. International Journal of Geographical Information Science, 19(2), 243–265.   
     Pourghasemi, H. R., & Moradi, E. (2021). Spatial modeling of flood susceptibility using data-driven ensemble models. Natural Hazards, 108(3), 2567–2590.
     Pham, B. T., Tien Bui, D., & Pradhan, B. (2023). Hybrid decision models for spatial flood risk prediction under climate change. Catena, 224, 107–146.                                                                                                          
                                                                                                        
     Rahmati, O., & Zeinivand, H. (2023). Dynamic flood hazard prediction using Marcos Chain and Fuzzy-AHP hybrid modeling. Journal of Hydrology, 619, 129–145.
    Taghvayi Salimi, S., Baghizadeh, A., & Pourghasemi, H. R. (2022). Flood susceptibility assessment in northern Iran using hybrid data-driven models. Environmental Monitoring and Assessment, 194(8), 557–572.
    Tehrany, M. S., Jang, C., & Pham, B. T. (2022). Comparative flood susceptibility assessment using multicriteria decision analysis and ensemble learning. Science of the Total Environment, 805, 150–168.
    Youssef, A. M., Pourghasemi, H. R., & Al-Katheeri, M. (2022). Flood hazard prediction using Marcos Chain integrated with data-driven models in arid basins. Geomatics, Natural Hazards and Risk, 13(1), 700–722.             
    Xiong, L., Chen, W., & Li, H. (2023). Spatio-temporal transition of flood risk using Marcos Chain integration with spatial susceptibility models. Hydrological Sciences Journal, 68(2), 101–116