Fractal Analysis of Geometric Turbulence in Clay Microforms of the Eshtehard Plain Using the Perimeter-Area Model"
Document Type : Original Article
Authors
Department of Geomorphology, Faculty of Geographical Sciences, University of Kharazmi Tehran, Iran.
10.22034/gmpj.2025.542549.1577
Abstract
Deserts, playa lakes, and similar landforms in many arid and semi-arid regions have experienced disturbance and turbulence due to human activities. Among these, the Eshtehard Plain, identified by the Ministry of Energy's reports as one of the critically restricted plains due to its groundwater resource conditions, is highly sensitive to active geomorphological processes and surface changes. This study aims to analyze the geometric patterns and degree of turbulence in clay microforms of the Eshtehard Plain using the perimeter-area fractal model as a tool for simulating unstable surface disturbances. This region, due to its unique geomorphological characteristics, has not previously been independently subjected to fractal analysis. To this end, during the winter of 2024, 403 surface microforms were imaged, of which 208 with distinct boundaries were selected, and their area and perimeter were precisely measured. The fractal dimension (DAP) for each form was calculated and analyzed using the logarithmic relationship between perimeter and area. The results showed that DAP values range from 1.60 to 1.90, indicating a high level of geometric turbulence and structural complexity in the region. The mean DAP value of 1.75 and a high correlation coefDeserts, playa lakes, and similar landforms in many arid and semi-arid regions have experienced disturbance and turbulence due to human activities. Among these, the Eshtehard Plain, identified by the Ministry of Energy's reports as one of the critically restricted plains due to its groundwater resource conditions, is highly sensitive to active geomorphological processes and surface changes. This study aims to analyze the geometric patterns and degree of turbulence in clay microforms of the Eshtehard Plain using the perimeter-area fractal model as a tool for simulating unstable surface disturbances.Deserts, playa lakes, and similar landforms in many arid and semi-arid regions have experienced disturbance and turbulence due to human activities. Among these, the Eshtehard Plain, identified by the Ministry of Energy's reports as one of the critically restricted plains due to its groundwater resource conditions, is highly sensitive to active geomorphological processes and surface changes. This study aims to analyze the geometric patterns and degree of turbulence in clay microforms of the Eshtehard Plain using the perimeter-area fractal model as a tool for simulating unstable surface disturbances.Deserts, playa lakes, and similar landforms in many arid and semi-arid regions have experienced disturbance and turbulence due to human activities. Among these, the Eshtehard Plain, identified by the Ministry of Energy's reports as one of the critically restricted plains due to its groundwater resource conditions, is highly sensitive to active geomorphological processes and surface changes. This study aims to analyze the geometric patterns and degree of turbulence in clay microforms of the Eshtehard Plain using the perimeter-area fractal model as a tool for simulating unstable surface disturbances.Deserts, playa lakes, and similar landforms in many arid and semi-arid regions have experienced disturbance and turbulence due to human activities. Among these, the Eshtehard Plain, identified by the Ministry of Energy's reports as one of the critically restricted plains due to its groundwater resource conditions, is highly sensitive to active geomorphological processes and surface changes. This study aims to analyze the geometric patterns and degree of turbulence in clay microforms of the Eshtehard Plain using the perimeter-area fractal model as a tool for simulating unstable surface disturbances.Deserts, playa lakes, and similar landforms in many arid and semi-arid regions have experienced disturbance and turbulence due to human activities. Among these, the Eshtehard Plain, identified by the Ministry of Energy's reports as one of the critically restricted plains due to its groundwater resource conditions, is highly sensitive to active geomorphological processes and surface changes. This study aims to analyze the geometric patterns and degree of turbulence in clay microforms of the Eshtehard Plain using the perimeter-area fractal model as a tool for simulating unstable surface disturbances.Deserts, playa lakes, and similar landforms in many arid and semi-arid regions have experienced disturbance and turbulence due to human activities. Among these, the Eshtehard Plain, identified by the Ministry of Energy's reports as one of the critically restricted plains due to its groundwater resource conditions, is highly sensitive to active geomorphological processes and surface changes. This study aims to analyze the geometric patterns and degree of turbulence in clay microforms of the Eshtehard Plain using the perimeter-area fractal model as a tool for simulating unstable surface disturbances.eserts, playa lakes, and similar landforms in many arid and semi-arid regions have experienced disturbance and turbulence due to human activities.mong these, the Eshtehard Plain, identified by theficient (above 0.96) confirm the model's validity and the data's alignment with the region's unstable conditions.
Keywords
آقانباتی، سیدعلی. (۱۳۸۳). زمینشناسی ایران، نشر سازمان زمینشناسی و اکتشافات معدنی کشور، ص ۵۵۶.
سازمان زمین شناسی. (۱۳۸۴). بررسی علت فرونشست زمین و آسیب های وارده به ساختمانهای مسکونی شهرک طالقانی – شهر اشتهارد، سازمان زمین شناسی کشور.
علمی زاده، هیوا ، ماه پیکر,امید، سعادتمند ومریم . (1397). بررسی نظریهی فرکتال در ژئومورفولوژی رودخانهای: مطالعهی موردی زرینهرود. پژوهشهای ژئومورفولوژی کمّی، 3(2)، 130-141.
علیمرادی، مهتاب، اختصاصی، محمدرضا ، تازه، مهدی و کریمی، حاجی . (1397). محاسبة بُعد فراکتال سازندهای زمینشناسی و بررسی ارتباط آن با حساسیت سازندها. پژوهش های جغرافیای طبیعی, 50(2), 241-253. doi: 10.22059/jphgr.2018.234333.1007060
کردوانی، پرویز. (۱۳۸۱). منابع و مسائل آب در ایران جلد اول، نشر دانشگاه تهران.
مصطفیزاده، رئوف؛ اسفندیاری، فریبا؛ ناصری، احمد؛عبیات،احمد و ادهمی، مریم . (1402). تعیین الگوی فرکتالی در بازهای از رودخانه قرهسو استان اردبیل. هیدروژئومورفولوژی 10(37)، 97-81. doi: 10.22034/hyd.2023.57428.1700
نوروزی، رعنا؛ افتخاری، سید مروت؛ احمدآبادی، علی. (۱۴۰۴). فرونشست دشتهای ممنوعه بحرانی (منطقه مورد مطالعه: دشت اشتهارد). نشریه تحقیقات کاربردی علوم جغرافیایی، ۴(۵۷)، ۶۶–۸۹. https://doi.org/10.61186/jgs.25.78.24
Alidoost, F., & Arefi, H. (2024). Vertical Accuracy Assessment and Improvement of Five High‑Resolution Open‑Source Digital Elevation Models Using ICESat‑2 Data and Random Forest: Case Study on Chongqing, China. Remote Sensing, 16(11), 1903. https://doi.org/10.3390/rs16111903
Arabameri, A., Rezaei, K., & Blaschke, T. (2019). Land-Subsidence Spatial Modeling Using the Random Forest Data-Mining Technique. In Spatial Modeling in GIS and R for Earth and Environmental Sciences (pp. 113-129). Elsevier. https://doi.org/10.1016/B978-0-12-815226-3.00006-5SpringerLink+1PubMed+1ResearchGate+1ScienceDirect+1
Cheng Q .The Perimeter–Area Fractal Model and Its Application to Geology. Math Geol Journal; 1995; 27(1):6
Cheng Q, Russell H, Sharpe D, Kenny F, Qin P. GIS-based statistical and fractal / multifractal analysis of surface stream patterns in the Oak Ridge’s Moraine. Computer Geoscience Journal; 2001; 27(5):513-526.
Dong, X., Zhang, Q., & Yan, J. (2025). Evaluating Machine Learning‑Based Approaches in Land Subsidence Susceptibility Mapping. Land, 13(3), 322.
https://doi.org/10.3390/land13030322
https://doi.org/10.3390/land13030322
Ewing, R. C., & Kocurek, G. A. (2019). Aeolian and subaqueous bedforms in dynamic equilibrium: Scaling using fractal dimensions. Earth Surface Processes and Landforms, 44(2), 541-553.
Galloway, D. L., & Burbey, T. J. (2011). Review: Regional land subsidence accompanying groundwater extraction. Hydrogeology Journal, 19(8), 1459–1486. https://doi.org/10.1007/s10040-011-0775-5
Ghahroudi Tali M, Alinoori K. Hazards Tracing Hoz-e Soltan Playa through Investigating Chaos in Micro-landforms. Iranian Journal of Hazards Science; 2015; 1 (2):241-252
Ghahroudi Tali M, Derafshi K. The study of chaos in the flood risk pattern of Tehran. Environmental Spatial Analysis Disaster Journal; 2015; 7 (2):1-16.
Ghahroudi Tali M, khedri gharibvand L. The Investigation of Chaos in Micro-Landforms in the Gavkhooni Everglade. Geodynamics Research International Bulletin (GRIB) Journal; 2014; 2 (3):44-51.
Goodchild M F. Lake on fractal surfaces: a null hypothesis for lake-rich landscapes. Math Geol Journal; 1988; 20(6):15–630.
Herrera-García, G., et al. (2021). The global risk of land subsidence. Nature Sustainability, 4(7), 671–679. https://doi.org/10.1038/s41893-021-00690-1
Imre, A. R., & Bogaert, J. (2006). The fractal dimension as a measure of the complexity of vegetation patterns. Ecological Complexity, 3(3), 201–209. https://doi.org/10.1016/j.ecocom.2006.02.001
Ku, C.-Y., & Liu, C.-Y. (2023). Land subsidence modeling using an artificial neural network with GIS in Yunlin County, Taiwan. Scientific Reports, 13, 4207. https://doi.org/10.1038/s41598-023-31390-5
Lovejoy S. Area–perimeter relation for rain and cloud areas. Science Journal; 1982; 216(4542):185-187
Mandelbrot B B, Passoja D E, Paullay A J. Fractal character of fracture surfaces of metals. Nature Journal; 1984; 308 (5961): 721.
Naghibi, S. A., Ahmadi, K., & Kalantar, B. (2024). Land subsidence risk assessment using GIS fuzzy logic spatial modeling in Varamin aquifer, Iran. Environmental Earth Sciences, 83(2), Article 115. https://doi.org/10.1007/s12665-023-11532-4
Ohenhen, L. O., Zhai, G., Lucy, J., Lee, J.-C., Zehsaz, S., & Shirzaei, M. (2025). Land subsidence risk to infrastructure in US metropolises. Nature Cities. https://doi.org/10.1038/s44284-025-00240-y
Phillips, J. D. (2022). Chaos, fractals, and geomorphology: A review and synthesis. Progress in Physical Geography: Earth and Environment, 46(4), 456-478.
Qin, Y., He, P., Zhang, J., & Xie, L. (2024). The Fractal Characteristics of Ground Subsidence Caused by Subway Excavation. Applied Sciences, 14(12), 5327. https://doi.org/10.3390/app14125327
Rahmati, O., Samadi, M., Pourghasemi, H. R., & Zeinivand, H. (2019). Land subsidence modelling using tree-based machine learning algorithms. Science of the Total Environment, 672, 239–252. https://doi.org/10.1016/j.scitotenv.2019.03
Rajabi, A. M., Edalat, A., Abolghasemi, Y., & Khodaparast, M. (2024). Ground subsidence modeling using Sentinel-1A SAR data and artificial neural network in Aliabad Plain, Iran. Journal of Mountain Science, 21(3), 589–603. https://doi.org/10.1007/s11629-023-8470-2.
Ramesht M H. Hazards Tracing Hoz-e Soltan Playa through Investigating Chaos in Microlandforms. Geography and Development Iranian Journal; 2003; 1 (1):13-36
Sun, T., Liu, Y., Wu, K., Zhang, H., Zhang, J., Jiang, X., Lin, Q., & Feng, M. (2024). Fractal-Based Multi-Criteria Feature Selection to Enhance Predictive Capability of AI-Driven Mineral Prospectivity Mapping. Fractal and Fractional, 8(4), 224. https://doi.org/10.3390/fractalfract8040224
United Nations Environment Programme (UNEP). (2022). Global Environmental Outlook 6: Regional assessments for West Asia and North Africa. Nairobi, Kenya: UNEP.
Vogel, H. J., et al. (2020). Quantitative morphology of desiccation cracks in soils: A fractal approach. Geoderma, 374, 114424.
Wang Z, Cheng Q, Cao L et al. Fractal modelling of the microstructure property of quartz mylonite during deformation process. Math Geol Journal; 2006; 39(1):53
Yang, K., Hu, Z. Q., Liang, Y. S., Fu, Y. K., Yuan, D. Z., Guo, J. X., et al. (2022). Automated extraction of ground fissures due to coal mining subsidence based on UAV photogrammetry. Remote Sensing, 14, 1071. https://doi.org/10.3390/rs14051071
Yu, B., Xing, H., & Yan, J. (2024). Susceptibility assessment of multi-hazards using random forest–back propagation neural network coupling model: A Hangzhou city case study. Scientific Reports, 14, 21783. https://doi.org/10.1038/s41598-024-71053-7
Yu, B., Xing, H., & Yan, J. (2024). Susceptibility assessment of multi-hazards using random forest–back propagation neural network coupling model: A Hangzhou city case study. Scientific Reports, 14, 21783. https://doi.org/10.1038/s41598-024-71053-7
Zhan, Y., Zhang, Y., Zhang, J., Xu, J., Chen, H., Liu, G., & Wan, Z. (2025). Ground subsidence risk assessment using AHP and entropy weight method in Shanghai Municipality. Scientific Reports, 15(1), 7339. https://doi.org/10.1038/s41598-025-91109-6
Zhao, Y. X., Xu, D., Sun, B., Jiang, Y. D., Zhang, C., & He, X. (2021). Investigation on ground fissure identification using UAV infrared remote sensing and edge detection technology. Journal of China Coal Society, 46, 624–637. https://doi.org/10.13225/j.cnki.jccs.xr20.1948
Zhou, Y., Wang, Y., & Li, X. (2023). Integrating SBAS-InSAR and Random Forest for Identifying Land Subsidence Areas in the North China Plain. Remote Sensing, 15(5), 830. https://doi.org/10.3390/rs15050830MDPI
